TSTP Solution File: ALG017^7 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ALG017^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.bwYkkHxwSd true
% Computer : n002.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 : Wed Aug 30 17:10:06 EDT 2023
% Result : Theorem 157.95s 20.91s
% Output : Refutation 158.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG017^7 : TPTP v8.1.2. Released v5.5.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.bwYkkHxwSd true
% 0.15/0.35 % Computer : n002.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 03:20:49 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.35 % Number of cores: 8
% 0.15/0.35 % Python version: Python 3.6.8
% 0.15/0.36 % Running in HO mode
% 0.21/0.65 % Total configuration time : 828
% 0.21/0.65 % Estimated wc time : 1656
% 0.21/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.23/0.82 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.42/0.82 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.43/1.17 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 157.95/20.91 % Solved by lams/30_b.l.sh.
% 157.95/20.91 % done 0 iterations in 19.490s
% 157.95/20.91 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 157.95/20.91 % SZS output start Refutation
% 157.95/20.91 thf(mu_type, type, mu: $tType).
% 157.95/20.91 thf(e0_type, type, e0: mu).
% 157.95/20.91 thf('#form3_type', type, '#form3': mu > mu > $i > $o).
% 157.95/20.91 thf(op_type, type, op: mu > mu > mu).
% 157.95/20.91 thf(rel_s4_type, type, rel_s4: $i > $i > $o).
% 157.95/20.91 thf('#sk2_type', type, '#sk2': mu > mu > $i > $i).
% 157.95/20.91 thf(mreflexive_type, type, mreflexive: ($i > $i > $o) > $o).
% 157.95/20.91 thf(mforall_ind_type, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 157.95/20.91 thf(e3_type, type, e3: mu).
% 157.95/20.91 thf(e2_type, type, e2: mu).
% 157.95/20.91 thf('#sk5_type', type, '#sk5': $i).
% 157.95/20.91 thf(mnot_type, type, mnot: ($i > $o) > $i > $o).
% 157.95/20.91 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 157.95/20.91 thf(e1_type, type, e1: mu).
% 157.95/20.91 thf('#form6_type', type, '#form6': $o).
% 157.95/20.91 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 157.95/20.91 thf(mbox_s4_type, type, mbox_s4: ($i > $o) > $i > $o).
% 157.95/20.91 thf('#sk4_type', type, '#sk4': $i).
% 157.95/20.91 thf(exists_in_world_type, type, exists_in_world: mu > $i > $o).
% 157.95/20.91 thf(qmltpeq_type, type, qmltpeq: mu > mu > $i > $o).
% 157.95/20.91 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 157.95/20.91 thf(mvalid_type, type, mvalid: ($i > $o) > $o).
% 157.95/20.91 thf(co1, conjecture,
% 157.95/20.91 (mvalid @
% 157.95/20.91 ( mbox_s4 @
% 157.95/20.91 ( mnot @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mor @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @
% 157.95/20.91 ( mor @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @
% 157.95/20.91 ( mor @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) @
% 157.95/20.91 ( mbox_s4 @
% 157.95/20.91 ( mnot @
% 157.95/20.91 ( mor @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @
% 157.95/20.91 ( mor @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @
% 157.95/20.91 ( mor @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 157.95/20.91 thf(zf_stmt_0, negated_conjecture,
% 157.95/20.91 (~( mvalid @
% 157.95/20.91 ( mbox_s4 @
% 157.95/20.91 ( mnot @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mor @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @
% 157.95/20.91 ( mor @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @
% 157.95/20.91 ( mor @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) @
% 157.95/20.91 ( mbox_s4 @
% 157.95/20.91 ( mnot @
% 157.95/20.91 ( mor @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @
% 157.95/20.91 ( mor @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @
% 157.95/20.91 ( mor @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 157.95/20.91 inference('cnf.neg', [status(esa)], [co1])).
% 157.95/20.91 thf(zip_derived_cl28, plain,
% 157.95/20.91 (~ (mvalid @
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))))))),
% 157.95/20.91 inference('cnf', [status(esa)], [zf_stmt_0])).
% 157.95/20.91 thf(mvalid, axiom, ~ (mvalid @ X0) =>
% 157.95/20.91 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) != ($true))).
% 157.95/20.91 thf('0', plain,
% 157.95/20.91 (![X0:( $i > $o )]:
% 157.95/20.91 ( ( ~( mvalid @ X0 ) ) <=> ( ~( ![X5:$i]: ( X0 @ X5 ) ) ) )),
% 157.95/20.91 inference('rw.lit', [status(esa)], [mvalid])).
% 157.95/20.91 thf(zip_derived_cl2501, plain,
% 157.95/20.91 (~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))))) @
% 157.95/20.91 Y0))))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl28, '0'])).
% 157.95/20.91 thf(zip_derived_cl2502, plain,
% 157.95/20.91 (~ (mbox_s4 @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))))) @
% 157.95/20.91 '#sk4')),
% 157.95/20.91 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2501])).
% 157.95/20.91 thf(mbox_s4, axiom, ~ (mbox_s4 @ X0 @ X1) =>
% 157.95/20.91 ((((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s4 @ X1 @ Y0))) | (X0 @ Y0)))))) !=
% 157.95/20.91 ($true))).
% 157.95/20.91 thf('1', plain,
% 157.95/20.91 (![X0:( $i > $o ),X1:$i]:
% 157.95/20.91 ( ( ~( mbox_s4 @ X0 @ X1 ) ) <=>
% 157.95/20.91 ( ~( ![X6:$i]: ( ( ~( rel_s4 @ X1 @ X6 ) ) | ( X0 @ X6 ) ) ) ) )),
% 157.95/20.91 inference('rw.lit', [status(esa)], [mbox_s4])).
% 157.95/20.91 thf(zip_derived_cl2503, plain,
% 157.95/20.91 (~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | (mnot @
% 157.95/20.91 (mand @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))) @
% 157.95/20.91 Y0))))))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2502, '1'])).
% 157.95/20.91 thf(zip_derived_cl2504, plain,
% 157.95/20.91 (~ (((((~) @ (rel_s4 @ '#sk4' @ '#sk5'))) | (mnot @
% 157.95/20.91 (mand @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))) @
% 157.95/20.91 '#sk5')))),
% 157.95/20.91 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2503])).
% 157.95/20.91 thf(zip_derived_cl2506, plain,
% 157.95/20.91 (~ (mnot @
% 157.95/20.91 (mand @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))) @
% 157.95/20.91 '#sk5')),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2504])).
% 157.95/20.91 thf(mnot, axiom, ~ (mnot @ X0 @ X1) => ((X0 @ X1) = ($true))).
% 157.95/20.91 thf('2', plain,
% 157.95/20.91 (![X0:( $i > $o ),X1:$i]: ( ( ~( mnot @ X0 @ X1 ) ) <=> ( X0 @ X1 ) )),
% 157.95/20.91 inference('rw.lit', [status(esa)], [mnot])).
% 157.95/20.91 thf(zip_derived_cl2507, plain,
% 157.95/20.91 ( (mand @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))) @
% 157.95/20.91 '#sk5')),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2506, '2'])).
% 157.95/20.91 thf(mand, axiom,(( mand @ (X0)@ (X1)@ (X2)) =
% 157.95/20.91 ((mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)) @ X2)))).
% 157.95/20.91 thf('3', plain,
% 157.95/20.91 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]:
% 157.95/20.91 ( ( mand @ X0 @ X1 @ X2 ) =
% 157.95/20.91 ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) @ X2 ) )),
% 157.95/20.91 define([status(thm)])).
% 157.95/20.91 thf(zip_derived_cl2508, plain,
% 157.95/20.91 ( (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))))) @
% 157.95/20.91 '#sk5')),
% 157.95/20.91 inference('rw', [status(thm)], [zip_derived_cl2507, '3'])).
% 157.95/20.91 thf(mnot, axiom, (mnot @ X0 @ X1) => ((X0 @ X1) != ($true))).
% 157.95/20.91 thf('4', plain,
% 157.95/20.91 (![X0:( $i > $o ),X1:$i]: ( ( mnot @ X0 @ X1 ) <=> ( ~( X0 @ X1 ) ) )),
% 157.95/20.91 inference('rw.lit', [status(esa)], [mnot])).
% 157.95/20.91 thf(zip_derived_cl2509, plain,
% 157.95/20.91 (~ (mor @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))) @
% 157.95/20.91 '#sk5')),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2508, '4'])).
% 157.95/20.91 thf(mor, axiom, ~ (mor @ X0 @ X1 @ X2) =>
% 157.95/20.91 ((((X1 @ X2) | (X0 @ X2))) != ($true))).
% 157.95/20.91 thf('5', plain,
% 157.95/20.91 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 157.95/20.91 ( ( ~( mor @ X0 @ X1 @ X2 ) ) <=> ( ~( ( X1 @ X2 ) | ( X0 @ X2 ) ) ) )),
% 157.95/20.91 inference('rw.lit', [status(esa)], [mor])).
% 157.95/20.91 thf(zip_derived_cl2510, plain,
% 157.95/20.91 (~ (((mnot @
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @
% 157.95/20.91 '#sk5')))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2509, '5'])).
% 157.95/20.91 thf(zip_derived_cl2512, plain,
% 157.95/20.91 (~ (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @
% 157.95/20.91 '#sk5')),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2510])).
% 157.95/20.91 thf(zip_derived_cl2514, plain,
% 157.95/20.91 ( (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))) @
% 157.95/20.91 '#sk5')),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2512, '2'])).
% 157.95/20.91 thf(mor, axiom, (mor @ X0 @ X1 @ X2) =>
% 157.95/20.91 ((((X1 @ X2) | (X0 @ X2))) = ($true))).
% 157.95/20.91 thf('6', plain,
% 157.95/20.91 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 157.95/20.91 ( ( mor @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) | ( X1 @ X2 ) ) )),
% 157.95/20.91 inference('rw.lit', [status(esa)], [mor])).
% 157.95/20.91 thf(zip_derived_cl2516, plain,
% 157.95/20.91 ( (((mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.91 '#sk5') | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @
% 157.95/20.91 '#sk5')))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2514, '6'])).
% 157.95/20.91 thf(zip_derived_cl2518, plain,
% 157.95/20.91 ( (((mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))))) @
% 157.95/20.91 '#sk5')))),
% 157.95/20.91 inference('rw', [status(thm)], [zip_derived_cl2516, '3'])).
% 157.95/20.91 thf(zip_derived_cl2519, plain,
% 157.95/20.91 (( (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))))) @
% 157.95/20.91 '#sk5'))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2518])).
% 157.95/20.91 thf(zip_derived_cl2521, plain,
% 157.95/20.91 (( (((mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.91 '#sk5') | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.91 '#sk5')))
% 157.95/20.91 | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))))) @
% 157.95/20.91 '#sk5'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2519, '6'])).
% 157.95/20.91 thf(zip_derived_cl2523, plain,
% 157.95/20.91 (( (((mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.91 '#sk5')))
% 157.95/20.91 | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))))) @
% 157.95/20.91 '#sk5'))),
% 157.95/20.91 inference('rw', [status(thm)], [zip_derived_cl2521, '3'])).
% 157.95/20.91 thf(zip_derived_cl2524, plain,
% 157.95/20.91 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | (((mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.91 '#sk5'))))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2523, '4'])).
% 157.95/20.91 thf(zip_derived_cl2526, plain,
% 157.95/20.91 ((~ (((mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @
% 157.95/20.91 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 '#sk5')))
% 157.95/20.91 | (((mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.91 '#sk5'))))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2524, '5'])).
% 157.95/20.91 thf(zip_derived_cl2531, plain,
% 157.95/20.91 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ '#sk5')
% 157.95/20.91 | (((mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.91 '#sk5'))))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2526])).
% 157.95/20.91 thf(zip_derived_cl2535, plain,
% 157.95/20.91 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0) @ '#sk5')
% 157.95/20.91 | (((mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.91 '#sk5'))))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2531, '2'])).
% 157.95/20.91 thf(mbox_s4, axiom, (mbox_s4 @ X0 @ X1) =>
% 157.95/20.91 ((((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s4 @ X1 @ Y0))) | (X0 @ Y0)))))) =
% 157.95/20.91 ($true))).
% 157.95/20.91 thf('7', plain,
% 157.95/20.91 (![X0:( $i > $o ),X1:$i]:
% 157.95/20.91 ( ( mbox_s4 @ X0 @ X1 ) <=>
% 157.95/20.91 ( ![X6:$i]: ( ( ~( rel_s4 @ X1 @ X6 ) ) | ( X0 @ X6 ) ) ) )),
% 157.95/20.91 inference('rw.lit', [status(esa)], [mbox_s4])).
% 157.95/20.91 thf(zip_derived_cl2542, plain,
% 157.95/20.91 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.91 (op @ e0 @ e0) @ e0 @ Y0))))))
% 157.95/20.91 | (((mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.91 '#sk5'))))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2535, '7'])).
% 157.95/20.91 thf(transitivity, axiom,
% 157.95/20.91 (mvalid @
% 157.95/20.91 ( mbox_s4 @
% 157.95/20.91 ( mforall_ind @
% 157.95/20.91 ( ^[X:mu]:
% 157.95/20.91 ( mbox_s4 @
% 157.95/20.91 ( mforall_ind @
% 157.95/20.91 ( ^[Y:mu]:
% 157.95/20.91 ( mbox_s4 @
% 157.95/20.91 ( mforall_ind @
% 157.95/20.91 ( ^[Z:mu]:
% 157.95/20.91 ( mbox_s4 @
% 157.95/20.91 ( mimplies @
% 157.95/20.91 ( mand @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ Y @ Z ) ) ) @
% 157.95/20.91 ( mbox_s4 @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 157.95/20.91 thf(zip_derived_cl13, plain,
% 157.95/20.91 ( (mvalid @
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y0 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y2 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ Y0 @ Y1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y1 @ Y2))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y0 @ Y2))))))))))))))),
% 157.95/20.91 inference('cnf', [status(esa)], [transitivity])).
% 157.95/20.91 thf(mvalid, axiom, (mvalid @ X0) =>
% 157.95/20.91 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) = ($true))).
% 157.95/20.91 thf('8', plain,
% 157.95/20.91 (![X0:( $i > $o )]: ( ( mvalid @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 ) ) )),
% 157.95/20.91 inference('rw.lit', [status(esa)], [mvalid])).
% 157.95/20.91 thf(zip_derived_cl228, plain,
% 157.95/20.91 ( (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y2 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y3 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ Y1 @ Y2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y2 @ Y3))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y1 @ Y3)))))))))))) @
% 157.95/20.91 Y0))))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl13, '8'])).
% 157.95/20.91 thf(zip_derived_cl229, plain,
% 157.95/20.91 (![X2 : $i]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y0 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y2 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ Y0 @ Y1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y1 @ Y2))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y0 @ Y2)))))))))))) @
% 157.95/20.91 X2)),
% 157.95/20.91 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl228])).
% 157.95/20.91 thf(zip_derived_cl230, plain,
% 157.95/20.91 (![X0 : $i]:
% 157.95/20.91 (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @
% 157.95/20.91 (^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y2 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y3 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y1 @ Y2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y2 @ Y3))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y1 @ Y3))))))))))) @
% 157.95/20.91 Y0))))))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl229, '7'])).
% 157.95/20.91 thf(zip_derived_cl231, plain,
% 157.95/20.91 (![X0 : $i, X2 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X0 @ X2))) | (mforall_ind @
% 157.95/20.91 (^[Y0 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y2 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ Y0 @ Y1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y1 @ Y2))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y0 @ Y2))))))))))) @
% 157.95/20.91 X2)))),
% 157.95/20.91 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl230])).
% 157.95/20.91 thf(zip_derived_cl232, plain,
% 157.95/20.91 (![X0 : $i, X2 : $i]:
% 157.95/20.91 (~ (rel_s4 @ X0 @ X2)
% 157.95/20.91 | (mforall_ind @
% 157.95/20.91 (^[Y0 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y2 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ Y0 @ Y1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y1 @ Y2))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y0 @ Y2))))))))))) @
% 157.95/20.91 X2))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl231])).
% 157.95/20.91 thf(mforall_ind, axiom, (mforall_ind @ X0 @ X1) =>
% 157.95/20.91 ((((!!) @ (^[Y0 : mu]: (((exists_in_world @ Y0 @ X1) => (X0 @ Y0 @ X1))))))
% 157.95/20.91 = ($true))).
% 157.95/20.91 thf('9', plain,
% 157.95/20.91 (![X0:( mu > $i > $o ),X1:$i]:
% 157.95/20.91 ( ( mforall_ind @ X0 @ X1 ) <=>
% 157.95/20.91 ( ![X6:mu]: ( ( exists_in_world @ X6 @ X1 ) => ( X0 @ X6 @ X1 ) ) ) )),
% 157.95/20.91 inference('rw.lit', [status(esa)], [mforall_ind])).
% 157.95/20.91 thf(zip_derived_cl233, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i]:
% 157.95/20.91 ( (((!!) @ (^[Y0 : mu]:
% 157.95/20.91 (((exists_in_world @ Y0 @ X0) =>
% 157.95/20.91 ((^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y2 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y3 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y1 @ Y2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y2 @ Y3))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y1 @ Y3))))))))))) @
% 157.95/20.91 Y0 @ X0))))))
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl232, '9'])).
% 157.95/20.91 thf(zip_derived_cl234, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i]:
% 157.95/20.91 ( (((!!) @ (^[Y0 : mu]:
% 157.95/20.91 (((exists_in_world @ Y0 @ X0) => (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y2 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ Y0 @ Y1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y1 @ Y2))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y0 @ Y2))))))))) @
% 157.95/20.91 X0))))))
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0))),
% 157.95/20.91 inference('ho_norm', [status(thm)], [zip_derived_cl233])).
% 157.95/20.91 thf(zip_derived_cl235, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X3 : mu]:
% 157.95/20.91 ( (((exists_in_world @ X3 @ X0) => (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y0 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ Y0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y0 @ Y1))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X3 @ Y1))))))))) @
% 157.95/20.91 X0)))
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0))),
% 157.95/20.91 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl234])).
% 157.95/20.91 thf(zip_derived_cl236, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X3 : mu]:
% 157.95/20.91 (~ (exists_in_world @ X3 @ X0)
% 157.95/20.91 | (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y0 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ Y0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y0 @ Y1))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X3 @ Y1))))))))) @
% 157.95/20.91 X0)
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0))),
% 157.95/20.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl235])).
% 157.95/20.91 thf(zip_derived_cl237, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : mu]:
% 157.95/20.91 ( (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @
% 157.95/20.91 (^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y2 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X2 @ Y1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y1 @ Y2))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X2 @ Y2)))))))) @
% 157.95/20.91 Y0))))))
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0)
% 157.95/20.91 | ~ (exists_in_world @ X2 @ X0))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl236, '7'])).
% 157.95/20.91 thf(zip_derived_cl238, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]:
% 157.95/20.91 ( (((((~) @ (rel_s4 @ X0 @ X4))) | (mforall_ind @
% 157.95/20.91 (^[Y0 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X2 @ Y0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y0 @ Y1))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X2 @ Y1)))))))) @
% 157.95/20.91 X4)))
% 157.95/20.91 | ~ (exists_in_world @ X2 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0))),
% 157.95/20.91 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl237])).
% 157.95/20.91 thf(zip_derived_cl239, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]:
% 157.95/20.91 (~ (rel_s4 @ X0 @ X4)
% 157.95/20.91 | (mforall_ind @
% 157.95/20.91 (^[Y0 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X2 @ Y0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y0 @ Y1))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X2 @ Y1)))))))) @
% 157.95/20.91 X4)
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0)
% 157.95/20.91 | ~ (exists_in_world @ X2 @ X0))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl238])).
% 157.95/20.91 thf(zip_derived_cl240, plain,
% 157.95/20.91 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i]:
% 157.95/20.91 ( (((!!) @ (^[Y0 : mu]:
% 157.95/20.91 (((exists_in_world @ Y0 @ X3) =>
% 157.95/20.91 ((^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y2 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X1 @ Y1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y1 @ Y2))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X1 @ Y2)))))))) @
% 157.95/20.91 Y0 @ X3))))))
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X0 @ X3))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl239, '9'])).
% 157.95/20.91 thf(zip_derived_cl241, plain,
% 157.95/20.91 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i]:
% 157.95/20.91 ( (((!!) @ (^[Y0 : mu]:
% 157.95/20.91 (((exists_in_world @ Y0 @ X3) => (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X1 @ Y0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ Y0 @ Y1))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X1 @ Y1)))))) @
% 157.95/20.91 X3))))))
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X0 @ X3))),
% 157.95/20.91 inference('ho_norm', [status(thm)], [zip_derived_cl240])).
% 157.95/20.91 thf(zip_derived_cl242, plain,
% 157.95/20.91 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i, X5 : mu]:
% 157.95/20.91 ( (((exists_in_world @ X5 @ X3) => (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y0 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X1 @ X5)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X5 @ Y0))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X1 @ Y0)))))) @
% 157.95/20.91 X3)))
% 157.95/20.91 | ~ (rel_s4 @ X0 @ X3)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X0)
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X0))),
% 157.95/20.91 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl241])).
% 157.95/20.91 thf(zip_derived_cl243, plain,
% 157.95/20.91 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i, X5 : mu]:
% 157.95/20.91 (~ (exists_in_world @ X5 @ X3)
% 157.95/20.91 | (mbox_s4 @
% 157.95/20.91 (mforall_ind @
% 157.95/20.91 (^[Y0 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X1 @ X5)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X5 @ Y0))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X1 @ Y0)))))) @
% 157.95/20.91 X3)
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X0 @ X3))),
% 157.95/20.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl242])).
% 157.95/20.91 thf(zip_derived_cl244, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu]:
% 157.95/20.91 ( (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @
% 157.95/20.91 (^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ X4)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X4 @ Y1))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X3 @ Y1))))) @
% 157.95/20.91 Y0))))))
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X1)
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X1)
% 157.95/20.91 | ~ (exists_in_world @ X4 @ X0))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl243, '7'])).
% 157.95/20.91 thf(zip_derived_cl245, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu, X6 : $i]:
% 157.95/20.91 ( (((((~) @ (rel_s4 @ X0 @ X6))) | (mforall_ind @
% 157.95/20.91 (^[Y0 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ X4)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X4 @ Y0))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X3 @ Y0))))) @
% 157.95/20.91 X6)))
% 157.95/20.91 | ~ (exists_in_world @ X4 @ X0)
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X1)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X1)
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0))),
% 157.95/20.91 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl244])).
% 157.95/20.91 thf(zip_derived_cl246, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu, X6 : $i]:
% 157.95/20.91 (~ (rel_s4 @ X0 @ X6)
% 157.95/20.91 | (mforall_ind @
% 157.95/20.91 (^[Y0 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ X4)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X4 @ Y0))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X3 @ Y0))))) @
% 157.95/20.91 X6)
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X1)
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X1)
% 157.95/20.91 | ~ (exists_in_world @ X4 @ X0))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl245])).
% 157.95/20.91 thf(zip_derived_cl247, plain,
% 157.95/20.91 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]:
% 157.95/20.91 ( (((!!) @ (^[Y0 : mu]:
% 157.95/20.91 (((exists_in_world @ Y0 @ X5) =>
% 157.95/20.91 ((^[Y1 : mu]:
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ X1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X1 @ Y1))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X3 @ Y1))))) @
% 157.95/20.91 Y0 @ X5))))))
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X0)
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X0 @ X5))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl246, '9'])).
% 157.95/20.91 thf(zip_derived_cl248, plain,
% 157.95/20.91 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]:
% 157.95/20.91 ( (((!!) @ (^[Y0 : mu]:
% 157.95/20.91 (((exists_in_world @ Y0 @ X5) => (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ X1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X1 @ Y0))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X3 @ Y0))) @
% 157.95/20.91 X5))))))
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X0)
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X0 @ X5))),
% 157.95/20.91 inference('ho_norm', [status(thm)], [zip_derived_cl247])).
% 157.95/20.91 thf(zip_derived_cl249, plain,
% 157.95/20.91 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i, X7 : mu]:
% 157.95/20.91 ( (((exists_in_world @ X7 @ X5) => (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ X1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X1 @ X7))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X3 @ X7))) @
% 157.95/20.91 X5)))
% 157.95/20.91 | ~ (rel_s4 @ X0 @ X5)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X2)
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X2)
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X0))),
% 157.95/20.91 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl248])).
% 157.95/20.91 thf(zip_derived_cl250, plain,
% 157.95/20.91 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i, X7 : mu]:
% 157.95/20.91 (~ (exists_in_world @ X7 @ X5)
% 157.95/20.91 | (mbox_s4 @
% 157.95/20.91 (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ X1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X1 @ X7))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X3 @ X7))) @
% 157.95/20.91 X5)
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X0)
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X0 @ X5))),
% 157.95/20.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl249])).
% 157.95/20.91 thf(zip_derived_cl251, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : mu, X5 : mu, X6 : mu]:
% 157.95/20.91 ( (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X4 @ X5)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X5 @ X6))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X4 @ X6)) @ Y0))))))
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X1)
% 157.95/20.91 | ~ (rel_s4 @ X3 @ X2)
% 157.95/20.91 | ~ (exists_in_world @ X4 @ X2)
% 157.95/20.91 | ~ (exists_in_world @ X5 @ X1)
% 157.95/20.91 | ~ (exists_in_world @ X6 @ X0))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl250, '7'])).
% 157.95/20.91 thf(zip_derived_cl252, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : mu, X5 : mu, X6 : mu, X8 : $i]:
% 157.95/20.91 ( (((((~) @ (rel_s4 @ X0 @ X8))) | (mimplies @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X4 @ X5)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X5 @ X6))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X4 @ X6)) @ X8)))
% 157.95/20.91 | ~ (exists_in_world @ X6 @ X0)
% 157.95/20.91 | ~ (exists_in_world @ X5 @ X1)
% 157.95/20.91 | ~ (exists_in_world @ X4 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X3 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X1)
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0))),
% 157.95/20.91 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl251])).
% 157.95/20.91 thf(mimplies, axiom,(( mimplies @ (X0)@ (X1)@ (X2)) =
% 157.95/20.91 ((mor @ (mnot @ X0) @ X1 @ X2)))).
% 157.95/20.91 thf('10', plain,
% 157.95/20.91 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]:
% 157.95/20.91 ( ( mimplies @ X0 @ X1 @ X2 ) = ( mor @ ( mnot @ X0 ) @ X1 @ X2 ) )),
% 157.95/20.91 define([status(thm)])).
% 157.95/20.91 thf(zip_derived_cl253, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : mu, X5 : mu, X6 : mu, X8 : $i]:
% 157.95/20.91 ( (((((~) @ (rel_s4 @ X0 @ X8))) | (mor @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X4 @ X5)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X5 @ X6)))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X4 @ X6)) @ X8)))
% 157.95/20.91 | ~ (exists_in_world @ X6 @ X0)
% 157.95/20.91 | ~ (exists_in_world @ X5 @ X1)
% 157.95/20.91 | ~ (exists_in_world @ X4 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X3 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X1)
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0))),
% 157.95/20.91 inference('rw', [status(thm)], [zip_derived_cl252, '10'])).
% 157.95/20.91 thf(zip_derived_cl254, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : mu, X5 : mu, X6 : mu, X8 : $i]:
% 157.95/20.91 (~ (rel_s4 @ X0 @ X8)
% 157.95/20.91 | (mor @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X4 @ X5)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X5 @ X6)))) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X4 @ X6)) @ X8)
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X1)
% 157.95/20.91 | ~ (rel_s4 @ X3 @ X2)
% 157.95/20.91 | ~ (exists_in_world @ X4 @ X2)
% 157.95/20.91 | ~ (exists_in_world @ X5 @ X1)
% 157.95/20.91 | ~ (exists_in_world @ X6 @ X0))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl253])).
% 157.95/20.91 thf(zip_derived_cl255, plain,
% 157.95/20.91 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : mu, X6 : $i, X7 : $i]:
% 157.95/20.91 ( (((mbox_s4 @ (qmltpeq @ X5 @ X1) @ X7) | (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X5 @ X3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X3 @ X1))) @
% 157.95/20.91 X7)))
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X0)
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X2)
% 157.95/20.91 | ~ (exists_in_world @ X5 @ X4)
% 157.95/20.91 | ~ (rel_s4 @ X6 @ X4)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X0 @ X7))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl254, '6'])).
% 157.95/20.91 thf(zip_derived_cl256, plain,
% 157.95/20.91 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : mu, X6 : $i, X7 : $i]:
% 157.95/20.91 ( (mbox_s4 @ (qmltpeq @ X5 @ X1) @ X7)
% 157.95/20.91 | (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X5 @ X3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X3 @ X1))) @
% 157.95/20.91 X7)
% 157.95/20.91 | ~ (rel_s4 @ X0 @ X7)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X6 @ X4)
% 157.95/20.91 | ~ (exists_in_world @ X5 @ X4)
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X2)
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X0))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl255])).
% 157.95/20.91 thf(zip_derived_cl257, plain,
% 157.95/20.91 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : mu, X6 : $i, X7 : $i]:
% 157.95/20.91 ( (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X7 @ Y0))) | (qmltpeq @ X5 @ X1 @
% 157.95/20.91 Y0))))))
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X0)
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X2)
% 157.95/20.91 | ~ (exists_in_world @ X5 @ X4)
% 157.95/20.91 | ~ (rel_s4 @ X6 @ X4)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X0 @ X7)
% 157.95/20.91 | (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ X5 @ X3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X3 @ X1))) @
% 157.95/20.91 X7))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl256, '7'])).
% 157.95/20.91 thf(zip_derived_cl258, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : mu, X6 : mu, X7 : mu]:
% 157.95/20.91 (~ (mand @ (mbox_s4 @ (qmltpeq @ X5 @ X6)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X6 @ X7)) @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X1)
% 157.95/20.91 | ~ (rel_s4 @ X3 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X3)
% 157.95/20.91 | ~ (exists_in_world @ X5 @ X3)
% 157.95/20.91 | ~ (exists_in_world @ X6 @ X2)
% 157.95/20.91 | ~ (exists_in_world @ X7 @ X1)
% 157.95/20.91 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X5 @ X7 @
% 157.95/20.91 Y0)))))))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl257, '4'])).
% 157.95/20.91 thf(zip_derived_cl259, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : mu, X6 : mu, X7 : mu]:
% 157.95/20.91 (~ (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ X5 @ X6))) @
% 157.95/20.91 (mnot @ (mbox_s4 @ (qmltpeq @ X6 @ X7)))) @
% 157.95/20.91 X0)
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X1)
% 157.95/20.91 | ~ (rel_s4 @ X3 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X3)
% 157.95/20.91 | ~ (exists_in_world @ X5 @ X3)
% 157.95/20.91 | ~ (exists_in_world @ X6 @ X2)
% 157.95/20.91 | ~ (exists_in_world @ X7 @ X1)
% 157.95/20.91 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X5 @ X7 @
% 157.95/20.91 Y0)))))))),
% 157.95/20.91 inference('rw', [status(thm)], [zip_derived_cl258, '3'])).
% 157.95/20.91 thf(zip_derived_cl260, plain,
% 157.95/20.91 (![X0 : mu, X1 : mu, X2 : $i, X3 : $i, X4 : $i, X5 : mu, X6 : $i, X7 : $i]:
% 157.95/20.91 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ X1 @ X5))) @
% 157.95/20.91 (mnot @ (mbox_s4 @ (qmltpeq @ X5 @ X0))) @ X2)
% 157.95/20.91 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.91 Y0))))))
% 157.95/20.91 | ~ (exists_in_world @ X0 @ X3)
% 157.95/20.91 | ~ (exists_in_world @ X5 @ X4)
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X6)
% 157.95/20.91 | ~ (rel_s4 @ X7 @ X6)
% 157.95/20.91 | ~ (rel_s4 @ X6 @ X4)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X3)
% 157.95/20.91 | ~ (rel_s4 @ X3 @ X2))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl259, '2'])).
% 157.95/20.91 thf(zip_derived_cl261, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : mu, X6 : mu, X7 : mu]:
% 157.95/20.91 ( (((mnot @ (mbox_s4 @ (qmltpeq @ X6 @ X7)) @ X0) | (mnot @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ X5 @ X6)) @ X0)))
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X1)
% 157.95/20.91 | ~ (rel_s4 @ X3 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X3)
% 157.95/20.91 | ~ (exists_in_world @ X5 @ X3)
% 157.95/20.91 | ~ (exists_in_world @ X6 @ X2)
% 157.95/20.91 | ~ (exists_in_world @ X7 @ X1)
% 157.95/20.91 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X5 @ X7 @
% 157.95/20.91 Y0)))))))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl260, '6'])).
% 157.95/20.91 thf(zip_derived_cl262, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : mu, X6 : mu, X7 : mu]:
% 157.95/20.91 ( (mnot @ (mbox_s4 @ (qmltpeq @ X6 @ X7)) @ X0)
% 157.95/20.91 | (mnot @ (mbox_s4 @ (qmltpeq @ X5 @ X6)) @ X0)
% 157.95/20.91 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X5 @ X7 @
% 157.95/20.91 Y0))))))
% 157.95/20.91 | ~ (exists_in_world @ X7 @ X1)
% 157.95/20.91 | ~ (exists_in_world @ X6 @ X2)
% 157.95/20.91 | ~ (exists_in_world @ X5 @ X3)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X3)
% 157.95/20.91 | ~ (rel_s4 @ X3 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X1)
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl261])).
% 157.95/20.91 thf(zip_derived_cl263, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : mu, X6 : mu, X7 : mu]:
% 157.95/20.91 (~ (mbox_s4 @ (qmltpeq @ X6 @ X7) @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X1)
% 157.95/20.91 | ~ (rel_s4 @ X3 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X3)
% 157.95/20.91 | ~ (exists_in_world @ X5 @ X3)
% 157.95/20.91 | ~ (exists_in_world @ X6 @ X2)
% 157.95/20.91 | ~ (exists_in_world @ X7 @ X1)
% 157.95/20.91 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X5 @ X7 @
% 157.95/20.91 Y0))))))
% 157.95/20.91 | (mnot @ (mbox_s4 @ (qmltpeq @ X5 @ X6)) @ X0))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl262, '4'])).
% 157.95/20.91 thf(zip_derived_cl264, plain,
% 157.95/20.91 (![X0 : $i, X1 : mu, X2 : mu, X3 : mu, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 157.95/20.91 (~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X1 @ X3 @
% 157.95/20.91 Y0))))))
% 157.95/20.91 | (mnot @ (mbox_s4 @ (qmltpeq @ X2 @ X1)) @ X0)
% 157.95/20.91 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X2 @ X3 @
% 157.95/20.91 Y0))))))
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X4)
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X5)
% 157.95/20.91 | ~ (exists_in_world @ X2 @ X6)
% 157.95/20.91 | ~ (rel_s4 @ X7 @ X6)
% 157.95/20.91 | ~ (rel_s4 @ X6 @ X5)
% 157.95/20.91 | ~ (rel_s4 @ X5 @ X4)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X0))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl263, '1'])).
% 157.95/20.91 thf(zip_derived_cl265, plain,
% 157.95/20.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : mu, X6 : mu, X7 : mu]:
% 157.95/20.91 (~ (mbox_s4 @ (qmltpeq @ X5 @ X6) @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X1 @ X0)
% 157.95/20.91 | ~ (rel_s4 @ X2 @ X1)
% 157.95/20.91 | ~ (rel_s4 @ X3 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X3)
% 157.95/20.91 | ~ (exists_in_world @ X5 @ X3)
% 157.95/20.91 | ~ (exists_in_world @ X6 @ X2)
% 157.95/20.91 | ~ (exists_in_world @ X7 @ X1)
% 157.95/20.91 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X5 @ X7 @
% 157.95/20.91 Y0))))))
% 157.95/20.91 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X6 @
% 157.95/20.91 X7 @ Y0)))))))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl264, '4'])).
% 157.95/20.91 thf(zip_derived_cl266, plain,
% 157.95/20.91 (![X0 : mu, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 157.95/20.91 (~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X3 @ X1 @
% 157.95/20.91 Y0))))))
% 157.95/20.91 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.91 X0 @ Y0))))))
% 157.95/20.91 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X3 @ X0 @
% 157.95/20.91 Y0))))))
% 157.95/20.91 | ~ (exists_in_world @ X0 @ X4)
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X5)
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X6)
% 157.95/20.91 | ~ (rel_s4 @ X7 @ X6)
% 157.95/20.91 | ~ (rel_s4 @ X6 @ X5)
% 157.95/20.91 | ~ (rel_s4 @ X5 @ X4)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X2))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl265, '1'])).
% 157.95/20.91 thf(zip_derived_cl267, plain,
% 157.95/20.91 (![X0 : mu, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 157.95/20.91 (~ (((((~) @ (rel_s4 @ X2 @ ('#sk2' @ X3 @ X1 @ X2)))) | (qmltpeq @
% 157.95/20.91 X3 @ X1 @ ('#sk2' @ X3 @ X1 @ X2))))
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X5 @ X4)
% 157.95/20.91 | ~ (rel_s4 @ X6 @ X5)
% 157.95/20.91 | ~ (rel_s4 @ X7 @ X6)
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X6)
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X5)
% 157.95/20.91 | ~ (exists_in_world @ X0 @ X4)
% 157.95/20.91 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X3 @ X0 @
% 157.95/20.91 Y0))))))
% 157.95/20.91 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.91 X0 @ Y0)))))))),
% 157.95/20.91 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl266])).
% 157.95/20.91 thf(zip_derived_cl268, plain,
% 157.95/20.91 (![X0 : mu, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 157.95/20.91 ( (rel_s4 @ X2 @ ('#sk2' @ X3 @ X1 @ X2))
% 157.95/20.91 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.91 X0 @ Y0))))))
% 157.95/20.91 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X3 @ X0 @
% 157.95/20.91 Y0))))))
% 157.95/20.91 | ~ (exists_in_world @ X0 @ X4)
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X5)
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X6)
% 157.95/20.91 | ~ (rel_s4 @ X7 @ X6)
% 157.95/20.91 | ~ (rel_s4 @ X6 @ X5)
% 157.95/20.91 | ~ (rel_s4 @ X5 @ X4)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X2))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl267])).
% 157.95/20.91 thf(zip_derived_cl268, plain,
% 157.95/20.91 (![X0 : mu, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 157.95/20.91 ( (rel_s4 @ X2 @ ('#sk2' @ X3 @ X1 @ X2))
% 157.95/20.91 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.91 X0 @ Y0))))))
% 157.95/20.91 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X3 @ X0 @
% 157.95/20.91 Y0))))))
% 157.95/20.91 | ~ (exists_in_world @ X0 @ X4)
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X5)
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X6)
% 157.95/20.91 | ~ (rel_s4 @ X7 @ X6)
% 157.95/20.91 | ~ (rel_s4 @ X6 @ X5)
% 157.95/20.91 | ~ (rel_s4 @ X5 @ X4)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X2))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl267])).
% 157.95/20.91 thf(zip_derived_cl270, plain,
% 157.95/20.91 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.91 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.91 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.91 X0 @ Y0)))))))),
% 157.95/20.91 define([status(thm)])).
% 157.95/20.91 thf(zip_derived_cl272, plain,
% 157.95/20.91 (![X0 : mu, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 157.95/20.91 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X4 @ X2)
% 157.95/20.91 | ~ (rel_s4 @ X5 @ X4)
% 157.95/20.91 | ~ (rel_s4 @ X6 @ X5)
% 157.95/20.91 | ~ (rel_s4 @ X7 @ X6)
% 157.95/20.91 | ~ (exists_in_world @ X3 @ X6)
% 157.95/20.91 | ~ (exists_in_world @ X1 @ X5)
% 157.95/20.91 | ~ (exists_in_world @ X0 @ X4)
% 157.95/20.91 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X3 @ X0 @
% 157.95/20.91 Y0))))))
% 157.95/20.91 | (rel_s4 @ X2 @ ('#sk2' @ X3 @ X1 @ X2)))),
% 157.95/20.91 inference('renaming', [status(thm)],
% 157.95/20.91 [zip_derived_cl268, zip_derived_cl270])).
% 157.95/20.91 thf(zip_derived_cl274, plain,
% 157.95/20.91 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.91 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.91 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.91 Y0)))))))),
% 157.95/20.91 define([status(thm)])).
% 157.95/20.91 thf(zip_derived_cl270, plain,
% 157.95/20.91 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.91 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.91 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.91 X0 @ Y0)))))))),
% 157.95/20.91 define([status(thm)])).
% 157.95/20.91 thf(zip_derived_cl2547, plain,
% 157.95/20.91 (( ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | (((mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.91 '#sk5'))))),
% 157.95/20.91 inference('renaming', [status(thm)],
% 157.95/20.91 [zip_derived_cl2542, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.91 thf(zip_derived_cl2555, plain,
% 157.95/20.91 (( (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2547])).
% 157.95/20.91 thf(zip_derived_cl2563, plain,
% 157.95/20.91 (( (((mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.91 '#sk5') | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.91 '#sk5')))
% 157.95/20.91 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.91 '#sk5'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2555, '6'])).
% 157.95/20.91 thf(zip_derived_cl2571, plain,
% 157.95/20.91 (( (((mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.91 '#sk5')))
% 157.95/20.91 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.91 '#sk5'))),
% 157.95/20.91 inference('rw', [status(thm)], [zip_derived_cl2563, '3', '3'])).
% 157.95/20.91 thf(zip_derived_cl2572, plain,
% 157.95/20.91 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | (((mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.91 '#sk5'))))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2571, '4'])).
% 157.95/20.91 thf(zip_derived_cl2580, plain,
% 157.95/20.91 ((~ (((mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.91 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 '#sk5')))
% 157.95/20.91 | (((mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.91 '#sk5')))
% 157.95/20.91 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2572, '5'])).
% 157.95/20.91 thf(zip_derived_cl2589, plain,
% 157.95/20.91 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ '#sk5')
% 157.95/20.91 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | (((mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.91 '#sk5'))))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2580])).
% 157.95/20.91 thf(zip_derived_cl2600, plain,
% 157.95/20.91 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk5')
% 157.95/20.91 | (((mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.91 '#sk5')))
% 157.95/20.91 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2589, '2'])).
% 157.95/20.91 thf(zip_derived_cl2611, plain,
% 157.95/20.91 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.91 (op @ e0 @ e0) @ e1 @ Y0))))))
% 157.95/20.91 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | (((mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.91 '#sk5'))))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2600, '7'])).
% 157.95/20.91 thf(zip_derived_cl274, plain,
% 157.95/20.91 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.91 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.91 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.91 Y0)))))))),
% 157.95/20.91 define([status(thm)])).
% 157.95/20.91 thf(zip_derived_cl270, plain,
% 157.95/20.91 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.91 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.91 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.91 X0 @ Y0)))))))),
% 157.95/20.91 define([status(thm)])).
% 157.95/20.91 thf(zip_derived_cl2620, plain,
% 157.95/20.91 (( ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | (((mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.91 '#sk5') | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.91 '#sk5')))
% 157.95/20.91 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.91 inference('renaming', [status(thm)],
% 157.95/20.91 [zip_derived_cl2611, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.91 thf(zip_derived_cl2632, plain,
% 157.95/20.91 (( (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2620])).
% 157.95/20.91 thf(zip_derived_cl2643, plain,
% 157.95/20.91 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.91 '#sk5'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2632, '4'])).
% 157.95/20.91 thf(zip_derived_cl2659, plain,
% 157.95/20.91 ((~ (((mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.91 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 '#sk5')))
% 157.95/20.91 | (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2643, '5'])).
% 157.95/20.91 thf(zip_derived_cl2670, plain,
% 157.95/20.91 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | ~ (((mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.91 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 '#sk5'))))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2659, '4'])).
% 157.95/20.91 thf(zip_derived_cl2687, plain,
% 157.95/20.91 ((~ (((mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.91 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 '#sk5')))
% 157.95/20.91 | ~ (((mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.91 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 '#sk5')))
% 157.95/20.91 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2670, '5'])).
% 157.95/20.91 thf(zip_derived_cl2702, plain,
% 157.95/20.91 ((~ (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.91 | ~ (((mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.91 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 '#sk5'))))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2687])).
% 157.95/20.91 thf(zip_derived_cl2721, plain,
% 157.95/20.91 (( ('#form6')
% 157.95/20.91 | ~ (((mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.91 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 '#sk5'))))),
% 157.95/20.91 define([status(thm)])).
% 157.95/20.91 thf(zip_derived_cl2722, plain,
% 157.95/20.91 ((~ (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2721])).
% 157.95/20.91 thf(zip_derived_cl2741, plain,
% 157.95/20.91 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2722, '2'])).
% 157.95/20.91 thf(zip_derived_cl2763, plain,
% 157.95/20.91 (( (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('rw', [status(thm)], [zip_derived_cl2741, '3'])).
% 157.95/20.91 thf(zip_derived_cl2764, plain,
% 157.95/20.91 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3))) @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2763, '4'])).
% 157.95/20.91 thf(zip_derived_cl2785, plain,
% 157.95/20.91 ((~ (((mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @
% 157.95/20.91 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 '#sk5')))
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2764, '5'])).
% 157.95/20.91 thf(zip_derived_cl2811, plain,
% 157.95/20.91 ((~ (mnot @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2785])).
% 157.95/20.91 thf(zip_derived_cl2835, plain,
% 157.95/20.91 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ '#sk5')
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2811, '2'])).
% 157.95/20.91 thf(zip_derived_cl2862, plain,
% 157.95/20.91 (( (mnot @
% 157.95/20.91 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3))) @
% 157.95/20.91 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.91 '#sk5')
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('rw', [status(thm)], [zip_derived_cl2835, '3'])).
% 157.95/20.91 thf(zip_derived_cl2863, plain,
% 157.95/20.91 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3))) @
% 157.95/20.91 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ '#sk5')
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2862, '4'])).
% 157.95/20.91 thf(zip_derived_cl2887, plain,
% 157.95/20.91 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ '#sk5') |
% 157.95/20.91 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ '#sk5')))
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2863, '5'])).
% 157.95/20.91 thf(zip_derived_cl2915, plain,
% 157.95/20.91 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ '#sk5')
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2887])).
% 157.95/20.91 thf(zip_derived_cl2944, plain,
% 157.95/20.91 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3) @ '#sk5') | ('#form6'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2915, '2'])).
% 157.95/20.91 thf(zip_derived_cl2977, plain,
% 157.95/20.91 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.91 (op @ e3 @ e3) @ e3 @ Y0))))))
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2944, '7'])).
% 157.95/20.91 thf(zip_derived_cl3003, plain,
% 157.95/20.91 (![X2 : $i]:
% 157.95/20.91 ( (((((~) @ (rel_s4 @ '#sk5' @ X2))) | (qmltpeq @ (op @ e3 @ e3) @
% 157.95/20.91 e3 @ X2)))
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2977])).
% 157.95/20.91 thf(zip_derived_cl3031, plain,
% 157.95/20.91 (![X2 : $i]:
% 157.95/20.91 (~ (rel_s4 @ '#sk5' @ X2)
% 157.95/20.91 | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X2)
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3003])).
% 157.95/20.91 thf(zip_derived_cl2916, plain,
% 157.95/20.91 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ '#sk5')
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2887])).
% 157.95/20.91 thf(zip_derived_cl2945, plain,
% 157.95/20.91 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3) @ '#sk5') | ('#form6'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2916, '2'])).
% 157.95/20.91 thf(zip_derived_cl2978, plain,
% 157.95/20.91 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.91 (op @ e2 @ e2) @ e3 @ Y0))))))
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2945, '7'])).
% 157.95/20.91 thf(zip_derived_cl3004, plain,
% 157.95/20.91 (![X2 : $i]:
% 157.95/20.91 ( (((((~) @ (rel_s4 @ '#sk5' @ X2))) | (qmltpeq @ (op @ e2 @ e2) @
% 157.95/20.91 e3 @ X2)))
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2978])).
% 157.95/20.91 thf(zip_derived_cl3032, plain,
% 157.95/20.91 (![X2 : $i]:
% 157.95/20.91 (~ (rel_s4 @ '#sk5' @ X2)
% 157.95/20.91 | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X2)
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3004])).
% 157.95/20.91 thf(zip_derived_cl270, plain,
% 157.95/20.91 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.91 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.91 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.91 X0 @ Y0)))))))),
% 157.95/20.91 define([status(thm)])).
% 157.95/20.91 thf(zip_derived_cl271, plain,
% 157.95/20.91 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.91 (~ (((((~) @ (rel_s4 @ X2 @ ('#sk2' @ X1 @ X0 @ X2)))) | (qmltpeq @
% 157.95/20.91 X1 @ X0 @ ('#sk2' @ X1 @ X0 @ X2))))
% 157.95/20.91 | ('#form3' @ X0 @ X1 @ X2))),
% 157.95/20.91 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl270])).
% 157.95/20.91 thf(zip_derived_cl277, plain,
% 157.95/20.91 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.91 ( (rel_s4 @ X2 @ ('#sk2' @ X1 @ X0 @ X2)) | ('#form3' @ X0 @ X1 @ X2))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl271])).
% 157.95/20.91 thf(zip_derived_cl2812, plain,
% 157.95/20.91 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ '#sk5')
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2785])).
% 157.95/20.91 thf(zip_derived_cl2836, plain,
% 157.95/20.91 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3) @ '#sk5') | ('#form6'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2812, '2'])).
% 157.95/20.91 thf(zip_derived_cl2864, plain,
% 157.95/20.91 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.91 (op @ e1 @ e1) @ e3 @ Y0))))))
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2836, '7'])).
% 157.95/20.91 thf(zip_derived_cl2888, plain,
% 157.95/20.91 (![X2 : $i]:
% 157.95/20.91 ( (((((~) @ (rel_s4 @ '#sk5' @ X2))) | (qmltpeq @ (op @ e1 @ e1) @
% 157.95/20.91 e3 @ X2)))
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2864])).
% 157.95/20.91 thf(zip_derived_cl2917, plain,
% 157.95/20.91 (![X2 : $i]:
% 157.95/20.91 (~ (rel_s4 @ '#sk5' @ X2)
% 157.95/20.91 | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)
% 157.95/20.91 | ('#form6'))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2888])).
% 157.95/20.91 thf(zip_derived_cl2511, plain,
% 157.95/20.91 (~ (mnot @
% 157.95/20.91 (mbox_s4 @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))) @
% 157.95/20.91 '#sk5')),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2510])).
% 157.95/20.91 thf(zip_derived_cl2513, plain,
% 157.95/20.91 ( (mbox_s4 @
% 157.95/20.91 (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))) @
% 157.95/20.91 '#sk5')),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2511, '2'])).
% 157.95/20.91 thf(zip_derived_cl2515, plain,
% 157.95/20.91 ( (((!!) @ (^[Y0 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @
% 157.95/20.91 Y0))))))),
% 157.95/20.91 inference('rw_clause', [status(thm)], [zip_derived_cl2513, '7'])).
% 157.95/20.91 thf(zip_derived_cl2517, plain,
% 157.95/20.91 (![X2 : $i]:
% 157.95/20.91 (((((~) @ (rel_s4 @ '#sk5' @ X2))) | (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @
% 157.95/20.91 X2)))),
% 157.95/20.91 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2515])).
% 157.95/20.91 thf(zip_derived_cl2520, plain,
% 157.95/20.91 (![X2 : $i]:
% 157.95/20.91 (~ (rel_s4 @ '#sk5' @ X2)
% 157.95/20.91 | (mnot @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.91 (mor @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.91 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.91 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @
% 157.95/20.91 X2))),
% 157.95/20.91 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2517])).
% 157.95/20.92 thf(zip_derived_cl2522, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.92 (mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.92 (mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))) @
% 157.95/20.92 X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2520, '4'])).
% 157.95/20.92 thf(zip_derived_cl2525, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.92 (mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 X0) | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @
% 157.95/20.92 X0)))
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2522, '5'])).
% 157.95/20.92 thf(zip_derived_cl2527, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.92 (mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 X0) | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))))) @
% 157.95/20.92 X0)))
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2525, '3'])).
% 157.95/20.92 thf(zip_derived_cl2528, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.92 (mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2527])).
% 157.95/20.92 thf(zip_derived_cl2532, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 X0) | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 X0)))
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2528, '5'])).
% 157.95/20.92 thf(zip_derived_cl2536, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 X0) | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 X0)))
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2532, '3'])).
% 157.95/20.92 thf(zip_derived_cl2537, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2536])).
% 157.95/20.92 thf(zip_derived_cl2543, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (((mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 X0) | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 X0)))
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2537, '5'])).
% 157.95/20.92 thf(zip_derived_cl2548, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 X0) | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 X0)))
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2543, '3', '3'])).
% 157.95/20.92 thf(zip_derived_cl2549, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2548])).
% 157.95/20.92 thf(zip_derived_cl2556, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2549, '2'])).
% 157.95/20.92 thf(zip_derived_cl2564, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 ( (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ X0)))
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2556, '6'])).
% 157.95/20.92 thf(zip_derived_cl2573, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 ( (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 X0)
% 157.95/20.92 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2564])).
% 157.95/20.92 thf(zip_derived_cl2581, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @
% 157.95/20.92 X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2573, '4'])).
% 157.95/20.92 thf(zip_derived_cl2590, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ X0))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2581, '3'])).
% 157.95/20.92 thf(zip_derived_cl2591, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 X0)
% 157.95/20.92 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2590, '2'])).
% 157.95/20.92 thf(zip_derived_cl2601, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 ( (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @
% 157.95/20.92 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0)))
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2591, '6'])).
% 157.95/20.92 thf(zip_derived_cl2612, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @
% 157.95/20.92 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2601, '4'])).
% 157.95/20.92 thf(zip_derived_cl2621, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e0 @ e0) @ e3 @ Y0))))))
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @
% 157.95/20.92 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0)))
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2612, '1'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl2633, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @
% 157.95/20.92 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0))))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl2621, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2644, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 ( (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @
% 157.95/20.92 X0)
% 157.95/20.92 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2633])).
% 157.95/20.92 thf(zip_derived_cl2660, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2644, '4'])).
% 157.95/20.92 thf(zip_derived_cl2671, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2660, '3'])).
% 157.95/20.92 thf(zip_derived_cl2672, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ X0)
% 157.95/20.92 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2671, '2'])).
% 157.95/20.92 thf(zip_derived_cl2688, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 ( (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0) |
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0)))
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2672, '6'])).
% 157.95/20.92 thf(zip_derived_cl2704, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0)
% 157.95/20.92 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0) |
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2688, '4'])).
% 157.95/20.92 thf(zip_derived_cl2726, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e1 @ e1) @ e3 @ Y0))))))
% 157.95/20.92 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0) |
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0)))
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2704, '1'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl2744, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0)
% 157.95/20.92 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0) |
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0))))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl2726, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2767, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 ( (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0)
% 157.95/20.92 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2744])).
% 157.95/20.92 thf(zip_derived_cl2788, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3) @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0)
% 157.95/20.92 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2767, '4'])).
% 157.95/20.92 thf(zip_derived_cl2814, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e3 @ e3) @ e3 @ Y0))))))
% 157.95/20.92 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2788, '1'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl2837, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ ('#form3' @ e3 @ (op @ e3 @ e3) @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0)
% 157.95/20.92 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl2814, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2865, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3) @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e3 @ e3) @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2837, '4'])).
% 157.95/20.92 thf(zip_derived_cl2889, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e2 @ e2) @ e3 @ Y0))))))
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e3 @ e3) @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2865, '1'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl2918, plain,
% 157.95/20.92 (![X0 : $i]:
% 157.95/20.92 (~ ('#form3' @ e3 @ (op @ e2 @ e2) @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0)
% 157.95/20.92 | ~ (rel_s4 @ '#sk5' @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0)
% 157.95/20.92 | ~ ('#form3' @ e3 @ (op @ e3 @ e3) @ X0))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl2889, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2723, plain,
% 157.95/20.92 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ '#sk5')
% 157.95/20.92 | ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2721])).
% 157.95/20.92 thf(zip_derived_cl2742, plain,
% 157.95/20.92 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk5') | ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2723, '2'])).
% 157.95/20.92 thf(zip_derived_cl2765, plain,
% 157.95/20.92 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e0 @ e0) @ e3 @ Y0))))))
% 157.95/20.92 | ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2742, '7'])).
% 157.95/20.92 thf(zip_derived_cl2786, plain,
% 157.95/20.92 (![X2 : $i]:
% 157.95/20.92 ( (((((~) @ (rel_s4 @ '#sk5' @ X2))) | (qmltpeq @ (op @ e0 @ e0) @
% 157.95/20.92 e3 @ X2)))
% 157.95/20.92 | ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2765])).
% 157.95/20.92 thf(zip_derived_cl2813, plain,
% 157.95/20.92 (![X2 : $i]:
% 157.95/20.92 (~ (rel_s4 @ '#sk5' @ X2)
% 157.95/20.92 | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2)
% 157.95/20.92 | ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2786])).
% 157.95/20.92 thf(zip_derived_cl278, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ (qmltpeq @ X1 @ X0 @ ('#sk2' @ X1 @ X0 @ X2))
% 157.95/20.92 | ('#form3' @ X0 @ X1 @ X2))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl271])).
% 157.95/20.92 thf(zip_derived_cl2530, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2526])).
% 157.95/20.92 thf(zip_derived_cl2534, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2530, '2'])).
% 157.95/20.92 thf(zip_derived_cl2540, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2534, '3'])).
% 157.95/20.92 thf(zip_derived_cl2541, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2540, '4'])).
% 157.95/20.92 thf(zip_derived_cl2546, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2541, '5'])).
% 157.95/20.92 thf(zip_derived_cl2553, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2546])).
% 157.95/20.92 thf(zip_derived_cl2561, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2553, '2'])).
% 157.95/20.92 thf(zip_derived_cl2568, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2561, '3'])).
% 157.95/20.92 thf(zip_derived_cl2569, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2568, '4'])).
% 157.95/20.92 thf(zip_derived_cl2578, plain,
% 157.95/20.92 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ '#sk5') |
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ '#sk5')))
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2569, '5'])).
% 157.95/20.92 thf(zip_derived_cl2586, plain,
% 157.95/20.92 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2578])).
% 157.95/20.92 thf(zip_derived_cl2597, plain,
% 157.95/20.92 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0) @ '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2586, '2'])).
% 157.95/20.92 thf(zip_derived_cl2606, plain,
% 157.95/20.92 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e2 @ e2) @ e0 @ Y0))))))
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2597, '7'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl2617, plain,
% 157.95/20.92 (( ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl2606, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2627, plain,
% 157.95/20.92 (( (mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2617])).
% 157.95/20.92 thf(zip_derived_cl2638, plain,
% 157.95/20.92 (( (((mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 '#sk5') | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2627, '6'])).
% 157.95/20.92 thf(zip_derived_cl2651, plain,
% 157.95/20.92 (( (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2638, '3', '3'])).
% 157.95/20.92 thf(zip_derived_cl2652, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2651, '4'])).
% 157.95/20.92 thf(zip_derived_cl2665, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2652, '5'])).
% 157.95/20.92 thf(zip_derived_cl2679, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2665])).
% 157.95/20.92 thf(zip_derived_cl2694, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2679, '2'])).
% 157.95/20.92 thf(zip_derived_cl2711, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2694, '3'])).
% 157.95/20.92 thf(zip_derived_cl2712, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2711, '4'])).
% 157.95/20.92 thf(zip_derived_cl2732, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2712, '5'])).
% 157.95/20.92 thf(zip_derived_cl2751, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2732])).
% 157.95/20.92 thf(zip_derived_cl2774, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2751, '2'])).
% 157.95/20.92 thf(zip_derived_cl2796, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2774, '3'])).
% 157.95/20.92 thf(zip_derived_cl2797, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2796, '4'])).
% 157.95/20.92 thf(zip_derived_cl2821, plain,
% 157.95/20.92 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') |
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5')))
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2797, '5'])).
% 157.95/20.92 thf(zip_derived_cl2845, plain,
% 157.95/20.92 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2821])).
% 157.95/20.92 thf(zip_derived_cl2873, plain,
% 157.95/20.92 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2845, '2'])).
% 157.95/20.92 thf(zip_derived_cl2897, plain,
% 157.95/20.92 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e2 @ e2) @ e1 @ Y0))))))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2873, '7'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl2926, plain,
% 157.95/20.92 (( ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl2897, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2953, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2926])).
% 157.95/20.92 thf(zip_derived_cl2985, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2953, '4'])).
% 157.95/20.92 thf(zip_derived_cl3012, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2985, '5'])).
% 157.95/20.92 thf(zip_derived_cl2721, plain,
% 157.95/20.92 (( ('#form6')
% 157.95/20.92 | ~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl3040, plain,
% 157.95/20.92 ((~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl3012, zip_derived_cl2721])).
% 157.95/20.92 thf(zip_derived_cl3068, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3040, '4'])).
% 157.95/20.92 thf(zip_derived_cl3101, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3068, '5'])).
% 157.95/20.92 thf(zip_derived_cl3130, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3101])).
% 157.95/20.92 thf(zip_derived_cl3156, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3130, '2'])).
% 157.95/20.92 thf(zip_derived_cl3186, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl3156, '3'])).
% 157.95/20.92 thf(zip_derived_cl3187, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3186, '4'])).
% 157.95/20.92 thf(zip_derived_cl3216, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3187, '5'])).
% 157.95/20.92 thf(zip_derived_cl3240, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3216])).
% 157.95/20.92 thf(zip_derived_cl3256, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3240, '2'])).
% 157.95/20.92 thf(zip_derived_cl3275, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl3256, '3'])).
% 157.95/20.92 thf(zip_derived_cl3276, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3275, '4'])).
% 157.95/20.92 thf(zip_derived_cl3292, plain,
% 157.95/20.92 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3276, '5'])).
% 157.95/20.92 thf(zip_derived_cl3307, plain,
% 157.95/20.92 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3292])).
% 157.95/20.92 thf(zip_derived_cl3315, plain,
% 157.95/20.92 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3307, '2'])).
% 157.95/20.92 thf(zip_derived_cl3323, plain,
% 157.95/20.92 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e2 @ e2) @ e2 @ Y0))))))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3315, '7'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl3331, plain,
% 157.95/20.92 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl3323, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2554, plain,
% 157.95/20.92 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2546])).
% 157.95/20.92 thf(zip_derived_cl2562, plain,
% 157.95/20.92 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0) @ '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2554, '2'])).
% 157.95/20.92 thf(zip_derived_cl2570, plain,
% 157.95/20.92 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e1 @ e1) @ e0 @ Y0))))))
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2562, '7'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl2579, plain,
% 157.95/20.92 (( ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl2570, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2587, plain,
% 157.95/20.92 (( (mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2579])).
% 157.95/20.92 thf(zip_derived_cl2598, plain,
% 157.95/20.92 (( (((mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 '#sk5') | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2587, '6'])).
% 157.95/20.92 thf(zip_derived_cl2607, plain,
% 157.95/20.92 (( (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2598, '3', '3'])).
% 157.95/20.92 thf(zip_derived_cl2608, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2607, '4'])).
% 157.95/20.92 thf(zip_derived_cl2618, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2608, '5'])).
% 157.95/20.92 thf(zip_derived_cl2628, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2618])).
% 157.95/20.92 thf(zip_derived_cl2639, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2628, '2'])).
% 157.95/20.92 thf(zip_derived_cl2653, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2639, '3'])).
% 157.95/20.92 thf(zip_derived_cl2654, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2653, '4'])).
% 157.95/20.92 thf(zip_derived_cl2666, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2654, '5'])).
% 157.95/20.92 thf(zip_derived_cl2681, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2666])).
% 157.95/20.92 thf(zip_derived_cl2696, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2681, '2'])).
% 157.95/20.92 thf(zip_derived_cl2714, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2696, '3'])).
% 157.95/20.92 thf(zip_derived_cl2715, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2714, '4'])).
% 157.95/20.92 thf(zip_derived_cl2734, plain,
% 157.95/20.92 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') |
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5')))
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2715, '5'])).
% 157.95/20.92 thf(zip_derived_cl2755, plain,
% 157.95/20.92 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2734])).
% 157.95/20.92 thf(zip_derived_cl2778, plain,
% 157.95/20.92 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2755, '2'])).
% 157.95/20.92 thf(zip_derived_cl2801, plain,
% 157.95/20.92 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e2 @ e2) @ e1 @ Y0))))))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2778, '7'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl2825, plain,
% 157.95/20.92 (( ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl2801, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2849, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2825])).
% 157.95/20.92 thf(zip_derived_cl2877, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2849, '4'])).
% 157.95/20.92 thf(zip_derived_cl2902, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2877, '5'])).
% 157.95/20.92 thf(zip_derived_cl2721, plain,
% 157.95/20.92 (( ('#form6')
% 157.95/20.92 | ~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl2931, plain,
% 157.95/20.92 ((~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl2902, zip_derived_cl2721])).
% 157.95/20.92 thf(zip_derived_cl2959, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2931, '4'])).
% 157.95/20.92 thf(zip_derived_cl2990, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2959, '5'])).
% 157.95/20.92 thf(zip_derived_cl3019, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2990])).
% 157.95/20.92 thf(zip_derived_cl3047, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3019, '2'])).
% 157.95/20.92 thf(zip_derived_cl3078, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl3047, '3'])).
% 157.95/20.92 thf(zip_derived_cl3079, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3078, '4'])).
% 157.95/20.92 thf(zip_derived_cl3108, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3079, '5'])).
% 157.95/20.92 thf(zip_derived_cl3138, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3108])).
% 157.95/20.92 thf(zip_derived_cl3164, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3138, '2'])).
% 157.95/20.92 thf(zip_derived_cl3197, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl3164, '3'])).
% 157.95/20.92 thf(zip_derived_cl3198, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3197, '4'])).
% 157.95/20.92 thf(zip_derived_cl3224, plain,
% 157.95/20.92 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3198, '5'])).
% 157.95/20.92 thf(zip_derived_cl3247, plain,
% 157.95/20.92 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3224])).
% 157.95/20.92 thf(zip_derived_cl3263, plain,
% 157.95/20.92 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3247, '2'])).
% 157.95/20.92 thf(zip_derived_cl3283, plain,
% 157.95/20.92 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e2 @ e2) @ e2 @ Y0))))))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3263, '7'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl3299, plain,
% 157.95/20.92 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl3283, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2588, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2580])).
% 157.95/20.92 thf(zip_derived_cl2599, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2588, '2'])).
% 157.95/20.92 thf(zip_derived_cl2609, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2599, '3'])).
% 157.95/20.92 thf(zip_derived_cl2610, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2609, '4'])).
% 157.95/20.92 thf(zip_derived_cl2619, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2610, '5'])).
% 157.95/20.92 thf(zip_derived_cl2630, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2619])).
% 157.95/20.92 thf(zip_derived_cl2641, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2630, '2'])).
% 157.95/20.92 thf(zip_derived_cl2656, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2641, '3'])).
% 157.95/20.92 thf(zip_derived_cl2657, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2656, '4'])).
% 157.95/20.92 thf(zip_derived_cl2668, plain,
% 157.95/20.92 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') |
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5')))
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2657, '5'])).
% 157.95/20.92 thf(zip_derived_cl2685, plain,
% 157.95/20.92 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2668])).
% 157.95/20.92 thf(zip_derived_cl2700, plain,
% 157.95/20.92 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2685, '2'])).
% 157.95/20.92 thf(zip_derived_cl2719, plain,
% 157.95/20.92 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e2 @ e2) @ e1 @ Y0))))))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2700, '7'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl2738, plain,
% 157.95/20.92 (( ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl2719, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2759, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2738])).
% 157.95/20.92 thf(zip_derived_cl2782, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2759, '4'])).
% 157.95/20.92 thf(zip_derived_cl2806, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2782, '5'])).
% 157.95/20.92 thf(zip_derived_cl2721, plain,
% 157.95/20.92 (( ('#form6')
% 157.95/20.92 | ~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl2830, plain,
% 157.95/20.92 ((~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl2806, zip_derived_cl2721])).
% 157.95/20.92 thf(zip_derived_cl2855, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2830, '4'])).
% 157.95/20.92 thf(zip_derived_cl2882, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2855, '5'])).
% 157.95/20.92 thf(zip_derived_cl2909, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2882])).
% 157.95/20.92 thf(zip_derived_cl2938, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2909, '2'])).
% 157.95/20.92 thf(zip_derived_cl2969, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2938, '3'])).
% 157.95/20.92 thf(zip_derived_cl2970, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2969, '4'])).
% 157.95/20.92 thf(zip_derived_cl2997, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2970, '5'])).
% 157.95/20.92 thf(zip_derived_cl3027, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2997])).
% 157.95/20.92 thf(zip_derived_cl3055, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3027, '2'])).
% 157.95/20.92 thf(zip_derived_cl3089, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl3055, '3'])).
% 157.95/20.92 thf(zip_derived_cl3090, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3089, '4'])).
% 157.95/20.92 thf(zip_derived_cl3116, plain,
% 157.95/20.92 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3090, '5'])).
% 157.95/20.92 thf(zip_derived_cl3145, plain,
% 157.95/20.92 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3116])).
% 157.95/20.92 thf(zip_derived_cl3171, plain,
% 157.95/20.92 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3145, '2'])).
% 157.95/20.92 thf(zip_derived_cl3205, plain,
% 157.95/20.92 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e2 @ e2) @ e2 @ Y0))))))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3171, '7'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl3231, plain,
% 157.95/20.92 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl3205, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2585, plain,
% 157.95/20.92 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2578])).
% 157.95/20.92 thf(zip_derived_cl2596, plain,
% 157.95/20.92 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0) @ '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2585, '2'])).
% 157.95/20.92 thf(zip_derived_cl2605, plain,
% 157.95/20.92 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e3 @ e3) @ e0 @ Y0))))))
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2596, '7'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl2616, plain,
% 157.95/20.92 (( ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | (((mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl2605, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2626, plain,
% 157.95/20.92 (( (mor @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2616])).
% 157.95/20.92 thf(zip_derived_cl2637, plain,
% 157.95/20.92 (( (((mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 '#sk5') | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2626, '6'])).
% 157.95/20.92 thf(zip_derived_cl2649, plain,
% 157.95/20.92 (( (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2637, '3', '3'])).
% 157.95/20.92 thf(zip_derived_cl2650, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2649, '4'])).
% 157.95/20.92 thf(zip_derived_cl2664, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2650, '5'])).
% 157.95/20.92 thf(zip_derived_cl2677, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2664])).
% 157.95/20.92 thf(zip_derived_cl2692, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2677, '2'])).
% 157.95/20.92 thf(zip_derived_cl2708, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2692, '3'])).
% 157.95/20.92 thf(zip_derived_cl2709, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2708, '4'])).
% 157.95/20.92 thf(zip_derived_cl2730, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2709, '5'])).
% 157.95/20.92 thf(zip_derived_cl2748, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2730])).
% 157.95/20.92 thf(zip_derived_cl2771, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2748, '2'])).
% 157.95/20.92 thf(zip_derived_cl2792, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl2771, '3'])).
% 157.95/20.92 thf(zip_derived_cl2793, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2792, '4'])).
% 157.95/20.92 thf(zip_derived_cl2818, plain,
% 157.95/20.92 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') |
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5')))
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2793, '5'])).
% 157.95/20.92 thf(zip_derived_cl2841, plain,
% 157.95/20.92 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2818])).
% 157.95/20.92 thf(zip_derived_cl2869, plain,
% 157.95/20.92 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2841, '2'])).
% 157.95/20.92 thf(zip_derived_cl2892, plain,
% 157.95/20.92 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e2 @ e2) @ e1 @ Y0))))))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2869, '7'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl2921, plain,
% 157.95/20.92 (( ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl2892, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2947, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2921])).
% 157.95/20.92 thf(zip_derived_cl2980, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2947, '4'])).
% 157.95/20.92 thf(zip_derived_cl3006, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2980, '5'])).
% 157.95/20.92 thf(zip_derived_cl2721, plain,
% 157.95/20.92 (( ('#form6')
% 157.95/20.92 | ~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl3034, plain,
% 157.95/20.92 ((~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl3006, zip_derived_cl2721])).
% 157.95/20.92 thf(zip_derived_cl3060, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3034, '4'])).
% 157.95/20.92 thf(zip_derived_cl3095, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3060, '5'])).
% 157.95/20.92 thf(zip_derived_cl3122, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3095])).
% 157.95/20.92 thf(zip_derived_cl3148, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3122, '2'])).
% 157.95/20.92 thf(zip_derived_cl3175, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl3148, '3'])).
% 157.95/20.92 thf(zip_derived_cl3176, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3175, '4'])).
% 157.95/20.92 thf(zip_derived_cl3208, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3176, '5'])).
% 157.95/20.92 thf(zip_derived_cl3234, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3208])).
% 157.95/20.92 thf(zip_derived_cl3250, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3234, '2'])).
% 157.95/20.92 thf(zip_derived_cl3267, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl3250, '3'])).
% 157.95/20.92 thf(zip_derived_cl3268, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3267, '4'])).
% 157.95/20.92 thf(zip_derived_cl3286, plain,
% 157.95/20.92 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3268, '5'])).
% 157.95/20.92 thf(zip_derived_cl3303, plain,
% 157.95/20.92 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3286])).
% 157.95/20.92 thf(zip_derived_cl3311, plain,
% 157.95/20.92 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3303, '2'])).
% 157.95/20.92 thf(zip_derived_cl3319, plain,
% 157.95/20.92 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e2 @ e2) @ e2 @ Y0))))))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3311, '7'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl3327, plain,
% 157.95/20.92 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl3319, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2752, plain,
% 157.95/20.92 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2732])).
% 157.95/20.92 thf(zip_derived_cl2775, plain,
% 157.95/20.92 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2752, '2'])).
% 157.95/20.92 thf(zip_derived_cl2798, plain,
% 157.95/20.92 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.92 (op @ e1 @ e1) @ e1 @ Y0))))))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2775, '7'])).
% 157.95/20.92 thf(zip_derived_cl274, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.92 Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl270, plain,
% 157.95/20.92 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.92 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.92 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.92 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.92 X0 @ Y0)))))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl2822, plain,
% 157.95/20.92 (( ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | (((mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5') | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl2798, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.92 thf(zip_derived_cl2846, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2822])).
% 157.95/20.92 thf(zip_derived_cl2874, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2846, '4'])).
% 157.95/20.92 thf(zip_derived_cl2898, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2874, '5'])).
% 157.95/20.92 thf(zip_derived_cl2721, plain,
% 157.95/20.92 (( ('#form6')
% 157.95/20.92 | ~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.92 '#sk5'))))),
% 157.95/20.92 define([status(thm)])).
% 157.95/20.92 thf(zip_derived_cl2927, plain,
% 157.95/20.92 ((~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.92 '#sk5'))),
% 157.95/20.92 inference('renaming', [status(thm)],
% 157.95/20.92 [zip_derived_cl2898, zip_derived_cl2721])).
% 157.95/20.92 thf(zip_derived_cl2954, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2927, '4'])).
% 157.95/20.92 thf(zip_derived_cl2986, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl2954, '5'])).
% 157.95/20.92 thf(zip_derived_cl3013, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2986])).
% 157.95/20.92 thf(zip_derived_cl3041, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3013, '2'])).
% 157.95/20.92 thf(zip_derived_cl3069, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl3041, '3'])).
% 157.95/20.92 thf(zip_derived_cl3070, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.92 (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3069, '4'])).
% 157.95/20.92 thf(zip_derived_cl3102, plain,
% 157.95/20.92 ((~ (((mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.92 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.92 '#sk5')))
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3070, '5'])).
% 157.95/20.92 thf(zip_derived_cl3132, plain,
% 157.95/20.92 ((~ (mnot @
% 157.95/20.92 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3102])).
% 157.95/20.92 thf(zip_derived_cl3158, plain,
% 157.95/20.92 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.92 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3132, '2'])).
% 157.95/20.92 thf(zip_derived_cl3189, plain,
% 157.95/20.92 (( (mnot @
% 157.95/20.92 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.92 '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw', [status(thm)], [zip_derived_cl3158, '3'])).
% 157.95/20.92 thf(zip_derived_cl3190, plain,
% 157.95/20.92 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3189, '4'])).
% 157.95/20.92 thf(zip_derived_cl3218, plain,
% 157.95/20.92 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 157.95/20.92 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3190, '5'])).
% 157.95/20.92 thf(zip_derived_cl3243, plain,
% 157.95/20.92 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ~ ('#form6'))),
% 157.95/20.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3218])).
% 157.95/20.92 thf(zip_derived_cl3259, plain,
% 157.95/20.92 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 157.95/20.92 | ~ ('#form6')
% 157.95/20.92 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.92 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.92 inference('rw_clause', [status(thm)], [zip_derived_cl3243, '2'])).
% 157.95/20.92 thf(zip_derived_cl3279, plain,
% 157.95/20.93 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.93 (op @ e2 @ e2) @ e2 @ Y0))))))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3259, '7'])).
% 157.95/20.93 thf(zip_derived_cl274, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.93 Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl270, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.93 X0 @ Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl3295, plain,
% 157.95/20.93 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl3279, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.93 thf(zip_derived_cl2682, plain,
% 157.95/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2666])).
% 157.95/20.93 thf(zip_derived_cl2697, plain,
% 157.95/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2682, '2'])).
% 157.95/20.93 thf(zip_derived_cl2716, plain,
% 157.95/20.93 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.93 (op @ e1 @ e1) @ e1 @ Y0))))))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2697, '7'])).
% 157.95/20.93 thf(zip_derived_cl274, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.93 Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl270, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.93 X0 @ Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl2735, plain,
% 157.95/20.93 (( ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl2716, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.93 thf(zip_derived_cl2756, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2735])).
% 157.95/20.93 thf(zip_derived_cl2779, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2756, '4'])).
% 157.95/20.93 thf(zip_derived_cl2802, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2779, '5'])).
% 157.95/20.93 thf(zip_derived_cl2721, plain,
% 157.95/20.93 (( ('#form6')
% 157.95/20.93 | ~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl2826, plain,
% 157.95/20.93 ((~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl2802, zip_derived_cl2721])).
% 157.95/20.93 thf(zip_derived_cl2850, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2826, '4'])).
% 157.95/20.93 thf(zip_derived_cl2878, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2850, '5'])).
% 157.95/20.93 thf(zip_derived_cl2903, plain,
% 157.95/20.93 ((~ (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2878])).
% 157.95/20.93 thf(zip_derived_cl2932, plain,
% 157.95/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2903, '2'])).
% 157.95/20.93 thf(zip_derived_cl2960, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw', [status(thm)], [zip_derived_cl2932, '3'])).
% 157.95/20.93 thf(zip_derived_cl2961, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2960, '4'])).
% 157.95/20.93 thf(zip_derived_cl2991, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2961, '5'])).
% 157.95/20.93 thf(zip_derived_cl3021, plain,
% 157.95/20.93 ((~ (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2991])).
% 157.95/20.93 thf(zip_derived_cl3049, plain,
% 157.95/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3021, '2'])).
% 157.95/20.93 thf(zip_derived_cl3081, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw', [status(thm)], [zip_derived_cl3049, '3'])).
% 157.95/20.93 thf(zip_derived_cl3082, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3081, '4'])).
% 157.95/20.93 thf(zip_derived_cl3110, plain,
% 157.95/20.93 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3082, '5'])).
% 157.95/20.93 thf(zip_derived_cl3141, plain,
% 157.95/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3110])).
% 157.95/20.93 thf(zip_derived_cl3167, plain,
% 157.95/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3141, '2'])).
% 157.95/20.93 thf(zip_derived_cl3201, plain,
% 157.95/20.93 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.93 (op @ e2 @ e2) @ e2 @ Y0))))))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3167, '7'])).
% 157.95/20.93 thf(zip_derived_cl274, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.93 Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl270, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.93 X0 @ Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl3227, plain,
% 157.95/20.93 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl3201, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.93 thf(zip_derived_cl2631, plain,
% 157.95/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2619])).
% 157.95/20.93 thf(zip_derived_cl2642, plain,
% 157.95/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2631, '2'])).
% 157.95/20.93 thf(zip_derived_cl2658, plain,
% 157.95/20.93 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.93 (op @ e1 @ e1) @ e1 @ Y0))))))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2642, '7'])).
% 157.95/20.93 thf(zip_derived_cl274, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.93 Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl270, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.93 X0 @ Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl2669, plain,
% 157.95/20.93 (( ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl2658, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.93 thf(zip_derived_cl2686, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2669])).
% 157.95/20.93 thf(zip_derived_cl2701, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2686, '4'])).
% 157.95/20.93 thf(zip_derived_cl2720, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2701, '5'])).
% 157.95/20.93 thf(zip_derived_cl2721, plain,
% 157.95/20.93 (( ('#form6')
% 157.95/20.93 | ~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl2739, plain,
% 157.95/20.93 ((~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl2720, zip_derived_cl2721])).
% 157.95/20.93 thf(zip_derived_cl2760, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2739, '4'])).
% 157.95/20.93 thf(zip_derived_cl2783, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2760, '5'])).
% 157.95/20.93 thf(zip_derived_cl2807, plain,
% 157.95/20.93 ((~ (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2783])).
% 157.95/20.93 thf(zip_derived_cl2831, plain,
% 157.95/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2807, '2'])).
% 157.95/20.93 thf(zip_derived_cl2856, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('rw', [status(thm)], [zip_derived_cl2831, '3'])).
% 157.95/20.93 thf(zip_derived_cl2857, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2856, '4'])).
% 157.95/20.93 thf(zip_derived_cl2883, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2857, '5'])).
% 157.95/20.93 thf(zip_derived_cl2911, plain,
% 157.95/20.93 ((~ (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2883])).
% 157.95/20.93 thf(zip_derived_cl2940, plain,
% 157.95/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2911, '2'])).
% 157.95/20.93 thf(zip_derived_cl2972, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('rw', [status(thm)], [zip_derived_cl2940, '3'])).
% 157.95/20.93 thf(zip_derived_cl2973, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2972, '4'])).
% 157.95/20.93 thf(zip_derived_cl2999, plain,
% 157.95/20.93 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2973, '5'])).
% 157.95/20.93 thf(zip_derived_cl3030, plain,
% 157.95/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2999])).
% 157.95/20.93 thf(zip_derived_cl3058, plain,
% 157.95/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3030, '2'])).
% 157.95/20.93 thf(zip_derived_cl3093, plain,
% 157.95/20.93 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.93 (op @ e2 @ e2) @ e2 @ Y0))))))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3058, '7'])).
% 157.95/20.93 thf(zip_derived_cl274, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.93 Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl270, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.93 X0 @ Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl3119, plain,
% 157.95/20.93 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl3093, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.93 thf(zip_derived_cl2749, plain,
% 157.95/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2730])).
% 157.95/20.93 thf(zip_derived_cl2772, plain,
% 157.95/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2749, '2'])).
% 157.95/20.93 thf(zip_derived_cl2794, plain,
% 157.95/20.93 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.93 (op @ e1 @ e1) @ e1 @ Y0))))))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2772, '7'])).
% 157.95/20.93 thf(zip_derived_cl274, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.93 Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl270, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.93 X0 @ Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl2819, plain,
% 157.95/20.93 (( ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl2794, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.93 thf(zip_derived_cl2842, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2819])).
% 157.95/20.93 thf(zip_derived_cl2870, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2842, '4'])).
% 157.95/20.93 thf(zip_derived_cl2893, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2870, '5'])).
% 157.95/20.93 thf(zip_derived_cl2721, plain,
% 157.95/20.93 (( ('#form6')
% 157.95/20.93 | ~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl2922, plain,
% 157.95/20.93 ((~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl2893, zip_derived_cl2721])).
% 157.95/20.93 thf(zip_derived_cl2948, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2922, '4'])).
% 157.95/20.93 thf(zip_derived_cl2981, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2948, '5'])).
% 157.95/20.93 thf(zip_derived_cl3007, plain,
% 157.95/20.93 ((~ (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2981])).
% 157.95/20.93 thf(zip_derived_cl3035, plain,
% 157.95/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3007, '2'])).
% 157.95/20.93 thf(zip_derived_cl3061, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.93 inference('rw', [status(thm)], [zip_derived_cl3035, '3'])).
% 157.95/20.93 thf(zip_derived_cl3062, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3061, '4'])).
% 157.95/20.93 thf(zip_derived_cl3096, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3062, '5'])).
% 157.95/20.93 thf(zip_derived_cl3124, plain,
% 157.95/20.93 ((~ (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3096])).
% 157.95/20.93 thf(zip_derived_cl3150, plain,
% 157.95/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3124, '2'])).
% 157.95/20.93 thf(zip_derived_cl3178, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.93 inference('rw', [status(thm)], [zip_derived_cl3150, '3'])).
% 157.95/20.93 thf(zip_derived_cl3179, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3178, '4'])).
% 157.95/20.93 thf(zip_derived_cl3210, plain,
% 157.95/20.93 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3179, '5'])).
% 157.95/20.93 thf(zip_derived_cl3237, plain,
% 157.95/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3210])).
% 157.95/20.93 thf(zip_derived_cl3253, plain,
% 157.95/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3237, '2'])).
% 157.95/20.93 thf(zip_derived_cl3271, plain,
% 157.95/20.93 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.93 (op @ e2 @ e2) @ e2 @ Y0))))))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3253, '7'])).
% 157.95/20.93 thf(zip_derived_cl274, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.93 Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl270, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.93 X0 @ Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl3289, plain,
% 157.95/20.93 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl3271, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.93 thf(zip_derived_cl2680, plain,
% 157.95/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2665])).
% 157.95/20.93 thf(zip_derived_cl2695, plain,
% 157.95/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2680, '2'])).
% 157.95/20.93 thf(zip_derived_cl2713, plain,
% 157.95/20.93 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.93 (op @ e0 @ e0) @ e1 @ Y0))))))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2695, '7'])).
% 157.95/20.93 thf(zip_derived_cl274, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.93 Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl270, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.93 X0 @ Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl2733, plain,
% 157.95/20.93 (( ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl2713, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.93 thf(zip_derived_cl2753, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2733])).
% 157.95/20.93 thf(zip_derived_cl2776, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2753, '4'])).
% 157.95/20.93 thf(zip_derived_cl2799, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2776, '5'])).
% 157.95/20.93 thf(zip_derived_cl2721, plain,
% 157.95/20.93 (( ('#form6')
% 157.95/20.93 | ~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl2823, plain,
% 157.95/20.93 ((~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl2799, zip_derived_cl2721])).
% 157.95/20.93 thf(zip_derived_cl2847, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2823, '4'])).
% 157.95/20.93 thf(zip_derived_cl2875, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2847, '5'])).
% 157.95/20.93 thf(zip_derived_cl2899, plain,
% 157.95/20.93 ((~ (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2875])).
% 157.95/20.93 thf(zip_derived_cl2928, plain,
% 157.95/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2899, '2'])).
% 157.95/20.93 thf(zip_derived_cl2955, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.93 inference('rw', [status(thm)], [zip_derived_cl2928, '3'])).
% 157.95/20.93 thf(zip_derived_cl2956, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2955, '4'])).
% 157.95/20.93 thf(zip_derived_cl2987, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2956, '5'])).
% 157.95/20.93 thf(zip_derived_cl3015, plain,
% 157.95/20.93 ((~ (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2987])).
% 157.95/20.93 thf(zip_derived_cl3043, plain,
% 157.95/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3015, '2'])).
% 157.95/20.93 thf(zip_derived_cl3072, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.93 inference('rw', [status(thm)], [zip_derived_cl3043, '3'])).
% 157.95/20.93 thf(zip_derived_cl3073, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3072, '4'])).
% 157.95/20.93 thf(zip_derived_cl3104, plain,
% 157.95/20.93 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3073, '5'])).
% 157.95/20.93 thf(zip_derived_cl3135, plain,
% 157.95/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3104])).
% 157.95/20.93 thf(zip_derived_cl3161, plain,
% 157.95/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3135, '2'])).
% 157.95/20.93 thf(zip_derived_cl3193, plain,
% 157.95/20.93 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.93 (op @ e2 @ e2) @ e2 @ Y0))))))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3161, '7'])).
% 157.95/20.93 thf(zip_derived_cl274, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.93 Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl270, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.93 X0 @ Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl3221, plain,
% 157.95/20.93 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl3193, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.93 thf(zip_derived_cl2629, plain,
% 157.95/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2618])).
% 157.95/20.93 thf(zip_derived_cl2640, plain,
% 157.95/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2629, '2'])).
% 157.95/20.93 thf(zip_derived_cl2655, plain,
% 157.95/20.93 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.93 (op @ e0 @ e0) @ e1 @ Y0))))))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2640, '7'])).
% 157.95/20.93 thf(zip_derived_cl274, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.93 Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl270, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.93 X0 @ Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl2667, plain,
% 157.95/20.93 (( ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | (((mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5') | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl2655, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.93 thf(zip_derived_cl2683, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2667])).
% 157.95/20.93 thf(zip_derived_cl2698, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2683, '4'])).
% 157.95/20.93 thf(zip_derived_cl2717, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2698, '5'])).
% 157.95/20.93 thf(zip_derived_cl2721, plain,
% 157.95/20.93 (( ('#form6')
% 157.95/20.93 | ~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl2736, plain,
% 157.95/20.93 ((~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 157.95/20.93 '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl2717, zip_derived_cl2721])).
% 157.95/20.93 thf(zip_derived_cl2757, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2736, '4'])).
% 157.95/20.93 thf(zip_derived_cl2780, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2757, '5'])).
% 157.95/20.93 thf(zip_derived_cl2803, plain,
% 157.95/20.93 ((~ (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2780])).
% 157.95/20.93 thf(zip_derived_cl2827, plain,
% 157.95/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2803, '2'])).
% 157.95/20.93 thf(zip_derived_cl2851, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw', [status(thm)], [zip_derived_cl2827, '3'])).
% 157.95/20.93 thf(zip_derived_cl2852, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2851, '4'])).
% 157.95/20.93 thf(zip_derived_cl2879, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2852, '5'])).
% 157.95/20.93 thf(zip_derived_cl2905, plain,
% 157.95/20.93 ((~ (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2879])).
% 157.95/20.93 thf(zip_derived_cl2934, plain,
% 157.95/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2905, '2'])).
% 157.95/20.93 thf(zip_derived_cl2963, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw', [status(thm)], [zip_derived_cl2934, '3'])).
% 157.95/20.93 thf(zip_derived_cl2964, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2963, '4'])).
% 157.95/20.93 thf(zip_derived_cl2993, plain,
% 157.95/20.93 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2964, '5'])).
% 157.95/20.93 thf(zip_derived_cl3024, plain,
% 157.95/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2993])).
% 157.95/20.93 thf(zip_derived_cl3052, plain,
% 157.95/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3024, '2'])).
% 157.95/20.93 thf(zip_derived_cl3085, plain,
% 157.95/20.93 (( (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 157.95/20.93 (op @ e2 @ e2) @ e2 @ Y0))))))
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3052, '7'])).
% 157.95/20.93 thf(zip_derived_cl274, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 157.95/20.93 Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl270, plain,
% 157.95/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 157.95/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 157.95/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 157.95/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 157.95/20.93 X0 @ Y0)))))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl3113, plain,
% 157.95/20.93 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl3085, zip_derived_cl274, zip_derived_cl270])).
% 157.95/20.93 thf(zip_derived_cl2702, plain,
% 157.95/20.93 ((~ (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2687])).
% 157.95/20.93 thf(zip_derived_cl2721, plain,
% 157.95/20.93 (( ('#form6')
% 157.95/20.93 | ~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 157.95/20.93 '#sk5'))))),
% 157.95/20.93 define([status(thm)])).
% 157.95/20.93 thf(zip_derived_cl2724, plain,
% 157.95/20.93 ((~ ('#form6')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5'))),
% 157.95/20.93 inference('renaming', [status(thm)],
% 157.95/20.93 [zip_derived_cl2702, zip_derived_cl2721])).
% 157.95/20.93 thf(zip_derived_cl2740, plain,
% 157.95/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2724, '2'])).
% 157.95/20.93 thf(zip_derived_cl2761, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw', [status(thm)], [zip_derived_cl2740, '3'])).
% 157.95/20.93 thf(zip_derived_cl2762, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 157.95/20.93 (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2761, '4'])).
% 157.95/20.93 thf(zip_derived_cl2784, plain,
% 157.95/20.93 ((~ (((mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 157.95/20.93 '#sk5')))
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2762, '5'])).
% 157.95/20.93 thf(zip_derived_cl2809, plain,
% 157.95/20.93 ((~ (mnot @
% 157.95/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2784])).
% 157.95/20.93 thf(zip_derived_cl2833, plain,
% 157.95/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 157.95/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2809, '2'])).
% 157.95/20.93 thf(zip_derived_cl2859, plain,
% 157.95/20.93 (( (mnot @
% 157.95/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 157.95/20.93 '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw', [status(thm)], [zip_derived_cl2833, '3'])).
% 157.95/20.93 thf(zip_derived_cl2860, plain,
% 157.95/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2859, '4'])).
% 157.95/20.93 thf(zip_derived_cl2885, plain,
% 157.95/20.93 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 157.95/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2860, '5'])).
% 157.95/20.93 thf(zip_derived_cl2914, plain,
% 157.95/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 157.95/20.93 | ~ ('#form6')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 157.95/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2885])).
% 157.95/20.93 thf(zip_derived_cl2943, plain,
% 157.95/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 157.95/20.93 | ~ ('#form6'))),
% 157.95/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2914, '2'])).
% 158.22/20.93 thf(zip_derived_cl2976, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e2 @ e2) @ e2 @ Y0))))))
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2943, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3002, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2976, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2678, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2664])).
% 158.22/20.93 thf(zip_derived_cl2693, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2678, '2'])).
% 158.22/20.93 thf(zip_derived_cl2710, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e0 @ e0) @ e1 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2693, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2731, plain,
% 158.22/20.93 (( ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2710, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2750, plain,
% 158.22/20.93 (( (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2731])).
% 158.22/20.93 thf(zip_derived_cl2773, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2750, '4'])).
% 158.22/20.93 thf(zip_derived_cl2795, plain,
% 158.22/20.93 ((~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2773, '5'])).
% 158.22/20.93 thf(zip_derived_cl2721, plain,
% 158.22/20.93 (( ('#form6')
% 158.22/20.93 | ~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 158.22/20.93 '#sk5'))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2820, plain,
% 158.22/20.93 ((~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2795, zip_derived_cl2721])).
% 158.22/20.93 thf(zip_derived_cl2843, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2820, '4'])).
% 158.22/20.93 thf(zip_derived_cl2871, plain,
% 158.22/20.93 ((~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2843, '5'])).
% 158.22/20.93 thf(zip_derived_cl2894, plain,
% 158.22/20.93 ((~ (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2871])).
% 158.22/20.93 thf(zip_derived_cl2923, plain,
% 158.22/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2894, '2'])).
% 158.22/20.93 thf(zip_derived_cl2949, plain,
% 158.22/20.93 (( (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw', [status(thm)], [zip_derived_cl2923, '3'])).
% 158.22/20.93 thf(zip_derived_cl2950, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2949, '4'])).
% 158.22/20.93 thf(zip_derived_cl2982, plain,
% 158.22/20.93 ((~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2950, '5'])).
% 158.22/20.93 thf(zip_derived_cl3009, plain,
% 158.22/20.93 ((~ (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2982])).
% 158.22/20.93 thf(zip_derived_cl3037, plain,
% 158.22/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3009, '2'])).
% 158.22/20.93 thf(zip_derived_cl3064, plain,
% 158.22/20.93 (( (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 158.22/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw', [status(thm)], [zip_derived_cl3037, '3'])).
% 158.22/20.93 thf(zip_derived_cl3065, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 158.22/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3064, '4'])).
% 158.22/20.93 thf(zip_derived_cl3098, plain,
% 158.22/20.93 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 158.22/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3065, '5'])).
% 158.22/20.93 thf(zip_derived_cl3127, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3098])).
% 158.22/20.93 thf(zip_derived_cl3153, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3127, '2'])).
% 158.22/20.93 thf(zip_derived_cl3182, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e2 @ e2) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3153, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3213, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3182, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl3241, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3216])).
% 158.22/20.93 thf(zip_derived_cl3257, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3241, '2'])).
% 158.22/20.93 thf(zip_derived_cl3277, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3257, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3293, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3277, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl3139, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3108])).
% 158.22/20.93 thf(zip_derived_cl3165, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3139, '2'])).
% 158.22/20.93 thf(zip_derived_cl3199, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3165, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3225, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3199, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl3028, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2997])).
% 158.22/20.93 thf(zip_derived_cl3056, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3028, '2'])).
% 158.22/20.93 thf(zip_derived_cl3091, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3056, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3117, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3091, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl3235, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3208])).
% 158.22/20.93 thf(zip_derived_cl3251, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3235, '2'])).
% 158.22/20.93 thf(zip_derived_cl3269, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3251, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3287, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3269, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl3133, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3102])).
% 158.22/20.93 thf(zip_derived_cl3159, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3133, '2'])).
% 158.22/20.93 thf(zip_derived_cl3191, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3159, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3219, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3191, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl3022, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2991])).
% 158.22/20.93 thf(zip_derived_cl3050, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3022, '2'])).
% 158.22/20.93 thf(zip_derived_cl3083, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3050, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3111, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3083, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2912, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2883])).
% 158.22/20.93 thf(zip_derived_cl2941, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2912, '2'])).
% 158.22/20.93 thf(zip_derived_cl2974, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2941, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3000, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2974, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl3125, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3096])).
% 158.22/20.93 thf(zip_derived_cl3151, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3125, '2'])).
% 158.22/20.93 thf(zip_derived_cl3180, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3151, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3211, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3180, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl3016, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2987])).
% 158.22/20.93 thf(zip_derived_cl3044, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3016, '2'])).
% 158.22/20.93 thf(zip_derived_cl3074, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3044, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3105, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3074, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2906, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2879])).
% 158.22/20.93 thf(zip_derived_cl2935, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2906, '2'])).
% 158.22/20.93 thf(zip_derived_cl2965, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2935, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2994, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2965, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2810, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2784])).
% 158.22/20.93 thf(zip_derived_cl2834, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2810, '2'])).
% 158.22/20.93 thf(zip_derived_cl2861, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2834, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2886, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2861, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl3010, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2982])).
% 158.22/20.93 thf(zip_derived_cl3038, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3010, '2'])).
% 158.22/20.93 thf(zip_derived_cl3066, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3038, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3099, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3066, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl3131, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3101])).
% 158.22/20.93 thf(zip_derived_cl3157, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3131, '2'])).
% 158.22/20.93 thf(zip_derived_cl3188, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3157, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3217, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3188, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl3020, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2990])).
% 158.22/20.93 thf(zip_derived_cl3048, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3020, '2'])).
% 158.22/20.93 thf(zip_derived_cl3080, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3048, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3109, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3080, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2910, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2882])).
% 158.22/20.93 thf(zip_derived_cl2939, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2910, '2'])).
% 158.22/20.93 thf(zip_derived_cl2971, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2939, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2998, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2971, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl3123, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3095])).
% 158.22/20.93 thf(zip_derived_cl3149, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3123, '2'])).
% 158.22/20.93 thf(zip_derived_cl3177, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3149, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3209, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3177, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl3014, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2986])).
% 158.22/20.93 thf(zip_derived_cl3042, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3014, '2'])).
% 158.22/20.93 thf(zip_derived_cl3071, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3042, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3103, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3071, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2904, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2878])).
% 158.22/20.93 thf(zip_derived_cl2933, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2904, '2'])).
% 158.22/20.93 thf(zip_derived_cl2962, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2933, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2992, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2962, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2808, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2783])).
% 158.22/20.93 thf(zip_derived_cl2832, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2808, '2'])).
% 158.22/20.93 thf(zip_derived_cl2858, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2832, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2884, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2858, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl3008, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2981])).
% 158.22/20.93 thf(zip_derived_cl3036, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3008, '2'])).
% 158.22/20.93 thf(zip_derived_cl3063, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3036, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3097, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3063, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2900, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2875])).
% 158.22/20.93 thf(zip_derived_cl2929, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2900, '2'])).
% 158.22/20.93 thf(zip_derived_cl2957, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2929, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2988, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2957, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2804, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2780])).
% 158.22/20.93 thf(zip_derived_cl2828, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2804, '2'])).
% 158.22/20.93 thf(zip_derived_cl2853, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2828, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2880, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2853, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2703, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 158.22/20.93 '#sk5'))))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2687])).
% 158.22/20.93 thf(zip_derived_cl2721, plain,
% 158.22/20.93 (( ('#form6')
% 158.22/20.93 | ~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 158.22/20.93 '#sk5'))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2725, plain,
% 158.22/20.93 ((~ ('#form6')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2703, zip_derived_cl2721])).
% 158.22/20.93 thf(zip_derived_cl2743, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2725, '2'])).
% 158.22/20.93 thf(zip_derived_cl2766, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2743, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2787, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2766, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2895, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2871])).
% 158.22/20.93 thf(zip_derived_cl2924, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2895, '2'])).
% 158.22/20.93 thf(zip_derived_cl2951, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2924, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2983, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2951, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2844, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2821])).
% 158.22/20.93 thf(zip_derived_cl2872, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2844, '2'])).
% 158.22/20.93 thf(zip_derived_cl2896, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e3 @ e3) @ e1 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2872, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2925, plain,
% 158.22/20.93 (( ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2896, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2952, plain,
% 158.22/20.93 (( (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2925])).
% 158.22/20.93 thf(zip_derived_cl2984, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2952, '4'])).
% 158.22/20.93 thf(zip_derived_cl3011, plain,
% 158.22/20.93 ((~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2984, '5'])).
% 158.22/20.93 thf(zip_derived_cl2721, plain,
% 158.22/20.93 (( ('#form6')
% 158.22/20.93 | ~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 158.22/20.93 '#sk5'))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3039, plain,
% 158.22/20.93 ((~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3011, zip_derived_cl2721])).
% 158.22/20.93 thf(zip_derived_cl3067, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3039, '4'])).
% 158.22/20.93 thf(zip_derived_cl3100, plain,
% 158.22/20.93 ((~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3067, '5'])).
% 158.22/20.93 thf(zip_derived_cl3128, plain,
% 158.22/20.93 ((~ (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3100])).
% 158.22/20.93 thf(zip_derived_cl3154, plain,
% 158.22/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3128, '2'])).
% 158.22/20.93 thf(zip_derived_cl3183, plain,
% 158.22/20.93 (( (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('rw', [status(thm)], [zip_derived_cl3154, '3'])).
% 158.22/20.93 thf(zip_derived_cl3184, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3183, '4'])).
% 158.22/20.93 thf(zip_derived_cl3214, plain,
% 158.22/20.93 ((~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3184, '5'])).
% 158.22/20.93 thf(zip_derived_cl3238, plain,
% 158.22/20.93 ((~ (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3214])).
% 158.22/20.93 thf(zip_derived_cl3254, plain,
% 158.22/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3238, '2'])).
% 158.22/20.93 thf(zip_derived_cl3272, plain,
% 158.22/20.93 (( (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 158.22/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('rw', [status(thm)], [zip_derived_cl3254, '3'])).
% 158.22/20.93 thf(zip_derived_cl3273, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 158.22/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3272, '4'])).
% 158.22/20.93 thf(zip_derived_cl3290, plain,
% 158.22/20.93 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 158.22/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3273, '5'])).
% 158.22/20.93 thf(zip_derived_cl3305, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3290])).
% 158.22/20.93 thf(zip_derived_cl3313, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3305, '2'])).
% 158.22/20.93 thf(zip_derived_cl3321, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e2 @ e2) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3313, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3329, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3321, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2754, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2734])).
% 158.22/20.93 thf(zip_derived_cl2777, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2754, '2'])).
% 158.22/20.93 thf(zip_derived_cl2800, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e3 @ e3) @ e1 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2777, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2824, plain,
% 158.22/20.93 (( ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2800, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2848, plain,
% 158.22/20.93 (( (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2824])).
% 158.22/20.93 thf(zip_derived_cl2876, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2848, '4'])).
% 158.22/20.93 thf(zip_derived_cl2901, plain,
% 158.22/20.93 ((~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2876, '5'])).
% 158.22/20.93 thf(zip_derived_cl2721, plain,
% 158.22/20.93 (( ('#form6')
% 158.22/20.93 | ~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 158.22/20.93 '#sk5'))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2930, plain,
% 158.22/20.93 ((~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2901, zip_derived_cl2721])).
% 158.22/20.93 thf(zip_derived_cl2958, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2930, '4'])).
% 158.22/20.93 thf(zip_derived_cl2989, plain,
% 158.22/20.93 ((~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2958, '5'])).
% 158.22/20.93 thf(zip_derived_cl3017, plain,
% 158.22/20.93 ((~ (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2989])).
% 158.22/20.93 thf(zip_derived_cl3045, plain,
% 158.22/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3017, '2'])).
% 158.22/20.93 thf(zip_derived_cl3075, plain,
% 158.22/20.93 (( (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('rw', [status(thm)], [zip_derived_cl3045, '3'])).
% 158.22/20.93 thf(zip_derived_cl3076, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3075, '4'])).
% 158.22/20.93 thf(zip_derived_cl3106, plain,
% 158.22/20.93 ((~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3076, '5'])).
% 158.22/20.93 thf(zip_derived_cl3136, plain,
% 158.22/20.93 ((~ (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3106])).
% 158.22/20.93 thf(zip_derived_cl3162, plain,
% 158.22/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3136, '2'])).
% 158.22/20.93 thf(zip_derived_cl3194, plain,
% 158.22/20.93 (( (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 158.22/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('rw', [status(thm)], [zip_derived_cl3162, '3'])).
% 158.22/20.93 thf(zip_derived_cl3195, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 158.22/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3194, '4'])).
% 158.22/20.93 thf(zip_derived_cl3222, plain,
% 158.22/20.93 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 158.22/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3195, '5'])).
% 158.22/20.93 thf(zip_derived_cl3245, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3222])).
% 158.22/20.93 thf(zip_derived_cl3261, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3245, '2'])).
% 158.22/20.93 thf(zip_derived_cl3281, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e2 @ e2) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3261, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3297, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3281, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2684, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2668])).
% 158.22/20.93 thf(zip_derived_cl2699, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2684, '2'])).
% 158.22/20.93 thf(zip_derived_cl2718, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e3 @ e3) @ e1 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2699, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2737, plain,
% 158.22/20.93 (( ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2718, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2758, plain,
% 158.22/20.93 (( (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2737])).
% 158.22/20.93 thf(zip_derived_cl2781, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2758, '4'])).
% 158.22/20.93 thf(zip_derived_cl2805, plain,
% 158.22/20.93 ((~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2781, '5'])).
% 158.22/20.93 thf(zip_derived_cl2721, plain,
% 158.22/20.93 (( ('#form6')
% 158.22/20.93 | ~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 158.22/20.93 '#sk5'))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl2829, plain,
% 158.22/20.93 ((~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl2805, zip_derived_cl2721])).
% 158.22/20.93 thf(zip_derived_cl2854, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2829, '4'])).
% 158.22/20.93 thf(zip_derived_cl2881, plain,
% 158.22/20.93 ((~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2854, '5'])).
% 158.22/20.93 thf(zip_derived_cl2907, plain,
% 158.22/20.93 ((~ (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2881])).
% 158.22/20.93 thf(zip_derived_cl2936, plain,
% 158.22/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2907, '2'])).
% 158.22/20.93 thf(zip_derived_cl2966, plain,
% 158.22/20.93 (( (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw', [status(thm)], [zip_derived_cl2936, '3'])).
% 158.22/20.93 thf(zip_derived_cl2967, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2966, '4'])).
% 158.22/20.93 thf(zip_derived_cl2995, plain,
% 158.22/20.93 ((~ (((mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.93 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2967, '5'])).
% 158.22/20.93 thf(zip_derived_cl3025, plain,
% 158.22/20.93 ((~ (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2995])).
% 158.22/20.93 thf(zip_derived_cl3053, plain,
% 158.22/20.93 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3025, '2'])).
% 158.22/20.93 thf(zip_derived_cl3086, plain,
% 158.22/20.93 (( (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 158.22/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.93 '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw', [status(thm)], [zip_derived_cl3053, '3'])).
% 158.22/20.93 thf(zip_derived_cl3087, plain,
% 158.22/20.93 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 158.22/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3086, '4'])).
% 158.22/20.93 thf(zip_derived_cl3114, plain,
% 158.22/20.93 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 158.22/20.93 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3087, '5'])).
% 158.22/20.93 thf(zip_derived_cl3143, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3114])).
% 158.22/20.93 thf(zip_derived_cl3169, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3143, '2'])).
% 158.22/20.93 thf(zip_derived_cl3203, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e2 @ e2) @ e2 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ~ ('#form6'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl3169, '7'])).
% 158.22/20.93 thf(zip_derived_cl274, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.93 Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl270, plain,
% 158.22/20.93 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.93 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.93 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.93 X0 @ Y0)))))))),
% 158.22/20.93 define([status(thm)])).
% 158.22/20.93 thf(zip_derived_cl3229, plain,
% 158.22/20.93 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.93 | ~ ('#form6')
% 158.22/20.93 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.93 inference('renaming', [status(thm)],
% 158.22/20.93 [zip_derived_cl3203, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.93 thf(zip_derived_cl2840, plain,
% 158.22/20.93 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5')
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5'))))),
% 158.22/20.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2818])).
% 158.22/20.93 thf(zip_derived_cl2868, plain,
% 158.22/20.93 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk5')
% 158.22/20.93 | (((mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.93 '#sk5') | (mnot @
% 158.22/20.93 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.93 (mnot @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.93 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.93 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.93 '#sk5')))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.93 inference('rw_clause', [status(thm)], [zip_derived_cl2840, '2'])).
% 158.22/20.93 thf(zip_derived_cl2891, plain,
% 158.22/20.93 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.93 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.93 (op @ e3 @ e3) @ e1 @ Y0))))))
% 158.22/20.93 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | (((mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.94 '#sk5') | (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.94 '#sk5'))))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2868, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl2920, plain,
% 158.22/20.94 (( ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | (((mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.94 '#sk5') | (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.94 '#sk5')))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl2891, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl2946, plain,
% 158.22/20.94 (( (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @
% 158.22/20.94 '#sk5')
% 158.22/20.94 | (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.94 '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2920])).
% 158.22/20.94 thf(zip_derived_cl2979, plain,
% 158.22/20.94 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @
% 158.22/20.94 '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.94 '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2946, '4'])).
% 158.22/20.94 thf(zip_derived_cl3005, plain,
% 158.22/20.94 ((~ (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 158.22/20.94 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 158.22/20.94 '#sk5')))
% 158.22/20.94 | (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.94 '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2979, '5'])).
% 158.22/20.94 thf(zip_derived_cl2721, plain,
% 158.22/20.94 (( ('#form6')
% 158.22/20.94 | ~ (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @
% 158.22/20.94 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @
% 158.22/20.94 '#sk5'))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3033, plain,
% 158.22/20.94 ((~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.94 '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3005, zip_derived_cl2721])).
% 158.22/20.94 thf(zip_derived_cl3059, plain,
% 158.22/20.94 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 158.22/20.94 '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3033, '4'])).
% 158.22/20.94 thf(zip_derived_cl3094, plain,
% 158.22/20.94 ((~ (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.94 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @
% 158.22/20.94 '#sk5')))
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3059, '5'])).
% 158.22/20.94 thf(zip_derived_cl3120, plain,
% 158.22/20.94 ((~ (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.94 '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3094])).
% 158.22/20.94 thf(zip_derived_cl3146, plain,
% 158.22/20.94 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.94 '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3120, '2'])).
% 158.22/20.94 thf(zip_derived_cl3172, plain,
% 158.22/20.94 (( (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 158.22/20.94 '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('rw', [status(thm)], [zip_derived_cl3146, '3'])).
% 158.22/20.94 thf(zip_derived_cl3173, plain,
% 158.22/20.94 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.94 '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3172, '4'])).
% 158.22/20.94 thf(zip_derived_cl3206, plain,
% 158.22/20.94 ((~ (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.94 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 '#sk5')))
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3173, '5'])).
% 158.22/20.94 thf(zip_derived_cl3232, plain,
% 158.22/20.94 ((~ (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.94 '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3206])).
% 158.22/20.94 thf(zip_derived_cl3248, plain,
% 158.22/20.94 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3232, '2'])).
% 158.22/20.94 thf(zip_derived_cl3264, plain,
% 158.22/20.94 (( (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.94 '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('rw', [status(thm)], [zip_derived_cl3248, '3'])).
% 158.22/20.94 thf(zip_derived_cl3265, plain,
% 158.22/20.94 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3264, '4'])).
% 158.22/20.94 thf(zip_derived_cl3284, plain,
% 158.22/20.94 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') |
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')))
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3265, '5'])).
% 158.22/20.94 thf(zip_derived_cl3301, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3284])).
% 158.22/20.94 thf(zip_derived_cl3309, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3301, '2'])).
% 158.22/20.94 thf(zip_derived_cl3317, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e2 @ e2) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3309, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3325, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3317, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3239, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3214])).
% 158.22/20.94 thf(zip_derived_cl3255, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3239, '2'])).
% 158.22/20.94 thf(zip_derived_cl3274, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3255, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3291, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3274, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3137, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3106])).
% 158.22/20.94 thf(zip_derived_cl3163, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3137, '2'])).
% 158.22/20.94 thf(zip_derived_cl3196, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3163, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3223, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3196, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3026, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2995])).
% 158.22/20.94 thf(zip_derived_cl3054, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3026, '2'])).
% 158.22/20.94 thf(zip_derived_cl3088, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3054, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3115, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3088, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3233, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3206])).
% 158.22/20.94 thf(zip_derived_cl3249, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3233, '2'])).
% 158.22/20.94 thf(zip_derived_cl3266, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3249, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3285, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3266, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3129, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3100])).
% 158.22/20.94 thf(zip_derived_cl3155, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3129, '2'])).
% 158.22/20.94 thf(zip_derived_cl3185, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3155, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3215, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3185, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3018, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2989])).
% 158.22/20.94 thf(zip_derived_cl3046, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3018, '2'])).
% 158.22/20.94 thf(zip_derived_cl3077, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3046, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3107, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3077, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl2908, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2881])).
% 158.22/20.94 thf(zip_derived_cl2937, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2908, '2'])).
% 158.22/20.94 thf(zip_derived_cl2968, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2937, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl2996, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl2968, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3121, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3094])).
% 158.22/20.94 thf(zip_derived_cl3147, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3121, '2'])).
% 158.22/20.94 thf(zip_derived_cl3174, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3147, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3207, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3174, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3306, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3292])).
% 158.22/20.94 thf(zip_derived_cl3314, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3306, '2'])).
% 158.22/20.94 thf(zip_derived_cl3322, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3314, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3330, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3322, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3246, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3224])).
% 158.22/20.94 thf(zip_derived_cl3262, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3246, '2'])).
% 158.22/20.94 thf(zip_derived_cl3282, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3262, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3298, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3282, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3144, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3116])).
% 158.22/20.94 thf(zip_derived_cl3170, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3144, '2'])).
% 158.22/20.94 thf(zip_derived_cl3204, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3170, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3230, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3204, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3302, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3286])).
% 158.22/20.94 thf(zip_derived_cl3310, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3302, '2'])).
% 158.22/20.94 thf(zip_derived_cl3318, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3310, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3326, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3318, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3242, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3218])).
% 158.22/20.94 thf(zip_derived_cl3258, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3242, '2'])).
% 158.22/20.94 thf(zip_derived_cl3278, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3258, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3294, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3278, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3140, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3110])).
% 158.22/20.94 thf(zip_derived_cl3166, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3140, '2'])).
% 158.22/20.94 thf(zip_derived_cl3200, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3166, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3226, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3200, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3029, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2999])).
% 158.22/20.94 thf(zip_derived_cl3057, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3029, '2'])).
% 158.22/20.94 thf(zip_derived_cl3092, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3057, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3118, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3092, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3236, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3210])).
% 158.22/20.94 thf(zip_derived_cl3252, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3236, '2'])).
% 158.22/20.94 thf(zip_derived_cl3270, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3252, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3288, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3270, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3134, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3104])).
% 158.22/20.94 thf(zip_derived_cl3160, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3134, '2'])).
% 158.22/20.94 thf(zip_derived_cl3192, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3160, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3220, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3192, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3023, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2993])).
% 158.22/20.94 thf(zip_derived_cl3051, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3023, '2'])).
% 158.22/20.94 thf(zip_derived_cl3084, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3051, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3112, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3084, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl2913, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2885])).
% 158.22/20.94 thf(zip_derived_cl2942, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2913, '2'])).
% 158.22/20.94 thf(zip_derived_cl2975, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2942, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3001, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl2975, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3126, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3098])).
% 158.22/20.94 thf(zip_derived_cl3152, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3126, '2'])).
% 158.22/20.94 thf(zip_derived_cl3181, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3152, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3212, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3181, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl2550, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @
% 158.22/20.94 X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2548])).
% 158.22/20.94 thf(zip_derived_cl2557, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 158.22/20.94 X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2550, '2'])).
% 158.22/20.94 thf(zip_derived_cl2565, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.94 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ X0)))
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2557, '6'])).
% 158.22/20.94 thf(zip_derived_cl2574, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.94 X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2565])).
% 158.22/20.94 thf(zip_derived_cl2582, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.94 X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2574, '4'])).
% 158.22/20.94 thf(zip_derived_cl2592, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @
% 158.22/20.94 X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ X0))),
% 158.22/20.94 inference('rw', [status(thm)], [zip_derived_cl2582, '3'])).
% 158.22/20.94 thf(zip_derived_cl2593, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.94 X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2592, '2'])).
% 158.22/20.94 thf(zip_derived_cl2602, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.94 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0)))
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2593, '6'])).
% 158.22/20.94 thf(zip_derived_cl2613, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.94 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0))))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2602, '4'])).
% 158.22/20.94 thf(zip_derived_cl2622, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e0 @ e0) @ e2 @ Y0))))))
% 158.22/20.94 | (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.94 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0)))
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2613, '1'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl2634, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.94 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0))))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl2622, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl2645, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @
% 158.22/20.94 X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2634])).
% 158.22/20.94 thf(zip_derived_cl2661, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2645, '4'])).
% 158.22/20.94 thf(zip_derived_cl2673, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @
% 158.22/20.94 X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0))),
% 158.22/20.94 inference('rw', [status(thm)], [zip_derived_cl2661, '3'])).
% 158.22/20.94 thf(zip_derived_cl2674, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2673, '2'])).
% 158.22/20.94 thf(zip_derived_cl2689, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0) |
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0)))
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2674, '6'])).
% 158.22/20.94 thf(zip_derived_cl2705, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0) |
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0))))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2689, '4'])).
% 158.22/20.94 thf(zip_derived_cl2727, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e1 @ e1) @ e2 @ Y0))))))
% 158.22/20.94 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0) |
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0)))
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2705, '1'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl2745, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0) |
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0))))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl2727, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl2768, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2745])).
% 158.22/20.94 thf(zip_derived_cl2789, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2768, '4'])).
% 158.22/20.94 thf(zip_derived_cl2815, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2789, '1'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl2838, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ ('#form3' @ e2 @ (op @ e3 @ e3) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl2815, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl2866, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e3 @ e3) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2838, '4'])).
% 158.22/20.94 thf(zip_derived_cl2890, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e2 @ e2) @ e2 @ Y0))))))
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e3 @ e3) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2866, '1'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl2919, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ ('#form3' @ e2 @ (op @ e2 @ e2) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e2 @ (op @ e3 @ e3) @ X0))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl2890, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3304, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3290])).
% 158.22/20.94 thf(zip_derived_cl3312, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3304, '2'])).
% 158.22/20.94 thf(zip_derived_cl3320, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3312, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3328, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3320, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3244, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3222])).
% 158.22/20.94 thf(zip_derived_cl3260, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3244, '2'])).
% 158.22/20.94 thf(zip_derived_cl3280, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3260, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3296, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3280, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3142, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3114])).
% 158.22/20.94 thf(zip_derived_cl3168, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3142, '2'])).
% 158.22/20.94 thf(zip_derived_cl3202, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3168, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3228, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3202, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3300, plain,
% 158.22/20.94 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3284])).
% 158.22/20.94 thf(zip_derived_cl3308, plain,
% 158.22/20.94 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3300, '2'])).
% 158.22/20.94 thf(zip_derived_cl3316, plain,
% 158.22/20.94 (( (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e2 @ Y0))))))
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6'))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl3308, '7'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl3324, plain,
% 158.22/20.94 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ~ ('#form6')
% 158.22/20.94 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5')
% 158.22/20.94 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl3316, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(a1, axiom, (mreflexive @ rel_s4)).
% 158.22/20.94 thf(zip_derived_cl1, plain, ( (mreflexive @ rel_s4)),
% 158.22/20.94 inference('cnf', [status(esa)], [a1])).
% 158.22/20.94 thf(mreflexive, axiom, (mreflexive @ X0) =>
% 158.22/20.94 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0 @ Y0)))) = ($true))).
% 158.22/20.94 thf('11', plain,
% 158.22/20.94 (![X0:( $i > $i > $o )]:
% 158.22/20.94 ( ( mreflexive @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 @ X5 ) ) )),
% 158.22/20.94 inference('rw.lit', [status(esa)], [mreflexive])).
% 158.22/20.94 thf(zip_derived_cl29, plain, ( (((!!) @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl1, '11'])).
% 158.22/20.94 thf(zip_derived_cl30, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)),
% 158.22/20.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])).
% 158.22/20.94 thf(zip_derived_cl2538, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @
% 158.22/20.94 X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2536])).
% 158.22/20.94 thf(zip_derived_cl2544, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 158.22/20.94 X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2538, '2'])).
% 158.22/20.94 thf(zip_derived_cl2551, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 158.22/20.94 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ X0)))
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2544, '6'])).
% 158.22/20.94 thf(zip_derived_cl2558, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 158.22/20.94 X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2551])).
% 158.22/20.94 thf(zip_derived_cl2566, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 158.22/20.94 X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2558, '4'])).
% 158.22/20.94 thf(zip_derived_cl2575, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @
% 158.22/20.94 X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ X0))),
% 158.22/20.94 inference('rw', [status(thm)], [zip_derived_cl2566, '3'])).
% 158.22/20.94 thf(zip_derived_cl2576, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 158.22/20.94 X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2575, '2'])).
% 158.22/20.94 thf(zip_derived_cl2583, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 158.22/20.94 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0)))
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2576, '6'])).
% 158.22/20.94 thf(zip_derived_cl2594, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 158.22/20.94 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0))))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2583, '4'])).
% 158.22/20.94 thf(zip_derived_cl2603, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e0 @ e0) @ e1 @ Y0))))))
% 158.22/20.94 | (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 158.22/20.94 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0)))
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2594, '1'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl2614, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 158.22/20.94 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0))))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl2603, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl2623, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @
% 158.22/20.94 X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2614])).
% 158.22/20.94 thf(zip_derived_cl2635, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2623, '4'])).
% 158.22/20.94 thf(zip_derived_cl2646, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @
% 158.22/20.94 X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0))),
% 158.22/20.94 inference('rw', [status(thm)], [zip_derived_cl2635, '3'])).
% 158.22/20.94 thf(zip_derived_cl2647, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2646, '2'])).
% 158.22/20.94 thf(zip_derived_cl2662, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0) |
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0)))
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2647, '6'])).
% 158.22/20.94 thf(zip_derived_cl2675, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0) |
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0))))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2662, '4'])).
% 158.22/20.94 thf(zip_derived_cl2690, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e1 @ e1) @ e1 @ Y0))))))
% 158.22/20.94 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0) |
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0)))
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2675, '1'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl2706, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0) |
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0))))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl2690, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl2728, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2706])).
% 158.22/20.94 thf(zip_derived_cl2746, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2728, '4'])).
% 158.22/20.94 thf(zip_derived_cl2769, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e1 @ Y0))))))
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2746, '1'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl2790, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ ('#form3' @ e1 @ (op @ e3 @ e3) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl2769, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl2816, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e3 @ e3) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2790, '4'])).
% 158.22/20.94 thf(zip_derived_cl2839, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e2 @ e2) @ e1 @ Y0))))))
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e3 @ e3) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2816, '1'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl2867, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ ('#form3' @ e1 @ (op @ e2 @ e2) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e1 @ (op @ e3 @ e3) @ X0))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl2839, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl2529, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))))) @
% 158.22/20.94 X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2527])).
% 158.22/20.94 thf(zip_derived_cl2533, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 158.22/20.94 X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2529, '2'])).
% 158.22/20.94 thf(zip_derived_cl2539, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @
% 158.22/20.94 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ X0)))
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2533, '6'])).
% 158.22/20.94 thf(zip_derived_cl2545, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @
% 158.22/20.94 X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2539])).
% 158.22/20.94 thf(zip_derived_cl2552, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @
% 158.22/20.94 X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2545, '4'])).
% 158.22/20.94 thf(zip_derived_cl2559, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @
% 158.22/20.94 X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ X0))),
% 158.22/20.94 inference('rw', [status(thm)], [zip_derived_cl2552, '3'])).
% 158.22/20.94 thf(zip_derived_cl2560, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0))) @
% 158.22/20.94 (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @
% 158.22/20.94 X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2559, '2'])).
% 158.22/20.94 thf(zip_derived_cl2567, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @
% 158.22/20.94 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0)))
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2560, '6'])).
% 158.22/20.94 thf(zip_derived_cl2577, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @
% 158.22/20.94 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0))))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2567, '4'])).
% 158.22/20.94 thf(zip_derived_cl2584, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e0 @ e0) @ e0 @ Y0))))))
% 158.22/20.94 | (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @
% 158.22/20.94 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0)))
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2577, '1'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl2595, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (((mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @
% 158.22/20.94 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0))))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl2584, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl2604, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mnot @
% 158.22/20.94 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @
% 158.22/20.94 X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2595])).
% 158.22/20.94 thf(zip_derived_cl2615, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @
% 158.22/20.94 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2604, '4'])).
% 158.22/20.94 thf(zip_derived_cl2624, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mnot @
% 158.22/20.94 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0))) @
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @
% 158.22/20.94 X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0))),
% 158.22/20.94 inference('rw', [status(thm)], [zip_derived_cl2615, '3'])).
% 158.22/20.94 thf(zip_derived_cl2625, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0))) @
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2624, '2'])).
% 158.22/20.94 thf(zip_derived_cl2636, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0) |
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0)))
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2625, '6'])).
% 158.22/20.94 thf(zip_derived_cl2648, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0) |
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0))))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2636, '4'])).
% 158.22/20.94 thf(zip_derived_cl2663, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e1 @ e1) @ e0 @ Y0))))))
% 158.22/20.94 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0) |
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0)))
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2648, '1'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl2676, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0) |
% 158.22/20.94 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0))))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl2663, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl2691, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 ( (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0))),
% 158.22/20.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2676])).
% 158.22/20.94 thf(zip_derived_cl2707, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2691, '4'])).
% 158.22/20.94 thf(zip_derived_cl2729, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e3 @ e3) @ e0 @ Y0))))))
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2707, '1'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl2747, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ ('#form3' @ e0 @ (op @ e3 @ e3) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl2729, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl2770, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e3 @ e3) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2747, '4'])).
% 158.22/20.94 thf(zip_derived_cl2791, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @
% 158.22/20.94 (op @ e2 @ e2) @ e0 @ Y0))))))
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e3 @ e3) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0))),
% 158.22/20.94 inference('rw_clause', [status(thm)], [zip_derived_cl2770, '1'])).
% 158.22/20.94 thf(zip_derived_cl274, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 (~ ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @
% 158.22/20.94 Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl270, plain,
% 158.22/20.94 (![X0 : mu, X1 : mu, X2 : $i]:
% 158.22/20.94 ( ('#form3' @ X0 @ X1 @ X2)
% 158.22/20.94 | ~ (((!!) @ (^[Y0 : $i]:
% 158.22/20.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @
% 158.22/20.94 X0 @ Y0)))))))),
% 158.22/20.94 define([status(thm)])).
% 158.22/20.94 thf(zip_derived_cl2817, plain,
% 158.22/20.94 (![X0 : $i]:
% 158.22/20.94 (~ ('#form3' @ e0 @ (op @ e2 @ e2) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0)
% 158.22/20.94 | ~ (rel_s4 @ '#sk5' @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0)
% 158.22/20.94 | ~ ('#form3' @ e0 @ (op @ e3 @ e3) @ X0))),
% 158.22/20.94 inference('renaming', [status(thm)],
% 158.22/20.94 [zip_derived_cl2791, zip_derived_cl274, zip_derived_cl270])).
% 158.22/20.94 thf(zip_derived_cl3332, plain, ($false),
% 158.22/20.94 inference('eprover', [status(thm)],
% 158.22/20.94 [zip_derived_cl3031, zip_derived_cl3032, zip_derived_cl277,
% 158.22/20.94 zip_derived_cl2917, zip_derived_cl2918, zip_derived_cl2813,
% 158.22/20.94 zip_derived_cl278, zip_derived_cl3331, zip_derived_cl3299,
% 158.22/20.94 zip_derived_cl3231, zip_derived_cl3327, zip_derived_cl3295,
% 158.22/20.94 zip_derived_cl3227, zip_derived_cl3119, zip_derived_cl3289,
% 158.22/20.94 zip_derived_cl3221, zip_derived_cl3113, zip_derived_cl3002,
% 158.22/20.94 zip_derived_cl3213, zip_derived_cl3293, zip_derived_cl3225,
% 158.22/20.94 zip_derived_cl3117, zip_derived_cl3287, zip_derived_cl3219,
% 158.22/20.94 zip_derived_cl3111, zip_derived_cl3000, zip_derived_cl3211,
% 158.22/20.94 zip_derived_cl3105, zip_derived_cl2994, zip_derived_cl2886,
% 158.22/20.94 zip_derived_cl3099, zip_derived_cl3217, zip_derived_cl3109,
% 158.22/20.94 zip_derived_cl2998, zip_derived_cl3209, zip_derived_cl3103,
% 158.22/20.94 zip_derived_cl2992, zip_derived_cl2884, zip_derived_cl3097,
% 158.22/20.94 zip_derived_cl2988, zip_derived_cl2880, zip_derived_cl2787,
% 158.22/20.94 zip_derived_cl2983, zip_derived_cl3329, zip_derived_cl3297,
% 158.22/20.94 zip_derived_cl3229, zip_derived_cl3325, zip_derived_cl3291,
% 158.22/20.94 zip_derived_cl3223, zip_derived_cl3115, zip_derived_cl3285,
% 158.22/20.94 zip_derived_cl3215, zip_derived_cl3107, zip_derived_cl2996,
% 158.22/20.94 zip_derived_cl3207, zip_derived_cl3330, zip_derived_cl3298,
% 158.22/20.94 zip_derived_cl3230, zip_derived_cl3326, zip_derived_cl3294,
% 158.22/20.94 zip_derived_cl3226, zip_derived_cl3118, zip_derived_cl3288,
% 158.22/20.94 zip_derived_cl3220, zip_derived_cl3112, zip_derived_cl3001,
% 158.22/20.94 zip_derived_cl3212, zip_derived_cl2919, zip_derived_cl3328,
% 158.22/20.94 zip_derived_cl3296, zip_derived_cl3228, zip_derived_cl3324,
% 158.22/20.94 zip_derived_cl30, zip_derived_cl2867, zip_derived_cl2817])).
% 158.22/20.94
% 158.22/20.94 % SZS output end Refutation
% 158.22/20.94
% 158.22/20.94
% 158.22/20.94 % Terminating...
% 158.85/21.09 % Runner terminated.
% 158.85/21.10 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------