0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.AkfGarRdtj true 0.14/0.36 % Computer : n017.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 1440 0.14/0.36 % WCLimit : 180 0.14/0.36 % DateTime : Thu Jul 4 08:36:09 EDT 2024 0.14/0.36 % CPUTime : 0.14/0.36 % Running portfolio for 1440 s 0.14/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.36 % Number of cores: 8 0.14/0.36 % Python version: Python 3.6.8 0.14/0.36 % Running in HO mode 0.53/0.66 % Total configuration time : 828 0.53/0.66 % Estimated wc time : 1656 0.53/0.66 % Estimated cpu time (8 cpus) : 207.0 0.53/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.53/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.54/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 4.49/1.19 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 156.28/20.45 % Solved by lams/30_b.l.sh. 156.28/20.45 % done 0 iterations in 19.046s 156.28/20.45 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 156.28/20.45 % SZS output start Refutation 156.28/20.45 thf(mu_type, type, mu: $tType). 156.28/20.45 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 156.28/20.45 thf(mreflexive_type, type, mreflexive: ($i > $i > $o) > $o). 156.28/20.45 thf('#form3_type', type, '#form3': mu > mu > $i > $o). 156.28/20.45 thf(e2_type, type, e2: mu). 156.28/20.45 thf(rel_s4_type, type, rel_s4: $i > $i > $o). 156.28/20.45 thf('#sk2_type', type, '#sk2': mu > mu > $i > $i). 156.28/20.45 thf(e0_type, type, e0: mu). 156.28/20.45 thf('#sk5_type', type, '#sk5': $i). 156.28/20.45 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 156.28/20.45 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 156.28/20.45 thf('#form6_type', type, '#form6': $o). 156.28/20.45 thf(op_type, type, op: mu > mu > mu). 156.28/20.45 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 156.28/20.45 thf(e3_type, type, e3: mu). 156.28/20.45 thf(mbox_s4_type, type, mbox_s4: ($i > $o) > $i > $o). 156.28/20.45 thf('#sk4_type', type, '#sk4': $i). 156.28/20.45 thf(exists_in_world_type, type, exists_in_world: mu > $i > $o). 156.28/20.45 thf(qmltpeq_type, type, qmltpeq: mu > mu > $i > $o). 156.28/20.45 thf(mforall_ind_type, type, mforall_ind: (mu > $i > $o) > $i > $o). 156.28/20.45 thf(e1_type, type, e1: mu). 156.28/20.45 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 156.28/20.45 thf(co1, conjecture, 156.28/20.45 (mvalid @ 156.28/20.45 ( mbox_s4 @ 156.28/20.45 ( mnot @ 156.28/20.45 ( mand @ 156.28/20.45 ( mor @ 156.28/20.45 ( mand @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ 156.28/20.45 ( mand @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ 156.28/20.45 ( mand @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ 156.28/20.45 ( mor @ 156.28/20.45 ( mand @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ 156.28/20.45 ( mand @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ 156.28/20.45 ( mand @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ 156.28/20.45 ( mor @ 156.28/20.45 ( mand @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ 156.28/20.45 ( mand @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ 156.28/20.45 ( mand @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ 156.28/20.45 ( mand @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ 156.28/20.45 ( mand @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ 156.28/20.45 ( mand @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) @ 156.28/20.45 ( mbox_s4 @ 156.28/20.45 ( mnot @ 156.28/20.45 ( mor @ 156.28/20.45 ( mand @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ 156.28/20.45 ( mand @ 156.28/20.45 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ 156.28/20.45 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ 156.28/20.46 ( mor @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ 156.28/20.46 ( mor @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ))). 156.28/20.46 thf(zf_stmt_0, negated_conjecture, 156.28/20.46 (~( mvalid @ 156.28/20.46 ( mbox_s4 @ 156.28/20.46 ( mnot @ 156.28/20.46 ( mand @ 156.28/20.46 ( mor @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ 156.28/20.46 ( mor @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ 156.28/20.46 ( mor @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) @ 156.28/20.46 ( mbox_s4 @ 156.28/20.46 ( mnot @ 156.28/20.46 ( mor @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ 156.28/20.46 ( mor @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ 156.28/20.46 ( mor @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ 156.28/20.46 ( mand @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ 156.28/20.46 ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) )), 156.28/20.46 inference('cnf.neg', [status(esa)], [co1])). 156.28/20.46 thf(zip_derived_cl28, plain, 156.28/20.46 (~ (mvalid @ 156.28/20.46 (mbox_s4 @ 156.28/20.46 (mnot @ 156.28/20.46 (mand @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 156.28/20.46 (mbox_s4 @ 156.28/20.46 (mnot @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))))))), 156.28/20.46 inference('cnf', [status(esa)], [zf_stmt_0])). 156.28/20.46 thf(mvalid, axiom, ~ (mvalid @ X0) => 156.28/20.46 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) != ($true))). 156.28/20.46 thf('0', plain, 156.28/20.46 (![X0:( $i > $o )]: 156.28/20.46 ( ( ~( mvalid @ X0 ) ) <=> ( ~( ![X5:$i]: ( X0 @ X5 ) ) ) )), 156.28/20.46 inference('rw.lit', [status(esa)], [mvalid])). 156.28/20.46 thf(zip_derived_cl2501, plain, 156.28/20.46 (~ (((!!) @ (^[Y0 : $i]: 156.28/20.46 (mbox_s4 @ 156.28/20.46 (mnot @ 156.28/20.46 (mand @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 156.28/20.46 (mbox_s4 @ 156.28/20.46 (mnot @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))))) @ 156.28/20.46 Y0))))), 156.28/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl28, '0'])). 156.28/20.46 thf(zip_derived_cl2502, plain, 156.28/20.46 (~ (mbox_s4 @ 156.28/20.46 (mnot @ 156.28/20.46 (mand @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 156.28/20.46 (mbox_s4 @ 156.28/20.46 (mnot @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))))) @ 156.28/20.46 '#sk4')), 156.28/20.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2501])). 156.28/20.46 thf(mbox_s4, axiom, ~ (mbox_s4 @ X0 @ X1) => 156.28/20.46 ((((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s4 @ X1 @ Y0))) | (X0 @ Y0)))))) != 156.28/20.46 ($true))). 156.28/20.46 thf('1', plain, 156.28/20.46 (![X0:( $i > $o ),X1:$i]: 156.28/20.46 ( ( ~( mbox_s4 @ X0 @ X1 ) ) <=> 156.28/20.46 ( ~( ![X6:$i]: ( ( ~( rel_s4 @ X1 @ X6 ) ) | ( X0 @ X6 ) ) ) ) )), 156.28/20.46 inference('rw.lit', [status(esa)], [mbox_s4])). 156.28/20.46 thf(zip_derived_cl2503, plain, 156.28/20.46 (~ (((!!) @ (^[Y0 : $i]: 156.28/20.46 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | (mnot @ 156.28/20.46 (mand @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 156.28/20.46 (mbox_s4 @ 156.28/20.46 (mnot @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))) @ 156.28/20.46 Y0))))))), 156.28/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2502, '1'])). 156.28/20.46 thf(zip_derived_cl2504, plain, 156.28/20.46 (~ (((((~) @ (rel_s4 @ '#sk4' @ '#sk5'))) | (mnot @ 156.28/20.46 (mand @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 156.28/20.46 (mbox_s4 @ 156.28/20.46 (mnot @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))) @ 156.28/20.46 '#sk5')))), 156.28/20.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2503])). 156.28/20.46 thf(zip_derived_cl2506, plain, 156.28/20.46 (~ (mnot @ 156.28/20.46 (mand @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 156.28/20.46 (mbox_s4 @ 156.28/20.46 (mnot @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))) @ 156.28/20.46 '#sk5')), 156.28/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2504])). 156.28/20.46 thf(mnot, axiom, ~ (mnot @ X0 @ X1) => ((X0 @ X1) = ($true))). 156.28/20.46 thf('2', plain, 156.28/20.46 (![X0:( $i > $o ),X1:$i]: ( ( ~( mnot @ X0 @ X1 ) ) <=> ( X0 @ X1 ) )), 156.28/20.46 inference('rw.lit', [status(esa)], [mnot])). 156.28/20.46 thf(zip_derived_cl2507, plain, 156.28/20.46 ( (mand @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 156.28/20.46 (mbox_s4 @ 156.28/20.46 (mnot @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))) @ 156.28/20.46 '#sk5')), 156.28/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2506, '2'])). 156.28/20.46 thf(mand, axiom,(( mand @ (X0)@ (X1)@ (X2)) = 156.28/20.46 ((mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)) @ X2)))). 156.28/20.46 thf('3', plain, 156.28/20.46 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]: 156.28/20.46 ( ( mand @ X0 @ X1 @ X2 ) = 156.28/20.46 ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) @ X2 ) )), 156.28/20.46 define([status(thm)])). 156.28/20.46 thf(zip_derived_cl2508, plain, 156.28/20.46 ( (mnot @ 156.28/20.46 (mor @ 156.28/20.46 (mnot @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))) @ 156.28/20.46 (mnot @ 156.28/20.46 (mbox_s4 @ 156.28/20.46 (mnot @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))))) @ 156.28/20.46 '#sk5')), 156.28/20.46 inference('rw', [status(thm)], [zip_derived_cl2507, '3'])). 156.28/20.46 thf(mnot, axiom, (mnot @ X0 @ X1) => ((X0 @ X1) != ($true))). 156.28/20.46 thf('4', plain, 156.28/20.46 (![X0:( $i > $o ),X1:$i]: ( ( mnot @ X0 @ X1 ) <=> ( ~( X0 @ X1 ) ) )), 156.28/20.46 inference('rw.lit', [status(esa)], [mnot])). 156.28/20.46 thf(zip_derived_cl2509, plain, 156.28/20.46 (~ (mor @ 156.28/20.46 (mnot @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))) @ 156.28/20.46 (mnot @ 156.28/20.46 (mbox_s4 @ 156.28/20.46 (mnot @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))) @ 156.28/20.46 '#sk5')), 156.28/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2508, '4'])). 156.28/20.46 thf(mor, axiom, ~ (mor @ X0 @ X1 @ X2) => 156.28/20.46 ((((X1 @ X2) | (X0 @ X2))) != ($true))). 156.28/20.46 thf('5', plain, 156.28/20.46 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]: 156.28/20.46 ( ( ~( mor @ X0 @ X1 @ X2 ) ) <=> ( ~( ( X1 @ X2 ) | ( X0 @ X2 ) ) ) )), 156.28/20.46 inference('rw.lit', [status(esa)], [mor])). 156.28/20.46 thf(zip_derived_cl2510, plain, 156.28/20.46 (~ (((mnot @ 156.28/20.46 (mbox_s4 @ 156.28/20.46 (mnot @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))) @ 156.28/20.46 '#sk5') | (mnot @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 156.28/20.46 '#sk5')))), 156.28/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2509, '5'])). 156.28/20.46 thf(zip_derived_cl2512, plain, 156.28/20.46 (~ (mnot @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.28/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.28/20.46 (mor @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.28/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 156.89/20.46 '#sk5')), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2510])). 156.89/20.46 thf(zip_derived_cl2514, plain, 156.89/20.46 ( (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))) @ 156.89/20.46 '#sk5')), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2512, '2'])). 156.89/20.46 thf(mor, axiom, (mor @ X0 @ X1 @ X2) => 156.89/20.46 ((((X1 @ X2) | (X0 @ X2))) = ($true))). 156.89/20.46 thf('6', plain, 156.89/20.46 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]: 156.89/20.46 ( ( mor @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) | ( X1 @ X2 ) ) )), 156.89/20.46 inference('rw.lit', [status(esa)], [mor])). 156.89/20.46 thf(zip_derived_cl2516, plain, 156.89/20.46 ( (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @ 156.89/20.46 '#sk5')))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2514, '6'])). 156.89/20.46 thf(zip_derived_cl2518, plain, 156.89/20.46 ( (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))))) @ 156.89/20.46 '#sk5')))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2516, '3'])). 156.89/20.46 thf(zip_derived_cl2519, plain, 156.89/20.46 (( (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))))) @ 156.89/20.46 '#sk5'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2518])). 156.89/20.46 thf(zip_derived_cl2521, plain, 156.89/20.46 (( (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))))) @ 156.89/20.46 '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2519, '6'])). 156.89/20.46 thf(zip_derived_cl2523, plain, 156.89/20.46 (( (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))))) @ 156.89/20.46 '#sk5'))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2521, '3'])). 156.89/20.46 thf(zip_derived_cl2524, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2523, '4'])). 156.89/20.46 thf(zip_derived_cl2526, plain, 156.89/20.46 ((~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2524, '5'])). 156.89/20.46 thf(zip_derived_cl2531, plain, 156.89/20.46 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2526])). 156.89/20.46 thf(zip_derived_cl2535, plain, 156.89/20.46 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0) @ '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2531, '2'])). 156.89/20.46 thf(mbox_s4, axiom, (mbox_s4 @ X0 @ X1) => 156.89/20.46 ((((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s4 @ X1 @ Y0))) | (X0 @ Y0)))))) = 156.89/20.46 ($true))). 156.89/20.46 thf('7', plain, 156.89/20.46 (![X0:( $i > $o ),X1:$i]: 156.89/20.46 ( ( mbox_s4 @ X0 @ X1 ) <=> 156.89/20.46 ( ![X6:$i]: ( ( ~( rel_s4 @ X1 @ X6 ) ) | ( X0 @ X6 ) ) ) )), 156.89/20.46 inference('rw.lit', [status(esa)], [mbox_s4])). 156.89/20.46 thf(zip_derived_cl2542, plain, 156.89/20.46 (( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.46 (op @ e0 @ e0) @ e0 @ Y0)))))) 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2535, '7'])). 156.89/20.46 thf(transitivity, axiom, 156.89/20.46 (mvalid @ 156.89/20.46 ( mbox_s4 @ 156.89/20.46 ( mforall_ind @ 156.89/20.46 ( ^[X:mu]: 156.89/20.46 ( mbox_s4 @ 156.89/20.46 ( mforall_ind @ 156.89/20.46 ( ^[Y:mu]: 156.89/20.46 ( mbox_s4 @ 156.89/20.46 ( mforall_ind @ 156.89/20.46 ( ^[Z:mu]: 156.89/20.46 ( mbox_s4 @ 156.89/20.46 ( mimplies @ 156.89/20.46 ( mand @ 156.89/20.46 ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ 156.89/20.46 ( mbox_s4 @ ( qmltpeq @ Y @ Z ) ) ) @ 156.89/20.46 ( mbox_s4 @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ) ))). 156.89/20.46 thf(zip_derived_cl6, plain, 156.89/20.46 ( (mvalid @ 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y0 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y2 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ Y0 @ Y1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y1 @ Y2))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y0 @ Y2))))))))))))))), 156.89/20.46 inference('cnf', [status(esa)], [transitivity])). 156.89/20.46 thf(mvalid, axiom, (mvalid @ X0) => 156.89/20.46 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) = ($true))). 156.89/20.46 thf('8', plain, 156.89/20.46 (![X0:( $i > $o )]: ( ( mvalid @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 ) ) )), 156.89/20.46 inference('rw.lit', [status(esa)], [mvalid])). 156.89/20.46 thf(zip_derived_cl228, plain, 156.89/20.46 ( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y2 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y3 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ Y1 @ Y2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y2 @ Y3))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y1 @ Y3)))))))))))) @ 156.89/20.46 Y0))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl6, '8'])). 156.89/20.46 thf(zip_derived_cl229, plain, 156.89/20.46 (![X2 : $i]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y0 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y2 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ Y0 @ Y1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y1 @ Y2))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y0 @ Y2)))))))))))) @ 156.89/20.46 X2)), 156.89/20.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl228])). 156.89/20.46 thf(zip_derived_cl230, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 156.89/20.46 (^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y2 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y3 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y1 @ Y2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y2 @ Y3))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y1 @ Y3))))))))))) @ 156.89/20.46 Y0))))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl229, '7'])). 156.89/20.46 thf(zip_derived_cl231, plain, 156.89/20.46 (![X0 : $i, X2 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ X2))) | (mforall_ind @ 156.89/20.46 (^[Y0 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y2 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ Y0 @ Y1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y1 @ Y2))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y0 @ Y2))))))))))) @ 156.89/20.46 X2)))), 156.89/20.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl230])). 156.89/20.46 thf(zip_derived_cl232, plain, 156.89/20.46 (![X0 : $i, X2 : $i]: 156.89/20.46 (~ (rel_s4 @ X0 @ X2) 156.89/20.46 | (mforall_ind @ 156.89/20.46 (^[Y0 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y2 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ Y0 @ Y1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y1 @ Y2))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y0 @ Y2))))))))))) @ 156.89/20.46 X2))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl231])). 156.89/20.46 thf(mforall_ind, axiom, (mforall_ind @ X0 @ X1) => 156.89/20.46 ((((!!) @ (^[Y0 : mu]: (((exists_in_world @ Y0 @ X1) => (X0 @ Y0 @ X1)))))) 156.89/20.46 = ($true))). 156.89/20.46 thf('9', plain, 156.89/20.46 (![X0:( mu > $i > $o ),X1:$i]: 156.89/20.46 ( ( mforall_ind @ X0 @ X1 ) <=> 156.89/20.46 ( ![X6:mu]: ( ( exists_in_world @ X6 @ X1 ) => ( X0 @ X6 @ X1 ) ) ) )), 156.89/20.46 inference('rw.lit', [status(esa)], [mforall_ind])). 156.89/20.46 thf(zip_derived_cl233, plain, 156.89/20.46 (![X0 : $i, X1 : $i]: 156.89/20.46 ( (((!!) @ (^[Y0 : mu]: 156.89/20.46 (((exists_in_world @ Y0 @ X0) => 156.89/20.46 ((^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y2 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y3 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y1 @ Y2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y2 @ Y3))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y1 @ Y3))))))))))) @ 156.89/20.46 Y0 @ X0)))))) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl232, '9'])). 156.89/20.46 thf(zip_derived_cl234, plain, 156.89/20.46 (![X0 : $i, X1 : $i]: 156.89/20.46 ( (((!!) @ (^[Y0 : mu]: 156.89/20.46 (((exists_in_world @ Y0 @ X0) => (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y2 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ Y0 @ Y1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y1 @ Y2))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y0 @ Y2))))))))) @ 156.89/20.46 X0)))))) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0))), 156.89/20.46 inference('ho_norm', [status(thm)], [zip_derived_cl233])). 156.89/20.46 thf(zip_derived_cl235, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X3 : mu]: 156.89/20.46 ( (((exists_in_world @ X3 @ X0) => (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y0 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ Y0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y0 @ Y1))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X3 @ Y1))))))))) @ 156.89/20.46 X0))) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0))), 156.89/20.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl234])). 156.89/20.46 thf(zip_derived_cl236, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X3 : mu]: 156.89/20.46 (~ (exists_in_world @ X3 @ X0) 156.89/20.46 | (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y0 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ Y0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y0 @ Y1))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X3 @ Y1))))))))) @ 156.89/20.46 X0) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0))), 156.89/20.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl235])). 156.89/20.46 thf(zip_derived_cl237, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : mu]: 156.89/20.46 ( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 156.89/20.46 (^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y2 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X2 @ Y1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y1 @ Y2))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X2 @ Y2)))))))) @ 156.89/20.46 Y0)))))) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0) 156.89/20.46 | ~ (exists_in_world @ X2 @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl236, '7'])). 156.89/20.46 thf(zip_derived_cl238, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]: 156.89/20.46 ( (((((~) @ (rel_s4 @ X0 @ X4))) | (mforall_ind @ 156.89/20.46 (^[Y0 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X2 @ Y0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y0 @ Y1))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X2 @ Y1)))))))) @ 156.89/20.46 X4))) 156.89/20.46 | ~ (exists_in_world @ X2 @ X0) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0))), 156.89/20.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl237])). 156.89/20.46 thf(zip_derived_cl239, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]: 156.89/20.46 (~ (rel_s4 @ X0 @ X4) 156.89/20.46 | (mforall_ind @ 156.89/20.46 (^[Y0 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X2 @ Y0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y0 @ Y1))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X2 @ Y1)))))))) @ 156.89/20.46 X4) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0) 156.89/20.46 | ~ (exists_in_world @ X2 @ X0))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl238])). 156.89/20.46 thf(zip_derived_cl240, plain, 156.89/20.46 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i]: 156.89/20.46 ( (((!!) @ (^[Y0 : mu]: 156.89/20.46 (((exists_in_world @ Y0 @ X3) => 156.89/20.46 ((^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y2 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X1 @ Y1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y1 @ Y2))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X1 @ Y2)))))))) @ 156.89/20.46 Y0 @ X3)))))) 156.89/20.46 | ~ (exists_in_world @ X1 @ X0) 156.89/20.46 | ~ (rel_s4 @ X2 @ X0) 156.89/20.46 | ~ (rel_s4 @ X0 @ X3))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl239, '9'])). 156.89/20.46 thf(zip_derived_cl241, plain, 156.89/20.46 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i]: 156.89/20.46 ( (((!!) @ (^[Y0 : mu]: 156.89/20.46 (((exists_in_world @ Y0 @ X3) => (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X1 @ Y0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ Y0 @ Y1))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X1 @ Y1)))))) @ 156.89/20.46 X3)))))) 156.89/20.46 | ~ (exists_in_world @ X1 @ X0) 156.89/20.46 | ~ (rel_s4 @ X2 @ X0) 156.89/20.46 | ~ (rel_s4 @ X0 @ X3))), 156.89/20.46 inference('ho_norm', [status(thm)], [zip_derived_cl240])). 156.89/20.46 thf(zip_derived_cl242, plain, 156.89/20.46 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i, X5 : mu]: 156.89/20.46 ( (((exists_in_world @ X5 @ X3) => (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y0 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X1 @ X5)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X5 @ Y0))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X1 @ Y0)))))) @ 156.89/20.46 X3))) 156.89/20.46 | ~ (rel_s4 @ X0 @ X3) 156.89/20.46 | ~ (rel_s4 @ X2 @ X0) 156.89/20.46 | ~ (exists_in_world @ X1 @ X0))), 156.89/20.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl241])). 156.89/20.46 thf(zip_derived_cl243, plain, 156.89/20.46 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i, X5 : mu]: 156.89/20.46 (~ (exists_in_world @ X5 @ X3) 156.89/20.46 | (mbox_s4 @ 156.89/20.46 (mforall_ind @ 156.89/20.46 (^[Y0 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X1 @ X5)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X5 @ Y0))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X1 @ Y0)))))) @ 156.89/20.46 X3) 156.89/20.46 | ~ (exists_in_world @ X1 @ X0) 156.89/20.46 | ~ (rel_s4 @ X2 @ X0) 156.89/20.46 | ~ (rel_s4 @ X0 @ X3))), 156.89/20.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl242])). 156.89/20.46 thf(zip_derived_cl244, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu]: 156.89/20.46 ( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 156.89/20.46 (^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ X4)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X4 @ Y1))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X3 @ Y1))))) @ 156.89/20.46 Y0)))))) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0) 156.89/20.46 | ~ (rel_s4 @ X2 @ X1) 156.89/20.46 | ~ (exists_in_world @ X3 @ X1) 156.89/20.46 | ~ (exists_in_world @ X4 @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl243, '7'])). 156.89/20.46 thf(zip_derived_cl245, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu, X6 : $i]: 156.89/20.46 ( (((((~) @ (rel_s4 @ X0 @ X6))) | (mforall_ind @ 156.89/20.46 (^[Y0 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ X4)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X4 @ Y0))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X3 @ Y0))))) @ 156.89/20.46 X6))) 156.89/20.46 | ~ (exists_in_world @ X4 @ X0) 156.89/20.46 | ~ (exists_in_world @ X3 @ X1) 156.89/20.46 | ~ (rel_s4 @ X2 @ X1) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0))), 156.89/20.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl244])). 156.89/20.46 thf(zip_derived_cl246, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu, X6 : $i]: 156.89/20.46 (~ (rel_s4 @ X0 @ X6) 156.89/20.46 | (mforall_ind @ 156.89/20.46 (^[Y0 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ X4)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X4 @ Y0))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X3 @ Y0))))) @ 156.89/20.46 X6) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0) 156.89/20.46 | ~ (rel_s4 @ X2 @ X1) 156.89/20.46 | ~ (exists_in_world @ X3 @ X1) 156.89/20.46 | ~ (exists_in_world @ X4 @ X0))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl245])). 156.89/20.46 thf(zip_derived_cl247, plain, 156.89/20.46 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]: 156.89/20.46 ( (((!!) @ (^[Y0 : mu]: 156.89/20.46 (((exists_in_world @ Y0 @ X5) => 156.89/20.46 ((^[Y1 : mu]: 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ X1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X1 @ Y1))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X3 @ Y1))))) @ 156.89/20.46 Y0 @ X5)))))) 156.89/20.46 | ~ (exists_in_world @ X1 @ X0) 156.89/20.46 | ~ (exists_in_world @ X3 @ X2) 156.89/20.46 | ~ (rel_s4 @ X4 @ X2) 156.89/20.46 | ~ (rel_s4 @ X2 @ X0) 156.89/20.46 | ~ (rel_s4 @ X0 @ X5))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl246, '9'])). 156.89/20.46 thf(zip_derived_cl248, plain, 156.89/20.46 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]: 156.89/20.46 ( (((!!) @ (^[Y0 : mu]: 156.89/20.46 (((exists_in_world @ Y0 @ X5) => (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ X1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X1 @ Y0))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X3 @ Y0))) @ 156.89/20.46 X5)))))) 156.89/20.46 | ~ (exists_in_world @ X1 @ X0) 156.89/20.46 | ~ (exists_in_world @ X3 @ X2) 156.89/20.46 | ~ (rel_s4 @ X4 @ X2) 156.89/20.46 | ~ (rel_s4 @ X2 @ X0) 156.89/20.46 | ~ (rel_s4 @ X0 @ X5))), 156.89/20.46 inference('ho_norm', [status(thm)], [zip_derived_cl247])). 156.89/20.46 thf(zip_derived_cl249, plain, 156.89/20.46 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i, X7 : mu]: 156.89/20.46 ( (((exists_in_world @ X7 @ X5) => (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ X1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X1 @ X7))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X3 @ X7))) @ 156.89/20.46 X5))) 156.89/20.46 | ~ (rel_s4 @ X0 @ X5) 156.89/20.46 | ~ (rel_s4 @ X2 @ X0) 156.89/20.46 | ~ (rel_s4 @ X4 @ X2) 156.89/20.46 | ~ (exists_in_world @ X3 @ X2) 156.89/20.46 | ~ (exists_in_world @ X1 @ X0))), 156.89/20.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl248])). 156.89/20.46 thf(zip_derived_cl250, plain, 156.89/20.46 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i, X7 : mu]: 156.89/20.46 (~ (exists_in_world @ X7 @ X5) 156.89/20.46 | (mbox_s4 @ 156.89/20.46 (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X3 @ X1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X1 @ X7))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X3 @ X7))) @ 156.89/20.46 X5) 156.89/20.46 | ~ (exists_in_world @ X1 @ X0) 156.89/20.46 | ~ (exists_in_world @ X3 @ X2) 156.89/20.46 | ~ (rel_s4 @ X4 @ X2) 156.89/20.46 | ~ (rel_s4 @ X2 @ X0) 156.89/20.46 | ~ (rel_s4 @ X0 @ X5))), 156.89/20.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl249])). 156.89/20.46 thf(zip_derived_cl251, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : mu, X5 : mu, X6 : mu]: 156.89/20.46 ( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X4 @ X5)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X5 @ X6))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X4 @ X6)) @ Y0)))))) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0) 156.89/20.46 | ~ (rel_s4 @ X2 @ X1) 156.89/20.46 | ~ (rel_s4 @ X3 @ X2) 156.89/20.46 | ~ (exists_in_world @ X4 @ X2) 156.89/20.46 | ~ (exists_in_world @ X5 @ X1) 156.89/20.46 | ~ (exists_in_world @ X6 @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl250, '7'])). 156.89/20.46 thf(zip_derived_cl252, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : mu, X5 : mu, X6 : mu, X8 : $i]: 156.89/20.46 ( (((((~) @ (rel_s4 @ X0 @ X8))) | (mimplies @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X4 @ X5)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X5 @ X6))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X4 @ X6)) @ X8))) 156.89/20.46 | ~ (exists_in_world @ X6 @ X0) 156.89/20.46 | ~ (exists_in_world @ X5 @ X1) 156.89/20.46 | ~ (exists_in_world @ X4 @ X2) 156.89/20.46 | ~ (rel_s4 @ X3 @ X2) 156.89/20.46 | ~ (rel_s4 @ X2 @ X1) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0))), 156.89/20.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl251])). 156.89/20.46 thf(mimplies, axiom,(( mimplies @ (X0)@ (X1)@ (X2)) = 156.89/20.46 ((mor @ (mnot @ X0) @ X1 @ X2)))). 156.89/20.46 thf('10', plain, 156.89/20.46 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]: 156.89/20.46 ( ( mimplies @ X0 @ X1 @ X2 ) = ( mor @ ( mnot @ X0 ) @ X1 @ X2 ) )), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl253, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : mu, X5 : mu, X6 : mu, X8 : $i]: 156.89/20.46 ( (((((~) @ (rel_s4 @ X0 @ X8))) | (mor @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X4 @ X5)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X5 @ X6)))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X4 @ X6)) @ X8))) 156.89/20.46 | ~ (exists_in_world @ X6 @ X0) 156.89/20.46 | ~ (exists_in_world @ X5 @ X1) 156.89/20.46 | ~ (exists_in_world @ X4 @ X2) 156.89/20.46 | ~ (rel_s4 @ X3 @ X2) 156.89/20.46 | ~ (rel_s4 @ X2 @ X1) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl252, '10'])). 156.89/20.46 thf(zip_derived_cl254, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : mu, X5 : mu, X6 : mu, X8 : $i]: 156.89/20.46 (~ (rel_s4 @ X0 @ X8) 156.89/20.46 | (mor @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X4 @ X5)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X5 @ X6)))) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X4 @ X6)) @ X8) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0) 156.89/20.46 | ~ (rel_s4 @ X2 @ X1) 156.89/20.46 | ~ (rel_s4 @ X3 @ X2) 156.89/20.46 | ~ (exists_in_world @ X4 @ X2) 156.89/20.46 | ~ (exists_in_world @ X5 @ X1) 156.89/20.46 | ~ (exists_in_world @ X6 @ X0))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl253])). 156.89/20.46 thf(zip_derived_cl255, plain, 156.89/20.46 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : mu, X6 : $i, X7 : $i]: 156.89/20.46 ( (((mbox_s4 @ (qmltpeq @ X5 @ X1) @ X7) | (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X5 @ X3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X3 @ X1))) @ 156.89/20.46 X7))) 156.89/20.46 | ~ (exists_in_world @ X1 @ X0) 156.89/20.46 | ~ (exists_in_world @ X3 @ X2) 156.89/20.46 | ~ (exists_in_world @ X5 @ X4) 156.89/20.46 | ~ (rel_s4 @ X6 @ X4) 156.89/20.46 | ~ (rel_s4 @ X4 @ X2) 156.89/20.46 | ~ (rel_s4 @ X2 @ X0) 156.89/20.46 | ~ (rel_s4 @ X0 @ X7))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl254, '6'])). 156.89/20.46 thf(zip_derived_cl256, plain, 156.89/20.46 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : mu, X6 : $i, X7 : $i]: 156.89/20.46 ( (mbox_s4 @ (qmltpeq @ X5 @ X1) @ X7) 156.89/20.46 | (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X5 @ X3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X3 @ X1))) @ 156.89/20.46 X7) 156.89/20.46 | ~ (rel_s4 @ X0 @ X7) 156.89/20.46 | ~ (rel_s4 @ X2 @ X0) 156.89/20.46 | ~ (rel_s4 @ X4 @ X2) 156.89/20.46 | ~ (rel_s4 @ X6 @ X4) 156.89/20.46 | ~ (exists_in_world @ X5 @ X4) 156.89/20.46 | ~ (exists_in_world @ X3 @ X2) 156.89/20.46 | ~ (exists_in_world @ X1 @ X0))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl255])). 156.89/20.46 thf(zip_derived_cl257, plain, 156.89/20.46 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : mu, X6 : $i, X7 : $i]: 156.89/20.46 ( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X7 @ Y0))) | (qmltpeq @ X5 @ X1 @ 156.89/20.46 Y0)))))) 156.89/20.46 | ~ (exists_in_world @ X1 @ X0) 156.89/20.46 | ~ (exists_in_world @ X3 @ X2) 156.89/20.46 | ~ (exists_in_world @ X5 @ X4) 156.89/20.46 | ~ (rel_s4 @ X6 @ X4) 156.89/20.46 | ~ (rel_s4 @ X4 @ X2) 156.89/20.46 | ~ (rel_s4 @ X2 @ X0) 156.89/20.46 | ~ (rel_s4 @ X0 @ X7) 156.89/20.46 | (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ X5 @ X3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X3 @ X1))) @ 156.89/20.46 X7))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl256, '7'])). 156.89/20.46 thf(zip_derived_cl258, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : mu, X6 : mu, X7 : mu]: 156.89/20.46 (~ (mand @ (mbox_s4 @ (qmltpeq @ X5 @ X6)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X6 @ X7)) @ X0) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0) 156.89/20.46 | ~ (rel_s4 @ X2 @ X1) 156.89/20.46 | ~ (rel_s4 @ X3 @ X2) 156.89/20.46 | ~ (rel_s4 @ X4 @ X3) 156.89/20.46 | ~ (exists_in_world @ X5 @ X3) 156.89/20.46 | ~ (exists_in_world @ X6 @ X2) 156.89/20.46 | ~ (exists_in_world @ X7 @ X1) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X5 @ X7 @ 156.89/20.46 Y0)))))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl257, '4'])). 156.89/20.46 thf(zip_derived_cl259, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : mu, X6 : mu, X7 : mu]: 156.89/20.46 (~ (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ X5 @ X6))) @ 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ X6 @ X7)))) @ 156.89/20.46 X0) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0) 156.89/20.46 | ~ (rel_s4 @ X2 @ X1) 156.89/20.46 | ~ (rel_s4 @ X3 @ X2) 156.89/20.46 | ~ (rel_s4 @ X4 @ X3) 156.89/20.46 | ~ (exists_in_world @ X5 @ X3) 156.89/20.46 | ~ (exists_in_world @ X6 @ X2) 156.89/20.46 | ~ (exists_in_world @ X7 @ X1) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X5 @ X7 @ 156.89/20.46 Y0)))))))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl258, '3'])). 156.89/20.46 thf(zip_derived_cl260, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i, X3 : $i, X4 : $i, X5 : mu, X6 : $i, X7 : $i]: 156.89/20.46 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ X1 @ X5))) @ 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ X5 @ X0))) @ X2) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.46 Y0)))))) 156.89/20.46 | ~ (exists_in_world @ X0 @ X3) 156.89/20.46 | ~ (exists_in_world @ X5 @ X4) 156.89/20.46 | ~ (exists_in_world @ X1 @ X6) 156.89/20.46 | ~ (rel_s4 @ X7 @ X6) 156.89/20.46 | ~ (rel_s4 @ X6 @ X4) 156.89/20.46 | ~ (rel_s4 @ X4 @ X3) 156.89/20.46 | ~ (rel_s4 @ X3 @ X2))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl259, '2'])). 156.89/20.46 thf(zip_derived_cl261, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : mu, X6 : mu, X7 : mu]: 156.89/20.46 ( (((mnot @ (mbox_s4 @ (qmltpeq @ X6 @ X7)) @ X0) | (mnot @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ X5 @ X6)) @ X0))) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0) 156.89/20.46 | ~ (rel_s4 @ X2 @ X1) 156.89/20.46 | ~ (rel_s4 @ X3 @ X2) 156.89/20.46 | ~ (rel_s4 @ X4 @ X3) 156.89/20.46 | ~ (exists_in_world @ X5 @ X3) 156.89/20.46 | ~ (exists_in_world @ X6 @ X2) 156.89/20.46 | ~ (exists_in_world @ X7 @ X1) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X5 @ X7 @ 156.89/20.46 Y0)))))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl260, '6'])). 156.89/20.46 thf(zip_derived_cl262, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : mu, X6 : mu, X7 : mu]: 156.89/20.46 ( (mnot @ (mbox_s4 @ (qmltpeq @ X6 @ X7)) @ X0) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ X5 @ X6)) @ X0) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X5 @ X7 @ 156.89/20.46 Y0)))))) 156.89/20.46 | ~ (exists_in_world @ X7 @ X1) 156.89/20.46 | ~ (exists_in_world @ X6 @ X2) 156.89/20.46 | ~ (exists_in_world @ X5 @ X3) 156.89/20.46 | ~ (rel_s4 @ X4 @ X3) 156.89/20.46 | ~ (rel_s4 @ X3 @ X2) 156.89/20.46 | ~ (rel_s4 @ X2 @ X1) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl261])). 156.89/20.46 thf(zip_derived_cl263, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : mu, X6 : mu, X7 : mu]: 156.89/20.46 (~ (mbox_s4 @ (qmltpeq @ X6 @ X7) @ X0) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0) 156.89/20.46 | ~ (rel_s4 @ X2 @ X1) 156.89/20.46 | ~ (rel_s4 @ X3 @ X2) 156.89/20.46 | ~ (rel_s4 @ X4 @ X3) 156.89/20.46 | ~ (exists_in_world @ X5 @ X3) 156.89/20.46 | ~ (exists_in_world @ X6 @ X2) 156.89/20.46 | ~ (exists_in_world @ X7 @ X1) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X5 @ X7 @ 156.89/20.46 Y0)))))) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ X5 @ X6)) @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl262, '4'])). 156.89/20.46 thf(zip_derived_cl264, plain, 156.89/20.46 (![X0 : $i, X1 : mu, X2 : mu, X3 : mu, X4 : $i, X5 : $i, X6 : $i, X7 : $i]: 156.89/20.46 (~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X1 @ X3 @ 156.89/20.46 Y0)))))) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ X2 @ X1)) @ X0) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X2 @ X3 @ 156.89/20.46 Y0)))))) 156.89/20.46 | ~ (exists_in_world @ X3 @ X4) 156.89/20.46 | ~ (exists_in_world @ X1 @ X5) 156.89/20.46 | ~ (exists_in_world @ X2 @ X6) 156.89/20.46 | ~ (rel_s4 @ X7 @ X6) 156.89/20.46 | ~ (rel_s4 @ X6 @ X5) 156.89/20.46 | ~ (rel_s4 @ X5 @ X4) 156.89/20.46 | ~ (rel_s4 @ X4 @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl263, '1'])). 156.89/20.46 thf(zip_derived_cl265, plain, 156.89/20.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : mu, X6 : mu, X7 : mu]: 156.89/20.46 (~ (mbox_s4 @ (qmltpeq @ X5 @ X6) @ X0) 156.89/20.46 | ~ (rel_s4 @ X1 @ X0) 156.89/20.46 | ~ (rel_s4 @ X2 @ X1) 156.89/20.46 | ~ (rel_s4 @ X3 @ X2) 156.89/20.46 | ~ (rel_s4 @ X4 @ X3) 156.89/20.46 | ~ (exists_in_world @ X5 @ X3) 156.89/20.46 | ~ (exists_in_world @ X6 @ X2) 156.89/20.46 | ~ (exists_in_world @ X7 @ X1) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X5 @ X7 @ 156.89/20.46 Y0)))))) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ X6 @ 156.89/20.46 X7 @ Y0)))))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl264, '4'])). 156.89/20.46 thf(zip_derived_cl266, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i, X6 : $i, X7 : $i]: 156.89/20.46 (~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X3 @ X1 @ 156.89/20.46 Y0)))))) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X3 @ X0 @ 156.89/20.46 Y0)))))) 156.89/20.46 | ~ (exists_in_world @ X0 @ X4) 156.89/20.46 | ~ (exists_in_world @ X1 @ X5) 156.89/20.46 | ~ (exists_in_world @ X3 @ X6) 156.89/20.46 | ~ (rel_s4 @ X7 @ X6) 156.89/20.46 | ~ (rel_s4 @ X6 @ X5) 156.89/20.46 | ~ (rel_s4 @ X5 @ X4) 156.89/20.46 | ~ (rel_s4 @ X4 @ X2))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl265, '1'])). 156.89/20.46 thf(zip_derived_cl267, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i, X6 : $i, X7 : $i]: 156.89/20.46 (~ (((((~) @ (rel_s4 @ X2 @ ('#sk2' @ X3 @ X1 @ X2)))) | (qmltpeq @ 156.89/20.46 X3 @ X1 @ ('#sk2' @ X3 @ X1 @ X2)))) 156.89/20.46 | ~ (rel_s4 @ X4 @ X2) 156.89/20.46 | ~ (rel_s4 @ X5 @ X4) 156.89/20.46 | ~ (rel_s4 @ X6 @ X5) 156.89/20.46 | ~ (rel_s4 @ X7 @ X6) 156.89/20.46 | ~ (exists_in_world @ X3 @ X6) 156.89/20.46 | ~ (exists_in_world @ X1 @ X5) 156.89/20.46 | ~ (exists_in_world @ X0 @ X4) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X3 @ X0 @ 156.89/20.46 Y0)))))) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))))), 156.89/20.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl266])). 156.89/20.46 thf(zip_derived_cl268, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i, X6 : $i, X7 : $i]: 156.89/20.46 ( (rel_s4 @ X2 @ ('#sk2' @ X3 @ X1 @ X2)) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X3 @ X0 @ 156.89/20.46 Y0)))))) 156.89/20.46 | ~ (exists_in_world @ X0 @ X4) 156.89/20.46 | ~ (exists_in_world @ X1 @ X5) 156.89/20.46 | ~ (exists_in_world @ X3 @ X6) 156.89/20.46 | ~ (rel_s4 @ X7 @ X6) 156.89/20.46 | ~ (rel_s4 @ X6 @ X5) 156.89/20.46 | ~ (rel_s4 @ X5 @ X4) 156.89/20.46 | ~ (rel_s4 @ X4 @ X2))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl267])). 156.89/20.46 thf(zip_derived_cl268, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i, X6 : $i, X7 : $i]: 156.89/20.46 ( (rel_s4 @ X2 @ ('#sk2' @ X3 @ X1 @ X2)) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X3 @ X0 @ 156.89/20.46 Y0)))))) 156.89/20.46 | ~ (exists_in_world @ X0 @ X4) 156.89/20.46 | ~ (exists_in_world @ X1 @ X5) 156.89/20.46 | ~ (exists_in_world @ X3 @ X6) 156.89/20.46 | ~ (rel_s4 @ X7 @ X6) 156.89/20.46 | ~ (rel_s4 @ X6 @ X5) 156.89/20.46 | ~ (rel_s4 @ X5 @ X4) 156.89/20.46 | ~ (rel_s4 @ X4 @ X2))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl267])). 156.89/20.46 thf(zip_derived_cl270, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl272, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i, X6 : $i, X7 : $i]: 156.89/20.46 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | ~ (rel_s4 @ X4 @ X2) 156.89/20.46 | ~ (rel_s4 @ X5 @ X4) 156.89/20.46 | ~ (rel_s4 @ X6 @ X5) 156.89/20.46 | ~ (rel_s4 @ X7 @ X6) 156.89/20.46 | ~ (exists_in_world @ X3 @ X6) 156.89/20.46 | ~ (exists_in_world @ X1 @ X5) 156.89/20.46 | ~ (exists_in_world @ X0 @ X4) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X3 @ X0 @ 156.89/20.46 Y0)))))) 156.89/20.46 | (rel_s4 @ X2 @ ('#sk2' @ X3 @ X1 @ X2)))), 156.89/20.46 inference('renaming', [status(thm)], 156.89/20.46 [zip_derived_cl268, zip_derived_cl270])). 156.89/20.46 thf(zip_derived_cl274, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.46 Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl270, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl2547, plain, 156.89/20.46 (( ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('renaming', [status(thm)], 156.89/20.46 [zip_derived_cl2542, zip_derived_cl274, zip_derived_cl270])). 156.89/20.46 thf(zip_derived_cl2555, plain, 156.89/20.46 (( (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2547])). 156.89/20.46 thf(zip_derived_cl2563, plain, 156.89/20.46 (( (((mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 '#sk5') | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2555, '6'])). 156.89/20.46 thf(zip_derived_cl2571, plain, 156.89/20.46 (( (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2563, '3', '3'])). 156.89/20.46 thf(zip_derived_cl2572, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2571, '4'])). 156.89/20.46 thf(zip_derived_cl2580, plain, 156.89/20.46 ((~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2572, '5'])). 156.89/20.46 thf(zip_derived_cl2589, plain, 156.89/20.46 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2580])). 156.89/20.46 thf(zip_derived_cl2600, plain, 156.89/20.46 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2589, '2'])). 156.89/20.46 thf(zip_derived_cl2611, plain, 156.89/20.46 (( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.46 (op @ e0 @ e0) @ e1 @ Y0)))))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2600, '7'])). 156.89/20.46 thf(zip_derived_cl274, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.46 Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl270, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl2620, plain, 156.89/20.46 (( ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.46 inference('renaming', [status(thm)], 156.89/20.46 [zip_derived_cl2611, zip_derived_cl274, zip_derived_cl270])). 156.89/20.46 thf(zip_derived_cl2632, plain, 156.89/20.46 (( (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2620])). 156.89/20.46 thf(zip_derived_cl2643, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2632, '4'])). 156.89/20.46 thf(zip_derived_cl2659, plain, 156.89/20.46 ((~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2643, '5'])). 156.89/20.46 thf(zip_derived_cl2670, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | ~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2659, '4'])). 156.89/20.46 thf(zip_derived_cl2687, plain, 156.89/20.46 ((~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2670, '5'])). 156.89/20.46 thf(zip_derived_cl2702, plain, 156.89/20.46 ((~ (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.46 | ~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2687])). 156.89/20.46 thf(zip_derived_cl2721, plain, 156.89/20.46 (( ('#form6') 156.89/20.46 | ~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl2722, plain, 156.89/20.46 ((~ (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2721])). 156.89/20.46 thf(zip_derived_cl2741, plain, 156.89/20.46 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2722, '2'])). 156.89/20.46 thf(zip_derived_cl2763, plain, 156.89/20.46 (( (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2741, '3'])). 156.89/20.46 thf(zip_derived_cl2764, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2763, '4'])). 156.89/20.46 thf(zip_derived_cl2785, plain, 156.89/20.46 ((~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2764, '5'])). 156.89/20.46 thf(zip_derived_cl2811, plain, 156.89/20.46 ((~ (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2785])). 156.89/20.46 thf(zip_derived_cl2835, plain, 156.89/20.46 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ '#sk5') 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2811, '2'])). 156.89/20.46 thf(zip_derived_cl2862, plain, 156.89/20.46 (( (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3))) @ 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2835, '3'])). 156.89/20.46 thf(zip_derived_cl2863, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3))) @ 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ '#sk5') 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2862, '4'])). 156.89/20.46 thf(zip_derived_cl2887, plain, 156.89/20.46 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ '#sk5') | 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ '#sk5'))) 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2863, '5'])). 156.89/20.46 thf(zip_derived_cl2915, plain, 156.89/20.46 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ '#sk5') 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2887])). 156.89/20.46 thf(zip_derived_cl2944, plain, 156.89/20.46 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3) @ '#sk5') | ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2915, '2'])). 156.89/20.46 thf(zip_derived_cl2977, plain, 156.89/20.46 (( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.46 (op @ e3 @ e3) @ e3 @ Y0)))))) 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2944, '7'])). 156.89/20.46 thf(zip_derived_cl3003, plain, 156.89/20.46 (![X2 : $i]: 156.89/20.46 ( (((((~) @ (rel_s4 @ '#sk5' @ X2))) | (qmltpeq @ (op @ e3 @ e3) @ 156.89/20.46 e3 @ X2))) 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2977])). 156.89/20.46 thf(zip_derived_cl3031, plain, 156.89/20.46 (![X2 : $i]: 156.89/20.46 (~ (rel_s4 @ '#sk5' @ X2) 156.89/20.46 | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X2) 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3003])). 156.89/20.46 thf(zip_derived_cl2916, plain, 156.89/20.46 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ '#sk5') 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2887])). 156.89/20.46 thf(zip_derived_cl2945, plain, 156.89/20.46 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3) @ '#sk5') | ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2916, '2'])). 156.89/20.46 thf(zip_derived_cl2978, plain, 156.89/20.46 (( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.46 (op @ e2 @ e2) @ e3 @ Y0)))))) 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2945, '7'])). 156.89/20.46 thf(zip_derived_cl3004, plain, 156.89/20.46 (![X2 : $i]: 156.89/20.46 ( (((((~) @ (rel_s4 @ '#sk5' @ X2))) | (qmltpeq @ (op @ e2 @ e2) @ 156.89/20.46 e3 @ X2))) 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2978])). 156.89/20.46 thf(zip_derived_cl3032, plain, 156.89/20.46 (![X2 : $i]: 156.89/20.46 (~ (rel_s4 @ '#sk5' @ X2) 156.89/20.46 | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X2) 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3004])). 156.89/20.46 thf(zip_derived_cl270, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl271, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 (~ (((((~) @ (rel_s4 @ X2 @ ('#sk2' @ X1 @ X0 @ X2)))) | (qmltpeq @ 156.89/20.46 X1 @ X0 @ ('#sk2' @ X1 @ X0 @ X2)))) 156.89/20.46 | ('#form3' @ X0 @ X1 @ X2))), 156.89/20.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl270])). 156.89/20.46 thf(zip_derived_cl277, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 ( (rel_s4 @ X2 @ ('#sk2' @ X1 @ X0 @ X2)) | ('#form3' @ X0 @ X1 @ X2))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl271])). 156.89/20.46 thf(zip_derived_cl2812, plain, 156.89/20.46 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ '#sk5') 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2785])). 156.89/20.46 thf(zip_derived_cl2836, plain, 156.89/20.46 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3) @ '#sk5') | ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2812, '2'])). 156.89/20.46 thf(zip_derived_cl2864, plain, 156.89/20.46 (( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.46 (op @ e1 @ e1) @ e3 @ Y0)))))) 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2836, '7'])). 156.89/20.46 thf(zip_derived_cl2888, plain, 156.89/20.46 (![X2 : $i]: 156.89/20.46 ( (((((~) @ (rel_s4 @ '#sk5' @ X2))) | (qmltpeq @ (op @ e1 @ e1) @ 156.89/20.46 e3 @ X2))) 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2864])). 156.89/20.46 thf(zip_derived_cl2917, plain, 156.89/20.46 (![X2 : $i]: 156.89/20.46 (~ (rel_s4 @ '#sk5' @ X2) 156.89/20.46 | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2) 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2888])). 156.89/20.46 thf(zip_derived_cl2511, plain, 156.89/20.46 (~ (mnot @ 156.89/20.46 (mbox_s4 @ 156.89/20.46 (mnot @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))) @ 156.89/20.46 '#sk5')), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2510])). 156.89/20.46 thf(zip_derived_cl2513, plain, 156.89/20.46 ( (mbox_s4 @ 156.89/20.46 (mnot @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))) @ 156.89/20.46 '#sk5')), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2511, '2'])). 156.89/20.46 thf(zip_derived_cl2515, plain, 156.89/20.46 ( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (mnot @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 156.89/20.46 Y0))))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2513, '7'])). 156.89/20.46 thf(zip_derived_cl2517, plain, 156.89/20.46 (![X2 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ '#sk5' @ X2))) | (mnot @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 156.89/20.46 X2)))), 156.89/20.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2515])). 156.89/20.46 thf(zip_derived_cl2520, plain, 156.89/20.46 (![X2 : $i]: 156.89/20.46 (~ (rel_s4 @ '#sk5' @ X2) 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 156.89/20.46 X2))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2517])). 156.89/20.46 thf(zip_derived_cl2522, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))) @ 156.89/20.46 X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2520, '4'])). 156.89/20.46 thf(zip_derived_cl2525, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 X0) | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @ 156.89/20.46 X0))) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2522, '5'])). 156.89/20.46 thf(zip_derived_cl2527, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 X0) | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))))) @ 156.89/20.46 X0))) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2525, '3'])). 156.89/20.46 thf(zip_derived_cl2528, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2527])). 156.89/20.46 thf(zip_derived_cl2532, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 X0) | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.46 X0))) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2528, '5'])). 156.89/20.46 thf(zip_derived_cl2536, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 X0) | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 X0))) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2532, '3'])). 156.89/20.46 thf(zip_derived_cl2537, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2536])). 156.89/20.46 thf(zip_derived_cl2543, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (((mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 X0) | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.46 X0))) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2537, '5'])). 156.89/20.46 thf(zip_derived_cl2548, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 X0) | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 X0))) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2543, '3', '3'])). 156.89/20.46 thf(zip_derived_cl2549, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2548])). 156.89/20.46 thf(zip_derived_cl2556, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2549, '2'])). 156.89/20.46 thf(zip_derived_cl2564, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 ( (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ X0))) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2556, '6'])). 156.89/20.46 thf(zip_derived_cl2573, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 ( (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 X0) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2564])). 156.89/20.46 thf(zip_derived_cl2581, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 156.89/20.46 X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2573, '4'])). 156.89/20.46 thf(zip_derived_cl2590, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ X0))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2581, '3'])). 156.89/20.46 thf(zip_derived_cl2591, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 X0) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2590, '2'])). 156.89/20.46 thf(zip_derived_cl2601, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 ( (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 156.89/20.46 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0))) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2591, '6'])). 156.89/20.46 thf(zip_derived_cl2612, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 156.89/20.46 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2601, '4'])). 156.89/20.46 thf(zip_derived_cl2621, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 156.89/20.46 (op @ e0 @ e0) @ e3 @ Y0)))))) 156.89/20.46 | (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 156.89/20.46 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0))) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2612, '1'])). 156.89/20.46 thf(zip_derived_cl274, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.46 Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl270, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl2633, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 156.89/20.46 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0))))), 156.89/20.46 inference('renaming', [status(thm)], 156.89/20.46 [zip_derived_cl2621, zip_derived_cl274, zip_derived_cl270])). 156.89/20.46 thf(zip_derived_cl2644, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 ( (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 156.89/20.46 X0) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2633])). 156.89/20.46 thf(zip_derived_cl2660, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2644, '4'])). 156.89/20.46 thf(zip_derived_cl2671, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3))) @ 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2660, '3'])). 156.89/20.46 thf(zip_derived_cl2672, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3))) @ 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ X0) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2671, '2'])). 156.89/20.46 thf(zip_derived_cl2688, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 ( (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0) | 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0))) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2672, '6'])). 156.89/20.46 thf(zip_derived_cl2704, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0) 156.89/20.46 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0) | 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2688, '4'])). 156.89/20.46 thf(zip_derived_cl2726, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 156.89/20.46 (op @ e1 @ e1) @ e3 @ Y0)))))) 156.89/20.46 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0) | 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0))) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2704, '1'])). 156.89/20.46 thf(zip_derived_cl274, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.46 Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl270, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl2744, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0) 156.89/20.46 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0) | 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0))))), 156.89/20.46 inference('renaming', [status(thm)], 156.89/20.46 [zip_derived_cl2726, zip_derived_cl274, zip_derived_cl270])). 156.89/20.46 thf(zip_derived_cl2767, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 ( (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2744])). 156.89/20.46 thf(zip_derived_cl2788, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3) @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2767, '4'])). 156.89/20.46 thf(zip_derived_cl2814, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 156.89/20.46 (op @ e3 @ e3) @ e3 @ Y0)))))) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2788, '1'])). 156.89/20.46 thf(zip_derived_cl274, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.46 Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl270, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl2837, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ ('#form3' @ e3 @ (op @ e3 @ e3) @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0) 156.89/20.46 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ X0))), 156.89/20.46 inference('renaming', [status(thm)], 156.89/20.46 [zip_derived_cl2814, zip_derived_cl274, zip_derived_cl270])). 156.89/20.46 thf(zip_derived_cl2865, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3) @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e3 @ e3) @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2837, '4'])). 156.89/20.46 thf(zip_derived_cl2889, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 156.89/20.46 (op @ e2 @ e2) @ e3 @ Y0)))))) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e3 @ e3) @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2865, '1'])). 156.89/20.46 thf(zip_derived_cl274, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.46 Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl270, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl2918, plain, 156.89/20.46 (![X0 : $i]: 156.89/20.46 (~ ('#form3' @ e3 @ (op @ e2 @ e2) @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e0 @ e0) @ X0) 156.89/20.46 | ~ (rel_s4 @ '#sk5' @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e1 @ e1) @ X0) 156.89/20.46 | ~ ('#form3' @ e3 @ (op @ e3 @ e3) @ X0))), 156.89/20.46 inference('renaming', [status(thm)], 156.89/20.46 [zip_derived_cl2889, zip_derived_cl274, zip_derived_cl270])). 156.89/20.46 thf(zip_derived_cl2723, plain, 156.89/20.46 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ '#sk5') 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2721])). 156.89/20.46 thf(zip_derived_cl2742, plain, 156.89/20.46 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk5') | ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2723, '2'])). 156.89/20.46 thf(zip_derived_cl2765, plain, 156.89/20.46 (( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.46 (op @ e0 @ e0) @ e3 @ Y0)))))) 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2742, '7'])). 156.89/20.46 thf(zip_derived_cl2786, plain, 156.89/20.46 (![X2 : $i]: 156.89/20.46 ( (((((~) @ (rel_s4 @ '#sk5' @ X2))) | (qmltpeq @ (op @ e0 @ e0) @ 156.89/20.46 e3 @ X2))) 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2765])). 156.89/20.46 thf(zip_derived_cl2813, plain, 156.89/20.46 (![X2 : $i]: 156.89/20.46 (~ (rel_s4 @ '#sk5' @ X2) 156.89/20.46 | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2) 156.89/20.46 | ('#form6'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2786])). 156.89/20.46 thf(zip_derived_cl278, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 (~ (qmltpeq @ X1 @ X0 @ ('#sk2' @ X1 @ X0 @ X2)) 156.89/20.46 | ('#form3' @ X0 @ X1 @ X2))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl271])). 156.89/20.46 thf(zip_derived_cl2530, plain, 156.89/20.46 ((~ (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2526])). 156.89/20.46 thf(zip_derived_cl2534, plain, 156.89/20.46 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2530, '2'])). 156.89/20.46 thf(zip_derived_cl2540, plain, 156.89/20.46 (( (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2534, '3'])). 156.89/20.46 thf(zip_derived_cl2541, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2540, '4'])). 156.89/20.46 thf(zip_derived_cl2546, plain, 156.89/20.46 ((~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2541, '5'])). 156.89/20.46 thf(zip_derived_cl2553, plain, 156.89/20.46 ((~ (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2546])). 156.89/20.46 thf(zip_derived_cl2561, plain, 156.89/20.46 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2553, '2'])). 156.89/20.46 thf(zip_derived_cl2568, plain, 156.89/20.46 (( (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0))) @ 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2561, '3'])). 156.89/20.46 thf(zip_derived_cl2569, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0))) @ 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2568, '4'])). 156.89/20.46 thf(zip_derived_cl2578, plain, 156.89/20.46 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ '#sk5') | 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ '#sk5'))) 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2569, '5'])). 156.89/20.46 thf(zip_derived_cl2586, plain, 156.89/20.46 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2578])). 156.89/20.46 thf(zip_derived_cl2597, plain, 156.89/20.46 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0) @ '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2586, '2'])). 156.89/20.46 thf(zip_derived_cl2606, plain, 156.89/20.46 (( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.46 (op @ e2 @ e2) @ e0 @ Y0)))))) 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2597, '7'])). 156.89/20.46 thf(zip_derived_cl274, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.46 Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl270, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl2617, plain, 156.89/20.46 (( ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('renaming', [status(thm)], 156.89/20.46 [zip_derived_cl2606, zip_derived_cl274, zip_derived_cl270])). 156.89/20.46 thf(zip_derived_cl2627, plain, 156.89/20.46 (( (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2617])). 156.89/20.46 thf(zip_derived_cl2638, plain, 156.89/20.46 (( (((mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 '#sk5') | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2627, '6'])). 156.89/20.46 thf(zip_derived_cl2651, plain, 156.89/20.46 (( (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2638, '3', '3'])). 156.89/20.46 thf(zip_derived_cl2652, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2651, '4'])). 156.89/20.46 thf(zip_derived_cl2665, plain, 156.89/20.46 ((~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2652, '5'])). 156.89/20.46 thf(zip_derived_cl2679, plain, 156.89/20.46 ((~ (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2665])). 156.89/20.46 thf(zip_derived_cl2694, plain, 156.89/20.46 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2679, '2'])). 156.89/20.46 thf(zip_derived_cl2711, plain, 156.89/20.46 (( (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2694, '3'])). 156.89/20.46 thf(zip_derived_cl2712, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2711, '4'])). 156.89/20.46 thf(zip_derived_cl2732, plain, 156.89/20.46 ((~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2712, '5'])). 156.89/20.46 thf(zip_derived_cl2751, plain, 156.89/20.46 ((~ (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2732])). 156.89/20.46 thf(zip_derived_cl2774, plain, 156.89/20.46 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2751, '2'])). 156.89/20.46 thf(zip_derived_cl2796, plain, 156.89/20.46 (( (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @ 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2774, '3'])). 156.89/20.46 thf(zip_derived_cl2797, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @ 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2796, '4'])). 156.89/20.46 thf(zip_derived_cl2821, plain, 156.89/20.46 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') | 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5'))) 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2797, '5'])). 156.89/20.46 thf(zip_derived_cl2845, plain, 156.89/20.46 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2821])). 156.89/20.46 thf(zip_derived_cl2873, plain, 156.89/20.46 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2845, '2'])). 156.89/20.46 thf(zip_derived_cl2897, plain, 156.89/20.46 (( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.46 (op @ e2 @ e2) @ e1 @ Y0)))))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2873, '7'])). 156.89/20.46 thf(zip_derived_cl274, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.46 Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl270, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl2926, plain, 156.89/20.46 (( ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('renaming', [status(thm)], 156.89/20.46 [zip_derived_cl2897, zip_derived_cl274, zip_derived_cl270])). 156.89/20.46 thf(zip_derived_cl2953, plain, 156.89/20.46 (( (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2926])). 156.89/20.46 thf(zip_derived_cl2985, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2953, '4'])). 156.89/20.46 thf(zip_derived_cl3012, plain, 156.89/20.46 ((~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2985, '5'])). 156.89/20.46 thf(zip_derived_cl2721, plain, 156.89/20.46 (( ('#form6') 156.89/20.46 | ~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl3040, plain, 156.89/20.46 ((~ ('#form6') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))), 156.89/20.46 inference('renaming', [status(thm)], 156.89/20.46 [zip_derived_cl3012, zip_derived_cl2721])). 156.89/20.46 thf(zip_derived_cl3068, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ~ ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl3040, '4'])). 156.89/20.46 thf(zip_derived_cl3101, plain, 156.89/20.46 ((~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ~ ('#form6') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl3068, '5'])). 156.89/20.46 thf(zip_derived_cl3130, plain, 156.89/20.46 ((~ (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ~ ('#form6'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3101])). 156.89/20.46 thf(zip_derived_cl3156, plain, 156.89/20.46 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ~ ('#form6') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl3130, '2'])). 156.89/20.46 thf(zip_derived_cl3186, plain, 156.89/20.46 (( (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ~ ('#form6') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl3156, '3'])). 156.89/20.46 thf(zip_derived_cl3187, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ~ ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl3186, '4'])). 156.89/20.46 thf(zip_derived_cl3216, plain, 156.89/20.46 ((~ (((mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.46 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ~ ('#form6') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl3187, '5'])). 156.89/20.46 thf(zip_derived_cl3240, plain, 156.89/20.46 ((~ (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ~ ('#form6'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3216])). 156.89/20.46 thf(zip_derived_cl3256, plain, 156.89/20.46 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.46 | ~ ('#form6') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl3240, '2'])). 156.89/20.46 thf(zip_derived_cl3275, plain, 156.89/20.46 (( (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ~ ('#form6') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl3256, '3'])). 156.89/20.46 thf(zip_derived_cl3276, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ~ ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl3275, '4'])). 156.89/20.46 thf(zip_derived_cl3292, plain, 156.89/20.46 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.46 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.46 | ~ ('#form6') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl3276, '5'])). 156.89/20.46 thf(zip_derived_cl3307, plain, 156.89/20.46 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ~ ('#form6'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3292])). 156.89/20.46 thf(zip_derived_cl3315, plain, 156.89/20.46 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 156.89/20.46 | ~ ('#form6') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl3307, '2'])). 156.89/20.46 thf(zip_derived_cl3323, plain, 156.89/20.46 (( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.46 (op @ e2 @ e2) @ e2 @ Y0)))))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ~ ('#form6'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl3315, '7'])). 156.89/20.46 thf(zip_derived_cl274, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.46 Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl270, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl3331, plain, 156.89/20.46 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ~ ('#form6') 156.89/20.46 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.46 inference('renaming', [status(thm)], 156.89/20.46 [zip_derived_cl3323, zip_derived_cl274, zip_derived_cl270])). 156.89/20.46 thf(zip_derived_cl2554, plain, 156.89/20.46 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2546])). 156.89/20.46 thf(zip_derived_cl2562, plain, 156.89/20.46 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0) @ '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2554, '2'])). 156.89/20.46 thf(zip_derived_cl2570, plain, 156.89/20.46 (( (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.46 (op @ e1 @ e1) @ e0 @ Y0)))))) 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2562, '7'])). 156.89/20.46 thf(zip_derived_cl274, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.46 Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl270, plain, 156.89/20.46 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.46 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.46 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.46 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.46 X0 @ Y0)))))))), 156.89/20.46 define([status(thm)])). 156.89/20.46 thf(zip_derived_cl2579, plain, 156.89/20.46 (( ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.46 | (((mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))))), 156.89/20.46 inference('renaming', [status(thm)], 156.89/20.46 [zip_derived_cl2570, zip_derived_cl274, zip_derived_cl270])). 156.89/20.46 thf(zip_derived_cl2587, plain, 156.89/20.46 (( (mor @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5') 156.89/20.46 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2579])). 156.89/20.46 thf(zip_derived_cl2598, plain, 156.89/20.46 (( (((mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.46 '#sk5') | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))), 156.89/20.46 inference('rw_clause', [status(thm)], [zip_derived_cl2587, '6'])). 156.89/20.46 thf(zip_derived_cl2607, plain, 156.89/20.46 (( (((mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.46 '#sk5') | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.46 '#sk5'))) 156.89/20.46 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.46 | (mnot @ 156.89/20.46 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.46 '#sk5'))), 156.89/20.46 inference('rw', [status(thm)], [zip_derived_cl2598, '3', '3'])). 156.89/20.46 thf(zip_derived_cl2608, plain, 156.89/20.46 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.46 (mnot @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.46 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.46 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.46 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2607, '4'])). 156.89/20.47 thf(zip_derived_cl2618, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2608, '5'])). 156.89/20.47 thf(zip_derived_cl2628, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2618])). 156.89/20.47 thf(zip_derived_cl2639, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2628, '2'])). 156.89/20.47 thf(zip_derived_cl2653, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2639, '3'])). 156.89/20.47 thf(zip_derived_cl2654, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2653, '4'])). 156.89/20.47 thf(zip_derived_cl2666, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2654, '5'])). 156.89/20.47 thf(zip_derived_cl2681, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2666])). 156.89/20.47 thf(zip_derived_cl2696, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2681, '2'])). 156.89/20.47 thf(zip_derived_cl2714, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2696, '3'])). 156.89/20.47 thf(zip_derived_cl2715, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2714, '4'])). 156.89/20.47 thf(zip_derived_cl2734, plain, 156.89/20.47 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') | 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5'))) 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2715, '5'])). 156.89/20.47 thf(zip_derived_cl2755, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2734])). 156.89/20.47 thf(zip_derived_cl2778, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2755, '2'])). 156.89/20.47 thf(zip_derived_cl2801, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e2 @ e2) @ e1 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2778, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2825, plain, 156.89/20.47 (( ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2801, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2849, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2825])). 156.89/20.47 thf(zip_derived_cl2877, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2849, '4'])). 156.89/20.47 thf(zip_derived_cl2902, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2877, '5'])). 156.89/20.47 thf(zip_derived_cl2721, plain, 156.89/20.47 (( ('#form6') 156.89/20.47 | ~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2931, plain, 156.89/20.47 ((~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2902, zip_derived_cl2721])). 156.89/20.47 thf(zip_derived_cl2959, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2931, '4'])). 156.89/20.47 thf(zip_derived_cl2990, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2959, '5'])). 156.89/20.47 thf(zip_derived_cl3019, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2990])). 156.89/20.47 thf(zip_derived_cl3047, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3019, '2'])). 156.89/20.47 thf(zip_derived_cl3078, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl3047, '3'])). 156.89/20.47 thf(zip_derived_cl3079, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3078, '4'])). 156.89/20.47 thf(zip_derived_cl3108, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3079, '5'])). 156.89/20.47 thf(zip_derived_cl3138, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3108])). 156.89/20.47 thf(zip_derived_cl3164, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3138, '2'])). 156.89/20.47 thf(zip_derived_cl3197, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl3164, '3'])). 156.89/20.47 thf(zip_derived_cl3198, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3197, '4'])). 156.89/20.47 thf(zip_derived_cl3224, plain, 156.89/20.47 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3198, '5'])). 156.89/20.47 thf(zip_derived_cl3247, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3224])). 156.89/20.47 thf(zip_derived_cl3263, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3247, '2'])). 156.89/20.47 thf(zip_derived_cl3283, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e2 @ e2) @ e2 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3263, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl3299, plain, 156.89/20.47 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl3283, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2588, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2580])). 156.89/20.47 thf(zip_derived_cl2599, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2588, '2'])). 156.89/20.47 thf(zip_derived_cl2609, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2599, '3'])). 156.89/20.47 thf(zip_derived_cl2610, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2609, '4'])). 156.89/20.47 thf(zip_derived_cl2619, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2610, '5'])). 156.89/20.47 thf(zip_derived_cl2630, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2619])). 156.89/20.47 thf(zip_derived_cl2641, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2630, '2'])). 156.89/20.47 thf(zip_derived_cl2656, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2641, '3'])). 156.89/20.47 thf(zip_derived_cl2657, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2656, '4'])). 156.89/20.47 thf(zip_derived_cl2668, plain, 156.89/20.47 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') | 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5'))) 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2657, '5'])). 156.89/20.47 thf(zip_derived_cl2685, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2668])). 156.89/20.47 thf(zip_derived_cl2700, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2685, '2'])). 156.89/20.47 thf(zip_derived_cl2719, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e2 @ e2) @ e1 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2700, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2738, plain, 156.89/20.47 (( ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2719, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2759, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2738])). 156.89/20.47 thf(zip_derived_cl2782, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2759, '4'])). 156.89/20.47 thf(zip_derived_cl2806, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2782, '5'])). 156.89/20.47 thf(zip_derived_cl2721, plain, 156.89/20.47 (( ('#form6') 156.89/20.47 | ~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2830, plain, 156.89/20.47 ((~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2806, zip_derived_cl2721])). 156.89/20.47 thf(zip_derived_cl2855, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2830, '4'])). 156.89/20.47 thf(zip_derived_cl2882, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2855, '5'])). 156.89/20.47 thf(zip_derived_cl2909, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2882])). 156.89/20.47 thf(zip_derived_cl2938, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2909, '2'])). 156.89/20.47 thf(zip_derived_cl2969, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2938, '3'])). 156.89/20.47 thf(zip_derived_cl2970, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2969, '4'])). 156.89/20.47 thf(zip_derived_cl2997, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2970, '5'])). 156.89/20.47 thf(zip_derived_cl3027, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2997])). 156.89/20.47 thf(zip_derived_cl3055, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3027, '2'])). 156.89/20.47 thf(zip_derived_cl3089, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl3055, '3'])). 156.89/20.47 thf(zip_derived_cl3090, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3089, '4'])). 156.89/20.47 thf(zip_derived_cl3116, plain, 156.89/20.47 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3090, '5'])). 156.89/20.47 thf(zip_derived_cl3145, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3116])). 156.89/20.47 thf(zip_derived_cl3171, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3145, '2'])). 156.89/20.47 thf(zip_derived_cl3205, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e2 @ e2) @ e2 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3171, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl3231, plain, 156.89/20.47 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl3205, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2585, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ '#sk5') 156.89/20.47 | (((mor @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2578])). 156.89/20.47 thf(zip_derived_cl2596, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0) @ '#sk5') 156.89/20.47 | (((mor @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2585, '2'])). 156.89/20.47 thf(zip_derived_cl2605, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e3 @ e3) @ e0 @ Y0)))))) 156.89/20.47 | (((mor @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2596, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2616, plain, 156.89/20.47 (( ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (((mor @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2605, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2626, plain, 156.89/20.47 (( (mor @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2616])). 156.89/20.47 thf(zip_derived_cl2637, plain, 156.89/20.47 (( (((mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mand @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2626, '6'])). 156.89/20.47 thf(zip_derived_cl2649, plain, 156.89/20.47 (( (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2637, '3', '3'])). 156.89/20.47 thf(zip_derived_cl2650, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2649, '4'])). 156.89/20.47 thf(zip_derived_cl2664, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2650, '5'])). 156.89/20.47 thf(zip_derived_cl2677, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2664])). 156.89/20.47 thf(zip_derived_cl2692, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2677, '2'])). 156.89/20.47 thf(zip_derived_cl2708, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2692, '3'])). 156.89/20.47 thf(zip_derived_cl2709, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2708, '4'])). 156.89/20.47 thf(zip_derived_cl2730, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2709, '5'])). 156.89/20.47 thf(zip_derived_cl2748, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2730])). 156.89/20.47 thf(zip_derived_cl2771, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2748, '2'])). 156.89/20.47 thf(zip_derived_cl2792, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2771, '3'])). 156.89/20.47 thf(zip_derived_cl2793, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2792, '4'])). 156.89/20.47 thf(zip_derived_cl2818, plain, 156.89/20.47 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') | 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5'))) 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2793, '5'])). 156.89/20.47 thf(zip_derived_cl2841, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2818])). 156.89/20.47 thf(zip_derived_cl2869, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2841, '2'])). 156.89/20.47 thf(zip_derived_cl2892, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e2 @ e2) @ e1 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2869, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2921, plain, 156.89/20.47 (( ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2892, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2947, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2921])). 156.89/20.47 thf(zip_derived_cl2980, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2947, '4'])). 156.89/20.47 thf(zip_derived_cl3006, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2980, '5'])). 156.89/20.47 thf(zip_derived_cl2721, plain, 156.89/20.47 (( ('#form6') 156.89/20.47 | ~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl3034, plain, 156.89/20.47 ((~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl3006, zip_derived_cl2721])). 156.89/20.47 thf(zip_derived_cl3060, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3034, '4'])). 156.89/20.47 thf(zip_derived_cl3095, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3060, '5'])). 156.89/20.47 thf(zip_derived_cl3122, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3095])). 156.89/20.47 thf(zip_derived_cl3148, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3122, '2'])). 156.89/20.47 thf(zip_derived_cl3175, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl3148, '3'])). 156.89/20.47 thf(zip_derived_cl3176, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3175, '4'])). 156.89/20.47 thf(zip_derived_cl3208, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3176, '5'])). 156.89/20.47 thf(zip_derived_cl3234, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3208])). 156.89/20.47 thf(zip_derived_cl3250, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3234, '2'])). 156.89/20.47 thf(zip_derived_cl3267, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl3250, '3'])). 156.89/20.47 thf(zip_derived_cl3268, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3267, '4'])). 156.89/20.47 thf(zip_derived_cl3286, plain, 156.89/20.47 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3268, '5'])). 156.89/20.47 thf(zip_derived_cl3303, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3286])). 156.89/20.47 thf(zip_derived_cl3311, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3303, '2'])). 156.89/20.47 thf(zip_derived_cl3319, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e2 @ e2) @ e2 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3311, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl3327, plain, 156.89/20.47 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl3319, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2752, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2732])). 156.89/20.47 thf(zip_derived_cl2775, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2752, '2'])). 156.89/20.47 thf(zip_derived_cl2798, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e1 @ e1) @ e1 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2775, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2822, plain, 156.89/20.47 (( ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2798, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2846, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2822])). 156.89/20.47 thf(zip_derived_cl2874, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2846, '4'])). 156.89/20.47 thf(zip_derived_cl2898, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2874, '5'])). 156.89/20.47 thf(zip_derived_cl2721, plain, 156.89/20.47 (( ('#form6') 156.89/20.47 | ~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2927, plain, 156.89/20.47 ((~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2898, zip_derived_cl2721])). 156.89/20.47 thf(zip_derived_cl2954, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2927, '4'])). 156.89/20.47 thf(zip_derived_cl2986, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2954, '5'])). 156.89/20.47 thf(zip_derived_cl3013, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2986])). 156.89/20.47 thf(zip_derived_cl3041, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3013, '2'])). 156.89/20.47 thf(zip_derived_cl3069, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl3041, '3'])). 156.89/20.47 thf(zip_derived_cl3070, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3069, '4'])). 156.89/20.47 thf(zip_derived_cl3102, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3070, '5'])). 156.89/20.47 thf(zip_derived_cl3132, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3102])). 156.89/20.47 thf(zip_derived_cl3158, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3132, '2'])). 156.89/20.47 thf(zip_derived_cl3189, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl3158, '3'])). 156.89/20.47 thf(zip_derived_cl3190, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3189, '4'])). 156.89/20.47 thf(zip_derived_cl3218, plain, 156.89/20.47 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3190, '5'])). 156.89/20.47 thf(zip_derived_cl3243, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3218])). 156.89/20.47 thf(zip_derived_cl3259, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3243, '2'])). 156.89/20.47 thf(zip_derived_cl3279, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e2 @ e2) @ e2 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3259, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl3295, plain, 156.89/20.47 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl3279, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2682, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2666])). 156.89/20.47 thf(zip_derived_cl2697, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2682, '2'])). 156.89/20.47 thf(zip_derived_cl2716, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e1 @ e1) @ e1 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2697, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2735, plain, 156.89/20.47 (( ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2716, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2756, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2735])). 156.89/20.47 thf(zip_derived_cl2779, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2756, '4'])). 156.89/20.47 thf(zip_derived_cl2802, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2779, '5'])). 156.89/20.47 thf(zip_derived_cl2721, plain, 156.89/20.47 (( ('#form6') 156.89/20.47 | ~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2826, plain, 156.89/20.47 ((~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2802, zip_derived_cl2721])). 156.89/20.47 thf(zip_derived_cl2850, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2826, '4'])). 156.89/20.47 thf(zip_derived_cl2878, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2850, '5'])). 156.89/20.47 thf(zip_derived_cl2903, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2878])). 156.89/20.47 thf(zip_derived_cl2932, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2903, '2'])). 156.89/20.47 thf(zip_derived_cl2960, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2932, '3'])). 156.89/20.47 thf(zip_derived_cl2961, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2960, '4'])). 156.89/20.47 thf(zip_derived_cl2991, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2961, '5'])). 156.89/20.47 thf(zip_derived_cl3021, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2991])). 156.89/20.47 thf(zip_derived_cl3049, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3021, '2'])). 156.89/20.47 thf(zip_derived_cl3081, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl3049, '3'])). 156.89/20.47 thf(zip_derived_cl3082, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3081, '4'])). 156.89/20.47 thf(zip_derived_cl3110, plain, 156.89/20.47 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3082, '5'])). 156.89/20.47 thf(zip_derived_cl3141, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3110])). 156.89/20.47 thf(zip_derived_cl3167, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3141, '2'])). 156.89/20.47 thf(zip_derived_cl3201, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e2 @ e2) @ e2 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3167, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl3227, plain, 156.89/20.47 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl3201, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2631, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2619])). 156.89/20.47 thf(zip_derived_cl2642, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2631, '2'])). 156.89/20.47 thf(zip_derived_cl2658, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e1 @ e1) @ e1 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2642, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2669, plain, 156.89/20.47 (( ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2658, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2686, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2669])). 156.89/20.47 thf(zip_derived_cl2701, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2686, '4'])). 156.89/20.47 thf(zip_derived_cl2720, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2701, '5'])). 156.89/20.47 thf(zip_derived_cl2721, plain, 156.89/20.47 (( ('#form6') 156.89/20.47 | ~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2739, plain, 156.89/20.47 ((~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2720, zip_derived_cl2721])). 156.89/20.47 thf(zip_derived_cl2760, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2739, '4'])). 156.89/20.47 thf(zip_derived_cl2783, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2760, '5'])). 156.89/20.47 thf(zip_derived_cl2807, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2783])). 156.89/20.47 thf(zip_derived_cl2831, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2807, '2'])). 156.89/20.47 thf(zip_derived_cl2856, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2831, '3'])). 156.89/20.47 thf(zip_derived_cl2857, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2856, '4'])). 156.89/20.47 thf(zip_derived_cl2883, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2857, '5'])). 156.89/20.47 thf(zip_derived_cl2911, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2883])). 156.89/20.47 thf(zip_derived_cl2940, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2911, '2'])). 156.89/20.47 thf(zip_derived_cl2972, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2940, '3'])). 156.89/20.47 thf(zip_derived_cl2973, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2972, '4'])). 156.89/20.47 thf(zip_derived_cl2999, plain, 156.89/20.47 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2973, '5'])). 156.89/20.47 thf(zip_derived_cl3030, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2999])). 156.89/20.47 thf(zip_derived_cl3058, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3030, '2'])). 156.89/20.47 thf(zip_derived_cl3093, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e2 @ e2) @ e2 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3058, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl3119, plain, 156.89/20.47 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl3093, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2749, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2730])). 156.89/20.47 thf(zip_derived_cl2772, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2749, '2'])). 156.89/20.47 thf(zip_derived_cl2794, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e1 @ e1) @ e1 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2772, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2819, plain, 156.89/20.47 (( ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2794, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2842, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2819])). 156.89/20.47 thf(zip_derived_cl2870, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2842, '4'])). 156.89/20.47 thf(zip_derived_cl2893, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2870, '5'])). 156.89/20.47 thf(zip_derived_cl2721, plain, 156.89/20.47 (( ('#form6') 156.89/20.47 | ~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2922, plain, 156.89/20.47 ((~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2893, zip_derived_cl2721])). 156.89/20.47 thf(zip_derived_cl2948, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2922, '4'])). 156.89/20.47 thf(zip_derived_cl2981, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2948, '5'])). 156.89/20.47 thf(zip_derived_cl3007, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2981])). 156.89/20.47 thf(zip_derived_cl3035, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3007, '2'])). 156.89/20.47 thf(zip_derived_cl3061, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl3035, '3'])). 156.89/20.47 thf(zip_derived_cl3062, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3061, '4'])). 156.89/20.47 thf(zip_derived_cl3096, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3062, '5'])). 156.89/20.47 thf(zip_derived_cl3124, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3096])). 156.89/20.47 thf(zip_derived_cl3150, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3124, '2'])). 156.89/20.47 thf(zip_derived_cl3178, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl3150, '3'])). 156.89/20.47 thf(zip_derived_cl3179, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3178, '4'])). 156.89/20.47 thf(zip_derived_cl3210, plain, 156.89/20.47 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3179, '5'])). 156.89/20.47 thf(zip_derived_cl3237, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3210])). 156.89/20.47 thf(zip_derived_cl3253, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3237, '2'])). 156.89/20.47 thf(zip_derived_cl3271, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e2 @ e2) @ e2 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3253, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl3289, plain, 156.89/20.47 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl3271, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2680, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2665])). 156.89/20.47 thf(zip_derived_cl2695, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2680, '2'])). 156.89/20.47 thf(zip_derived_cl2713, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e0 @ e0) @ e1 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2695, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2733, plain, 156.89/20.47 (( ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2713, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2753, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2733])). 156.89/20.47 thf(zip_derived_cl2776, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2753, '4'])). 156.89/20.47 thf(zip_derived_cl2799, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2776, '5'])). 156.89/20.47 thf(zip_derived_cl2721, plain, 156.89/20.47 (( ('#form6') 156.89/20.47 | ~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2823, plain, 156.89/20.47 ((~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2799, zip_derived_cl2721])). 156.89/20.47 thf(zip_derived_cl2847, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2823, '4'])). 156.89/20.47 thf(zip_derived_cl2875, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2847, '5'])). 156.89/20.47 thf(zip_derived_cl2899, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2875])). 156.89/20.47 thf(zip_derived_cl2928, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2899, '2'])). 156.89/20.47 thf(zip_derived_cl2955, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2928, '3'])). 156.89/20.47 thf(zip_derived_cl2956, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2955, '4'])). 156.89/20.47 thf(zip_derived_cl2987, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2956, '5'])). 156.89/20.47 thf(zip_derived_cl3015, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2987])). 156.89/20.47 thf(zip_derived_cl3043, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3015, '2'])). 156.89/20.47 thf(zip_derived_cl3072, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl3043, '3'])). 156.89/20.47 thf(zip_derived_cl3073, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3072, '4'])). 156.89/20.47 thf(zip_derived_cl3104, plain, 156.89/20.47 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3073, '5'])). 156.89/20.47 thf(zip_derived_cl3135, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3104])). 156.89/20.47 thf(zip_derived_cl3161, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3135, '2'])). 156.89/20.47 thf(zip_derived_cl3193, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e2 @ e2) @ e2 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3161, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl3221, plain, 156.89/20.47 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl3193, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2629, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2618])). 156.89/20.47 thf(zip_derived_cl2640, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2629, '2'])). 156.89/20.47 thf(zip_derived_cl2655, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e0 @ e0) @ e1 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2640, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2667, plain, 156.89/20.47 (( ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2655, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2683, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2667])). 156.89/20.47 thf(zip_derived_cl2698, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2683, '4'])). 156.89/20.47 thf(zip_derived_cl2717, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2698, '5'])). 156.89/20.47 thf(zip_derived_cl2721, plain, 156.89/20.47 (( ('#form6') 156.89/20.47 | ~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2736, plain, 156.89/20.47 ((~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2717, zip_derived_cl2721])). 156.89/20.47 thf(zip_derived_cl2757, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2736, '4'])). 156.89/20.47 thf(zip_derived_cl2780, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2757, '5'])). 156.89/20.47 thf(zip_derived_cl2803, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2780])). 156.89/20.47 thf(zip_derived_cl2827, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2803, '2'])). 156.89/20.47 thf(zip_derived_cl2851, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2827, '3'])). 156.89/20.47 thf(zip_derived_cl2852, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2851, '4'])). 156.89/20.47 thf(zip_derived_cl2879, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2852, '5'])). 156.89/20.47 thf(zip_derived_cl2905, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2879])). 156.89/20.47 thf(zip_derived_cl2934, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2905, '2'])). 156.89/20.47 thf(zip_derived_cl2963, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2934, '3'])). 156.89/20.47 thf(zip_derived_cl2964, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2963, '4'])). 156.89/20.47 thf(zip_derived_cl2993, plain, 156.89/20.47 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2964, '5'])). 156.89/20.47 thf(zip_derived_cl3024, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2993])). 156.89/20.47 thf(zip_derived_cl3052, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3024, '2'])). 156.89/20.47 thf(zip_derived_cl3085, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e2 @ e2) @ e2 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl3052, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl3113, plain, 156.89/20.47 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl3085, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2702, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2687])). 156.89/20.47 thf(zip_derived_cl2721, plain, 156.89/20.47 (( ('#form6') 156.89/20.47 | ~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2724, plain, 156.89/20.47 ((~ ('#form6') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2702, zip_derived_cl2721])). 156.89/20.47 thf(zip_derived_cl2740, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2724, '2'])). 156.89/20.47 thf(zip_derived_cl2761, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2740, '3'])). 156.89/20.47 thf(zip_derived_cl2762, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2761, '4'])). 156.89/20.47 thf(zip_derived_cl2784, plain, 156.89/20.47 ((~ (((mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2762, '5'])). 156.89/20.47 thf(zip_derived_cl2809, plain, 156.89/20.47 ((~ (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2784])). 156.89/20.47 thf(zip_derived_cl2833, plain, 156.89/20.47 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2809, '2'])). 156.89/20.47 thf(zip_derived_cl2859, plain, 156.89/20.47 (( (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.47 '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw', [status(thm)], [zip_derived_cl2833, '3'])). 156.89/20.47 thf(zip_derived_cl2860, plain, 156.89/20.47 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2859, '4'])). 156.89/20.47 thf(zip_derived_cl2885, plain, 156.89/20.47 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.47 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2860, '5'])). 156.89/20.47 thf(zip_derived_cl2914, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2885])). 156.89/20.47 thf(zip_derived_cl2943, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2914, '2'])). 156.89/20.47 thf(zip_derived_cl2976, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e2 @ e2) @ e2 @ Y0)))))) 156.89/20.47 | ~ ('#form6') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2943, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl3002, plain, 156.89/20.47 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.47 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | ~ ('#form6'))), 156.89/20.47 inference('renaming', [status(thm)], 156.89/20.47 [zip_derived_cl2976, zip_derived_cl274, zip_derived_cl270])). 156.89/20.47 thf(zip_derived_cl2678, plain, 156.89/20.47 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ '#sk5') 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2664])). 156.89/20.47 thf(zip_derived_cl2693, plain, 156.89/20.47 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2678, '2'])). 156.89/20.47 thf(zip_derived_cl2710, plain, 156.89/20.47 (( (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.47 (op @ e0 @ e0) @ e1 @ Y0)))))) 156.89/20.47 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.47 '#sk5'))))), 156.89/20.47 inference('rw_clause', [status(thm)], [zip_derived_cl2693, '7'])). 156.89/20.47 thf(zip_derived_cl274, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.47 Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl270, plain, 156.89/20.47 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.47 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.47 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.47 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.47 X0 @ Y0)))))))), 156.89/20.47 define([status(thm)])). 156.89/20.47 thf(zip_derived_cl2731, plain, 156.89/20.47 (( ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.47 | (((mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.47 (mnot @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.47 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.47 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.47 '#sk5') | (mnot @ 156.89/20.47 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.47 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2710, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2750, plain, 156.89/20.48 (( (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2731])). 156.89/20.48 thf(zip_derived_cl2773, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2750, '4'])). 156.89/20.48 thf(zip_derived_cl2795, plain, 156.89/20.48 ((~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2773, '5'])). 156.89/20.48 thf(zip_derived_cl2721, plain, 156.89/20.48 (( ('#form6') 156.89/20.48 | ~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.48 '#sk5'))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2820, plain, 156.89/20.48 ((~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2795, zip_derived_cl2721])). 156.89/20.48 thf(zip_derived_cl2843, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2820, '4'])). 156.89/20.48 thf(zip_derived_cl2871, plain, 156.89/20.48 ((~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2843, '5'])). 156.89/20.48 thf(zip_derived_cl2894, plain, 156.89/20.48 ((~ (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2871])). 156.89/20.48 thf(zip_derived_cl2923, plain, 156.89/20.48 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2894, '2'])). 156.89/20.48 thf(zip_derived_cl2949, plain, 156.89/20.48 (( (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw', [status(thm)], [zip_derived_cl2923, '3'])). 156.89/20.48 thf(zip_derived_cl2950, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2949, '4'])). 156.89/20.48 thf(zip_derived_cl2982, plain, 156.89/20.48 ((~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2950, '5'])). 156.89/20.48 thf(zip_derived_cl3009, plain, 156.89/20.48 ((~ (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2982])). 156.89/20.48 thf(zip_derived_cl3037, plain, 156.89/20.48 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3009, '2'])). 156.89/20.48 thf(zip_derived_cl3064, plain, 156.89/20.48 (( (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw', [status(thm)], [zip_derived_cl3037, '3'])). 156.89/20.48 thf(zip_derived_cl3065, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3064, '4'])). 156.89/20.48 thf(zip_derived_cl3098, plain, 156.89/20.48 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3065, '5'])). 156.89/20.48 thf(zip_derived_cl3127, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3098])). 156.89/20.48 thf(zip_derived_cl3153, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3127, '2'])). 156.89/20.48 thf(zip_derived_cl3182, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e2 @ e2) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3153, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3213, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3182, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl3241, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3216])). 156.89/20.48 thf(zip_derived_cl3257, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3241, '2'])). 156.89/20.48 thf(zip_derived_cl3277, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3257, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3293, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3277, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl3139, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3108])). 156.89/20.48 thf(zip_derived_cl3165, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3139, '2'])). 156.89/20.48 thf(zip_derived_cl3199, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3165, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3225, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3199, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl3028, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2997])). 156.89/20.48 thf(zip_derived_cl3056, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3028, '2'])). 156.89/20.48 thf(zip_derived_cl3091, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3056, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3117, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3091, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl3235, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3208])). 156.89/20.48 thf(zip_derived_cl3251, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3235, '2'])). 156.89/20.48 thf(zip_derived_cl3269, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3251, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3287, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3269, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl3133, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3102])). 156.89/20.48 thf(zip_derived_cl3159, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3133, '2'])). 156.89/20.48 thf(zip_derived_cl3191, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3159, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3219, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3191, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl3022, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2991])). 156.89/20.48 thf(zip_derived_cl3050, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3022, '2'])). 156.89/20.48 thf(zip_derived_cl3083, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3050, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3111, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3083, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2912, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2883])). 156.89/20.48 thf(zip_derived_cl2941, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2912, '2'])). 156.89/20.48 thf(zip_derived_cl2974, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2941, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3000, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2974, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl3125, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3096])). 156.89/20.48 thf(zip_derived_cl3151, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3125, '2'])). 156.89/20.48 thf(zip_derived_cl3180, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3151, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3211, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3180, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl3016, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2987])). 156.89/20.48 thf(zip_derived_cl3044, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3016, '2'])). 156.89/20.48 thf(zip_derived_cl3074, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3044, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3105, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3074, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2906, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2879])). 156.89/20.48 thf(zip_derived_cl2935, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2906, '2'])). 156.89/20.48 thf(zip_derived_cl2965, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2935, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2994, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2965, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2810, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2784])). 156.89/20.48 thf(zip_derived_cl2834, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2810, '2'])). 156.89/20.48 thf(zip_derived_cl2861, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2834, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2886, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2861, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl3010, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2982])). 156.89/20.48 thf(zip_derived_cl3038, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3010, '2'])). 156.89/20.48 thf(zip_derived_cl3066, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3038, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3099, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3066, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl3131, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3101])). 156.89/20.48 thf(zip_derived_cl3157, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3131, '2'])). 156.89/20.48 thf(zip_derived_cl3188, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3157, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3217, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3188, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl3020, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2990])). 156.89/20.48 thf(zip_derived_cl3048, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3020, '2'])). 156.89/20.48 thf(zip_derived_cl3080, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3048, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3109, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3080, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2910, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2882])). 156.89/20.48 thf(zip_derived_cl2939, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2910, '2'])). 156.89/20.48 thf(zip_derived_cl2971, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2939, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2998, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2971, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl3123, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3095])). 156.89/20.48 thf(zip_derived_cl3149, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3123, '2'])). 156.89/20.48 thf(zip_derived_cl3177, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3149, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3209, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3177, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl3014, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2986])). 156.89/20.48 thf(zip_derived_cl3042, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3014, '2'])). 156.89/20.48 thf(zip_derived_cl3071, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3042, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3103, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3071, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2904, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2878])). 156.89/20.48 thf(zip_derived_cl2933, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2904, '2'])). 156.89/20.48 thf(zip_derived_cl2962, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2933, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2992, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2962, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2808, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2783])). 156.89/20.48 thf(zip_derived_cl2832, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2808, '2'])). 156.89/20.48 thf(zip_derived_cl2858, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2832, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2884, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2858, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl3008, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2981])). 156.89/20.48 thf(zip_derived_cl3036, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3008, '2'])). 156.89/20.48 thf(zip_derived_cl3063, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3036, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3097, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3063, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2900, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2875])). 156.89/20.48 thf(zip_derived_cl2929, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2900, '2'])). 156.89/20.48 thf(zip_derived_cl2957, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2929, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2988, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2957, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2804, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2780])). 156.89/20.48 thf(zip_derived_cl2828, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2804, '2'])). 156.89/20.48 thf(zip_derived_cl2853, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2828, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2880, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2853, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2703, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.48 '#sk5'))))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2687])). 156.89/20.48 thf(zip_derived_cl2721, plain, 156.89/20.48 (( ('#form6') 156.89/20.48 | ~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.48 '#sk5'))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2725, plain, 156.89/20.48 ((~ ('#form6') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2703, zip_derived_cl2721])). 156.89/20.48 thf(zip_derived_cl2743, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2725, '2'])). 156.89/20.48 thf(zip_derived_cl2766, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2743, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2787, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2766, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2895, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2871])). 156.89/20.48 thf(zip_derived_cl2924, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2895, '2'])). 156.89/20.48 thf(zip_derived_cl2951, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2924, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2983, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2951, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2844, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2821])). 156.89/20.48 thf(zip_derived_cl2872, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2844, '2'])). 156.89/20.48 thf(zip_derived_cl2896, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e3 @ e3) @ e1 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2872, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2925, plain, 156.89/20.48 (( ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2896, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2952, plain, 156.89/20.48 (( (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2925])). 156.89/20.48 thf(zip_derived_cl2984, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2952, '4'])). 156.89/20.48 thf(zip_derived_cl3011, plain, 156.89/20.48 ((~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2984, '5'])). 156.89/20.48 thf(zip_derived_cl2721, plain, 156.89/20.48 (( ('#form6') 156.89/20.48 | ~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.48 '#sk5'))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3039, plain, 156.89/20.48 ((~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3011, zip_derived_cl2721])). 156.89/20.48 thf(zip_derived_cl3067, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3039, '4'])). 156.89/20.48 thf(zip_derived_cl3100, plain, 156.89/20.48 ((~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3067, '5'])). 156.89/20.48 thf(zip_derived_cl3128, plain, 156.89/20.48 ((~ (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3100])). 156.89/20.48 thf(zip_derived_cl3154, plain, 156.89/20.48 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3128, '2'])). 156.89/20.48 thf(zip_derived_cl3183, plain, 156.89/20.48 (( (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('rw', [status(thm)], [zip_derived_cl3154, '3'])). 156.89/20.48 thf(zip_derived_cl3184, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3183, '4'])). 156.89/20.48 thf(zip_derived_cl3214, plain, 156.89/20.48 ((~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3184, '5'])). 156.89/20.48 thf(zip_derived_cl3238, plain, 156.89/20.48 ((~ (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3214])). 156.89/20.48 thf(zip_derived_cl3254, plain, 156.89/20.48 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3238, '2'])). 156.89/20.48 thf(zip_derived_cl3272, plain, 156.89/20.48 (( (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('rw', [status(thm)], [zip_derived_cl3254, '3'])). 156.89/20.48 thf(zip_derived_cl3273, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3272, '4'])). 156.89/20.48 thf(zip_derived_cl3290, plain, 156.89/20.48 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3273, '5'])). 156.89/20.48 thf(zip_derived_cl3305, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3290])). 156.89/20.48 thf(zip_derived_cl3313, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3305, '2'])). 156.89/20.48 thf(zip_derived_cl3321, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e2 @ e2) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3313, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3329, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3321, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2754, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2734])). 156.89/20.48 thf(zip_derived_cl2777, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2754, '2'])). 156.89/20.48 thf(zip_derived_cl2800, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e3 @ e3) @ e1 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2777, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2824, plain, 156.89/20.48 (( ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2800, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2848, plain, 156.89/20.48 (( (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2824])). 156.89/20.48 thf(zip_derived_cl2876, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2848, '4'])). 156.89/20.48 thf(zip_derived_cl2901, plain, 156.89/20.48 ((~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2876, '5'])). 156.89/20.48 thf(zip_derived_cl2721, plain, 156.89/20.48 (( ('#form6') 156.89/20.48 | ~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.48 '#sk5'))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2930, plain, 156.89/20.48 ((~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2901, zip_derived_cl2721])). 156.89/20.48 thf(zip_derived_cl2958, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2930, '4'])). 156.89/20.48 thf(zip_derived_cl2989, plain, 156.89/20.48 ((~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2958, '5'])). 156.89/20.48 thf(zip_derived_cl3017, plain, 156.89/20.48 ((~ (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2989])). 156.89/20.48 thf(zip_derived_cl3045, plain, 156.89/20.48 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3017, '2'])). 156.89/20.48 thf(zip_derived_cl3075, plain, 156.89/20.48 (( (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('rw', [status(thm)], [zip_derived_cl3045, '3'])). 156.89/20.48 thf(zip_derived_cl3076, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3075, '4'])). 156.89/20.48 thf(zip_derived_cl3106, plain, 156.89/20.48 ((~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3076, '5'])). 156.89/20.48 thf(zip_derived_cl3136, plain, 156.89/20.48 ((~ (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3106])). 156.89/20.48 thf(zip_derived_cl3162, plain, 156.89/20.48 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3136, '2'])). 156.89/20.48 thf(zip_derived_cl3194, plain, 156.89/20.48 (( (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('rw', [status(thm)], [zip_derived_cl3162, '3'])). 156.89/20.48 thf(zip_derived_cl3195, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3194, '4'])). 156.89/20.48 thf(zip_derived_cl3222, plain, 156.89/20.48 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3195, '5'])). 156.89/20.48 thf(zip_derived_cl3245, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3222])). 156.89/20.48 thf(zip_derived_cl3261, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3245, '2'])). 156.89/20.48 thf(zip_derived_cl3281, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e2 @ e2) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3261, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3297, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3281, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2684, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2668])). 156.89/20.48 thf(zip_derived_cl2699, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2684, '2'])). 156.89/20.48 thf(zip_derived_cl2718, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e3 @ e3) @ e1 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2699, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2737, plain, 156.89/20.48 (( ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2718, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2758, plain, 156.89/20.48 (( (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2737])). 156.89/20.48 thf(zip_derived_cl2781, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2758, '4'])). 156.89/20.48 thf(zip_derived_cl2805, plain, 156.89/20.48 ((~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2781, '5'])). 156.89/20.48 thf(zip_derived_cl2721, plain, 156.89/20.48 (( ('#form6') 156.89/20.48 | ~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.48 '#sk5'))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2829, plain, 156.89/20.48 ((~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2805, zip_derived_cl2721])). 156.89/20.48 thf(zip_derived_cl2854, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2829, '4'])). 156.89/20.48 thf(zip_derived_cl2881, plain, 156.89/20.48 ((~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2854, '5'])). 156.89/20.48 thf(zip_derived_cl2907, plain, 156.89/20.48 ((~ (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2881])). 156.89/20.48 thf(zip_derived_cl2936, plain, 156.89/20.48 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2907, '2'])). 156.89/20.48 thf(zip_derived_cl2966, plain, 156.89/20.48 (( (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw', [status(thm)], [zip_derived_cl2936, '3'])). 156.89/20.48 thf(zip_derived_cl2967, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2966, '4'])). 156.89/20.48 thf(zip_derived_cl2995, plain, 156.89/20.48 ((~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2967, '5'])). 156.89/20.48 thf(zip_derived_cl3025, plain, 156.89/20.48 ((~ (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2995])). 156.89/20.48 thf(zip_derived_cl3053, plain, 156.89/20.48 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3025, '2'])). 156.89/20.48 thf(zip_derived_cl3086, plain, 156.89/20.48 (( (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw', [status(thm)], [zip_derived_cl3053, '3'])). 156.89/20.48 thf(zip_derived_cl3087, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3086, '4'])). 156.89/20.48 thf(zip_derived_cl3114, plain, 156.89/20.48 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3087, '5'])). 156.89/20.48 thf(zip_derived_cl3143, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3114])). 156.89/20.48 thf(zip_derived_cl3169, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3143, '2'])). 156.89/20.48 thf(zip_derived_cl3203, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e2 @ e2) @ e2 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3169, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3229, plain, 156.89/20.48 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3203, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2840, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2818])). 156.89/20.48 thf(zip_derived_cl2868, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2840, '2'])). 156.89/20.48 thf(zip_derived_cl2891, plain, 156.89/20.48 (( (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 156.89/20.48 (op @ e3 @ e3) @ e1 @ Y0)))))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2868, '7'])). 156.89/20.48 thf(zip_derived_cl274, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 156.89/20.48 Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl270, plain, 156.89/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 156.89/20.48 ( ('#form3' @ X0 @ X1 @ X2) 156.89/20.48 | ~ (((!!) @ (^[Y0 : $i]: 156.89/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 156.89/20.48 X0 @ Y0)))))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl2920, plain, 156.89/20.48 (( ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | (((mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl2891, zip_derived_cl274, zip_derived_cl270])). 156.89/20.48 thf(zip_derived_cl2946, plain, 156.89/20.48 (( (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2920])). 156.89/20.48 thf(zip_derived_cl2979, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2946, '4'])). 156.89/20.48 thf(zip_derived_cl3005, plain, 156.89/20.48 ((~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2979, '5'])). 156.89/20.48 thf(zip_derived_cl2721, plain, 156.89/20.48 (( ('#form6') 156.89/20.48 | ~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 156.89/20.48 '#sk5'))))), 156.89/20.48 define([status(thm)])). 156.89/20.48 thf(zip_derived_cl3033, plain, 156.89/20.48 ((~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 156.89/20.48 '#sk5'))), 156.89/20.48 inference('renaming', [status(thm)], 156.89/20.48 [zip_derived_cl3005, zip_derived_cl2721])). 156.89/20.48 thf(zip_derived_cl3059, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3033, '4'])). 156.89/20.48 thf(zip_derived_cl3094, plain, 156.89/20.48 ((~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3059, '5'])). 156.89/20.48 thf(zip_derived_cl3120, plain, 156.89/20.48 ((~ (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3094])). 156.89/20.48 thf(zip_derived_cl3146, plain, 156.89/20.48 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3120, '2'])). 156.89/20.48 thf(zip_derived_cl3172, plain, 156.89/20.48 (( (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw', [status(thm)], [zip_derived_cl3146, '3'])). 156.89/20.48 thf(zip_derived_cl3173, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 156.89/20.48 (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3172, '4'])). 156.89/20.48 thf(zip_derived_cl3206, plain, 156.89/20.48 ((~ (((mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.48 '#sk5') | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 156.89/20.48 '#sk5'))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3173, '5'])). 156.89/20.48 thf(zip_derived_cl3232, plain, 156.89/20.48 ((~ (mnot @ 156.89/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3206])). 156.89/20.48 thf(zip_derived_cl3248, plain, 156.89/20.48 (( (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 156.89/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3232, '2'])). 156.89/20.48 thf(zip_derived_cl3264, plain, 156.89/20.48 (( (mnot @ 156.89/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 156.89/20.48 '#sk5') 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw', [status(thm)], [zip_derived_cl3248, '3'])). 156.89/20.48 thf(zip_derived_cl3265, plain, 156.89/20.48 ((~ (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 156.89/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3264, '4'])). 156.89/20.48 thf(zip_derived_cl3284, plain, 156.89/20.48 ((~ (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') | 156.89/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5'))) 156.89/20.48 | ~ ('#form6') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 156.89/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3265, '5'])). 156.89/20.48 thf(zip_derived_cl3301, plain, 156.89/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ '#sk5') 156.89/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 156.89/20.48 | ~ ('#form6'))), 156.89/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3284])). 156.89/20.48 thf(zip_derived_cl3309, plain, 156.89/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3301, '2'])). 157.06/20.48 thf(zip_derived_cl3317, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e2 @ e2) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3309, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3325, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3317, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3239, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3214])). 157.06/20.48 thf(zip_derived_cl3255, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3239, '2'])). 157.06/20.48 thf(zip_derived_cl3274, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3255, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3291, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3274, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3137, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3106])). 157.06/20.48 thf(zip_derived_cl3163, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3137, '2'])). 157.06/20.48 thf(zip_derived_cl3196, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3163, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3223, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3196, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3026, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2995])). 157.06/20.48 thf(zip_derived_cl3054, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3026, '2'])). 157.06/20.48 thf(zip_derived_cl3088, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3054, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3115, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3088, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3233, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3206])). 157.06/20.48 thf(zip_derived_cl3249, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3233, '2'])). 157.06/20.48 thf(zip_derived_cl3266, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e1 @ e1) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3249, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3285, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3266, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3129, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3100])). 157.06/20.48 thf(zip_derived_cl3155, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3129, '2'])). 157.06/20.48 thf(zip_derived_cl3185, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3155, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3215, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3185, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3018, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2989])). 157.06/20.48 thf(zip_derived_cl3046, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3018, '2'])). 157.06/20.48 thf(zip_derived_cl3077, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3046, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3107, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3077, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl2908, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2881])). 157.06/20.48 thf(zip_derived_cl2937, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2908, '2'])). 157.06/20.48 thf(zip_derived_cl2968, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2937, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl2996, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl2968, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3121, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3094])). 157.06/20.48 thf(zip_derived_cl3147, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3121, '2'])). 157.06/20.48 thf(zip_derived_cl3174, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3147, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3207, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3174, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3306, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3292])). 157.06/20.48 thf(zip_derived_cl3314, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3306, '2'])). 157.06/20.48 thf(zip_derived_cl3322, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3314, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3330, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3322, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3246, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3224])). 157.06/20.48 thf(zip_derived_cl3262, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3246, '2'])). 157.06/20.48 thf(zip_derived_cl3282, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3262, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3298, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3282, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3144, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3116])). 157.06/20.48 thf(zip_derived_cl3170, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3144, '2'])). 157.06/20.48 thf(zip_derived_cl3204, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3170, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3230, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3204, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3302, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3286])). 157.06/20.48 thf(zip_derived_cl3310, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3302, '2'])). 157.06/20.48 thf(zip_derived_cl3318, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3310, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3326, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3318, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3242, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3218])). 157.06/20.48 thf(zip_derived_cl3258, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3242, '2'])). 157.06/20.48 thf(zip_derived_cl3278, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3258, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3294, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3278, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3140, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3110])). 157.06/20.48 thf(zip_derived_cl3166, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3140, '2'])). 157.06/20.48 thf(zip_derived_cl3200, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3166, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3226, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3200, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3029, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2999])). 157.06/20.48 thf(zip_derived_cl3057, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3029, '2'])). 157.06/20.48 thf(zip_derived_cl3092, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3057, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3118, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3092, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3236, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3210])). 157.06/20.48 thf(zip_derived_cl3252, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3236, '2'])). 157.06/20.48 thf(zip_derived_cl3270, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3252, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3288, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3270, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3134, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3104])). 157.06/20.48 thf(zip_derived_cl3160, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3134, '2'])). 157.06/20.48 thf(zip_derived_cl3192, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3160, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3220, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3192, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3023, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2993])). 157.06/20.48 thf(zip_derived_cl3051, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3023, '2'])). 157.06/20.48 thf(zip_derived_cl3084, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3051, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3112, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3084, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl2913, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2885])). 157.06/20.48 thf(zip_derived_cl2942, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2913, '2'])). 157.06/20.48 thf(zip_derived_cl2975, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2942, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3001, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl2975, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl3126, plain, 157.06/20.48 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3098])). 157.06/20.48 thf(zip_derived_cl3152, plain, 157.06/20.48 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3126, '2'])). 157.06/20.48 thf(zip_derived_cl3181, plain, 157.06/20.48 (( (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ~ ('#form6'))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl3152, '7'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl3212, plain, 157.06/20.48 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.48 | ~ ('#form6') 157.06/20.48 | ('#form3' @ e1 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.48 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl3181, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl2550, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 (~ (mnot @ 157.06/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 157.06/20.48 (mnot @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 157.06/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))))) @ 157.06/20.48 X0) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2548])). 157.06/20.48 thf(zip_derived_cl2557, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2))) @ 157.06/20.48 (mnot @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 157.06/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 157.06/20.48 X0) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2550, '2'])). 157.06/20.48 thf(zip_derived_cl2565, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 ( (((mnot @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 157.06/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 157.06/20.48 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ X0))) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2557, '6'])). 157.06/20.48 thf(zip_derived_cl2574, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 ( (mnot @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 157.06/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 157.06/20.48 X0) 157.06/20.48 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ X0) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2565])). 157.06/20.48 thf(zip_derived_cl2582, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 157.06/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 157.06/20.48 X0) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.48 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ X0))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2574, '4'])). 157.06/20.48 thf(zip_derived_cl2592, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 (~ (mnot @ 157.06/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 157.06/20.48 (mnot @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 157.06/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 157.06/20.48 X0) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.48 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ X0))), 157.06/20.48 inference('rw', [status(thm)], [zip_derived_cl2582, '3'])). 157.06/20.48 thf(zip_derived_cl2593, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2))) @ 157.06/20.48 (mnot @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 157.06/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 157.06/20.48 X0) 157.06/20.48 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ X0) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2592, '2'])). 157.06/20.48 thf(zip_derived_cl2602, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 ( (((mnot @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 157.06/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 157.06/20.48 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0))) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.48 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ X0))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2593, '6'])). 157.06/20.48 thf(zip_derived_cl2613, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 (~ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ X0) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.48 | (((mnot @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 157.06/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 157.06/20.48 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0))))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2602, '4'])). 157.06/20.48 thf(zip_derived_cl2622, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 (~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 157.06/20.48 (op @ e0 @ e0) @ e2 @ Y0)))))) 157.06/20.48 | (((mnot @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 157.06/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 157.06/20.48 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0))) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2613, '1'])). 157.06/20.48 thf(zip_derived_cl274, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.48 Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl270, plain, 157.06/20.48 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.48 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.48 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.48 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.48 X0 @ Y0)))))))), 157.06/20.48 define([status(thm)])). 157.06/20.48 thf(zip_derived_cl2634, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 (~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.48 | (((mnot @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 157.06/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 157.06/20.48 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0))))), 157.06/20.48 inference('renaming', [status(thm)], 157.06/20.48 [zip_derived_cl2622, zip_derived_cl274, zip_derived_cl270])). 157.06/20.48 thf(zip_derived_cl2645, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 ( (mnot @ 157.06/20.48 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 157.06/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 157.06/20.48 X0) 157.06/20.48 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.48 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0))), 157.06/20.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2634])). 157.06/20.48 thf(zip_derived_cl2661, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 157.06/20.48 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0) 157.06/20.48 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.48 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2645, '4'])). 157.06/20.48 thf(zip_derived_cl2673, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 (~ (mnot @ 157.06/20.48 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 157.06/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 157.06/20.48 X0) 157.06/20.48 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.48 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0))), 157.06/20.48 inference('rw', [status(thm)], [zip_derived_cl2661, '3'])). 157.06/20.48 thf(zip_derived_cl2674, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2))) @ 157.06/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ X0) 157.06/20.48 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.48 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2673, '2'])). 157.06/20.48 thf(zip_derived_cl2689, plain, 157.06/20.48 (![X0 : $i]: 157.06/20.48 ( (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0) | 157.06/20.48 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0))) 157.06/20.48 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0) 157.06/20.48 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.48 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ X0))), 157.06/20.48 inference('rw_clause', [status(thm)], [zip_derived_cl2674, '6'])). 157.06/20.48 thf(zip_derived_cl2705, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0) | 157.06/20.49 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0))))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2689, '4'])). 157.06/20.49 thf(zip_derived_cl2727, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 157.06/20.49 (op @ e1 @ e1) @ e2 @ Y0)))))) 157.06/20.49 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0) | 157.06/20.49 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0))) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2705, '1'])). 157.06/20.49 thf(zip_derived_cl274, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.49 Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl270, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.49 X0 @ Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl2745, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0) | 157.06/20.49 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0))))), 157.06/20.49 inference('renaming', [status(thm)], 157.06/20.49 [zip_derived_cl2727, zip_derived_cl274, zip_derived_cl270])). 157.06/20.49 thf(zip_derived_cl2768, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0))), 157.06/20.49 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2745])). 157.06/20.49 thf(zip_derived_cl2789, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2768, '4'])). 157.06/20.49 thf(zip_derived_cl2815, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 157.06/20.49 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2789, '1'])). 157.06/20.49 thf(zip_derived_cl274, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.49 Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl270, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.49 X0 @ Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl2838, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ ('#form3' @ e2 @ (op @ e3 @ e3) @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ X0))), 157.06/20.49 inference('renaming', [status(thm)], 157.06/20.49 [zip_derived_cl2815, zip_derived_cl274, zip_derived_cl270])). 157.06/20.49 thf(zip_derived_cl2866, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e3 @ e3) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2838, '4'])). 157.06/20.49 thf(zip_derived_cl2890, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 157.06/20.49 (op @ e2 @ e2) @ e2 @ Y0)))))) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e3 @ e3) @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2866, '1'])). 157.06/20.49 thf(zip_derived_cl274, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.49 Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl270, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.49 X0 @ Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl2919, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ ('#form3' @ e2 @ (op @ e2 @ e2) @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ ('#form3' @ e2 @ (op @ e3 @ e3) @ X0))), 157.06/20.49 inference('renaming', [status(thm)], 157.06/20.49 [zip_derived_cl2890, zip_derived_cl274, zip_derived_cl270])). 157.06/20.49 thf(zip_derived_cl3304, plain, 157.06/20.49 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.49 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ~ ('#form6'))), 157.06/20.49 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3290])). 157.06/20.49 thf(zip_derived_cl3312, plain, 157.06/20.49 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.49 | ~ ('#form6') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl3304, '2'])). 157.06/20.49 thf(zip_derived_cl3320, plain, 157.06/20.49 (( (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.49 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.49 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ~ ('#form6'))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl3312, '7'])). 157.06/20.49 thf(zip_derived_cl274, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.49 Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl270, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.49 X0 @ Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl3328, plain, 157.06/20.49 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ~ ('#form6') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ('#form3' @ e0 @ (op @ e2 @ e2) @ '#sk5'))), 157.06/20.49 inference('renaming', [status(thm)], 157.06/20.49 [zip_derived_cl3320, zip_derived_cl274, zip_derived_cl270])). 157.06/20.49 thf(zip_derived_cl3244, plain, 157.06/20.49 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.49 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ~ ('#form6'))), 157.06/20.49 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3222])). 157.06/20.49 thf(zip_derived_cl3260, plain, 157.06/20.49 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.49 | ~ ('#form6') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl3244, '2'])). 157.06/20.49 thf(zip_derived_cl3280, plain, 157.06/20.49 (( (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.49 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.49 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ~ ('#form6'))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl3260, '7'])). 157.06/20.49 thf(zip_derived_cl274, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.49 Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl270, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.49 X0 @ Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl3296, plain, 157.06/20.49 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ~ ('#form6') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ('#form3' @ e0 @ (op @ e1 @ e1) @ '#sk5'))), 157.06/20.49 inference('renaming', [status(thm)], 157.06/20.49 [zip_derived_cl3280, zip_derived_cl274, zip_derived_cl270])). 157.06/20.49 thf(zip_derived_cl3142, plain, 157.06/20.49 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.49 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ~ ('#form6'))), 157.06/20.49 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3114])). 157.06/20.49 thf(zip_derived_cl3168, plain, 157.06/20.49 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.49 | ~ ('#form6') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl3142, '2'])). 157.06/20.49 thf(zip_derived_cl3202, plain, 157.06/20.49 (( (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.49 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.49 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ~ ('#form6'))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl3168, '7'])). 157.06/20.49 thf(zip_derived_cl274, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.49 Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl270, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.49 X0 @ Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl3228, plain, 157.06/20.49 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ~ ('#form6') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ('#form3' @ e0 @ (op @ e0 @ e0) @ '#sk5'))), 157.06/20.49 inference('renaming', [status(thm)], 157.06/20.49 [zip_derived_cl3202, zip_derived_cl274, zip_derived_cl270])). 157.06/20.49 thf(zip_derived_cl3300, plain, 157.06/20.49 ((~ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk5') 157.06/20.49 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ~ ('#form6'))), 157.06/20.49 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3284])). 157.06/20.49 thf(zip_derived_cl3308, plain, 157.06/20.49 (( (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk5') 157.06/20.49 | ~ ('#form6') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl3300, '2'])). 157.06/20.49 thf(zip_derived_cl3316, plain, 157.06/20.49 (( (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (qmltpeq @ 157.06/20.49 (op @ e3 @ e3) @ e2 @ Y0)))))) 157.06/20.49 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ~ ('#form6'))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl3308, '7'])). 157.06/20.49 thf(zip_derived_cl274, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.49 Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl270, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.49 X0 @ Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl3324, plain, 157.06/20.49 (( ('#form3' @ e2 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ~ ('#form6') 157.06/20.49 | ('#form3' @ e1 @ (op @ e3 @ e3) @ '#sk5') 157.06/20.49 | ('#form3' @ e0 @ (op @ e3 @ e3) @ '#sk5'))), 157.06/20.49 inference('renaming', [status(thm)], 157.06/20.49 [zip_derived_cl3316, zip_derived_cl274, zip_derived_cl270])). 157.06/20.49 thf(a1, axiom, (mreflexive @ rel_s4)). 157.06/20.49 thf(zip_derived_cl2, plain, ( (mreflexive @ rel_s4)), 157.06/20.49 inference('cnf', [status(esa)], [a1])). 157.06/20.49 thf(mreflexive, axiom, (mreflexive @ X0) => 157.06/20.49 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0 @ Y0)))) = ($true))). 157.06/20.49 thf('11', plain, 157.06/20.49 (![X0:( $i > $i > $o )]: 157.06/20.49 ( ( mreflexive @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 @ X5 ) ) )), 157.06/20.49 inference('rw.lit', [status(esa)], [mreflexive])). 157.06/20.49 thf(zip_derived_cl35, plain, ( (((!!) @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2, '11'])). 157.06/20.49 thf(zip_derived_cl36, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 157.06/20.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl35])). 157.06/20.49 thf(zip_derived_cl2538, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mnot @ 157.06/20.49 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 157.06/20.49 (mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))))) @ 157.06/20.49 X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.49 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2536])). 157.06/20.49 thf(zip_derived_cl2544, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1))) @ 157.06/20.49 (mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 157.06/20.49 X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2538, '2'])). 157.06/20.49 thf(zip_derived_cl2551, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (((mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 157.06/20.49 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ X0))) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2544, '6'])). 157.06/20.49 thf(zip_derived_cl2558, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 157.06/20.49 X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.49 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2551])). 157.06/20.49 thf(zip_derived_cl2566, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 157.06/20.49 X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2558, '4'])). 157.06/20.49 thf(zip_derived_cl2575, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mnot @ 157.06/20.49 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @ 157.06/20.49 (mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 157.06/20.49 X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ X0))), 157.06/20.49 inference('rw', [status(thm)], [zip_derived_cl2566, '3'])). 157.06/20.49 thf(zip_derived_cl2576, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1))) @ 157.06/20.49 (mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 157.06/20.49 X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2575, '2'])). 157.06/20.49 thf(zip_derived_cl2583, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (((mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 157.06/20.49 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0))) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2576, '6'])). 157.06/20.49 thf(zip_derived_cl2594, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (((mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 157.06/20.49 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0))))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2583, '4'])). 157.06/20.49 thf(zip_derived_cl2603, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 157.06/20.49 (op @ e0 @ e0) @ e1 @ Y0)))))) 157.06/20.49 | (((mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 157.06/20.49 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0))) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2594, '1'])). 157.06/20.49 thf(zip_derived_cl274, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.49 Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl270, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.49 X0 @ Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl2614, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (((mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 157.06/20.49 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0))))), 157.06/20.49 inference('renaming', [status(thm)], 157.06/20.49 [zip_derived_cl2603, zip_derived_cl274, zip_derived_cl270])). 157.06/20.49 thf(zip_derived_cl2623, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 157.06/20.49 X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0))), 157.06/20.49 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2614])). 157.06/20.49 thf(zip_derived_cl2635, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2623, '4'])). 157.06/20.49 thf(zip_derived_cl2646, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mnot @ 157.06/20.49 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @ 157.06/20.49 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 157.06/20.49 X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0))), 157.06/20.49 inference('rw', [status(thm)], [zip_derived_cl2635, '3'])). 157.06/20.49 thf(zip_derived_cl2647, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1))) @ 157.06/20.49 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2646, '2'])). 157.06/20.49 thf(zip_derived_cl2662, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0) | 157.06/20.49 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0))) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2647, '6'])). 157.06/20.49 thf(zip_derived_cl2675, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0) | 157.06/20.49 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0))))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2662, '4'])). 157.06/20.49 thf(zip_derived_cl2690, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 157.06/20.49 (op @ e1 @ e1) @ e1 @ Y0)))))) 157.06/20.49 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0) | 157.06/20.49 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0))) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2675, '1'])). 157.06/20.49 thf(zip_derived_cl274, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.49 Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl270, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.49 X0 @ Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl2706, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0) | 157.06/20.49 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0))))), 157.06/20.49 inference('renaming', [status(thm)], 157.06/20.49 [zip_derived_cl2690, zip_derived_cl274, zip_derived_cl270])). 157.06/20.49 thf(zip_derived_cl2728, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0))), 157.06/20.49 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2706])). 157.06/20.49 thf(zip_derived_cl2746, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2728, '4'])). 157.06/20.49 thf(zip_derived_cl2769, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 157.06/20.49 (op @ e3 @ e3) @ e1 @ Y0)))))) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2746, '1'])). 157.06/20.49 thf(zip_derived_cl274, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.49 Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl270, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.49 X0 @ Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl2790, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ ('#form3' @ e1 @ (op @ e3 @ e3) @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ X0))), 157.06/20.49 inference('renaming', [status(thm)], 157.06/20.49 [zip_derived_cl2769, zip_derived_cl274, zip_derived_cl270])). 157.06/20.49 thf(zip_derived_cl2816, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e3 @ e3) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2790, '4'])). 157.06/20.49 thf(zip_derived_cl2839, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 157.06/20.49 (op @ e2 @ e2) @ e1 @ Y0)))))) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e3 @ e3) @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2816, '1'])). 157.06/20.49 thf(zip_derived_cl274, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.49 Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl270, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.49 X0 @ Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl2867, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ ('#form3' @ e1 @ (op @ e2 @ e2) @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ ('#form3' @ e1 @ (op @ e3 @ e3) @ X0))), 157.06/20.49 inference('renaming', [status(thm)], 157.06/20.49 [zip_derived_cl2839, zip_derived_cl274, zip_derived_cl270])). 157.06/20.49 thf(zip_derived_cl2529, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mnot @ 157.06/20.49 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @ 157.06/20.49 (mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))))) @ 157.06/20.49 X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.49 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2527])). 157.06/20.49 thf(zip_derived_cl2533, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0))) @ 157.06/20.49 (mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 157.06/20.49 X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2529, '2'])). 157.06/20.49 thf(zip_derived_cl2539, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (((mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @ 157.06/20.49 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ X0))) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2533, '6'])). 157.06/20.49 thf(zip_derived_cl2545, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @ 157.06/20.49 X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.49 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2539])). 157.06/20.49 thf(zip_derived_cl2552, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ 157.06/20.49 X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2545, '4'])). 157.06/20.49 thf(zip_derived_cl2559, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mnot @ 157.06/20.49 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0))) @ 157.06/20.49 (mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 157.06/20.49 X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ X0))), 157.06/20.49 inference('rw', [status(thm)], [zip_derived_cl2552, '3'])). 157.06/20.49 thf(zip_derived_cl2560, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0))) @ 157.06/20.49 (mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @ 157.06/20.49 X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2559, '2'])). 157.06/20.49 thf(zip_derived_cl2567, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (((mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ 157.06/20.49 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0))) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2560, '6'])). 157.06/20.49 thf(zip_derived_cl2577, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mbox_s4 @ (qmltpeq @ (op @ e0 @ e0) @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (((mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ 157.06/20.49 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0))))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2567, '4'])). 157.06/20.49 thf(zip_derived_cl2584, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 157.06/20.49 (op @ e0 @ e0) @ e0 @ Y0)))))) 157.06/20.49 | (((mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ 157.06/20.49 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0))) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2577, '1'])). 157.06/20.49 thf(zip_derived_cl274, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.49 Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl270, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.49 X0 @ Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl2595, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (((mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ 157.06/20.49 X0) | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0))))), 157.06/20.49 inference('renaming', [status(thm)], 157.06/20.49 [zip_derived_cl2584, zip_derived_cl274, zip_derived_cl270])). 157.06/20.49 thf(zip_derived_cl2604, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (mnot @ 157.06/20.49 (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ 157.06/20.49 X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0))), 157.06/20.49 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2595])). 157.06/20.49 thf(zip_derived_cl2615, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mand @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 157.06/20.49 (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2604, '4'])). 157.06/20.49 thf(zip_derived_cl2624, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mnot @ 157.06/20.49 (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0))) @ 157.06/20.49 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @ 157.06/20.49 X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0))), 157.06/20.49 inference('rw', [status(thm)], [zip_derived_cl2615, '3'])). 157.06/20.49 thf(zip_derived_cl2625, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (mor @ (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0))) @ 157.06/20.49 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2624, '2'])). 157.06/20.49 thf(zip_derived_cl2636, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0) | 157.06/20.49 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0))) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2625, '6'])). 157.06/20.49 thf(zip_derived_cl2648, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mbox_s4 @ (qmltpeq @ (op @ e1 @ e1) @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0) | 157.06/20.49 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0))))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2636, '4'])). 157.06/20.49 thf(zip_derived_cl2663, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 157.06/20.49 (op @ e1 @ e1) @ e0 @ Y0)))))) 157.06/20.49 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0) | 157.06/20.49 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0))) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2648, '1'])). 157.06/20.49 thf(zip_derived_cl274, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.49 Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl270, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.49 X0 @ Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl2676, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | (((mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0) | 157.06/20.49 (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0))))), 157.06/20.49 inference('renaming', [status(thm)], 157.06/20.49 [zip_derived_cl2663, zip_derived_cl274, zip_derived_cl270])). 157.06/20.49 thf(zip_derived_cl2691, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 ( (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0))), 157.06/20.49 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2676])). 157.06/20.49 thf(zip_derived_cl2707, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mbox_s4 @ (qmltpeq @ (op @ e3 @ e3) @ e0) @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2691, '4'])). 157.06/20.49 thf(zip_derived_cl2729, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 157.06/20.49 (op @ e3 @ e3) @ e0 @ Y0)))))) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2707, '1'])). 157.06/20.49 thf(zip_derived_cl274, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.49 Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl270, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.49 X0 @ Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl2747, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ ('#form3' @ e0 @ (op @ e3 @ e3) @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | (mnot @ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ X0))), 157.06/20.49 inference('renaming', [status(thm)], 157.06/20.49 [zip_derived_cl2729, zip_derived_cl274, zip_derived_cl270])). 157.06/20.49 thf(zip_derived_cl2770, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (mbox_s4 @ (qmltpeq @ (op @ e2 @ e2) @ e0) @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e3 @ e3) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2747, '4'])). 157.06/20.49 thf(zip_derived_cl2791, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X0 @ Y0))) | (qmltpeq @ 157.06/20.49 (op @ e2 @ e2) @ e0 @ Y0)))))) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e3 @ e3) @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0))), 157.06/20.49 inference('rw_clause', [status(thm)], [zip_derived_cl2770, '1'])). 157.06/20.49 thf(zip_derived_cl274, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 (~ ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ X0 @ 157.06/20.49 Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl270, plain, 157.06/20.49 (![X0 : mu, X1 : mu, X2 : $i]: 157.06/20.49 ( ('#form3' @ X0 @ X1 @ X2) 157.06/20.49 | ~ (((!!) @ (^[Y0 : $i]: 157.06/20.49 (((((~) @ (rel_s4 @ X2 @ Y0))) | (qmltpeq @ X1 @ 157.06/20.49 X0 @ Y0)))))))), 157.06/20.49 define([status(thm)])). 157.06/20.49 thf(zip_derived_cl2817, plain, 157.06/20.49 (![X0 : $i]: 157.06/20.49 (~ ('#form3' @ e0 @ (op @ e2 @ e2) @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e0 @ e0) @ X0) 157.06/20.49 | ~ (rel_s4 @ '#sk5' @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e1 @ e1) @ X0) 157.06/20.49 | ~ ('#form3' @ e0 @ (op @ e3 @ e3) @ X0))), 157.06/20.49 inference('renaming', [status(thm)], 157.06/20.49 [zip_derived_cl2791, zip_derived_cl274, zip_derived_cl270])). 157.06/20.49 thf(zip_derived_cl3332, plain, ($false), 157.06/20.49 inference('eprover', [status(thm)], 157.06/20.49 [zip_derived_cl3031, zip_derived_cl3032, zip_derived_cl277, 157.06/20.49 zip_derived_cl2917, zip_derived_cl2918, zip_derived_cl2813, 157.06/20.49 zip_derived_cl278, zip_derived_cl3331, zip_derived_cl3299, 157.06/20.49 zip_derived_cl3231, zip_derived_cl3327, zip_derived_cl3295, 157.06/20.49 zip_derived_cl3227, zip_derived_cl3119, zip_derived_cl3289, 157.06/20.49 zip_derived_cl3221, zip_derived_cl3113, zip_derived_cl3002, 157.06/20.49 zip_derived_cl3213, zip_derived_cl3293, zip_derived_cl3225, 157.06/20.49 zip_derived_cl3117, zip_derived_cl3287, zip_derived_cl3219, 157.06/20.49 zip_derived_cl3111, zip_derived_cl3000, zip_derived_cl3211, 157.06/20.49 zip_derived_cl3105, zip_derived_cl2994, zip_derived_cl2886, 157.06/20.49 zip_derived_cl3099, zip_derived_cl3217, zip_derived_cl3109, 157.06/20.49 zip_derived_cl2998, zip_derived_cl3209, zip_derived_cl3103, 157.06/20.49 zip_derived_cl2992, zip_derived_cl2884, zip_derived_cl3097, 157.06/20.49 zip_derived_cl2988, zip_derived_cl2880, zip_derived_cl2787, 157.06/20.49 zip_derived_cl2983, zip_derived_cl3329, zip_derived_cl3297, 157.06/20.49 zip_derived_cl3229, zip_derived_cl3325, zip_derived_cl3291, 157.06/20.49 zip_derived_cl3223, zip_derived_cl3115, zip_derived_cl3285, 157.06/20.49 zip_derived_cl3215, zip_derived_cl3107, zip_derived_cl2996, 157.06/20.49 zip_derived_cl3207, zip_derived_cl3330, zip_derived_cl3298, 157.06/20.49 zip_derived_cl3230, zip_derived_cl3326, zip_derived_cl3294, 157.06/20.49 zip_derived_cl3226, zip_derived_cl3118, zip_derived_cl3288, 157.06/20.49 zip_derived_cl3220, zip_derived_cl3112, zip_derived_cl3001, 157.06/20.49 zip_derived_cl3212, zip_derived_cl2919, zip_derived_cl3328, 157.06/20.49 zip_derived_cl3296, zip_derived_cl3228, zip_derived_cl3324, 157.06/20.49 zip_derived_cl36, zip_derived_cl2867, zip_derived_cl2817])). 157.06/20.49 157.06/20.49 % SZS output end Refutation 157.06/20.49 157.06/20.49 157.06/20.49 % Terminating... 157.48/20.60 % Runner terminated. 157.48/20.60 % Zipperpin 1.5 exiting 157.48/20.61 EOF