0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.uJryQ9KJva true 0.14/0.35 % Computer : n023.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 960 0.14/0.35 % WCLimit : 120 0.14/0.35 % DateTime : Tue Aug 9 07:00:13 EDT 2022 0.14/0.36 % CPUTime : 0.14/0.36 % Running portfolio for 960 s 0.14/0.36 % File : /export/starexec/sandbox/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 0.54/0.67 % Total configuration time : 828 0.54/0.67 % Estimated wc time : 1656 0.54/0.67 % Estimated cpu time (8 cpus) : 207.0 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.58/0.80 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 4.96/1.24 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 242.94/31.46 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s 274.84/35.47 % Solved by lams/30_b.l.sh. 274.84/35.47 % done 1170 iterations in 34.009s 274.84/35.47 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 274.84/35.47 % SZS output start Refutation 274.84/35.47 thf(mworld_type, type, mworld: $tType). 274.84/35.47 thf(mforall_di_type, type, mforall_di: ($i > mworld > $o) > mworld > $o). 274.84/35.47 thf(mimplies_type, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o). 274.84/35.47 thf(e0_type, type, e0: $i). 274.84/35.47 thf(mbox_type, type, mbox: (mworld > $o) > mworld > $o). 274.84/35.47 thf(op_type, type, op: $i > $i > $i). 274.84/35.47 thf(inv_type, type, inv: $i > $i). 274.84/35.47 thf('#sk3_type', type, '#sk3': mworld). 274.84/35.47 thf(mactual_type, type, mactual: mworld). 274.84/35.47 thf(mand_type, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o). 274.84/35.47 thf(mor_type, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o). 274.84/35.47 thf('#form4_type', type, '#form4': $o). 274.84/35.47 thf(mnot_type, type, mnot: (mworld > $o) > mworld > $o). 274.84/35.47 thf('#sk1_type', type, '#sk1': mworld > $i > $i > mworld). 274.84/35.47 thf(qmltpeq_type, type, qmltpeq: $i > $i > mworld > $o). 274.84/35.47 thf(mlocal_type, type, mlocal: (mworld > $o) > $o). 274.84/35.47 thf(e2_type, type, e2: $i). 274.84/35.47 thf(mrel_type, type, mrel: mworld > mworld > $o). 274.84/35.47 thf('#form2_type', type, '#form2': mworld > $i > $i > $o). 274.84/35.47 thf(e3_type, type, e3: $i). 274.84/35.47 thf(e1_type, type, e1: $i). 274.84/35.47 thf(co1, conjecture, 274.84/35.47 (mlocal @ 274.84/35.47 ( mbox @ 274.84/35.47 ( mnot @ 274.84/35.47 ( mand @ 274.84/35.47 ( mor @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ 274.84/35.47 ( mor @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ 274.84/35.47 ( mor @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) @ 274.84/35.47 ( mbox @ 274.84/35.47 ( mnot @ 274.84/35.47 ( mor @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ 274.84/35.47 ( mor @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ 274.84/35.47 ( mor @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ))). 274.84/35.47 thf(zf_stmt_0, negated_conjecture, 274.84/35.47 (~( mlocal @ 274.84/35.47 ( mbox @ 274.84/35.47 ( mnot @ 274.84/35.47 ( mand @ 274.84/35.47 ( mor @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ 274.84/35.47 ( mor @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ 274.84/35.47 ( mor @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) @ 274.84/35.47 ( mbox @ 274.84/35.47 ( mnot @ 274.84/35.47 ( mor @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ 274.84/35.47 ( mor @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ 274.84/35.47 ( mor @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) )), 274.84/35.47 inference('cnf.neg', [status(esa)], [co1])). 274.84/35.47 thf(zip_derived_cl15, plain, 274.84/35.47 (~ (mlocal @ 274.84/35.47 (mbox @ 274.84/35.47 (mnot @ 274.84/35.47 (mand @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 274.84/35.47 (mbox @ 274.84/35.47 (mnot @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))))))), 274.84/35.47 inference('cnf', [status(esa)], [zf_stmt_0])). 274.84/35.47 thf(mlocal_def, axiom,(( mlocal @ (X0)) = ((X0 @ mactual)))). 274.84/35.47 thf('0', plain, 274.84/35.47 (![X0:( mworld > $o )]: ( ( mlocal @ X0 ) = ( X0 @ mactual ) )), 274.84/35.47 define([status(thm)])). 274.84/35.47 thf(zip_derived_cl800, plain, 274.84/35.47 (~ (mbox @ 274.84/35.47 (mnot @ 274.84/35.47 (mand @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 274.84/35.47 (mbox @ 274.84/35.47 (mnot @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))))) @ 274.84/35.47 mactual)), 274.84/35.47 inference('rw', [status(thm)], [zip_derived_cl15, '0'])). 274.84/35.47 thf(mbox_def, axiom, ~ (mbox @ X0 @ X1) => 274.84/35.47 ((((!!) @ (^[Y0 : mworld]: (((mrel @ X1 @ Y0) => (X0 @ Y0)))))) != ($true))). 274.84/35.47 thf('1', plain, 274.84/35.47 (![X0:( mworld > $o ),X1:mworld]: 274.84/35.47 ( ( ~( mbox @ X0 @ X1 ) ) <=> 274.84/35.47 ( ~( ![X6:mworld]: ( ( mrel @ X1 @ X6 ) => ( X0 @ X6 ) ) ) ) )), 274.84/35.47 inference('rw.lit', [status(esa)], [mbox_def])). 274.84/35.47 thf(zip_derived_cl801, plain, 274.84/35.47 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ mactual @ Y0) => (mnot @ 274.84/35.47 (mand @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 274.84/35.47 (mbox @ 274.84/35.47 (mnot @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))) @ 274.84/35.47 Y0))))))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl800, '1'])). 274.84/35.47 thf(zip_derived_cl802, plain, 274.84/35.47 (~ (((mrel @ mactual @ '#sk3') => (mnot @ 274.84/35.47 (mand @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 274.84/35.47 (mbox @ 274.84/35.47 (mnot @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))) @ 274.84/35.47 '#sk3')))), 274.84/35.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl801])). 274.84/35.47 thf(zip_derived_cl804, plain, 274.84/35.47 (~ (mnot @ 274.84/35.47 (mand @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 274.84/35.47 (mbox @ 274.84/35.47 (mnot @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))) @ 274.84/35.47 '#sk3')), 274.84/35.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl802])). 274.84/35.47 thf(mnot_def, axiom, ~ (mnot @ X0 @ X1) => ((X0 @ X1) = ($true))). 274.84/35.47 thf('2', plain, 274.84/35.47 (![X0:( mworld > $o ),X1:mworld]: 274.84/35.47 ( ( ~( mnot @ X0 @ X1 ) ) <=> ( X0 @ X1 ) )), 274.84/35.47 inference('rw.lit', [status(esa)], [mnot_def])). 274.84/35.47 thf(zip_derived_cl805, plain, 274.84/35.47 ( (mand @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 274.84/35.47 (mbox @ 274.84/35.47 (mnot @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))) @ 274.84/35.47 '#sk3')), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl804, '2'])). 274.84/35.47 thf(mand_def, axiom, (mand @ X0 @ X1 @ X2) => 274.84/35.47 ((((X1 @ X2) & (X0 @ X2))) = ($true))). 274.84/35.47 thf('3', plain, 274.84/35.47 (![X0:( mworld > $o ),X1:( mworld > $o ),X2:mworld]: 274.84/35.47 ( ( mand @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) & ( X1 @ X2 ) ) )), 274.84/35.47 inference('rw.lit', [status(esa)], [mand_def])). 274.84/35.47 thf(zip_derived_cl806, plain, 274.84/35.47 ( (((mbox @ 274.84/35.47 (mnot @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))) @ 274.84/35.47 '#sk3') & (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))) @ 274.84/35.47 '#sk3')))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl805, '3'])). 274.84/35.47 thf(zip_derived_cl807, plain, 274.84/35.47 ( (mbox @ 274.84/35.47 (mnot @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))) @ 274.84/35.47 '#sk3')), 274.84/35.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl806])). 274.84/35.47 thf(mbox_def, axiom, (mbox @ X0 @ X1) => 274.84/35.47 ((((!!) @ (^[Y0 : mworld]: (((mrel @ X1 @ Y0) => (X0 @ Y0)))))) = ($true))). 274.84/35.47 thf('4', plain, 274.84/35.47 (![X0:( mworld > $o ),X1:mworld]: 274.84/35.47 ( ( mbox @ X0 @ X1 ) <=> 274.84/35.47 ( ![X6:mworld]: ( ( mrel @ X1 @ X6 ) => ( X0 @ X6 ) ) ) )), 274.84/35.47 inference('rw.lit', [status(esa)], [mbox_def])). 274.84/35.47 thf(zip_derived_cl809, plain, 274.84/35.47 ( (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ '#sk3' @ Y0) => (mnot @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 274.84/35.47 Y0))))))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl807, '4'])). 274.84/35.47 thf(zip_derived_cl811, plain, 274.84/35.47 (![X2 : mworld]: 274.84/35.47 (((mrel @ '#sk3' @ X2) => (mnot @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 274.84/35.47 X2)))), 274.84/35.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl809])). 274.84/35.47 thf(zip_derived_cl813, plain, 274.84/35.47 (![X2 : mworld]: 274.84/35.47 (~ (mrel @ '#sk3' @ X2) 274.84/35.47 | (mnot @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))) @ 274.84/35.47 X2))), 274.84/35.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl811])). 274.84/35.47 thf(mnot_def, axiom, (mnot @ X0 @ X1) => ((X0 @ X1) != ($true))). 274.84/35.47 thf('5', plain, 274.84/35.47 (![X0:( mworld > $o ),X1:mworld]: 274.84/35.47 ( ( mnot @ X0 @ X1 ) <=> ( ~( X0 @ X1 ) ) )), 274.84/35.47 inference('rw.lit', [status(esa)], [mnot_def])). 274.84/35.47 thf(zip_derived_cl815, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))) @ 274.84/35.47 X0) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl813, '5'])). 274.84/35.47 thf(mor_def, axiom, ~ (mor @ X0 @ X1 @ X2) => 274.84/35.47 ((((X1 @ X2) | (X0 @ X2))) != ($true))). 274.84/35.47 thf('6', plain, 274.84/35.47 (![X0:( mworld > $o ),X1:( mworld > $o ),X2:mworld]: 274.84/35.47 ( ( ~( mor @ X0 @ X1 @ X2 ) ) <=> ( ~( ( X1 @ X2 ) | ( X0 @ X2 ) ) ) )), 274.84/35.47 inference('rw.lit', [status(esa)], [mor_def])). 274.84/35.47 thf(zip_derived_cl817, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (((mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 274.84/35.47 X0) | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @ 274.84/35.47 X0))) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl815, '6'])). 274.84/35.47 thf(zip_derived_cl820, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 274.84/35.47 X0) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl817])). 274.84/35.47 thf(zip_derived_cl824, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (((mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.47 X0) | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.47 X0))) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl820, '6'])). 274.84/35.47 thf(zip_derived_cl829, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.47 X0) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl824])). 274.84/35.47 thf(zip_derived_cl835, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.47 X0) | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.47 X0))) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl829, '6'])). 274.84/35.47 thf(zip_derived_cl843, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.47 X0) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl835])). 274.84/35.47 thf(mand_def, axiom, ~ (mand @ X0 @ X1 @ X2) => 274.84/35.47 ((((X0 @ X2) & (X1 @ X2))) != ($true))). 274.84/35.47 thf('7', plain, 274.84/35.47 (![X0:( mworld > $o ),X1:( mworld > $o ),X2:mworld]: 274.84/35.47 ( ( ~( mand @ X0 @ X1 @ X2 ) ) <=> ( ~( ( X0 @ X2 ) & ( X1 @ X2 ) ) ) )), 274.84/35.47 inference('rw.lit', [status(esa)], [mand_def])). 274.84/35.47 thf(zip_derived_cl851, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (((mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ X0) & (mand @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.47 X0))) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl843, '7'])). 274.84/35.47 thf(zip_derived_cl860, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ X0) 274.84/35.47 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.47 X0) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl851])). 274.84/35.47 thf(zip_derived_cl869, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ 274.84/35.47 Y0)))))) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0) 274.84/35.47 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.47 X0))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl860, '1'])). 274.84/35.47 thf(ax6, axiom, 274.84/35.47 (mlocal @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 ) ) @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 ) ) ) ) ))). 274.84/35.47 thf(zip_derived_cl13, plain, 274.84/35.47 ( (mlocal @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (inv @ (inv @ e0)) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (inv @ (inv @ e1)) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (inv @ (inv @ e2)) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (inv @ (inv @ e3)) @ e3))))))), 274.84/35.47 inference('cnf', [status(esa)], [ax6])). 274.84/35.47 thf(zip_derived_cl248, plain, 274.84/35.47 ( (mand @ (mbox @ (qmltpeq @ (inv @ (inv @ e0)) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (inv @ (inv @ e1)) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (inv @ (inv @ e2)) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (inv @ (inv @ e3)) @ e3)))) @ 274.84/35.47 mactual)), 274.84/35.47 inference('rw', [status(thm)], [zip_derived_cl13, '0'])). 274.84/35.47 thf(zip_derived_cl249, plain, 274.84/35.47 ( (((mand @ (mbox @ (qmltpeq @ (inv @ (inv @ e1)) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (inv @ (inv @ e2)) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (inv @ (inv @ e3)) @ e3))) @ 274.84/35.47 mactual) & (mbox @ (qmltpeq @ (inv @ (inv @ e0)) @ e0) @ mactual)))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl248, '3'])). 274.84/35.47 thf(zip_derived_cl251, plain, 274.84/35.47 ( (mbox @ (qmltpeq @ (inv @ (inv @ e0)) @ e0) @ mactual)), 274.84/35.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl249])). 274.84/35.47 thf(zip_derived_cl253, plain, 274.84/35.47 ( (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ mactual @ Y0) => (qmltpeq @ (inv @ (inv @ e0)) @ 274.84/35.47 e0 @ Y0))))))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl251, '4'])). 274.84/35.47 thf(zip_derived_cl256, plain, 274.84/35.47 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.47 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.47 | (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.47 define([status(thm)])). 274.84/35.47 thf(transitivity, axiom, 274.84/35.47 (mlocal @ 274.84/35.47 ( mbox @ 274.84/35.47 ( mforall_di @ 274.84/35.47 ( ^[X:$i]: 274.84/35.47 ( mbox @ 274.84/35.47 ( mforall_di @ 274.84/35.47 ( ^[Y:$i]: 274.84/35.47 ( mbox @ 274.84/35.47 ( mforall_di @ 274.84/35.47 ( ^[Z:$i]: 274.84/35.47 ( mbox @ 274.84/35.47 ( mimplies @ 274.84/35.47 ( mand @ 274.84/35.47 ( mbox @ ( qmltpeq @ X @ Y ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ Y @ Z ) ) ) @ 274.84/35.47 ( mbox @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ) ))). 274.84/35.47 thf(zip_derived_cl6, plain, 274.84/35.47 ( (mlocal @ 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y0 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y1 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y2 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ Y0 @ Y1)) @ 274.84/35.47 (mbox @ (qmltpeq @ Y1 @ Y2))) @ 274.84/35.47 (mbox @ (qmltpeq @ Y0 @ Y2))))))))))))))), 274.84/35.47 inference('cnf', [status(esa)], [transitivity])). 274.84/35.47 thf(zip_derived_cl156, plain, 274.84/35.47 ( (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y0 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y1 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y2 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ Y0 @ Y1)) @ 274.84/35.47 (mbox @ (qmltpeq @ Y1 @ Y2))) @ 274.84/35.47 (mbox @ (qmltpeq @ Y0 @ Y2)))))))))))) @ 274.84/35.47 mactual)), 274.84/35.47 inference('rw', [status(thm)], [zip_derived_cl6, '0'])). 274.84/35.47 thf(zip_derived_cl157, plain, 274.84/35.47 ( (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ mactual @ Y0) => (mforall_di @ 274.84/35.47 (^[Y1 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y2 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y3 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ Y1 @ Y2)) @ 274.84/35.47 (mbox @ (qmltpeq @ Y2 @ Y3))) @ 274.84/35.47 (mbox @ (qmltpeq @ Y1 @ Y3))))))))))) @ 274.84/35.47 Y0))))))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl156, '4'])). 274.84/35.47 thf(zip_derived_cl158, plain, 274.84/35.47 (![X2 : mworld]: 274.84/35.47 (((mrel @ mactual @ X2) => (mforall_di @ 274.84/35.47 (^[Y0 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y1 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y2 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ Y0 @ Y1)) @ 274.84/35.47 (mbox @ (qmltpeq @ Y1 @ Y2))) @ 274.84/35.47 (mbox @ (qmltpeq @ Y0 @ Y2))))))))))) @ 274.84/35.47 X2)))), 274.84/35.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl157])). 274.84/35.47 thf(zip_derived_cl159, plain, 274.84/35.47 (![X2 : mworld]: 274.84/35.47 (~ (mrel @ mactual @ X2) 274.84/35.47 | (mforall_di @ 274.84/35.47 (^[Y0 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y1 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y2 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ Y0 @ Y1)) @ 274.84/35.47 (mbox @ (qmltpeq @ Y1 @ Y2))) @ 274.84/35.47 (mbox @ (qmltpeq @ Y0 @ Y2))))))))))) @ 274.84/35.47 X2))), 274.84/35.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])). 274.84/35.47 thf(mforall_di_def, axiom, (mforall_di @ X0 @ X1) => 274.84/35.47 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0 @ X1)))) = ($true))). 274.84/35.47 thf('8', plain, 274.84/35.47 (![X0:( $i > mworld > $o ),X1:mworld]: 274.84/35.47 ( ( mforall_di @ X0 @ X1 ) <=> ( ![X6:$i]: ( X0 @ X6 @ X1 ) ) )), 274.84/35.47 inference('rw.lit', [status(esa)], [mforall_di_def])). 274.84/35.47 thf(zip_derived_cl160, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 ( (((!!) @ (^[Y0 : $i]: 274.84/35.47 ((^[Y1 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y2 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y3 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ Y1 @ Y2)) @ 274.84/35.47 (mbox @ (qmltpeq @ Y2 @ Y3))) @ 274.84/35.47 (mbox @ (qmltpeq @ Y1 @ Y3))))))))))) @ 274.84/35.47 Y0 @ X0)))) 274.84/35.47 | ~ (mrel @ mactual @ X0))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl159, '8'])). 274.84/35.47 thf(zip_derived_cl161, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 ( (((!!) @ (^[Y0 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y1 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y2 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ Y0 @ Y1)) @ 274.84/35.47 (mbox @ (qmltpeq @ Y1 @ Y2))) @ 274.84/35.47 (mbox @ (qmltpeq @ Y0 @ Y2))))))))) @ 274.84/35.47 X0)))) 274.84/35.47 | ~ (mrel @ mactual @ X0))), 274.84/35.47 inference('ho_norm', [status(thm)], [zip_derived_cl160])). 274.84/35.47 thf(zip_derived_cl162, plain, 274.84/35.47 (![X0 : mworld, X2 : $i]: 274.84/35.47 ( (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y0 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y1 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X2 @ Y0)) @ 274.84/35.47 (mbox @ (qmltpeq @ Y0 @ Y1))) @ 274.84/35.47 (mbox @ (qmltpeq @ X2 @ Y1))))))))) @ 274.84/35.47 X0) 274.84/35.47 | ~ (mrel @ mactual @ X0))), 274.84/35.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl161])). 274.84/35.47 thf(zip_derived_cl163, plain, 274.84/35.47 (![X0 : mworld, X1 : $i]: 274.84/35.47 ( (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X0 @ Y0) => (mforall_di @ 274.84/35.47 (^[Y1 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y2 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X1 @ Y1)) @ 274.84/35.47 (mbox @ (qmltpeq @ Y1 @ Y2))) @ 274.84/35.47 (mbox @ (qmltpeq @ X1 @ Y2)))))))) @ 274.84/35.47 Y0)))))) 274.84/35.47 | ~ (mrel @ mactual @ X0))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl162, '4'])). 274.84/35.47 thf(zip_derived_cl164, plain, 274.84/35.47 (![X0 : mworld, X1 : $i, X3 : mworld]: 274.84/35.47 ( (((mrel @ X0 @ X3) => (mforall_di @ 274.84/35.47 (^[Y0 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y1 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X1 @ Y0)) @ 274.84/35.47 (mbox @ (qmltpeq @ Y0 @ Y1))) @ 274.84/35.47 (mbox @ (qmltpeq @ X1 @ Y1)))))))) @ 274.84/35.47 X3))) 274.84/35.47 | ~ (mrel @ mactual @ X0))), 274.84/35.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl163])). 274.84/35.47 thf(zip_derived_cl165, plain, 274.84/35.47 (![X0 : mworld, X1 : $i, X3 : mworld]: 274.84/35.47 (~ (mrel @ X0 @ X3) 274.84/35.47 | (mforall_di @ 274.84/35.47 (^[Y0 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y1 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X1 @ Y0)) @ 274.84/35.47 (mbox @ (qmltpeq @ Y0 @ Y1))) @ 274.84/35.47 (mbox @ (qmltpeq @ X1 @ Y1)))))))) @ 274.84/35.47 X3) 274.84/35.47 | ~ (mrel @ mactual @ X0))), 274.84/35.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])). 274.84/35.47 thf(zip_derived_cl166, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : $i]: 274.84/35.47 ( (((!!) @ (^[Y0 : $i]: 274.84/35.47 ((^[Y1 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y2 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X2 @ Y1)) @ 274.84/35.47 (mbox @ (qmltpeq @ Y1 @ Y2))) @ 274.84/35.47 (mbox @ (qmltpeq @ X2 @ Y2)))))))) @ 274.84/35.47 Y0 @ X1)))) 274.84/35.47 | ~ (mrel @ mactual @ X0) 274.84/35.47 | ~ (mrel @ X0 @ X1))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl165, '8'])). 274.84/35.47 thf(zip_derived_cl167, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : $i]: 274.84/35.47 ( (((!!) @ (^[Y0 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y1 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X2 @ Y0)) @ 274.84/35.47 (mbox @ (qmltpeq @ Y0 @ Y1))) @ 274.84/35.47 (mbox @ (qmltpeq @ X2 @ Y1)))))) @ 274.84/35.47 X1)))) 274.84/35.47 | ~ (mrel @ mactual @ X0) 274.84/35.47 | ~ (mrel @ X0 @ X1))), 274.84/35.47 inference('ho_norm', [status(thm)], [zip_derived_cl166])). 274.84/35.47 thf(zip_derived_cl168, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : $i, X4 : $i]: 274.84/35.47 ( (mbox @ 274.84/35.47 (mforall_di @ 274.84/35.47 (^[Y0 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X2 @ X4)) @ 274.84/35.47 (mbox @ (qmltpeq @ X4 @ Y0))) @ 274.84/35.47 (mbox @ (qmltpeq @ X2 @ Y0)))))) @ 274.84/35.47 X1) 274.84/35.47 | ~ (mrel @ X0 @ X1) 274.84/35.47 | ~ (mrel @ mactual @ X0))), 274.84/35.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl167])). 274.84/35.47 thf(zip_derived_cl169, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : $i, X3 : $i]: 274.84/35.47 ( (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X1 @ Y0) => (mforall_di @ 274.84/35.47 (^[Y1 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X2 @ X3)) @ 274.84/35.47 (mbox @ (qmltpeq @ X3 @ Y1))) @ 274.84/35.47 (mbox @ (qmltpeq @ X2 @ Y1))))) @ 274.84/35.47 Y0)))))) 274.84/35.47 | ~ (mrel @ mactual @ X0) 274.84/35.47 | ~ (mrel @ X0 @ X1))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl168, '4'])). 274.84/35.47 thf(zip_derived_cl170, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : $i, X3 : $i, X5 : mworld]: 274.84/35.47 ( (((mrel @ X1 @ X5) => (mforall_di @ 274.84/35.47 (^[Y0 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X2 @ X3)) @ 274.84/35.47 (mbox @ (qmltpeq @ X3 @ Y0))) @ 274.84/35.47 (mbox @ (qmltpeq @ X2 @ Y0))))) @ 274.84/35.47 X5))) 274.84/35.47 | ~ (mrel @ X0 @ X1) 274.84/35.47 | ~ (mrel @ mactual @ X0))), 274.84/35.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl169])). 274.84/35.47 thf(zip_derived_cl171, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : $i, X3 : $i, X5 : mworld]: 274.84/35.47 (~ (mrel @ X1 @ X5) 274.84/35.47 | (mforall_di @ 274.84/35.47 (^[Y0 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X2 @ X3)) @ 274.84/35.47 (mbox @ (qmltpeq @ X3 @ Y0))) @ 274.84/35.47 (mbox @ (qmltpeq @ X2 @ Y0))))) @ 274.84/35.47 X5) 274.84/35.47 | ~ (mrel @ mactual @ X0) 274.84/35.47 | ~ (mrel @ X0 @ X1))), 274.84/35.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl170])). 274.84/35.47 thf(zip_derived_cl172, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : $i, X4 : $i]: 274.84/35.47 ( (((!!) @ (^[Y0 : $i]: 274.84/35.47 ((^[Y1 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X3 @ X4)) @ 274.84/35.47 (mbox @ (qmltpeq @ X4 @ Y1))) @ 274.84/35.47 (mbox @ (qmltpeq @ X3 @ Y1))))) @ 274.84/35.47 Y0 @ X2)))) 274.84/35.47 | ~ (mrel @ X1 @ X0) 274.84/35.47 | ~ (mrel @ mactual @ X1) 274.84/35.47 | ~ (mrel @ X0 @ X2))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl171, '8'])). 274.84/35.47 thf(zip_derived_cl173, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : $i, X4 : $i]: 274.84/35.47 ( (((!!) @ (^[Y0 : $i]: 274.84/35.47 (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X3 @ X4)) @ 274.84/35.47 (mbox @ (qmltpeq @ X4 @ Y0))) @ 274.84/35.47 (mbox @ (qmltpeq @ X3 @ Y0))) @ 274.84/35.47 X2)))) 274.84/35.47 | ~ (mrel @ X1 @ X0) 274.84/35.47 | ~ (mrel @ mactual @ X1) 274.84/35.47 | ~ (mrel @ X0 @ X2))), 274.84/35.47 inference('ho_norm', [status(thm)], [zip_derived_cl172])). 274.84/35.47 thf(zip_derived_cl174, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : $i, X4 : $i, X6 : $i]: 274.84/35.47 ( (mbox @ 274.84/35.47 (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X3 @ X4)) @ 274.84/35.47 (mbox @ (qmltpeq @ X4 @ X6))) @ 274.84/35.47 (mbox @ (qmltpeq @ X3 @ X6))) @ 274.84/35.47 X2) 274.84/35.47 | ~ (mrel @ X0 @ X2) 274.84/35.47 | ~ (mrel @ mactual @ X1) 274.84/35.47 | ~ (mrel @ X1 @ X0))), 274.84/35.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl173])). 274.84/35.47 thf(zip_derived_cl175, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : $i, X4 : $i, X5 : $i]: 274.84/35.47 ( (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X2 @ Y0) => (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X4 @ X5)) @ 274.84/35.47 (mbox @ (qmltpeq @ X5 @ X3))) @ 274.84/35.47 (mbox @ (qmltpeq @ X4 @ X3)) @ Y0)))))) 274.84/35.47 | ~ (mrel @ X1 @ X0) 274.84/35.47 | ~ (mrel @ mactual @ X1) 274.84/35.47 | ~ (mrel @ X0 @ X2))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl174, '4'])). 274.84/35.47 thf(zip_derived_cl176, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : $i, X4 : $i, X5 : $i, 274.84/35.47 X7 : mworld]: 274.84/35.47 ( (((mrel @ X2 @ X7) => (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X4 @ X5)) @ 274.84/35.47 (mbox @ (qmltpeq @ X5 @ X3))) @ 274.84/35.47 (mbox @ (qmltpeq @ X4 @ X3)) @ X7))) 274.84/35.47 | ~ (mrel @ X0 @ X2) 274.84/35.47 | ~ (mrel @ mactual @ X1) 274.84/35.47 | ~ (mrel @ X1 @ X0))), 274.84/35.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl175])). 274.84/35.47 thf(zip_derived_cl177, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : $i, X4 : $i, X5 : $i, 274.84/35.47 X7 : mworld]: 274.84/35.47 (~ (mrel @ X2 @ X7) 274.84/35.47 | (mimplies @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ X4 @ X5)) @ 274.84/35.47 (mbox @ (qmltpeq @ X5 @ X3))) @ 274.84/35.47 (mbox @ (qmltpeq @ X4 @ X3)) @ X7) 274.84/35.47 | ~ (mrel @ X1 @ X0) 274.84/35.47 | ~ (mrel @ mactual @ X1) 274.84/35.47 | ~ (mrel @ X0 @ X2))), 274.84/35.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl176])). 274.84/35.47 thf(mimplies_def, axiom, (mimplies @ X0 @ X1 @ X2) => 274.84/35.47 ((((X0 @ X2) => (X1 @ X2))) = ($true))). 274.84/35.47 thf('9', plain, 274.84/35.47 (![X0:( mworld > $o ),X1:( mworld > $o ),X2:mworld]: 274.84/35.47 ( ( mimplies @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) => ( X1 @ X2 ) ) )), 274.84/35.47 inference('rw.lit', [status(esa)], [mimplies_def])). 274.84/35.47 thf(zip_derived_cl178, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : mworld, X4 : $i, X5 : $i, 274.84/35.47 X6 : $i]: 274.84/35.47 ( (((mand @ (mbox @ (qmltpeq @ X5 @ X6)) @ 274.84/35.47 (mbox @ (qmltpeq @ X6 @ X4)) @ X3) => (mbox @ 274.84/35.47 (qmltpeq @ X5 @ X4) @ X3))) 274.84/35.47 | ~ (mrel @ X1 @ X0) 274.84/35.47 | ~ (mrel @ mactual @ X2) 274.84/35.47 | ~ (mrel @ X2 @ X1) 274.84/35.47 | ~ (mrel @ X0 @ X3))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl177, '9'])). 274.84/35.47 thf(zip_derived_cl179, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : mworld, X4 : $i, X5 : $i, 274.84/35.47 X6 : $i]: 274.84/35.47 (~ (mand @ (mbox @ (qmltpeq @ X5 @ X6)) @ 274.84/35.47 (mbox @ (qmltpeq @ X6 @ X4)) @ X3) 274.84/35.47 | (mbox @ (qmltpeq @ X5 @ X4) @ X3) 274.84/35.47 | ~ (mrel @ X0 @ X3) 274.84/35.47 | ~ (mrel @ X2 @ X1) 274.84/35.47 | ~ (mrel @ mactual @ X2) 274.84/35.47 | ~ (mrel @ X1 @ X0))), 274.84/35.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl178])). 274.84/35.47 thf(zip_derived_cl180, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : mworld, X4 : $i, X5 : $i, 274.84/35.47 X6 : $i]: 274.84/35.47 (~ (((mbox @ (qmltpeq @ X5 @ X6) @ X3) & (mbox @ 274.84/35.47 (qmltpeq @ X6 @ X4) @ X3))) 274.84/35.47 | ~ (mrel @ X1 @ X0) 274.84/35.47 | ~ (mrel @ mactual @ X2) 274.84/35.47 | ~ (mrel @ X2 @ X1) 274.84/35.47 | ~ (mrel @ X0 @ X3) 274.84/35.47 | (mbox @ (qmltpeq @ X5 @ X4) @ X3))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl179, '7'])). 274.84/35.47 thf(zip_derived_cl181, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : mworld, X4 : $i, X5 : $i, 274.84/35.47 X6 : $i]: 274.84/35.47 ( (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X0 @ Y0) => (qmltpeq @ X6 @ X4 @ Y0)))))) 274.84/35.47 | ~ (mrel @ X1 @ X0) 274.84/35.47 | ~ (mrel @ X3 @ X2) 274.84/35.47 | ~ (mrel @ mactual @ X3) 274.84/35.47 | ~ (mrel @ X2 @ X1) 274.84/35.47 | ~ (((mbox @ (qmltpeq @ X6 @ X5) @ X0) & (mbox @ 274.84/35.47 (qmltpeq @ X5 @ X4) @ X0))))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl180, '4'])). 274.84/35.47 thf(zip_derived_cl182, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : mworld, X4 : $i, X5 : $i, 274.84/35.47 X6 : $i, X8 : mworld]: 274.84/35.47 ( (((mrel @ X0 @ X8) => (qmltpeq @ X6 @ X4 @ X8))) 274.84/35.47 | ~ (((mbox @ (qmltpeq @ X6 @ X5) @ X0) & (mbox @ 274.84/35.47 (qmltpeq @ X5 @ X4) @ X0))) 274.84/35.47 | ~ (mrel @ X2 @ X1) 274.84/35.47 | ~ (mrel @ mactual @ X3) 274.84/35.47 | ~ (mrel @ X3 @ X2) 274.84/35.47 | ~ (mrel @ X1 @ X0))), 274.84/35.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl181])). 274.84/35.47 thf(zip_derived_cl183, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : mworld, X4 : $i, X5 : $i, 274.84/35.47 X6 : $i, X8 : mworld]: 274.84/35.47 (~ (mrel @ X0 @ X8) 274.84/35.47 | (qmltpeq @ X6 @ X4 @ X8) 274.84/35.47 | ~ (mrel @ X1 @ X0) 274.84/35.47 | ~ (mrel @ X3 @ X2) 274.84/35.47 | ~ (mrel @ mactual @ X3) 274.84/35.47 | ~ (mrel @ X2 @ X1) 274.84/35.47 | ~ (((mbox @ (qmltpeq @ X6 @ X5) @ X0) & (mbox @ 274.84/35.47 (qmltpeq @ X5 @ X4) @ X0))))), 274.84/35.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl182])). 274.84/35.47 thf(zip_derived_cl184, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : mworld, X4 : $i, X5 : $i, 274.84/35.47 X6 : $i, X8 : mworld]: 274.84/35.47 (~ (mbox @ (qmltpeq @ X6 @ X5) @ X0) 274.84/35.47 | ~ (mbox @ (qmltpeq @ X5 @ X4) @ X0) 274.84/35.47 | ~ (mrel @ X2 @ X1) 274.84/35.47 | ~ (mrel @ mactual @ X3) 274.84/35.47 | ~ (mrel @ X3 @ X2) 274.84/35.47 | ~ (mrel @ X1 @ X0) 274.84/35.47 | (qmltpeq @ X6 @ X4 @ X8) 274.84/35.47 | ~ (mrel @ X0 @ X8))), 274.84/35.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl183])). 274.84/35.47 thf(zip_derived_cl185, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : $i, X3 : $i, X4 : mworld, X5 : mworld, 274.84/35.47 X6 : mworld, X7 : $i]: 274.84/35.47 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X1 @ Y0) => (qmltpeq @ X3 @ X7 @ Y0)))))) 274.84/35.47 | ~ (mrel @ X1 @ X0) 274.84/35.47 | (qmltpeq @ X3 @ X2 @ X0) 274.84/35.47 | ~ (mrel @ X4 @ X1) 274.84/35.47 | ~ (mrel @ X6 @ X5) 274.84/35.47 | ~ (mrel @ mactual @ X6) 274.84/35.47 | ~ (mrel @ X5 @ X4) 274.84/35.47 | ~ (mbox @ (qmltpeq @ X7 @ X2) @ X1))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl184, '1'])). 274.84/35.47 thf(zip_derived_cl186, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : mworld, X4 : mworld, 274.84/35.47 X5 : $i, X6 : $i, X7 : $i]: 274.84/35.47 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X3 @ Y0) => (qmltpeq @ X7 @ X5 @ Y0)))))) 274.84/35.47 | ~ (mrel @ X1 @ X0) 274.84/35.47 | ~ (mrel @ mactual @ X2) 274.84/35.47 | ~ (mrel @ X2 @ X1) 274.84/35.47 | ~ (mrel @ X0 @ X3) 274.84/35.47 | (qmltpeq @ X6 @ X5 @ X4) 274.84/35.47 | ~ (mrel @ X3 @ X4) 274.84/35.47 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl185, '1'])). 274.84/35.47 thf(zip_derived_cl187, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : mworld, X4 : mworld, 274.84/35.47 X5 : $i, X6 : $i, X7 : $i]: 274.84/35.47 (~ (((mrel @ X3 @ ('#sk1' @ X3 @ X5 @ X7)) => (qmltpeq @ X7 @ X5 @ 274.84/35.47 ('#sk1' @ X3 @ X5 @ X7)))) 274.84/35.47 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))) 274.84/35.47 | ~ (mrel @ X3 @ X4) 274.84/35.47 | (qmltpeq @ X6 @ X5 @ X4) 274.84/35.47 | ~ (mrel @ X0 @ X3) 274.84/35.47 | ~ (mrel @ X2 @ X1) 274.84/35.47 | ~ (mrel @ mactual @ X2) 274.84/35.47 | ~ (mrel @ X1 @ X0))), 274.84/35.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl186])). 274.84/35.47 thf(zip_derived_cl188, plain, 274.84/35.47 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : mworld, X4 : mworld, 274.84/35.47 X5 : $i, X6 : $i, X7 : $i]: 274.84/35.47 ( (mrel @ X3 @ ('#sk1' @ X3 @ X5 @ X7)) 274.84/35.47 | ~ (mrel @ X1 @ X0) 274.84/35.47 | ~ (mrel @ mactual @ X2) 274.84/35.47 | ~ (mrel @ X2 @ X1) 274.84/35.47 | ~ (mrel @ X0 @ X3) 274.84/35.47 | (qmltpeq @ X6 @ X5 @ X4) 274.84/35.47 | ~ (mrel @ X3 @ X4) 274.84/35.47 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl187])). 274.84/35.47 thf(zip_derived_cl190, plain, 274.84/35.47 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.47 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.47 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.47 define([status(thm)])). 274.84/35.47 thf(zip_derived_cl880, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.47 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.47 X0) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.47 inference('renaming', [status(thm)], 274.84/35.47 [zip_derived_cl869, zip_derived_cl256, zip_derived_cl190])). 274.84/35.47 thf(zip_derived_cl891, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (((mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ X0) & (mand @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0))) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl880, '7'])). 274.84/35.47 thf(zip_derived_cl906, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ X0) 274.84/35.47 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl891])). 274.84/35.47 thf(zip_derived_cl921, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ 274.84/35.47 Y0)))))) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.47 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl906, '1'])). 274.84/35.47 thf(zip_derived_cl256, plain, 274.84/35.47 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.47 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.47 | (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.47 define([status(thm)])). 274.84/35.47 thf(zip_derived_cl190, plain, 274.84/35.47 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.47 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.47 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.47 define([status(thm)])). 274.84/35.47 thf(zip_derived_cl940, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.47 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ X0) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.47 inference('renaming', [status(thm)], 274.84/35.47 [zip_derived_cl921, zip_derived_cl256, zip_derived_cl190])). 274.84/35.47 thf(zip_derived_cl962, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (((mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ X0) & (mbox @ 274.84/35.47 (qmltpeq @ (op @ e3 @ e3) @ e2) @ X0))) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl940, '7'])). 274.84/35.47 thf(zip_derived_cl985, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ X0) 274.84/35.47 | ~ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ X0) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl962])). 274.84/35.47 thf(zip_derived_cl1012, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ 274.84/35.47 Y0)))))) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.47 | ~ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ X0))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl985, '1'])). 274.84/35.47 thf(zip_derived_cl256, plain, 274.84/35.47 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.47 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.47 | (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.47 define([status(thm)])). 274.84/35.47 thf(zip_derived_cl190, plain, 274.84/35.47 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.47 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.47 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.47 define([status(thm)])). 274.84/35.47 thf(zip_derived_cl1037, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.47 | ~ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ X0) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.47 inference('renaming', [status(thm)], 274.84/35.47 [zip_derived_cl1012, zip_derived_cl256, zip_derived_cl190])). 274.84/35.47 thf(zip_derived_cl1070, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ 274.84/35.47 Y0)))))) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl1037, '1'])). 274.84/35.47 thf(zip_derived_cl256, plain, 274.84/35.47 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.47 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.47 | (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.47 define([status(thm)])). 274.84/35.47 thf(zip_derived_cl190, plain, 274.84/35.47 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.47 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.47 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.47 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.47 define([status(thm)])). 274.84/35.47 thf(zip_derived_cl1099, plain, 274.84/35.47 (![X0 : mworld]: 274.84/35.47 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.47 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.47 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.47 inference('renaming', [status(thm)], 274.84/35.47 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.47 thf(zip_derived_cl808, plain, 274.84/35.47 ( (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))) @ 274.84/35.47 '#sk3')), 274.84/35.47 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl806])). 274.84/35.47 thf(mor_def, axiom, (mor @ X0 @ X1 @ X2) => 274.84/35.47 ((((X1 @ X2) | (X0 @ X2))) = ($true))). 274.84/35.47 thf('10', plain, 274.84/35.47 (![X0:( mworld > $o ),X1:( mworld > $o ),X2:mworld]: 274.84/35.47 ( ( mor @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) | ( X1 @ X2 ) ) )), 274.84/35.47 inference('rw.lit', [status(esa)], [mor_def])). 274.84/35.47 thf(zip_derived_cl810, plain, 274.84/35.47 ( (((mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 274.84/35.47 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @ 274.84/35.47 '#sk3')))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl808, '10'])). 274.84/35.47 thf(zip_derived_cl812, plain, 274.84/35.47 (( (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ 274.84/35.47 (mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))) @ 274.84/35.47 '#sk3') 274.84/35.47 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @ 274.84/35.47 '#sk3'))), 274.84/35.47 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl810])). 274.84/35.47 thf(zip_derived_cl814, plain, 274.84/35.47 (( (((mor @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.47 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.47 '#sk3'))) 274.84/35.47 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.47 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @ 274.84/35.47 '#sk3'))), 274.84/35.47 inference('rw_clause', [status(thm)], [zip_derived_cl812, '10'])). 274.84/35.47 thf(zip_derived_cl816, plain, 274.84/35.47 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.47 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0) @ '#sk3'))) 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl814, '3'])). 274.84/35.48 thf(zip_derived_cl818, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl816])). 274.84/35.48 thf(zip_derived_cl822, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e1 @ e1) @ e0) @ '#sk3'))) 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl818, '3'])). 274.84/35.48 thf(zip_derived_cl826, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ '#sk3') 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl822])). 274.84/35.48 thf(zip_derived_cl832, plain, 274.84/35.48 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e2 @ e2) @ e0) @ '#sk3'))) 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl826, '3'])). 274.84/35.48 thf(zip_derived_cl839, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0) @ '#sk3') 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl832])). 274.84/35.48 thf(zip_derived_cl847, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.48 e0 @ Y0)))))) 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl839, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl855, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl847, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl864, plain, 274.84/35.48 (( (mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl855])). 274.84/35.48 thf(zip_derived_cl873, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl864, '10'])). 274.84/35.48 thf(zip_derived_cl884, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl873, '3'])). 274.84/35.48 thf(zip_derived_cl896, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl884])). 274.84/35.48 thf(zip_derived_cl911, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl896, '3'])). 274.84/35.48 thf(zip_derived_cl927, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl911])). 274.84/35.48 thf(zip_derived_cl946, plain, 274.84/35.48 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl927, '3'])). 274.84/35.48 thf(zip_derived_cl970, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl946])). 274.84/35.48 thf(zip_derived_cl993, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl970, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1019, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl993, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl1045, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1019])). 274.84/35.48 thf(zip_derived_cl1077, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1045, '3'])). 274.84/35.48 thf(zip_derived_cl827, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0) @ '#sk3') 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl822])). 274.84/35.48 thf(zip_derived_cl833, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.48 e0 @ Y0)))))) 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl827, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl840, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl833, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl848, plain, 274.84/35.48 (( (mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl840])). 274.84/35.48 thf(zip_derived_cl856, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl848, '10'])). 274.84/35.48 thf(zip_derived_cl865, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl856, '3'])). 274.84/35.48 thf(zip_derived_cl875, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl865])). 274.84/35.48 thf(zip_derived_cl886, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl875, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl900, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl886, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl915, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl900])). 274.84/35.48 thf(zip_derived_cl933, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl915, '3'])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1108, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1077, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl1144, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1108, '3'])). 274.84/35.48 thf(zip_derived_cl1177, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1144])). 274.84/35.48 thf(zip_derived_cl1214, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1177, '3'])). 274.84/35.48 thf(zip_derived_cl1244, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1214])). 274.84/35.48 thf(zip_derived_cl1272, plain, 274.84/35.48 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1244, '3'])). 274.84/35.48 thf(zip_derived_cl1291, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1272])). 274.84/35.48 thf(zip_derived_cl1306, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1291, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1314, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1306, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl191, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ (((mrel @ X3 @ ('#sk1' @ X3 @ X7 @ X6)) => (qmltpeq @ X6 @ X7 @ 274.84/35.48 ('#sk1' @ X3 @ X7 @ X6)))) 274.84/35.48 | ('#form2' @ X3 @ X6 @ X7))), 274.84/35.48 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl194, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( (mrel @ X3 @ ('#sk1' @ X3 @ X7 @ X6)) | ('#form2' @ X3 @ X6 @ X7))), 274.84/35.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl953, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl977, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e1 @ e1) @ e3) @ '#sk3'))) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl953, '3'])). 274.84/35.48 thf(zip_derived_cl1001, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ '#sk3') 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl977])). 274.84/35.48 thf(zip_derived_cl1027, plain, 274.84/35.48 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e2 @ e2) @ e3) @ '#sk3'))) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1001, '3'])). 274.84/35.48 thf(zip_derived_cl1057, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3) @ '#sk3') | ~ ('#form4'))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1027])). 274.84/35.48 thf(zip_derived_cl1088, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.48 e3 @ Y0)))))) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1057, '4'])). 274.84/35.48 thf(zip_derived_cl1125, plain, 274.84/35.48 (![X2 : mworld]: 274.84/35.48 ( (((mrel @ '#sk3' @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X2))) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1088])). 274.84/35.48 thf(zip_derived_cl1158, plain, 274.84/35.48 (![X2 : mworld]: 274.84/35.48 (~ (mrel @ '#sk3' @ X2) 274.84/35.48 | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X2) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1125])). 274.84/35.48 thf(zip_derived_cl195, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ (qmltpeq @ X6 @ X7 @ ('#sk1' @ X3 @ X7 @ X6)) 274.84/35.48 | ('#form2' @ X3 @ X6 @ X7))), 274.84/35.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])). 274.84/35.48 thf(zip_derived_cl4468, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form4') 274.84/35.48 | ~ (mrel @ '#sk3' @ ('#sk1' @ X0 @ e3 @ (op @ e2 @ e2))) 274.84/35.48 | ('#form2' @ X0 @ (op @ e2 @ e2) @ e3))), 274.84/35.48 inference('sup-', [status(thm)], [zip_derived_cl1158, zip_derived_cl195])). 274.84/35.48 thf(zip_derived_cl5000, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e3) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e3) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('sup-', [status(thm)], [zip_derived_cl194, zip_derived_cl4468])). 274.84/35.48 thf(zip_derived_cl5006, plain, 274.84/35.48 ((~ ('#form4') | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e3))), 274.84/35.48 inference('simplify', [status(thm)], [zip_derived_cl5000])). 274.84/35.48 thf(zip_derived_cl842, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 X0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl835])). 274.84/35.48 thf(zip_derived_cl850, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ X0) & (mand @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 X0))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl842, '7'])). 274.84/35.48 thf(zip_derived_cl859, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ X0) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 X0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl850])). 274.84/35.48 thf(zip_derived_cl868, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ 274.84/35.48 Y0)))))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 X0))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl859, '1'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl879, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e3) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 X0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl868, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl890, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3) @ X0) & (mand @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e3))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl879, '7'])). 274.84/35.48 thf(zip_derived_cl905, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3) @ X0) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e3) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl890])). 274.84/35.48 thf(zip_derived_cl920, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ 274.84/35.48 Y0)))))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e3) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl905, '1'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl939, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e3) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)) @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e3) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl920, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl961, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3) @ X0) & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e3 @ e3) @ e3) @ X0))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e3) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e3))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl939, '7'])). 274.84/35.48 thf(zip_derived_cl984, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3) @ X0) 274.84/35.48 | ~ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3) @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e3) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e3) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl961])). 274.84/35.48 thf(zip_derived_cl1011, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ 274.84/35.48 Y0)))))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e3) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e3) 274.84/35.48 | ~ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3) @ X0))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl984, '1'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1036, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e3) 274.84/35.48 | ~ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3) @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e3) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e3) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1011, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl1069, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ 274.84/35.48 Y0)))))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e3) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e3) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e3))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1036, '1'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1098, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e3) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e3) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e3) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e3) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1069, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl194, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( (mrel @ X3 @ ('#sk1' @ X3 @ X7 @ X6)) | ('#form2' @ X3 @ X6 @ X7))), 274.84/35.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])). 274.84/35.48 thf(zip_derived_cl1056, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3) @ '#sk3') | ~ ('#form4'))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1027])). 274.84/35.48 thf(zip_derived_cl1087, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.48 e3 @ Y0)))))) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1056, '4'])). 274.84/35.48 thf(zip_derived_cl1124, plain, 274.84/35.48 (![X2 : mworld]: 274.84/35.48 ( (((mrel @ '#sk3' @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X2))) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1087])). 274.84/35.48 thf(zip_derived_cl1157, plain, 274.84/35.48 (![X2 : mworld]: 274.84/35.48 (~ (mrel @ '#sk3' @ X2) 274.84/35.48 | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X2) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1124])). 274.84/35.48 thf(zip_derived_cl195, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ (qmltpeq @ X6 @ X7 @ ('#sk1' @ X3 @ X7 @ X6)) 274.84/35.48 | ('#form2' @ X3 @ X6 @ X7))), 274.84/35.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])). 274.84/35.48 thf(zip_derived_cl4436, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form4') 274.84/35.48 | ~ (mrel @ '#sk3' @ ('#sk1' @ X0 @ e3 @ (op @ e3 @ e3))) 274.84/35.48 | ('#form2' @ X0 @ (op @ e3 @ e3) @ e3))), 274.84/35.48 inference('sup-', [status(thm)], [zip_derived_cl1157, zip_derived_cl195])). 274.84/35.48 thf(zip_derived_cl4948, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e3) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e3) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('sup-', [status(thm)], [zip_derived_cl194, zip_derived_cl4436])). 274.84/35.48 thf(zip_derived_cl4954, plain, 274.84/35.48 ((~ ('#form4') | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e3))), 274.84/35.48 inference('simplify', [status(thm)], [zip_derived_cl4948])). 274.84/35.48 thf(zip_derived_cl4959, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e3) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e3) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e3) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl1098, zip_derived_cl4954])). 274.84/35.48 thf(mrel_reflexive, axiom, (![W:mworld]: ( mrel @ W @ W ))). 274.84/35.48 thf(zip_derived_cl10, plain, 274.84/35.48 ( (((!!) @ (^[Y0 : mworld]: (mrel @ Y0 @ Y0))))), 274.84/35.48 inference('cnf', [status(esa)], [mrel_reflexive])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl4962, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e3) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e3) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e3) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl4959, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl194, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( (mrel @ X3 @ ('#sk1' @ X3 @ X7 @ X6)) | ('#form2' @ X3 @ X6 @ X7))), 274.84/35.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])). 274.84/35.48 thf(zip_derived_cl954, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3') | ~ ('#form4'))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl978, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e3 @ Y0)))))) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl954, '4'])). 274.84/35.48 thf(zip_derived_cl1003, plain, 274.84/35.48 (![X2 : mworld]: 274.84/35.48 ( (((mrel @ '#sk3' @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl978])). 274.84/35.48 thf(zip_derived_cl1029, plain, 274.84/35.48 (![X2 : mworld]: 274.84/35.48 (~ (mrel @ '#sk3' @ X2) 274.84/35.48 | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1003])). 274.84/35.48 thf(zip_derived_cl195, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ (qmltpeq @ X6 @ X7 @ ('#sk1' @ X3 @ X7 @ X6)) 274.84/35.48 | ('#form2' @ X3 @ X6 @ X7))), 274.84/35.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])). 274.84/35.48 thf(zip_derived_cl4352, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form4') 274.84/35.48 | ~ (mrel @ '#sk3' @ ('#sk1' @ X0 @ e3 @ (op @ e0 @ e0))) 274.84/35.48 | ('#form2' @ X0 @ (op @ e0 @ e0) @ e3))), 274.84/35.48 inference('sup-', [status(thm)], [zip_derived_cl1029, zip_derived_cl195])). 274.84/35.48 thf(zip_derived_cl4876, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e3) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e3) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('sup-', [status(thm)], [zip_derived_cl194, zip_derived_cl4352])). 274.84/35.48 thf(zip_derived_cl4882, plain, 274.84/35.48 ((~ ('#form4') | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e3))), 274.84/35.48 inference('simplify', [status(thm)], [zip_derived_cl4876])). 274.84/35.48 thf(zip_derived_cl4974, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e3) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e3))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl4962, zip_derived_cl4882])). 274.84/35.48 thf(zip_derived_cl194, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( (mrel @ X3 @ ('#sk1' @ X3 @ X7 @ X6)) | ('#form2' @ X3 @ X6 @ X7))), 274.84/35.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])). 274.84/35.48 thf(zip_derived_cl1002, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3) @ '#sk3') | ~ ('#form4'))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl977])). 274.84/35.48 thf(zip_derived_cl1028, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.48 e3 @ Y0)))))) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1002, '4'])). 274.84/35.48 thf(zip_derived_cl1058, plain, 274.84/35.48 (![X2 : mworld]: 274.84/35.48 ( (((mrel @ '#sk3' @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2))) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1028])). 274.84/35.48 thf(zip_derived_cl1089, plain, 274.84/35.48 (![X2 : mworld]: 274.84/35.48 (~ (mrel @ '#sk3' @ X2) 274.84/35.48 | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1058])). 274.84/35.48 thf(zip_derived_cl195, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ (qmltpeq @ X6 @ X7 @ ('#sk1' @ X3 @ X7 @ X6)) 274.84/35.48 | ('#form2' @ X3 @ X6 @ X7))), 274.84/35.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])). 274.84/35.48 thf(zip_derived_cl4404, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form4') 274.84/35.48 | ~ (mrel @ '#sk3' @ ('#sk1' @ X0 @ e3 @ (op @ e1 @ e1))) 274.84/35.48 | ('#form2' @ X0 @ (op @ e1 @ e1) @ e3))), 274.84/35.48 inference('sup-', [status(thm)], [zip_derived_cl1089, zip_derived_cl195])). 274.84/35.48 thf(zip_derived_cl4916, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e3) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e3) 274.84/35.48 | ~ ('#form4'))), 274.84/35.48 inference('sup-', [status(thm)], [zip_derived_cl194, zip_derived_cl4404])). 274.84/35.48 thf(zip_derived_cl4922, plain, 274.84/35.48 ((~ ('#form4') | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e3))), 274.84/35.48 inference('simplify', [status(thm)], [zip_derived_cl4916])). 274.84/35.48 thf(zip_derived_cl4975, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e3) | ~ ('#form4'))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl4974, zip_derived_cl4922])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5620, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1314, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl821, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0)))) @ 274.84/35.48 X0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl817])). 274.84/35.48 thf(zip_derived_cl825, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0) @ X0) & (mand @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ 274.84/35.48 X0))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl821, '7'])). 274.84/35.48 thf(zip_derived_cl831, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0) @ X0) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ 274.84/35.48 X0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl825])). 274.84/35.48 thf(zip_derived_cl837, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ 274.84/35.48 Y0)))))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ 274.84/35.48 X0))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl831, '1'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl845, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))) @ 274.84/35.48 X0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl837, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl853, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0) @ X0) & (mand @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl845, '7'])). 274.84/35.48 thf(zip_derived_cl862, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0) @ X0) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl853])). 274.84/35.48 thf(zip_derived_cl871, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ 274.84/35.48 Y0)))))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl862, '1'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl882, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0)) @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl871, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl893, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0) @ X0) & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e3 @ e3) @ e0) @ X0))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl882, '7'])). 274.84/35.48 thf(zip_derived_cl908, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0) @ X0) 274.84/35.48 | ~ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0) @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl893])). 274.84/35.48 thf(zip_derived_cl923, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ 274.84/35.48 Y0)))))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0) @ X0))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl908, '1'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl942, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ~ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0) @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl923, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl964, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ 274.84/35.48 Y0)))))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl942, '1'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl987, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl964, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl1099, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl838, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0) @ '#sk3') 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl832])). 274.84/35.48 thf(zip_derived_cl846, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.48 e0 @ Y0)))))) 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl838, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl854, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl846, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl863, plain, 274.84/35.48 (( (mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl854])). 274.84/35.48 thf(zip_derived_cl872, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl863, '10'])). 274.84/35.48 thf(zip_derived_cl883, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl872, '3'])). 274.84/35.48 thf(zip_derived_cl894, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl883])). 274.84/35.48 thf(zip_derived_cl909, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl894, '3'])). 274.84/35.48 thf(zip_derived_cl924, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl909])). 274.84/35.48 thf(zip_derived_cl943, plain, 274.84/35.48 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl924, '3'])). 274.84/35.48 thf(zip_derived_cl966, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl943])). 274.84/35.48 thf(zip_derived_cl989, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl966, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1015, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl989, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl1040, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1015])). 274.84/35.48 thf(zip_derived_cl1072, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1040, '3'])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1101, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1072, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl1138, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1101, '3'])). 274.84/35.48 thf(zip_derived_cl1167, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1138])). 274.84/35.48 thf(zip_derived_cl1206, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1167, '3'])). 274.84/35.48 thf(zip_derived_cl1233, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1206])). 274.84/35.48 thf(zip_derived_cl1266, plain, 274.84/35.48 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1233, '3'])). 274.84/35.48 thf(zip_derived_cl1283, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1266])). 274.84/35.48 thf(zip_derived_cl1302, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1283, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1310, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1302, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5580, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1310, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5582, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl5580])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl5585, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl5582, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl987, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl964, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl830, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 X0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl824])). 274.84/35.48 thf(zip_derived_cl836, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ X0) & (mand @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 274.84/35.48 X0))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl830, '7'])). 274.84/35.48 thf(zip_derived_cl844, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ X0) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 274.84/35.48 X0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl836])). 274.84/35.48 thf(zip_derived_cl852, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ 274.84/35.48 Y0)))))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 274.84/35.48 X0))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl844, '1'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl861, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 274.84/35.48 X0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl852, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl870, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ X0) & (mand @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl861, '7'])). 274.84/35.48 thf(zip_derived_cl881, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ X0) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl870])). 274.84/35.48 thf(zip_derived_cl892, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ 274.84/35.48 Y0)))))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl881, '1'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl907, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl892, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl922, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ X0) & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e3 @ e3) @ e1) @ X0))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl907, '7'])). 274.84/35.48 thf(zip_derived_cl941, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ X0) 274.84/35.48 | ~ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl922])). 274.84/35.48 thf(zip_derived_cl963, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ 274.84/35.48 Y0)))))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ X0))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl941, '1'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl986, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ~ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl963, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl1013, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X0 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ 274.84/35.48 Y0)))))) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl986, '1'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1038, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1013, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl965, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl943])). 274.84/35.48 thf(zip_derived_cl988, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl965, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1014, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl988, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl1039, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1014])). 274.84/35.48 thf(zip_derived_cl1071, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1039, '3'])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1100, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1071, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl1137, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1100, '3'])). 274.84/35.48 thf(zip_derived_cl1166, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1137])). 274.84/35.48 thf(zip_derived_cl1205, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1166, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1232, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1205, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5152, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1232, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5154, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl5152])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl5157, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl5154, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl987, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl964, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl895, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl883])). 274.84/35.48 thf(zip_derived_cl910, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl895, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl926, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl910, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl945, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl926])). 274.84/35.48 thf(zip_derived_cl968, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl945, '3'])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl991, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl968, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl1017, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl991, '3'])). 274.84/35.48 thf(zip_derived_cl1043, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1017])). 274.84/35.48 thf(zip_derived_cl1075, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1043, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1106, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1075, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5015, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1106, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5064, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl987, zip_derived_cl5015])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl5067, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl5064, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl819, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0) @ '#sk3') 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl816])). 274.84/35.48 thf(zip_derived_cl823, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e0 @ Y0)))))) 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl819, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl828, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | (((mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl823, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl834, plain, 274.84/35.48 (( (mor @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl828])). 274.84/35.48 thf(zip_derived_cl841, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl834, '10'])). 274.84/35.48 thf(zip_derived_cl849, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl841, '3'])). 274.84/35.48 thf(zip_derived_cl858, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl849])). 274.84/35.48 thf(zip_derived_cl867, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl858, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl878, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl867, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl889, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl878])). 274.84/35.48 thf(zip_derived_cl904, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl889, '3'])). 274.84/35.48 thf(zip_derived_cl919, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl904, '3'])). 274.84/35.48 thf(zip_derived_cl938, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl919])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl960, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl938, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl983, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl960, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1010, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl983, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5011, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1010, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5708, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5067, zip_derived_cl5011])). 274.84/35.48 thf(zip_derived_cl897, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl884])). 274.84/35.48 thf(zip_derived_cl912, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl897, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl929, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl912, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl948, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl929])). 274.84/35.48 thf(zip_derived_cl972, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl948, '3'])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl995, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl972, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl1021, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl995, '3'])). 274.84/35.48 thf(zip_derived_cl1048, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1021])). 274.84/35.48 thf(zip_derived_cl1080, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1048, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1113, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1080, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5016, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1113, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5709, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5708, zip_derived_cl5016])). 274.84/35.48 thf(zip_derived_cl933, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl915, '3'])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl955, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl933, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl976, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl955, '3'])). 274.84/35.48 thf(zip_derived_cl1000, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl976])). 274.84/35.48 thf(zip_derived_cl1026, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1000, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1055, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1026, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5012, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1055, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5710, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5709, zip_derived_cl5012])). 274.84/35.48 thf(zip_derived_cl6114, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5157, zip_derived_cl5710])). 274.84/35.48 thf(zip_derived_cl1168, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1138])). 274.84/35.48 thf(zip_derived_cl1207, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1168, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1235, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1207, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5177, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1235, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl6115, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6114, zip_derived_cl5177])). 274.84/35.48 thf(zip_derived_cl925, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl909])). 274.84/35.48 thf(zip_derived_cl944, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl925, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl967, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl944, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl990, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl967])). 274.84/35.48 thf(zip_derived_cl1016, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl990, '3'])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1041, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1016, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl1073, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1041, '3'])). 274.84/35.48 thf(zip_derived_cl1103, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1073])). 274.84/35.48 thf(zip_derived_cl1140, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1103, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1171, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1140, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5024, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1171, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl6116, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6115, zip_derived_cl5024])). 274.84/35.48 thf(zip_derived_cl6118, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl987, zip_derived_cl6116])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl6121, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl6118, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl1038, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1013, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl857, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl849])). 274.84/35.48 thf(zip_derived_cl866, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl857, '3'])). 274.84/35.48 thf(zip_derived_cl876, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl866])). 274.84/35.48 thf(zip_derived_cl887, plain, 274.84/35.48 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl876, '3'])). 274.84/35.48 thf(zip_derived_cl901, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl887])). 274.84/35.48 thf(zip_derived_cl916, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl901, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl934, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl916, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl956, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl934])). 274.84/35.48 thf(zip_derived_cl979, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl956, '3'])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1004, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl979, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl1030, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1004, '3'])). 274.84/35.48 thf(zip_derived_cl1060, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1030])). 274.84/35.48 thf(zip_derived_cl1091, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1060, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1128, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1091, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5019, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1128, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5073, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl5019])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl5076, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl5073, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl5710, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5709, zip_derived_cl5012])). 274.84/35.48 thf(zip_derived_cl6026, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5076, zip_derived_cl5710])). 274.84/35.48 thf(zip_derived_cl902, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl887])). 274.84/35.48 thf(zip_derived_cl917, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl902, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl935, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl917, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl957, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl935])). 274.84/35.48 thf(zip_derived_cl980, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl957, '3'])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1005, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl980, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl1031, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1005, '3'])). 274.84/35.48 thf(zip_derived_cl1062, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1031])). 274.84/35.48 thf(zip_derived_cl1093, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1062, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1131, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1093, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5020, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1131, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl6027, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6026, zip_derived_cl5020])). 274.84/35.48 thf(zip_derived_cl1099, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl877, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl866])). 274.84/35.48 thf(zip_derived_cl888, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl877, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl903, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl888, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl918, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl903])). 274.84/35.48 thf(zip_derived_cl936, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl918, '3'])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl958, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl936, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl981, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl958, '3'])). 274.84/35.48 thf(zip_derived_cl1006, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl981])). 274.84/35.48 thf(zip_derived_cl1032, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1006, '3'])). 274.84/35.48 thf(zip_derived_cl1063, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1032])). 274.84/35.48 thf(zip_derived_cl1094, plain, 274.84/35.48 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1063, '3'])). 274.84/35.48 thf(zip_derived_cl1132, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1094])). 274.84/35.48 thf(zip_derived_cl1163, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1132, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1202, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1163, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5054, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1202, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5056, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl5054])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl5059, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl5056, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl1007, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl981])). 274.84/35.48 thf(zip_derived_cl1033, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1007, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1065, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1033, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5013, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1065, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5696, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5059, zip_derived_cl5013])). 274.84/35.48 thf(zip_derived_cl1133, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1094])). 274.84/35.48 thf(zip_derived_cl1164, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1133, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1203, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1164, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5071, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1203, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5697, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5696, zip_derived_cl5071])). 274.84/35.48 thf(zip_derived_cl1064, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1032])). 274.84/35.48 thf(zip_derived_cl1095, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1064, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1134, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1095, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5021, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1134, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5698, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5697, zip_derived_cl5021])). 274.84/35.48 thf(zip_derived_cl6028, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6027, zip_derived_cl5698])). 274.84/35.48 thf(zip_derived_cl6125, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6121, zip_derived_cl6028])). 274.84/35.48 thf(zip_derived_cl1038, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1013, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl969, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl946])). 274.84/35.48 thf(zip_derived_cl992, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl969, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1018, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl992, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl1044, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1018])). 274.84/35.48 thf(zip_derived_cl1076, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1044, '3'])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1107, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1076, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl1143, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1107, '3'])). 274.84/35.48 thf(zip_derived_cl1176, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1143])). 274.84/35.48 thf(zip_derived_cl1213, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1176, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1243, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1213, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5253, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1243, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5255, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl5253])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl5258, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl5255, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl5710, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5709, zip_derived_cl5012])). 274.84/35.48 thf(zip_derived_cl7000, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5258, zip_derived_cl5710])). 274.84/35.48 thf(zip_derived_cl1178, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1144])). 274.84/35.48 thf(zip_derived_cl1215, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1178, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1246, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1215, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5262, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1246, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl7001, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl7000, zip_derived_cl5262])). 274.84/35.48 thf(zip_derived_cl928, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl911])). 274.84/35.48 thf(zip_derived_cl947, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl928, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl971, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl947, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl994, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl971])). 274.84/35.48 thf(zip_derived_cl1020, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl994, '3'])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1046, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1020, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl1078, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1046, '3'])). 274.84/35.48 thf(zip_derived_cl1110, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1078])). 274.84/35.48 thf(zip_derived_cl1146, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1110, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1181, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1146, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5026, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1181, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl6125, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6121, zip_derived_cl6028])). 274.84/35.48 thf(zip_derived_cl6131, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('sup-', [status(thm)], [zip_derived_cl5026, zip_derived_cl6125])). 274.84/35.48 thf(zip_derived_cl6138, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('simplify', [status(thm)], [zip_derived_cl6131])). 274.84/35.48 thf(zip_derived_cl874, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl865])). 274.84/35.48 thf(zip_derived_cl885, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl874, '3'])). 274.84/35.48 thf(zip_derived_cl899, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl885])). 274.84/35.48 thf(zip_derived_cl914, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl899, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl932, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl914, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl951, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl932])). 274.84/35.48 thf(zip_derived_cl975, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl951, '3'])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl998, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl975, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl1024, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl998, '3'])). 274.84/35.48 thf(zip_derived_cl1052, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1024])). 274.84/35.48 thf(zip_derived_cl1084, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1052, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1120, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1084, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5017, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1120, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl6208, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6138, zip_derived_cl5017])). 274.84/35.48 thf(zip_derived_cl7002, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl7001, zip_derived_cl6208])). 274.84/35.48 thf(zip_derived_cl7006, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl6125, zip_derived_cl7002])). 274.84/35.48 thf(zip_derived_cl7011, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('simplify', [status(thm)], [zip_derived_cl7006])). 274.84/35.48 thf(zip_derived_cl1038, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1013, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl898, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1)) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl885])). 274.84/35.48 thf(zip_derived_cl913, plain, 274.84/35.48 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl898, '3'])). 274.84/35.48 thf(zip_derived_cl930, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl913])). 274.84/35.48 thf(zip_derived_cl949, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl930, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl973, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl949, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl996, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl973])). 274.84/35.48 thf(zip_derived_cl1022, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl996, '3'])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1049, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1022, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl1081, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1049, '3'])). 274.84/35.48 thf(zip_derived_cl1115, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1081])). 274.84/35.48 thf(zip_derived_cl1150, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1115, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1187, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1150, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5028, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1187, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5187, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl5028])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl5190, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl5187, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl5710, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5709, zip_derived_cl5012])). 274.84/35.48 thf(zip_derived_cl6308, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5190, zip_derived_cl5710])). 274.84/35.48 thf(zip_derived_cl931, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1) @ '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl913])). 274.84/35.48 thf(zip_derived_cl950, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.48 e1 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl931, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl974, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl950, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl997, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl974])). 274.84/35.48 thf(zip_derived_cl1023, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl997, '3'])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1050, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1023, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl1082, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1050, '3'])). 274.84/35.48 thf(zip_derived_cl1117, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1082])). 274.84/35.48 thf(zip_derived_cl1152, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1117, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1190, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1152, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5029, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1190, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl6309, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6308, zip_derived_cl5029])). 274.84/35.48 thf(zip_derived_cl6208, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6138, zip_derived_cl5017])). 274.84/35.48 thf(zip_derived_cl6310, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6309, zip_derived_cl6208])). 274.84/35.48 thf(zip_derived_cl7015, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2)), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl7011, zip_derived_cl6310])). 274.84/35.48 thf(zip_derived_cl1245, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1214])). 274.84/35.48 thf(zip_derived_cl1273, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1245, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1293, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1273, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5480, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1293, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl1038, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1013, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl1175, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1143])). 274.84/35.48 thf(zip_derived_cl1212, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1175, '3'])). 274.84/35.48 thf(zip_derived_cl1242, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1212])). 274.84/35.48 thf(zip_derived_cl1271, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1242, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1290, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1271, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5438, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1290, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5440, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl5438])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl5443, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl5440, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl1047, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1021])). 274.84/35.48 thf(zip_derived_cl1079, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1047, '3'])). 274.84/35.48 thf(zip_derived_cl1111, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1079])). 274.84/35.48 thf(zip_derived_cl1147, plain, 274.84/35.48 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1111, '3'])). 274.84/35.48 thf(zip_derived_cl1183, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1147])). 274.84/35.48 thf(zip_derived_cl1219, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1183, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1251, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1219, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5273, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1251, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl1099, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl1182, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1147])). 274.84/35.48 thf(zip_derived_cl1218, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1182, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1250, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1218, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5264, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1250, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5266, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl5264])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl5269, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl5266, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl7015, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2)), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl7011, zip_derived_cl6310])). 274.84/35.48 thf(zip_derived_cl7494, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl5269, zip_derived_cl7015])). 274.84/35.48 thf(zip_derived_cl987, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl964, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl1042, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1017])). 274.84/35.48 thf(zip_derived_cl1074, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1042, '3'])). 274.84/35.48 thf(zip_derived_cl1105, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1074])). 274.84/35.48 thf(zip_derived_cl1142, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1105, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1174, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1142, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5025, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1174, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5170, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl987, zip_derived_cl5025])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl5173, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl5170, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl1099, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl937, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl919])). 274.84/35.48 thf(zip_derived_cl952, plain, 274.84/35.48 ((~ ('#form4') 274.84/35.48 | (((mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))) @ 274.84/35.48 '#sk3') & (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3) @ '#sk3'))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl959, plain, 274.84/35.48 (( ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3'))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl937, zip_derived_cl952])). 274.84/35.48 thf(zip_derived_cl982, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl959, '3'])). 274.84/35.48 thf(zip_derived_cl1008, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl982])). 274.84/35.48 thf(zip_derived_cl1034, plain, 274.84/35.48 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1008, '3'])). 274.84/35.48 thf(zip_derived_cl1066, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1034])). 274.84/35.48 thf(zip_derived_cl1096, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1066, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1135, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1096, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5022, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1135, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5081, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl5022])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl5084, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl5081, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl5710, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5709, zip_derived_cl5012])). 274.84/35.48 thf(zip_derived_cl6038, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5084, zip_derived_cl5710])). 274.84/35.48 thf(zip_derived_cl1067, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1034])). 274.84/35.48 thf(zip_derived_cl1097, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1067, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1136, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1097, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5023, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1136, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl6039, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6038, zip_derived_cl5023])). 274.84/35.48 thf(zip_derived_cl1009, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl982])). 274.84/35.48 thf(zip_derived_cl1035, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1009, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1068, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1035, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5014, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1068, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl6040, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6039, zip_derived_cl5014])). 274.84/35.48 thf(zip_derived_cl6236, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5173, zip_derived_cl6040])). 274.84/35.48 thf(zip_derived_cl1112, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1079])). 274.84/35.48 thf(zip_derived_cl1148, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1112, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1184, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1148, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5027, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1184, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl6237, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6236, zip_derived_cl5027])). 274.84/35.48 thf(zip_derived_cl999, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl976])). 274.84/35.48 thf(zip_derived_cl1025, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl999, '3'])). 274.84/35.48 thf(zip_derived_cl1054, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1025])). 274.84/35.48 thf(zip_derived_cl1086, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1054, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1123, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1086, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5018, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1123, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl6238, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6237, zip_derived_cl5018])). 274.84/35.48 thf(zip_derived_cl7495, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl7494, zip_derived_cl6238])). 274.84/35.48 thf(zip_derived_cl987, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl964, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl1099, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl1104, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1074])). 274.84/35.48 thf(zip_derived_cl1141, plain, 274.84/35.48 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1104, '3'])). 274.84/35.48 thf(zip_derived_cl1172, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1141])). 274.84/35.48 thf(zip_derived_cl1210, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1172, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1239, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1210, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5235, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1239, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5237, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl5235])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl5240, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl5237, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl5710, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5709, zip_derived_cl5012])). 274.84/35.48 thf(zip_derived_cl6444, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5240, zip_derived_cl5710])). 274.84/35.48 thf(zip_derived_cl1173, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1141])). 274.84/35.48 thf(zip_derived_cl1211, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1173, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1240, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1211, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5244, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1240, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl6445, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6444, zip_derived_cl5244])). 274.84/35.48 thf(zip_derived_cl6238, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6237, zip_derived_cl5018])). 274.84/35.48 thf(zip_derived_cl6446, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6445, zip_derived_cl6238])). 274.84/35.48 thf(zip_derived_cl6448, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl987, zip_derived_cl6446])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl6451, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl6448, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl6040, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6039, zip_derived_cl5014])). 274.84/35.48 thf(zip_derived_cl6455, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6451, zip_derived_cl6040])). 274.84/35.48 thf(zip_derived_cl1099, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl1053, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1025])). 274.84/35.48 thf(zip_derived_cl1085, plain, 274.84/35.48 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1053, '3'])). 274.84/35.48 thf(zip_derived_cl1121, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1085])). 274.84/35.48 thf(zip_derived_cl1155, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1121, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1194, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1155, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5031, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1194, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl5220, plain, 274.84/35.48 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl5031])). 274.84/35.48 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.48 thf(zip_derived_cl5223, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('demod', [status(thm)], [zip_derived_cl5220, zip_derived_cl23])). 274.84/35.48 thf(zip_derived_cl5710, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5709, zip_derived_cl5012])). 274.84/35.48 thf(zip_derived_cl6340, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5223, zip_derived_cl5710])). 274.84/35.48 thf(zip_derived_cl1122, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1085])). 274.84/35.48 thf(zip_derived_cl1156, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1122, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1195, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1156, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5032, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl1195, zip_derived_cl5010])). 274.84/35.48 thf(zip_derived_cl6341, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6340, zip_derived_cl5032])). 274.84/35.48 thf(zip_derived_cl6238, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6237, zip_derived_cl5018])). 274.84/35.48 thf(zip_derived_cl6342, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6341, zip_derived_cl6238])). 274.84/35.48 thf(zip_derived_cl6456, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6455, zip_derived_cl6342])). 274.84/35.48 thf(zip_derived_cl7496, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl7495, zip_derived_cl6456])). 274.84/35.48 thf(zip_derived_cl7508, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('sup-', [status(thm)], [zip_derived_cl5273, zip_derived_cl7496])). 274.84/35.48 thf(zip_derived_cl7509, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('simplify', [status(thm)], [zip_derived_cl7508])). 274.84/35.48 thf(zip_derived_cl6456, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl6455, zip_derived_cl6342])). 274.84/35.48 thf(zip_derived_cl7511, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1)), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl7509, zip_derived_cl6456])). 274.84/35.48 thf(zip_derived_cl9510, plain, 274.84/35.48 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.48 inference('demod', [status(thm)], 274.84/35.48 [zip_derived_cl5443, zip_derived_cl7511])). 274.84/35.48 thf(zip_derived_cl987, plain, 274.84/35.48 (![X0 : mworld]: 274.84/35.48 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e0) 274.84/35.48 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.48 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl964, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl1102, plain, 274.84/35.48 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.48 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.48 '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1073])). 274.84/35.48 thf(zip_derived_cl1139, plain, 274.84/35.48 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.48 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.48 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1102, '3'])). 274.84/35.48 thf(zip_derived_cl1170, plain, 274.84/35.48 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1139])). 274.84/35.48 thf(zip_derived_cl1209, plain, 274.84/35.48 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.48 e2 @ Y0)))))) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form4'))), 274.84/35.48 inference('rw_clause', [status(thm)], [zip_derived_cl1170, '4'])). 274.84/35.48 thf(zip_derived_cl256, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl190, plain, 274.84/35.48 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.48 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.48 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.48 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.48 define([status(thm)])). 274.84/35.48 thf(zip_derived_cl1238, plain, 274.84/35.48 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.48 | ('#form4') 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.48 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.48 inference('renaming', [status(thm)], 274.84/35.48 [zip_derived_cl1209, zip_derived_cl256, zip_derived_cl190])). 274.84/35.48 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.48 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.48 thf(zip_derived_cl5210, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1238, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl5212, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl987, zip_derived_cl5210])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl5215, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('demod', [status(thm)], [zip_derived_cl5212, zip_derived_cl23])). 274.84/35.49 thf(zip_derived_cl5698, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5697, zip_derived_cl5021])). 274.84/35.49 thf(zip_derived_cl6320, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5215, zip_derived_cl5698])). 274.84/35.49 thf(zip_derived_cl1109, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.49 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.49 '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1078])). 274.84/35.49 thf(zip_derived_cl1145, plain, 274.84/35.49 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1109, '3'])). 274.84/35.49 thf(zip_derived_cl1180, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1145])). 274.84/35.49 thf(zip_derived_cl1217, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1180, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1249, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1217, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5263, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1249, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl6321, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl6320, zip_derived_cl5263])). 274.84/35.49 thf(zip_derived_cl1051, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.49 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.49 '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1024])). 274.84/35.49 thf(zip_derived_cl1083, plain, 274.84/35.49 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1051, '3'])). 274.84/35.49 thf(zip_derived_cl1119, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1083])). 274.84/35.49 thf(zip_derived_cl1154, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1119, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1193, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1154, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5030, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1193, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl6322, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl6321, zip_derived_cl5030])). 274.84/35.49 thf(zip_derived_cl9511, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9510, zip_derived_cl6322])). 274.84/35.49 thf(zip_derived_cl987, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl964, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1038, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1013, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1165, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.49 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.49 '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1137])). 274.84/35.49 thf(zip_derived_cl1204, plain, 274.84/35.49 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1165, '3'])). 274.84/35.49 thf(zip_derived_cl1231, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1204])). 274.84/35.49 thf(zip_derived_cl1265, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1231, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1282, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1265, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5402, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1282, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl5404, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl5402])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl5407, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('demod', [status(thm)], [zip_derived_cl5404, zip_derived_cl23])). 274.84/35.49 thf(zip_derived_cl7511, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7509, zip_derived_cl6456])). 274.84/35.49 thf(zip_derived_cl8840, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5407, zip_derived_cl7511])). 274.84/35.49 thf(zip_derived_cl6322, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl6321, zip_derived_cl5030])). 274.84/35.49 thf(zip_derived_cl8841, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl8840, zip_derived_cl6322])). 274.84/35.49 thf(zip_derived_cl1234, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1206])). 274.84/35.49 thf(zip_derived_cl1267, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1234, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1285, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1267, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5411, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1285, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl8842, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl8841, zip_derived_cl5411])). 274.84/35.49 thf(zip_derived_cl8844, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl987, zip_derived_cl8842])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl1061, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.49 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.49 '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1031])). 274.84/35.49 thf(zip_derived_cl1092, plain, 274.84/35.49 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1061, '3'])). 274.84/35.49 thf(zip_derived_cl1129, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1092])). 274.84/35.49 thf(zip_derived_cl1161, plain, 274.84/35.49 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1129, '3'])). 274.84/35.49 thf(zip_derived_cl1200, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1161])). 274.84/35.49 thf(zip_derived_cl1229, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1200, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1263, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1229, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5398, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1263, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl1099, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1199, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1161])). 274.84/35.49 thf(zip_derived_cl1228, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1199, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1262, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1228, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5389, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1262, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl5391, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl5389])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl5394, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.49 inference('demod', [status(thm)], [zip_derived_cl5391, zip_derived_cl23])). 274.84/35.49 thf(zip_derived_cl7015, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7011, zip_derived_cl6310])). 274.84/35.49 thf(zip_derived_cl8808, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5394, zip_derived_cl7015])). 274.84/35.49 thf(zip_derived_cl1038, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1013, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1059, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.49 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.49 '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1030])). 274.84/35.49 thf(zip_derived_cl1090, plain, 274.84/35.49 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1059, '3'])). 274.84/35.49 thf(zip_derived_cl1127, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1090])). 274.84/35.49 thf(zip_derived_cl1160, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1127, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1198, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1160, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5033, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1198, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl5228, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl5033])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl5231, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('demod', [status(thm)], [zip_derived_cl5228, zip_derived_cl23])). 274.84/35.49 thf(zip_derived_cl6238, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl6237, zip_derived_cl5018])). 274.84/35.49 thf(zip_derived_cl6428, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5231, zip_derived_cl6238])). 274.84/35.49 thf(zip_derived_cl1130, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1092])). 274.84/35.49 thf(zip_derived_cl1162, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1130, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1201, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1162, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5041, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1201, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl6429, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl6428, zip_derived_cl5041])). 274.84/35.49 thf(zip_derived_cl5698, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5697, zip_derived_cl5021])). 274.84/35.49 thf(zip_derived_cl6430, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl6429, zip_derived_cl5698])). 274.84/35.49 thf(zip_derived_cl8809, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl8808, zip_derived_cl6430])). 274.84/35.49 thf(zip_derived_cl1038, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1013, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1099, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1126, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1090])). 274.84/35.49 thf(zip_derived_cl1159, plain, 274.84/35.49 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1126, '3'])). 274.84/35.49 thf(zip_derived_cl1196, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1159])). 274.84/35.49 thf(zip_derived_cl1226, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1196, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1260, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1226, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5371, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1260, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl5373, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl5371])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl5376, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.49 inference('demod', [status(thm)], [zip_derived_cl5373, zip_derived_cl23])). 274.84/35.49 thf(zip_derived_cl7015, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7011, zip_derived_cl6310])). 274.84/35.49 thf(zip_derived_cl8006, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5376, zip_derived_cl7015])). 274.84/35.49 thf(zip_derived_cl6430, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl6429, zip_derived_cl5698])). 274.84/35.49 thf(zip_derived_cl8007, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl8006, zip_derived_cl6430])). 274.84/35.49 thf(zip_derived_cl1197, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1159])). 274.84/35.49 thf(zip_derived_cl1227, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1197, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1261, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1227, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5380, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1261, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl8008, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl8007, zip_derived_cl5380])). 274.84/35.49 thf(zip_derived_cl8010, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl8008])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl7511, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7509, zip_derived_cl6456])). 274.84/35.49 thf(zip_derived_cl8013, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl8010, zip_derived_cl23, zip_derived_cl7511])). 274.84/35.49 thf(zip_derived_cl5698, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5697, zip_derived_cl5021])). 274.84/35.49 thf(zip_derived_cl8019, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl8013, zip_derived_cl5698])). 274.84/35.49 thf(zip_derived_cl8810, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl8809, zip_derived_cl8019])). 274.84/35.49 thf(zip_derived_cl8818, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0))), 274.84/35.49 inference('sup-', [status(thm)], [zip_derived_cl5398, zip_derived_cl8810])). 274.84/35.49 thf(zip_derived_cl8827, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('simplify', [status(thm)], [zip_derived_cl8818])). 274.84/35.49 thf(zip_derived_cl8019, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl8013, zip_derived_cl5698])). 274.84/35.49 thf(zip_derived_cl8831, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl8827, zip_derived_cl8019])). 274.84/35.49 thf(zip_derived_cl8847, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl8844, zip_derived_cl23, zip_derived_cl8831])). 274.84/35.49 thf(zip_derived_cl1038, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1013, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1114, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.49 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.49 '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1081])). 274.84/35.49 thf(zip_derived_cl1149, plain, 274.84/35.49 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1114, '3'])). 274.84/35.49 thf(zip_derived_cl1186, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1149])). 274.84/35.49 thf(zip_derived_cl1221, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1186, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1254, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1221, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5274, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1254, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl5276, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl5274])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl5279, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('demod', [status(thm)], [zip_derived_cl5276, zip_derived_cl23])). 274.84/35.49 thf(zip_derived_cl7511, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7509, zip_derived_cl6456])). 274.84/35.49 thf(zip_derived_cl7974, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5279, zip_derived_cl7511])). 274.84/35.49 thf(zip_derived_cl6322, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl6321, zip_derived_cl5030])). 274.84/35.49 thf(zip_derived_cl7975, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7974, zip_derived_cl6322])). 274.84/35.49 thf(zip_derived_cl1116, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ 274.84/35.49 (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))) @ 274.84/35.49 '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1082])). 274.84/35.49 thf(zip_derived_cl1151, plain, 274.84/35.49 (( (((mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1116, '3'])). 274.84/35.49 thf(zip_derived_cl1189, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1151])). 274.84/35.49 thf(zip_derived_cl1223, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1189, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1257, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1223, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5283, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1257, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl7976, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7975, zip_derived_cl5283])). 274.84/35.49 thf(zip_derived_cl8853, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl8847, zip_derived_cl7976])). 274.84/35.49 thf(zip_derived_cl9512, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9511, zip_derived_cl8853])). 274.84/35.49 thf(zip_derived_cl9514, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('sup-', [status(thm)], [zip_derived_cl5480, zip_derived_cl9512])). 274.84/35.49 thf(zip_derived_cl9517, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.49 inference('simplify', [status(thm)], [zip_derived_cl9514])). 274.84/35.49 thf(zip_derived_cl8853, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl8847, zip_derived_cl7976])). 274.84/35.49 thf(zip_derived_cl9521, plain, ( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9517, zip_derived_cl8853])). 274.84/35.49 thf(zip_derived_cl9797, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5585, zip_derived_cl7015, zip_derived_cl9521])). 274.84/35.49 thf(zip_derived_cl1038, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1013, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1230, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1204])). 274.84/35.49 thf(zip_derived_cl1264, plain, 274.84/35.49 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1230, '3'])). 274.84/35.49 thf(zip_derived_cl1281, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1264])). 274.84/35.49 thf(zip_derived_cl1301, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1281, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1309, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1301, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5571, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1309, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl5573, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl5571])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl5576, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2))), 274.84/35.49 inference('demod', [status(thm)], [zip_derived_cl5573, zip_derived_cl23])). 274.84/35.49 thf(zip_derived_cl7511, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7509, zip_derived_cl6456])). 274.84/35.49 thf(zip_derived_cl1099, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1179, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1145])). 274.84/35.49 thf(zip_derived_cl1216, plain, 274.84/35.49 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1179, '3'])). 274.84/35.49 thf(zip_derived_cl1247, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1216])). 274.84/35.49 thf(zip_derived_cl1274, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1247, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1294, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1274, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5481, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1294, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl5483, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl5481])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl5486, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.49 inference('demod', [status(thm)], [zip_derived_cl5483, zip_derived_cl23])). 274.84/35.49 thf(zip_derived_cl7015, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7011, zip_derived_cl6310])). 274.84/35.49 thf(zip_derived_cl9521, plain, ( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9517, zip_derived_cl8853])). 274.84/35.49 thf(zip_derived_cl9533, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5486, zip_derived_cl7015, zip_derived_cl9521])). 274.84/35.49 thf(zip_derived_cl1248, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1216])). 274.84/35.49 thf(zip_derived_cl1275, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1248, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1295, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1275, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5490, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1295, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl9534, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9533, zip_derived_cl5490])). 274.84/35.49 thf(zip_derived_cl987, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl964, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1099, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1169, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1139])). 274.84/35.49 thf(zip_derived_cl1208, plain, 274.84/35.49 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1169, '3'])). 274.84/35.49 thf(zip_derived_cl1236, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1208])). 274.84/35.49 thf(zip_derived_cl1268, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1236, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1286, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1268, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5420, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1286, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl5422, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl5420])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl5425, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.49 inference('demod', [status(thm)], [zip_derived_cl5422, zip_derived_cl23])). 274.84/35.49 thf(zip_derived_cl7015, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7011, zip_derived_cl6310])). 274.84/35.49 thf(zip_derived_cl9250, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5425, zip_derived_cl7015])). 274.84/35.49 thf(zip_derived_cl8842, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl8841, zip_derived_cl5411])). 274.84/35.49 thf(zip_derived_cl9251, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9250, zip_derived_cl8842])). 274.84/35.49 thf(zip_derived_cl1237, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1208])). 274.84/35.49 thf(zip_derived_cl1269, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1237, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1287, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1269, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5429, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1287, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl9252, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9251, zip_derived_cl5429])). 274.84/35.49 thf(zip_derived_cl9254, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl987, zip_derived_cl9252])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl8831, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl8827, zip_derived_cl8019])). 274.84/35.49 thf(zip_derived_cl9257, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl9254, zip_derived_cl23, zip_derived_cl8831])). 274.84/35.49 thf(zip_derived_cl1099, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1118, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1083])). 274.84/35.49 thf(zip_derived_cl1153, plain, 274.84/35.49 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1118, '3'])). 274.84/35.49 thf(zip_derived_cl1191, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1153])). 274.84/35.49 thf(zip_derived_cl1224, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1191, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1258, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1224, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5284, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1258, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl5286, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl5284])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl5289, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.49 inference('demod', [status(thm)], [zip_derived_cl5286, zip_derived_cl23])). 274.84/35.49 thf(zip_derived_cl7015, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7011, zip_derived_cl6310])). 274.84/35.49 thf(zip_derived_cl7986, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5289, zip_derived_cl7015])). 274.84/35.49 thf(zip_derived_cl7976, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7975, zip_derived_cl5283])). 274.84/35.49 thf(zip_derived_cl7987, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7986, zip_derived_cl7976])). 274.84/35.49 thf(zip_derived_cl1192, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1153])). 274.84/35.49 thf(zip_derived_cl1225, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1192, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1259, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1225, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5370, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1259, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl7988, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7987, zip_derived_cl5370])). 274.84/35.49 thf(zip_derived_cl9309, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9257, zip_derived_cl7988])). 274.84/35.49 thf(zip_derived_cl9535, plain, ( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9534, zip_derived_cl9309])). 274.84/35.49 thf(zip_derived_cl9780, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5576, zip_derived_cl7511, zip_derived_cl9535])). 274.84/35.49 thf(zip_derived_cl1284, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1266])). 274.84/35.49 thf(zip_derived_cl1303, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1284, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1311, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1303, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5593, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1311, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl9781, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9780, zip_derived_cl5593])). 274.84/35.49 thf(zip_derived_cl9798, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9797, zip_derived_cl9781])). 274.84/35.49 thf(zip_derived_cl1038, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1013, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1099, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1280, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1264])). 274.84/35.49 thf(zip_derived_cl1300, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1280, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1308, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1300, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5562, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1308, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl5564, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl5562])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl5567, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.49 inference('demod', [status(thm)], [zip_derived_cl5564, zip_derived_cl23])). 274.84/35.49 thf(zip_derived_cl7015, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7011, zip_derived_cl6310])). 274.84/35.49 thf(zip_derived_cl9521, plain, ( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9517, zip_derived_cl8853])). 274.84/35.49 thf(zip_derived_cl9598, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5567, zip_derived_cl7015, zip_derived_cl9521])). 274.84/35.49 thf(zip_derived_cl5571, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1309, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl9599, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9598, zip_derived_cl5571])). 274.84/35.49 thf(zip_derived_cl9601, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl9599])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl7511, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7509, zip_derived_cl6456])). 274.84/35.49 thf(zip_derived_cl9535, plain, ( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9534, zip_derived_cl9309])). 274.84/35.49 thf(zip_derived_cl9604, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl9601, zip_derived_cl23, zip_derived_cl7511, 274.84/35.49 zip_derived_cl9535])). 274.84/35.49 thf(zip_derived_cl9799, plain, ( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e0)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9798, zip_derived_cl9604])). 274.84/35.49 thf(zip_derived_cl9801, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl987, zip_derived_cl9799])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl8831, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e0)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl8827, zip_derived_cl8019])). 274.84/35.49 thf(zip_derived_cl1099, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1188, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1151])). 274.84/35.49 thf(zip_derived_cl1222, plain, 274.84/35.49 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1188, '3'])). 274.84/35.49 thf(zip_derived_cl1255, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1222])). 274.84/35.49 thf(zip_derived_cl1278, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1255, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1298, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1278, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5552, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1298, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl5554, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl5552])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl5557, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.49 inference('demod', [status(thm)], [zip_derived_cl5554, zip_derived_cl23])). 274.84/35.49 thf(zip_derived_cl7015, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7011, zip_derived_cl6310])). 274.84/35.49 thf(zip_derived_cl9521, plain, ( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9517, zip_derived_cl8853])). 274.84/35.49 thf(zip_derived_cl9582, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5557, zip_derived_cl7015, zip_derived_cl9521])). 274.84/35.49 thf(zip_derived_cl1038, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1013, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1185, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1149])). 274.84/35.49 thf(zip_derived_cl1220, plain, 274.84/35.49 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1185, '3'])). 274.84/35.49 thf(zip_derived_cl1253, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1220])). 274.84/35.49 thf(zip_derived_cl1277, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1253, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1297, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1277, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5500, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1297, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl5502, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl5500])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl5505, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2))), 274.84/35.49 inference('demod', [status(thm)], [zip_derived_cl5502, zip_derived_cl23])). 274.84/35.49 thf(zip_derived_cl7511, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7509, zip_derived_cl6456])). 274.84/35.49 thf(zip_derived_cl9535, plain, ( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9534, zip_derived_cl9309])). 274.84/35.49 thf(zip_derived_cl9567, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5505, zip_derived_cl7511, zip_derived_cl9535])). 274.84/35.49 thf(zip_derived_cl1256, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1222])). 274.84/35.49 thf(zip_derived_cl1279, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1256, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1299, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1279, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5561, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1299, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl9568, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9567, zip_derived_cl5561])). 274.84/35.49 thf(zip_derived_cl9583, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9582, zip_derived_cl9568])). 274.84/35.49 thf(zip_derived_cl1038, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1013, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1099, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1252, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1220])). 274.84/35.49 thf(zip_derived_cl1276, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1252, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1296, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1276, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5491, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1296, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl5493, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl5491])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl5496, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.49 inference('demod', [status(thm)], [zip_derived_cl5493, zip_derived_cl23])). 274.84/35.49 thf(zip_derived_cl7015, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7011, zip_derived_cl6310])). 274.84/35.49 thf(zip_derived_cl9521, plain, ( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9517, zip_derived_cl8853])). 274.84/35.49 thf(zip_derived_cl9543, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5496, zip_derived_cl7015, zip_derived_cl9521])). 274.84/35.49 thf(zip_derived_cl5500, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1297, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl9544, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9543, zip_derived_cl5500])). 274.84/35.49 thf(zip_derived_cl9546, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl9544])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl7511, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7509, zip_derived_cl6456])). 274.84/35.49 thf(zip_derived_cl9535, plain, ( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9534, zip_derived_cl9309])). 274.84/35.49 thf(zip_derived_cl9549, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl9546, zip_derived_cl23, zip_derived_cl7511, 274.84/35.49 zip_derived_cl9535])). 274.84/35.49 thf(zip_derived_cl9584, plain, ( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e0)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9583, zip_derived_cl9549])). 274.84/35.49 thf(zip_derived_cl9804, plain, (~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0)), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl9801, zip_derived_cl23, zip_derived_cl8831, 274.84/35.49 zip_derived_cl9584])). 274.84/35.49 thf(zip_derived_cl9870, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5620, zip_derived_cl9804])). 274.84/35.49 thf(zip_derived_cl1038, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1013, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1241, plain, 274.84/35.49 (( (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ 274.84/35.49 (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2)) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1212])). 274.84/35.49 thf(zip_derived_cl1270, plain, 274.84/35.49 (( (((mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') & (mbox @ 274.84/35.49 (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3'))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1241, '3'])). 274.84/35.49 thf(zip_derived_cl1289, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1270])). 274.84/35.49 thf(zip_derived_cl1305, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1289, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1313, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1305, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5611, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1313, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl9804, plain, (~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0)), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl9801, zip_derived_cl23, zip_derived_cl8831, 274.84/35.49 zip_derived_cl9584])). 274.84/35.49 thf(zip_derived_cl9869, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5611, zip_derived_cl9804])). 274.84/35.49 thf(zip_derived_cl1099, plain, 274.84/35.49 (![X0 : mworld]: 274.84/35.49 (~ ('#form2' @ X0 @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ X0 @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ (mrel @ '#sk3' @ X0))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1070, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl1288, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1270])). 274.84/35.49 thf(zip_derived_cl1304, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1288, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1312, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1304, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5602, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1312, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl9804, plain, (~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0)), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl9801, zip_derived_cl23, zip_derived_cl8831, 274.84/35.49 zip_derived_cl9584])). 274.84/35.49 thf(zip_derived_cl9868, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5602, zip_derived_cl9804])). 274.84/35.49 thf(zip_derived_cl9873, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1099, zip_derived_cl9868])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl7015, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7011, zip_derived_cl6310])). 274.84/35.49 thf(zip_derived_cl9521, plain, ( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9517, zip_derived_cl8853])). 274.84/35.49 thf(zip_derived_cl9876, plain, 274.84/35.49 ((~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl9873, zip_derived_cl23, zip_derived_cl7015, 274.84/35.49 zip_derived_cl9521])). 274.84/35.49 thf(zip_derived_cl9888, plain, ( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e1)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9869, zip_derived_cl9876])). 274.84/35.49 thf(zip_derived_cl9890, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl9888])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl7511, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e1)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7509, zip_derived_cl6456])). 274.84/35.49 thf(zip_derived_cl9535, plain, ( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e1)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9534, zip_derived_cl9309])). 274.84/35.49 thf(zip_derived_cl9893, plain, (~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1)), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl9890, zip_derived_cl23, zip_derived_cl7511, 274.84/35.49 zip_derived_cl9535])). 274.84/35.49 thf(zip_derived_cl10477, plain, ( ('#form2' @ '#sk3' @ (op @ e3 @ e3) @ e2)), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl9870, zip_derived_cl9893])). 274.84/35.49 thf(zip_derived_cl10479, plain, 274.84/35.49 ((~ (mrel @ '#sk3' @ '#sk3') 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2) 274.84/35.49 | ~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2))), 274.84/35.49 inference('sup+', [status(thm)], 274.84/35.49 [zip_derived_cl1099, zip_derived_cl10477])). 274.84/35.49 thf(zip_derived_cl23, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 274.84/35.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 274.84/35.49 thf(zip_derived_cl7015, plain, ( ('#form2' @ '#sk3' @ (op @ e0 @ e0) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl7011, zip_derived_cl6310])). 274.84/35.49 thf(zip_derived_cl9521, plain, ( ('#form2' @ '#sk3' @ (op @ e1 @ e1) @ e2)), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl9517, zip_derived_cl8853])). 274.84/35.49 thf(zip_derived_cl10482, plain, 274.84/35.49 (~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2)), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl10479, zip_derived_cl23, zip_derived_cl7015, 274.84/35.49 zip_derived_cl9521])). 274.84/35.49 thf(zip_derived_cl1292, plain, 274.84/35.49 (( (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2) @ '#sk3') 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1272])). 274.84/35.49 thf(zip_derived_cl1307, plain, 274.84/35.49 (( (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ '#sk3' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 274.84/35.49 e2 @ Y0)))))) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form4'))), 274.84/35.49 inference('rw_clause', [status(thm)], [zip_derived_cl1292, '4'])). 274.84/35.49 thf(zip_derived_cl256, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 (~ ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl190, plain, 274.84/35.49 (![X3 : mworld, X6 : $i, X7 : $i]: 274.84/35.49 ( ('#form2' @ X3 @ X6 @ X7) 274.84/35.49 | ~ (((!!) @ (^[Y0 : mworld]: 274.84/35.49 (((mrel @ X3 @ Y0) => (qmltpeq @ X6 @ X7 @ Y0)))))))), 274.84/35.49 define([status(thm)])). 274.84/35.49 thf(zip_derived_cl1315, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form4') 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('renaming', [status(thm)], 274.84/35.49 [zip_derived_cl1307, zip_derived_cl256, zip_derived_cl190])). 274.84/35.49 thf(zip_derived_cl5010, plain, (~ ('#form4')), 274.84/35.49 inference('clc', [status(thm)], [zip_derived_cl5006, zip_derived_cl4975])). 274.84/35.49 thf(zip_derived_cl5629, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl1315, zip_derived_cl5010])). 274.84/35.49 thf(zip_derived_cl9804, plain, (~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e0)), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl9801, zip_derived_cl23, zip_derived_cl8831, 274.84/35.49 zip_derived_cl9584])). 274.84/35.49 thf(zip_derived_cl9871, plain, 274.84/35.49 (( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2) 274.84/35.49 | ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1))), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl5629, zip_derived_cl9804])). 274.84/35.49 thf(zip_derived_cl9893, plain, (~ ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e1)), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl9890, zip_derived_cl23, zip_derived_cl7511, 274.84/35.49 zip_derived_cl9535])). 274.84/35.49 thf(zip_derived_cl10546, plain, ( ('#form2' @ '#sk3' @ (op @ e2 @ e2) @ e2)), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl9871, zip_derived_cl9893])). 274.84/35.49 thf(zip_derived_cl10547, plain, ($false), 274.84/35.49 inference('demod', [status(thm)], 274.84/35.49 [zip_derived_cl10482, zip_derived_cl10546])). 274.84/35.49 274.84/35.49 % SZS output end Refutation 274.84/35.49 274.84/35.49 274.84/35.49 % Terminating... 274.84/35.56 % Runner terminated. 274.84/35.56 % Zipperpin 1.5 exiting 274.84/35.57 EOF