0.02/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.9iUscxQltG true 0.12/0.32 % Computer : n013.cluster.edu 0.12/0.32 % Model : x86_64 x86_64 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.32 % Memory : 8042.1875MB 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.32 % CPULimit : 960 0.12/0.32 % WCLimit : 120 0.12/0.32 % DateTime : Tue Aug 9 07:22:30 EDT 2022 0.12/0.33 % CPUTime : 0.12/0.33 % Running portfolio for 960 s 0.12/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.12/0.33 % Number of cores: 8 0.12/0.33 % Python version: Python 3.6.8 0.12/0.33 % Running in HO mode 0.44/0.62 % Total configuration time : 828 0.44/0.62 % Estimated wc time : 1656 0.44/0.62 % Estimated cpu time (8 cpus) : 207.0 0.46/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.46/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.46/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.46/0.71 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.46/0.71 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.46/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.46/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.46/0.72 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.48/0.98 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 244.08/31.58 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 477.59/61.30 % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s 572.12/73.75 % /export/starexec/sandbox2/solver/bin/lams/15_lifting3.sh running for 30s 632.62/81.38 % /export/starexec/sandbox2/solver/bin/lams/33_shallow_sine.sh running for 66s 632.96/81.45 % /export/starexec/sandbox2/solver/bin/lams/40_e_lift.sh running for 80s 633.69/81.58 % /export/starexec/sandbox2/solver/bin/lams/15_lifting1.sh running for 30s 685.19/88.20 % /export/starexec/sandbox2/solver/bin/lams/8_new_cnf.sh running for 16s 689.25/88.71 % /export/starexec/sandbox2/solver/bin/lams/10_e_short2.sh running for 20s 711.20/91.61 % /export/starexec/sandbox2/solver/bin/lams/8_add_var_l_av.sh running for 16s 711.20/91.66 % /export/starexec/sandbox2/solver/bin/lams/8_new_sh_or.sh running for 16s 795.25/103.82 % /export/starexec/sandbox2/solver/bin/lams/30_old_zip1.sh running for 36s 799.16/104.43 % /export/starexec/sandbox2/solver/bin/lams/10_shallow_lift.sh running for 30s 822.93/107.66 % /export/starexec/sandbox2/solver/bin/lams/15_lcnf_noform.sh running for 30s 827.73/108.45 % /export/starexec/sandbox2/solver/bin/lams/8_sh.eqenc2.sh running for 10s 843.83/110.68 % /export/starexec/sandbox2/solver/bin/lams/8_cmb.lcnf4.sh running for 10s 853.00/111.87 % /export/starexec/sandbox2/solver/bin/lams/8_new_l_av.sh running for 24s 869.37/113.97 % Solved by lams/8_new_l_av.sh. 869.37/113.97 % done 264 iterations in 1.982s 869.37/113.97 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 869.37/113.97 % SZS output start Refutation 869.37/113.97 thf(mworld_type, type, mworld: $tType). 869.37/113.97 thf(mlocal_type, type, mlocal: (mworld > $o) > $o). 869.37/113.97 thf(op_type, type, op: $i > $i > $i). 869.37/113.97 thf(mor_type, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o). 869.37/113.97 thf('#sk2_type', type, '#sk2': mworld). 869.37/113.97 thf(qmltpeq_type, type, qmltpeq: $i > $i > mworld > $o). 869.37/113.97 thf(mrel_type, type, mrel: mworld > mworld > $o). 869.37/113.97 thf(mnot_type, type, mnot: (mworld > $o) > mworld > $o). 869.37/113.97 thf(mand_type, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o). 869.37/113.97 thf(e3_type, type, e3: $i). 869.37/113.97 thf(mactual_type, type, mactual: mworld). 869.37/113.97 thf(e1_type, type, e1: $i). 869.37/113.97 thf(e2_type, type, e2: $i). 869.37/113.97 thf('#sk1_type', type, '#sk1': $i > $i > mworld > mworld). 869.37/113.97 thf(mbox_type, type, mbox: (mworld > $o) > mworld > $o). 869.37/113.97 thf(e0_type, type, e0: $i). 869.37/113.97 thf(mbox_def, axiom,(( mbox ) = 869.37/113.97 (^[Phi:( mworld > $o ),W:mworld]: 869.37/113.97 ( ![V:mworld]: ( ( mrel @ W @ V ) => ( Phi @ V ) ) )))). 869.37/113.97 thf('0', plain, 869.37/113.97 (( mbox ) = 869.37/113.97 ( ^[Phi:( mworld > $o ),W:mworld]: 869.37/113.97 ( ![V:mworld]: ( ( mrel @ W @ V ) => ( Phi @ V ) ) ) )), 869.37/113.97 inference('simplify_rw_rule', [status(thm)], [mbox_def])). 869.37/113.97 thf('1', plain, 869.37/113.97 (( mbox ) = 869.37/113.97 ( ^[V_1:( mworld > $o ),V_2:mworld]: 869.37/113.97 ( ![X4:mworld]: ( ( mrel @ V_2 @ X4 ) => ( V_1 @ X4 ) ) ) )), 869.37/113.97 define([status(thm)])). 869.37/113.97 thf(mor_def, axiom,(( mor ) = 869.37/113.97 (^[A:( mworld > $o ),B:( mworld > $o ),W:mworld]: ( ( A @ W ) | ( B @ W ) )))). 869.37/113.97 thf('2', plain, 869.37/113.97 (( mor ) = 869.37/113.97 ( ^[A:( mworld > $o ),B:( mworld > $o ),W:mworld]: 869.37/113.97 ( ( A @ W ) | ( B @ W ) ) )), 869.37/113.97 inference('simplify_rw_rule', [status(thm)], [mor_def])). 869.37/113.97 thf('3', plain, 869.37/113.97 (( mor ) = 869.37/113.97 ( ^[V_1:( mworld > $o ),V_2:( mworld > $o ),V_3:mworld]: 869.37/113.97 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 869.37/113.97 define([status(thm)])). 869.37/113.97 thf(mand_def, axiom,(( mand ) = 869.37/113.97 (^[A:( mworld > $o ),B:( mworld > $o ),W:mworld]: ( ( A @ W ) & ( B @ W ) )))). 869.37/113.97 thf('4', plain, 869.37/113.97 (( mand ) = 869.37/113.97 ( ^[A:( mworld > $o ),B:( mworld > $o ),W:mworld]: 869.37/113.97 ( ( A @ W ) & ( B @ W ) ) )), 869.37/113.97 inference('simplify_rw_rule', [status(thm)], [mand_def])). 869.37/113.97 thf('5', plain, 869.37/113.97 (( mand ) = 869.37/113.97 ( ^[V_1:( mworld > $o ),V_2:( mworld > $o ),V_3:mworld]: 869.37/113.97 ( ( V_1 @ V_3 ) & ( V_2 @ V_3 ) ) )), 869.37/113.97 define([status(thm)])). 869.37/113.97 thf(mnot_def, axiom,(( mnot ) = 869.37/113.97 (^[A:( mworld > $o ),W:mworld]: ( ~( A @ W ) )))). 869.37/113.97 thf('6', plain, 869.37/113.97 (( mnot ) = ( ^[A:( mworld > $o ),W:mworld]: ( ~( A @ W ) ) )), 869.37/113.97 inference('simplify_rw_rule', [status(thm)], [mnot_def])). 869.37/113.97 thf('7', plain, 869.37/113.97 (( mnot ) = ( ^[V_1:( mworld > $o ),V_2:mworld]: ( ~( V_1 @ V_2 ) ) )), 869.37/113.97 define([status(thm)])). 869.37/113.97 thf(mlocal_def, axiom,(( mlocal ) = 869.37/113.97 (^[Phi:( mworld > $o )]: ( Phi @ mactual )))). 869.37/113.97 thf('8', plain, (( mlocal ) = ( ^[Phi:( mworld > $o )]: ( Phi @ mactual ) )), 869.37/113.97 inference('simplify_rw_rule', [status(thm)], [mlocal_def])). 869.37/113.97 thf('9', plain, (( mlocal ) = ( ^[V_1:( mworld > $o )]: ( V_1 @ mactual ) )), 869.37/113.97 define([status(thm)])). 869.37/113.97 thf(co1, conjecture, 869.37/113.97 (mlocal @ 869.37/113.97 ( mor @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ 869.37/113.97 ( mor @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ 869.37/113.97 ( mor @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ 869.37/113.97 ( mor @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) @ 869.37/113.97 ( mbox @ 869.37/113.97 ( mnot @ 869.37/113.97 ( mor @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ 869.37/113.97 ( mor @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ 869.37/113.97 ( mor @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ 869.37/113.97 ( mand @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ 869.37/113.97 ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 869.37/113.97 thf(zf_stmt_0, conjecture, 869.37/113.97 (( ![X36:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X36 ) => 869.37/113.97 ( ~( ( ( ![X68:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X68 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X68 ) ) ) & 869.37/113.97 ( ![X66:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X66 ) => 869.37/113.97 ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X66 ) ) ) & 869.37/113.97 ( ![X64:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X64 ) => 869.37/113.97 ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X64 ) ) ) & 869.37/113.97 ( ![X62:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X62 ) => 869.37/113.97 ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X62 ) ) ) ) | 869.37/113.97 ( ( ![X60:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X60 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X60 ) ) ) & 869.37/113.97 ( ![X58:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X58 ) => 869.37/113.97 ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X58 ) ) ) & 869.37/113.97 ( ![X56:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X56 ) => 869.37/113.97 ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X56 ) ) ) & 869.37/113.97 ( ![X54:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X54 ) => 869.37/113.97 ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X54 ) ) ) ) | 869.37/113.97 ( ( ![X52:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X52 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X52 ) ) ) & 869.37/113.97 ( ![X50:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X50 ) => 869.37/113.97 ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X50 ) ) ) & 869.37/113.97 ( ![X48:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X48 ) => 869.37/113.97 ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X48 ) ) ) & 869.37/113.97 ( ![X46:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X46 ) => 869.37/113.97 ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X46 ) ) ) ) | 869.37/113.97 ( ( ![X44:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X44 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X44 ) ) ) & 869.37/113.97 ( ![X42:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X42 ) => 869.37/113.97 ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X42 ) ) ) & 869.37/113.97 ( ![X40:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X40 ) => 869.37/113.97 ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X40 ) ) ) & 869.37/113.97 ( ![X38:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X38 ) => 869.37/113.97 ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X38 ) ) ) ) ) ) ) ) | 869.37/113.97 ( ( ![X34:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X34 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X34 ) ) ) & 869.37/113.97 ( ![X32:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X32 ) => 869.37/113.97 ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X32 ) ) ) & 869.37/113.97 ( ![X30:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X30 ) => 869.37/113.97 ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X30 ) ) ) & 869.37/113.97 ( ![X28:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X28 ) => 869.37/113.97 ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X28 ) ) ) ) | 869.37/113.97 ( ( ![X26:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X26 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X26 ) ) ) & 869.37/113.97 ( ![X24:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X24 ) => 869.37/113.97 ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X24 ) ) ) & 869.37/113.97 ( ![X22:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X22 ) => 869.37/113.97 ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X22 ) ) ) & 869.37/113.97 ( ![X20:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X20 ) => 869.37/113.97 ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X20 ) ) ) ) | 869.37/113.97 ( ( ![X18:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X18 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X18 ) ) ) & 869.37/113.97 ( ![X16:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X16 ) => 869.37/113.97 ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X16 ) ) ) & 869.37/113.97 ( ![X14:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X14 ) => 869.37/113.97 ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X14 ) ) ) & 869.37/113.97 ( ![X12:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X12 ) => 869.37/113.97 ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X12 ) ) ) ) | 869.37/113.97 ( ( ![X10:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X10 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X10 ) ) ) & 869.37/113.97 ( ![X8:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X8 ) => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X8 ) ) ) & 869.37/113.97 ( ![X6:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X6 ) => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X6 ) ) ) & 869.37/113.97 ( ![X4:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X4 ) => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X4 ) ) ) ))). 869.37/113.97 thf(zf_stmt_1, negated_conjecture, 869.37/113.97 (~( ( ![X36:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X36 ) => 869.37/113.97 ( ~( ( ( ![X68:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X68 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X68 ) ) ) & 869.37/113.97 ( ![X66:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X66 ) => 869.37/113.97 ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X66 ) ) ) & 869.37/113.97 ( ![X64:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X64 ) => 869.37/113.97 ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X64 ) ) ) & 869.37/113.97 ( ![X62:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X62 ) => 869.37/113.97 ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X62 ) ) ) ) | 869.37/113.97 ( ( ![X60:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X60 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X60 ) ) ) & 869.37/113.97 ( ![X58:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X58 ) => 869.37/113.97 ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X58 ) ) ) & 869.37/113.97 ( ![X56:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X56 ) => 869.37/113.97 ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X56 ) ) ) & 869.37/113.97 ( ![X54:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X54 ) => 869.37/113.97 ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X54 ) ) ) ) | 869.37/113.97 ( ( ![X52:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X52 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X52 ) ) ) & 869.37/113.97 ( ![X50:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X50 ) => 869.37/113.97 ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X50 ) ) ) & 869.37/113.97 ( ![X48:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X48 ) => 869.37/113.97 ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X48 ) ) ) & 869.37/113.97 ( ![X46:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X46 ) => 869.37/113.97 ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X46 ) ) ) ) | 869.37/113.97 ( ( ![X44:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X44 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X44 ) ) ) & 869.37/113.97 ( ![X42:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X42 ) => 869.37/113.97 ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X42 ) ) ) & 869.37/113.97 ( ![X40:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X40 ) => 869.37/113.97 ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X40 ) ) ) & 869.37/113.97 ( ![X38:mworld]: 869.37/113.97 ( ( mrel @ X36 @ X38 ) => 869.37/113.97 ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X38 ) ) ) ) ) ) ) ) | 869.37/113.97 ( ( ![X34:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X34 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X34 ) ) ) & 869.37/113.97 ( ![X32:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X32 ) => 869.37/113.97 ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X32 ) ) ) & 869.37/113.97 ( ![X30:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X30 ) => 869.37/113.97 ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X30 ) ) ) & 869.37/113.97 ( ![X28:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X28 ) => 869.37/113.97 ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X28 ) ) ) ) | 869.37/113.97 ( ( ![X26:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X26 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X26 ) ) ) & 869.37/113.97 ( ![X24:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X24 ) => 869.37/113.97 ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X24 ) ) ) & 869.37/113.97 ( ![X22:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X22 ) => 869.37/113.97 ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X22 ) ) ) & 869.37/113.97 ( ![X20:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X20 ) => 869.37/113.97 ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X20 ) ) ) ) | 869.37/113.97 ( ( ![X18:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X18 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X18 ) ) ) & 869.37/113.97 ( ![X16:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X16 ) => 869.37/113.97 ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X16 ) ) ) & 869.37/113.97 ( ![X14:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X14 ) => 869.37/113.97 ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X14 ) ) ) & 869.37/113.97 ( ![X12:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X12 ) => 869.37/113.97 ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X12 ) ) ) ) | 869.37/113.97 ( ( ![X10:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X10 ) => 869.37/113.97 ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X10 ) ) ) & 869.37/113.97 ( ![X8:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X8 ) => 869.37/113.97 ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X8 ) ) ) & 869.37/113.97 ( ![X6:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X6 ) => 869.37/113.97 ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X6 ) ) ) & 869.37/113.97 ( ![X4:mworld]: 869.37/113.97 ( ( mrel @ mactual @ X4 ) => 869.37/113.97 ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X4 ) ) ) ) )), 869.37/113.97 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 869.37/113.97 thf(zip_derived_cl17, plain, 869.37/113.97 (~ (((((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => 869.37/113.97 (((~) @ (((((((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.97 e3 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.97 e3 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.97 e3 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.97 e3 @ Y1)))))))) | 869.37/113.97 (((((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.97 e2 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.97 e2 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.97 e2 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.97 e2 @ Y1)))))))) | 869.37/113.97 (((((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.97 e1 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.97 e1 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.97 e1 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.97 e1 @ Y1)))))))) | 869.37/113.97 (((((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.97 e0 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.97 e0 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.97 e0 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.97 e0 @ Y1))))))))))))))))) | 869.37/113.97 (((((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e0 @ e0) @ e3 @ Y0)))))))) | 869.37/113.97 (((((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e0 @ e0) @ e2 @ Y0)))))))) | 869.37/113.97 (((((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e0 @ e0) @ e1 @ Y0)))))))) | 869.37/113.97 (((((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.97 inference('cnf', [status(esa)], [zf_stmt_1])). 869.37/113.97 thf(zip_derived_cl495, plain, 869.37/113.97 (~ (((((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.97 e3 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.97 e3 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.97 e3 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.97 e3 @ Y0))))))))), 869.37/113.97 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl17])). 869.37/113.97 thf(zip_derived_cl500, plain, 869.37/113.97 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.97 e3 @ Y0)))))) 869.37/113.97 | ~ (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.97 e3 @ Y0)))))) 869.37/113.97 | ~ (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.97 e3 @ Y0)))))) 869.37/113.97 | ~ (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.97 e3 @ Y0)))))))), 869.37/113.97 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl495])). 869.37/113.97 thf(zip_derived_cl508, plain, 869.37/113.97 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.97 e3 @ Y0))))))) 869.37/113.97 <= (~ 869.37/113.97 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e1 @ e1) @ e3 @ Y0))))))))), 869.37/113.97 inference('split', [status(esa)], [zip_derived_cl500])). 869.37/113.97 thf(zip_derived_cl525, plain, 869.37/113.97 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e1 @ e1) @ e3 @ mactual)) => 869.37/113.97 (qmltpeq @ (op @ e1 @ e1) @ e3 @ 869.37/113.97 ('#sk1' @ (op @ e1 @ e1) @ e3 @ mactual))))) 869.37/113.97 <= (~ 869.37/113.97 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e1 @ e1) @ e3 @ Y0))))))))), 869.37/113.97 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl508])). 869.37/113.97 thf(zip_derived_cl548, plain, 869.37/113.97 ((~ (qmltpeq @ (op @ e1 @ e1) @ e3 @ 869.37/113.97 ('#sk1' @ (op @ e1 @ e1) @ e3 @ mactual))) 869.37/113.97 <= (~ 869.37/113.97 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e1 @ e1) @ e3 @ Y0))))))))), 869.37/113.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl525])). 869.37/113.97 thf(zip_derived_cl494, plain, 869.37/113.97 (~ (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ mactual @ Y0) => 869.37/113.97 (((~) @ (((((((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.97 e3 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.97 e3 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.97 e3 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.97 e3 @ Y1)))))))) | 869.37/113.97 (((((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.97 e2 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.97 e2 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.97 e2 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.97 e2 @ Y1)))))))) | 869.37/113.97 (((((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.97 e1 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.97 e1 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.97 e1 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.97 e1 @ Y1)))))))) | 869.37/113.97 (((((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.97 e0 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.97 e0 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.97 e0 @ Y1)))))) & 869.37/113.97 (((!!) @ (^[Y1 : mworld]: 869.37/113.97 (((mrel @ Y0 @ Y1) => 869.37/113.97 (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.97 e0 @ Y1)))))))))))))))))), 869.37/113.97 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl17])). 869.37/113.97 thf(zip_derived_cl499, plain, 869.37/113.97 (~ (((mrel @ mactual @ '#sk2') => 869.37/113.97 (((~) @ (((((((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e0 @ e0) @ e3 @ Y0)))))))) | 869.37/113.97 (((((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e0 @ e0) @ e2 @ Y0)))))))) | 869.37/113.97 (((((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e0 @ e0) @ e1 @ Y0)))))))) | 869.37/113.97 (((((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.97 (op @ e0 @ e0) @ e0 @ Y0))))))))))))))), 869.37/113.97 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl494])). 869.37/113.97 thf(zip_derived_cl505, plain, 869.37/113.97 ( (((((((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.97 e3 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.97 e3 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.97 e3 @ Y0)))))) & 869.37/113.97 (((!!) @ (^[Y0 : mworld]: 869.37/113.97 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e3 @ Y0)))))))) | 869.37/113.98 (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e2 @ Y0)))))))) | 869.37/113.98 (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e1 @ Y0)))))))) | 869.37/113.98 (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e0 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl499])). 869.37/113.98 thf(zip_derived_cl522, plain, 869.37/113.98 (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e3 @ Y0)))))))) 869.37/113.98 | (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e2 @ Y0)))))))) 869.37/113.98 | (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e1 @ Y0)))))))) 869.37/113.98 | (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e0 @ Y0)))))))))), 869.37/113.98 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl505])). 869.37/113.98 thf(zip_derived_cl542, plain, 869.37/113.98 (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e3 @ Y0))))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl522])). 869.37/113.98 thf(zip_derived_cl589, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e3 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl542])). 869.37/113.98 thf(zip_derived_cl605, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl589])). 869.37/113.98 thf(zip_derived_cl621, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl605])). 869.37/113.98 thf(zip_derived_cl3385, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e1 @ e1) @ e3 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('sup+', [status(thm)], [zip_derived_cl548, zip_derived_cl621])). 869.37/113.98 thf(zip_derived_cl547, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e1 @ e1) @ e3 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl525])). 869.37/113.98 thf(zip_derived_cl504, plain, ( (mrel @ mactual @ '#sk2')), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl499])). 869.37/113.98 thf(mrel_euclidean, axiom, 869.37/113.98 (![W:mworld,V:mworld,U:mworld]: 869.37/113.98 ( ( ( mrel @ W @ U ) & ( mrel @ W @ V ) ) => ( mrel @ U @ V ) ))). 869.37/113.98 thf(zip_derived_cl0, plain, 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((!!) @ (^[Y1 : mworld]: 869.37/113.98 (((!!) @ (^[Y2 : mworld]: 869.37/113.98 (((((mrel @ Y0 @ Y2) & (mrel @ 869.37/113.98 Y0 @ Y1))) => 869.37/113.98 (mrel @ Y2 @ Y1))))))))))))), 869.37/113.98 inference('cnf', [status(esa)], [mrel_euclidean])). 869.37/113.98 thf(zip_derived_cl25, plain, 869.37/113.98 (![X2 : mworld]: 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((!!) @ (^[Y1 : mworld]: 869.37/113.98 (((((mrel @ X2 @ Y1) & (mrel @ X2 @ Y0))) => 869.37/113.98 (mrel @ Y1 @ Y0)))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 869.37/113.98 thf(zip_derived_cl26, plain, 869.37/113.98 (![X2 : mworld, X4 : mworld]: 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((((mrel @ X2 @ Y0) & (mrel @ X2 @ X4))) => (mrel @ 869.37/113.98 Y0 @ X4))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl25])). 869.37/113.98 thf(zip_derived_cl27, plain, 869.37/113.98 (![X2 : mworld, X4 : mworld, X6 : mworld]: 869.37/113.98 (((((mrel @ X2 @ X6) & (mrel @ X2 @ X4))) => (mrel @ X6 @ X4)))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])). 869.37/113.98 thf(zip_derived_cl28, plain, 869.37/113.98 (![X2 : mworld, X4 : mworld, X6 : mworld]: 869.37/113.98 (~ (((mrel @ X2 @ X6) & (mrel @ X2 @ X4))) | (mrel @ X6 @ X4))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 869.37/113.98 thf(zip_derived_cl29, plain, 869.37/113.98 (![X2 : mworld, X4 : mworld, X6 : mworld]: 869.37/113.98 (~ (mrel @ X2 @ X6) | ~ (mrel @ X2 @ X4) | (mrel @ X6 @ X4))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl28])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl1593, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e1 @ e1) @ e3 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl547, zip_derived_cl629])). 869.37/113.98 thf('10', plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e3 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e3 @ Y0)))))))))), 869.37/113.98 inference('demod', [status(thm)], 869.37/113.98 [zip_derived_cl3385, zip_derived_cl1593])). 869.37/113.98 thf(zip_derived_cl509, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e3 @ Y0))))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl500])). 869.37/113.98 thf(zip_derived_cl526, plain, 869.37/113.98 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e0 @ e0) @ e3 @ mactual)) => 869.37/113.98 (qmltpeq @ (op @ e0 @ e0) @ e3 @ 869.37/113.98 ('#sk1' @ (op @ e0 @ e0) @ e3 @ mactual))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl509])). 869.37/113.98 thf(zip_derived_cl550, plain, 869.37/113.98 ((~ (qmltpeq @ (op @ e0 @ e0) @ e3 @ 869.37/113.98 ('#sk1' @ (op @ e0 @ e0) @ e3 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl526])). 869.37/113.98 thf(zip_derived_cl590, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e3 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl542])). 869.37/113.98 thf(zip_derived_cl606, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl590])). 869.37/113.98 thf(zip_derived_cl622, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl606])). 869.37/113.98 thf(zip_derived_cl3443, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e0 @ e0) @ e3 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('sup+', [status(thm)], [zip_derived_cl550, zip_derived_cl622])). 869.37/113.98 thf(zip_derived_cl549, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e0 @ e0) @ e3 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl526])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl1673, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e0 @ e0) @ e3 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl549, zip_derived_cl629])). 869.37/113.98 thf('11', plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e3 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e3 @ Y0)))))))))), 869.37/113.98 inference('demod', [status(thm)], 869.37/113.98 [zip_derived_cl3443, zip_derived_cl1673])). 869.37/113.98 thf(zip_derived_cl506, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e3 @ Y0))))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl500])). 869.37/113.98 thf(zip_derived_cl523, plain, 869.37/113.98 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e3 @ e3) @ e3 @ mactual)) => 869.37/113.98 (qmltpeq @ (op @ e3 @ e3) @ e3 @ 869.37/113.98 ('#sk1' @ (op @ e3 @ e3) @ e3 @ mactual))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl506])). 869.37/113.98 thf(zip_derived_cl544, plain, 869.37/113.98 ((~ (qmltpeq @ (op @ e3 @ e3) @ e3 @ 869.37/113.98 ('#sk1' @ (op @ e3 @ e3) @ e3 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl523])). 869.37/113.98 thf(zip_derived_cl587, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e3 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl542])). 869.37/113.98 thf(zip_derived_cl603, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl587])). 869.37/113.98 thf(zip_derived_cl619, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e3 @ e3) @ e3 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl603])). 869.37/113.98 thf(zip_derived_cl3169, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e3 @ e3) @ e3 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('sup+', [status(thm)], [zip_derived_cl544, zip_derived_cl619])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl543, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e3 @ e3) @ e3 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl523])). 869.37/113.98 thf(zip_derived_cl1473, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e3 @ e3) @ e3 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0))))))))), 869.37/113.98 inference('sup+', [status(thm)], [zip_derived_cl629, zip_derived_cl543])). 869.37/113.98 thf('12', plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e3 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e3 @ Y0)))))))))), 869.37/113.98 inference('demod', [status(thm)], 869.37/113.98 [zip_derived_cl3169, zip_derived_cl1473])). 869.37/113.98 thf(zip_derived_cl497, plain, 869.37/113.98 (~ (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e1 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl17])). 869.37/113.98 thf(zip_derived_cl502, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e1 @ Y0)))))) 869.37/113.98 | ~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e1 @ Y0)))))) 869.37/113.98 | ~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e1 @ Y0)))))) 869.37/113.98 | ~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e1 @ Y0)))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl497])). 869.37/113.98 thf(zip_derived_cl517, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e1 @ Y0))))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl502])). 869.37/113.98 thf(zip_derived_cl534, plain, 869.37/113.98 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e0 @ e0) @ e1 @ mactual)) => 869.37/113.98 (qmltpeq @ (op @ e0 @ e0) @ e1 @ 869.37/113.98 ('#sk1' @ (op @ e0 @ e0) @ e1 @ mactual))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl517])). 869.37/113.98 thf(zip_derived_cl565, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e0 @ e0) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl534])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl1921, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e0 @ e0) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl565, zip_derived_cl629])). 869.37/113.98 thf(zip_derived_cl540, plain, 869.37/113.98 (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e1 @ Y0))))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl522])). 869.37/113.98 thf(zip_derived_cl582, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e1 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl540])). 869.37/113.98 thf(zip_derived_cl598, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl582])). 869.37/113.98 thf(zip_derived_cl614, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl598])). 869.37/113.98 thf(zip_derived_cl566, plain, 869.37/113.98 ((~ (qmltpeq @ (op @ e0 @ e0) @ e1 @ 869.37/113.98 ('#sk1' @ (op @ e0 @ e0) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl534])). 869.37/113.98 thf(zip_derived_cl2659, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e0 @ e0) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl614, zip_derived_cl566])). 869.37/113.98 thf('13', plain, 869.37/113.98 (~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e1 @ Y0))))))))) | 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e1 @ Y0)))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl1921, zip_derived_cl2659])). 869.37/113.98 thf(zip_derived_cl516, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e1 @ Y0))))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl502])). 869.37/113.98 thf(zip_derived_cl533, plain, 869.37/113.98 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e1 @ e1) @ e1 @ mactual)) => 869.37/113.98 (qmltpeq @ (op @ e1 @ e1) @ e1 @ 869.37/113.98 ('#sk1' @ (op @ e1 @ e1) @ e1 @ mactual))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl516])). 869.37/113.98 thf(zip_derived_cl563, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e1 @ e1) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl533])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl1893, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e1 @ e1) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl563, zip_derived_cl629])). 869.37/113.98 thf(zip_derived_cl581, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e1 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl540])). 869.37/113.98 thf(zip_derived_cl597, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl581])). 869.37/113.98 thf(zip_derived_cl613, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl597])). 869.37/113.98 thf(zip_derived_cl564, plain, 869.37/113.98 ((~ (qmltpeq @ (op @ e1 @ e1) @ e1 @ 869.37/113.98 ('#sk1' @ (op @ e1 @ e1) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl533])). 869.37/113.98 thf(zip_derived_cl2501, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e1 @ e1) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl613, zip_derived_cl564])). 869.37/113.98 thf('14', plain, 869.37/113.98 (~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e1 @ Y0))))))))) | 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e1 @ Y0)))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl1893, zip_derived_cl2501])). 869.37/113.98 thf(zip_derived_cl515, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e1 @ Y0))))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl502])). 869.37/113.98 thf(zip_derived_cl532, plain, 869.37/113.98 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e2 @ e2) @ e1 @ mactual)) => 869.37/113.98 (qmltpeq @ (op @ e2 @ e2) @ e1 @ 869.37/113.98 ('#sk1' @ (op @ e2 @ e2) @ e1 @ mactual))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl515])). 869.37/113.98 thf(zip_derived_cl561, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e2 @ e2) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl532])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl1829, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e2 @ e2) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl561, zip_derived_cl629])). 869.37/113.98 thf(zip_derived_cl580, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e1 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl540])). 869.37/113.98 thf(zip_derived_cl596, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl580])). 869.37/113.98 thf(zip_derived_cl612, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl596])). 869.37/113.98 thf(zip_derived_cl562, plain, 869.37/113.98 ((~ (qmltpeq @ (op @ e2 @ e2) @ e1 @ 869.37/113.98 ('#sk1' @ (op @ e2 @ e2) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl532])). 869.37/113.98 thf(zip_derived_cl2403, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e2 @ e2) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl612, zip_derived_cl562])). 869.37/113.98 thf('15', plain, 869.37/113.98 (~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e1 @ Y0))))))))) | 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e1 @ Y0)))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl1829, zip_derived_cl2403])). 869.37/113.98 thf(zip_derived_cl514, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e1 @ Y0))))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl502])). 869.37/113.98 thf(zip_derived_cl531, plain, 869.37/113.98 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e3 @ e3) @ e1 @ mactual)) => 869.37/113.98 (qmltpeq @ (op @ e3 @ e3) @ e1 @ 869.37/113.98 ('#sk1' @ (op @ e3 @ e3) @ e1 @ mactual))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl514])). 869.37/113.98 thf(zip_derived_cl559, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e3 @ e3) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl531])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl1803, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e3 @ e3) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl559, zip_derived_cl629])). 869.37/113.98 thf(zip_derived_cl579, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e1 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl540])). 869.37/113.98 thf(zip_derived_cl595, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl579])). 869.37/113.98 thf(zip_derived_cl611, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl595])). 869.37/113.98 thf(zip_derived_cl560, plain, 869.37/113.98 ((~ (qmltpeq @ (op @ e3 @ e3) @ e1 @ 869.37/113.98 ('#sk1' @ (op @ e3 @ e3) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl531])). 869.37/113.98 thf(zip_derived_cl2335, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e3 @ e3) @ e1 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e1 @ Y0))))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl611, zip_derived_cl560])). 869.37/113.98 thf('16', plain, 869.37/113.98 (~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e1 @ Y0))))))))) | 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e1 @ Y0)))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl1803, zip_derived_cl2335])). 869.37/113.98 thf('17', plain, 869.37/113.98 (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e1 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e1 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e1 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e1 @ Y0)))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl502])). 869.37/113.98 thf(zip_derived_cl496, plain, 869.37/113.98 (~ (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e2 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl17])). 869.37/113.98 thf(zip_derived_cl501, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e2 @ Y0)))))) 869.37/113.98 | ~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e2 @ Y0)))))) 869.37/113.98 | ~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e2 @ Y0)))))) 869.37/113.98 | ~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e2 @ Y0)))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl496])). 869.37/113.98 thf(zip_derived_cl513, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e2 @ Y0))))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl501])). 869.37/113.98 thf(zip_derived_cl530, plain, 869.37/113.98 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e0 @ e0) @ e2 @ mactual)) => 869.37/113.98 (qmltpeq @ (op @ e0 @ e0) @ e2 @ 869.37/113.98 ('#sk1' @ (op @ e0 @ e0) @ e2 @ mactual))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl513])). 869.37/113.98 thf(zip_derived_cl558, plain, 869.37/113.98 ((~ (qmltpeq @ (op @ e0 @ e0) @ e2 @ 869.37/113.98 ('#sk1' @ (op @ e0 @ e0) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl530])). 869.37/113.98 thf(zip_derived_cl541, plain, 869.37/113.98 (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e2 @ Y0))))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl522])). 869.37/113.98 thf(zip_derived_cl586, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e2 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl541])). 869.37/113.98 thf(zip_derived_cl602, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl586])). 869.37/113.98 thf(zip_derived_cl618, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl602])). 869.37/113.98 thf(zip_derived_cl2977, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e0 @ e0) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('sup+', [status(thm)], [zip_derived_cl558, zip_derived_cl618])). 869.37/113.98 thf(zip_derived_cl557, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e0 @ e0) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl530])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl1777, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e0 @ e0) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl557, zip_derived_cl629])). 869.37/113.98 thf('18', plain, 869.37/113.98 (~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e2 @ Y0))))))))) | 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e2 @ Y0)))))))), 869.37/113.98 inference('demod', [status(thm)], 869.37/113.98 [zip_derived_cl2977, zip_derived_cl1777])). 869.37/113.98 thf(zip_derived_cl512, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e2 @ Y0))))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl501])). 869.37/113.98 thf(zip_derived_cl529, plain, 869.37/113.98 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e1 @ e1) @ e2 @ mactual)) => 869.37/113.98 (qmltpeq @ (op @ e1 @ e1) @ e2 @ 869.37/113.98 ('#sk1' @ (op @ e1 @ e1) @ e2 @ mactual))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl512])). 869.37/113.98 thf(zip_derived_cl556, plain, 869.37/113.98 ((~ (qmltpeq @ (op @ e1 @ e1) @ e2 @ 869.37/113.98 ('#sk1' @ (op @ e1 @ e1) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl529])). 869.37/113.98 thf(zip_derived_cl585, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e2 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl541])). 869.37/113.98 thf(zip_derived_cl601, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl585])). 869.37/113.98 thf(zip_derived_cl617, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl601])). 869.37/113.98 thf(zip_derived_cl2849, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e1 @ e1) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('sup+', [status(thm)], [zip_derived_cl556, zip_derived_cl617])). 869.37/113.98 thf(zip_derived_cl555, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e1 @ e1) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl529])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl1751, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e1 @ e1) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl555, zip_derived_cl629])). 869.37/113.98 thf('19', plain, 869.37/113.98 (~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e2 @ Y0))))))))) | 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e2 @ Y0)))))))), 869.37/113.98 inference('demod', [status(thm)], 869.37/113.98 [zip_derived_cl2849, zip_derived_cl1751])). 869.37/113.98 thf(zip_derived_cl511, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e2 @ Y0))))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl501])). 869.37/113.98 thf(zip_derived_cl528, plain, 869.37/113.98 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e2 @ e2) @ e2 @ mactual)) => 869.37/113.98 (qmltpeq @ (op @ e2 @ e2) @ e2 @ 869.37/113.98 ('#sk1' @ (op @ e2 @ e2) @ e2 @ mactual))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl511])). 869.37/113.98 thf(zip_derived_cl554, plain, 869.37/113.98 ((~ (qmltpeq @ (op @ e2 @ e2) @ e2 @ 869.37/113.98 ('#sk1' @ (op @ e2 @ e2) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])). 869.37/113.98 thf(zip_derived_cl584, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e2 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl541])). 869.37/113.98 thf(zip_derived_cl600, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl584])). 869.37/113.98 thf(zip_derived_cl616, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl600])). 869.37/113.98 thf(zip_derived_cl2754, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e2 @ e2) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('sup+', [status(thm)], [zip_derived_cl554, zip_derived_cl616])). 869.37/113.98 thf(zip_derived_cl553, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e2 @ e2) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl1725, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e2 @ e2) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl553, zip_derived_cl629])). 869.37/113.98 thf('20', plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e2 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e2 @ Y0)))))))))), 869.37/113.98 inference('demod', [status(thm)], 869.37/113.98 [zip_derived_cl2754, zip_derived_cl1725])). 869.37/113.98 thf(zip_derived_cl510, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e2 @ Y0))))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl501])). 869.37/113.98 thf(zip_derived_cl527, plain, 869.37/113.98 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e3 @ e3) @ e2 @ mactual)) => 869.37/113.98 (qmltpeq @ (op @ e3 @ e3) @ e2 @ 869.37/113.98 ('#sk1' @ (op @ e3 @ e3) @ e2 @ mactual))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl510])). 869.37/113.98 thf(zip_derived_cl552, plain, 869.37/113.98 ((~ (qmltpeq @ (op @ e3 @ e3) @ e2 @ 869.37/113.98 ('#sk1' @ (op @ e3 @ e3) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl527])). 869.37/113.98 thf(zip_derived_cl583, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e2 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl541])). 869.37/113.98 thf(zip_derived_cl599, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl583])). 869.37/113.98 thf(zip_derived_cl615, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e3 @ e3) @ e2 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl599])). 869.37/113.98 thf(zip_derived_cl2706, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e3 @ e3) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e2 @ Y0))))))))))), 869.37/113.98 inference('sup+', [status(thm)], [zip_derived_cl552, zip_derived_cl615])). 869.37/113.98 thf(zip_derived_cl551, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e3 @ e3) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl527])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl1699, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e3 @ e3) @ e2 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e2 @ Y0))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl551, zip_derived_cl629])). 869.37/113.98 thf('21', plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e2 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e2 @ Y0)))))))))), 869.37/113.98 inference('demod', [status(thm)], 869.37/113.98 [zip_derived_cl2706, zip_derived_cl1699])). 869.37/113.98 thf('22', plain, 869.37/113.98 (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e2 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e2 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e2 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e2 @ Y0)))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl501])). 869.37/113.98 thf(zip_derived_cl498, plain, 869.37/113.98 (~ (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e0 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl17])). 869.37/113.98 thf(zip_derived_cl503, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e0 @ Y0)))))) 869.37/113.98 | ~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e0 @ Y0)))))) 869.37/113.98 | ~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e0 @ Y0)))))) 869.37/113.98 | ~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e0 @ Y0)))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl498])). 869.37/113.98 thf(zip_derived_cl521, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e0 @ Y0))))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl503])). 869.37/113.98 thf(zip_derived_cl538, plain, 869.37/113.98 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e0 @ e0) @ e0 @ mactual)) => 869.37/113.98 (qmltpeq @ (op @ e0 @ e0) @ e0 @ 869.37/113.98 ('#sk1' @ (op @ e0 @ e0) @ e0 @ mactual))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl521])). 869.37/113.98 thf(zip_derived_cl573, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e0 @ e0) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl538])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl2033, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e0 @ e0) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl573, zip_derived_cl629])). 869.37/113.98 thf(zip_derived_cl539, plain, 869.37/113.98 (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e0 @ Y0))))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl522])). 869.37/113.98 thf(zip_derived_cl578, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e0 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl539])). 869.37/113.98 thf(zip_derived_cl594, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl578])). 869.37/113.98 thf(zip_derived_cl610, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl594])). 869.37/113.98 thf(zip_derived_cl574, plain, 869.37/113.98 ((~ (qmltpeq @ (op @ e0 @ e0) @ e0 @ 869.37/113.98 ('#sk1' @ (op @ e0 @ e0) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl538])). 869.37/113.98 thf(zip_derived_cl2277, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e0 @ e0) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl610, zip_derived_cl574])). 869.37/113.98 thf('23', plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e0 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e0 @ Y0)))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl2033, zip_derived_cl2277])). 869.37/113.98 thf(zip_derived_cl520, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e0 @ Y0))))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl503])). 869.37/113.98 thf(zip_derived_cl537, plain, 869.37/113.98 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e1 @ e1) @ e0 @ mactual)) => 869.37/113.98 (qmltpeq @ (op @ e1 @ e1) @ e0 @ 869.37/113.98 ('#sk1' @ (op @ e1 @ e1) @ e0 @ mactual))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl520])). 869.37/113.98 thf(zip_derived_cl571, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e1 @ e1) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl537])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl2005, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e1 @ e1) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl571, zip_derived_cl629])). 869.37/113.98 thf(zip_derived_cl577, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e0 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl539])). 869.37/113.98 thf(zip_derived_cl593, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl577])). 869.37/113.98 thf(zip_derived_cl609, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e1 @ e1) @ e0 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl593])). 869.37/113.98 thf(zip_derived_cl572, plain, 869.37/113.98 ((~ (qmltpeq @ (op @ e1 @ e1) @ e0 @ 869.37/113.98 ('#sk1' @ (op @ e1 @ e1) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl537])). 869.37/113.98 thf(zip_derived_cl2245, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e1 @ e1) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl609, zip_derived_cl572])). 869.37/113.98 thf('24', plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e0 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e0 @ Y0)))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl2005, zip_derived_cl2245])). 869.37/113.98 thf(zip_derived_cl519, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e0 @ Y0))))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl503])). 869.37/113.98 thf(zip_derived_cl536, plain, 869.37/113.98 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e2 @ e2) @ e0 @ mactual)) => 869.37/113.98 (qmltpeq @ (op @ e2 @ e2) @ e0 @ 869.37/113.98 ('#sk1' @ (op @ e2 @ e2) @ e0 @ mactual))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl519])). 869.37/113.98 thf(zip_derived_cl569, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e2 @ e2) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl536])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl1977, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e2 @ e2) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl569, zip_derived_cl629])). 869.37/113.98 thf(zip_derived_cl576, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e0 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl539])). 869.37/113.98 thf(zip_derived_cl592, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl576])). 869.37/113.98 thf(zip_derived_cl608, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl592])). 869.37/113.98 thf(zip_derived_cl570, plain, 869.37/113.98 ((~ (qmltpeq @ (op @ e2 @ e2) @ e0 @ 869.37/113.98 ('#sk1' @ (op @ e2 @ e2) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl536])). 869.37/113.98 thf(zip_derived_cl2213, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e2 @ e2) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl608, zip_derived_cl570])). 869.37/113.98 thf('25', plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e0 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e0 @ Y0)))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl1977, zip_derived_cl2213])). 869.37/113.98 thf(zip_derived_cl518, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e0 @ Y0))))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl503])). 869.37/113.98 thf(zip_derived_cl535, plain, 869.37/113.98 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e3 @ e3) @ e0 @ mactual)) => 869.37/113.98 (qmltpeq @ (op @ e3 @ e3) @ e0 @ 869.37/113.98 ('#sk1' @ (op @ e3 @ e3) @ e0 @ mactual))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl518])). 869.37/113.98 thf(zip_derived_cl567, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e3 @ e3) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl535])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl1949, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e3 @ e3) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl567, zip_derived_cl629])). 869.37/113.98 thf(zip_derived_cl575, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e0 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl539])). 869.37/113.98 thf(zip_derived_cl591, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl575])). 869.37/113.98 thf(zip_derived_cl607, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl591])). 869.37/113.98 thf(zip_derived_cl568, plain, 869.37/113.98 ((~ (qmltpeq @ (op @ e3 @ e3) @ e0 @ 869.37/113.98 ('#sk1' @ (op @ e3 @ e3) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl535])). 869.37/113.98 thf(zip_derived_cl2091, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e3 @ e3) @ e0 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e0 @ Y0))))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl607, zip_derived_cl568])). 869.37/113.98 thf('26', plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e0 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e0 @ Y0)))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl1949, zip_derived_cl2091])). 869.37/113.98 thf('27', plain, 869.37/113.98 (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e0 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e0 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e0 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e0 @ Y0)))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl503])). 869.37/113.98 thf('28', plain, 869.37/113.98 (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e3 @ Y0))))))))) | 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e0 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e0 @ Y0))))))))) | 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e2 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e2 @ Y0))))))))) | 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e1 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e1 @ Y0)))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl522])). 869.37/113.98 thf(zip_derived_cl507, plain, 869.37/113.98 ((~ (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e3 @ Y0))))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0))))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl500])). 869.37/113.98 thf(zip_derived_cl524, plain, 869.37/113.98 ((~ (((mrel @ mactual @ ('#sk1' @ (op @ e2 @ e2) @ e3 @ mactual)) => 869.37/113.98 (qmltpeq @ (op @ e2 @ e2) @ e3 @ 869.37/113.98 ('#sk1' @ (op @ e2 @ e2) @ e3 @ mactual))))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl507])). 869.37/113.98 thf(zip_derived_cl546, plain, 869.37/113.98 ((~ (qmltpeq @ (op @ e2 @ e2) @ e3 @ 869.37/113.98 ('#sk1' @ (op @ e2 @ e2) @ e3 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl524])). 869.37/113.98 thf(zip_derived_cl588, plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e3 @ Y0))))))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl542])). 869.37/113.98 thf(zip_derived_cl604, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X2)))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl588])). 869.37/113.98 thf(zip_derived_cl620, plain, 869.37/113.98 ((![X2 : mworld]: 869.37/113.98 (~ (mrel @ '#sk2' @ X2) | (qmltpeq @ (op @ e2 @ e2) @ e3 @ X2))) 869.37/113.98 <= (( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl604])). 869.37/113.98 thf(zip_derived_cl3237, plain, 869.37/113.98 ((~ (mrel @ '#sk2' @ ('#sk1' @ (op @ e2 @ e2) @ e3 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0))))))) & 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e3 @ e3) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e1 @ e1) @ e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e0 @ e0) @ e3 @ Y0))))))))))), 869.37/113.98 inference('sup+', [status(thm)], [zip_derived_cl546, zip_derived_cl620])). 869.37/113.98 thf(zip_derived_cl545, plain, 869.37/113.98 (( (mrel @ mactual @ ('#sk1' @ (op @ e2 @ e2) @ e3 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0))))))))), 869.37/113.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl524])). 869.37/113.98 thf(zip_derived_cl629, plain, 869.37/113.98 (![X0 : mworld]: ( (mrel @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl504, zip_derived_cl29])). 869.37/113.98 thf(zip_derived_cl1567, plain, 869.37/113.98 (( (mrel @ '#sk2' @ ('#sk1' @ (op @ e2 @ e2) @ e3 @ mactual))) 869.37/113.98 <= (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ 869.37/113.98 (op @ e2 @ e2) @ e3 @ Y0))))))))), 869.37/113.98 inference('sup-', [status(thm)], [zip_derived_cl545, zip_derived_cl629])). 869.37/113.98 thf('29', plain, 869.37/113.98 (( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e3 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e3 @ Y0)))))) & 869.37/113.98 (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ '#sk2' @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e3 @ Y0)))))))))), 869.37/113.98 inference('demod', [status(thm)], 869.37/113.98 [zip_derived_cl3237, zip_derived_cl1567])). 869.37/113.98 thf('30', plain, 869.37/113.98 (~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ 869.37/113.98 e3 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ 869.37/113.98 e3 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ 869.37/113.98 e3 @ Y0))))))) | 869.37/113.98 ~ 869.37/113.98 ( (((!!) @ (^[Y0 : mworld]: 869.37/113.98 (((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ 869.37/113.98 e3 @ Y0)))))))), 869.37/113.98 inference('split', [status(esa)], [zip_derived_cl500])). 869.37/113.98 thf(zip_derived_cl3453, plain, ($false), 869.37/113.98 inference('sat_resolution*', [status(thm)], 869.37/113.98 ['10', '11', '12', '13', '14', '15', '16', '17', '18', '19', 869.37/113.98 '20', '21', '22', '23', '24', '25', '26', '27', '28', '29', 869.37/113.98 '30'])). 869.37/113.98 869.37/113.98 % SZS output end Refutation 869.37/113.98 869.37/113.98 869.37/113.98 % Terminating... 870.01/114.09 % Runner terminated. 870.01/114.09 % Zipperpin 1.5 exiting 870.01/114.11 EOF