0.08/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.K0co8uTGGA true 0.10/0.31 % Computer : n029.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 1440 0.10/0.31 % WCLimit : 180 0.10/0.31 % DateTime : Thu Jul 4 09:45:39 EDT 2024 0.10/0.31 % CPUTime : 0.10/0.31 % Running portfolio for 1440 s 0.10/0.31 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.10/0.31 % Number of cores: 8 0.10/0.32 % Python version: Python 3.6.8 0.14/0.32 % Running in HO mode 0.44/0.69 % Total configuration time : 828 0.44/0.69 % Estimated wc time : 1656 0.44/0.69 % Estimated cpu time (8 cpus) : 207.0 0.47/0.85 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.47/0.86 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.47/0.86 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.47/0.86 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.47/0.88 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.47/0.88 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.47/0.97 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.47/0.99 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.48/1.10 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 0.48/1.17 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s 3.18/1.35 % /export/starexec/sandbox/solver/bin/lams/15_old_s4.sh running for 30s 3.80/1.51 % /export/starexec/sandbox/solver/bin/lams/15_lifting3.sh running for 30s 197.18/30.86 % /export/starexec/sandbox/solver/bin/lams/33_shallow_sine.sh running for 66s 198.09/30.94 % /export/starexec/sandbox/solver/bin/lams/40_e_lift.sh running for 80s 202.62/31.66 % /export/starexec/sandbox/solver/bin/lams/15_lifting1.sh running for 30s 202.72/31.69 % /export/starexec/sandbox/solver/bin/lams/8_new_cnf.sh running for 16s 313.72/47.71 % /export/starexec/sandbox/solver/bin/lams/10_e_short2.sh running for 20s 382.20/57.19 % /export/starexec/sandbox/solver/bin/lams/8_add_var_l_av.sh running for 16s 411.24/61.18 % /export/starexec/sandbox/solver/bin/lams/8_new_sh_or.sh running for 16s 411.74/61.30 % /export/starexec/sandbox/solver/bin/lams/30_old_zip1.sh running for 36s 413.95/61.57 % /export/starexec/sandbox/solver/bin/lams/10_shallow_lift.sh running for 30s 414.48/61.67 % /export/starexec/sandbox/solver/bin/lams/15_lcnf_noform.sh running for 30s 465.60/68.10 % /export/starexec/sandbox/solver/bin/lams/8_sh.eqenc2.sh running for 10s 505.02/73.10 % /export/starexec/sandbox/solver/bin/lams/8_cmb.lcnf4.sh running for 10s 545.48/78.17 % /export/starexec/sandbox/solver/bin/lams/8_new_l_av.sh running for 24s 550.56/78.87 % /export/starexec/sandbox/solver/bin/lams/10_forms1.sh running for 20s 565.33/80.71 % /export/starexec/sandbox/solver/bin/lams/10_forms4.sh running for 20s 566.22/80.86 % /export/starexec/sandbox/solver/bin/lams/15_ch_av2.sh running for 26s 575.14/81.95 % /export/starexec/sandbox/solver/bin/lams/15_sine_deep.sh running for 44s 584.75/83.19 % /export/starexec/sandbox/solver/bin/lams/10_shallow_sine.sh running for 30s 585.79/83.35 % /export/starexec/sandbox/solver/bin/lams/20_new_c.s3.sh running for 40s 644.51/90.78 % /export/starexec/sandbox/solver/bin/lams/10_forms2.sh running for 20s 650.76/91.63 % /export/starexec/sandbox/solver/bin/lams/8_sh.or.sh running for 24s 653.09/91.91 % /export/starexec/sandbox/solver/bin/lams/15_combs_pe.sh running for 20s 695.88/97.37 % /export/starexec/sandbox/solver/bin/lams/15_b.split.li.sh running for 44s 722.41/100.76 % /export/starexec/sandbox/solver/bin/lams/18_sh1.sh running for 36s 770.86/106.93 % /export/starexec/sandbox/solver/bin/lams/8_no_ord.sh running for 10s 794.02/109.91 % Solved by lams/15_combs_pe.sh. 794.02/109.91 % done 1313 iterations in 17.943s 794.02/109.91 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 794.02/109.91 % SZS output start Refutation 794.02/109.91 thf(individuals_type, type, individuals: $tType). 794.02/109.91 thf('#sk369_type', type, '#sk369': $i). 794.02/109.91 thf('#sk368_type', type, '#sk368': $i). 794.02/109.91 thf(cs4_atom_type, type, cs4_atom: ($i > $o) > $i > $o). 794.02/109.91 thf(cs4_impl_type, type, cs4_impl: ($i > $o) > ($i > $o) > $i > $o). 794.02/109.91 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 794.02/109.91 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 794.02/109.91 thf(reli_type, type, reli: $i > $i > $o). 794.02/109.91 thf('#sk372_type', type, '#sk372': $i). 794.02/109.91 thf('#sk73_type', type, '#sk73': ($i > $o) > $i > $i). 794.02/109.91 thf('#sk5_type', type, '#sk5': ($i > $o) > $i > $i). 794.02/109.91 thf(relr_type, type, relr: $i > $i > $o). 794.02/109.91 thf(mimpl_type, type, mimpl: ($i > $o) > ($i > $o) > $i > $o). 794.02/109.91 thf(bl_valid_type, type, bl_valid: ($i > $o) > $o). 794.02/109.91 thf(bl_atom_type, type, bl_atom: ($i > $o) > $i > $o). 794.02/109.91 thf(cs4_box_type, type, cs4_box: ($i > $o) > $i > $o). 794.02/109.91 thf(bl_impl_type, type, bl_impl: ($i > $o) > ($i > $o) > $i > $o). 794.02/109.91 thf(bl_says_type, type, bl_says: individuals > ($i > $o) > $i > $o). 794.02/109.91 thf(bl_princ_type, type, bl_princ: ($i > $o) > $i > $o). 794.02/109.91 thf('#sk367_type', type, '#sk367': $i > $o). 794.02/109.91 thf('#sk366_type', type, '#sk366': individuals). 794.02/109.91 thf('#sk371_type', type, '#sk371': $i). 794.02/109.91 thf('#sk370_type', type, '#sk370': $i). 794.02/109.91 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 794.02/109.91 thf(princ_inj_type, type, princ_inj: individuals > $i > $o). 794.02/109.91 thf(mbox_type, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o). 794.02/109.91 thf(bl_valid_def, axiom,(( bl_valid ) = (mvalid))). 794.02/109.91 thf(mvalid, axiom,(( mvalid ) = (^[P:( $i > $o )]: ( ![W:$i]: ( P @ W ) )))). 794.02/109.91 thf('0', plain, (( mvalid ) = ( ^[P:( $i > $o )]: ( ![W:$i]: ( P @ W ) ) )), 794.02/109.91 inference('simplify_rw_rule', [status(thm)], [mvalid])). 794.02/109.91 thf('1', plain, 794.02/109.91 (( mvalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 794.02/109.91 define([status(thm)])). 794.02/109.91 thf('2', plain, (( bl_valid ) = ( mvalid )), 794.02/109.91 inference('simplify_rw_rule', [status(thm)], [bl_valid_def, '1'])). 794.02/109.91 thf('3', plain, (( bl_valid ) = ( mvalid )), define([status(thm)])). 794.02/109.91 thf(bl_says, axiom,(( bl_says ) = 794.02/109.91 (^[K:individuals,A:( $i > $o )]: 794.02/109.91 ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ K ) ) @ A ) )))). 794.02/109.91 thf(bl_princ, axiom,(( bl_princ ) = (^[P:( $i > $o )]: ( cs4_atom @ P )))). 794.02/109.91 thf(cs4_atom, axiom,(( cs4_atom ) = 794.02/109.91 (^[P:( $i > $o )]: ( mbox @ reli @ P )))). 794.02/109.91 thf(mbox, axiom,(( mbox ) = 794.02/109.91 (^[R:( $i > $i > $o ),P:( $i > $o ),X:$i]: 794.02/109.91 ( ![Y:$i]: ( ( R @ X @ Y ) => ( P @ Y ) ) )))). 794.02/109.91 thf('4', plain, 794.02/109.91 (( mbox ) = 794.02/109.91 ( ^[R:( $i > $i > $o ),P:( $i > $o ),X:$i]: 794.02/109.91 ( ![Y:$i]: ( ( R @ X @ Y ) => ( P @ Y ) ) ) )), 794.02/109.91 inference('simplify_rw_rule', [status(thm)], [mbox])). 794.02/109.91 thf('5', plain, 794.02/109.91 (( mbox ) = 794.02/109.91 ( ^[V_1:( $i > $i > $o ),V_2:( $i > $o ),V_3:$i]: 794.02/109.91 ( ![X4:$i]: ( ( V_1 @ V_3 @ X4 ) => ( V_2 @ X4 ) ) ) )), 794.02/109.91 define([status(thm)])). 794.02/109.91 thf('6', plain, (( cs4_atom ) = ( ^[P:( $i > $o )]: ( mbox @ reli @ P ) )), 794.02/109.91 inference('simplify_rw_rule', [status(thm)], [cs4_atom, '5'])). 794.02/109.91 thf('7', plain, 794.02/109.91 (( cs4_atom ) = ( ^[V_1:( $i > $o )]: ( mbox @ reli @ V_1 ) )), 794.02/109.91 define([status(thm)])). 794.02/109.91 thf('8', plain, (( bl_princ ) = ( ^[P:( $i > $o )]: ( cs4_atom @ P ) )), 794.02/109.91 inference('simplify_rw_rule', [status(thm)], [bl_princ, '7', '5'])). 794.02/109.91 thf('9', plain, (( bl_princ ) = ( ^[V_1:( $i > $o )]: ( cs4_atom @ V_1 ) )), 794.02/109.91 define([status(thm)])). 794.02/109.91 thf(cs4_box, axiom,(( cs4_box ) = 794.02/109.91 (^[A:( $i > $o )]: ( mbox @ reli @ ( mbox @ relr @ A ) )))). 794.02/109.91 thf('10', plain, 794.02/109.91 (( cs4_box ) = 794.02/109.91 ( ^[A:( $i > $o )]: ( mbox @ reli @ ( mbox @ relr @ A ) ) )), 794.02/109.91 inference('simplify_rw_rule', [status(thm)], [cs4_box, '5'])). 794.02/109.91 thf('11', plain, 794.02/109.91 (( cs4_box ) = 794.02/109.91 ( ^[V_1:( $i > $o )]: ( mbox @ reli @ ( mbox @ relr @ V_1 ) ) )), 794.02/109.91 define([status(thm)])). 794.02/109.91 thf(cs4_impl, axiom,(( cs4_impl ) = 794.02/109.91 (^[A:( $i > $o ),B:( $i > $o )]: ( mbox @ reli @ ( mimpl @ A @ B ) )))). 794.02/109.91 thf(mimpl, axiom,(( mimpl ) = 794.02/109.91 (^[U:( $i > $o ),V:( $i > $o )]: ( mor @ ( mnot @ U ) @ V )))). 794.02/109.91 thf(mor, axiom,(( mor ) = 794.02/109.91 (^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) | ( Y @ U ) )))). 794.02/109.91 thf('12', plain, 794.02/109.91 (( mor ) = 794.02/109.91 ( ^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) | ( Y @ U ) ) )), 794.02/109.91 inference('simplify_rw_rule', [status(thm)], [mor])). 794.02/109.91 thf('13', plain, 794.02/109.91 (( mor ) = 794.02/109.91 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 794.02/109.91 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 794.02/109.91 define([status(thm)])). 794.02/109.91 thf(mnot, axiom,(( mnot ) = (^[X:( $i > $o ),U:$i]: ( ~( X @ U ) )))). 794.02/109.91 thf('14', plain, (( mnot ) = ( ^[X:( $i > $o ),U:$i]: ( ~( X @ U ) ) )), 794.02/109.91 inference('simplify_rw_rule', [status(thm)], [mnot])). 794.02/109.91 thf('15', plain, 794.02/109.91 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )), 794.02/109.91 define([status(thm)])). 794.02/109.91 thf('16', plain, 794.02/109.91 (( mimpl ) = 794.02/109.91 ( ^[U:( $i > $o ),V:( $i > $o )]: ( mor @ ( mnot @ U ) @ V ) )), 794.02/109.91 inference('simplify_rw_rule', [status(thm)], [mimpl, '13', '15'])). 794.02/109.91 thf('17', plain, 794.02/109.91 (( mimpl ) = 794.02/109.91 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )), 794.02/109.91 define([status(thm)])). 794.02/109.91 thf('18', plain, 794.02/109.91 (( cs4_impl ) = 794.02/109.91 ( ^[A:( $i > $o ),B:( $i > $o )]: ( mbox @ reli @ ( mimpl @ A @ B ) ) )), 794.02/109.91 inference('simplify_rw_rule', [status(thm)], 794.02/109.91 [cs4_impl, '5', '17', '13', '15'])). 794.02/109.91 thf('19', plain, 794.02/109.91 (( cs4_impl ) = 794.02/109.91 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 794.02/109.91 ( mbox @ reli @ ( mimpl @ V_1 @ V_2 ) ) )), 794.02/109.91 define([status(thm)])). 794.02/109.91 thf('20', plain, 794.02/109.91 (( bl_says ) = 794.02/109.91 ( ^[K:individuals,A:( $i > $o )]: 794.02/109.91 ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ K ) ) @ A ) ) )), 794.02/109.91 inference('simplify_rw_rule', [status(thm)], 794.02/109.91 [bl_says, '9', '11', '19', '7', '5', '17', '13', '15'])). 794.02/109.91 thf('21', plain, 794.02/109.91 (( bl_says ) = 794.02/109.91 ( ^[V_1:individuals,V_2:( $i > $o )]: 794.02/109.91 ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ V_1 ) ) @ V_2 ) ) )), 794.02/109.91 define([status(thm)])). 794.02/109.91 thf(bl_impl, axiom,(( bl_impl ) = 794.02/109.91 (^[A:( $i > $o ),B:( $i > $o )]: ( cs4_impl @ A @ B )))). 794.02/109.91 thf('22', plain, 794.02/109.91 (( bl_impl ) = ( ^[A:( $i > $o ),B:( $i > $o )]: ( cs4_impl @ A @ B ) )), 794.02/109.91 inference('simplify_rw_rule', [status(thm)], 794.02/109.91 [bl_impl, '19', '5', '17', '13', '15'])). 794.02/109.91 thf('23', plain, 794.02/109.91 (( bl_impl ) = 794.02/109.91 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( cs4_impl @ V_1 @ V_2 ) )), 794.02/109.91 define([status(thm)])). 794.02/109.91 thf(bl_atom, axiom,(( bl_atom ) = (^[P:( $i > $o )]: ( cs4_atom @ P )))). 794.02/109.91 thf('24', plain, (( bl_atom ) = ( ^[P:( $i > $o )]: ( cs4_atom @ P ) )), 794.02/109.91 inference('simplify_rw_rule', [status(thm)], [bl_atom, '7', '5'])). 794.02/109.91 thf('25', plain, (( bl_atom ) = ( ^[V_1:( $i > $o )]: ( cs4_atom @ V_1 ) )), 794.02/109.91 define([status(thm)])). 794.02/109.91 thf(bl_c4, conjecture, 794.02/109.91 (![K:individuals,A:( $i > $o )]: 794.02/109.91 ( bl_valid @ 794.02/109.91 ( bl_impl @ 794.02/109.91 ( bl_says @ K @ ( bl_says @ K @ ( bl_atom @ A ) ) ) @ 794.02/109.91 ( bl_says @ K @ ( bl_atom @ A ) ) ) ))). 794.02/109.91 thf(zf_stmt_0, conjecture, 794.02/109.91 (![X4:individuals,X6:( $i > $o ),X8:$i,X10:$i]: 794.02/109.91 ( ( reli @ X8 @ X10 ) => 794.02/109.91 ( ( ![X30:$i]: 794.02/109.91 ( ( reli @ X10 @ X30 ) => 794.02/109.91 ( ![X32:$i]: 794.02/109.91 ( ( relr @ X30 @ X32 ) => 794.02/109.91 ( ![X34:$i]: 794.02/109.91 ( ( reli @ X32 @ X34 ) => 794.02/109.91 ( ( ![X38:$i]: ( ( reli @ X34 @ X38 ) => ( X6 @ X38 ) ) ) | 794.02/109.91 ( ~( ![X36:$i]: 794.02/109.91 ( ( reli @ X34 @ X36 ) => ( princ_inj @ X4 @ X36 ) ) ) ) ) ) ) ) ) ) ) | 794.02/109.91 ( ~( ![X12:$i]: 794.02/109.91 ( ( reli @ X10 @ X12 ) => 794.02/109.91 ( ![X14:$i]: 794.02/109.91 ( ( relr @ X12 @ X14 ) => 794.02/109.91 ( ![X16:$i]: 794.02/109.91 ( ( reli @ X14 @ X16 ) => 794.02/109.91 ( ( ![X20:$i]: 794.02/109.91 ( ( reli @ X16 @ X20 ) => 794.02/109.91 ( ![X22:$i]: 794.02/109.91 ( ( relr @ X20 @ X22 ) => 794.02/109.91 ( ![X24:$i]: 794.02/109.91 ( ( reli @ X22 @ X24 ) => 794.02/109.91 ( ( ![X28:$i]: 794.02/109.91 ( ( reli @ X24 @ X28 ) => 794.02/109.91 ( X6 @ X28 ) ) ) | 794.02/109.91 ( ~( ![X26:$i]: 794.02/109.91 ( ( reli @ X24 @ X26 ) => 794.02/109.91 ( princ_inj @ X4 @ X26 ) ) ) ) ) ) ) ) ) ) ) | 794.02/109.91 ( ~( ![X18:$i]: 794.02/109.91 ( ( reli @ X16 @ X18 ) => 794.02/109.91 ( princ_inj @ X4 @ X18 ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 794.02/109.91 thf(zf_stmt_1, negated_conjecture, 794.02/109.91 (~( ![X4:individuals,X6:( $i > $o ),X8:$i,X10:$i]: 794.02/109.91 ( ( reli @ X8 @ X10 ) => 794.02/109.91 ( ( ![X30:$i]: 794.02/109.91 ( ( reli @ X10 @ X30 ) => 794.02/109.91 ( ![X32:$i]: 794.02/109.91 ( ( relr @ X30 @ X32 ) => 794.02/109.91 ( ![X34:$i]: 794.02/109.91 ( ( reli @ X32 @ X34 ) => 794.02/109.91 ( ( ![X38:$i]: ( ( reli @ X34 @ X38 ) => ( X6 @ X38 ) ) ) | 794.02/109.91 ( ~( ![X36:$i]: 794.02/109.91 ( ( reli @ X34 @ X36 ) => 794.02/109.91 ( princ_inj @ X4 @ X36 ) ) ) ) ) ) ) ) ) ) ) | 794.02/109.91 ( ~( ![X12:$i]: 794.02/109.91 ( ( reli @ X10 @ X12 ) => 794.02/109.91 ( ![X14:$i]: 794.02/109.91 ( ( relr @ X12 @ X14 ) => 794.02/109.91 ( ![X16:$i]: 794.02/109.91 ( ( reli @ X14 @ X16 ) => 794.02/109.91 ( ( ![X20:$i]: 794.02/109.91 ( ( reli @ X16 @ X20 ) => 794.02/109.91 ( ![X22:$i]: 794.02/109.91 ( ( relr @ X20 @ X22 ) => 794.02/109.91 ( ![X24:$i]: 794.02/109.91 ( ( reli @ X22 @ X24 ) => 794.02/109.91 ( ( ![X28:$i]: 794.02/109.91 ( ( reli @ X24 @ X28 ) => 794.02/109.91 ( X6 @ X28 ) ) ) | 794.02/109.91 ( ~( ![X26:$i]: 794.02/109.91 ( ( reli @ X24 @ X26 ) => 794.02/109.91 ( princ_inj @ X4 @ X26 ) ) ) ) ) ) ) ) ) ) ) | 794.02/109.91 ( ~( ![X18:$i]: 794.02/109.91 ( ( reli @ X16 @ X18 ) => 794.02/109.91 ( princ_inj @ X4 @ X18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 794.02/109.91 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 794.02/109.91 thf(zip_derived_cl6, plain, 794.02/109.91 (~ (((!!) @ (^[Y0 : individuals]: 794.02/109.91 (((!!) @ (^[Y1 : $i > $o]: 794.02/109.91 (((!!) @ (^[Y2 : $i]: 794.02/109.91 (((!!) @ (^[Y3 : $i]: 794.02/109.91 (((reli @ Y2 @ Y3) => 794.02/109.91 (((((!!) @ ( 794.02/109.91 ^[Y4 : $i]: 794.02/109.91 (((reli @ 794.02/109.91 Y3 @ Y4) => 794.02/109.91 (((!!) @ ( 794.02/109.91 ^[Y5 : $i]: 794.02/109.91 (( 794.02/109.91 (relr @ 794.02/109.91 Y4 @ 794.02/109.91 Y5) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y6 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y5 @ 794.02/109.91 Y6) => 794.02/109.91 (( 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y7 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y6 @ 794.02/109.91 Y7) => 794.02/109.91 (Y1 @ Y7)))))) | 794.02/109.91 (( 794.02/109.91 (~) @ ( 794.02/109.91 ( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y7 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y6 @ 794.02/109.91 Y7) => 794.02/109.91 (princ_inj @ 794.02/109.91 Y0 @ Y7))))))))))))))))))))))))) | 794.02/109.91 (((~) @ (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y4 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y3 @ 794.02/109.91 Y4) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y5 : $i]: 794.02/109.91 (( 794.02/109.91 (relr @ 794.02/109.91 Y4 @ 794.02/109.91 Y5) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y6 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y5 @ 794.02/109.91 Y6) => 794.02/109.91 (( 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y7 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y6 @ 794.02/109.91 Y7) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y8 : $i]: 794.02/109.91 (( 794.02/109.91 (relr @ 794.02/109.91 Y7 @ 794.02/109.91 Y8) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y9 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y8 @ 794.02/109.91 Y9) => 794.02/109.91 (( 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y10 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y9 @ 794.02/109.91 Y10) => 794.02/109.91 (Y1 @ 794.02/109.91 Y10)))))) | 794.02/109.91 (( 794.02/109.91 (~) @ ( 794.02/109.91 ( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y10 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y9 @ 794.02/109.91 Y10) => 794.02/109.91 (princ_inj @ 794.02/109.91 Y0 @ Y10))))))))))))))))))))))))) | 794.02/109.91 (( 794.02/109.91 (~) @ ( 794.02/109.91 ( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y7 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y6 @ 794.02/109.91 Y7) => 794.02/109.91 (princ_inj @ 794.02/109.91 Y0 @ Y7)))))))))))))))))))))))))))))))))))))))))))), 794.02/109.91 inference('cnf', [status(esa)], [zf_stmt_1])). 794.02/109.91 thf(zip_derived_cl295, plain, 794.02/109.91 (~ (((!!) @ (^[Y0 : $i > $o]: 794.02/109.91 (((!!) @ (^[Y1 : $i]: 794.02/109.91 (((!!) @ (^[Y2 : $i]: 794.02/109.91 (((reli @ Y1 @ Y2) => 794.02/109.91 (((((!!) @ (^[Y3 : $i]: 794.02/109.91 (((reli @ Y2 @ 794.02/109.91 Y3) => 794.02/109.91 (((!!) @ ( 794.02/109.91 ^[Y4 : $i]: 794.02/109.91 (((relr @ 794.02/109.91 Y3 @ 794.02/109.91 Y4) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y5 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y4 @ 794.02/109.91 Y5) => 794.02/109.91 (( 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y6 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y5 @ 794.02/109.91 Y6) => 794.02/109.91 (Y0 @ Y6)))))) | 794.02/109.91 (( 794.02/109.91 (~) @ ( 794.02/109.91 ( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y6 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y5 @ 794.02/109.91 Y6) => 794.02/109.91 (princ_inj @ 794.02/109.91 '#sk366' @ 794.02/109.91 Y6))))))))))))))))))))))))) | 794.02/109.91 (((~) @ (((!!) @ (^[Y3 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y2 @ 794.02/109.91 Y3) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y4 : $i]: 794.02/109.91 (( 794.02/109.91 (relr @ 794.02/109.91 Y3 @ 794.02/109.91 Y4) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y5 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y4 @ 794.02/109.91 Y5) => 794.02/109.91 (( 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y6 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y5 @ 794.02/109.91 Y6) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y7 : $i]: 794.02/109.91 (( 794.02/109.91 (relr @ 794.02/109.91 Y6 @ 794.02/109.91 Y7) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y8 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y7 @ 794.02/109.91 Y8) => 794.02/109.91 (( 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y9 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y8 @ 794.02/109.91 Y9) => 794.02/109.91 (Y0 @ Y9)))))) | 794.02/109.91 (( 794.02/109.91 (~) @ ( 794.02/109.91 ( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y9 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y8 @ 794.02/109.91 Y9) => 794.02/109.91 (princ_inj @ 794.02/109.91 '#sk366' @ 794.02/109.91 Y9))))))))))))))))))))))))) | 794.02/109.91 (( 794.02/109.91 (~) @ ( 794.02/109.91 ( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y6 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y5 @ 794.02/109.91 Y6) => 794.02/109.91 (princ_inj @ 794.02/109.91 '#sk366' @ 794.02/109.91 Y6))))))))))))))))))))))))))))))))))))))))), 794.02/109.91 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 794.02/109.91 thf(zip_derived_cl296, plain, 794.02/109.91 (~ (((!!) @ (^[Y0 : $i]: 794.02/109.91 (((!!) @ (^[Y1 : $i]: 794.02/109.91 (((reli @ Y0 @ Y1) => 794.02/109.91 (((((!!) @ (^[Y2 : $i]: 794.02/109.91 (((reli @ Y1 @ Y2) => 794.02/109.91 (((!!) @ (^[Y3 : $i]: 794.02/109.91 (((relr @ Y2 @ 794.02/109.91 Y3) => 794.02/109.91 (((!!) @ ( 794.02/109.91 ^[Y4 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y3 @ 794.02/109.91 Y4) => 794.02/109.91 (( 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y5 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y4 @ 794.02/109.91 Y5) => 794.02/109.91 ('#sk367' @ 794.02/109.91 Y5)))))) | 794.02/109.91 (( 794.02/109.91 (~) @ ( 794.02/109.91 ( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y5 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y4 @ 794.02/109.91 Y5) => 794.02/109.91 (princ_inj @ 794.02/109.91 '#sk366' @ 794.02/109.91 Y5))))))))))))))))))))))))) | 794.02/109.91 (((~) @ (((!!) @ (^[Y2 : $i]: 794.02/109.91 (((reli @ Y1 @ Y2) => 794.02/109.91 (((!!) @ (^[Y3 : $i]: 794.02/109.91 (( 794.02/109.91 (relr @ 794.02/109.91 Y2 @ 794.02/109.91 Y3) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y4 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y3 @ 794.02/109.91 Y4) => 794.02/109.91 (( 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y5 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y4 @ 794.02/109.91 Y5) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y6 : $i]: 794.02/109.91 (( 794.02/109.91 (relr @ 794.02/109.91 Y5 @ 794.02/109.91 Y6) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y7 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y6 @ 794.02/109.91 Y7) => 794.02/109.91 (( 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y8 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y7 @ 794.02/109.91 Y8) => 794.02/109.91 ('#sk367' @ 794.02/109.91 Y8)))))) | 794.02/109.91 (( 794.02/109.91 (~) @ ( 794.02/109.91 ( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y8 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y7 @ 794.02/109.91 Y8) => 794.02/109.91 (princ_inj @ 794.02/109.91 '#sk366' @ 794.02/109.91 Y8))))))))))))))))))))))))) | 794.02/109.91 (( 794.02/109.91 (~) @ ( 794.02/109.91 ( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y5 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y4 @ 794.02/109.91 Y5) => 794.02/109.91 (princ_inj @ 794.02/109.91 '#sk366' @ 794.02/109.91 Y5)))))))))))))))))))))))))))))))))))))), 794.02/109.91 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl295])). 794.02/109.91 thf(zip_derived_cl297, plain, 794.02/109.91 (~ (((!!) @ (^[Y0 : $i]: 794.02/109.91 (((reli @ '#sk368' @ Y0) => 794.02/109.91 (((((!!) @ (^[Y1 : $i]: 794.02/109.91 (((reli @ Y0 @ Y1) => 794.02/109.91 (((!!) @ (^[Y2 : $i]: 794.02/109.91 (((relr @ Y1 @ Y2) => 794.02/109.91 (((!!) @ (^[Y3 : $i]: 794.02/109.91 (((reli @ 794.02/109.91 Y2 @ Y3) => 794.02/109.91 (((( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y4 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y3 @ 794.02/109.91 Y4) => 794.02/109.91 ('#sk367' @ 794.02/109.91 Y4)))))) | 794.02/109.91 (( 794.02/109.91 (~) @ ( 794.02/109.91 ((!!) @ ( 794.02/109.91 ^[Y4 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y3 @ 794.02/109.91 Y4) => 794.02/109.91 (princ_inj @ 794.02/109.91 '#sk366' @ 794.02/109.91 Y4))))))))))))))))))))))))) | 794.02/109.91 (((~) @ (((!!) @ (^[Y1 : $i]: 794.02/109.91 (((reli @ Y0 @ Y1) => 794.02/109.91 (((!!) @ (^[Y2 : $i]: 794.02/109.91 (((relr @ Y1 @ 794.02/109.91 Y2) => 794.02/109.91 (((!!) @ ( 794.02/109.91 ^[Y3 : $i]: 794.02/109.91 (((reli @ 794.02/109.91 Y2 @ Y3) => 794.02/109.91 (((( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y4 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y3 @ 794.02/109.91 Y4) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y5 : $i]: 794.02/109.91 (( 794.02/109.91 (relr @ 794.02/109.91 Y4 @ 794.02/109.91 Y5) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y6 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y5 @ 794.02/109.91 Y6) => 794.02/109.91 (( 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y7 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y6 @ 794.02/109.91 Y7) => 794.02/109.91 ('#sk367' @ 794.02/109.91 Y7)))))) | 794.02/109.91 (( 794.02/109.91 (~) @ ( 794.02/109.91 ( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y7 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y6 @ 794.02/109.91 Y7) => 794.02/109.91 (princ_inj @ 794.02/109.91 '#sk366' @ 794.02/109.91 Y7))))))))))))))))))))))))) | 794.02/109.91 (( 794.02/109.91 (~) @ ( 794.02/109.91 ((!!) @ ( 794.02/109.91 ^[Y4 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y3 @ 794.02/109.91 Y4) => 794.02/109.91 (princ_inj @ 794.02/109.91 '#sk366' @ 794.02/109.91 Y4))))))))))))))))))))))))))))))))))), 794.02/109.91 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl296])). 794.02/109.91 thf(zip_derived_cl298, plain, 794.02/109.91 (~ (((reli @ '#sk368' @ '#sk369') => 794.02/109.91 (((((!!) @ (^[Y0 : $i]: 794.02/109.91 (((reli @ '#sk369' @ Y0) => 794.02/109.91 (((!!) @ (^[Y1 : $i]: 794.02/109.91 (((relr @ Y0 @ Y1) => 794.02/109.91 (((!!) @ (^[Y2 : $i]: 794.02/109.91 (((reli @ Y1 @ Y2) => 794.02/109.91 (((((!!) @ (^[Y3 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y2 @ 794.02/109.91 Y3) => 794.02/109.91 ('#sk367' @ 794.02/109.91 Y3)))))) | 794.02/109.91 (((~) @ (((!!) @ ( 794.02/109.91 ^[Y3 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y2 @ 794.02/109.91 Y3) => 794.02/109.91 (princ_inj @ 794.02/109.91 '#sk366' @ 794.02/109.91 Y3))))))))))))))))))))))))) | 794.02/109.91 (((~) @ (((!!) @ (^[Y0 : $i]: 794.02/109.91 (((reli @ '#sk369' @ Y0) => 794.02/109.91 (((!!) @ (^[Y1 : $i]: 794.02/109.91 (((relr @ Y0 @ Y1) => 794.02/109.91 (((!!) @ (^[Y2 : $i]: 794.02/109.91 (((reli @ Y1 @ 794.02/109.91 Y2) => 794.02/109.91 (((((!!) @ ( 794.02/109.91 ^[Y3 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y2 @ 794.02/109.91 Y3) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y4 : $i]: 794.02/109.91 (( 794.02/109.91 (relr @ 794.02/109.91 Y3 @ 794.02/109.91 Y4) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y5 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y4 @ 794.02/109.91 Y5) => 794.02/109.91 (( 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y6 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y5 @ 794.02/109.91 Y6) => 794.02/109.91 ('#sk367' @ 794.02/109.91 Y6)))))) | 794.02/109.91 (( 794.02/109.91 (~) @ ( 794.02/109.91 ( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y6 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y5 @ 794.02/109.91 Y6) => 794.02/109.91 (princ_inj @ 794.02/109.91 '#sk366' @ 794.02/109.91 Y6))))))))))))))))))))))))) | 794.02/109.91 (((~) @ ( 794.02/109.91 ((!!) @ ( 794.02/109.91 ^[Y3 : $i]: 794.02/109.91 ( 794.02/109.91 ( 794.02/109.91 (reli @ 794.02/109.91 Y2 @ 794.02/109.91 Y3) => 794.02/109.91 (princ_inj @ 794.02/109.91 '#sk366' @ 794.02/109.91 Y3)))))))))))))))))))))))))))))))), 794.02/109.91 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl297])). 794.02/109.91 thf(zip_derived_cl300, plain, 794.02/109.91 (~ (((((!!) @ (^[Y0 : $i]: 794.02/109.91 (((reli @ '#sk369' @ Y0) => 794.02/109.91 (((!!) @ (^[Y1 : $i]: 794.02/109.91 (((relr @ Y0 @ Y1) => 794.02/109.91 (((!!) @ (^[Y2 : $i]: 794.02/109.91 (((reli @ Y1 @ Y2) => 794.02/109.91 (((((!!) @ (^[Y3 : $i]: 794.02/109.91 (((reli @ 794.02/109.91 Y2 @ 794.02/109.91 Y3) => 794.02/109.91 ('#sk367' @ 794.02/109.91 Y3)))))) | 794.02/109.91 (((~) @ (((!!) @ ( 794.02/109.91 ^[Y3 : $i]: 794.02/109.91 (((reli @ 794.02/109.91 Y2 @ 794.02/109.91 Y3) => 794.02/109.91 (princ_inj @ 794.02/109.91 '#sk366' @ 794.02/109.91 Y3))))))))))))))))))))))))) | 794.02/109.91 (((~) @ (((!!) @ (^[Y0 : $i]: 794.02/109.91 (((reli @ '#sk369' @ Y0) => 794.02/109.91 (((!!) @ (^[Y1 : $i]: 794.02/109.91 (((relr @ Y0 @ Y1) => 794.02/109.91 (((!!) @ (^[Y2 : $i]: 794.02/109.91 (((reli @ Y1 @ 794.02/109.91 Y2) => 794.02/109.91 (((((!!) @ ( 794.02/109.91 ^[Y3 : $i]: 794.02/109.91 (((reli @ 794.02/109.91 Y2 @ 794.02/109.91 Y3) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y4 : $i]: 794.02/109.91 (( 794.02/109.91 (relr @ 794.02/109.91 Y3 @ 794.02/109.91 Y4) => 794.02/109.91 (( 794.02/109.91 (!!) @ ( 794.02/109.91 ^[Y5 : $i]: 794.02/109.91 (( 794.02/109.91 (reli @ 794.02/109.91 Y4 @ 794.02/109.91 Y5) => 794.02/109.91 (( 794.02/109.91 (( 794.02/109.92 (!!) @ ( 794.02/109.92 ^[Y6 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y5 @ 794.02/109.92 Y6) => 794.02/109.92 ('#sk367' @ 794.02/109.92 Y6)))))) | 794.02/109.92 (( 794.02/109.92 (~) @ ( 794.02/109.92 ( 794.02/109.92 (!!) @ ( 794.02/109.92 ^[Y6 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y5 @ 794.02/109.92 Y6) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ 794.02/109.92 Y6))))))))))))))))))))))))) | 794.02/109.92 (((~) @ ( 794.02/109.92 ((!!) @ ( 794.02/109.92 ^[Y3 : $i]: 794.02/109.92 (((reli @ 794.02/109.92 Y2 @ 794.02/109.92 Y3) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ 794.02/109.92 Y3)))))))))))))))))))))))))))))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl298])). 794.02/109.92 thf(zip_derived_cl301, plain, 794.02/109.92 (~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ '#sk369' @ Y0) => 794.02/109.92 (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((relr @ Y0 @ Y1) => 794.02/109.92 (((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ Y2) => 794.02/109.92 (((((!!) @ (^[Y3 : $i]: 794.02/109.92 (((reli @ 794.02/109.92 Y2 @ Y3) => 794.02/109.92 ('#sk367' @ 794.02/109.92 Y3)))))) | 794.02/109.92 (((~) @ (((!!) @ ( 794.02/109.92 ^[Y3 : $i]: 794.02/109.92 (((reli @ 794.02/109.92 Y2 @ Y3) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ 794.02/109.92 Y3)))))))))))))))))))))))))), 794.02/109.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl300])). 794.02/109.92 thf(zip_derived_cl303, plain, 794.02/109.92 (~ (((reli @ '#sk369' @ '#sk370') => 794.02/109.92 (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((relr @ '#sk370' @ Y0) => 794.02/109.92 (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => 794.02/109.92 (((((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ Y2) => 794.02/109.92 ('#sk367' @ Y2)))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ 794.02/109.92 Y2) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ Y2))))))))))))))))))))))), 794.02/109.92 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl301])). 794.02/109.92 thf(zip_derived_cl306, plain, 794.02/109.92 (~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((relr @ '#sk370' @ Y0) => 794.02/109.92 (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => 794.02/109.92 (((((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ Y2) => 794.02/109.92 ('#sk367' @ Y2)))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ 794.02/109.92 Y2) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ Y2))))))))))))))))))))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl303])). 794.02/109.92 thf(zip_derived_cl308, plain, 794.02/109.92 (~ (((relr @ '#sk370' @ '#sk371') => 794.02/109.92 (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ '#sk371' @ Y0) => 794.02/109.92 (((((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => ('#sk367' @ Y1)))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => 794.02/109.92 (princ_inj @ '#sk366' @ Y1)))))))))))))))))), 794.02/109.92 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl306])). 794.02/109.92 thf(zip_derived_cl310, plain, ( (relr @ '#sk370' @ '#sk371')), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl308])). 794.02/109.92 thf(refl_axiom_i, axiom, 794.02/109.92 (![A:( $i > $o )]: ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ A ) ))). 794.02/109.92 thf(zf_stmt_2, axiom, 794.02/109.92 (![X4:( $i > $o ),X6:$i]: 794.02/109.92 ( ( X4 @ X6 ) | ( ~( ![X8:$i]: ( ( reli @ X6 @ X8 ) => ( X4 @ X8 ) ) ) ) ))). 794.02/109.92 thf(zip_derived_cl1, plain, 794.02/109.92 ( (((!!) @ (^[Y0 : $i > $o]: 794.02/109.92 (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((Y0 @ Y1) | 794.02/109.92 (((~) @ (((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ Y2) => 794.02/109.92 (Y0 @ Y2))))))))))))))))), 794.02/109.92 inference('cnf', [status(esa)], [zf_stmt_2])). 794.02/109.92 thf(zip_derived_cl46, plain, 794.02/109.92 (![X2 : $i > $o]: 794.02/109.92 (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((X2 @ Y0) | 794.02/109.92 (((~) @ (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => (X2 @ Y1)))))))))))))), 794.02/109.92 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 794.02/109.92 thf(zip_derived_cl47, plain, 794.02/109.92 (![X2 : $i > $o, X4 : $i]: 794.02/109.92 (((X2 @ X4) | 794.02/109.92 (((~) @ (((!!) @ (^[Y0 : $i]: (((reli @ X4 @ Y0) => (X2 @ Y0))))))))))), 794.02/109.92 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl46])). 794.02/109.92 thf(zip_derived_cl48, plain, 794.02/109.92 (![X2 : $i > $o, X4 : $i]: 794.02/109.92 ( (X2 @ X4) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: (((reli @ X4 @ Y0) => (X2 @ Y0)))))))), 794.02/109.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl47])). 794.02/109.92 thf(zip_derived_cl49, plain, 794.02/109.92 (![X2 : $i > $o, X4 : $i]: 794.02/109.92 (~ (((reli @ X4 @ ('#sk73' @ X2 @ X4)) => (X2 @ ('#sk73' @ X2 @ X4)))) 794.02/109.92 | (X2 @ X4))), 794.02/109.92 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl48])). 794.02/109.92 thf(zip_derived_cl50, plain, 794.02/109.92 (![X2 : $i > $o, X4 : $i]: 794.02/109.92 ( (reli @ X4 @ ('#sk73' @ X2 @ X4)) | (X2 @ X4))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 794.02/109.92 thf(zip_derived_cl51, plain, 794.02/109.92 (![X2 : $i > $o, X4 : $i]: (~ (X2 @ ('#sk73' @ X2 @ X4)) | (X2 @ X4))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 794.02/109.92 thf(zip_derived_cl149, plain, 794.02/109.92 (![X0 : $i]: ( (reli @ X0 @ X0) | (reli @ X0 @ X0))), 794.02/109.92 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl51])). 794.02/109.92 thf(zip_derived_cl171, plain, (![X0 : $i]: (reli @ X0 @ X0)), 794.02/109.92 inference('simplify', [status(thm)], [zip_derived_cl149])). 794.02/109.92 thf(zip_derived_cl311, plain, 794.02/109.92 (~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ '#sk371' @ Y0) => 794.02/109.92 (((((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => ('#sk367' @ Y1)))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => 794.02/109.92 (princ_inj @ '#sk366' @ Y1)))))))))))))))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl308])). 794.02/109.92 thf(zip_derived_cl313, plain, 794.02/109.92 (~ (((reli @ '#sk371' @ '#sk372') => 794.02/109.92 (((((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ '#sk372' @ Y0) => ('#sk367' @ Y0)))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ '#sk372' @ Y0) => (princ_inj @ 794.02/109.92 '#sk366' @ Y0))))))))))))), 794.02/109.92 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl311])). 794.02/109.92 thf(zip_derived_cl316, plain, 794.02/109.92 (~ (((((!!) @ (^[Y0 : $i]: (((reli @ '#sk372' @ Y0) => ('#sk367' @ Y0)))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ '#sk372' @ Y0) => (princ_inj @ 794.02/109.92 '#sk366' @ Y0))))))))))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl313])). 794.02/109.92 thf(zip_derived_cl318, plain, 794.02/109.92 (~ (((!!) @ (^[Y0 : $i]: (((reli @ '#sk372' @ Y0) => ('#sk367' @ Y0))))))), 794.02/109.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl316])). 794.02/109.92 thf(zip_derived_cl321, plain, 794.02/109.92 (~ (((reli @ '#sk372' @ ('#sk73' @ '#sk367' @ '#sk372')) => ('#sk367' @ 794.02/109.92 ('#sk73' @ '#sk367' @ '#sk372'))))), 794.02/109.92 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl318])). 794.02/109.92 thf(zip_derived_cl324, plain, 794.02/109.92 ( (reli @ '#sk372' @ ('#sk73' @ '#sk367' @ '#sk372'))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl321])). 794.02/109.92 thf(refl_axiom_r, axiom, 794.02/109.92 (![A:( $i > $o )]: ( mvalid @ ( mimpl @ ( mbox @ relr @ A ) @ A ) ))). 794.02/109.92 thf(zf_stmt_3, axiom, 794.02/109.92 (![X4:( $i > $o ),X6:$i]: 794.02/109.92 ( ( X4 @ X6 ) | ( ~( ![X8:$i]: ( ( relr @ X6 @ X8 ) => ( X4 @ X8 ) ) ) ) ))). 794.02/109.92 thf(zip_derived_cl0, plain, 794.02/109.92 ( (((!!) @ (^[Y0 : $i > $o]: 794.02/109.92 (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((Y0 @ Y1) | 794.02/109.92 (((~) @ (((!!) @ (^[Y2 : $i]: 794.02/109.92 (((relr @ Y1 @ Y2) => 794.02/109.92 (Y0 @ Y2))))))))))))))))), 794.02/109.92 inference('cnf', [status(esa)], [zf_stmt_3])). 794.02/109.92 thf(zip_derived_cl7, plain, 794.02/109.92 (![X2 : $i > $o]: 794.02/109.92 (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((X2 @ Y0) | 794.02/109.92 (((~) @ (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((relr @ Y0 @ Y1) => (X2 @ Y1)))))))))))))), 794.02/109.92 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 794.02/109.92 thf(zip_derived_cl8, plain, 794.02/109.92 (![X2 : $i > $o, X4 : $i]: 794.02/109.92 (((X2 @ X4) | 794.02/109.92 (((~) @ (((!!) @ (^[Y0 : $i]: (((relr @ X4 @ Y0) => (X2 @ Y0))))))))))), 794.02/109.92 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 794.02/109.92 thf(zip_derived_cl9, plain, 794.02/109.92 (![X2 : $i > $o, X4 : $i]: 794.02/109.92 ( (X2 @ X4) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: (((relr @ X4 @ Y0) => (X2 @ Y0)))))))), 794.02/109.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl8])). 794.02/109.92 thf(zip_derived_cl10, plain, 794.02/109.92 (![X2 : $i > $o, X4 : $i]: 794.02/109.92 (~ (((relr @ X4 @ ('#sk5' @ X2 @ X4)) => (X2 @ ('#sk5' @ X2 @ X4)))) 794.02/109.92 | (X2 @ X4))), 794.02/109.92 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl9])). 794.02/109.92 thf(zip_derived_cl11, plain, 794.02/109.92 (![X2 : $i > $o, X4 : $i]: 794.02/109.92 ( (relr @ X4 @ ('#sk5' @ X2 @ X4)) | (X2 @ X4))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl10])). 794.02/109.92 thf(zip_derived_cl12, plain, 794.02/109.92 (![X2 : $i > $o, X4 : $i]: (~ (X2 @ ('#sk5' @ X2 @ X4)) | (X2 @ X4))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl10])). 794.02/109.92 thf(zip_derived_cl86, plain, 794.02/109.92 (![X0 : $i]: ( (relr @ X0 @ X0) | (relr @ X0 @ X0))), 794.02/109.92 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl12])). 794.02/109.92 thf(zip_derived_cl107, plain, (![X0 : $i]: (relr @ X0 @ X0)), 794.02/109.92 inference('simplify', [status(thm)], [zip_derived_cl86])). 794.02/109.92 thf(zip_derived_cl315, plain, ( (reli @ '#sk371' @ '#sk372')), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl313])). 794.02/109.92 thf(zip_derived_cl171, plain, (![X0 : $i]: (reli @ X0 @ X0)), 794.02/109.92 inference('simplify', [status(thm)], [zip_derived_cl149])). 794.02/109.92 thf(zip_derived_cl324, plain, 794.02/109.92 ( (reli @ '#sk372' @ ('#sk73' @ '#sk367' @ '#sk372'))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl321])). 794.02/109.92 thf(zip_derived_cl107, plain, (![X0 : $i]: (relr @ X0 @ X0)), 794.02/109.92 inference('simplify', [status(thm)], [zip_derived_cl86])). 794.02/109.92 thf(zip_derived_cl310, plain, ( (relr @ '#sk370' @ '#sk371')), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl308])). 794.02/109.92 thf(zip_derived_cl302, plain, 794.02/109.92 ( (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ '#sk369' @ Y0) => 794.02/109.92 (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((relr @ Y0 @ Y1) => 794.02/109.92 (((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ Y2) => 794.02/109.92 (((((!!) @ (^[Y3 : $i]: 794.02/109.92 (((reli @ Y2 @ 794.02/109.92 Y3) => 794.02/109.92 (((!!) @ ( 794.02/109.92 ^[Y4 : $i]: 794.02/109.92 ( 794.02/109.92 ( 794.02/109.92 (relr @ 794.02/109.92 Y3 @ 794.02/109.92 Y4) => 794.02/109.92 (( 794.02/109.92 (!!) @ ( 794.02/109.92 ^[Y5 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y4 @ 794.02/109.92 Y5) => 794.02/109.92 (( 794.02/109.92 (( 794.02/109.92 (!!) @ ( 794.02/109.92 ^[Y6 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y5 @ 794.02/109.92 Y6) => 794.02/109.92 ('#sk367' @ 794.02/109.92 Y6)))))) | 794.02/109.92 (( 794.02/109.92 (~) @ ( 794.02/109.92 ( 794.02/109.92 (!!) @ ( 794.02/109.92 ^[Y6 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y5 @ 794.02/109.92 Y6) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ 794.02/109.92 Y6))))))))))))))))))))))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y3 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y2 @ 794.02/109.92 Y3) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ 794.02/109.92 Y3)))))))))))))))))))))))))), 794.02/109.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl300])). 794.02/109.92 thf(zip_derived_cl304, plain, 794.02/109.92 (![X2 : $i]: 794.02/109.92 (((reli @ '#sk369' @ X2) => 794.02/109.92 (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((relr @ X2 @ Y0) => 794.02/109.92 (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => 794.02/109.92 (((((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ Y2) => 794.02/109.92 (((!!) @ (^[Y3 : $i]: 794.02/109.92 (((relr @ 794.02/109.92 Y2 @ 794.02/109.92 Y3) => 794.02/109.92 (( 794.02/109.92 (!!) @ ( 794.02/109.92 ^[Y4 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y3 @ 794.02/109.92 Y4) => 794.02/109.92 (( 794.02/109.92 (( 794.02/109.92 (!!) @ ( 794.02/109.92 ^[Y5 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y4 @ 794.02/109.92 Y5) => 794.02/109.92 ('#sk367' @ 794.02/109.92 Y5)))))) | 794.02/109.92 (( 794.02/109.92 (~) @ ( 794.02/109.92 ( 794.02/109.92 (!!) @ ( 794.02/109.92 ^[Y5 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y4 @ 794.02/109.92 Y5) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ 794.02/109.92 Y5))))))))))))))))))))))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ 794.02/109.92 Y2) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ Y2))))))))))))))))))))))), 794.02/109.92 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl302])). 794.02/109.92 thf(zip_derived_cl307, plain, 794.02/109.92 (![X2 : $i]: 794.02/109.92 (~ (reli @ '#sk369' @ X2) 794.02/109.92 | (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((relr @ X2 @ Y0) => 794.02/109.92 (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => 794.02/109.92 (((((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ Y2) => 794.02/109.92 (((!!) @ (^[Y3 : $i]: 794.02/109.92 (( 794.02/109.92 (relr @ 794.02/109.92 Y2 @ 794.02/109.92 Y3) => 794.02/109.92 (( 794.02/109.92 (!!) @ ( 794.02/109.92 ^[Y4 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y3 @ 794.02/109.92 Y4) => 794.02/109.92 (( 794.02/109.92 (( 794.02/109.92 (!!) @ ( 794.02/109.92 ^[Y5 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y4 @ 794.02/109.92 Y5) => 794.02/109.92 ('#sk367' @ 794.02/109.92 Y5)))))) | 794.02/109.92 (( 794.02/109.92 (~) @ ( 794.02/109.92 ( 794.02/109.92 (!!) @ ( 794.02/109.92 ^[Y5 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y4 @ 794.02/109.92 Y5) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ 794.02/109.92 Y5))))))))))))))))))))))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ 794.02/109.92 Y2) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ Y2)))))))))))))))))))))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl304])). 794.02/109.92 thf(zip_derived_cl309, plain, 794.02/109.92 (![X2 : $i, X4 : $i]: 794.02/109.92 ( (((relr @ X2 @ X4) => 794.02/109.92 (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X4 @ Y0) => 794.02/109.92 (((((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => 794.02/109.92 (((!!) @ (^[Y2 : $i]: 794.02/109.92 (((relr @ Y1 @ Y2) => 794.02/109.92 (((!!) @ (^[Y3 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y2 @ 794.02/109.92 Y3) => 794.02/109.92 (( 794.02/109.92 (( 794.02/109.92 (!!) @ ( 794.02/109.92 ^[Y4 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y3 @ 794.02/109.92 Y4) => 794.02/109.92 ('#sk367' @ 794.02/109.92 Y4)))))) | 794.02/109.92 (( 794.02/109.92 (~) @ ( 794.02/109.92 ( 794.02/109.92 (!!) @ ( 794.02/109.92 ^[Y4 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y3 @ 794.02/109.92 Y4) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ 794.02/109.92 Y4))))))))))))))))))))))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => 794.02/109.92 (princ_inj @ '#sk366' @ Y1))))))))))))))))) 794.02/109.92 | ~ (reli @ '#sk369' @ X2))), 794.02/109.92 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl307])). 794.02/109.92 thf(zip_derived_cl312, plain, 794.02/109.92 (![X2 : $i, X4 : $i]: 794.02/109.92 (~ (relr @ X2 @ X4) 794.02/109.92 | (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X4 @ Y0) => 794.02/109.92 (((((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => 794.02/109.92 (((!!) @ (^[Y2 : $i]: 794.02/109.92 (((relr @ Y1 @ Y2) => 794.02/109.92 (((!!) @ (^[Y3 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y2 @ 794.02/109.92 Y3) => 794.02/109.92 (( 794.02/109.92 (( 794.02/109.92 (!!) @ ( 794.02/109.92 ^[Y4 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y3 @ 794.02/109.92 Y4) => 794.02/109.92 ('#sk367' @ 794.02/109.92 Y4)))))) | 794.02/109.92 (( 794.02/109.92 (~) @ ( 794.02/109.92 ( 794.02/109.92 (!!) @ ( 794.02/109.92 ^[Y4 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y3 @ 794.02/109.92 Y4) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ 794.02/109.92 Y4))))))))))))))))))))))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => 794.02/109.92 (princ_inj @ '#sk366' @ Y1))))))))))))))) 794.02/109.92 | ~ (reli @ '#sk369' @ X2))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl309])). 794.02/109.92 thf(zip_derived_cl314, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i]: 794.02/109.92 ( (((reli @ X4 @ X6) => 794.02/109.92 (((((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => 794.02/109.92 (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((relr @ Y0 @ Y1) => 794.02/109.92 (((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ Y2) => 794.02/109.92 (((((!!) @ (^[Y3 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y2 @ 794.02/109.92 Y3) => 794.02/109.92 ('#sk367' @ 794.02/109.92 Y3)))))) | 794.02/109.92 (((~) @ (((!!) @ ( 794.02/109.92 ^[Y3 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y2 @ 794.02/109.92 Y3) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ 794.02/109.92 Y3))))))))))))))))))))))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => (princ_inj @ 794.02/109.92 '#sk366' @ Y0)))))))))))) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (relr @ X2 @ X4))), 794.02/109.92 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl312])). 794.02/109.92 thf(zip_derived_cl317, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i]: 794.02/109.92 (~ (reli @ X4 @ X6) 794.02/109.92 | (((((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => 794.02/109.92 (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((relr @ Y0 @ Y1) => 794.02/109.92 (((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ Y2) => 794.02/109.92 (((((!!) @ (^[Y3 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y2 @ 794.02/109.92 Y3) => 794.02/109.92 ('#sk367' @ 794.02/109.92 Y3)))))) | 794.02/109.92 (((~) @ (((!!) @ ( 794.02/109.92 ^[Y3 : $i]: 794.02/109.92 (( 794.02/109.92 (reli @ 794.02/109.92 Y2 @ 794.02/109.92 Y3) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ 794.02/109.92 Y3))))))))))))))))))))))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => (princ_inj @ 794.02/109.92 '#sk366' @ Y0)))))))))) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ '#sk369' @ X2))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl314])). 794.02/109.92 thf(zip_derived_cl320, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i]: 794.02/109.92 ( (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => 794.02/109.92 (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((relr @ Y0 @ Y1) => 794.02/109.92 (((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ Y2) => 794.02/109.92 (((((!!) @ (^[Y3 : $i]: 794.02/109.92 (((reli @ 794.02/109.92 Y2 @ 794.02/109.92 Y3) => 794.02/109.92 ('#sk367' @ 794.02/109.92 Y3)))))) | 794.02/109.92 (((~) @ (((!!) @ ( 794.02/109.92 ^[Y3 : $i]: 794.02/109.92 (((reli @ 794.02/109.92 Y2 @ 794.02/109.92 Y3) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ 794.02/109.92 Y3))))))))))))))))))))))))) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ X4 @ X6))), 794.02/109.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl317])). 794.02/109.92 thf(zip_derived_cl323, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 794.02/109.92 ( (((reli @ X6 @ X8) => 794.02/109.92 (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((relr @ X8 @ Y0) => 794.02/109.92 (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => 794.02/109.92 (((((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ Y2) => 794.02/109.92 ('#sk367' @ Y2)))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ 794.02/109.92 Y2) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ Y2)))))))))))))))))))))) 794.02/109.92 | ~ (reli @ X4 @ X6) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))))), 794.02/109.92 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl320])). 794.02/109.92 thf(zip_derived_cl327, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 794.02/109.92 (~ (reli @ X6 @ X8) 794.02/109.92 | (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((relr @ X8 @ Y0) => 794.02/109.92 (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => 794.02/109.92 (((((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ Y2) => 794.02/109.92 ('#sk367' @ Y2)))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y2 : $i]: 794.02/109.92 (((reli @ Y1 @ 794.02/109.92 Y2) => 794.02/109.92 (princ_inj @ 794.02/109.92 '#sk366' @ Y2)))))))))))))))))))) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ X4 @ X6))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl323])). 794.02/109.92 thf(zip_derived_cl328, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 794.02/109.92 ( (((relr @ X8 @ X10) => 794.02/109.92 (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X10 @ Y0) => 794.02/109.92 (((((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => ('#sk367' @ Y1)))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => 794.02/109.92 (princ_inj @ '#sk366' @ Y1))))))))))))))))) 794.02/109.92 | ~ (reli @ X4 @ X6) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))) 794.02/109.92 | ~ (reli @ X6 @ X8))), 794.02/109.92 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl327])). 794.02/109.92 thf(zip_derived_cl329, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 794.02/109.92 (~ (relr @ X8 @ X10) 794.02/109.92 | (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X10 @ Y0) => 794.02/109.92 (((((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => ('#sk367' @ Y1)))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y1 : $i]: 794.02/109.92 (((reli @ Y0 @ Y1) => 794.02/109.92 (princ_inj @ '#sk366' @ Y1))))))))))))))) 794.02/109.92 | ~ (reli @ X6 @ X8) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ X4 @ X6))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl328])). 794.02/109.92 thf(zip_derived_cl330, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 794.02/109.92 ( (((reli @ X10 @ X12) => 794.02/109.92 (((((!!) @ (^[Y0 : $i]: (((reli @ X12 @ Y0) => ('#sk367' @ Y0)))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X12 @ Y0) => (princ_inj @ 794.02/109.92 '#sk366' @ Y0)))))))))))) 794.02/109.92 | ~ (reli @ X4 @ X6) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))) 794.02/109.92 | ~ (reli @ X6 @ X8) 794.02/109.92 | ~ (relr @ X8 @ X10))), 794.02/109.92 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl329])). 794.02/109.92 thf(zip_derived_cl331, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 794.02/109.92 (~ (reli @ X10 @ X12) 794.02/109.92 | (((((!!) @ (^[Y0 : $i]: (((reli @ X12 @ Y0) => ('#sk367' @ Y0)))))) | 794.02/109.92 (((~) @ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X12 @ Y0) => (princ_inj @ 794.02/109.92 '#sk366' @ Y0)))))))))) 794.02/109.92 | ~ (relr @ X8 @ X10) 794.02/109.92 | ~ (reli @ X6 @ X8) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ X4 @ X6))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl330])). 794.02/109.92 thf(zip_derived_cl332, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 794.02/109.92 ( (((!!) @ (^[Y0 : $i]: (((reli @ X12 @ Y0) => ('#sk367' @ Y0)))))) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X12 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))) 794.02/109.92 | ~ (reli @ X4 @ X6) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))) 794.02/109.92 | ~ (reli @ X6 @ X8) 794.02/109.92 | ~ (relr @ X8 @ X10) 794.02/109.92 | ~ (reli @ X10 @ X12))), 794.02/109.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl331])). 794.02/109.92 thf(zip_derived_cl333, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 794.02/109.92 ( (((reli @ X12 @ X14) => ('#sk367' @ X14))) 794.02/109.92 | ~ (reli @ X10 @ X12) 794.02/109.92 | ~ (relr @ X8 @ X10) 794.02/109.92 | ~ (reli @ X6 @ X8) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ X4 @ X6) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X12 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))))), 794.02/109.92 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl332])). 794.02/109.92 thf(zip_derived_cl334, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 794.02/109.92 (~ (reli @ X12 @ X14) 794.02/109.92 | ('#sk367' @ X14) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X12 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))) 794.02/109.92 | ~ (reli @ X4 @ X6) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))) 794.02/109.92 | ~ (reli @ X6 @ X8) 794.02/109.92 | ~ (relr @ X8 @ X10) 794.02/109.92 | ~ (reli @ X10 @ X12))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl333])). 794.02/109.92 thf(zip_derived_cl335, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 794.02/109.92 (~ (((reli @ X12 @ ('#sk73' @ (princ_inj @ '#sk366') @ X12)) => 794.02/109.92 (princ_inj @ '#sk366' @ ('#sk73' @ (princ_inj @ '#sk366') @ X12)))) 794.02/109.92 | ~ (reli @ X10 @ X12) 794.02/109.92 | ~ (relr @ X8 @ X10) 794.02/109.92 | ~ (reli @ X6 @ X8) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ X4 @ X6) 794.02/109.92 | ('#sk367' @ X14) 794.02/109.92 | ~ (reli @ X12 @ X14))), 794.02/109.92 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl334])). 794.02/109.92 thf(zip_derived_cl336, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 794.02/109.92 ( (reli @ X12 @ ('#sk73' @ (princ_inj @ '#sk366') @ X12)) 794.02/109.92 | ~ (reli @ X12 @ X14) 794.02/109.92 | ('#sk367' @ X14) 794.02/109.92 | ~ (reli @ X4 @ X6) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))) 794.02/109.92 | ~ (reli @ X6 @ X8) 794.02/109.92 | ~ (relr @ X8 @ X10) 794.02/109.92 | ~ (reli @ X10 @ X12))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl335])). 794.02/109.92 thf(zip_derived_cl338, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 794.02/109.92 (~ (((reli @ X6 @ ('#sk73' @ (princ_inj @ '#sk366') @ X6)) => 794.02/109.92 (princ_inj @ '#sk366' @ ('#sk73' @ (princ_inj @ '#sk366') @ X6)))) 794.02/109.92 | ~ (reli @ X10 @ X12) 794.02/109.92 | ~ (relr @ X8 @ X10) 794.02/109.92 | ~ (reli @ X6 @ X8) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ X4 @ X6) 794.02/109.92 | ('#sk367' @ X14) 794.02/109.92 | ~ (reli @ X12 @ X14) 794.02/109.92 | (reli @ X12 @ ('#sk73' @ (princ_inj @ '#sk366') @ X12)))), 794.02/109.92 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl336])). 794.02/109.92 thf(zip_derived_cl340, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 794.02/109.92 ( (reli @ X6 @ ('#sk73' @ (princ_inj @ '#sk366') @ X6)) 794.02/109.92 | (reli @ X12 @ ('#sk73' @ (princ_inj @ '#sk366') @ X12)) 794.02/109.92 | ~ (reli @ X12 @ X14) 794.02/109.92 | ('#sk367' @ X14) 794.02/109.92 | ~ (reli @ X4 @ X6) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (reli @ X6 @ X8) 794.02/109.92 | ~ (relr @ X8 @ X10) 794.02/109.92 | ~ (reli @ X10 @ X12))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl338])). 794.02/109.92 thf(zip_derived_cl1903, plain, 794.02/109.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 794.02/109.92 (~ (reli @ X1 @ X0) 794.02/109.92 | ~ (relr @ X2 @ X1) 794.02/109.92 | ~ (reli @ X3 @ X2) 794.02/109.92 | ~ (reli @ '#sk369' @ '#sk370') 794.02/109.92 | ~ (reli @ '#sk371' @ X3) 794.02/109.92 | ('#sk367' @ X4) 794.02/109.92 | ~ (reli @ X0 @ X4) 794.02/109.92 | (reli @ X0 @ ('#sk73' @ (princ_inj @ '#sk366') @ X0)) 794.02/109.92 | (reli @ X3 @ ('#sk73' @ (princ_inj @ '#sk366') @ X3)))), 794.02/109.92 inference('sup-', [status(thm)], [zip_derived_cl310, zip_derived_cl340])). 794.02/109.92 thf(zip_derived_cl305, plain, ( (reli @ '#sk369' @ '#sk370')), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl303])). 794.02/109.92 thf(zip_derived_cl1936, plain, 794.02/109.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 794.02/109.92 (~ (reli @ X1 @ X0) 794.02/109.92 | ~ (relr @ X2 @ X1) 794.02/109.92 | ~ (reli @ X3 @ X2) 794.02/109.92 | ~ (reli @ '#sk371' @ X3) 794.02/109.92 | ('#sk367' @ X4) 794.02/109.92 | ~ (reli @ X0 @ X4) 794.02/109.92 | (reli @ X0 @ ('#sk73' @ (princ_inj @ '#sk366') @ X0)) 794.02/109.92 | (reli @ X3 @ ('#sk73' @ (princ_inj @ '#sk366') @ X3)))), 794.02/109.92 inference('demod', [status(thm)], [zip_derived_cl1903, zip_derived_cl305])). 794.02/109.92 thf(zip_derived_cl1950, plain, 794.02/109.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 794.02/109.92 ( (reli @ X1 @ ('#sk73' @ (princ_inj @ '#sk366') @ X1)) 794.02/109.92 | (reli @ X2 @ ('#sk73' @ (princ_inj @ '#sk366') @ X2)) 794.02/109.92 | ~ (reli @ X2 @ X3) 794.02/109.92 | ('#sk367' @ X3) 794.02/109.92 | ~ (reli @ '#sk371' @ X1) 794.02/109.92 | ~ (reli @ X1 @ X0) 794.02/109.92 | ~ (reli @ X0 @ X2))), 794.02/109.92 inference('sup-', [status(thm)], [zip_derived_cl107, zip_derived_cl1936])). 794.02/109.92 thf(zip_derived_cl13112, plain, 794.02/109.92 (![X0 : $i, X1 : $i]: 794.02/109.92 (~ (reli @ X0 @ '#sk372') 794.02/109.92 | ~ (reli @ X1 @ X0) 794.02/109.92 | ~ (reli @ '#sk371' @ X1) 794.02/109.92 | ('#sk367' @ ('#sk73' @ '#sk367' @ '#sk372')) 794.02/109.92 | (reli @ '#sk372' @ ('#sk73' @ (princ_inj @ '#sk366') @ '#sk372')) 794.02/109.92 | (reli @ X1 @ ('#sk73' @ (princ_inj @ '#sk366') @ X1)))), 794.02/109.92 inference('sup-', [status(thm)], [zip_derived_cl324, zip_derived_cl1950])). 794.02/109.92 thf(zip_derived_cl325, plain, 794.02/109.92 (~ ('#sk367' @ ('#sk73' @ '#sk367' @ '#sk372'))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl321])). 794.02/109.92 thf(zip_derived_cl13198, plain, 794.02/109.92 (![X0 : $i, X1 : $i]: 794.02/109.92 (~ (reli @ X0 @ '#sk372') 794.02/109.92 | ~ (reli @ X1 @ X0) 794.02/109.92 | ~ (reli @ '#sk371' @ X1) 794.02/109.92 | (reli @ '#sk372' @ ('#sk73' @ (princ_inj @ '#sk366') @ '#sk372')) 794.02/109.92 | (reli @ X1 @ ('#sk73' @ (princ_inj @ '#sk366') @ X1)))), 794.02/109.92 inference('demod', [status(thm)], 794.02/109.92 [zip_derived_cl13112, zip_derived_cl325])). 794.02/109.92 thf(zip_derived_cl16148, plain, 794.02/109.92 (![X0 : $i]: 794.02/109.92 ( (reli @ X0 @ ('#sk73' @ (princ_inj @ '#sk366') @ X0)) 794.02/109.92 | (reli @ '#sk372' @ ('#sk73' @ (princ_inj @ '#sk366') @ '#sk372')) 794.02/109.92 | ~ (reli @ '#sk371' @ X0) 794.02/109.92 | ~ (reli @ X0 @ '#sk372'))), 794.02/109.92 inference('sup-', [status(thm)], [zip_derived_cl171, zip_derived_cl13198])). 794.02/109.92 thf(zip_derived_cl17456, plain, 794.02/109.92 ((~ (reli @ '#sk372' @ '#sk372') 794.02/109.92 | (reli @ '#sk372' @ ('#sk73' @ (princ_inj @ '#sk366') @ '#sk372')) 794.02/109.92 | (reli @ '#sk372' @ ('#sk73' @ (princ_inj @ '#sk366') @ '#sk372')))), 794.02/109.92 inference('sup-', [status(thm)], [zip_derived_cl315, zip_derived_cl16148])). 794.02/109.92 thf(zip_derived_cl171, plain, (![X0 : $i]: (reli @ X0 @ X0)), 794.02/109.92 inference('simplify', [status(thm)], [zip_derived_cl149])). 794.02/109.92 thf(zip_derived_cl17489, plain, 794.02/109.92 (( (reli @ '#sk372' @ ('#sk73' @ (princ_inj @ '#sk366') @ '#sk372')) 794.02/109.92 | (reli @ '#sk372' @ ('#sk73' @ (princ_inj @ '#sk366') @ '#sk372')))), 794.02/109.92 inference('demod', [status(thm)], 794.02/109.92 [zip_derived_cl17456, zip_derived_cl171])). 794.02/109.92 thf(zip_derived_cl17490, plain, 794.02/109.92 ( (reli @ '#sk372' @ ('#sk73' @ (princ_inj @ '#sk366') @ '#sk372'))), 794.02/109.92 inference('simplify', [status(thm)], [zip_derived_cl17489])). 794.02/109.92 thf(zip_derived_cl319, plain, 794.02/109.92 ( (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ '#sk372' @ Y0) => (princ_inj @ '#sk366' @ Y0))))))), 794.02/109.92 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl316])). 794.02/109.92 thf(zip_derived_cl322, plain, 794.02/109.92 (![X2 : $i]: (((reli @ '#sk372' @ X2) => (princ_inj @ '#sk366' @ X2)))), 794.02/109.92 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl319])). 794.02/109.92 thf(zip_derived_cl326, plain, 794.02/109.92 (![X2 : $i]: (~ (reli @ '#sk372' @ X2) | (princ_inj @ '#sk366' @ X2))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl322])). 794.02/109.92 thf(zip_derived_cl337, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 794.02/109.92 (~ (princ_inj @ '#sk366' @ ('#sk73' @ (princ_inj @ '#sk366') @ X12)) 794.02/109.92 | ~ (reli @ X12 @ X14) 794.02/109.92 | ('#sk367' @ X14) 794.02/109.92 | ~ (reli @ X4 @ X6) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (((!!) @ (^[Y0 : $i]: 794.02/109.92 (((reli @ X6 @ Y0) => (princ_inj @ '#sk366' @ Y0)))))) 794.02/109.92 | ~ (reli @ X6 @ X8) 794.02/109.92 | ~ (relr @ X8 @ X10) 794.02/109.92 | ~ (reli @ X10 @ X12))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl335])). 794.02/109.92 thf(zip_derived_cl339, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 794.02/109.92 (~ (((reli @ X6 @ ('#sk73' @ (princ_inj @ '#sk366') @ X6)) => 794.02/109.92 (princ_inj @ '#sk366' @ ('#sk73' @ (princ_inj @ '#sk366') @ X6)))) 794.02/109.92 | ~ (reli @ X10 @ X12) 794.02/109.92 | ~ (relr @ X8 @ X10) 794.02/109.92 | ~ (reli @ X6 @ X8) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ X4 @ X6) 794.02/109.92 | ('#sk367' @ X14) 794.02/109.92 | ~ (reli @ X12 @ X14) 794.02/109.92 | ~ (princ_inj @ '#sk366' @ ('#sk73' @ (princ_inj @ '#sk366') @ X12)))), 794.02/109.92 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl337])). 794.02/109.92 thf(zip_derived_cl343, plain, 794.02/109.92 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 794.02/109.92 (~ (princ_inj @ '#sk366' @ ('#sk73' @ (princ_inj @ '#sk366') @ X6)) 794.02/109.92 | ~ (princ_inj @ '#sk366' @ ('#sk73' @ (princ_inj @ '#sk366') @ X12)) 794.02/109.92 | ~ (reli @ X12 @ X14) 794.02/109.92 | ('#sk367' @ X14) 794.02/109.92 | ~ (reli @ X4 @ X6) 794.02/109.92 | ~ (relr @ X2 @ X4) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (reli @ X6 @ X8) 794.02/109.92 | ~ (relr @ X8 @ X10) 794.02/109.92 | ~ (reli @ X10 @ X12))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl339])). 794.02/109.92 thf(zip_derived_cl449, plain, 794.02/109.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 794.02/109.92 (~ (reli @ X1 @ X0) 794.02/109.92 | ~ (relr @ X2 @ X1) 794.02/109.92 | ~ (reli @ X0 @ X2) 794.02/109.92 | ~ (reli @ '#sk369' @ X3) 794.02/109.92 | ~ (relr @ X3 @ X4) 794.02/109.92 | ~ (reli @ X4 @ X0) 794.02/109.92 | ('#sk367' @ X5) 794.02/109.92 | ~ (reli @ X0 @ X5) 794.02/109.92 | ~ (princ_inj @ '#sk366' @ ('#sk73' @ (princ_inj @ '#sk366') @ X0)))), 794.02/109.92 inference('eq_fact', [status(thm)], [zip_derived_cl343])). 794.02/109.92 thf(zip_derived_cl452, plain, 794.02/109.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 794.02/109.92 (~ (reli @ '#sk372' @ ('#sk73' @ (princ_inj @ '#sk366') @ X0)) 794.02/109.92 | ~ (reli @ X0 @ X1) 794.02/109.92 | ('#sk367' @ X1) 794.02/109.92 | ~ (reli @ X2 @ X0) 794.02/109.92 | ~ (relr @ X3 @ X2) 794.02/109.92 | ~ (reli @ '#sk369' @ X3) 794.02/109.92 | ~ (reli @ X0 @ X4) 794.02/109.92 | ~ (relr @ X4 @ X5) 794.02/109.92 | ~ (reli @ X5 @ X0))), 794.02/109.92 inference('sup-', [status(thm)], [zip_derived_cl326, zip_derived_cl449])). 794.02/109.92 thf(zip_derived_cl17516, plain, 794.02/109.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 794.02/109.92 (~ (reli @ X0 @ '#sk372') 794.02/109.92 | ~ (relr @ X1 @ X0) 794.02/109.92 | ~ (reli @ '#sk372' @ X1) 794.02/109.92 | ~ (reli @ '#sk369' @ X2) 794.02/109.92 | ~ (relr @ X2 @ X3) 794.02/109.92 | ~ (reli @ X3 @ '#sk372') 794.02/109.92 | ('#sk367' @ X4) 794.02/109.92 | ~ (reli @ '#sk372' @ X4))), 794.02/109.92 inference('sup-', [status(thm)], [zip_derived_cl17490, zip_derived_cl452])). 794.02/109.92 thf(zip_derived_cl20784, plain, 794.02/109.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 794.02/109.92 (~ (reli @ '#sk372' @ X1) 794.02/109.92 | ('#sk367' @ X1) 794.02/109.92 | ~ (reli @ X2 @ '#sk372') 794.02/109.92 | ~ (relr @ X3 @ X2) 794.02/109.92 | ~ (reli @ '#sk369' @ X3) 794.02/109.92 | ~ (reli @ '#sk372' @ X0) 794.02/109.92 | ~ (reli @ X0 @ '#sk372'))), 794.02/109.92 inference('sup-', [status(thm)], [zip_derived_cl107, zip_derived_cl17516])). 794.02/109.92 thf(zip_derived_cl23762, plain, 794.02/109.92 (![X0 : $i, X1 : $i, X2 : $i]: 794.02/109.92 (~ (reli @ X0 @ '#sk372') 794.02/109.92 | ~ (reli @ '#sk372' @ X0) 794.02/109.92 | ~ (reli @ '#sk369' @ X1) 794.02/109.92 | ~ (relr @ X1 @ X2) 794.02/109.92 | ~ (reli @ X2 @ '#sk372') 794.02/109.92 | ('#sk367' @ ('#sk73' @ '#sk367' @ '#sk372')))), 794.02/109.92 inference('sup-', [status(thm)], [zip_derived_cl324, zip_derived_cl20784])). 794.02/109.92 thf(zip_derived_cl325, plain, 794.02/109.92 (~ ('#sk367' @ ('#sk73' @ '#sk367' @ '#sk372'))), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl321])). 794.02/109.92 thf(zip_derived_cl23795, plain, 794.02/109.92 (![X0 : $i, X1 : $i, X2 : $i]: 794.02/109.92 (~ (reli @ X0 @ '#sk372') 794.02/109.92 | ~ (reli @ '#sk372' @ X0) 794.02/109.92 | ~ (reli @ '#sk369' @ X1) 794.02/109.92 | ~ (relr @ X1 @ X2) 794.02/109.92 | ~ (reli @ X2 @ '#sk372'))), 794.02/109.92 inference('demod', [status(thm)], 794.02/109.92 [zip_derived_cl23762, zip_derived_cl325])). 794.02/109.92 thf(zip_derived_cl23799, plain, 794.02/109.92 (![X0 : $i, X1 : $i]: 794.02/109.92 (~ (reli @ X0 @ '#sk372') 794.02/109.92 | ~ (relr @ X1 @ X0) 794.02/109.92 | ~ (reli @ '#sk369' @ X1) 794.02/109.92 | ~ (reli @ '#sk372' @ '#sk372'))), 794.02/109.92 inference('sup-', [status(thm)], [zip_derived_cl171, zip_derived_cl23795])). 794.02/109.92 thf(zip_derived_cl171, plain, (![X0 : $i]: (reli @ X0 @ X0)), 794.02/109.92 inference('simplify', [status(thm)], [zip_derived_cl149])). 794.02/109.92 thf(zip_derived_cl23811, plain, 794.02/109.92 (![X0 : $i, X1 : $i]: 794.02/109.92 (~ (reli @ X0 @ '#sk372') 794.02/109.92 | ~ (relr @ X1 @ X0) 794.02/109.92 | ~ (reli @ '#sk369' @ X1))), 794.02/109.92 inference('demod', [status(thm)], 794.02/109.92 [zip_derived_cl23799, zip_derived_cl171])). 794.02/109.92 thf(zip_derived_cl23876, plain, 794.02/109.92 ((~ (reli @ '#sk369' @ '#sk370') | ~ (reli @ '#sk371' @ '#sk372'))), 794.02/109.92 inference('sup-', [status(thm)], [zip_derived_cl310, zip_derived_cl23811])). 794.02/109.92 thf(zip_derived_cl305, plain, ( (reli @ '#sk369' @ '#sk370')), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl303])). 794.02/109.92 thf(zip_derived_cl315, plain, ( (reli @ '#sk371' @ '#sk372')), 794.02/109.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl313])). 794.02/109.92 thf(zip_derived_cl23942, plain, ($false), 794.02/109.92 inference('demod', [status(thm)], 794.02/109.92 [zip_derived_cl23876, zip_derived_cl305, zip_derived_cl315])). 794.02/109.92 794.02/109.92 % SZS output end Refutation 794.02/109.92 794.02/109.92 794.02/109.92 % Terminating... 795.05/110.02 % Runner terminated. 795.05/110.04 % Zipperpin 1.5 exiting 795.05/110.04 EOF