0.09/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.2FCP1GJvXT true 0.10/0.32 % Computer : n015.cluster.edu 0.10/0.32 % Model : x86_64 x86_64 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.32 % Memory : 8042.1875MB 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.32 % CPULimit : 960 0.10/0.32 % WCLimit : 120 0.10/0.32 % DateTime : Tue Aug 9 04:27:26 EDT 2022 0.10/0.32 % CPUTime : 0.10/0.32 % Running portfolio for 960 s 0.10/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.10/0.32 % Number of cores: 8 0.10/0.33 % Python version: Python 3.6.8 0.10/0.33 % Running in HO mode 0.73/0.64 % Total configuration time : 828 0.73/0.64 % Estimated wc time : 1656 0.73/0.64 % Estimated cpu time (8 cpus) : 207.0 0.73/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.73/0.70 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.73/0.70 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.73/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 1.03/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 1.04/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 1.04/0.81 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 1.10/0.91 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 1.10/0.96 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 1.18/1.15 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 3.10/1.20 % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s 3.23/1.24 % /export/starexec/sandbox2/solver/bin/lams/15_lifting3.sh running for 30s 81.19/14.44 % Solved by lams/15_lifting3.sh. 81.19/14.44 % done 349 iterations in 13.014s 81.19/14.44 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 81.19/14.44 % SZS output start Refutation 81.19/14.44 thf(individuals_type, type, individuals: $tType). 81.19/14.44 thf(cs4_impl_type, type, cs4_impl: ($i > $o) > ($i > $o) > $i > $o). 81.19/14.44 thf(relr_type, type, relr: $i > $i > $o). 81.19/14.44 thf('#sk8_type', type, '#sk8': $i). 81.19/14.44 thf('#sk7_type', type, '#sk7': $i). 81.19/14.44 thf('#sk4_type', type, '#sk4': $i). 81.19/14.44 thf('#sk6_type', type, '#sk6': $i). 81.19/14.44 thf('#sk5_type', type, '#sk5': individuals). 81.19/14.44 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 81.19/14.44 thf('#sk2_type', type, '#sk2': $i). 81.19/14.44 thf(reli_type, type, reli: $i > $i > $o). 81.19/14.44 thf('#sk11_type', type, '#sk11': ($i > $o) > $i > $i). 81.19/14.44 thf('#sk3_type', type, '#sk3': $i). 81.19/14.44 thf(cs4_box_type, type, cs4_box: ($i > $o) > $i > $o). 81.19/14.44 thf(cs4_all_type, type, cs4_all: (individuals > $i > $o) > $i > $o). 81.19/14.44 thf('#sk1_type', type, '#sk1': individuals > $i > $o). 81.19/14.44 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 81.19/14.44 thf(mbox_type, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o). 81.19/14.44 thf(cs4_atom_type, type, cs4_atom: ($i > $o) > $i > $o). 81.19/14.44 thf(mall_type, type, mall: (individuals > $i > $o) > $i > $o). 81.19/14.44 thf(cs4_valid_type, type, cs4_valid: ($i > $o) > $o). 81.19/14.44 thf(mimpl_type, type, mimpl: ($i > $o) > ($i > $o) > $i > $o). 81.19/14.44 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 81.19/14.44 thf(cs4_valid_def, axiom,(( cs4_valid ) = 81.19/14.44 (^[A:( $i > $o )]: ( mvalid @ A )))). 81.19/14.44 thf(mvalid, axiom,(( mvalid ) = (^[P:( $i > $o )]: ( ![W:$i]: ( P @ W ) )))). 81.19/14.44 thf('0', plain, (( mvalid ) = ( ^[P:( $i > $o )]: ( ![W:$i]: ( P @ W ) ) )), 81.19/14.44 inference('simplify_rw_rule', [status(thm)], [mvalid])). 81.19/14.44 thf('1', plain, 81.19/14.44 (( mvalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 81.19/14.44 define([status(thm)])). 81.19/14.44 thf('2', plain, (( cs4_valid ) = ( ^[A:( $i > $o )]: ( mvalid @ A ) )), 81.19/14.44 inference('simplify_rw_rule', [status(thm)], [cs4_valid_def, '1'])). 81.19/14.44 thf('3', plain, (( cs4_valid ) = ( ^[V_1:( $i > $o )]: ( mvalid @ V_1 ) )), 81.19/14.44 define([status(thm)])). 81.19/14.44 thf(cs4_box, axiom,(( cs4_box ) = 81.19/14.44 (^[A:( $i > $o )]: ( mbox @ reli @ ( mbox @ relr @ A ) )))). 81.19/14.44 thf(mbox, axiom,(( mbox ) = 81.19/14.44 (^[R:( $i > $i > $o ),P:( $i > $o ),X:$i]: 81.19/14.44 ( ![Y:$i]: ( ( R @ X @ Y ) => ( P @ Y ) ) )))). 81.19/14.44 thf('4', plain, 81.19/14.44 (( mbox ) = 81.19/14.44 ( ^[R:( $i > $i > $o ),P:( $i > $o ),X:$i]: 81.19/14.44 ( ![Y:$i]: ( ( R @ X @ Y ) => ( P @ Y ) ) ) )), 81.19/14.44 inference('simplify_rw_rule', [status(thm)], [mbox])). 81.19/14.44 thf('5', plain, 81.19/14.44 (( mbox ) = 81.19/14.44 ( ^[V_1:( $i > $i > $o ),V_2:( $i > $o ),V_3:$i]: 81.19/14.44 ( ![X4:$i]: ( ( V_1 @ V_3 @ X4 ) => ( V_2 @ X4 ) ) ) )), 81.19/14.44 define([status(thm)])). 81.19/14.44 thf('6', plain, 81.19/14.44 (( cs4_box ) = 81.19/14.44 ( ^[A:( $i > $o )]: ( mbox @ reli @ ( mbox @ relr @ A ) ) )), 81.19/14.44 inference('simplify_rw_rule', [status(thm)], [cs4_box, '5'])). 81.19/14.44 thf('7', plain, 81.19/14.44 (( cs4_box ) = 81.19/14.44 ( ^[V_1:( $i > $o )]: ( mbox @ reli @ ( mbox @ relr @ V_1 ) ) )), 81.19/14.44 define([status(thm)])). 81.19/14.44 thf(cs4_all, axiom,(( cs4_all ) = 81.19/14.44 (^[A:( individuals > $i > $o )]: ( mbox @ reli @ ( mall @ A ) )))). 81.19/14.44 thf(mall, axiom,(( mall ) = 81.19/14.44 (^[P:( individuals > $i > $o ),W:$i]: ( ![X:individuals]: ( P @ X @ W ) )))). 81.19/14.44 thf('8', plain, 81.19/14.44 (( mall ) = 81.19/14.44 ( ^[P:( individuals > $i > $o ),W:$i]: 81.19/14.44 ( ![X:individuals]: ( P @ X @ W ) ) )), 81.19/14.44 inference('simplify_rw_rule', [status(thm)], [mall])). 81.19/14.44 thf('9', plain, 81.19/14.44 (( mall ) = 81.19/14.44 ( ^[V_1:( individuals > $i > $o ),V_2:$i]: 81.19/14.44 ( ![X4:individuals]: ( V_1 @ X4 @ V_2 ) ) )), 81.19/14.44 define([status(thm)])). 81.19/14.44 thf('10', plain, 81.19/14.44 (( cs4_all ) = 81.19/14.44 ( ^[A:( individuals > $i > $o )]: ( mbox @ reli @ ( mall @ A ) ) )), 81.19/14.44 inference('simplify_rw_rule', [status(thm)], [cs4_all, '9', '5'])). 81.19/14.44 thf('11', plain, 81.19/14.44 (( cs4_all ) = 81.19/14.44 ( ^[V_1:( individuals > $i > $o )]: ( mbox @ reli @ ( mall @ V_1 ) ) )), 81.19/14.44 define([status(thm)])). 81.19/14.44 thf(cs4_impl, axiom,(( cs4_impl ) = 81.19/14.44 (^[A:( $i > $o ),B:( $i > $o )]: ( mbox @ reli @ ( mimpl @ A @ B ) )))). 81.19/14.44 thf(mimpl, axiom,(( mimpl ) = 81.19/14.44 (^[U:( $i > $o ),V:( $i > $o )]: ( mor @ ( mnot @ U ) @ V )))). 81.19/14.44 thf(mor, axiom,(( mor ) = 81.19/14.44 (^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) | ( Y @ U ) )))). 81.19/14.44 thf('12', plain, 81.19/14.44 (( mor ) = 81.19/14.44 ( ^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) | ( Y @ U ) ) )), 81.19/14.44 inference('simplify_rw_rule', [status(thm)], [mor])). 81.19/14.44 thf('13', plain, 81.19/14.44 (( mor ) = 81.19/14.44 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 81.19/14.44 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 81.19/14.44 define([status(thm)])). 81.19/14.44 thf(mnot, axiom,(( mnot ) = (^[X:( $i > $o ),U:$i]: ( ~( X @ U ) )))). 81.19/14.44 thf('14', plain, (( mnot ) = ( ^[X:( $i > $o ),U:$i]: ( ~( X @ U ) ) )), 81.19/14.44 inference('simplify_rw_rule', [status(thm)], [mnot])). 81.19/14.44 thf('15', plain, 81.19/14.44 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )), 81.19/14.44 define([status(thm)])). 81.19/14.44 thf('16', plain, 81.19/14.44 (( mimpl ) = 81.19/14.44 ( ^[U:( $i > $o ),V:( $i > $o )]: ( mor @ ( mnot @ U ) @ V ) )), 81.19/14.44 inference('simplify_rw_rule', [status(thm)], [mimpl, '13', '15'])). 81.19/14.44 thf('17', plain, 81.19/14.44 (( mimpl ) = 81.19/14.44 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )), 81.19/14.44 define([status(thm)])). 81.19/14.44 thf('18', plain, 81.19/14.44 (( cs4_impl ) = 81.19/14.44 ( ^[A:( $i > $o ),B:( $i > $o )]: ( mbox @ reli @ ( mimpl @ A @ B ) ) )), 81.19/14.44 inference('simplify_rw_rule', [status(thm)], 81.19/14.44 [cs4_impl, '5', '17', '13', '15'])). 81.19/14.44 thf('19', plain, 81.19/14.44 (( cs4_impl ) = 81.19/14.44 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 81.19/14.44 ( mbox @ reli @ ( mimpl @ V_1 @ V_2 ) ) )), 81.19/14.44 define([status(thm)])). 81.19/14.44 thf(cs4_atom, axiom,(( cs4_atom ) = 81.19/14.44 (^[P:( $i > $o )]: ( mbox @ reli @ P )))). 81.19/14.44 thf('20', plain, (( cs4_atom ) = ( ^[P:( $i > $o )]: ( mbox @ reli @ P ) )), 81.19/14.44 inference('simplify_rw_rule', [status(thm)], [cs4_atom, '5'])). 81.19/14.44 thf('21', plain, 81.19/14.44 (( cs4_atom ) = ( ^[V_1:( $i > $o )]: ( mbox @ reli @ V_1 ) )), 81.19/14.44 define([status(thm)])). 81.19/14.44 thf(cs4_cbarcan, conjecture, 81.19/14.44 (![A:( individuals > $i > $o )]: 81.19/14.44 ( cs4_valid @ 81.19/14.44 ( cs4_impl @ 81.19/14.44 ( cs4_box @ 81.19/14.44 ( cs4_all @ ( ^[I:individuals]: ( cs4_atom @ ( A @ I ) ) ) ) ) @ 81.19/14.44 ( cs4_all @ 81.19/14.44 ( ^[I:individuals]: ( cs4_box @ ( cs4_atom @ ( A @ I ) ) ) ) ) ) ))). 81.19/14.44 thf(zf_stmt_0, conjecture, 81.19/14.44 (![X4:( individuals > $i > $o ),X6:$i,X8:$i]: 81.19/14.44 ( ( reli @ X6 @ X8 ) => 81.19/14.44 ( ( ![X20:$i]: 81.19/14.44 ( ( reli @ X8 @ X20 ) => 81.19/14.44 ( ![X22:individuals,X24:$i]: 81.19/14.44 ( ( reli @ X20 @ X24 ) => 81.19/14.44 ( ![X26:$i]: 81.19/14.44 ( ( relr @ X24 @ X26 ) => 81.19/14.44 ( ![X28:$i]: 81.19/14.44 ( ( reli @ X26 @ X28 ) => ( X4 @ X22 @ X28 ) ) ) ) ) ) ) ) ) | 81.19/14.44 ( ~( ![X10:$i]: 81.19/14.44 ( ( reli @ X8 @ X10 ) => 81.19/14.44 ( ![X12:$i]: 81.19/14.44 ( ( relr @ X10 @ X12 ) => 81.19/14.44 ( ![X14:$i]: 81.19/14.44 ( ( reli @ X12 @ X14 ) => 81.19/14.44 ( ![X16:individuals,X18:$i]: 81.19/14.44 ( ( reli @ X14 @ X18 ) => ( X4 @ X16 @ X18 ) ) ) ) ) ) ) ) ) ) ) ))). 81.19/14.44 thf(zf_stmt_1, negated_conjecture, 81.19/14.44 (~( ![X4:( individuals > $i > $o ),X6:$i,X8:$i]: 81.19/14.44 ( ( reli @ X6 @ X8 ) => 81.19/14.44 ( ( ![X20:$i]: 81.19/14.44 ( ( reli @ X8 @ X20 ) => 81.19/14.44 ( ![X22:individuals,X24:$i]: 81.19/14.44 ( ( reli @ X20 @ X24 ) => 81.19/14.44 ( ![X26:$i]: 81.19/14.44 ( ( relr @ X24 @ X26 ) => 81.19/14.44 ( ![X28:$i]: 81.19/14.44 ( ( reli @ X26 @ X28 ) => ( X4 @ X22 @ X28 ) ) ) ) ) ) ) ) ) | 81.19/14.44 ( ~( ![X10:$i]: 81.19/14.44 ( ( reli @ X8 @ X10 ) => 81.19/14.44 ( ![X12:$i]: 81.19/14.44 ( ( relr @ X10 @ X12 ) => 81.19/14.44 ( ![X14:$i]: 81.19/14.44 ( ( reli @ X12 @ X14 ) => 81.19/14.44 ( ![X16:individuals,X18:$i]: 81.19/14.44 ( ( reli @ X14 @ X18 ) => ( X4 @ X16 @ X18 ) ) ) ) ) ) ) ) ) ) ) ) )), 81.19/14.44 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 81.19/14.44 thf(zip_derived_cl5, plain, 81.19/14.44 (~ (((!!) @ (^[Y0 : individuals > $i > $o]: 81.19/14.44 (((!!) @ (^[Y1 : $i]: 81.19/14.44 (((!!) @ (^[Y2 : $i]: 81.19/14.44 (((reli @ Y1 @ Y2) => 81.19/14.44 (((((!!) @ (^[Y3 : $i]: 81.19/14.44 (((reli @ Y2 @ 81.19/14.44 Y3) => 81.19/14.44 (((!!) @ ( 81.19/14.44 ^[Y4 : individuals]: 81.19/14.44 (((!!) @ ( 81.19/14.44 ^[Y5 : $i]: 81.19/14.44 (( 81.19/14.44 (reli @ 81.19/14.44 Y3 @ 81.19/14.44 Y5) => 81.19/14.44 (( 81.19/14.44 (!!) @ ( 81.19/14.44 ^[Y6 : $i]: 81.19/14.44 (( 81.19/14.44 (relr @ 81.19/14.44 Y5 @ 81.19/14.44 Y6) => 81.19/14.44 (( 81.19/14.44 (!!) @ ( 81.19/14.44 ^[Y7 : $i]: 81.19/14.44 (( 81.19/14.44 (reli @ 81.19/14.44 Y6 @ 81.19/14.44 Y7) => 81.19/14.44 (Y0 @ 81.19/14.44 Y4 @ Y7)))))))))))))))))))))))) | 81.19/14.44 (((~) @ (((!!) @ (^[Y3 : $i]: 81.19/14.44 (( 81.19/14.44 (reli @ 81.19/14.44 Y2 @ 81.19/14.44 Y3) => 81.19/14.44 (( 81.19/14.44 (!!) @ ( 81.19/14.44 ^[Y4 : $i]: 81.19/14.44 (( 81.19/14.44 (relr @ 81.19/14.44 Y3 @ 81.19/14.44 Y4) => 81.19/14.44 (( 81.19/14.44 (!!) @ ( 81.19/14.44 ^[Y5 : $i]: 81.19/14.44 (( 81.19/14.44 (reli @ 81.19/14.44 Y4 @ 81.19/14.44 Y5) => 81.19/14.44 (( 81.19/14.44 (!!) @ ( 81.19/14.44 ^[Y6 : individuals]: 81.19/14.44 (( 81.19/14.44 (!!) @ ( 81.19/14.44 ^[Y7 : $i]: 81.19/14.44 (( 81.19/14.44 (reli @ 81.19/14.44 Y5 @ 81.19/14.44 Y7) => 81.19/14.44 (Y0 @ 81.19/14.44 Y6 @ Y7)))))))))))))))))))))))))))))))))))))))), 81.19/14.44 inference('cnf', [status(esa)], [zf_stmt_1])). 81.19/14.44 thf(zip_derived_cl6, plain, 81.19/14.44 (~ (((!!) @ (^[Y0 : $i]: 81.19/14.44 (((!!) @ (^[Y1 : $i]: 81.19/14.44 (((reli @ Y0 @ Y1) => 81.19/14.44 (((((!!) @ (^[Y2 : $i]: 81.19/14.44 (((reli @ Y1 @ Y2) => 81.19/14.44 (((!!) @ (^[Y3 : individuals]: 81.19/14.44 (((!!) @ ( 81.19/14.44 ^[Y4 : $i]: 81.19/14.44 (((reli @ 81.19/14.44 Y2 @ 81.19/14.44 Y4) => 81.19/14.44 (( 81.19/14.44 (!!) @ ( 81.19/14.44 ^[Y5 : $i]: 81.19/14.44 (( 81.19/14.44 (relr @ 81.19/14.44 Y4 @ 81.19/14.44 Y5) => 81.19/14.44 (( 81.19/14.44 (!!) @ ( 81.19/14.44 ^[Y6 : $i]: 81.19/14.44 (( 81.19/14.44 (reli @ 81.19/14.44 Y5 @ 81.19/14.44 Y6) => 81.19/14.44 ('#sk1' @ 81.19/14.44 Y3 @ Y6)))))))))))))))))))))))) | 81.19/14.44 (((~) @ (((!!) @ (^[Y2 : $i]: 81.19/14.44 (((reli @ Y1 @ Y2) => 81.19/14.44 (((!!) @ (^[Y3 : $i]: 81.19/14.44 (( 81.19/14.44 (relr @ 81.19/14.44 Y2 @ 81.19/14.44 Y3) => 81.19/14.44 (( 81.19/14.44 (!!) @ ( 81.19/14.44 ^[Y4 : $i]: 81.19/14.44 (( 81.19/14.44 (reli @ 81.19/14.44 Y3 @ 81.19/14.44 Y4) => 81.19/14.44 (( 81.19/14.44 (!!) @ ( 81.19/14.44 ^[Y5 : individuals]: 81.19/14.44 (( 81.19/14.44 (!!) @ ( 81.19/14.44 ^[Y6 : $i]: 81.19/14.44 (( 81.19/14.44 (reli @ 81.19/14.44 Y4 @ 81.19/14.44 Y6) => 81.19/14.44 ('#sk1' @ 81.19/14.44 Y5 @ Y6))))))))))))))))))))))))))))))))))))), 81.19/14.44 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl5])). 81.19/14.44 thf(zip_derived_cl7, plain, 81.19/14.44 (~ (((!!) @ (^[Y0 : $i]: 81.19/14.44 (((reli @ '#sk2' @ Y0) => 81.19/14.44 (((((!!) @ (^[Y1 : $i]: 81.19/14.44 (((reli @ Y0 @ Y1) => 81.19/14.44 (((!!) @ (^[Y2 : individuals]: 81.19/14.44 (((!!) @ (^[Y3 : $i]: 81.19/14.44 (((reli @ Y1 @ 81.19/14.44 Y3) => 81.19/14.44 (((!!) @ ( 81.19/14.44 ^[Y4 : $i]: 81.19/14.44 (( 81.19/14.44 (relr @ 81.19/14.44 Y3 @ 81.19/14.44 Y4) => 81.19/14.44 (( 81.19/14.44 (!!) @ ( 81.19/14.44 ^[Y5 : $i]: 81.19/14.44 (( 81.19/14.44 (reli @ 81.19/14.44 Y4 @ 81.19/14.44 Y5) => 81.19/14.44 ('#sk1' @ 81.19/14.44 Y2 @ Y5)))))))))))))))))))))))) | 81.19/14.44 (((~) @ (((!!) @ (^[Y1 : $i]: 81.19/14.44 (((reli @ Y0 @ Y1) => 81.19/14.44 (((!!) @ (^[Y2 : $i]: 81.19/14.44 (((relr @ Y1 @ 81.19/14.44 Y2) => 81.19/14.44 (((!!) @ ( 81.19/14.44 ^[Y3 : $i]: 81.19/14.44 (((reli @ 81.19/14.44 Y2 @ Y3) => 81.19/14.44 (((!!) @ ( 81.19/14.44 ^[Y4 : individuals]: 81.19/14.44 (( 81.19/14.44 (!!) @ ( 81.19/14.44 ^[Y5 : $i]: 81.19/14.44 (( 81.19/14.44 (reli @ 81.19/14.44 Y3 @ 81.19/14.44 Y5) => 81.19/14.44 ('#sk1' @ 81.19/14.44 Y4 @ Y5)))))))))))))))))))))))))))))))))), 81.19/14.44 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 81.19/14.44 thf(zip_derived_cl8, plain, 81.19/14.44 (~ (((reli @ '#sk2' @ '#sk3') => 81.19/14.44 (((((!!) @ (^[Y0 : $i]: 81.19/14.44 (((reli @ '#sk3' @ Y0) => 81.19/14.44 (((!!) @ (^[Y1 : individuals]: 81.19/14.44 (((!!) @ (^[Y2 : $i]: 81.19/14.44 (((reli @ Y0 @ Y2) => 81.19/14.44 (((!!) @ (^[Y3 : $i]: 81.19/14.44 (((relr @ 81.19/14.44 Y2 @ Y3) => 81.19/14.44 (((!!) @ ( 81.19/14.44 ^[Y4 : $i]: 81.19/14.44 (( 81.19/14.44 (reli @ 81.19/14.44 Y3 @ 81.19/14.44 Y4) => 81.19/14.44 ('#sk1' @ 81.19/14.44 Y1 @ Y4)))))))))))))))))))))))) | 81.19/14.44 (((~) @ (((!!) @ (^[Y0 : $i]: 81.19/14.44 (((reli @ '#sk3' @ Y0) => 81.19/14.44 (((!!) @ (^[Y1 : $i]: 81.19/14.44 (((relr @ Y0 @ Y1) => 81.19/14.44 (((!!) @ (^[Y2 : $i]: 81.19/14.44 (((reli @ Y1 @ 81.19/14.44 Y2) => 81.19/14.44 (((!!) @ ( 81.19/14.44 ^[Y3 : individuals]: 81.19/14.44 (((!!) @ ( 81.19/14.44 ^[Y4 : $i]: 81.19/14.44 (( 81.19/14.44 (reli @ 81.19/14.44 Y2 @ 81.19/14.44 Y4) => 81.19/14.44 ('#sk1' @ 81.19/14.44 Y3 @ Y4))))))))))))))))))))))))))))))), 81.19/14.44 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl7])). 81.19/14.44 thf(zip_derived_cl10, plain, 81.19/14.44 (~ (((((!!) @ (^[Y0 : $i]: 81.19/14.44 (((reli @ '#sk3' @ Y0) => 81.19/14.44 (((!!) @ (^[Y1 : individuals]: 81.19/14.44 (((!!) @ (^[Y2 : $i]: 81.19/14.44 (((reli @ Y0 @ Y2) => 81.19/14.44 (((!!) @ (^[Y3 : $i]: 81.19/14.44 (((relr @ Y2 @ 81.19/14.45 Y3) => 81.19/14.45 (((!!) @ ( 81.19/14.45 ^[Y4 : $i]: 81.19/14.45 (( 81.19/14.45 (reli @ 81.19/14.45 Y3 @ 81.19/14.45 Y4) => 81.19/14.45 ('#sk1' @ 81.19/14.45 Y1 @ Y4)))))))))))))))))))))))) | 81.19/14.45 (((~) @ (((!!) @ (^[Y0 : $i]: 81.19/14.45 (((reli @ '#sk3' @ Y0) => 81.19/14.45 (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((relr @ Y0 @ Y1) => 81.19/14.45 (((!!) @ (^[Y2 : $i]: 81.19/14.45 (((reli @ Y1 @ 81.19/14.45 Y2) => 81.19/14.45 (((!!) @ ( 81.19/14.45 ^[Y3 : individuals]: 81.19/14.45 (((!!) @ ( 81.19/14.45 ^[Y4 : $i]: 81.19/14.45 (( 81.19/14.45 (reli @ 81.19/14.45 Y2 @ 81.19/14.45 Y4) => 81.19/14.45 ('#sk1' @ 81.19/14.45 Y3 @ Y4))))))))))))))))))))))))))))), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 81.19/14.45 thf(zip_derived_cl11, plain, 81.19/14.45 (~ (((!!) @ (^[Y0 : $i]: 81.19/14.45 (((reli @ '#sk3' @ Y0) => 81.19/14.45 (((!!) @ (^[Y1 : individuals]: 81.19/14.45 (((!!) @ (^[Y2 : $i]: 81.19/14.45 (((reli @ Y0 @ Y2) => 81.19/14.45 (((!!) @ (^[Y3 : $i]: 81.19/14.45 (((relr @ Y2 @ 81.19/14.45 Y3) => 81.19/14.45 (((!!) @ ( 81.19/14.45 ^[Y4 : $i]: 81.19/14.45 (((reli @ 81.19/14.45 Y3 @ 81.19/14.45 Y4) => 81.19/14.45 ('#sk1' @ 81.19/14.45 Y1 @ Y4))))))))))))))))))))))))), 81.19/14.45 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl10])). 81.19/14.45 thf(zip_derived_cl13, plain, 81.19/14.45 (~ (((reli @ '#sk3' @ '#sk4') => 81.19/14.45 (((!!) @ (^[Y0 : individuals]: 81.19/14.45 (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((reli @ '#sk4' @ Y1) => 81.19/14.45 (((!!) @ (^[Y2 : $i]: 81.19/14.45 (((relr @ Y1 @ Y2) => 81.19/14.45 (((!!) @ (^[Y3 : $i]: 81.19/14.45 (((reli @ Y2 @ 81.19/14.45 Y3) => 81.19/14.45 ('#sk1' @ 81.19/14.45 Y0 @ Y3)))))))))))))))))))))), 81.19/14.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl11])). 81.19/14.45 thf(zip_derived_cl16, plain, 81.19/14.45 (~ (((!!) @ (^[Y0 : individuals]: 81.19/14.45 (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((reli @ '#sk4' @ Y1) => 81.19/14.45 (((!!) @ (^[Y2 : $i]: 81.19/14.45 (((relr @ Y1 @ Y2) => 81.19/14.45 (((!!) @ (^[Y3 : $i]: 81.19/14.45 (((reli @ Y2 @ 81.19/14.45 Y3) => 81.19/14.45 ('#sk1' @ Y0 @ 81.19/14.45 Y3)))))))))))))))))))), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 81.19/14.45 thf(zip_derived_cl18, plain, 81.19/14.45 (~ (((!!) @ (^[Y0 : $i]: 81.19/14.45 (((reli @ '#sk4' @ Y0) => 81.19/14.45 (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((relr @ Y0 @ Y1) => 81.19/14.45 (((!!) @ (^[Y2 : $i]: 81.19/14.45 (((reli @ Y1 @ Y2) => 81.19/14.45 ('#sk1' @ '#sk5' @ Y2))))))))))))))))), 81.19/14.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl16])). 81.19/14.45 thf(zip_derived_cl20, plain, 81.19/14.45 (~ (((reli @ '#sk4' @ '#sk6') => 81.19/14.45 (((!!) @ (^[Y0 : $i]: 81.19/14.45 (((relr @ '#sk6' @ Y0) => 81.19/14.45 (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((reli @ Y0 @ Y1) => ('#sk1' @ '#sk5' @ 81.19/14.45 Y1)))))))))))))), 81.19/14.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl18])). 81.19/14.45 thf(zip_derived_cl23, plain, 81.19/14.45 (~ (((!!) @ (^[Y0 : $i]: 81.19/14.45 (((relr @ '#sk6' @ Y0) => 81.19/14.45 (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((reli @ Y0 @ Y1) => ('#sk1' @ '#sk5' @ Y1)))))))))))), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 81.19/14.45 thf(zip_derived_cl25, plain, 81.19/14.45 (~ (((relr @ '#sk6' @ '#sk7') => 81.19/14.45 (((!!) @ (^[Y0 : $i]: 81.19/14.45 (((reli @ '#sk7' @ Y0) => ('#sk1' @ '#sk5' @ Y0))))))))), 81.19/14.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl23])). 81.19/14.45 thf(zip_derived_cl28, plain, 81.19/14.45 (~ (((!!) @ (^[Y0 : $i]: 81.19/14.45 (((reli @ '#sk7' @ Y0) => ('#sk1' @ '#sk5' @ Y0))))))), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 81.19/14.45 thf(zip_derived_cl30, plain, 81.19/14.45 (~ (((reli @ '#sk7' @ '#sk8') => ('#sk1' @ '#sk5' @ '#sk8')))), 81.19/14.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])). 81.19/14.45 thf(zip_derived_cl33, plain, (~ ('#sk1' @ '#sk5' @ '#sk8')), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl30])). 81.19/14.45 thf(zip_derived_cl15, plain, ( (reli @ '#sk3' @ '#sk4')), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 81.19/14.45 thf(zip_derived_cl22, plain, ( (reli @ '#sk4' @ '#sk6')), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 81.19/14.45 thf(trans_axiom_i, axiom, 81.19/14.45 (![A:( $i > $o )]: 81.19/14.45 ( mvalid @ 81.19/14.45 ( mimpl @ ( mbox @ reli @ A ) @ ( mbox @ reli @ ( mbox @ reli @ A ) ) ) ))). 81.19/14.45 thf(zf_stmt_2, axiom, 81.19/14.45 (![X4:( $i > $o ),X6:$i]: 81.19/14.45 ( ( ![X10:$i]: 81.19/14.45 ( ( reli @ X6 @ X10 ) => 81.19/14.45 ( ![X12:$i]: ( ( reli @ X10 @ X12 ) => ( X4 @ X12 ) ) ) ) ) | 81.19/14.45 ( ~( ![X8:$i]: ( ( reli @ X6 @ X8 ) => ( X4 @ X8 ) ) ) ) ))). 81.19/14.45 thf(zip_derived_cl2, plain, 81.19/14.45 ( (((!!) @ (^[Y0 : $i > $o]: 81.19/14.45 (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((((!!) @ (^[Y2 : $i]: 81.19/14.45 (((reli @ Y1 @ Y2) => 81.19/14.45 (((!!) @ (^[Y3 : $i]: 81.19/14.45 (((reli @ Y2 @ 81.19/14.45 Y3) => (Y0 @ Y3))))))))))) | 81.19/14.45 (((~) @ (((!!) @ (^[Y2 : $i]: 81.19/14.45 (((reli @ Y1 @ Y2) => 81.19/14.45 (Y0 @ Y2))))))))))))))))), 81.19/14.45 inference('cnf', [status(esa)], [zf_stmt_2])). 81.19/14.45 thf(zip_derived_cl98, plain, 81.19/14.45 (![X2 : $i > $o]: 81.19/14.45 (((!!) @ (^[Y0 : $i]: 81.19/14.45 (((((!!) @ (^[Y1 : $i]: 81.19/14.45 (((reli @ Y0 @ Y1) => 81.19/14.45 (((!!) @ (^[Y2 : $i]: 81.19/14.45 (((reli @ Y1 @ Y2) => (X2 @ 81.19/14.45 Y2))))))))))) | 81.19/14.45 (((~) @ (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((reli @ Y0 @ Y1) => (X2 @ Y1)))))))))))))), 81.19/14.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 81.19/14.45 thf(zip_derived_cl99, plain, 81.19/14.45 (![X2 : $i > $o, X4 : $i]: 81.19/14.45 (((((!!) @ (^[Y0 : $i]: 81.19/14.45 (((reli @ X4 @ Y0) => 81.19/14.45 (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((reli @ Y0 @ Y1) => (X2 @ Y1))))))))))) | 81.19/14.45 (((~) @ (((!!) @ (^[Y0 : $i]: (((reli @ X4 @ Y0) => (X2 @ Y0))))))))))), 81.19/14.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl98])). 81.19/14.45 thf(zip_derived_cl100, plain, 81.19/14.45 (![X2 : $i > $o, X4 : $i]: 81.19/14.45 ( (((!!) @ (^[Y0 : $i]: 81.19/14.45 (((reli @ X4 @ Y0) => 81.19/14.45 (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((reli @ Y0 @ Y1) => (X2 @ Y1))))))))))) 81.19/14.45 | ~ (((!!) @ (^[Y0 : $i]: (((reli @ X4 @ Y0) => (X2 @ Y0)))))))), 81.19/14.45 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl99])). 81.19/14.45 thf(zip_derived_cl101, plain, 81.19/14.45 (![X2 : $i > $o, X4 : $i, X6 : $i]: 81.19/14.45 ( (((reli @ X4 @ X6) => 81.19/14.45 (((!!) @ (^[Y0 : $i]: (((reli @ X6 @ Y0) => (X2 @ Y0)))))))) 81.19/14.45 | ~ (((!!) @ (^[Y0 : $i]: (((reli @ X4 @ Y0) => (X2 @ Y0)))))))), 81.19/14.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl100])). 81.19/14.45 thf(zip_derived_cl102, plain, 81.19/14.45 (![X2 : $i > $o, X4 : $i, X6 : $i]: 81.19/14.45 (~ (reli @ X4 @ X6) 81.19/14.45 | (((!!) @ (^[Y0 : $i]: (((reli @ X6 @ Y0) => (X2 @ Y0)))))) 81.19/14.45 | ~ (((!!) @ (^[Y0 : $i]: (((reli @ X4 @ Y0) => (X2 @ Y0)))))))), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl101])). 81.19/14.45 thf(zip_derived_cl103, plain, 81.19/14.45 (![X2 : $i > $o, X4 : $i, X6 : $i, X8 : $i]: 81.19/14.45 ( (((reli @ X6 @ X8) => (X2 @ X8))) 81.19/14.45 | ~ (((!!) @ (^[Y0 : $i]: (((reli @ X4 @ Y0) => (X2 @ Y0)))))) 81.19/14.45 | ~ (reli @ X4 @ X6))), 81.19/14.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl102])). 81.19/14.45 thf(zip_derived_cl104, plain, 81.19/14.45 (![X2 : $i > $o, X4 : $i, X6 : $i, X8 : $i]: 81.19/14.45 (~ (reli @ X6 @ X8) 81.19/14.45 | (X2 @ X8) 81.19/14.45 | ~ (reli @ X4 @ X6) 81.19/14.45 | ~ (((!!) @ (^[Y0 : $i]: (((reli @ X4 @ Y0) => (X2 @ Y0)))))))), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])). 81.19/14.45 thf(zip_derived_cl105, plain, 81.19/14.45 (![X2 : $i > $o, X4 : $i, X6 : $i, X8 : $i]: 81.19/14.45 (~ (((reli @ X4 @ ('#sk11' @ X2 @ X4)) => (X2 @ ('#sk11' @ X2 @ X4)))) 81.19/14.45 | ~ (reli @ X4 @ X6) 81.19/14.45 | (X2 @ X8) 81.19/14.45 | ~ (reli @ X6 @ X8))), 81.19/14.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl104])). 81.19/14.45 thf(zip_derived_cl107, plain, 81.19/14.45 (![X2 : $i > $o, X4 : $i, X6 : $i, X8 : $i]: 81.19/14.45 (~ (X2 @ ('#sk11' @ X2 @ X4)) 81.19/14.45 | ~ (reli @ X6 @ X8) 81.19/14.45 | (X2 @ X8) 81.19/14.45 | ~ (reli @ X4 @ X6))), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])). 81.19/14.45 thf(zip_derived_cl140, plain, 81.19/14.45 (![X0 : $i, X1 : $i > $o]: 81.19/14.45 (~ (reli @ X0 @ '#sk4') 81.19/14.45 | (X1 @ '#sk6') 81.19/14.45 | ~ (X1 @ ('#sk11' @ X1 @ X0)))), 81.19/14.45 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl107])). 81.19/14.45 thf(zip_derived_cl566, plain, 81.19/14.45 (![X0 : $i > $o]: (~ (X0 @ ('#sk11' @ X0 @ '#sk3')) | (X0 @ '#sk6'))), 81.19/14.45 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl140])). 81.19/14.45 thf(zip_derived_cl15, plain, ( (reli @ '#sk3' @ '#sk4')), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 81.19/14.45 thf(zip_derived_cl22, plain, ( (reli @ '#sk4' @ '#sk6')), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 81.19/14.45 thf(zip_derived_cl106, plain, 81.19/14.45 (![X2 : $i > $o, X4 : $i, X6 : $i, X8 : $i]: 81.19/14.45 ( (reli @ X4 @ ('#sk11' @ X2 @ X4)) 81.19/14.45 | ~ (reli @ X6 @ X8) 81.19/14.45 | (X2 @ X8) 81.19/14.45 | ~ (reli @ X4 @ X6))), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])). 81.19/14.45 thf(zip_derived_cl111, plain, 81.19/14.45 (![X0 : $i, X1 : $i > $o]: 81.19/14.45 (~ (reli @ X0 @ '#sk4') 81.19/14.45 | (X1 @ '#sk6') 81.19/14.45 | (reli @ X0 @ ('#sk11' @ X1 @ X0)))), 81.19/14.45 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl106])). 81.19/14.45 thf(zip_derived_cl551, plain, 81.19/14.45 (![X0 : $i > $o]: 81.19/14.45 ( (reli @ '#sk3' @ ('#sk11' @ X0 @ '#sk3')) | (X0 @ '#sk6'))), 81.19/14.45 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl111])). 81.19/14.45 thf(zip_derived_cl5359, plain, 81.19/14.45 (( (reli @ '#sk3' @ '#sk6') | (reli @ '#sk3' @ '#sk6'))), 81.19/14.45 inference('sup+', [status(thm)], [zip_derived_cl566, zip_derived_cl551])). 81.19/14.45 thf(zip_derived_cl5360, plain, ( (reli @ '#sk3' @ '#sk6')), 81.19/14.45 inference('simplify', [status(thm)], [zip_derived_cl5359])). 81.19/14.45 thf(refl_axiom_i, axiom, 81.19/14.45 (![A:( $i > $o )]: ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ A ) ))). 81.19/14.45 thf(zf_stmt_3, axiom, 81.19/14.45 (![X4:( $i > $o ),X6:$i]: 81.19/14.45 ( ( X4 @ X6 ) | ( ~( ![X8:$i]: ( ( reli @ X6 @ X8 ) => ( X4 @ X8 ) ) ) ) ))). 81.19/14.45 thf(zip_derived_cl3, plain, 81.19/14.45 ( (((!!) @ (^[Y0 : $i > $o]: 81.19/14.45 (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((Y0 @ Y1) | 81.19/14.45 (((~) @ (((!!) @ (^[Y2 : $i]: 81.19/14.45 (((reli @ Y1 @ Y2) => 81.19/14.45 (Y0 @ Y2))))))))))))))))), 81.19/14.45 inference('cnf', [status(esa)], [zf_stmt_3])). 81.19/14.45 thf(zip_derived_cl79, plain, 81.19/14.45 (![X2 : $i > $o]: 81.19/14.45 (((!!) @ (^[Y0 : $i]: 81.19/14.45 (((X2 @ Y0) | 81.19/14.45 (((~) @ (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((reli @ Y0 @ Y1) => (X2 @ Y1)))))))))))))), 81.19/14.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 81.19/14.45 thf(zip_derived_cl80, plain, 81.19/14.45 (![X2 : $i > $o, X4 : $i]: 81.19/14.45 (((X2 @ X4) | 81.19/14.45 (((~) @ (((!!) @ (^[Y0 : $i]: (((reli @ X4 @ Y0) => (X2 @ Y0))))))))))), 81.19/14.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl79])). 81.19/14.45 thf(zip_derived_cl81, plain, 81.19/14.45 (![X2 : $i > $o, X4 : $i]: 81.19/14.45 ( (X2 @ X4) 81.19/14.45 | ~ (((!!) @ (^[Y0 : $i]: (((reli @ X4 @ Y0) => (X2 @ Y0)))))))), 81.19/14.45 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl80])). 81.19/14.45 thf(zip_derived_cl82, plain, 81.19/14.45 (![X2 : $i > $o, X4 : $i]: 81.19/14.45 (~ (((reli @ X4 @ ('#sk11' @ X2 @ X4)) => (X2 @ ('#sk11' @ X2 @ X4)))) 81.19/14.45 | (X2 @ X4))), 81.19/14.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl81])). 81.19/14.45 thf(zip_derived_cl83, plain, 81.19/14.45 (![X2 : $i > $o, X4 : $i]: 81.19/14.45 ( (reli @ X4 @ ('#sk11' @ X2 @ X4)) | (X2 @ X4))), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 81.19/14.45 thf(zip_derived_cl84, plain, 81.19/14.45 (![X2 : $i > $o, X4 : $i]: (~ (X2 @ ('#sk11' @ X2 @ X4)) | (X2 @ X4))), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 81.19/14.45 thf(zip_derived_cl92, plain, 81.19/14.45 (![X0 : $i]: ( (reli @ X0 @ X0) | (reli @ X0 @ X0))), 81.19/14.45 inference('sup-', [status(thm)], [zip_derived_cl83, zip_derived_cl84])). 81.19/14.45 thf(zip_derived_cl93, plain, (![X0 : $i]: (reli @ X0 @ X0)), 81.19/14.45 inference('simplify', [status(thm)], [zip_derived_cl92])). 81.19/14.45 thf(zip_derived_cl32, plain, ( (reli @ '#sk7' @ '#sk8')), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl30])). 81.19/14.45 thf(zip_derived_cl12, plain, 81.19/14.45 ( (((!!) @ (^[Y0 : $i]: 81.19/14.45 (((reli @ '#sk3' @ Y0) => 81.19/14.45 (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((relr @ Y0 @ Y1) => 81.19/14.45 (((!!) @ (^[Y2 : $i]: 81.19/14.45 (((reli @ Y1 @ Y2) => 81.19/14.45 (((!!) @ (^[Y3 : individuals]: 81.19/14.45 (((!!) @ ( 81.19/14.45 ^[Y4 : $i]: 81.19/14.45 (((reli @ 81.19/14.45 Y2 @ Y4) => 81.19/14.45 ('#sk1' @ 81.19/14.45 Y3 @ Y4))))))))))))))))))))))))), 81.19/14.45 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl10])). 81.19/14.45 thf(zip_derived_cl14, plain, 81.19/14.45 (![X2 : $i]: 81.19/14.45 (((reli @ '#sk3' @ X2) => 81.19/14.45 (((!!) @ (^[Y0 : $i]: 81.19/14.45 (((relr @ X2 @ Y0) => 81.19/14.45 (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((reli @ Y0 @ Y1) => 81.19/14.45 (((!!) @ (^[Y2 : individuals]: 81.19/14.45 (((!!) @ (^[Y3 : $i]: 81.19/14.45 (((reli @ Y1 @ 81.19/14.45 Y3) => 81.19/14.45 ('#sk1' @ 81.19/14.45 Y2 @ Y3)))))))))))))))))))))), 81.19/14.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 81.19/14.45 thf(zip_derived_cl17, plain, 81.19/14.45 (![X2 : $i]: 81.19/14.45 (~ (reli @ '#sk3' @ X2) 81.19/14.45 | (((!!) @ (^[Y0 : $i]: 81.19/14.45 (((relr @ X2 @ Y0) => 81.19/14.45 (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((reli @ Y0 @ Y1) => 81.19/14.45 (((!!) @ (^[Y2 : individuals]: 81.19/14.45 (((!!) @ (^[Y3 : $i]: 81.19/14.45 (((reli @ 81.19/14.45 Y1 @ Y3) => 81.19/14.45 ('#sk1' @ 81.19/14.45 Y2 @ Y3))))))))))))))))))))), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 81.19/14.45 thf(zip_derived_cl19, plain, 81.19/14.45 (![X2 : $i, X4 : $i]: 81.19/14.45 ( (((relr @ X2 @ X4) => 81.19/14.45 (((!!) @ (^[Y0 : $i]: 81.19/14.45 (((reli @ X4 @ Y0) => 81.19/14.45 (((!!) @ (^[Y1 : individuals]: 81.19/14.45 (((!!) @ (^[Y2 : $i]: 81.19/14.45 (((reli @ Y0 @ Y2) => 81.19/14.45 ('#sk1' @ Y1 @ Y2)))))))))))))))) 81.19/14.45 | ~ (reli @ '#sk3' @ X2))), 81.19/14.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 81.19/14.45 thf(zip_derived_cl21, plain, 81.19/14.45 (![X2 : $i, X4 : $i]: 81.19/14.45 (~ (relr @ X2 @ X4) 81.19/14.45 | (((!!) @ (^[Y0 : $i]: 81.19/14.45 (((reli @ X4 @ Y0) => 81.19/14.45 (((!!) @ (^[Y1 : individuals]: 81.19/14.45 (((!!) @ (^[Y2 : $i]: 81.19/14.45 (((reli @ Y0 @ Y2) => 81.19/14.45 ('#sk1' @ Y1 @ Y2)))))))))))))) 81.19/14.45 | ~ (reli @ '#sk3' @ X2))), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 81.19/14.45 thf(zip_derived_cl24, plain, 81.19/14.45 (![X2 : $i, X4 : $i, X6 : $i]: 81.19/14.45 ( (((reli @ X4 @ X6) => 81.19/14.45 (((!!) @ (^[Y0 : individuals]: 81.19/14.45 (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((reli @ X6 @ Y1) => ('#sk1' @ Y0 @ Y1))))))))))) 81.19/14.45 | ~ (reli @ '#sk3' @ X2) 81.19/14.45 | ~ (relr @ X2 @ X4))), 81.19/14.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])). 81.19/14.45 thf(zip_derived_cl26, plain, 81.19/14.45 (![X2 : $i, X4 : $i, X6 : $i]: 81.19/14.45 (~ (reli @ X4 @ X6) 81.19/14.45 | (((!!) @ (^[Y0 : individuals]: 81.19/14.45 (((!!) @ (^[Y1 : $i]: 81.19/14.45 (((reli @ X6 @ Y1) => ('#sk1' @ Y0 @ Y1))))))))) 81.19/14.45 | ~ (relr @ X2 @ X4) 81.19/14.45 | ~ (reli @ '#sk3' @ X2))), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 81.19/14.45 thf(zip_derived_cl29, plain, 81.19/14.45 (![X2 : $i, X4 : $i, X6 : $i, X8 : individuals]: 81.19/14.45 ( (((!!) @ (^[Y0 : $i]: (((reli @ X6 @ Y0) => ('#sk1' @ X8 @ Y0)))))) 81.19/14.45 | ~ (reli @ '#sk3' @ X2) 81.19/14.45 | ~ (relr @ X2 @ X4) 81.19/14.45 | ~ (reli @ X4 @ X6))), 81.19/14.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])). 81.19/14.45 thf(zip_derived_cl31, plain, 81.19/14.45 (![X2 : $i, X4 : $i, X6 : $i, X8 : individuals, X10 : $i]: 81.19/14.45 ( (((reli @ X6 @ X10) => ('#sk1' @ X8 @ X10))) 81.19/14.45 | ~ (reli @ X4 @ X6) 81.19/14.45 | ~ (relr @ X2 @ X4) 81.19/14.45 | ~ (reli @ '#sk3' @ X2))), 81.19/14.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])). 81.19/14.45 thf(zip_derived_cl34, plain, 81.19/14.45 (![X2 : $i, X4 : $i, X6 : $i, X8 : individuals, X10 : $i]: 81.19/14.45 (~ (reli @ X6 @ X10) 81.19/14.45 | ('#sk1' @ X8 @ X10) 81.19/14.45 | ~ (reli @ '#sk3' @ X2) 81.19/14.45 | ~ (relr @ X2 @ X4) 81.19/14.45 | ~ (reli @ X4 @ X6))), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl31])). 81.19/14.45 thf(zip_derived_cl45, plain, 81.19/14.45 (![X0 : $i, X1 : $i, X2 : individuals]: 81.19/14.45 (~ (reli @ X0 @ '#sk7') 81.19/14.45 | ~ (relr @ X1 @ X0) 81.19/14.45 | ~ (reli @ '#sk3' @ X1) 81.19/14.45 | ('#sk1' @ X2 @ '#sk8'))), 81.19/14.45 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl34])). 81.19/14.45 thf(zip_derived_cl192, plain, 81.19/14.45 (![X0 : individuals, X1 : $i]: 81.19/14.45 ( ('#sk1' @ X0 @ '#sk8') 81.19/14.45 | ~ (reli @ '#sk3' @ X1) 81.19/14.45 | ~ (relr @ X1 @ '#sk7'))), 81.19/14.45 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl45])). 81.19/14.45 thf(zip_derived_cl5391, plain, 81.19/14.45 (![X0 : individuals]: 81.19/14.45 (~ (relr @ '#sk6' @ '#sk7') | ('#sk1' @ X0 @ '#sk8'))), 81.19/14.45 inference('sup-', [status(thm)], [zip_derived_cl5360, zip_derived_cl192])). 81.19/14.45 thf(zip_derived_cl27, plain, ( (relr @ '#sk6' @ '#sk7')), 81.19/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 81.19/14.45 thf(zip_derived_cl5397, plain, 81.19/14.45 (![X0 : individuals]: ('#sk1' @ X0 @ '#sk8')), 81.19/14.45 inference('demod', [status(thm)], [zip_derived_cl5391, zip_derived_cl27])). 81.19/14.45 thf(zip_derived_cl5885, plain, ($false), 81.19/14.45 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl5397])). 81.19/14.45 81.19/14.45 % SZS output end Refutation 81.19/14.45 81.19/14.45 81.19/14.45 % Terminating... 82.06/14.66 % Runner terminated. 82.06/14.69 % Zipperpin 1.5 exiting 82.06/14.69 EOF