0.00/0.08 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.09 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.GHftx6RePK true 0.09/0.29 % Computer : n022.cluster.edu 0.09/0.29 % Model : x86_64 x86_64 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.29 % Memory : 8042.1875MB 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.29 % CPULimit : 1440 0.09/0.29 % WCLimit : 180 0.09/0.29 % DateTime : Mon Jul 3 08:29:59 EDT 2023 0.09/0.29 % CPUTime : 0.09/0.29 % Running portfolio for 1440 s 0.09/0.29 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.09/0.29 % Number of cores: 8 0.09/0.30 % Python version: Python 3.6.8 0.09/0.30 % Running in HO mode 0.45/0.60 % Total configuration time : 828 0.45/0.60 % Estimated wc time : 1656 0.45/0.60 % Estimated cpu time (8 cpus) : 207.0 0.46/0.66 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.46/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.46/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.46/0.68 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.46/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.46/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.47/0.71 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.47/0.72 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.48/0.76 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 0.48/0.78 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 0.49/0.92 % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s 129.96/17.26 % /export/starexec/sandbox2/solver/bin/lams/15_lifting3.sh running for 30s 153.58/20.42 % Solved by lams/15_lifting3.sh. 153.58/20.42 % done 469 iterations in 3.054s 153.58/20.42 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 153.58/20.42 % SZS output start Refutation 153.58/20.42 thf(mworld_type, type, mworld: $tType). 153.58/20.42 thf(eiw_di_type, type, eiw_di: $i > mworld > $o). 153.58/20.42 thf(mimplies_type, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o). 153.58/20.42 thf(r2_type, type, r2: mworld > $o). 153.58/20.42 thf(mbox_type, type, mbox: (mworld > $o) > mworld > $o). 153.58/20.42 thf(mforall_di_type, type, mforall_di: ($i > mworld > $o) > mworld > $o). 153.58/20.42 thf(mactual_type, type, mactual: mworld). 153.58/20.42 thf(mand_type, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o). 153.58/20.42 thf('#sk1_type', type, '#sk1': mworld). 153.58/20.42 thf(implies_type, type, implies: $i > $i > $i). 153.58/20.42 thf('#form57_type', type, '#form57': mworld > $o). 153.58/20.42 thf(or_2_type, type, or_2: mworld > $o). 153.58/20.42 thf(mlocal_type, type, mlocal: (mworld > $o) > $o). 153.58/20.42 thf(is_a_theorem_type, type, is_a_theorem: $i > mworld > $o). 153.58/20.42 thf(mrel_type, type, mrel: mworld > mworld > $o). 153.58/20.42 thf('#form59_type', type, '#form59': mworld > $o). 153.58/20.42 thf(or_type, type, or: $i > $i > $i). 153.58/20.42 thf('#form153_type', type, '#form153': mworld > $o). 153.58/20.42 thf(mbox_def, axiom,(( mbox ) = 153.58/20.42 (^[Phi:( mworld > $o ),W:mworld]: 153.58/20.42 ( ![V:mworld]: ( ( mrel @ W @ V ) => ( Phi @ V ) ) )))). 153.58/20.42 thf('0', plain, 153.58/20.42 (( mbox ) = 153.58/20.42 ( ^[Phi:( mworld > $o ),W:mworld]: 153.58/20.42 ( ![V:mworld]: ( ( mrel @ W @ V ) => ( Phi @ V ) ) ) )), 153.58/20.42 inference('simplify_rw_rule', [status(thm)], [mbox_def])). 153.58/20.42 thf('1', plain, 153.58/20.42 (( mbox ) = 153.58/20.42 ( ^[V_1:( mworld > $o ),V_2:mworld]: 153.58/20.42 ( ![X4:mworld]: ( ( mrel @ V_2 @ X4 ) => ( V_1 @ X4 ) ) ) )), 153.58/20.42 define([status(thm)])). 153.58/20.42 thf(mlocal_def, axiom,(( mlocal ) = 153.58/20.42 (^[Phi:( mworld > $o )]: ( Phi @ mactual )))). 153.58/20.42 thf('2', plain, (( mlocal ) = ( ^[Phi:( mworld > $o )]: ( Phi @ mactual ) )), 153.58/20.42 inference('simplify_rw_rule', [status(thm)], [mlocal_def])). 153.58/20.42 thf('3', plain, (( mlocal ) = ( ^[V_1:( mworld > $o )]: ( V_1 @ mactual ) )), 153.58/20.42 define([status(thm)])). 153.58/20.42 thf(principia_r2, conjecture, (mlocal @ ( mbox @ r2 ))). 153.58/20.42 thf(zf_stmt_0, conjecture, 153.58/20.42 (![X4:mworld]: ( ( mrel @ mactual @ X4 ) => ( r2 @ X4 ) ))). 153.58/20.42 thf(zf_stmt_1, negated_conjecture, 153.58/20.42 (~( ![X4:mworld]: ( ( mrel @ mactual @ X4 ) => ( r2 @ X4 ) ) )), 153.58/20.42 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 153.58/20.42 thf(zip_derived_cl52, plain, 153.58/20.42 (~ (((!!) @ (^[Y0 : mworld]: (((mrel @ mactual @ Y0) => (r2 @ Y0))))))), 153.58/20.42 inference('cnf', [status(esa)], [zf_stmt_1])). 153.58/20.42 thf(zip_derived_cl68, plain, 153.58/20.42 (~ (((mrel @ mactual @ '#sk1') => (r2 @ '#sk1')))), 153.58/20.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl52])). 153.58/20.42 thf(zip_derived_cl70, plain, (~ (r2 @ '#sk1')), 153.58/20.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 153.58/20.42 thf(zip_derived_cl69, plain, ( (mrel @ mactual @ '#sk1')), 153.58/20.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 153.58/20.42 thf(mforall_di_def, axiom,(( mforall_di ) = 153.58/20.42 (^[A:( $i > mworld > $o ),W:mworld]: 153.58/20.42 ( ![X:$i]: ( ( eiw_di @ X @ W ) => ( A @ X @ W ) ) )))). 153.58/20.42 thf('4', plain, 153.58/20.42 (( mforall_di ) = 153.58/20.42 ( ^[A:( $i > mworld > $o ),W:mworld]: 153.58/20.42 ( ![X:$i]: ( ( eiw_di @ X @ W ) => ( A @ X @ W ) ) ) )), 153.58/20.42 inference('simplify_rw_rule', [status(thm)], [mforall_di_def])). 153.58/20.42 thf('5', plain, 153.58/20.42 (( mforall_di ) = 153.58/20.42 ( ^[V_1:( $i > mworld > $o ),V_2:mworld]: 153.58/20.42 ( ![X4:$i]: ( ( eiw_di @ X4 @ V_2 ) => ( V_1 @ X4 @ V_2 ) ) ) )), 153.58/20.42 define([status(thm)])). 153.58/20.42 thf(mimplies_def, axiom,(( mimplies ) = 153.58/20.42 (^[A:( mworld > $o ),B:( mworld > $o ),W:mworld]: 153.58/20.42 ( ( A @ W ) => ( B @ W ) )))). 153.58/20.42 thf('6', plain, 153.58/20.42 (( mimplies ) = 153.58/20.42 ( ^[A:( mworld > $o ),B:( mworld > $o ),W:mworld]: 153.58/20.42 ( ( A @ W ) => ( B @ W ) ) )), 153.58/20.42 inference('simplify_rw_rule', [status(thm)], [mimplies_def])). 153.58/20.42 thf('7', plain, 153.58/20.42 (( mimplies ) = 153.58/20.42 ( ^[V_1:( mworld > $o ),V_2:( mworld > $o ),V_3:mworld]: 153.58/20.42 ( ( V_1 @ V_3 ) => ( V_2 @ V_3 ) ) )), 153.58/20.42 define([status(thm)])). 153.58/20.42 thf(mand_def, axiom,(( mand ) = 153.58/20.42 (^[A:( mworld > $o ),B:( mworld > $o ),W:mworld]: ( ( A @ W ) & ( B @ W ) )))). 153.58/20.42 thf('8', plain, 153.58/20.42 (( mand ) = 153.58/20.42 ( ^[A:( mworld > $o ),B:( mworld > $o ),W:mworld]: 153.58/20.42 ( ( A @ W ) & ( B @ W ) ) )), 153.58/20.42 inference('simplify_rw_rule', [status(thm)], [mand_def])). 153.58/20.42 thf('9', plain, 153.58/20.42 (( mand ) = 153.58/20.42 ( ^[V_1:( mworld > $o ),V_2:( mworld > $o ),V_3:mworld]: 153.58/20.42 ( ( V_1 @ V_3 ) & ( V_2 @ V_3 ) ) )), 153.58/20.42 define([status(thm)])). 153.58/20.42 thf(r2_0, axiom, 153.58/20.42 (mlocal @ 153.58/20.42 ( mand @ 153.58/20.42 ( mbox @ 153.58/20.42 ( mimplies @ 153.58/20.42 ( mbox @ r2 ) @ 153.58/20.42 ( mbox @ 153.58/20.42 ( mforall_di @ 153.58/20.42 ( ^[P:$i]: 153.58/20.42 ( mbox @ 153.58/20.42 ( mforall_di @ 153.58/20.42 ( ^[Q:$i]: 153.58/20.42 ( mbox @ 153.58/20.42 ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) ) ) ) ) ) ) ) ) @ 153.58/20.42 ( mbox @ 153.58/20.42 ( mimplies @ 153.58/20.42 ( mbox @ 153.58/20.42 ( mforall_di @ 153.58/20.42 ( ^[P:$i]: 153.58/20.42 ( mbox @ 153.58/20.42 ( mforall_di @ 153.58/20.42 ( ^[Q:$i]: 153.58/20.42 ( mbox @ 153.58/20.42 ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) ) ) ) ) ) ) @ 153.58/20.42 ( mbox @ r2 ) ) ) ))). 153.58/20.42 thf(zf_stmt_2, axiom, 153.58/20.42 (( ![X18:mworld]: 153.58/20.42 ( ( mrel @ mactual @ X18 ) => 153.58/20.42 ( ( ![X20:mworld]: 153.58/20.43 ( ( mrel @ X18 @ X20 ) => 153.58/20.43 ( ![X22:$i]: 153.58/20.43 ( ( eiw_di @ X22 @ X20 ) => 153.58/20.43 ( ![X24:mworld]: 153.58/20.43 ( ( mrel @ X20 @ X24 ) => 153.58/20.43 ( ![X26:$i]: 153.58/20.43 ( ( eiw_di @ X26 @ X24 ) => 153.58/20.43 ( ![X28:mworld]: 153.58/20.43 ( ( mrel @ X24 @ X28 ) => 153.58/20.43 ( is_a_theorem @ 153.58/20.43 ( implies @ X26 @ ( or @ X22 @ X26 ) ) @ X28 ) ) ) ) ) ) ) ) ) ) ) => 153.58/20.43 ( ![X30:mworld]: ( ( mrel @ X18 @ X30 ) => ( r2 @ X30 ) ) ) ) ) ) & 153.58/20.43 ( ![X4:mworld]: 153.58/20.43 ( ( mrel @ mactual @ X4 ) => 153.58/20.43 ( ( ![X6:mworld]: ( ( mrel @ X4 @ X6 ) => ( r2 @ X6 ) ) ) => 153.58/20.43 ( ![X8:mworld]: 153.58/20.43 ( ( mrel @ X4 @ X8 ) => 153.58/20.43 ( ![X10:$i]: 153.58/20.43 ( ( eiw_di @ X10 @ X8 ) => 153.58/20.43 ( ![X12:mworld]: 153.58/20.43 ( ( mrel @ X8 @ X12 ) => 153.58/20.43 ( ![X14:$i]: 153.58/20.43 ( ( eiw_di @ X14 @ X12 ) => 153.58/20.43 ( ![X16:mworld]: 153.58/20.43 ( ( mrel @ X12 @ X16 ) => 153.58/20.43 ( is_a_theorem @ 153.58/20.43 ( implies @ X14 @ ( or @ X10 @ X14 ) ) @ X16 ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 153.58/20.43 thf(zip_derived_cl51, plain, 153.58/20.43 ( (((((!!) @ (^[Y0 : mworld]: 153.58/20.43 (((mrel @ mactual @ Y0) => 153.58/20.43 (((((!!) @ (^[Y1 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y1) => 153.58/20.43 (((!!) @ (^[Y2 : $i]: 153.58/20.43 (((eiw_di @ Y2 @ Y1) => 153.58/20.43 (((!!) @ (^[Y3 : mworld]: 153.58/20.43 (((mrel @ 153.58/20.43 Y1 @ Y3) => 153.58/20.43 (((!!) @ ( 153.58/20.43 ^[Y4 : $i]: 153.58/20.43 (( 153.58/20.43 (eiw_di @ 153.58/20.43 Y4 @ 153.58/20.43 Y3) => 153.58/20.43 (( 153.58/20.43 (!!) @ ( 153.58/20.43 ^[Y5 : mworld]: 153.58/20.43 (( 153.58/20.43 (mrel @ 153.58/20.43 Y3 @ 153.58/20.43 Y5) => 153.58/20.43 (is_a_theorem @ 153.58/20.43 ( 153.58/20.43 implies @ 153.58/20.43 Y4 @ 153.58/20.43 ( 153.58/20.43 or @ 153.58/20.43 Y2 @ Y4)) @ 153.58/20.43 Y5)))))))))))))))))))))))))) => 153.58/20.43 (((!!) @ (^[Y1 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y1) => (r2 @ Y1))))))))))))) & 153.58/20.43 (((!!) @ (^[Y0 : mworld]: 153.58/20.43 (((mrel @ mactual @ Y0) => 153.58/20.43 (((((!!) @ (^[Y1 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y1) => (r2 @ Y1)))))) => 153.58/20.43 (((!!) @ (^[Y1 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y1) => 153.58/20.43 (((!!) @ (^[Y2 : $i]: 153.58/20.43 (((eiw_di @ Y2 @ Y1) => 153.58/20.43 (((!!) @ (^[Y3 : mworld]: 153.58/20.43 (((mrel @ 153.58/20.43 Y1 @ Y3) => 153.58/20.43 (((!!) @ ( 153.58/20.43 ^[Y4 : $i]: 153.58/20.43 (( 153.58/20.43 (eiw_di @ 153.58/20.43 Y4 @ 153.58/20.43 Y3) => 153.58/20.43 (( 153.58/20.43 (!!) @ ( 153.58/20.43 ^[Y5 : mworld]: 153.58/20.43 (( 153.58/20.43 (mrel @ 153.58/20.43 Y3 @ 153.58/20.43 Y5) => 153.58/20.43 (is_a_theorem @ 153.58/20.43 ( 153.58/20.43 implies @ 153.58/20.43 Y4 @ 153.58/20.43 ( 153.58/20.43 or @ 153.58/20.43 Y2 @ Y4)) @ 153.58/20.43 Y5)))))))))))))))))))))))))))))))))))), 153.58/20.43 inference('cnf', [status(esa)], [zf_stmt_2])). 153.58/20.43 thf(zip_derived_cl5502, plain, 153.58/20.43 ( (((!!) @ (^[Y0 : mworld]: 153.58/20.43 (((mrel @ mactual @ Y0) => 153.58/20.43 (((((!!) @ (^[Y1 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y1) => 153.58/20.43 (((!!) @ (^[Y2 : $i]: 153.58/20.43 (((eiw_di @ Y2 @ Y1) => 153.58/20.43 (((!!) @ (^[Y3 : mworld]: 153.58/20.43 (((mrel @ Y1 @ 153.58/20.43 Y3) => 153.58/20.43 (((!!) @ ( 153.58/20.43 ^[Y4 : $i]: 153.58/20.43 ( 153.58/20.43 ( 153.58/20.43 (eiw_di @ 153.58/20.43 Y4 @ 153.58/20.43 Y3) => 153.58/20.43 (( 153.58/20.43 (!!) @ ( 153.58/20.43 ^[Y5 : mworld]: 153.58/20.43 (( 153.58/20.43 (mrel @ 153.58/20.43 Y3 @ 153.58/20.43 Y5) => 153.58/20.43 (is_a_theorem @ 153.58/20.43 ( 153.58/20.43 implies @ 153.58/20.43 Y4 @ 153.58/20.43 ( 153.58/20.43 or @ 153.58/20.43 Y2 @ Y4)) @ 153.58/20.43 Y5)))))))))))))))))))))))))) => 153.58/20.43 (((!!) @ (^[Y1 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y1) => (r2 @ Y1)))))))))))))), 153.58/20.43 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl51])). 153.58/20.43 thf(zip_derived_cl5504, plain, 153.58/20.43 (![X2 : mworld]: 153.58/20.43 (((mrel @ mactual @ X2) => 153.58/20.43 (((((!!) @ (^[Y0 : mworld]: 153.58/20.43 (((mrel @ X2 @ Y0) => 153.58/20.43 (((!!) @ (^[Y1 : $i]: 153.58/20.43 (((eiw_di @ Y1 @ Y0) => 153.58/20.43 (((!!) @ (^[Y2 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y2) => 153.58/20.43 (((!!) @ (^[Y3 : $i]: 153.58/20.43 (((eiw_di @ 153.58/20.43 Y3 @ 153.58/20.43 Y2) => 153.58/20.43 (( 153.58/20.43 (!!) @ ( 153.58/20.43 ^[Y4 : mworld]: 153.58/20.43 (( 153.58/20.43 (mrel @ 153.58/20.43 Y2 @ 153.58/20.43 Y4) => 153.58/20.43 (is_a_theorem @ 153.58/20.43 ( 153.58/20.43 implies @ 153.58/20.43 Y3 @ 153.58/20.43 ( 153.58/20.43 or @ 153.58/20.43 Y1 @ Y3)) @ 153.58/20.43 Y4)))))))))))))))))))))))))) => 153.58/20.43 (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0))))))))))), 153.58/20.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5502])). 153.58/20.43 thf(zip_derived_cl5506, plain, 153.58/20.43 (![X2 : mworld]: 153.58/20.43 (~ (mrel @ mactual @ X2) 153.58/20.43 | (((((!!) @ (^[Y0 : mworld]: 153.58/20.43 (((mrel @ X2 @ Y0) => 153.58/20.43 (((!!) @ (^[Y1 : $i]: 153.58/20.43 (((eiw_di @ Y1 @ Y0) => 153.58/20.43 (((!!) @ (^[Y2 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y2) => 153.58/20.43 (((!!) @ (^[Y3 : $i]: 153.58/20.43 (( 153.58/20.43 (eiw_di @ 153.58/20.43 Y3 @ 153.58/20.43 Y2) => 153.58/20.43 (( 153.58/20.43 (!!) @ ( 153.58/20.43 ^[Y4 : mworld]: 153.58/20.43 (( 153.58/20.43 (mrel @ 153.58/20.43 Y2 @ 153.58/20.43 Y4) => 153.58/20.43 (is_a_theorem @ 153.58/20.43 ( 153.58/20.43 implies @ 153.58/20.43 Y3 @ 153.58/20.43 ( 153.58/20.43 or @ 153.58/20.43 Y1 @ Y3)) @ 153.58/20.43 Y4)))))))))))))))))))))))))) => 153.58/20.43 (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))))))), 153.58/20.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5504])). 153.58/20.43 thf(zip_derived_cl5508, plain, 153.58/20.43 (![X2 : mworld]: 153.58/20.43 (~ (((!!) @ (^[Y0 : mworld]: 153.58/20.43 (((mrel @ X2 @ Y0) => 153.58/20.43 (((!!) @ (^[Y1 : $i]: 153.58/20.43 (((eiw_di @ Y1 @ Y0) => 153.58/20.43 (((!!) @ (^[Y2 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y2) => 153.58/20.43 (((!!) @ (^[Y3 : $i]: 153.58/20.43 (((eiw_di @ 153.58/20.43 Y3 @ Y2) => 153.58/20.43 (((!!) @ ( 153.58/20.43 ^[Y4 : mworld]: 153.58/20.43 (( 153.58/20.43 (mrel @ 153.58/20.43 Y2 @ 153.58/20.43 Y4) => 153.58/20.43 (is_a_theorem @ 153.58/20.43 ( 153.58/20.43 implies @ 153.58/20.43 Y3 @ 153.58/20.43 ( 153.58/20.43 or @ 153.58/20.43 Y1 @ Y3)) @ 153.58/20.43 Y4)))))))))))))))))))))))))) 153.58/20.43 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))) 153.58/20.43 | ~ (mrel @ mactual @ X2))), 153.58/20.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5506])). 153.58/20.43 thf(or_2_0, axiom, 153.58/20.43 (mlocal @ 153.58/20.43 ( mand @ 153.58/20.43 ( mbox @ 153.58/20.43 ( mimplies @ 153.58/20.43 ( mbox @ or_2 ) @ 153.58/20.43 ( mbox @ 153.58/20.43 ( mforall_di @ 153.58/20.43 ( ^[X:$i]: 153.58/20.43 ( mbox @ 153.58/20.43 ( mforall_di @ 153.58/20.43 ( ^[Y:$i]: 153.58/20.43 ( mbox @ 153.58/20.43 ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) @ 153.58/20.43 ( mbox @ 153.58/20.43 ( mimplies @ 153.58/20.43 ( mbox @ 153.58/20.43 ( mforall_di @ 153.58/20.43 ( ^[X:$i]: 153.58/20.43 ( mbox @ 153.58/20.43 ( mforall_di @ 153.58/20.43 ( ^[Y:$i]: 153.58/20.43 ( mbox @ 153.58/20.43 ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) ) ) ) ) ) ) @ 153.58/20.43 ( mbox @ or_2 ) ) ) ))). 153.58/20.43 thf(zf_stmt_3, axiom, 153.58/20.43 (( ![X18:mworld]: 153.58/20.43 ( ( mrel @ mactual @ X18 ) => 153.58/20.43 ( ( ![X20:mworld]: 153.58/20.43 ( ( mrel @ X18 @ X20 ) => 153.58/20.43 ( ![X22:$i]: 153.58/20.43 ( ( eiw_di @ X22 @ X20 ) => 153.58/20.43 ( ![X24:mworld]: 153.58/20.43 ( ( mrel @ X20 @ X24 ) => 153.58/20.43 ( ![X26:$i]: 153.58/20.43 ( ( eiw_di @ X26 @ X24 ) => 153.58/20.43 ( ![X28:mworld]: 153.58/20.43 ( ( mrel @ X24 @ X28 ) => 153.58/20.43 ( is_a_theorem @ 153.58/20.43 ( implies @ X26 @ ( or @ X22 @ X26 ) ) @ X28 ) ) ) ) ) ) ) ) ) ) ) => 153.58/20.43 ( ![X30:mworld]: ( ( mrel @ X18 @ X30 ) => ( or_2 @ X30 ) ) ) ) ) ) & 153.58/20.43 ( ![X4:mworld]: 153.58/20.43 ( ( mrel @ mactual @ X4 ) => 153.58/20.43 ( ( ![X6:mworld]: ( ( mrel @ X4 @ X6 ) => ( or_2 @ X6 ) ) ) => 153.58/20.43 ( ![X8:mworld]: 153.58/20.43 ( ( mrel @ X4 @ X8 ) => 153.58/20.43 ( ![X10:$i]: 153.58/20.43 ( ( eiw_di @ X10 @ X8 ) => 153.58/20.43 ( ![X12:mworld]: 153.58/20.43 ( ( mrel @ X8 @ X12 ) => 153.58/20.43 ( ![X14:$i]: 153.58/20.43 ( ( eiw_di @ X14 @ X12 ) => 153.58/20.43 ( ![X16:mworld]: 153.58/20.43 ( ( mrel @ X12 @ X16 ) => 153.58/20.43 ( is_a_theorem @ 153.58/20.43 ( implies @ X14 @ ( or @ X10 @ X14 ) ) @ X16 ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 153.58/20.43 thf(zip_derived_cl13, plain, 153.58/20.43 ( (((((!!) @ (^[Y0 : mworld]: 153.58/20.43 (((mrel @ mactual @ Y0) => 153.58/20.43 (((((!!) @ (^[Y1 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y1) => 153.58/20.43 (((!!) @ (^[Y2 : $i]: 153.58/20.43 (((eiw_di @ Y2 @ Y1) => 153.58/20.43 (((!!) @ (^[Y3 : mworld]: 153.58/20.43 (((mrel @ 153.58/20.43 Y1 @ Y3) => 153.58/20.43 (((!!) @ ( 153.58/20.43 ^[Y4 : $i]: 153.58/20.43 (( 153.58/20.43 (eiw_di @ 153.58/20.43 Y4 @ 153.58/20.43 Y3) => 153.58/20.43 (( 153.58/20.43 (!!) @ ( 153.58/20.43 ^[Y5 : mworld]: 153.58/20.43 (( 153.58/20.43 (mrel @ 153.58/20.43 Y3 @ 153.58/20.43 Y5) => 153.58/20.43 (is_a_theorem @ 153.58/20.43 ( 153.58/20.43 implies @ 153.58/20.43 Y4 @ 153.58/20.43 ( 153.58/20.43 or @ 153.58/20.43 Y2 @ Y4)) @ 153.58/20.43 Y5)))))))))))))))))))))))))) => 153.58/20.43 (((!!) @ (^[Y1 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y1) => (or_2 @ Y1))))))))))))) & 153.58/20.43 (((!!) @ (^[Y0 : mworld]: 153.58/20.43 (((mrel @ mactual @ Y0) => 153.58/20.43 (((((!!) @ (^[Y1 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y1) => (or_2 @ Y1)))))) => 153.58/20.43 (((!!) @ (^[Y1 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y1) => 153.58/20.43 (((!!) @ (^[Y2 : $i]: 153.58/20.43 (((eiw_di @ Y2 @ Y1) => 153.58/20.43 (((!!) @ (^[Y3 : mworld]: 153.58/20.43 (((mrel @ 153.58/20.43 Y1 @ Y3) => 153.58/20.43 (((!!) @ ( 153.58/20.43 ^[Y4 : $i]: 153.58/20.43 (( 153.58/20.43 (eiw_di @ 153.58/20.43 Y4 @ 153.58/20.43 Y3) => 153.58/20.43 (( 153.58/20.43 (!!) @ ( 153.58/20.43 ^[Y5 : mworld]: 153.58/20.43 (( 153.58/20.43 (mrel @ 153.58/20.43 Y3 @ 153.58/20.43 Y5) => 153.58/20.43 (is_a_theorem @ 153.58/20.43 ( 153.58/20.43 implies @ 153.58/20.43 Y4 @ 153.58/20.43 ( 153.58/20.43 or @ 153.58/20.43 Y2 @ Y4)) @ 153.58/20.43 Y5)))))))))))))))))))))))))))))))))))), 153.58/20.43 inference('cnf', [status(esa)], [zf_stmt_3])). 153.58/20.43 thf(zip_derived_cl691, plain, 153.58/20.43 ( (((!!) @ (^[Y0 : mworld]: 153.58/20.43 (((mrel @ mactual @ Y0) => 153.58/20.43 (((((!!) @ (^[Y1 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y1) => (or_2 @ Y1)))))) => 153.58/20.43 (((!!) @ (^[Y1 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y1) => 153.58/20.43 (((!!) @ (^[Y2 : $i]: 153.58/20.43 (((eiw_di @ Y2 @ Y1) => 153.58/20.43 (((!!) @ (^[Y3 : mworld]: 153.58/20.43 (((mrel @ Y1 @ 153.58/20.43 Y3) => 153.58/20.43 (((!!) @ ( 153.58/20.43 ^[Y4 : $i]: 153.58/20.43 ( 153.58/20.43 ( 153.58/20.43 (eiw_di @ 153.58/20.43 Y4 @ 153.58/20.43 Y3) => 153.58/20.43 (( 153.58/20.43 (!!) @ ( 153.58/20.43 ^[Y5 : mworld]: 153.58/20.43 (( 153.58/20.43 (mrel @ 153.58/20.43 Y3 @ 153.58/20.43 Y5) => 153.58/20.43 (is_a_theorem @ 153.58/20.43 ( 153.58/20.43 implies @ 153.58/20.43 Y4 @ 153.58/20.43 ( 153.58/20.43 or @ 153.58/20.43 Y2 @ Y4)) @ 153.58/20.43 Y5)))))))))))))))))))))))))))))))))), 153.58/20.43 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl13])). 153.58/20.43 thf(zip_derived_cl693, plain, 153.58/20.43 (![X2 : mworld]: 153.58/20.43 (((mrel @ mactual @ X2) => 153.58/20.43 (((((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))) => 153.58/20.43 (((!!) @ (^[Y0 : mworld]: 153.58/20.43 (((mrel @ X2 @ Y0) => 153.58/20.43 (((!!) @ (^[Y1 : $i]: 153.58/20.43 (((eiw_di @ Y1 @ Y0) => 153.58/20.43 (((!!) @ (^[Y2 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y2) => 153.58/20.43 (((!!) @ (^[Y3 : $i]: 153.58/20.43 (((eiw_di @ 153.58/20.43 Y3 @ 153.58/20.43 Y2) => 153.58/20.43 (( 153.58/20.43 (!!) @ ( 153.58/20.43 ^[Y4 : mworld]: 153.58/20.43 (( 153.58/20.43 (mrel @ 153.58/20.43 Y2 @ 153.58/20.43 Y4) => 153.58/20.43 (is_a_theorem @ 153.58/20.43 ( 153.58/20.43 implies @ 153.58/20.43 Y3 @ 153.58/20.43 ( 153.58/20.43 or @ 153.58/20.43 Y1 @ Y3)) @ 153.58/20.43 Y4))))))))))))))))))))))))))))))), 153.58/20.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl691])). 153.58/20.43 thf(zip_derived_cl695, plain, 153.58/20.43 (![X2 : mworld]: 153.58/20.43 (~ (mrel @ mactual @ X2) 153.58/20.43 | (((((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))) => 153.58/20.43 (((!!) @ (^[Y0 : mworld]: 153.58/20.43 (((mrel @ X2 @ Y0) => 153.58/20.43 (((!!) @ (^[Y1 : $i]: 153.58/20.43 (((eiw_di @ Y1 @ Y0) => 153.58/20.43 (((!!) @ (^[Y2 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y2) => 153.58/20.43 (((!!) @ (^[Y3 : $i]: 153.58/20.43 (( 153.58/20.43 (eiw_di @ 153.58/20.43 Y3 @ 153.58/20.43 Y2) => 153.58/20.43 (( 153.58/20.43 (!!) @ ( 153.58/20.43 ^[Y4 : mworld]: 153.58/20.43 (( 153.58/20.43 (mrel @ 153.58/20.43 Y2 @ 153.58/20.43 Y4) => 153.58/20.43 (is_a_theorem @ 153.58/20.43 ( 153.58/20.43 implies @ 153.58/20.43 Y3 @ 153.58/20.43 ( 153.58/20.43 or @ 153.58/20.43 Y1 @ Y3)) @ 153.58/20.43 Y4)))))))))))))))))))))))))))))), 153.58/20.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl693])). 153.58/20.43 thf(zip_derived_cl697, plain, 153.58/20.43 (![X2 : mworld]: 153.58/20.43 (~ (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))) 153.58/20.43 | (((!!) @ (^[Y0 : mworld]: 153.58/20.43 (((mrel @ X2 @ Y0) => 153.58/20.43 (((!!) @ (^[Y1 : $i]: 153.58/20.43 (((eiw_di @ Y1 @ Y0) => 153.58/20.43 (((!!) @ (^[Y2 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y2) => 153.58/20.43 (((!!) @ (^[Y3 : $i]: 153.58/20.43 (((eiw_di @ 153.58/20.43 Y3 @ 153.58/20.43 Y2) => 153.58/20.43 (( 153.58/20.43 (!!) @ ( 153.58/20.43 ^[Y4 : mworld]: 153.58/20.43 (( 153.58/20.43 (mrel @ 153.58/20.43 Y2 @ 153.58/20.43 Y4) => 153.58/20.43 (is_a_theorem @ 153.58/20.43 ( 153.58/20.43 implies @ 153.58/20.43 Y3 @ 153.58/20.43 ( 153.58/20.43 or @ 153.58/20.43 Y1 @ Y3)) @ 153.58/20.43 Y4)))))))))))))))))))))))))) 153.58/20.43 | ~ (mrel @ mactual @ X2))), 153.58/20.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl695])). 153.58/20.43 thf(zip_derived_cl697, plain, 153.58/20.43 (![X2 : mworld]: 153.58/20.43 (~ (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))) 153.58/20.43 | (((!!) @ (^[Y0 : mworld]: 153.58/20.43 (((mrel @ X2 @ Y0) => 153.58/20.43 (((!!) @ (^[Y1 : $i]: 153.58/20.43 (((eiw_di @ Y1 @ Y0) => 153.58/20.43 (((!!) @ (^[Y2 : mworld]: 153.58/20.43 (((mrel @ Y0 @ Y2) => 153.58/20.43 (((!!) @ (^[Y3 : $i]: 153.58/20.43 (((eiw_di @ 153.58/20.43 Y3 @ 153.58/20.43 Y2) => 153.58/20.43 (( 153.58/20.43 (!!) @ ( 154.02/20.43 ^[Y4 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y2 @ 154.02/20.43 Y4) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y3 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y1 @ Y3)) @ 154.02/20.43 Y4)))))))))))))))))))))))))) 154.02/20.43 | ~ (mrel @ mactual @ X2))), 154.02/20.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl695])). 154.02/20.43 thf(zip_derived_cl701, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 ( ('#form59' @ X2) 154.02/20.43 | ~ (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))))), 154.02/20.43 define([status(thm)])). 154.02/20.43 thf(zip_derived_cl703, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (~ ('#form59' @ X2) 154.02/20.43 | ~ (mrel @ mactual @ X2) 154.02/20.43 | (((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ X2 @ Y0) => 154.02/20.43 (((!!) @ (^[Y1 : $i]: 154.02/20.43 (((eiw_di @ Y1 @ Y0) => 154.02/20.43 (((!!) @ (^[Y2 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y2) => 154.02/20.43 (((!!) @ (^[Y3 : $i]: 154.02/20.43 (((eiw_di @ 154.02/20.43 Y3 @ 154.02/20.43 Y2) => 154.02/20.43 (( 154.02/20.43 (!!) @ ( 154.02/20.43 ^[Y4 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y2 @ 154.02/20.43 Y4) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y3 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y1 @ Y3)) @ 154.02/20.43 Y4)))))))))))))))))))))))))))), 154.02/20.43 inference('renaming', [status(thm)], 154.02/20.43 [zip_derived_cl697, zip_derived_cl701])). 154.02/20.43 thf(zip_derived_cl709, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (~ ('#form57' @ X2) 154.02/20.43 | (((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ X2 @ Y0) => 154.02/20.43 (((!!) @ (^[Y1 : $i]: 154.02/20.43 (((eiw_di @ Y1 @ Y0) => 154.02/20.43 (((!!) @ (^[Y2 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y2) => 154.02/20.43 (((!!) @ (^[Y3 : $i]: 154.02/20.43 (((eiw_di @ 154.02/20.43 Y3 @ 154.02/20.43 Y2) => 154.02/20.43 (( 154.02/20.43 (!!) @ ( 154.02/20.43 ^[Y4 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y2 @ 154.02/20.43 Y4) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y3 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y1 @ Y3)) @ 154.02/20.43 Y4)))))))))))))))))))))))))))), 154.02/20.43 define([status(thm)])). 154.02/20.43 thf(zip_derived_cl690, plain, 154.02/20.43 ( (((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ mactual @ Y0) => 154.02/20.43 (((((!!) @ (^[Y1 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y1) => 154.02/20.43 (((!!) @ (^[Y2 : $i]: 154.02/20.43 (((eiw_di @ Y2 @ Y1) => 154.02/20.43 (((!!) @ (^[Y3 : mworld]: 154.02/20.43 (((mrel @ Y1 @ 154.02/20.43 Y3) => 154.02/20.43 (((!!) @ ( 154.02/20.43 ^[Y4 : $i]: 154.02/20.43 ( 154.02/20.43 ( 154.02/20.43 (eiw_di @ 154.02/20.43 Y4 @ 154.02/20.43 Y3) => 154.02/20.43 (( 154.02/20.43 (!!) @ ( 154.02/20.43 ^[Y5 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y3 @ 154.02/20.43 Y5) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y4 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y2 @ Y4)) @ 154.02/20.43 Y5)))))))))))))))))))))))))) => 154.02/20.43 (((!!) @ (^[Y1 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y1) => (or_2 @ Y1)))))))))))))), 154.02/20.43 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl13])). 154.02/20.43 thf(zip_derived_cl692, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (((mrel @ mactual @ X2) => 154.02/20.43 (((((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ X2 @ Y0) => 154.02/20.43 (((!!) @ (^[Y1 : $i]: 154.02/20.43 (((eiw_di @ Y1 @ Y0) => 154.02/20.43 (((!!) @ (^[Y2 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y2) => 154.02/20.43 (((!!) @ (^[Y3 : $i]: 154.02/20.43 (((eiw_di @ 154.02/20.43 Y3 @ 154.02/20.43 Y2) => 154.02/20.43 (( 154.02/20.43 (!!) @ ( 154.02/20.43 ^[Y4 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y2 @ 154.02/20.43 Y4) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y3 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y1 @ Y3)) @ 154.02/20.43 Y4)))))))))))))))))))))))))) => 154.02/20.43 (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0))))))))))), 154.02/20.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl690])). 154.02/20.43 thf(zip_derived_cl694, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (~ (mrel @ mactual @ X2) 154.02/20.43 | (((((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ X2 @ Y0) => 154.02/20.43 (((!!) @ (^[Y1 : $i]: 154.02/20.43 (((eiw_di @ Y1 @ Y0) => 154.02/20.43 (((!!) @ (^[Y2 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y2) => 154.02/20.43 (((!!) @ (^[Y3 : $i]: 154.02/20.43 (( 154.02/20.43 (eiw_di @ 154.02/20.43 Y3 @ 154.02/20.43 Y2) => 154.02/20.43 (( 154.02/20.43 (!!) @ ( 154.02/20.43 ^[Y4 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y2 @ 154.02/20.43 Y4) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y3 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y1 @ Y3)) @ 154.02/20.43 Y4)))))))))))))))))))))))))) => 154.02/20.43 (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))))))), 154.02/20.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl692])). 154.02/20.43 thf(zip_derived_cl696, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (~ (((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ X2 @ Y0) => 154.02/20.43 (((!!) @ (^[Y1 : $i]: 154.02/20.43 (((eiw_di @ Y1 @ Y0) => 154.02/20.43 (((!!) @ (^[Y2 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y2) => 154.02/20.43 (((!!) @ (^[Y3 : $i]: 154.02/20.43 (((eiw_di @ 154.02/20.43 Y3 @ Y2) => 154.02/20.43 (((!!) @ ( 154.02/20.43 ^[Y4 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y2 @ 154.02/20.43 Y4) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y3 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y1 @ Y3)) @ 154.02/20.43 Y4)))))))))))))))))))))))))) 154.02/20.43 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))) 154.02/20.43 | ~ (mrel @ mactual @ X2))), 154.02/20.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl694])). 154.02/20.43 thf(zip_derived_cl698, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 ( ('#form57' @ X2) 154.02/20.43 | ~ (((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ X2 @ Y0) => 154.02/20.43 (((!!) @ (^[Y1 : $i]: 154.02/20.43 (((eiw_di @ Y1 @ Y0) => 154.02/20.43 (((!!) @ (^[Y2 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y2) => 154.02/20.43 (((!!) @ (^[Y3 : $i]: 154.02/20.43 (((eiw_di @ 154.02/20.43 Y3 @ 154.02/20.43 Y2) => 154.02/20.43 (( 154.02/20.43 (!!) @ ( 154.02/20.43 ^[Y4 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y2 @ 154.02/20.43 Y4) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y3 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y1 @ Y3)) @ 154.02/20.43 Y4)))))))))))))))))))))))))))), 154.02/20.43 define([status(thm)])). 154.02/20.43 thf(zip_derived_cl5510, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (~ ('#form57' @ X2) 154.02/20.43 | ~ (mrel @ mactual @ X2) 154.02/20.43 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))))), 154.02/20.43 inference('renaming', [status(thm)], 154.02/20.43 [zip_derived_cl5508, zip_derived_cl709, zip_derived_cl698])). 154.02/20.43 thf(zip_derived_cl5514, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (~ ('#form153' @ X2) 154.02/20.43 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))))), 154.02/20.43 define([status(thm)])). 154.02/20.43 thf(zip_derived_cl5515, plain, 154.02/20.43 (![X2 : mworld, X4 : mworld]: 154.02/20.43 ( (((mrel @ X2 @ X4) => (r2 @ X4))) | ~ ('#form153' @ X2))), 154.02/20.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5514])). 154.02/20.43 thf(zip_derived_cl5520, plain, 154.02/20.43 (![X2 : mworld, X4 : mworld]: 154.02/20.43 (~ (mrel @ X2 @ X4) | (r2 @ X4) | ~ ('#form153' @ X2))), 154.02/20.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5515])). 154.02/20.43 thf(zip_derived_cl5576, plain, ((~ ('#form153' @ mactual) | (r2 @ '#sk1'))), 154.02/20.43 inference('sup-', [status(thm)], [zip_derived_cl69, zip_derived_cl5520])). 154.02/20.43 thf(mrel_reflexive, axiom, (![W:mworld]: ( mrel @ W @ W ))). 154.02/20.43 thf(zip_derived_cl47, plain, 154.02/20.43 ( (((!!) @ (^[Y0 : mworld]: (mrel @ Y0 @ Y0))))), 154.02/20.43 inference('cnf', [status(esa)], [mrel_reflexive])). 154.02/20.43 thf(zip_derived_cl71, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 154.02/20.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])). 154.02/20.43 thf(zip_derived_cl5510, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (~ ('#form57' @ X2) 154.02/20.43 | ~ (mrel @ mactual @ X2) 154.02/20.43 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))))), 154.02/20.43 inference('renaming', [status(thm)], 154.02/20.43 [zip_derived_cl5508, zip_derived_cl709, zip_derived_cl698])). 154.02/20.43 thf(zip_derived_cl5514, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (~ ('#form153' @ X2) 154.02/20.43 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))))), 154.02/20.43 define([status(thm)])). 154.02/20.43 thf(zip_derived_cl5503, plain, 154.02/20.43 ( (((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ mactual @ Y0) => 154.02/20.43 (((((!!) @ (^[Y1 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y1) => (r2 @ Y1)))))) => 154.02/20.43 (((!!) @ (^[Y1 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y1) => 154.02/20.43 (((!!) @ (^[Y2 : $i]: 154.02/20.43 (((eiw_di @ Y2 @ Y1) => 154.02/20.43 (((!!) @ (^[Y3 : mworld]: 154.02/20.43 (((mrel @ Y1 @ 154.02/20.43 Y3) => 154.02/20.43 (((!!) @ ( 154.02/20.43 ^[Y4 : $i]: 154.02/20.43 ( 154.02/20.43 ( 154.02/20.43 (eiw_di @ 154.02/20.43 Y4 @ 154.02/20.43 Y3) => 154.02/20.43 (( 154.02/20.43 (!!) @ ( 154.02/20.43 ^[Y5 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y3 @ 154.02/20.43 Y5) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y4 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y2 @ Y4)) @ 154.02/20.43 Y5)))))))))))))))))))))))))))))))))), 154.02/20.43 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl51])). 154.02/20.43 thf(zip_derived_cl5505, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (((mrel @ mactual @ X2) => 154.02/20.43 (((((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))) => 154.02/20.43 (((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ X2 @ Y0) => 154.02/20.43 (((!!) @ (^[Y1 : $i]: 154.02/20.43 (((eiw_di @ Y1 @ Y0) => 154.02/20.43 (((!!) @ (^[Y2 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y2) => 154.02/20.43 (((!!) @ (^[Y3 : $i]: 154.02/20.43 (((eiw_di @ 154.02/20.43 Y3 @ 154.02/20.43 Y2) => 154.02/20.43 (( 154.02/20.43 (!!) @ ( 154.02/20.43 ^[Y4 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y2 @ 154.02/20.43 Y4) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y3 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y1 @ Y3)) @ 154.02/20.43 Y4))))))))))))))))))))))))))))))), 154.02/20.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5503])). 154.02/20.43 thf(zip_derived_cl5507, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (~ (mrel @ mactual @ X2) 154.02/20.43 | (((((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))) => 154.02/20.43 (((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ X2 @ Y0) => 154.02/20.43 (((!!) @ (^[Y1 : $i]: 154.02/20.43 (((eiw_di @ Y1 @ Y0) => 154.02/20.43 (((!!) @ (^[Y2 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y2) => 154.02/20.43 (((!!) @ (^[Y3 : $i]: 154.02/20.43 (( 154.02/20.43 (eiw_di @ 154.02/20.43 Y3 @ 154.02/20.43 Y2) => 154.02/20.43 (( 154.02/20.43 (!!) @ ( 154.02/20.43 ^[Y4 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y2 @ 154.02/20.43 Y4) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y3 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y1 @ Y3)) @ 154.02/20.43 Y4)))))))))))))))))))))))))))))), 154.02/20.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5505])). 154.02/20.43 thf(zip_derived_cl5509, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (~ (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))) 154.02/20.43 | (((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ X2 @ Y0) => 154.02/20.43 (((!!) @ (^[Y1 : $i]: 154.02/20.43 (((eiw_di @ Y1 @ Y0) => 154.02/20.43 (((!!) @ (^[Y2 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y2) => 154.02/20.43 (((!!) @ (^[Y3 : $i]: 154.02/20.43 (((eiw_di @ 154.02/20.43 Y3 @ 154.02/20.43 Y2) => 154.02/20.43 (( 154.02/20.43 (!!) @ ( 154.02/20.43 ^[Y4 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y2 @ 154.02/20.43 Y4) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y3 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y1 @ Y3)) @ 154.02/20.43 Y4)))))))))))))))))))))))))) 154.02/20.43 | ~ (mrel @ mactual @ X2))), 154.02/20.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5507])). 154.02/20.43 thf(zip_derived_cl5511, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 ( ('#form153' @ X2) 154.02/20.43 | ~ (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))))), 154.02/20.43 define([status(thm)])). 154.02/20.43 thf(zip_derived_cl5516, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 ( ('#form153' @ X2) | ~ (mrel @ mactual @ X2) | ~ ('#form57' @ X2))), 154.02/20.43 inference('renaming', [status(thm)], 154.02/20.43 [zip_derived_cl5510, zip_derived_cl5514, zip_derived_cl5511])). 154.02/20.43 thf(zip_derived_cl5521, plain, 154.02/20.43 ((~ ('#form57' @ mactual) | ('#form153' @ mactual))), 154.02/20.43 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl5516])). 154.02/20.43 thf(zip_derived_cl71, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 154.02/20.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])). 154.02/20.43 thf(zip_derived_cl703, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (~ ('#form59' @ X2) 154.02/20.43 | ~ (mrel @ mactual @ X2) 154.02/20.43 | (((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ X2 @ Y0) => 154.02/20.43 (((!!) @ (^[Y1 : $i]: 154.02/20.43 (((eiw_di @ Y1 @ Y0) => 154.02/20.43 (((!!) @ (^[Y2 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y2) => 154.02/20.43 (((!!) @ (^[Y3 : $i]: 154.02/20.43 (((eiw_di @ 154.02/20.43 Y3 @ 154.02/20.43 Y2) => 154.02/20.43 (( 154.02/20.43 (!!) @ ( 154.02/20.43 ^[Y4 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y2 @ 154.02/20.43 Y4) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y3 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y1 @ Y3)) @ 154.02/20.43 Y4)))))))))))))))))))))))))))), 154.02/20.43 inference('renaming', [status(thm)], 154.02/20.43 [zip_derived_cl697, zip_derived_cl701])). 154.02/20.43 thf(zip_derived_cl709, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (~ ('#form57' @ X2) 154.02/20.43 | (((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ X2 @ Y0) => 154.02/20.43 (((!!) @ (^[Y1 : $i]: 154.02/20.43 (((eiw_di @ Y1 @ Y0) => 154.02/20.43 (((!!) @ (^[Y2 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y2) => 154.02/20.43 (((!!) @ (^[Y3 : $i]: 154.02/20.43 (((eiw_di @ 154.02/20.43 Y3 @ 154.02/20.43 Y2) => 154.02/20.43 (( 154.02/20.43 (!!) @ ( 154.02/20.43 ^[Y4 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y2 @ 154.02/20.43 Y4) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y3 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y1 @ Y3)) @ 154.02/20.43 Y4)))))))))))))))))))))))))))), 154.02/20.43 define([status(thm)])). 154.02/20.43 thf(zip_derived_cl698, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 ( ('#form57' @ X2) 154.02/20.43 | ~ (((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ X2 @ Y0) => 154.02/20.43 (((!!) @ (^[Y1 : $i]: 154.02/20.43 (((eiw_di @ Y1 @ Y0) => 154.02/20.43 (((!!) @ (^[Y2 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y2) => 154.02/20.43 (((!!) @ (^[Y3 : $i]: 154.02/20.43 (((eiw_di @ 154.02/20.43 Y3 @ 154.02/20.43 Y2) => 154.02/20.43 (( 154.02/20.43 (!!) @ ( 154.02/20.43 ^[Y4 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y2 @ 154.02/20.43 Y4) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y3 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y1 @ Y3)) @ 154.02/20.43 Y4)))))))))))))))))))))))))))), 154.02/20.43 define([status(thm)])). 154.02/20.43 thf(zip_derived_cl711, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 ( ('#form57' @ X2) | ~ (mrel @ mactual @ X2) | ~ ('#form59' @ X2))), 154.02/20.43 inference('renaming', [status(thm)], 154.02/20.43 [zip_derived_cl703, zip_derived_cl709, zip_derived_cl698])). 154.02/20.43 thf(zip_derived_cl1427, plain, 154.02/20.43 ((~ ('#form59' @ mactual) | ('#form57' @ mactual))), 154.02/20.43 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl711])). 154.02/20.43 thf(hilbert_or_2, axiom, (mlocal @ ( mbox @ or_2 ))). 154.02/20.43 thf(zf_stmt_4, axiom, 154.02/20.43 (![X4:mworld]: ( ( mrel @ mactual @ X4 ) => ( or_2 @ X4 ) ))). 154.02/20.43 thf(zip_derived_cl48, plain, 154.02/20.43 ( (((!!) @ (^[Y0 : mworld]: (((mrel @ mactual @ Y0) => (or_2 @ Y0))))))), 154.02/20.43 inference('cnf', [status(esa)], [zf_stmt_4])). 154.02/20.43 thf(zip_derived_cl696, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (~ (((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ X2 @ Y0) => 154.02/20.43 (((!!) @ (^[Y1 : $i]: 154.02/20.43 (((eiw_di @ Y1 @ Y0) => 154.02/20.43 (((!!) @ (^[Y2 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y2) => 154.02/20.43 (((!!) @ (^[Y3 : $i]: 154.02/20.43 (((eiw_di @ 154.02/20.43 Y3 @ Y2) => 154.02/20.43 (((!!) @ ( 154.02/20.43 ^[Y4 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y2 @ 154.02/20.43 Y4) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y3 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y1 @ Y3)) @ 154.02/20.43 Y4)))))))))))))))))))))))))) 154.02/20.43 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))) 154.02/20.43 | ~ (mrel @ mactual @ X2))), 154.02/20.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl694])). 154.02/20.43 thf(zip_derived_cl698, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 ( ('#form57' @ X2) 154.02/20.43 | ~ (((!!) @ (^[Y0 : mworld]: 154.02/20.43 (((mrel @ X2 @ Y0) => 154.02/20.43 (((!!) @ (^[Y1 : $i]: 154.02/20.43 (((eiw_di @ Y1 @ Y0) => 154.02/20.43 (((!!) @ (^[Y2 : mworld]: 154.02/20.43 (((mrel @ Y0 @ Y2) => 154.02/20.43 (((!!) @ (^[Y3 : $i]: 154.02/20.43 (((eiw_di @ 154.02/20.43 Y3 @ 154.02/20.43 Y2) => 154.02/20.43 (( 154.02/20.43 (!!) @ ( 154.02/20.43 ^[Y4 : mworld]: 154.02/20.43 (( 154.02/20.43 (mrel @ 154.02/20.43 Y2 @ 154.02/20.43 Y4) => 154.02/20.43 (is_a_theorem @ 154.02/20.43 ( 154.02/20.43 implies @ 154.02/20.43 Y3 @ 154.02/20.43 ( 154.02/20.43 or @ 154.02/20.43 Y1 @ Y3)) @ 154.02/20.43 Y4)))))))))))))))))))))))))))), 154.02/20.43 define([status(thm)])). 154.02/20.43 thf(zip_derived_cl700, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (~ ('#form57' @ X2) 154.02/20.43 | ~ (mrel @ mactual @ X2) 154.02/20.43 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))))), 154.02/20.43 inference('renaming', [status(thm)], 154.02/20.43 [zip_derived_cl696, zip_derived_cl698])). 154.02/20.43 thf(zip_derived_cl704, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 (~ ('#form59' @ X2) 154.02/20.43 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))))), 154.02/20.43 define([status(thm)])). 154.02/20.43 thf(zip_derived_cl701, plain, 154.02/20.43 (![X2 : mworld]: 154.02/20.43 ( ('#form59' @ X2) 154.02/20.43 | ~ (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))))), 154.02/20.43 define([status(thm)])). 154.02/20.43 thf(zip_derived_cl4810, plain, ( ('#form59' @ mactual)), 154.02/20.43 inference('renaming', [status(thm)], 154.02/20.43 [zip_derived_cl48, zip_derived_cl704, zip_derived_cl701])). 154.02/20.43 thf(zip_derived_cl4812, plain, ( ('#form57' @ mactual)), 154.02/20.43 inference('demod', [status(thm)], 154.02/20.43 [zip_derived_cl1427, zip_derived_cl4810])). 154.02/20.43 thf(zip_derived_cl5543, plain, ( ('#form153' @ mactual)), 154.02/20.43 inference('demod', [status(thm)], 154.02/20.43 [zip_derived_cl5521, zip_derived_cl4812])). 154.02/20.43 thf(zip_derived_cl5577, plain, ( (r2 @ '#sk1')), 154.02/20.43 inference('demod', [status(thm)], 154.02/20.43 [zip_derived_cl5576, zip_derived_cl5543])). 154.02/20.43 thf(zip_derived_cl5578, plain, ($false), 154.02/20.43 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl5577])). 154.02/20.43 154.02/20.43 % SZS output end Refutation 154.02/20.43 154.02/20.43 154.02/20.43 % Terminating... 154.83/20.59 % Runner terminated. 154.83/20.61 % Zipperpin 1.5 exiting 154.83/20.62 EOF