0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.anpyMKgjHs true 0.13/0.35 % Computer : n012.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 1440 0.13/0.35 % WCLimit : 180 0.13/0.35 % DateTime : Mon Jul 3 08:26:52 EDT 2023 0.13/0.35 % CPUTime : 0.13/0.35 % Running portfolio for 1440 s 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.35 % Number of cores: 8 0.13/0.36 % Python version: Python 3.6.8 0.13/0.36 % Running in HO mode 0.56/0.63 % Total configuration time : 828 0.56/0.63 % Estimated wc time : 1656 0.56/0.63 % Estimated cpu time (8 cpus) : 207.0 0.57/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.57/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.57/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.57/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.57/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.57/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.57/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.57/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.58/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 0.58/0.83 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 0.58/0.90 % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s 76.09/10.35 % /export/starexec/sandbox2/solver/bin/lams/15_lifting3.sh running for 30s 92.74/12.38 % Solved by lams/15_lifting3.sh. 92.74/12.38 % done 469 iterations in 1.995s 92.74/12.38 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 92.74/12.38 % SZS output start Refutation 92.74/12.38 thf(mworld_type, type, mworld: $tType). 92.74/12.38 thf(eiw_di_type, type, eiw_di: $i > mworld > $o). 92.74/12.38 thf(mimplies_type, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o). 92.74/12.38 thf(r2_type, type, r2: mworld > $o). 92.74/12.38 thf(mbox_type, type, mbox: (mworld > $o) > mworld > $o). 92.74/12.38 thf(mforall_di_type, type, mforall_di: ($i > mworld > $o) > mworld > $o). 92.74/12.38 thf(mactual_type, type, mactual: mworld). 92.74/12.38 thf(mand_type, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o). 92.74/12.38 thf('#sk1_type', type, '#sk1': mworld). 92.74/12.38 thf(implies_type, type, implies: $i > $i > $i). 92.74/12.38 thf('#form57_type', type, '#form57': mworld > $o). 92.74/12.38 thf(or_2_type, type, or_2: mworld > $o). 92.74/12.38 thf(mlocal_type, type, mlocal: (mworld > $o) > $o). 92.74/12.38 thf(is_a_theorem_type, type, is_a_theorem: $i > mworld > $o). 92.74/12.38 thf(mrel_type, type, mrel: mworld > mworld > $o). 92.74/12.38 thf('#form59_type', type, '#form59': mworld > $o). 92.74/12.38 thf(or_type, type, or: $i > $i > $i). 92.74/12.38 thf('#form153_type', type, '#form153': mworld > $o). 92.74/12.38 thf(mbox_def, axiom,(( mbox ) = 92.74/12.38 (^[Phi:( mworld > $o ),W:mworld]: 92.74/12.38 ( ![V:mworld]: ( ( mrel @ W @ V ) => ( Phi @ V ) ) )))). 92.74/12.38 thf('0', plain, 92.74/12.38 (( mbox ) = 92.74/12.38 ( ^[Phi:( mworld > $o ),W:mworld]: 92.74/12.38 ( ![V:mworld]: ( ( mrel @ W @ V ) => ( Phi @ V ) ) ) )), 92.74/12.38 inference('simplify_rw_rule', [status(thm)], [mbox_def])). 92.74/12.38 thf('1', plain, 92.74/12.38 (( mbox ) = 92.74/12.38 ( ^[V_1:( mworld > $o ),V_2:mworld]: 92.74/12.38 ( ![X4:mworld]: ( ( mrel @ V_2 @ X4 ) => ( V_1 @ X4 ) ) ) )), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(mlocal_def, axiom,(( mlocal ) = 92.74/12.38 (^[Phi:( mworld > $o )]: ( Phi @ mactual )))). 92.74/12.38 thf('2', plain, (( mlocal ) = ( ^[Phi:( mworld > $o )]: ( Phi @ mactual ) )), 92.74/12.38 inference('simplify_rw_rule', [status(thm)], [mlocal_def])). 92.74/12.38 thf('3', plain, (( mlocal ) = ( ^[V_1:( mworld > $o )]: ( V_1 @ mactual ) )), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(principia_r2, conjecture, (mlocal @ ( mbox @ r2 ))). 92.74/12.38 thf(zf_stmt_0, conjecture, 92.74/12.38 (![X4:mworld]: ( ( mrel @ mactual @ X4 ) => ( r2 @ X4 ) ))). 92.74/12.38 thf(zf_stmt_1, negated_conjecture, 92.74/12.38 (~( ![X4:mworld]: ( ( mrel @ mactual @ X4 ) => ( r2 @ X4 ) ) )), 92.74/12.38 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 92.74/12.38 thf(zip_derived_cl52, plain, 92.74/12.38 (~ (((!!) @ (^[Y0 : mworld]: (((mrel @ mactual @ Y0) => (r2 @ Y0))))))), 92.74/12.38 inference('cnf', [status(esa)], [zf_stmt_1])). 92.74/12.38 thf(zip_derived_cl68, plain, 92.74/12.38 (~ (((mrel @ mactual @ '#sk1') => (r2 @ '#sk1')))), 92.74/12.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl52])). 92.74/12.38 thf(zip_derived_cl70, plain, (~ (r2 @ '#sk1')), 92.74/12.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 92.74/12.38 thf(zip_derived_cl69, plain, ( (mrel @ mactual @ '#sk1')), 92.74/12.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 92.74/12.38 thf(mforall_di_def, axiom,(( mforall_di ) = 92.74/12.38 (^[A:( $i > mworld > $o ),W:mworld]: 92.74/12.38 ( ![X:$i]: ( ( eiw_di @ X @ W ) => ( A @ X @ W ) ) )))). 92.74/12.38 thf('4', plain, 92.74/12.38 (( mforall_di ) = 92.74/12.38 ( ^[A:( $i > mworld > $o ),W:mworld]: 92.74/12.38 ( ![X:$i]: ( ( eiw_di @ X @ W ) => ( A @ X @ W ) ) ) )), 92.74/12.38 inference('simplify_rw_rule', [status(thm)], [mforall_di_def])). 92.74/12.38 thf('5', plain, 92.74/12.38 (( mforall_di ) = 92.74/12.38 ( ^[V_1:( $i > mworld > $o ),V_2:mworld]: 92.74/12.38 ( ![X4:$i]: ( ( eiw_di @ X4 @ V_2 ) => ( V_1 @ X4 @ V_2 ) ) ) )), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(mimplies_def, axiom,(( mimplies ) = 92.74/12.38 (^[A:( mworld > $o ),B:( mworld > $o ),W:mworld]: 92.74/12.38 ( ( A @ W ) => ( B @ W ) )))). 92.74/12.38 thf('6', plain, 92.74/12.38 (( mimplies ) = 92.74/12.38 ( ^[A:( mworld > $o ),B:( mworld > $o ),W:mworld]: 92.74/12.38 ( ( A @ W ) => ( B @ W ) ) )), 92.74/12.38 inference('simplify_rw_rule', [status(thm)], [mimplies_def])). 92.74/12.38 thf('7', plain, 92.74/12.38 (( mimplies ) = 92.74/12.38 ( ^[V_1:( mworld > $o ),V_2:( mworld > $o ),V_3:mworld]: 92.74/12.38 ( ( V_1 @ V_3 ) => ( V_2 @ V_3 ) ) )), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(mand_def, axiom,(( mand ) = 92.74/12.38 (^[A:( mworld > $o ),B:( mworld > $o ),W:mworld]: ( ( A @ W ) & ( B @ W ) )))). 92.74/12.38 thf('8', plain, 92.74/12.38 (( mand ) = 92.74/12.38 ( ^[A:( mworld > $o ),B:( mworld > $o ),W:mworld]: 92.74/12.38 ( ( A @ W ) & ( B @ W ) ) )), 92.74/12.38 inference('simplify_rw_rule', [status(thm)], [mand_def])). 92.74/12.38 thf('9', plain, 92.74/12.38 (( mand ) = 92.74/12.38 ( ^[V_1:( mworld > $o ),V_2:( mworld > $o ),V_3:mworld]: 92.74/12.38 ( ( V_1 @ V_3 ) & ( V_2 @ V_3 ) ) )), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(r2_0, axiom, 92.74/12.38 (mlocal @ 92.74/12.38 ( mand @ 92.74/12.38 ( mbox @ 92.74/12.38 ( mimplies @ 92.74/12.38 ( mbox @ r2 ) @ 92.74/12.38 ( mbox @ 92.74/12.38 ( mforall_di @ 92.74/12.38 ( ^[P:$i]: 92.74/12.38 ( mbox @ 92.74/12.38 ( mforall_di @ 92.74/12.38 ( ^[Q:$i]: 92.74/12.38 ( mbox @ 92.74/12.38 ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) ) ) ) ) ) ) ) ) @ 92.74/12.38 ( mbox @ 92.74/12.38 ( mimplies @ 92.74/12.38 ( mbox @ 92.74/12.38 ( mforall_di @ 92.74/12.38 ( ^[P:$i]: 92.74/12.38 ( mbox @ 92.74/12.38 ( mforall_di @ 92.74/12.38 ( ^[Q:$i]: 92.74/12.38 ( mbox @ 92.74/12.38 ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) ) ) ) ) ) ) @ 92.74/12.38 ( mbox @ r2 ) ) ) ))). 92.74/12.38 thf(zf_stmt_2, axiom, 92.74/12.38 (( ![X18:mworld]: 92.74/12.38 ( ( mrel @ mactual @ X18 ) => 92.74/12.38 ( ( ![X20:mworld]: 92.74/12.38 ( ( mrel @ X18 @ X20 ) => 92.74/12.38 ( ![X22:$i]: 92.74/12.38 ( ( eiw_di @ X22 @ X20 ) => 92.74/12.38 ( ![X24:mworld]: 92.74/12.38 ( ( mrel @ X20 @ X24 ) => 92.74/12.38 ( ![X26:$i]: 92.74/12.38 ( ( eiw_di @ X26 @ X24 ) => 92.74/12.38 ( ![X28:mworld]: 92.74/12.38 ( ( mrel @ X24 @ X28 ) => 92.74/12.38 ( is_a_theorem @ 92.74/12.38 ( implies @ X26 @ ( or @ X22 @ X26 ) ) @ X28 ) ) ) ) ) ) ) ) ) ) ) => 92.74/12.38 ( ![X30:mworld]: ( ( mrel @ X18 @ X30 ) => ( r2 @ X30 ) ) ) ) ) ) & 92.74/12.38 ( ![X4:mworld]: 92.74/12.38 ( ( mrel @ mactual @ X4 ) => 92.74/12.38 ( ( ![X6:mworld]: ( ( mrel @ X4 @ X6 ) => ( r2 @ X6 ) ) ) => 92.74/12.38 ( ![X8:mworld]: 92.74/12.38 ( ( mrel @ X4 @ X8 ) => 92.74/12.38 ( ![X10:$i]: 92.74/12.38 ( ( eiw_di @ X10 @ X8 ) => 92.74/12.38 ( ![X12:mworld]: 92.74/12.38 ( ( mrel @ X8 @ X12 ) => 92.74/12.38 ( ![X14:$i]: 92.74/12.38 ( ( eiw_di @ X14 @ X12 ) => 92.74/12.38 ( ![X16:mworld]: 92.74/12.38 ( ( mrel @ X12 @ X16 ) => 92.74/12.38 ( is_a_theorem @ 92.74/12.38 ( implies @ X14 @ ( or @ X10 @ X14 ) ) @ X16 ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 92.74/12.38 thf(zip_derived_cl51, plain, 92.74/12.38 ( (((((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ mactual @ Y0) => 92.74/12.38 (((((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => 92.74/12.38 (((!!) @ (^[Y2 : $i]: 92.74/12.38 (((eiw_di @ Y2 @ Y1) => 92.74/12.38 (((!!) @ (^[Y3 : mworld]: 92.74/12.38 (((mrel @ 92.74/12.38 Y1 @ Y3) => 92.74/12.38 (((!!) @ ( 92.74/12.38 ^[Y4 : $i]: 92.74/12.38 (( 92.74/12.38 (eiw_di @ 92.74/12.38 Y4 @ 92.74/12.38 Y3) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y5 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y3 @ 92.74/12.38 Y5) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y4 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y2 @ Y4)) @ 92.74/12.38 Y5)))))))))))))))))))))))))) => 92.74/12.38 (((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => (r2 @ Y1))))))))))))) & 92.74/12.38 (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ mactual @ Y0) => 92.74/12.38 (((((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => (r2 @ Y1)))))) => 92.74/12.38 (((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => 92.74/12.38 (((!!) @ (^[Y2 : $i]: 92.74/12.38 (((eiw_di @ Y2 @ Y1) => 92.74/12.38 (((!!) @ (^[Y3 : mworld]: 92.74/12.38 (((mrel @ 92.74/12.38 Y1 @ Y3) => 92.74/12.38 (((!!) @ ( 92.74/12.38 ^[Y4 : $i]: 92.74/12.38 (( 92.74/12.38 (eiw_di @ 92.74/12.38 Y4 @ 92.74/12.38 Y3) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y5 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y3 @ 92.74/12.38 Y5) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y4 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y2 @ Y4)) @ 92.74/12.38 Y5)))))))))))))))))))))))))))))))))))), 92.74/12.38 inference('cnf', [status(esa)], [zf_stmt_2])). 92.74/12.38 thf(zip_derived_cl5502, plain, 92.74/12.38 ( (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ mactual @ Y0) => 92.74/12.38 (((((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => 92.74/12.38 (((!!) @ (^[Y2 : $i]: 92.74/12.38 (((eiw_di @ Y2 @ Y1) => 92.74/12.38 (((!!) @ (^[Y3 : mworld]: 92.74/12.38 (((mrel @ Y1 @ 92.74/12.38 Y3) => 92.74/12.38 (((!!) @ ( 92.74/12.38 ^[Y4 : $i]: 92.74/12.38 ( 92.74/12.38 ( 92.74/12.38 (eiw_di @ 92.74/12.38 Y4 @ 92.74/12.38 Y3) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y5 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y3 @ 92.74/12.38 Y5) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y4 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y2 @ Y4)) @ 92.74/12.38 Y5)))))))))))))))))))))))))) => 92.74/12.38 (((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => (r2 @ Y1)))))))))))))), 92.74/12.38 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl51])). 92.74/12.38 thf(zip_derived_cl5504, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (((mrel @ mactual @ X2) => 92.74/12.38 (((((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))) => 92.74/12.38 (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0))))))))))), 92.74/12.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5502])). 92.74/12.38 thf(zip_derived_cl5506, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ (mrel @ mactual @ X2) 92.74/12.38 | (((((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (( 92.74/12.38 (eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))) => 92.74/12.38 (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))))))), 92.74/12.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5504])). 92.74/12.38 thf(zip_derived_cl5508, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ Y2) => 92.74/12.38 (((!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))) 92.74/12.38 | ~ (mrel @ mactual @ X2))), 92.74/12.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5506])). 92.74/12.38 thf(or_2_0, axiom, 92.74/12.38 (mlocal @ 92.74/12.38 ( mand @ 92.74/12.38 ( mbox @ 92.74/12.38 ( mimplies @ 92.74/12.38 ( mbox @ or_2 ) @ 92.74/12.38 ( mbox @ 92.74/12.38 ( mforall_di @ 92.74/12.38 ( ^[X:$i]: 92.74/12.38 ( mbox @ 92.74/12.38 ( mforall_di @ 92.74/12.38 ( ^[Y:$i]: 92.74/12.38 ( mbox @ 92.74/12.38 ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) @ 92.74/12.38 ( mbox @ 92.74/12.38 ( mimplies @ 92.74/12.38 ( mbox @ 92.74/12.38 ( mforall_di @ 92.74/12.38 ( ^[X:$i]: 92.74/12.38 ( mbox @ 92.74/12.38 ( mforall_di @ 92.74/12.38 ( ^[Y:$i]: 92.74/12.38 ( mbox @ 92.74/12.38 ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) ) ) ) ) ) ) @ 92.74/12.38 ( mbox @ or_2 ) ) ) ))). 92.74/12.38 thf(zf_stmt_3, axiom, 92.74/12.38 (( ![X18:mworld]: 92.74/12.38 ( ( mrel @ mactual @ X18 ) => 92.74/12.38 ( ( ![X20:mworld]: 92.74/12.38 ( ( mrel @ X18 @ X20 ) => 92.74/12.38 ( ![X22:$i]: 92.74/12.38 ( ( eiw_di @ X22 @ X20 ) => 92.74/12.38 ( ![X24:mworld]: 92.74/12.38 ( ( mrel @ X20 @ X24 ) => 92.74/12.38 ( ![X26:$i]: 92.74/12.38 ( ( eiw_di @ X26 @ X24 ) => 92.74/12.38 ( ![X28:mworld]: 92.74/12.38 ( ( mrel @ X24 @ X28 ) => 92.74/12.38 ( is_a_theorem @ 92.74/12.38 ( implies @ X26 @ ( or @ X22 @ X26 ) ) @ X28 ) ) ) ) ) ) ) ) ) ) ) => 92.74/12.38 ( ![X30:mworld]: ( ( mrel @ X18 @ X30 ) => ( or_2 @ X30 ) ) ) ) ) ) & 92.74/12.38 ( ![X4:mworld]: 92.74/12.38 ( ( mrel @ mactual @ X4 ) => 92.74/12.38 ( ( ![X6:mworld]: ( ( mrel @ X4 @ X6 ) => ( or_2 @ X6 ) ) ) => 92.74/12.38 ( ![X8:mworld]: 92.74/12.38 ( ( mrel @ X4 @ X8 ) => 92.74/12.38 ( ![X10:$i]: 92.74/12.38 ( ( eiw_di @ X10 @ X8 ) => 92.74/12.38 ( ![X12:mworld]: 92.74/12.38 ( ( mrel @ X8 @ X12 ) => 92.74/12.38 ( ![X14:$i]: 92.74/12.38 ( ( eiw_di @ X14 @ X12 ) => 92.74/12.38 ( ![X16:mworld]: 92.74/12.38 ( ( mrel @ X12 @ X16 ) => 92.74/12.38 ( is_a_theorem @ 92.74/12.38 ( implies @ X14 @ ( or @ X10 @ X14 ) ) @ X16 ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 92.74/12.38 thf(zip_derived_cl13, plain, 92.74/12.38 ( (((((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ mactual @ Y0) => 92.74/12.38 (((((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => 92.74/12.38 (((!!) @ (^[Y2 : $i]: 92.74/12.38 (((eiw_di @ Y2 @ Y1) => 92.74/12.38 (((!!) @ (^[Y3 : mworld]: 92.74/12.38 (((mrel @ 92.74/12.38 Y1 @ Y3) => 92.74/12.38 (((!!) @ ( 92.74/12.38 ^[Y4 : $i]: 92.74/12.38 (( 92.74/12.38 (eiw_di @ 92.74/12.38 Y4 @ 92.74/12.38 Y3) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y5 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y3 @ 92.74/12.38 Y5) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y4 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y2 @ Y4)) @ 92.74/12.38 Y5)))))))))))))))))))))))))) => 92.74/12.38 (((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => (or_2 @ Y1))))))))))))) & 92.74/12.38 (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ mactual @ Y0) => 92.74/12.38 (((((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => (or_2 @ Y1)))))) => 92.74/12.38 (((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => 92.74/12.38 (((!!) @ (^[Y2 : $i]: 92.74/12.38 (((eiw_di @ Y2 @ Y1) => 92.74/12.38 (((!!) @ (^[Y3 : mworld]: 92.74/12.38 (((mrel @ 92.74/12.38 Y1 @ Y3) => 92.74/12.38 (((!!) @ ( 92.74/12.38 ^[Y4 : $i]: 92.74/12.38 (( 92.74/12.38 (eiw_di @ 92.74/12.38 Y4 @ 92.74/12.38 Y3) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y5 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y3 @ 92.74/12.38 Y5) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y4 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y2 @ Y4)) @ 92.74/12.38 Y5)))))))))))))))))))))))))))))))))))), 92.74/12.38 inference('cnf', [status(esa)], [zf_stmt_3])). 92.74/12.38 thf(zip_derived_cl691, plain, 92.74/12.38 ( (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ mactual @ Y0) => 92.74/12.38 (((((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => (or_2 @ Y1)))))) => 92.74/12.38 (((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => 92.74/12.38 (((!!) @ (^[Y2 : $i]: 92.74/12.38 (((eiw_di @ Y2 @ Y1) => 92.74/12.38 (((!!) @ (^[Y3 : mworld]: 92.74/12.38 (((mrel @ Y1 @ 92.74/12.38 Y3) => 92.74/12.38 (((!!) @ ( 92.74/12.38 ^[Y4 : $i]: 92.74/12.38 ( 92.74/12.38 ( 92.74/12.38 (eiw_di @ 92.74/12.38 Y4 @ 92.74/12.38 Y3) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y5 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y3 @ 92.74/12.38 Y5) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y4 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y2 @ Y4)) @ 92.74/12.38 Y5)))))))))))))))))))))))))))))))))), 92.74/12.38 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl13])). 92.74/12.38 thf(zip_derived_cl693, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (((mrel @ mactual @ X2) => 92.74/12.38 (((((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))) => 92.74/12.38 (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4))))))))))))))))))))))))))))))), 92.74/12.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl691])). 92.74/12.38 thf(zip_derived_cl695, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ (mrel @ mactual @ X2) 92.74/12.38 | (((((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))) => 92.74/12.38 (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (( 92.74/12.38 (eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))))))), 92.74/12.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl693])). 92.74/12.38 thf(zip_derived_cl697, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))) 92.74/12.38 | ~ (mrel @ mactual @ X2))), 92.74/12.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl695])). 92.74/12.38 thf(zip_derived_cl697, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))) 92.74/12.38 | ~ (mrel @ mactual @ X2))), 92.74/12.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl695])). 92.74/12.38 thf(zip_derived_cl701, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 ( ('#form59' @ X2) 92.74/12.38 | ~ (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))))), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(zip_derived_cl703, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ ('#form59' @ X2) 92.74/12.38 | ~ (mrel @ mactual @ X2) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))))), 92.74/12.38 inference('renaming', [status(thm)], 92.74/12.38 [zip_derived_cl697, zip_derived_cl701])). 92.74/12.38 thf(zip_derived_cl709, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ ('#form57' @ X2) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))))), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(zip_derived_cl690, plain, 92.74/12.38 ( (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ mactual @ Y0) => 92.74/12.38 (((((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => 92.74/12.38 (((!!) @ (^[Y2 : $i]: 92.74/12.38 (((eiw_di @ Y2 @ Y1) => 92.74/12.38 (((!!) @ (^[Y3 : mworld]: 92.74/12.38 (((mrel @ Y1 @ 92.74/12.38 Y3) => 92.74/12.38 (((!!) @ ( 92.74/12.38 ^[Y4 : $i]: 92.74/12.38 ( 92.74/12.38 ( 92.74/12.38 (eiw_di @ 92.74/12.38 Y4 @ 92.74/12.38 Y3) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y5 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y3 @ 92.74/12.38 Y5) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y4 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y2 @ Y4)) @ 92.74/12.38 Y5)))))))))))))))))))))))))) => 92.74/12.38 (((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => (or_2 @ Y1)))))))))))))), 92.74/12.38 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl13])). 92.74/12.38 thf(zip_derived_cl692, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (((mrel @ mactual @ X2) => 92.74/12.38 (((((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))) => 92.74/12.38 (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0))))))))))), 92.74/12.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl690])). 92.74/12.38 thf(zip_derived_cl694, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ (mrel @ mactual @ X2) 92.74/12.38 | (((((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (( 92.74/12.38 (eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))) => 92.74/12.38 (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))))))), 92.74/12.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl692])). 92.74/12.38 thf(zip_derived_cl696, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ Y2) => 92.74/12.38 (((!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))) 92.74/12.38 | ~ (mrel @ mactual @ X2))), 92.74/12.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl694])). 92.74/12.38 thf(zip_derived_cl698, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 ( ('#form57' @ X2) 92.74/12.38 | ~ (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))))), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(zip_derived_cl5510, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ ('#form57' @ X2) 92.74/12.38 | ~ (mrel @ mactual @ X2) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))))), 92.74/12.38 inference('renaming', [status(thm)], 92.74/12.38 [zip_derived_cl5508, zip_derived_cl709, zip_derived_cl698])). 92.74/12.38 thf(zip_derived_cl5514, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ ('#form153' @ X2) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))))), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(zip_derived_cl5515, plain, 92.74/12.38 (![X2 : mworld, X4 : mworld]: 92.74/12.38 ( (((mrel @ X2 @ X4) => (r2 @ X4))) | ~ ('#form153' @ X2))), 92.74/12.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5514])). 92.74/12.38 thf(zip_derived_cl5520, plain, 92.74/12.38 (![X2 : mworld, X4 : mworld]: 92.74/12.38 (~ (mrel @ X2 @ X4) | (r2 @ X4) | ~ ('#form153' @ X2))), 92.74/12.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5515])). 92.74/12.38 thf(zip_derived_cl5576, plain, ((~ ('#form153' @ mactual) | (r2 @ '#sk1'))), 92.74/12.38 inference('sup-', [status(thm)], [zip_derived_cl69, zip_derived_cl5520])). 92.74/12.38 thf(mrel_reflexive, axiom, (![W:mworld]: ( mrel @ W @ W ))). 92.74/12.38 thf(zip_derived_cl47, plain, 92.74/12.38 ( (((!!) @ (^[Y0 : mworld]: (mrel @ Y0 @ Y0))))), 92.74/12.38 inference('cnf', [status(esa)], [mrel_reflexive])). 92.74/12.38 thf(zip_derived_cl71, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 92.74/12.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])). 92.74/12.38 thf(zip_derived_cl5510, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ ('#form57' @ X2) 92.74/12.38 | ~ (mrel @ mactual @ X2) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))))), 92.74/12.38 inference('renaming', [status(thm)], 92.74/12.38 [zip_derived_cl5508, zip_derived_cl709, zip_derived_cl698])). 92.74/12.38 thf(zip_derived_cl5514, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ ('#form153' @ X2) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))))), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(zip_derived_cl5503, plain, 92.74/12.38 ( (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ mactual @ Y0) => 92.74/12.38 (((((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => (r2 @ Y1)))))) => 92.74/12.38 (((!!) @ (^[Y1 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y1) => 92.74/12.38 (((!!) @ (^[Y2 : $i]: 92.74/12.38 (((eiw_di @ Y2 @ Y1) => 92.74/12.38 (((!!) @ (^[Y3 : mworld]: 92.74/12.38 (((mrel @ Y1 @ 92.74/12.38 Y3) => 92.74/12.38 (((!!) @ ( 92.74/12.38 ^[Y4 : $i]: 92.74/12.38 ( 92.74/12.38 ( 92.74/12.38 (eiw_di @ 92.74/12.38 Y4 @ 92.74/12.38 Y3) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y5 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y3 @ 92.74/12.38 Y5) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y4 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y2 @ Y4)) @ 92.74/12.38 Y5)))))))))))))))))))))))))))))))))), 92.74/12.38 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl51])). 92.74/12.38 thf(zip_derived_cl5505, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (((mrel @ mactual @ X2) => 92.74/12.38 (((((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))) => 92.74/12.38 (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4))))))))))))))))))))))))))))))), 92.74/12.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5503])). 92.74/12.38 thf(zip_derived_cl5507, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ (mrel @ mactual @ X2) 92.74/12.38 | (((((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))) => 92.74/12.38 (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (( 92.74/12.38 (eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))))))), 92.74/12.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5505])). 92.74/12.38 thf(zip_derived_cl5509, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))) 92.74/12.38 | ~ (mrel @ mactual @ X2))), 92.74/12.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5507])). 92.74/12.38 thf(zip_derived_cl5511, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 ( ('#form153' @ X2) 92.74/12.38 | ~ (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (r2 @ Y0)))))))), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(zip_derived_cl5516, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 ( ('#form153' @ X2) | ~ (mrel @ mactual @ X2) | ~ ('#form57' @ X2))), 92.74/12.38 inference('renaming', [status(thm)], 92.74/12.38 [zip_derived_cl5510, zip_derived_cl5514, zip_derived_cl5511])). 92.74/12.38 thf(zip_derived_cl5521, plain, 92.74/12.38 ((~ ('#form57' @ mactual) | ('#form153' @ mactual))), 92.74/12.38 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl5516])). 92.74/12.38 thf(zip_derived_cl71, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 92.74/12.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])). 92.74/12.38 thf(zip_derived_cl703, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ ('#form59' @ X2) 92.74/12.38 | ~ (mrel @ mactual @ X2) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))))), 92.74/12.38 inference('renaming', [status(thm)], 92.74/12.38 [zip_derived_cl697, zip_derived_cl701])). 92.74/12.38 thf(zip_derived_cl709, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ ('#form57' @ X2) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))))), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(zip_derived_cl698, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 ( ('#form57' @ X2) 92.74/12.38 | ~ (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))))), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(zip_derived_cl711, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 ( ('#form57' @ X2) | ~ (mrel @ mactual @ X2) | ~ ('#form59' @ X2))), 92.74/12.38 inference('renaming', [status(thm)], 92.74/12.38 [zip_derived_cl703, zip_derived_cl709, zip_derived_cl698])). 92.74/12.38 thf(zip_derived_cl1427, plain, 92.74/12.38 ((~ ('#form59' @ mactual) | ('#form57' @ mactual))), 92.74/12.38 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl711])). 92.74/12.38 thf(hilbert_or_2, axiom, (mlocal @ ( mbox @ or_2 ))). 92.74/12.38 thf(zf_stmt_4, axiom, 92.74/12.38 (![X4:mworld]: ( ( mrel @ mactual @ X4 ) => ( or_2 @ X4 ) ))). 92.74/12.38 thf(zip_derived_cl48, plain, 92.74/12.38 ( (((!!) @ (^[Y0 : mworld]: (((mrel @ mactual @ Y0) => (or_2 @ Y0))))))), 92.74/12.38 inference('cnf', [status(esa)], [zf_stmt_4])). 92.74/12.38 thf(zip_derived_cl696, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ Y2) => 92.74/12.38 (((!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))) 92.74/12.38 | ~ (mrel @ mactual @ X2))), 92.74/12.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl694])). 92.74/12.38 thf(zip_derived_cl698, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 ( ('#form57' @ X2) 92.74/12.38 | ~ (((!!) @ (^[Y0 : mworld]: 92.74/12.38 (((mrel @ X2 @ Y0) => 92.74/12.38 (((!!) @ (^[Y1 : $i]: 92.74/12.38 (((eiw_di @ Y1 @ Y0) => 92.74/12.38 (((!!) @ (^[Y2 : mworld]: 92.74/12.38 (((mrel @ Y0 @ Y2) => 92.74/12.38 (((!!) @ (^[Y3 : $i]: 92.74/12.38 (((eiw_di @ 92.74/12.38 Y3 @ 92.74/12.38 Y2) => 92.74/12.38 (( 92.74/12.38 (!!) @ ( 92.74/12.38 ^[Y4 : mworld]: 92.74/12.38 (( 92.74/12.38 (mrel @ 92.74/12.38 Y2 @ 92.74/12.38 Y4) => 92.74/12.38 (is_a_theorem @ 92.74/12.38 ( 92.74/12.38 implies @ 92.74/12.38 Y3 @ 92.74/12.38 ( 92.74/12.38 or @ 92.74/12.38 Y1 @ Y3)) @ 92.74/12.38 Y4)))))))))))))))))))))))))))), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(zip_derived_cl700, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ ('#form57' @ X2) 92.74/12.38 | ~ (mrel @ mactual @ X2) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))))), 92.74/12.38 inference('renaming', [status(thm)], 92.74/12.38 [zip_derived_cl696, zip_derived_cl698])). 92.74/12.38 thf(zip_derived_cl704, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 (~ ('#form59' @ X2) 92.74/12.38 | (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))))), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(zip_derived_cl701, plain, 92.74/12.38 (![X2 : mworld]: 92.74/12.38 ( ('#form59' @ X2) 92.74/12.38 | ~ (((!!) @ (^[Y0 : mworld]: (((mrel @ X2 @ Y0) => (or_2 @ Y0)))))))), 92.74/12.38 define([status(thm)])). 92.74/12.38 thf(zip_derived_cl4810, plain, ( ('#form59' @ mactual)), 92.74/12.38 inference('renaming', [status(thm)], 92.74/12.38 [zip_derived_cl48, zip_derived_cl704, zip_derived_cl701])). 92.74/12.38 thf(zip_derived_cl4812, plain, ( ('#form57' @ mactual)), 92.74/12.38 inference('demod', [status(thm)], 92.74/12.38 [zip_derived_cl1427, zip_derived_cl4810])). 92.74/12.38 thf(zip_derived_cl5543, plain, ( ('#form153' @ mactual)), 92.74/12.38 inference('demod', [status(thm)], 92.74/12.38 [zip_derived_cl5521, zip_derived_cl4812])). 92.74/12.38 thf(zip_derived_cl5577, plain, ( (r2 @ '#sk1')), 92.74/12.38 inference('demod', [status(thm)], 92.74/12.38 [zip_derived_cl5576, zip_derived_cl5543])). 92.74/12.38 thf(zip_derived_cl5578, plain, ($false), 92.74/12.38 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl5577])). 92.74/12.38 92.74/12.38 % SZS output end Refutation 92.74/12.38 92.74/12.38 92.74/12.38 % Terminating... 92.74/12.48 % Runner terminated. 92.74/12.48 % Zipperpin 1.5 exiting 92.74/12.50 EOF