0.05/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.10 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.YsEVe7kZ8c true 0.09/0.30 % Computer : n006.cluster.edu 0.09/0.30 % Model : x86_64 x86_64 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 % Memory : 8042.1875MB 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.30 % CPULimit : 960 0.09/0.30 % WCLimit : 120 0.09/0.30 % DateTime : Tue Aug 9 07:06:44 EDT 2022 0.09/0.30 % CPUTime : 0.09/0.30 % Running portfolio for 960 s 0.09/0.30 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.09/0.30 % Number of cores: 8 0.09/0.30 % Python version: Python 3.6.8 0.09/0.30 % Running in HO mode 0.47/0.58 % Total configuration time : 828 0.47/0.58 % Estimated wc time : 1656 0.47/0.58 % Estimated cpu time (8 cpus) : 207.0 0.47/0.66 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.47/0.66 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.47/0.66 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.47/0.66 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.47/0.67 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.47/0.67 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.47/0.67 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.47/0.67 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.48/0.86 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 115.55/15.17 % Solved by lams/30_b.l.sh. 115.55/15.17 % running E: timeout 14 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.YsEVe7kZ8c/e_input980930 --cpu-limit=12 --auto -s -p 115.55/15.17 % done 3041 iterations in 14.244s 115.55/15.17 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 115.55/15.17 % SZS output start Refutation 115.55/15.17 thf(mworld_type, type, mworld: $tType). 115.55/15.17 thf('#sk4_type', type, '#sk4': mworld > $i > $i > $i > $i). 115.55/15.17 thf(mlocal_type, type, mlocal: (mworld > $o) > $o). 115.55/15.17 thf(entry_box_type, type, entry_box: $i > mworld > $o). 115.55/15.17 thf('#sk2_type', type, '#sk2': $i). 115.55/15.17 thf(do_type, type, do: $i > $i > $i > mworld > $o). 115.55/15.17 thf(in_type, type, in: $i > $i > $i > mworld > $o). 115.55/15.17 thf(eiw_di_type, type, eiw_di: $i > mworld > $o). 115.55/15.17 thf('#form7_type', type, '#form7': $i > $i > $o). 115.55/15.17 thf(mrel_type, type, mrel: mworld > mworld > $o). 115.55/15.17 thf('#sk8_type', type, '#sk8': $i > $i > mworld). 115.55/15.17 thf(mimplies_type, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o). 115.55/15.17 thf('#sk5_type', type, '#sk5': mworld). 115.55/15.17 thf(mand_type, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o). 115.55/15.17 thf('#sk3_type', type, '#sk3': mworld > $i). 115.55/15.17 thf(string_type, type, string: $i > mworld > $o). 115.55/15.17 thf(mactual_type, type, mactual: mworld). 115.55/15.17 thf(userid_type, type, userid: $i > $i > mworld > $o). 115.55/15.17 thf(one_type, type, one: $i). 115.55/15.17 thf(mexists_di_type, type, mexists_di: ($i > mworld > $o) > mworld > $o). 115.55/15.17 thf(number_type, type, number: $i > $i > mworld > $o). 115.55/15.17 thf(mforall_di_type, type, mforall_di: ($i > mworld > $o) > mworld > $o). 115.55/15.17 thf('#sk9_type', type, '#sk9': $i > $i > $i > $i > $i). 115.55/15.17 thf(mbox_type, type, mbox: (mworld > $o) > mworld > $o). 115.55/15.17 thf(u_type, type, u: $i). 115.55/15.17 thf('#sk6_type', type, '#sk6': $i > $i > $i > $i > mworld). 115.55/15.17 thf(eiw_di_decr, axiom, 115.55/15.17 (![W:mworld,V:mworld,X:$i]: 115.55/15.17 ( ( ( mrel @ V @ W ) & ( eiw_di @ X @ W ) ) => ( eiw_di @ X @ V ) ))). 115.55/15.17 thf(zip_derived_cl6, plain, 115.55/15.17 ( (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((!!) @ (^[Y1 : mworld]: 115.55/15.17 (((!!) @ (^[Y2 : $i]: 115.55/15.17 (((((mrel @ Y1 @ Y0) & (eiw_di @ 115.55/15.17 Y2 @ Y0))) => 115.55/15.17 (eiw_di @ Y2 @ Y1))))))))))))), 115.55/15.17 inference('cnf', [status(esa)], [eiw_di_decr])). 115.55/15.17 thf(zip_derived_cl43, plain, 115.55/15.17 (![X2 : mworld]: 115.55/15.17 (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((!!) @ (^[Y1 : $i]: 115.55/15.17 (((((mrel @ Y0 @ X2) & (eiw_di @ Y1 @ X2))) => 115.55/15.17 (eiw_di @ Y1 @ Y0)))))))))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 115.55/15.17 thf(zip_derived_cl44, plain, 115.55/15.17 (![X2 : mworld, X4 : mworld]: 115.55/15.17 (((!!) @ (^[Y0 : $i]: 115.55/15.17 (((((mrel @ X4 @ X2) & (eiw_di @ Y0 @ X2))) => (eiw_di @ 115.55/15.17 Y0 @ X4))))))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 115.55/15.17 thf(zip_derived_cl45, plain, 115.55/15.17 (![X2 : mworld, X4 : mworld, X6 : $i]: 115.55/15.17 (((((mrel @ X4 @ X2) & (eiw_di @ X6 @ X2))) => (eiw_di @ X6 @ X4)))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl44])). 115.55/15.17 thf(zip_derived_cl46, plain, 115.55/15.17 (![X2 : mworld, X4 : mworld, X6 : $i]: 115.55/15.17 (~ (((mrel @ X4 @ X2) & (eiw_di @ X6 @ X2))) | (eiw_di @ X6 @ X4))), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 115.55/15.17 thf(zip_derived_cl47, plain, 115.55/15.17 (![X2 : mworld, X4 : mworld, X6 : $i]: 115.55/15.17 (~ (mrel @ X4 @ X2) | ~ (eiw_di @ X6 @ X2) | (eiw_di @ X6 @ X4))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 115.55/15.17 thf(ax2, axiom, 115.55/15.17 (mlocal @ 115.55/15.17 ( mexists_di @ 115.55/15.17 ( ^[B:$i]: 115.55/15.17 ( mbox @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) ))). 115.55/15.17 thf(zip_derived_cl5, plain, 115.55/15.17 ( (mlocal @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y0 : $i]: (mbox @ (mand @ (entry_box @ Y0) @ (number @ Y0 @ one))))))), 115.55/15.17 inference('cnf', [status(esa)], [ax2])). 115.55/15.17 thf(mlocal_def, axiom,(( mlocal @ (X0)) = ((X0 @ mactual)))). 115.55/15.17 thf('0', plain, 115.55/15.17 (![X0:( mworld > $o )]: ( ( mlocal @ X0 ) = ( X0 @ mactual ) )), 115.55/15.17 define([status(thm)])). 115.55/15.17 thf(zip_derived_cl11, plain, 115.55/15.17 ( (mexists_di @ 115.55/15.17 (^[Y0 : $i]: (mbox @ (mand @ (entry_box @ Y0) @ (number @ Y0 @ one)))) @ 115.55/15.17 mactual)), 115.55/15.17 inference('rw', [status(thm)], [zip_derived_cl5, '0'])). 115.55/15.17 thf(mexists_di_def, axiom, (mexists_di @ X0 @ X1) => 115.55/15.17 ((((??) @ (^[Y0 : $i]: (((eiw_di @ Y0 @ X1) & (X0 @ Y0 @ X1)))))) = ($true))). 115.55/15.17 thf('1', plain, 115.55/15.17 (![X0:( $i > mworld > $o ),X1:mworld]: 115.55/15.17 ( ( mexists_di @ X0 @ X1 ) <=> 115.55/15.17 ( ?[X6:$i]: ( ( eiw_di @ X6 @ X1 ) & ( X0 @ X6 @ X1 ) ) ) )), 115.55/15.17 inference('rw.lit', [status(esa)], [mexists_di_def])). 115.55/15.17 thf(zip_derived_cl12, plain, 115.55/15.17 ( (((??) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ mactual) & 115.55/15.17 ((^[Y1 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ 115.55/15.17 Y0 @ mactual))))))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl11, '1'])). 115.55/15.17 thf(zip_derived_cl13, plain, 115.55/15.17 ( (((??) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ mactual) & (mbox @ 115.55/15.17 (mand @ (entry_box @ Y0) @ (number @ Y0 @ one)) @ 115.55/15.17 mactual))))))), 115.55/15.17 inference('ho_norm', [status(thm)], [zip_derived_cl12])). 115.55/15.17 thf(zip_derived_cl14, plain, 115.55/15.17 ( (((eiw_di @ '#sk2' @ mactual) & (mbox @ 115.55/15.17 (mand @ (entry_box @ '#sk2') @ (number @ '#sk2' @ one)) @ mactual)))), 115.55/15.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl13])). 115.55/15.17 thf(zip_derived_cl15, plain, ( (eiw_di @ '#sk2' @ mactual)), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl14])). 115.55/15.17 thf(zip_derived_cl266, plain, 115.55/15.17 (![X0 : mworld]: ( (eiw_di @ '#sk2' @ X0) | ~ (mrel @ X0 @ mactual))), 115.55/15.17 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl15])). 115.55/15.17 thf(zip_derived_cl16, plain, 115.55/15.17 ( (mbox @ (mand @ (entry_box @ '#sk2') @ (number @ '#sk2' @ one)) @ 115.55/15.17 mactual)), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl14])). 115.55/15.17 thf(mbox_def, axiom, (mbox @ X0 @ X1) => 115.55/15.17 ((((!!) @ (^[Y0 : mworld]: (((mrel @ X1 @ Y0) => (X0 @ Y0)))))) = ($true))). 115.55/15.17 thf('2', plain, 115.55/15.17 (![X0:( mworld > $o ),X1:mworld]: 115.55/15.17 ( ( mbox @ X0 @ X1 ) <=> 115.55/15.17 ( ![X6:mworld]: ( ( mrel @ X1 @ X6 ) => ( X0 @ X6 ) ) ) )), 115.55/15.17 inference('rw.lit', [status(esa)], [mbox_def])). 115.55/15.17 thf(zip_derived_cl17, plain, 115.55/15.17 ( (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((mrel @ mactual @ Y0) => (mand @ (entry_box @ '#sk2') @ 115.55/15.17 (number @ '#sk2' @ one) @ Y0))))))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl16, '2'])). 115.55/15.17 thf(zip_derived_cl18, plain, 115.55/15.17 (![X2 : mworld]: 115.55/15.17 (((mrel @ mactual @ X2) => (mand @ (entry_box @ '#sk2') @ 115.55/15.17 (number @ '#sk2' @ one) @ X2)))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 115.55/15.17 thf(zip_derived_cl19, plain, 115.55/15.17 (![X2 : mworld]: 115.55/15.17 (~ (mrel @ mactual @ X2) 115.55/15.17 | (mand @ (entry_box @ '#sk2') @ (number @ '#sk2' @ one) @ X2))), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 115.55/15.17 thf(mand_def, axiom, (mand @ X0 @ X1 @ X2) => 115.55/15.17 ((((X1 @ X2) & (X0 @ X2))) = ($true))). 115.55/15.17 thf('3', plain, 115.55/15.17 (![X0:( mworld > $o ),X1:( mworld > $o ),X2:mworld]: 115.55/15.17 ( ( mand @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) & ( X1 @ X2 ) ) )), 115.55/15.17 inference('rw.lit', [status(esa)], [mand_def])). 115.55/15.17 thf(zip_derived_cl20, plain, 115.55/15.17 (![X0 : mworld]: 115.55/15.17 ( (((number @ '#sk2' @ one @ X0) & (entry_box @ '#sk2' @ X0))) 115.55/15.17 | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl19, '3'])). 115.55/15.17 thf(zip_derived_cl22, plain, 115.55/15.17 (![X0 : mworld]: ( (entry_box @ '#sk2' @ X0) | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl20])). 115.55/15.17 thf(mrel_euclidean, axiom, 115.55/15.17 (![W:mworld,V:mworld,U:mworld]: 115.55/15.17 ( ( ( mrel @ W @ V ) & ( mrel @ W @ U ) ) => ( mrel @ U @ V ) ))). 115.55/15.17 thf(zip_derived_cl4, plain, 115.55/15.17 ( (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((!!) @ (^[Y1 : mworld]: 115.55/15.17 (((!!) @ (^[Y2 : mworld]: 115.55/15.17 (((((mrel @ Y0 @ Y1) & (mrel @ 115.55/15.17 Y0 @ Y2))) => 115.55/15.17 (mrel @ Y2 @ Y1))))))))))))), 115.55/15.17 inference('cnf', [status(esa)], [mrel_euclidean])). 115.55/15.17 thf(zip_derived_cl38, plain, 115.55/15.17 (![X2 : mworld]: 115.55/15.17 (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((!!) @ (^[Y1 : mworld]: 115.55/15.17 (((((mrel @ X2 @ Y0) & (mrel @ X2 @ Y1))) => 115.55/15.17 (mrel @ Y1 @ Y0)))))))))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 115.55/15.17 thf(zip_derived_cl39, plain, 115.55/15.17 (![X2 : mworld, X4 : mworld]: 115.55/15.17 (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((((mrel @ X2 @ X4) & (mrel @ X2 @ Y0))) => (mrel @ 115.55/15.17 Y0 @ X4))))))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl38])). 115.55/15.17 thf(zip_derived_cl40, plain, 115.55/15.17 (![X2 : mworld, X4 : mworld, X6 : mworld]: 115.55/15.17 (((((mrel @ X2 @ X4) & (mrel @ X2 @ X6))) => (mrel @ X6 @ X4)))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl39])). 115.55/15.17 thf(zip_derived_cl41, plain, 115.55/15.17 (![X2 : mworld, X4 : mworld, X6 : mworld]: 115.55/15.17 (~ (((mrel @ X2 @ X4) & (mrel @ X2 @ X6))) | (mrel @ X6 @ X4))), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])). 115.55/15.17 thf(zip_derived_cl42, plain, 115.55/15.17 (![X2 : mworld, X4 : mworld, X6 : mworld]: 115.55/15.17 (~ (mrel @ X2 @ X4) | ~ (mrel @ X2 @ X6) | (mrel @ X6 @ X4))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl41])). 115.55/15.17 thf(con, conjecture, 115.55/15.17 (mlocal @ 115.55/15.17 ( mbox @ 115.55/15.17 ( mexists_di @ 115.55/15.17 ( ^[I:$i]: 115.55/15.17 ( mexists_di @ 115.55/15.17 ( ^[B:$i]: 115.55/15.17 ( mexists_di @ 115.55/15.17 ( ^[A:$i]: 115.55/15.17 ( mexists_di @ 115.55/15.17 ( ^[S:$i]: 115.55/15.17 ( mand @ 115.55/15.17 ( mbox @ 115.55/15.17 ( mand @ 115.55/15.17 ( userid @ u @ I ) @ 115.55/15.17 ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) @ 115.55/15.17 ( mbox @ 115.55/15.17 ( mforall_di @ 115.55/15.17 ( ^[S2:$i]: 115.55/15.17 ( mimplies @ 115.55/15.17 ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 115.55/15.17 thf(zf_stmt_0, negated_conjecture, 115.55/15.17 (~( mlocal @ 115.55/15.17 ( mbox @ 115.55/15.17 ( mexists_di @ 115.55/15.17 ( ^[I:$i]: 115.55/15.17 ( mexists_di @ 115.55/15.17 ( ^[B:$i]: 115.55/15.17 ( mexists_di @ 115.55/15.17 ( ^[A:$i]: 115.55/15.17 ( mexists_di @ 115.55/15.17 ( ^[S:$i]: 115.55/15.17 ( mand @ 115.55/15.17 ( mbox @ 115.55/15.17 ( mand @ 115.55/15.17 ( userid @ u @ I ) @ 115.55/15.17 ( mand @ 115.55/15.17 ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) @ 115.55/15.17 ( mbox @ 115.55/15.17 ( mforall_di @ 115.55/15.17 ( ^[S2:$i]: 115.55/15.17 ( mimplies @ 115.55/15.17 ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 115.55/15.17 inference('cnf.neg', [status(esa)], [con])). 115.55/15.17 thf(zip_derived_cl2, plain, 115.55/15.17 (~ (mlocal @ 115.55/15.17 (mbox @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ Y0) @ 115.55/15.17 (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mimplies @ (do @ Y3 @ Y2 @ Y4) @ 115.55/15.17 (in @ Y0 @ Y1 @ Y4))))))))))))))))), 115.55/15.17 inference('cnf', [status(esa)], [zf_stmt_0])). 115.55/15.17 thf(zip_derived_cl83, plain, 115.55/15.17 (~ (mbox @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ Y0) @ 115.55/15.17 (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mimplies @ (do @ Y3 @ Y2 @ Y4) @ 115.55/15.17 (in @ Y0 @ Y1 @ Y4)))))))))))))) @ 115.55/15.17 mactual)), 115.55/15.17 inference('rw', [status(thm)], [zip_derived_cl2, '0'])). 115.55/15.17 thf(mbox_def, axiom, ~ (mbox @ X0 @ X1) => 115.55/15.17 ((((!!) @ (^[Y0 : mworld]: (((mrel @ X1 @ Y0) => (X0 @ Y0)))))) != ($true))). 115.55/15.17 thf('4', plain, 115.55/15.17 (![X0:( mworld > $o ),X1:mworld]: 115.55/15.17 ( ( ~( mbox @ X0 @ X1 ) ) <=> 115.55/15.17 ( ~( ![X6:mworld]: ( ( mrel @ X1 @ X6 ) => ( X0 @ X6 ) ) ) ) )), 115.55/15.17 inference('rw.lit', [status(esa)], [mbox_def])). 115.55/15.17 thf(zip_derived_cl84, plain, 115.55/15.17 (~ (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((mrel @ mactual @ Y0) => (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ Y1) @ 115.55/15.17 (mand @ (entry_box @ Y2) @ 115.55/15.17 (number @ Y2 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y5 : $i]: 115.55/15.17 (mimplies @ (do @ Y4 @ Y3 @ Y5) @ 115.55/15.17 (in @ Y1 @ Y2 @ Y5))))))))))))) @ 115.55/15.17 Y0))))))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl83, '4'])). 115.55/15.17 thf(zip_derived_cl85, plain, 115.55/15.17 (~ (((mrel @ mactual @ '#sk5') => (mexists_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ Y0) @ 115.55/15.17 (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mimplies @ (do @ Y3 @ Y2 @ Y4) @ 115.55/15.17 (in @ Y0 @ Y1 @ Y4))))))))))))) @ 115.55/15.17 '#sk5')))), 115.55/15.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl84])). 115.55/15.17 thf(zip_derived_cl86, plain, ( (mrel @ mactual @ '#sk5')), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl85])). 115.55/15.17 thf(zip_derived_cl131, plain, 115.55/15.17 (![X0 : mworld]: ( (mrel @ '#sk5' @ X0) | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('sup+', [status(thm)], [zip_derived_cl42, zip_derived_cl86])). 115.55/15.17 thf(mrel_reflexive, axiom, (![W:mworld]: ( mrel @ W @ W ))). 115.55/15.17 thf(zip_derived_cl0, plain, ( (((!!) @ (^[Y0 : mworld]: (mrel @ Y0 @ Y0))))), 115.55/15.17 inference('cnf', [status(esa)], [mrel_reflexive])). 115.55/15.17 thf(zip_derived_cl8, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 115.55/15.17 thf(zip_derived_cl181, plain, ( (mrel @ '#sk5' @ mactual)), 115.55/15.17 inference('sup+', [status(thm)], [zip_derived_cl131, zip_derived_cl8])). 115.55/15.17 thf(ax1, axiom, 115.55/15.17 (mlocal @ 115.55/15.17 ( mbox @ 115.55/15.17 ( mexists_di @ 115.55/15.17 ( ^[I:$i]: ( mbox @ ( mand @ ( userid @ u @ I ) @ ( string @ I ) ) ) ) ) ))). 115.55/15.17 thf(zip_derived_cl1, plain, 115.55/15.17 ( (mlocal @ 115.55/15.17 (mbox @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y0 : $i]: (mbox @ (mand @ (userid @ u @ Y0) @ (string @ Y0)))))))), 115.55/15.17 inference('cnf', [status(esa)], [ax1])). 115.55/15.17 thf(zip_derived_cl23, plain, 115.55/15.17 ( (mbox @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y0 : $i]: (mbox @ (mand @ (userid @ u @ Y0) @ (string @ Y0))))) @ 115.55/15.17 mactual)), 115.55/15.17 inference('rw', [status(thm)], [zip_derived_cl1, '0'])). 115.55/15.17 thf(zip_derived_cl24, plain, 115.55/15.17 ( (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((mrel @ mactual @ Y0) => (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mbox @ (mand @ (userid @ u @ Y1) @ (string @ Y1)))) @ 115.55/15.17 Y0))))))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl23, '2'])). 115.55/15.17 thf(zip_derived_cl25, plain, 115.55/15.17 (![X2 : mworld]: 115.55/15.17 (((mrel @ mactual @ X2) => (mexists_di @ 115.55/15.17 (^[Y0 : $i]: (mbox @ (mand @ (userid @ u @ Y0) @ (string @ Y0)))) @ 115.55/15.17 X2)))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl24])). 115.55/15.17 thf(zip_derived_cl26, plain, 115.55/15.17 (![X2 : mworld]: 115.55/15.17 (~ (mrel @ mactual @ X2) 115.55/15.17 | (mexists_di @ 115.55/15.17 (^[Y0 : $i]: (mbox @ (mand @ (userid @ u @ Y0) @ (string @ Y0)))) @ 115.55/15.17 X2))), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 115.55/15.17 thf(zip_derived_cl27, plain, 115.55/15.17 (![X0 : mworld]: 115.55/15.17 ( (((??) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ X0) & 115.55/15.17 ((^[Y1 : $i]: 115.55/15.17 (mbox @ (mand @ (userid @ u @ Y1) @ (string @ Y1)))) @ 115.55/15.17 Y0 @ X0)))))) 115.55/15.17 | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl26, '1'])). 115.55/15.17 thf(zip_derived_cl28, plain, 115.55/15.17 (![X0 : mworld]: 115.55/15.17 ( (((??) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ X0) & (mbox @ 115.55/15.17 (mand @ (userid @ u @ Y0) @ (string @ Y0)) @ X0)))))) 115.55/15.17 | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('ho_norm', [status(thm)], [zip_derived_cl27])). 115.55/15.17 thf(zip_derived_cl29, plain, 115.55/15.17 (![X0 : mworld]: 115.55/15.17 ( (((eiw_di @ ('#sk3' @ X0) @ X0) & (mbox @ 115.55/15.17 (mand @ (userid @ u @ ('#sk3' @ X0)) @ (string @ ('#sk3' @ X0))) @ 115.55/15.17 X0))) 115.55/15.17 | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])). 115.55/15.17 thf(zip_derived_cl31, plain, 115.55/15.17 (![X0 : mworld]: 115.55/15.17 ( (mbox @ 115.55/15.17 (mand @ (userid @ u @ ('#sk3' @ X0)) @ (string @ ('#sk3' @ X0))) @ 115.55/15.17 X0) 115.55/15.17 | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl29])). 115.55/15.17 thf(zip_derived_cl32, plain, 115.55/15.17 (![X0 : mworld]: 115.55/15.17 ( (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((mrel @ X0 @ Y0) => (mand @ 115.55/15.17 (userid @ u @ ('#sk3' @ X0)) @ 115.55/15.17 (string @ ('#sk3' @ X0)) @ Y0)))))) 115.55/15.17 | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl31, '2'])). 115.55/15.17 thf(zip_derived_cl33, plain, 115.55/15.17 (![X0 : mworld, X2 : mworld]: 115.55/15.17 ( (((mrel @ X0 @ X2) => (mand @ (userid @ u @ ('#sk3' @ X0)) @ 115.55/15.17 (string @ ('#sk3' @ X0)) @ X2))) 115.55/15.17 | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 115.55/15.17 thf(zip_derived_cl34, plain, 115.55/15.17 (![X0 : mworld, X2 : mworld]: 115.55/15.17 (~ (mrel @ X0 @ X2) 115.55/15.17 | (mand @ (userid @ u @ ('#sk3' @ X0)) @ (string @ ('#sk3' @ X0)) @ 115.55/15.17 X2) 115.55/15.17 | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 115.55/15.17 thf(zip_derived_cl35, plain, 115.55/15.17 (![X0 : mworld, X1 : mworld]: 115.55/15.17 ( (((string @ ('#sk3' @ X0) @ X1) & (userid @ u @ ('#sk3' @ X0) @ X1))) 115.55/15.17 | ~ (mrel @ mactual @ X0) 115.55/15.17 | ~ (mrel @ X0 @ X1))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl34, '3'])). 115.55/15.17 thf(zip_derived_cl36, plain, 115.55/15.17 (![X0 : mworld, X1 : mworld]: 115.55/15.17 ( (string @ ('#sk3' @ X0) @ X1) 115.55/15.17 | ~ (mrel @ X0 @ X1) 115.55/15.17 | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl35])). 115.55/15.17 thf(zip_derived_cl42, plain, 115.55/15.17 (![X2 : mworld, X4 : mworld, X6 : mworld]: 115.55/15.17 (~ (mrel @ X2 @ X4) | ~ (mrel @ X2 @ X6) | (mrel @ X6 @ X4))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl41])). 115.55/15.17 thf(zip_derived_cl21, plain, 115.55/15.17 (![X0 : mworld]: 115.55/15.17 ( (number @ '#sk2' @ one @ X0) | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl20])). 115.55/15.17 thf(zip_derived_cl87, plain, 115.55/15.17 (~ (mexists_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ Y0) @ 115.55/15.17 (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mimplies @ (do @ Y3 @ Y2 @ Y4) @ 115.55/15.17 (in @ Y0 @ Y1 @ Y4))))))))))))) @ 115.55/15.17 '#sk5')), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl85])). 115.55/15.17 thf(mexists_di_def, axiom, ~ (mexists_di @ X0 @ X1) => 115.55/15.17 ((((??) @ (^[Y0 : $i]: (((eiw_di @ Y0 @ X1) & (X0 @ Y0 @ X1)))))) != 115.55/15.17 ($true))). 115.55/15.17 thf('5', plain, 115.55/15.17 (![X0:( $i > mworld > $o ),X1:mworld]: 115.55/15.17 ( ( ~( mexists_di @ X0 @ X1 ) ) <=> 115.55/15.17 ( ~( ?[X6:$i]: ( ( eiw_di @ X6 @ X1 ) & ( X0 @ X6 @ X1 ) ) ) ) )), 115.55/15.17 inference('rw.lit', [status(esa)], [mexists_di_def])). 115.55/15.17 thf(zip_derived_cl88, plain, 115.55/15.17 (~ (((??) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ '#sk5') & 115.55/15.17 ((^[Y1 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ Y1) @ 115.55/15.17 (mand @ (entry_box @ Y2) @ 115.55/15.17 (number @ Y2 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y5 : $i]: 115.55/15.17 (mimplies @ (do @ Y4 @ Y3 @ Y5) @ 115.55/15.17 (in @ Y1 @ Y2 @ Y5))))))))))))) @ 115.55/15.17 Y0 @ '#sk5'))))))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl87, '5'])). 115.55/15.17 thf(zip_derived_cl89, plain, 115.55/15.17 (~ (((??) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ '#sk5') & (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ Y0) @ 115.55/15.17 (mand @ (entry_box @ Y1) @ 115.55/15.17 (number @ Y1 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mimplies @ (do @ Y3 @ Y2 @ Y4) @ 115.55/15.17 (in @ Y0 @ Y1 @ Y4))))))))))) @ 115.55/15.17 '#sk5'))))))), 115.55/15.17 inference('ho_norm', [status(thm)], [zip_derived_cl88])). 115.55/15.17 thf(zip_derived_cl90, plain, 115.55/15.17 (![X2 : $i]: 115.55/15.17 ~ (((eiw_di @ X2 @ '#sk5') & (mexists_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ X2) @ 115.55/15.17 (mand @ (entry_box @ Y0) @ (number @ Y0 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mimplies @ (do @ Y2 @ Y1 @ Y3) @ 115.55/15.17 (in @ X2 @ Y0 @ Y3))))))))))) @ 115.55/15.17 '#sk5')))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl89])). 115.55/15.17 thf(zip_derived_cl91, plain, 115.55/15.17 (![X2 : $i]: 115.55/15.17 (~ (eiw_di @ X2 @ '#sk5') 115.55/15.17 | ~ (mexists_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ X2) @ 115.55/15.17 (mand @ (entry_box @ Y0) @ (number @ Y0 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mimplies @ (do @ Y2 @ Y1 @ Y3) @ 115.55/15.17 (in @ X2 @ Y0 @ Y3))))))))))) @ 115.55/15.17 '#sk5'))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl90])). 115.55/15.17 thf(zip_derived_cl92, plain, 115.55/15.17 (![X0 : $i]: 115.55/15.17 (~ (((??) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ '#sk5') & 115.55/15.17 ((^[Y1 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ X0) @ 115.55/15.17 (mand @ (entry_box @ Y1) @ 115.55/15.17 (number @ Y1 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mimplies @ (do @ Y3 @ Y2 @ Y4) @ 115.55/15.17 (in @ X0 @ Y1 @ Y4))))))))))) @ 115.55/15.17 Y0 @ '#sk5')))))) 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5'))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl91, '5'])). 115.55/15.17 thf(zip_derived_cl93, plain, 115.55/15.17 (![X0 : $i]: 115.55/15.17 (~ (((??) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ '#sk5') & (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ X0) @ 115.55/15.17 (mand @ (entry_box @ Y0) @ 115.55/15.17 (number @ Y0 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mimplies @ (do @ Y2 @ Y1 @ Y3) @ 115.55/15.17 (in @ X0 @ Y0 @ Y3))))))))) @ 115.55/15.17 '#sk5')))))) 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5'))), 115.55/15.17 inference('ho_norm', [status(thm)], [zip_derived_cl92])). 115.55/15.17 thf(zip_derived_cl94, plain, 115.55/15.17 (![X0 : $i, X2 : $i]: 115.55/15.17 (~ (((eiw_di @ X2 @ '#sk5') & (mexists_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ X0) @ 115.55/15.17 (mand @ (entry_box @ X2) @ (number @ X2 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mimplies @ (do @ Y1 @ Y0 @ Y2) @ 115.55/15.17 (in @ X0 @ X2 @ Y2))))))))) @ 115.55/15.17 '#sk5'))) 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5'))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl93])). 115.55/15.17 thf(zip_derived_cl95, plain, 115.55/15.17 (![X0 : $i, X2 : $i]: 115.55/15.17 (~ (eiw_di @ X2 @ '#sk5') 115.55/15.17 | ~ (mexists_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ X0) @ 115.55/15.17 (mand @ (entry_box @ X2) @ (number @ X2 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mimplies @ (do @ Y1 @ Y0 @ Y2) @ 115.55/15.17 (in @ X0 @ X2 @ Y2))))))))) @ 115.55/15.17 '#sk5') 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5'))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl94])). 115.55/15.17 thf(zip_derived_cl96, plain, 115.55/15.17 (![X0 : $i, X1 : $i]: 115.55/15.17 (~ (((??) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ '#sk5') & 115.55/15.17 ((^[Y1 : $i]: 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ X0) @ 115.55/15.17 (mand @ (entry_box @ X1) @ 115.55/15.17 (number @ X1 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mimplies @ (do @ Y2 @ Y1 @ Y3) @ 115.55/15.17 (in @ X0 @ X1 @ Y3))))))))) @ 115.55/15.17 Y0 @ '#sk5')))))) 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X1 @ '#sk5'))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl95, '5'])). 115.55/15.17 thf(zip_derived_cl97, plain, 115.55/15.17 (![X0 : $i, X1 : $i]: 115.55/15.17 (~ (((??) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ '#sk5') & (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ X0) @ 115.55/15.17 (mand @ (entry_box @ X1) @ (number @ X1 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mimplies @ (do @ Y1 @ Y0 @ Y2) @ 115.55/15.17 (in @ X0 @ X1 @ Y2))))))) @ 115.55/15.17 '#sk5')))))) 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X1 @ '#sk5'))), 115.55/15.17 inference('ho_norm', [status(thm)], [zip_derived_cl96])). 115.55/15.17 thf(zip_derived_cl98, plain, 115.55/15.17 (![X0 : $i, X1 : $i, X3 : $i]: 115.55/15.17 (~ (((eiw_di @ X3 @ '#sk5') & (mexists_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ X0) @ 115.55/15.17 (mand @ (entry_box @ X1) @ (number @ X1 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mimplies @ (do @ Y0 @ X3 @ Y1) @ (in @ X0 @ X1 @ Y1))))))) @ 115.55/15.17 '#sk5'))) 115.55/15.17 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5'))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl97])). 115.55/15.17 thf(zip_derived_cl99, plain, 115.55/15.17 (![X0 : $i, X1 : $i, X3 : $i]: 115.55/15.17 (~ (eiw_di @ X3 @ '#sk5') 115.55/15.17 | ~ (mexists_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ X0) @ 115.55/15.17 (mand @ (entry_box @ X1) @ (number @ X1 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mimplies @ (do @ Y0 @ X3 @ Y1) @ (in @ X0 @ X1 @ Y1))))))) @ 115.55/15.17 '#sk5') 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X1 @ '#sk5'))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl98])). 115.55/15.17 thf(zip_derived_cl100, plain, 115.55/15.17 (![X0 : $i, X1 : $i, X2 : $i]: 115.55/15.17 (~ (((??) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ '#sk5') & 115.55/15.17 ((^[Y1 : $i]: 115.55/15.17 (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ X1) @ 115.55/15.17 (mand @ (entry_box @ X0) @ (number @ X0 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mimplies @ (do @ Y1 @ X2 @ Y2) @ 115.55/15.17 (in @ X1 @ X0 @ Y2))))))) @ 115.55/15.17 Y0 @ '#sk5')))))) 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X2 @ '#sk5'))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl99, '5'])). 115.55/15.17 thf(zip_derived_cl101, plain, 115.55/15.17 (![X0 : $i, X1 : $i, X2 : $i]: 115.55/15.17 (~ (((??) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ '#sk5') & (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ X1) @ 115.55/15.17 (mand @ (entry_box @ X0) @ (number @ X0 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mimplies @ (do @ Y0 @ X2 @ Y1) @ 115.55/15.17 (in @ X1 @ X0 @ Y1))))) @ 115.55/15.17 '#sk5')))))) 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X2 @ '#sk5'))), 115.55/15.17 inference('ho_norm', [status(thm)], [zip_derived_cl100])). 115.55/15.17 thf(zip_derived_cl102, plain, 115.55/15.17 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 115.55/15.17 (~ (((eiw_di @ X4 @ '#sk5') & (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ X1) @ 115.55/15.17 (mand @ (entry_box @ X0) @ (number @ X0 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mimplies @ (do @ X4 @ X2 @ Y0) @ (in @ X1 @ X0 @ Y0))))) @ 115.55/15.17 '#sk5'))) 115.55/15.17 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5'))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl101])). 115.55/15.17 thf(zip_derived_cl103, plain, 115.55/15.17 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 115.55/15.17 (~ (eiw_di @ X4 @ '#sk5') 115.55/15.17 | ~ (mand @ 115.55/15.17 (mbox @ 115.55/15.17 (mand @ (userid @ u @ X1) @ 115.55/15.17 (mand @ (entry_box @ X0) @ (number @ X0 @ one)))) @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mimplies @ (do @ X4 @ X2 @ Y0) @ (in @ X1 @ X0 @ Y0))))) @ 115.55/15.17 '#sk5') 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X2 @ '#sk5'))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl102])). 115.55/15.17 thf(mand_def, axiom, ~ (mand @ X0 @ X1 @ X2) => 115.55/15.17 ((((X0 @ X2) & (X1 @ X2))) != ($true))). 115.55/15.17 thf('6', plain, 115.55/15.17 (![X0:( mworld > $o ),X1:( mworld > $o ),X2:mworld]: 115.55/15.17 ( ( ~( mand @ X0 @ X1 @ X2 ) ) <=> ( ~( ( X0 @ X2 ) & ( X1 @ X2 ) ) ) )), 115.55/15.17 inference('rw.lit', [status(esa)], [mand_def])). 115.55/15.17 thf(zip_derived_cl104, plain, 115.55/15.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.17 (~ (((mbox @ 115.55/15.17 (mand @ (userid @ u @ X1) @ 115.55/15.17 (mand @ (entry_box @ X2) @ (number @ X2 @ one))) @ 115.55/15.17 '#sk5') & (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mimplies @ (do @ X3 @ X0 @ Y0) @ (in @ X1 @ X2 @ Y0)))) @ 115.55/15.17 '#sk5'))) 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X3 @ '#sk5'))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl103, '6'])). 115.55/15.17 thf(zip_derived_cl105, plain, 115.55/15.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.17 (~ (mbox @ 115.55/15.17 (mand @ (userid @ u @ X1) @ 115.55/15.17 (mand @ (entry_box @ X2) @ (number @ X2 @ one))) @ 115.55/15.17 '#sk5') 115.55/15.17 | ~ (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mimplies @ (do @ X3 @ X0 @ Y0) @ (in @ X1 @ X2 @ Y0)))) @ 115.55/15.17 '#sk5') 115.55/15.17 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5'))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl104])). 115.55/15.17 thf(zip_derived_cl106, plain, 115.55/15.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.17 (~ (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((mrel @ '#sk5' @ Y0) => (mand @ (userid @ u @ X1) @ 115.55/15.17 (mand @ (entry_box @ X2) @ (number @ X2 @ one)) @ Y0)))))) 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.17 | ~ (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mimplies @ (do @ X3 @ X0 @ Y0) @ (in @ X1 @ X2 @ Y0)))) @ 115.55/15.17 '#sk5'))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl105, '4'])). 115.55/15.17 thf(zip_derived_cl107, plain, 115.55/15.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.17 (~ (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((mrel @ '#sk5' @ Y0) => (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mimplies @ (do @ X0 @ X3 @ Y1) @ 115.55/15.17 (in @ X2 @ X1 @ Y1))) @ 115.55/15.17 Y0)))))) 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.17 | ~ (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((mrel @ '#sk5' @ Y0) => (mand @ 115.55/15.17 (userid @ u @ X2) @ 115.55/15.17 (mand @ (entry_box @ X1) @ (number @ X1 @ one)) @ 115.55/15.17 Y0)))))))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl106, '4'])). 115.55/15.17 thf(zip_derived_cl108, plain, 115.55/15.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.17 (~ (((mrel @ '#sk5' @ ('#sk6' @ X0 @ X1 @ X2 @ X3)) => (mforall_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mimplies @ (do @ X0 @ X3 @ Y0) @ (in @ X2 @ X1 @ Y0))) @ 115.55/15.17 ('#sk6' @ X0 @ X1 @ X2 @ X3)))) 115.55/15.17 | ~ (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((mrel @ '#sk5' @ Y0) => (mand @ 115.55/15.17 (userid @ u @ X2) @ 115.55/15.17 (mand @ (entry_box @ X1) @ (number @ X1 @ one)) @ 115.55/15.17 Y0)))))) 115.55/15.17 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5'))), 115.55/15.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl107])). 115.55/15.17 thf(zip_derived_cl109, plain, 115.55/15.17 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.17 ( (mrel @ '#sk5' @ ('#sk6' @ X0 @ X1 @ X2 @ X3)) 115.55/15.17 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.17 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.17 | ~ (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((mrel @ '#sk5' @ Y0) => (mand @ 115.55/15.17 (userid @ u @ X2) @ 115.55/15.17 (mand @ (entry_box @ X1) @ (number @ X1 @ one)) @ 115.55/15.17 Y0)))))))), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 115.55/15.17 thf(zip_derived_cl111, plain, 115.55/15.17 (![X1 : $i, X2 : $i]: 115.55/15.17 ( ('#form7' @ X1 @ X2) 115.55/15.17 | ~ (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((mrel @ '#sk5' @ Y0) => (mand @ 115.55/15.17 (userid @ u @ X2) @ 115.55/15.17 (mand @ (entry_box @ X1) @ (number @ X1 @ one)) @ 115.55/15.17 Y0)))))))), 115.55/15.17 define([status(thm)])). 115.55/15.17 thf(zip_derived_cl112, plain, 115.55/15.17 (![X1 : $i, X2 : $i]: 115.55/15.17 (~ (((mrel @ '#sk5' @ ('#sk8' @ X1 @ X2)) => (mand @ 115.55/15.17 (userid @ u @ X2) @ 115.55/15.17 (mand @ (entry_box @ X1) @ (number @ X1 @ one)) @ 115.55/15.17 ('#sk8' @ X1 @ X2)))) 115.55/15.17 | ('#form7' @ X1 @ X2))), 115.55/15.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl111])). 115.55/15.17 thf(zip_derived_cl116, plain, 115.55/15.17 (![X1 : $i, X2 : $i]: 115.55/15.17 (~ (mand @ (userid @ u @ X2) @ 115.55/15.17 (mand @ (entry_box @ X1) @ (number @ X1 @ one)) @ 115.55/15.17 ('#sk8' @ X1 @ X2)) 115.55/15.17 | ('#form7' @ X1 @ X2))), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl112])). 115.55/15.17 thf(zip_derived_cl118, plain, 115.55/15.17 (![X0 : $i, X1 : $i]: 115.55/15.17 (~ (((userid @ u @ X0 @ ('#sk8' @ X1 @ X0)) & (mand @ 115.55/15.17 (entry_box @ X1) @ (number @ X1 @ one) @ ('#sk8' @ X1 @ X0)))) 115.55/15.17 | ('#form7' @ X1 @ X0))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl116, '6'])). 115.55/15.17 thf(zip_derived_cl121, plain, 115.55/15.17 (![X0 : $i, X1 : $i]: 115.55/15.17 (~ (userid @ u @ X0 @ ('#sk8' @ X1 @ X0)) 115.55/15.17 | ~ (mand @ (entry_box @ X1) @ (number @ X1 @ one) @ 115.55/15.17 ('#sk8' @ X1 @ X0)) 115.55/15.17 | ('#form7' @ X1 @ X0))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl118])). 115.55/15.17 thf(zip_derived_cl124, plain, 115.55/15.17 (![X0 : $i, X1 : $i]: 115.55/15.17 (~ (((entry_box @ X1 @ ('#sk8' @ X1 @ X0)) & (number @ X1 @ one @ 115.55/15.17 ('#sk8' @ X1 @ X0)))) 115.55/15.17 | ('#form7' @ X1 @ X0) 115.55/15.17 | ~ (userid @ u @ X0 @ ('#sk8' @ X1 @ X0)))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl121, '6'])). 115.55/15.17 thf(zip_derived_cl126, plain, 115.55/15.17 (![X0 : $i, X1 : $i]: 115.55/15.17 (~ (entry_box @ X1 @ ('#sk8' @ X1 @ X0)) 115.55/15.17 | ~ (number @ X1 @ one @ ('#sk8' @ X1 @ X0)) 115.55/15.17 | ~ (userid @ u @ X0 @ ('#sk8' @ X1 @ X0)) 115.55/15.17 | ('#form7' @ X1 @ X0))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl124])). 115.55/15.17 thf(zip_derived_cl37, plain, 115.55/15.17 (![X0 : mworld, X1 : mworld]: 115.55/15.17 ( (userid @ u @ ('#sk3' @ X0) @ X1) 115.55/15.17 | ~ (mrel @ X0 @ X1) 115.55/15.17 | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl35])). 115.55/15.17 thf(zip_derived_cl754, plain, 115.55/15.17 (![X0 : mworld, X1 : $i]: 115.55/15.17 ( ('#form7' @ X1 @ ('#sk3' @ X0)) 115.55/15.17 | ~ (number @ X1 @ one @ ('#sk8' @ X1 @ ('#sk3' @ X0))) 115.55/15.17 | ~ (entry_box @ X1 @ ('#sk8' @ X1 @ ('#sk3' @ X0))) 115.55/15.17 | ~ (mrel @ mactual @ X0) 115.55/15.17 | ~ (mrel @ X0 @ ('#sk8' @ X1 @ ('#sk3' @ X0))))), 115.55/15.17 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl37])). 115.55/15.17 thf(zip_derived_cl30, plain, 115.55/15.17 (![X0 : mworld]: 115.55/15.17 ( (eiw_di @ ('#sk3' @ X0) @ X0) | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl29])). 115.55/15.17 thf(zip_derived_cl86, plain, ( (mrel @ mactual @ '#sk5')), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl85])). 115.55/15.17 thf(zip_derived_cl42, plain, 115.55/15.17 (![X2 : mworld, X4 : mworld, X6 : mworld]: 115.55/15.17 (~ (mrel @ X2 @ X4) | ~ (mrel @ X2 @ X6) | (mrel @ X6 @ X4))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl41])). 115.55/15.17 thf(zip_derived_cl8, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 115.55/15.17 thf(zip_derived_cl136, plain, 115.55/15.17 (![X0 : mworld, X1 : mworld]: ( (mrel @ X1 @ X0) | ~ (mrel @ X0 @ X1))), 115.55/15.17 inference('sup+', [status(thm)], [zip_derived_cl42, zip_derived_cl8])). 115.55/15.17 thf(zip_derived_cl42, plain, 115.55/15.17 (![X2 : mworld, X4 : mworld, X6 : mworld]: 115.55/15.17 (~ (mrel @ X2 @ X4) | ~ (mrel @ X2 @ X6) | (mrel @ X6 @ X4))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl41])). 115.55/15.17 thf(zip_derived_cl196, plain, 115.55/15.17 (![X0 : mworld, X1 : mworld, X2 : mworld]: 115.55/15.17 (~ (mrel @ X0 @ X1) | (mrel @ X0 @ X2) | ~ (mrel @ X1 @ X2))), 115.55/15.17 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl42])). 115.55/15.17 thf(zip_derived_cl115, plain, 115.55/15.17 (![X1 : $i, X2 : $i]: 115.55/15.17 ( (mrel @ '#sk5' @ ('#sk8' @ X1 @ X2)) | ('#form7' @ X1 @ X2))), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl112])). 115.55/15.17 thf(zip_derived_cl42, plain, 115.55/15.17 (![X2 : mworld, X4 : mworld, X6 : mworld]: 115.55/15.17 (~ (mrel @ X2 @ X4) | ~ (mrel @ X2 @ X6) | (mrel @ X6 @ X4))), 115.55/15.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl41])). 115.55/15.17 thf(zip_derived_cl619, plain, 115.55/15.17 (![X0 : $i, X1 : $i, X2 : mworld]: 115.55/15.17 ( ('#form7' @ X1 @ X0) 115.55/15.17 | (mrel @ X2 @ ('#sk8' @ X1 @ X0)) 115.55/15.17 | ~ (mrel @ '#sk5' @ X2))), 115.55/15.17 inference('sup-', [status(thm)], [zip_derived_cl115, zip_derived_cl42])). 115.55/15.17 thf(ax3, axiom, 115.55/15.17 (mlocal @ 115.55/15.17 ( mbox @ 115.55/15.17 ( mforall_di @ 115.55/15.17 ( ^[S:$i]: 115.55/15.17 ( mforall_di @ 115.55/15.17 ( ^[I:$i]: 115.55/15.17 ( mforall_di @ 115.55/15.17 ( ^[B:$i]: 115.55/15.17 ( mimplies @ 115.55/15.17 ( mand @ ( string @ I ) @ ( entry_box @ B ) ) @ 115.55/15.17 ( mexists_di @ 115.55/15.17 ( ^[A:$i]: 115.55/15.17 ( mbox @ 115.55/15.17 ( mforall_di @ 115.55/15.17 ( ^[S2:$i]: 115.55/15.17 ( mimplies @ 115.55/15.17 ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 115.55/15.17 thf(zip_derived_cl7, plain, 115.55/15.17 ( (mlocal @ 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mimplies @ (mand @ (string @ Y1) @ (entry_box @ Y2)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mimplies @ (do @ Y0 @ Y3 @ Y4) @ 115.55/15.17 (in @ Y1 @ Y2 @ Y4))))))))))))))))), 115.55/15.17 inference('cnf', [status(esa)], [ax3])). 115.55/15.17 thf(zip_derived_cl48, plain, 115.55/15.17 ( (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mimplies @ (mand @ (string @ Y1) @ (entry_box @ Y2)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mimplies @ (do @ Y0 @ Y3 @ Y4) @ 115.55/15.17 (in @ Y1 @ Y2 @ Y4)))))))))))))) @ 115.55/15.17 mactual)), 115.55/15.17 inference('rw', [status(thm)], [zip_derived_cl7, '0'])). 115.55/15.17 thf(zip_derived_cl49, plain, 115.55/15.17 ( (((!!) @ (^[Y0 : mworld]: 115.55/15.17 (((mrel @ mactual @ Y0) => (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mimplies @ 115.55/15.17 (mand @ (string @ Y2) @ (entry_box @ Y3)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y5 : $i]: 115.55/15.17 (mimplies @ (do @ Y1 @ Y4 @ Y5) @ 115.55/15.17 (in @ Y2 @ Y3 @ Y5))))))))))))) @ 115.55/15.17 Y0))))))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl48, '2'])). 115.55/15.17 thf(zip_derived_cl50, plain, 115.55/15.17 (![X2 : mworld]: 115.55/15.17 (((mrel @ mactual @ X2) => (mforall_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mimplies @ (mand @ (string @ Y1) @ (entry_box @ Y2)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mimplies @ (do @ Y0 @ Y3 @ Y4) @ 115.55/15.17 (in @ Y1 @ Y2 @ Y4))))))))))))) @ 115.55/15.17 X2)))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl49])). 115.55/15.17 thf(zip_derived_cl51, plain, 115.55/15.17 (![X2 : mworld]: 115.55/15.17 (~ (mrel @ mactual @ X2) 115.55/15.17 | (mforall_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mimplies @ 115.55/15.17 (mand @ (string @ Y1) @ (entry_box @ Y2)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mimplies @ (do @ Y0 @ Y3 @ Y4) @ 115.55/15.17 (in @ Y1 @ Y2 @ Y4))))))))))))) @ 115.55/15.17 X2))), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])). 115.55/15.17 thf(mforall_di_def, axiom, (mforall_di @ X0 @ X1) => 115.55/15.17 ((((!!) @ (^[Y0 : $i]: (((eiw_di @ Y0 @ X1) => (X0 @ Y0 @ X1)))))) = 115.55/15.17 ($true))). 115.55/15.17 thf('7', plain, 115.55/15.17 (![X0:( $i > mworld > $o ),X1:mworld]: 115.55/15.17 ( ( mforall_di @ X0 @ X1 ) <=> 115.55/15.17 ( ![X6:$i]: ( ( eiw_di @ X6 @ X1 ) => ( X0 @ X6 @ X1 ) ) ) )), 115.55/15.17 inference('rw.lit', [status(esa)], [mforall_di_def])). 115.55/15.17 thf(zip_derived_cl52, plain, 115.55/15.17 (![X0 : mworld]: 115.55/15.17 ( (((!!) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ X0) => 115.55/15.17 ((^[Y1 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mimplies @ 115.55/15.17 (mand @ (string @ Y2) @ (entry_box @ Y3)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y5 : $i]: 115.55/15.17 (mimplies @ 115.55/15.17 (do @ Y1 @ Y4 @ Y5) @ 115.55/15.17 (in @ Y2 @ Y3 @ Y5))))))))))))) @ 115.55/15.17 Y0 @ X0)))))) 115.55/15.17 | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl51, '7'])). 115.55/15.17 thf(zip_derived_cl53, plain, 115.55/15.17 (![X0 : mworld]: 115.55/15.17 ( (((!!) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ X0) => (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mimplies @ 115.55/15.17 (mand @ (string @ Y1) @ (entry_box @ Y2)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mimplies @ (do @ Y0 @ Y3 @ Y4) @ 115.55/15.17 (in @ Y1 @ Y2 @ Y4))))))))))) @ 115.55/15.17 X0)))))) 115.55/15.17 | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('ho_norm', [status(thm)], [zip_derived_cl52])). 115.55/15.17 thf(zip_derived_cl54, plain, 115.55/15.17 (![X0 : mworld, X2 : $i]: 115.55/15.17 ( (((eiw_di @ X2 @ X0) => (mforall_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mimplies @ (mand @ (string @ Y0) @ (entry_box @ Y1)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mimplies @ (do @ X2 @ Y2 @ Y3) @ 115.55/15.17 (in @ Y0 @ Y1 @ Y3))))))))))) @ 115.55/15.17 X0))) 115.55/15.17 | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl53])). 115.55/15.17 thf(zip_derived_cl55, plain, 115.55/15.17 (![X0 : mworld, X2 : $i]: 115.55/15.17 (~ (eiw_di @ X2 @ X0) 115.55/15.17 | (mforall_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mimplies @ (mand @ (string @ Y0) @ (entry_box @ Y1)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mimplies @ (do @ X2 @ Y2 @ Y3) @ 115.55/15.17 (in @ Y0 @ Y1 @ Y3))))))))))) @ 115.55/15.17 X0) 115.55/15.17 | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl54])). 115.55/15.17 thf(zip_derived_cl56, plain, 115.55/15.17 (![X0 : mworld, X1 : $i]: 115.55/15.17 ( (((!!) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ X0) => 115.55/15.17 ((^[Y1 : $i]: 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mimplies @ 115.55/15.17 (mand @ (string @ Y1) @ (entry_box @ Y2)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y4 : $i]: 115.55/15.17 (mimplies @ (do @ X1 @ Y3 @ Y4) @ 115.55/15.17 (in @ Y1 @ Y2 @ Y4))))))))))) @ 115.55/15.17 Y0 @ X0)))))) 115.55/15.17 | ~ (mrel @ mactual @ X0) 115.55/15.17 | ~ (eiw_di @ X1 @ X0))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl55, '7'])). 115.55/15.17 thf(zip_derived_cl57, plain, 115.55/15.17 (![X0 : mworld, X1 : $i]: 115.55/15.17 ( (((!!) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ X0) => (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mimplies @ 115.55/15.17 (mand @ (string @ Y0) @ (entry_box @ Y1)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mimplies @ (do @ X1 @ Y2 @ Y3) @ 115.55/15.17 (in @ Y0 @ Y1 @ Y3))))))))) @ 115.55/15.17 X0)))))) 115.55/15.17 | ~ (mrel @ mactual @ X0) 115.55/15.17 | ~ (eiw_di @ X1 @ X0))), 115.55/15.17 inference('ho_norm', [status(thm)], [zip_derived_cl56])). 115.55/15.17 thf(zip_derived_cl58, plain, 115.55/15.17 (![X0 : mworld, X1 : $i, X3 : $i]: 115.55/15.17 ( (((eiw_di @ X3 @ X0) => (mforall_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mimplies @ (mand @ (string @ X3) @ (entry_box @ Y0)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mimplies @ (do @ X1 @ Y1 @ Y2) @ (in @ X3 @ Y0 @ Y2))))))))) @ 115.55/15.17 X0))) 115.55/15.17 | ~ (eiw_di @ X1 @ X0) 115.55/15.17 | ~ (mrel @ mactual @ X0))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl57])). 115.55/15.17 thf(zip_derived_cl59, plain, 115.55/15.17 (![X0 : mworld, X1 : $i, X3 : $i]: 115.55/15.17 (~ (eiw_di @ X3 @ X0) 115.55/15.17 | (mforall_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mimplies @ (mand @ (string @ X3) @ (entry_box @ Y0)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mimplies @ (do @ X1 @ Y1 @ Y2) @ 115.55/15.17 (in @ X3 @ Y0 @ Y2))))))))) @ 115.55/15.17 X0) 115.55/15.17 | ~ (mrel @ mactual @ X0) 115.55/15.17 | ~ (eiw_di @ X1 @ X0))), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 115.55/15.17 thf(zip_derived_cl60, plain, 115.55/15.17 (![X0 : mworld, X1 : $i, X2 : $i]: 115.55/15.17 ( (((!!) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ X0) => 115.55/15.17 ((^[Y1 : $i]: 115.55/15.17 (mimplies @ 115.55/15.17 (mand @ (string @ X2) @ (entry_box @ Y1)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y3 : $i]: 115.55/15.17 (mimplies @ (do @ X1 @ Y2 @ Y3) @ 115.55/15.17 (in @ X2 @ Y1 @ Y3))))))))) @ 115.55/15.17 Y0 @ X0)))))) 115.55/15.17 | ~ (eiw_di @ X1 @ X0) 115.55/15.17 | ~ (mrel @ mactual @ X0) 115.55/15.17 | ~ (eiw_di @ X2 @ X0))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl59, '7'])). 115.55/15.17 thf(zip_derived_cl61, plain, 115.55/15.17 (![X0 : mworld, X1 : $i, X2 : $i]: 115.55/15.17 ( (((!!) @ (^[Y0 : $i]: 115.55/15.17 (((eiw_di @ Y0 @ X0) => (mimplies @ 115.55/15.17 (mand @ (string @ X2) @ (entry_box @ Y0)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y2 : $i]: 115.55/15.17 (mimplies @ (do @ X1 @ Y1 @ Y2) @ 115.55/15.17 (in @ X2 @ Y0 @ Y2))))))) @ 115.55/15.17 X0)))))) 115.55/15.17 | ~ (eiw_di @ X1 @ X0) 115.55/15.17 | ~ (mrel @ mactual @ X0) 115.55/15.17 | ~ (eiw_di @ X2 @ X0))), 115.55/15.17 inference('ho_norm', [status(thm)], [zip_derived_cl60])). 115.55/15.17 thf(zip_derived_cl62, plain, 115.55/15.17 (![X0 : mworld, X1 : $i, X2 : $i, X4 : $i]: 115.55/15.17 ( (((eiw_di @ X4 @ X0) => (mimplies @ 115.55/15.17 (mand @ (string @ X2) @ (entry_box @ X4)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mimplies @ (do @ X1 @ Y0 @ Y1) @ (in @ X2 @ X4 @ Y1))))))) @ 115.55/15.17 X0))) 115.55/15.17 | ~ (eiw_di @ X2 @ X0) 115.55/15.17 | ~ (mrel @ mactual @ X0) 115.55/15.17 | ~ (eiw_di @ X1 @ X0))), 115.55/15.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl61])). 115.55/15.17 thf(zip_derived_cl63, plain, 115.55/15.17 (![X0 : mworld, X1 : $i, X2 : $i, X4 : $i]: 115.55/15.17 (~ (eiw_di @ X4 @ X0) 115.55/15.17 | (mimplies @ (mand @ (string @ X2) @ (entry_box @ X4)) @ 115.55/15.17 (mexists_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mimplies @ (do @ X1 @ Y0 @ Y1) @ (in @ X2 @ X4 @ Y1))))))) @ 115.55/15.17 X0) 115.55/15.17 | ~ (eiw_di @ X1 @ X0) 115.55/15.17 | ~ (mrel @ mactual @ X0) 115.55/15.17 | ~ (eiw_di @ X2 @ X0))), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 115.55/15.17 thf(mimplies_def, axiom, (mimplies @ X0 @ X1 @ X2) => 115.55/15.17 ((((X0 @ X2) => (X1 @ X2))) = ($true))). 115.55/15.17 thf('8', plain, 115.55/15.17 (![X0:( mworld > $o ),X1:( mworld > $o ),X2:mworld]: 115.55/15.17 ( ( mimplies @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) => ( X1 @ X2 ) ) )), 115.55/15.17 inference('rw.lit', [status(esa)], [mimplies_def])). 115.55/15.17 thf(zip_derived_cl64, plain, 115.55/15.17 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.17 ( (((mand @ (string @ X1) @ (entry_box @ X3) @ X0) => (mexists_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mimplies @ (do @ X2 @ Y0 @ Y1) @ (in @ X1 @ X3 @ Y1)))))) @ 115.55/15.17 X0))) 115.55/15.17 | ~ (eiw_di @ X1 @ X0) 115.55/15.17 | ~ (mrel @ mactual @ X0) 115.55/15.17 | ~ (eiw_di @ X2 @ X0) 115.55/15.17 | ~ (eiw_di @ X3 @ X0))), 115.55/15.17 inference('rw_clause', [status(thm)], [zip_derived_cl63, '8'])). 115.55/15.17 thf(zip_derived_cl65, plain, 115.55/15.17 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.17 (~ (mand @ (string @ X1) @ (entry_box @ X3) @ X0) 115.55/15.17 | (mexists_di @ 115.55/15.17 (^[Y0 : $i]: 115.55/15.17 (mbox @ 115.55/15.17 (mforall_di @ 115.55/15.17 (^[Y1 : $i]: 115.55/15.17 (mimplies @ (do @ X2 @ Y0 @ Y1) @ (in @ X1 @ X3 @ Y1)))))) @ 115.55/15.17 X0) 115.55/15.17 | ~ (eiw_di @ X3 @ X0) 115.55/15.17 | ~ (eiw_di @ X2 @ X0) 115.55/15.17 | ~ (mrel @ mactual @ X0) 115.55/15.17 | ~ (eiw_di @ X1 @ X0))), 115.55/15.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])). 115.55/15.17 thf(zip_derived_cl66, plain, 115.55/15.17 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.17 (~ (((string @ X1 @ X0) & (entry_box @ X3 @ X0))) 115.55/15.17 | ~ (eiw_di @ X1 @ X0) 115.55/15.17 | ~ (mrel @ mactual @ X0) 115.55/15.17 | ~ (eiw_di @ X2 @ X0) 115.55/15.17 | ~ (eiw_di @ X3 @ X0) 115.55/15.18 | (mexists_di @ 115.55/15.18 (^[Y0 : $i]: 115.55/15.18 (mbox @ 115.55/15.18 (mforall_di @ 115.55/15.18 (^[Y1 : $i]: 115.55/15.18 (mimplies @ (do @ X2 @ Y0 @ Y1) @ (in @ X1 @ X3 @ Y1)))))) @ 115.55/15.18 X0))), 115.55/15.18 inference('rw_clause', [status(thm)], [zip_derived_cl65, '6'])). 115.55/15.18 thf(zip_derived_cl67, plain, 115.55/15.18 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 ( (((??) @ (^[Y0 : $i]: 115.55/15.18 (((eiw_di @ Y0 @ X0) & 115.55/15.18 ((^[Y1 : $i]: 115.55/15.18 (mbox @ 115.55/15.18 (mforall_di @ 115.55/15.18 (^[Y2 : $i]: 115.55/15.18 (mimplies @ (do @ X2 @ Y1 @ Y2) @ 115.55/15.18 (in @ X3 @ X1 @ Y2)))))) @ 115.55/15.18 Y0 @ X0)))))) 115.55/15.18 | ~ (eiw_di @ X1 @ X0) 115.55/15.18 | ~ (eiw_di @ X2 @ X0) 115.55/15.18 | ~ (mrel @ mactual @ X0) 115.55/15.18 | ~ (eiw_di @ X3 @ X0) 115.55/15.18 | ~ (((string @ X3 @ X0) & (entry_box @ X1 @ X0))))), 115.55/15.18 inference('rw_clause', [status(thm)], [zip_derived_cl66, '1'])). 115.55/15.18 thf(zip_derived_cl68, plain, 115.55/15.18 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 ( (((??) @ (^[Y0 : $i]: 115.55/15.18 (((eiw_di @ Y0 @ X0) & (mbox @ 115.55/15.18 (mforall_di @ 115.55/15.18 (^[Y1 : $i]: 115.55/15.18 (mimplies @ (do @ X2 @ Y0 @ Y1) @ 115.55/15.18 (in @ X3 @ X1 @ Y1)))) @ 115.55/15.18 X0)))))) 115.55/15.18 | ~ (eiw_di @ X1 @ X0) 115.55/15.18 | ~ (eiw_di @ X2 @ X0) 115.55/15.18 | ~ (mrel @ mactual @ X0) 115.55/15.18 | ~ (eiw_di @ X3 @ X0) 115.55/15.18 | ~ (((string @ X3 @ X0) & (entry_box @ X1 @ X0))))), 115.55/15.18 inference('ho_norm', [status(thm)], [zip_derived_cl67])). 115.55/15.18 thf(zip_derived_cl69, plain, 115.55/15.18 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 ( (((eiw_di @ ('#sk4' @ X0 @ X1 @ X2 @ X3) @ X0) & (mbox @ 115.55/15.18 (mforall_di @ 115.55/15.18 (^[Y0 : $i]: 115.55/15.18 (mimplies @ (do @ X2 @ ('#sk4' @ X0 @ X1 @ X2 @ X3) @ Y0) @ 115.55/15.18 (in @ X3 @ X1 @ Y0)))) @ 115.55/15.18 X0))) 115.55/15.18 | ~ (((string @ X3 @ X0) & (entry_box @ X1 @ X0))) 115.55/15.18 | ~ (eiw_di @ X3 @ X0) 115.55/15.18 | ~ (mrel @ mactual @ X0) 115.55/15.18 | ~ (eiw_di @ X2 @ X0) 115.55/15.18 | ~ (eiw_di @ X1 @ X0))), 115.55/15.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl68])). 115.55/15.18 thf(zip_derived_cl70, plain, 115.55/15.18 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 ( (eiw_di @ ('#sk4' @ X0 @ X1 @ X2 @ X3) @ X0) 115.55/15.18 | ~ (eiw_di @ X1 @ X0) 115.55/15.18 | ~ (eiw_di @ X2 @ X0) 115.55/15.18 | ~ (mrel @ mactual @ X0) 115.55/15.18 | ~ (eiw_di @ X3 @ X0) 115.55/15.18 | ~ (((string @ X3 @ X0) & (entry_box @ X1 @ X0))))), 115.55/15.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 115.55/15.18 thf(zip_derived_cl72, plain, 115.55/15.18 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 (~ (string @ X3 @ X0) 115.55/15.18 | ~ (entry_box @ X1 @ X0) 115.55/15.18 | ~ (eiw_di @ X3 @ X0) 115.55/15.18 | ~ (mrel @ mactual @ X0) 115.55/15.18 | ~ (eiw_di @ X2 @ X0) 115.55/15.18 | ~ (eiw_di @ X1 @ X0) 115.55/15.18 | (eiw_di @ ('#sk4' @ X0 @ X1 @ X2 @ X3) @ X0))), 115.55/15.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl70])). 115.55/15.18 thf(zip_derived_cl47, plain, 115.55/15.18 (![X2 : mworld, X4 : mworld, X6 : $i]: 115.55/15.18 (~ (mrel @ X4 @ X2) | ~ (eiw_di @ X6 @ X2) | (eiw_di @ X6 @ X4))), 115.55/15.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 115.55/15.18 thf(zip_derived_cl306, plain, 115.55/15.18 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i, X4 : mworld]: 115.55/15.18 (~ (eiw_di @ X3 @ X0) 115.55/15.18 | ~ (eiw_di @ X2 @ X0) 115.55/15.18 | ~ (mrel @ mactual @ X0) 115.55/15.18 | ~ (eiw_di @ X1 @ X0) 115.55/15.18 | ~ (entry_box @ X3 @ X0) 115.55/15.18 | ~ (string @ X1 @ X0) 115.55/15.18 | (eiw_di @ ('#sk4' @ X0 @ X3 @ X2 @ X1) @ X4) 115.55/15.18 | ~ (mrel @ X4 @ X0))), 115.55/15.18 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl47])). 115.55/15.18 thf(zip_derived_cl109, plain, 115.55/15.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 ( (mrel @ '#sk5' @ ('#sk6' @ X0 @ X1 @ X2 @ X3)) 115.55/15.18 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.18 | ~ (((!!) @ (^[Y0 : mworld]: 115.55/15.18 (((mrel @ '#sk5' @ Y0) => (mand @ 115.55/15.18 (userid @ u @ X2) @ 115.55/15.18 (mand @ (entry_box @ X1) @ (number @ X1 @ one)) @ 115.55/15.18 Y0)))))))), 115.55/15.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 115.55/15.18 thf(zip_derived_cl111, plain, 115.55/15.18 (![X1 : $i, X2 : $i]: 115.55/15.18 ( ('#form7' @ X1 @ X2) 115.55/15.18 | ~ (((!!) @ (^[Y0 : mworld]: 115.55/15.18 (((mrel @ '#sk5' @ Y0) => (mand @ 115.55/15.18 (userid @ u @ X2) @ 115.55/15.18 (mand @ (entry_box @ X1) @ (number @ X1 @ one)) @ 115.55/15.18 Y0)))))))), 115.55/15.18 define([status(thm)])). 115.55/15.18 thf(zip_derived_cl113, plain, 115.55/15.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 (~ ('#form7' @ X1 @ X2) 115.55/15.18 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.18 | (mrel @ '#sk5' @ ('#sk6' @ X0 @ X1 @ X2 @ X3)))), 115.55/15.18 inference('renaming', [status(thm)], 115.55/15.18 [zip_derived_cl109, zip_derived_cl111])). 115.55/15.18 thf(zip_derived_cl110, plain, 115.55/15.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 (~ (mforall_di @ 115.55/15.18 (^[Y0 : $i]: 115.55/15.18 (mimplies @ (do @ X0 @ X3 @ Y0) @ (in @ X2 @ X1 @ Y0))) @ 115.55/15.18 ('#sk6' @ X0 @ X1 @ X2 @ X3)) 115.55/15.18 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.18 | ~ (((!!) @ (^[Y0 : mworld]: 115.55/15.18 (((mrel @ '#sk5' @ Y0) => (mand @ 115.55/15.18 (userid @ u @ X2) @ 115.55/15.18 (mand @ (entry_box @ X1) @ (number @ X1 @ one)) @ 115.55/15.18 Y0)))))))), 115.55/15.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 115.55/15.18 thf(zip_derived_cl111, plain, 115.55/15.18 (![X1 : $i, X2 : $i]: 115.55/15.18 ( ('#form7' @ X1 @ X2) 115.55/15.18 | ~ (((!!) @ (^[Y0 : mworld]: 115.55/15.18 (((mrel @ '#sk5' @ Y0) => (mand @ 115.55/15.18 (userid @ u @ X2) @ 115.55/15.18 (mand @ (entry_box @ X1) @ (number @ X1 @ one)) @ 115.55/15.18 Y0)))))))), 115.55/15.18 define([status(thm)])). 115.55/15.18 thf(zip_derived_cl114, plain, 115.55/15.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 (~ ('#form7' @ X1 @ X2) 115.55/15.18 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.18 | ~ (mforall_di @ 115.55/15.18 (^[Y0 : $i]: 115.55/15.18 (mimplies @ (do @ X0 @ X3 @ Y0) @ (in @ X2 @ X1 @ Y0))) @ 115.55/15.18 ('#sk6' @ X0 @ X1 @ X2 @ X3)))), 115.55/15.18 inference('renaming', [status(thm)], 115.55/15.18 [zip_derived_cl110, zip_derived_cl111])). 115.55/15.18 thf(mforall_di_def, axiom, ~ (mforall_di @ X0 @ X1) => 115.55/15.18 ((((!!) @ (^[Y0 : $i]: (((eiw_di @ Y0 @ X1) => (X0 @ Y0 @ X1)))))) != 115.55/15.18 ($true))). 115.55/15.18 thf('9', plain, 115.55/15.18 (![X0:( $i > mworld > $o ),X1:mworld]: 115.55/15.18 ( ( ~( mforall_di @ X0 @ X1 ) ) <=> 115.55/15.18 ( ~( ![X6:$i]: ( ( eiw_di @ X6 @ X1 ) => ( X0 @ X6 @ X1 ) ) ) ) )), 115.55/15.18 inference('rw.lit', [status(esa)], [mforall_di_def])). 115.55/15.18 thf(zip_derived_cl117, plain, 115.55/15.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 (~ (((!!) @ (^[Y0 : $i]: 115.55/15.18 (((eiw_di @ Y0 @ ('#sk6' @ X0 @ X1 @ X2 @ X3)) => 115.55/15.18 ((^[Y1 : $i]: 115.55/15.18 (mimplies @ (do @ X0 @ X3 @ Y1) @ 115.55/15.18 (in @ X2 @ X1 @ Y1))) @ 115.55/15.18 Y0 @ ('#sk6' @ X0 @ X1 @ X2 @ X3))))))) 115.55/15.18 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.18 | ~ ('#form7' @ X1 @ X2))), 115.55/15.18 inference('rw_clause', [status(thm)], [zip_derived_cl114, '9'])). 115.55/15.18 thf(zip_derived_cl119, plain, 115.55/15.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 (~ (((!!) @ (^[Y0 : $i]: 115.55/15.18 (((eiw_di @ Y0 @ ('#sk6' @ X0 @ X1 @ X2 @ X3)) => 115.55/15.18 (mimplies @ (do @ X0 @ X3 @ Y0) @ 115.55/15.18 (in @ X2 @ X1 @ Y0) @ ('#sk6' @ X0 @ X1 @ X2 @ X3))))))) 115.55/15.18 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.18 | ~ ('#form7' @ X1 @ X2))), 115.55/15.18 inference('ho_norm', [status(thm)], [zip_derived_cl117])). 115.55/15.18 thf(zip_derived_cl120, plain, 115.55/15.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 (~ (((eiw_di @ ('#sk9' @ X0 @ X1 @ X2 @ X3) @ 115.55/15.18 ('#sk6' @ X0 @ X1 @ X2 @ X3)) => (mimplies @ 115.55/15.18 (do @ X0 @ X3 @ ('#sk9' @ X0 @ X1 @ X2 @ X3)) @ 115.55/15.18 (in @ X2 @ X1 @ ('#sk9' @ X0 @ X1 @ X2 @ X3)) @ 115.55/15.18 ('#sk6' @ X0 @ X1 @ X2 @ X3)))) 115.55/15.18 | ~ ('#form7' @ X1 @ X2) 115.55/15.18 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X0 @ '#sk5'))), 115.55/15.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl119])). 115.55/15.18 thf(zip_derived_cl123, plain, 115.55/15.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 (~ (mimplies @ (do @ X0 @ X3 @ ('#sk9' @ X0 @ X1 @ X2 @ X3)) @ 115.55/15.18 (in @ X2 @ X1 @ ('#sk9' @ X0 @ X1 @ X2 @ X3)) @ 115.55/15.18 ('#sk6' @ X0 @ X1 @ X2 @ X3)) 115.55/15.18 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.18 | ~ ('#form7' @ X1 @ X2))), 115.55/15.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl120])). 115.55/15.18 thf(mimplies_def, axiom, ~ (mimplies @ X0 @ X1 @ X2) => 115.55/15.18 ((((X0 @ X2) => (X1 @ X2))) != ($true))). 115.55/15.18 thf('10', plain, 115.55/15.18 (![X0:( mworld > $o ),X1:( mworld > $o ),X2:mworld]: 115.55/15.18 ( ( ~( mimplies @ X0 @ X1 @ X2 ) ) <=> 115.55/15.18 ( ~( ( X0 @ X2 ) => ( X1 @ X2 ) ) ) )), 115.55/15.18 inference('rw.lit', [status(esa)], [mimplies_def])). 115.55/15.18 thf(zip_derived_cl125, plain, 115.55/15.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 (~ (((do @ X3 @ X2 @ ('#sk9' @ X3 @ X1 @ X0 @ X2) @ 115.55/15.18 ('#sk6' @ X3 @ X1 @ X0 @ X2)) => (in @ X0 @ X1 @ 115.55/15.18 ('#sk9' @ X3 @ X1 @ X0 @ X2) @ ('#sk6' @ X3 @ X1 @ X0 @ X2)))) 115.55/15.18 | ~ ('#form7' @ X1 @ X0) 115.55/15.18 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X3 @ '#sk5'))), 115.55/15.18 inference('rw_clause', [status(thm)], [zip_derived_cl123, '10'])). 115.55/15.18 thf(zip_derived_cl128, plain, 115.55/15.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 (~ (in @ X0 @ X1 @ ('#sk9' @ X3 @ X1 @ X0 @ X2) @ 115.55/15.18 ('#sk6' @ X3 @ X1 @ X0 @ X2)) 115.55/15.18 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.18 | ~ ('#form7' @ X1 @ X0))), 115.55/15.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])). 115.55/15.18 thf(zip_derived_cl8, plain, (![X2 : mworld]: (mrel @ X2 @ X2)), 115.55/15.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 115.55/15.18 thf(zip_derived_cl47, plain, 115.55/15.18 (![X2 : mworld, X4 : mworld, X6 : $i]: 115.55/15.18 (~ (mrel @ X4 @ X2) | ~ (eiw_di @ X6 @ X2) | (eiw_di @ X6 @ X4))), 115.55/15.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 115.55/15.18 thf(zip_derived_cl42, plain, 115.55/15.18 (![X2 : mworld, X4 : mworld, X6 : mworld]: 115.55/15.18 (~ (mrel @ X2 @ X4) | ~ (mrel @ X2 @ X6) | (mrel @ X6 @ X4))), 115.55/15.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl41])). 115.55/15.18 thf(zip_derived_cl270, plain, 115.55/15.18 (![X0 : mworld, X1 : mworld, X2 : mworld, X3 : $i]: 115.55/15.18 ( (eiw_di @ X3 @ X1) 115.55/15.18 | ~ (eiw_di @ X3 @ X0) 115.55/15.18 | ~ (mrel @ X2 @ X1) 115.55/15.18 | ~ (mrel @ X2 @ X0))), 115.55/15.18 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl42])). 115.55/15.18 thf(zip_derived_cl42, plain, 115.55/15.18 (![X2 : mworld, X4 : mworld, X6 : mworld]: 115.55/15.18 (~ (mrel @ X2 @ X4) | ~ (mrel @ X2 @ X6) | (mrel @ X6 @ X4))), 115.55/15.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl41])). 115.55/15.18 thf(zip_derived_cl86, plain, ( (mrel @ mactual @ '#sk5')), 115.55/15.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl85])). 115.55/15.18 thf(zip_derived_cl134, plain, 115.55/15.18 (![X0 : mworld]: ( (mrel @ X0 @ '#sk5') | ~ (mrel @ mactual @ X0))), 115.55/15.18 inference('sup+', [status(thm)], [zip_derived_cl42, zip_derived_cl86])). 115.55/15.18 thf(zip_derived_cl3733, plain, 115.55/15.18 (![X0 : mworld, X1 : mworld, X2 : $i]: 115.55/15.18 (~ (mrel @ X0 @ X1) 115.55/15.18 | ~ (eiw_di @ X2 @ X1) 115.55/15.18 | (eiw_di @ X2 @ '#sk5') 115.55/15.18 | ~ (mrel @ mactual @ X0))), 115.55/15.18 inference('sup+', [status(thm)], [zip_derived_cl270, zip_derived_cl134])). 115.55/15.18 thf(zip_derived_cl122, plain, 115.55/15.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 ( (eiw_di @ ('#sk9' @ X0 @ X1 @ X2 @ X3) @ 115.55/15.18 ('#sk6' @ X0 @ X1 @ X2 @ X3)) 115.55/15.18 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.18 | ~ ('#form7' @ X1 @ X2))), 115.55/15.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl120])). 115.55/15.18 thf(zip_derived_cl127, plain, 115.55/15.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 ( (do @ X3 @ X2 @ ('#sk9' @ X3 @ X1 @ X0 @ X2) @ 115.55/15.18 ('#sk6' @ X3 @ X1 @ X0 @ X2)) 115.55/15.18 | ~ (eiw_di @ X3 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X0 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X2 @ '#sk5') 115.55/15.18 | ~ ('#form7' @ X1 @ X0))), 115.55/15.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])). 115.55/15.18 thf(zip_derived_cl71, plain, 115.55/15.18 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 ( (mbox @ 115.55/15.18 (mforall_di @ 115.55/15.18 (^[Y0 : $i]: 115.55/15.18 (mimplies @ (do @ X2 @ ('#sk4' @ X0 @ X1 @ X2 @ X3) @ Y0) @ 115.55/15.18 (in @ X3 @ X1 @ Y0)))) @ 115.55/15.18 X0) 115.55/15.18 | ~ (eiw_di @ X1 @ X0) 115.55/15.18 | ~ (eiw_di @ X2 @ X0) 115.55/15.18 | ~ (mrel @ mactual @ X0) 115.55/15.18 | ~ (eiw_di @ X3 @ X0) 115.55/15.18 | ~ (((string @ X3 @ X0) & (entry_box @ X1 @ X0))))), 115.55/15.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 115.55/15.18 thf(zip_derived_cl73, plain, 115.55/15.18 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i]: 115.55/15.18 ( (((!!) @ (^[Y0 : mworld]: 115.55/15.18 (((mrel @ X0 @ Y0) => (mforall_di @ 115.55/15.18 (^[Y1 : $i]: 115.55/15.18 (mimplies @ 115.55/15.18 (do @ X3 @ ('#sk4' @ X0 @ X1 @ X3 @ X2) @ Y1) @ 115.55/15.18 (in @ X2 @ X1 @ Y1))) @ 115.55/15.18 Y0)))))) 115.55/15.18 | ~ (((string @ X2 @ X0) & (entry_box @ X1 @ X0))) 115.55/15.18 | ~ (eiw_di @ X2 @ X0) 115.55/15.18 | ~ (mrel @ mactual @ X0) 115.55/15.18 | ~ (eiw_di @ X3 @ X0) 115.55/15.18 | ~ (eiw_di @ X1 @ X0))), 115.55/15.18 inference('rw_clause', [status(thm)], [zip_derived_cl71, '2'])). 115.55/15.18 thf(zip_derived_cl74, plain, 115.55/15.18 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i, X5 : mworld]: 115.55/15.18 ( (((mrel @ X0 @ X5) => (mforall_di @ 115.55/15.18 (^[Y0 : $i]: 115.55/15.18 (mimplies @ (do @ X3 @ ('#sk4' @ X0 @ X1 @ X3 @ X2) @ Y0) @ 115.55/15.18 (in @ X2 @ X1 @ Y0))) @ 115.55/15.18 X5))) 115.55/15.18 | ~ (eiw_di @ X1 @ X0) 115.55/15.18 | ~ (eiw_di @ X3 @ X0) 115.55/15.18 | ~ (mrel @ mactual @ X0) 115.55/15.18 | ~ (eiw_di @ X2 @ X0) 115.55/15.18 | ~ (((string @ X2 @ X0) & (entry_box @ X1 @ X0))))), 115.55/15.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl73])). 115.55/15.18 thf(zip_derived_cl75, plain, 115.55/15.18 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i, X5 : mworld]: 115.55/15.18 (~ (mrel @ X0 @ X5) 115.55/15.18 | (mforall_di @ 115.55/15.18 (^[Y0 : $i]: 115.55/15.18 (mimplies @ (do @ X3 @ ('#sk4' @ X0 @ X1 @ X3 @ X2) @ Y0) @ 115.55/15.18 (in @ X2 @ X1 @ Y0))) @ 115.55/15.18 X5) 115.55/15.18 | ~ (((string @ X2 @ X0) & (entry_box @ X1 @ X0))) 115.55/15.18 | ~ (eiw_di @ X2 @ X0) 115.55/15.18 | ~ (mrel @ mactual @ X0) 115.55/15.18 | ~ (eiw_di @ X3 @ X0) 115.55/15.18 | ~ (eiw_di @ X1 @ X0))), 115.55/15.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 115.55/15.18 thf(zip_derived_cl76, plain, 115.55/15.18 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i, X4 : mworld]: 115.55/15.18 ( (((!!) @ (^[Y0 : $i]: 115.55/15.18 (((eiw_di @ Y0 @ X4) => 115.55/15.18 ((^[Y1 : $i]: 115.55/15.18 (mimplies @ 115.55/15.18 (do @ X2 @ ('#sk4' @ X0 @ X1 @ X2 @ X3) @ Y1) @ 115.55/15.18 (in @ X3 @ X1 @ Y1))) @ 115.55/15.18 Y0 @ X4)))))) 115.55/15.18 | ~ (eiw_di @ X1 @ X0) 115.55/15.18 | ~ (eiw_di @ X2 @ X0) 115.55/15.18 | ~ (mrel @ mactual @ X0) 115.55/15.18 | ~ (eiw_di @ X3 @ X0) 115.55/15.18 | ~ (((string @ X3 @ X0) & (entry_box @ X1 @ X0))) 115.55/15.18 | ~ (mrel @ X0 @ X4))), 115.55/15.18 inference('rw_clause', [status(thm)], [zip_derived_cl75, '7'])). 115.55/15.18 thf(zip_derived_cl77, plain, 115.55/15.18 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i, X4 : mworld]: 115.55/15.18 ( (((!!) @ (^[Y0 : $i]: 115.55/15.18 (((eiw_di @ Y0 @ X4) => (mimplies @ 115.55/15.18 (do @ X2 @ ('#sk4' @ X0 @ X1 @ X2 @ X3) @ Y0) @ 115.55/15.18 (in @ X3 @ X1 @ Y0) @ X4)))))) 115.55/15.18 | ~ (eiw_di @ X1 @ X0) 115.55/15.18 | ~ (eiw_di @ X2 @ X0) 115.55/15.18 | ~ (mrel @ mactual @ X0) 115.55/15.18 | ~ (eiw_di @ X3 @ X0) 115.55/15.18 | ~ (((string @ X3 @ X0) & (entry_box @ X1 @ X0))) 115.55/15.18 | ~ (mrel @ X0 @ X4))), 115.55/15.18 inference('ho_norm', [status(thm)], [zip_derived_cl76])). 115.55/15.18 thf(zip_derived_cl78, plain, 115.55/15.18 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i, X4 : mworld, X6 : $i]: 115.55/15.18 ( (((eiw_di @ X6 @ X4) => (mimplies @ 115.55/15.18 (do @ X2 @ ('#sk4' @ X0 @ X1 @ X2 @ X3) @ X6) @ 115.55/15.18 (in @ X3 @ X1 @ X6) @ X4))) 115.55/15.18 | ~ (mrel @ X0 @ X4) 115.55/15.18 | ~ (((string @ X3 @ X0) & (entry_box @ X1 @ X0))) 115.55/15.18 | ~ (eiw_di @ X3 @ X0) 115.55/15.18 | ~ (mrel @ mactual @ X0) 115.55/15.18 | ~ (eiw_di @ X2 @ X0) 115.55/15.18 | ~ (eiw_di @ X1 @ X0))), 115.55/15.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl77])). 115.55/15.18 thf(zip_derived_cl79, plain, 115.55/15.18 (![X0 : mworld, X1 : $i, X2 : $i, X3 : $i, X4 : mworld, X6 : $i]: 115.55/15.18 (~ (eiw_di @ X6 @ X4) 115.55/15.18 | (mimplies @ (do @ X2 @ ('#sk4' @ X0 @ X1 @ X2 @ X3) @ X6) @ 115.55/15.18 (in @ X3 @ X1 @ X6) @ X4) 115.55/15.18 | ~ (eiw_di @ X1 @ X0) 115.55/15.18 | ~ (eiw_di @ X2 @ X0) 115.55/15.18 | ~ (mrel @ mactual @ X0) 115.55/15.18 | ~ (eiw_di @ X3 @ X0) 115.55/15.18 | ~ (((string @ X3 @ X0) & (entry_box @ X1 @ X0))) 115.55/15.18 | ~ (mrel @ X0 @ X4))), 115.55/15.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 115.55/15.18 thf(zip_derived_cl80, plain, 115.55/15.18 (![X0 : mworld, X1 : mworld, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 115.55/15.18 ( (((do @ X4 @ ('#sk4' @ X1 @ X2 @ X4 @ X3) @ X5 @ X0) => (in @ X3 @ 115.55/15.18 X2 @ X5 @ X0))) 115.55/15.18 | ~ (mrel @ X1 @ X0) 115.55/15.18 | ~ (((string @ X3 @ X1) & (entry_box @ X2 @ X1))) 115.55/15.18 | ~ (eiw_di @ X3 @ X1) 115.55/15.18 | ~ (mrel @ mactual @ X1) 115.55/15.18 | ~ (eiw_di @ X4 @ X1) 115.55/15.18 | ~ (eiw_di @ X2 @ X1) 115.55/15.18 | ~ (eiw_di @ X5 @ X0))), 115.55/15.18 inference('rw_clause', [status(thm)], [zip_derived_cl79, '8'])). 115.55/15.18 thf(zip_derived_cl81, plain, 115.55/15.18 (![X0 : mworld, X1 : mworld, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 115.55/15.18 (~ (do @ X4 @ ('#sk4' @ X1 @ X2 @ X4 @ X3) @ X5 @ X0) 115.55/15.18 | (in @ X3 @ X2 @ X5 @ X0) 115.55/15.18 | ~ (eiw_di @ X5 @ X0) 115.55/15.18 | ~ (eiw_di @ X2 @ X1) 115.55/15.18 | ~ (eiw_di @ X4 @ X1) 115.55/15.18 | ~ (mrel @ mactual @ X1) 115.55/15.18 | ~ (eiw_di @ X3 @ X1) 115.55/15.18 | ~ (((string @ X3 @ X1) & (entry_box @ X2 @ X1))) 115.55/15.18 | ~ (mrel @ X1 @ X0))), 115.55/15.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])). 115.55/15.18 thf(zip_derived_cl82, plain, 115.55/15.18 (![X0 : mworld, X1 : mworld, X2 : $i, X3 : $i, X4 : $i, X5 : $i]: 115.55/15.18 (~ (string @ X3 @ X1) 115.55/15.18 | ~ (entry_box @ X2 @ X1) 115.55/15.18 | ~ (mrel @ X1 @ X0) 115.55/15.18 | ~ (eiw_di @ X3 @ X1) 115.55/15.18 | ~ (mrel @ mactual @ X1) 115.55/15.18 | ~ (eiw_di @ X4 @ X1) 115.55/15.18 | ~ (eiw_di @ X2 @ X1) 115.55/15.18 | ~ (eiw_di @ X5 @ X0) 115.55/15.18 | (in @ X3 @ X2 @ X5 @ X0) 115.55/15.18 | ~ (do @ X4 @ ('#sk4' @ X1 @ X2 @ X4 @ X3) @ X5 @ X0))), 115.55/15.18 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl81])). 115.55/15.18 thf(zip_derived_cl758, plain, 115.55/15.18 (![X0 : $i, X1 : $i, X2 : $i, X3 : mworld, X4 : $i, X5 : $i]: 115.55/15.18 (~ ('#form7' @ X5 @ X4) 115.55/15.18 | ~ (eiw_di @ ('#sk4' @ X3 @ X2 @ X1 @ X0) @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X4 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X5 @ '#sk5') 115.55/15.18 | ~ (eiw_di @ X1 @ '#sk5') 115.55/15.18 | (in @ X0 @ X2 @ 115.55/15.18 ('#sk9' @ X1 @ X5 @ X4 @ ('#sk4' @ X3 @ X2 @ X1 @ X0)) @ 115.55/15.18 ('#sk6' @ X1 @ X5 @ X4 @ ('#sk4' @ X3 @ X2 @ X1 @ X0))) 115.55/15.18 | ~ (eiw_di @ 115.55/15.18 ('#sk9' @ X1 @ X5 @ X4 @ ('#sk4' @ X3 @ X2 @ X1 @ X0)) @ 115.55/15.18 ('#sk6' @ X1 @ X5 @ X4 @ ('#sk4' @ X3 @ X2 @ X1 @ X0))) 115.55/15.18 | ~ (eiw_di @ X2 @ X3) 115.55/15.18 | ~ (eiw_di @ X1 @ X3) 115.55/15.18 | ~ (mrel @ mactual @ X3) 115.55/15.18 | ~ (eiw_di @ X0 @ X3) 115.55/15.18 | ~ (mrel @ X3 @ 115.55/15.18 ('#sk6' @ X1 @ X5 @ X4 @ ('#sk4' @ X3 @ X2 @ X1 @ X0))) 115.55/15.18 | ~ (entry_box @ X2 @ X3) 115.55/15.18 | ~ (string @ X0 @ X3))), 115.55/15.18 inference('sup-', [status(thm)], [zip_derived_cl127, zip_derived_cl82])). 115.55/15.18 thf(zip_derived_cl34137, plain, ($false), 115.55/15.18 inference('eprover', [status(thm)], 115.55/15.18 [zip_derived_cl266, zip_derived_cl22, zip_derived_cl181, 115.55/15.18 zip_derived_cl36, zip_derived_cl42, zip_derived_cl21, 115.55/15.18 zip_derived_cl754, zip_derived_cl30, zip_derived_cl86, 115.55/15.18 zip_derived_cl196, zip_derived_cl619, zip_derived_cl306, 115.55/15.18 zip_derived_cl113, zip_derived_cl128, zip_derived_cl8, 115.55/15.18 zip_derived_cl3733, zip_derived_cl122, zip_derived_cl758])). 115.55/15.18 115.55/15.18 % SZS output end Refutation 115.55/15.18 115.55/15.18 115.55/15.18 % Terminating... 115.55/15.18 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s 116.12/15.36 % Runner terminated. 116.12/15.36 % Zipperpin 1.5 exiting 116.12/15.37 EOF