0.00/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.PxY5MYpGTp true 0.14/0.36 % Computer : n008.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 960 0.14/0.36 % WCLimit : 120 0.14/0.36 % DateTime : Tue Aug 9 07:03:39 EDT 2022 0.14/0.36 % CPUTime : 0.14/0.36 % Running portfolio for 960 s 0.14/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.36 % Number of cores: 8 0.14/0.36 % Python version: Python 3.6.8 0.14/0.37 % Running in HO mode 0.53/0.63 % Total configuration time : 828 0.53/0.63 % Estimated wc time : 1656 0.53/0.63 % Estimated cpu time (8 cpus) : 207.0 0.54/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.54/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.56/0.76 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.56/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 14.20/2.40 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 33.13/4.91 % Solved by lams/30_sp5.sh. 33.13/4.91 % done 181 iterations in 4.108s 33.13/4.91 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 33.13/4.91 % SZS output start Refutation 33.13/4.91 thf(emptyset_type, type, emptyset: $i). 33.13/4.91 thf(omega_type, type, omega: $i). 33.13/4.91 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 33.13/4.91 thf(in_type, type, in: $i > $i > $o). 33.13/4.91 thf('#sk51_type', type, '#sk51': $i). 33.13/4.91 thf('#sk52_type', type, '#sk52': $i). 33.13/4.91 thf(e_is_type, type, e_is: $i > $i > $i > $o). 33.13/4.91 thf(ap_type, type, ap: $i > $i > $i). 33.13/4.91 thf(nat_type, type, nat: $i). 33.13/4.91 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 33.13/4.91 thf('#sk50_type', type, '#sk50': $i). 33.13/4.91 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 33.13/4.91 thf(plus_type, type, plus: $i > $i). 33.13/4.91 thf(n_is_type, type, n_is: $i > $i > $o). 33.13/4.91 thf(n_pl_type, type, n_pl: $i > $i > $i). 33.13/4.91 thf(def_n_pl, axiom,(( n_pl ) = (^[X0:$i]: ( ap @ ( plus @ X0 ) )))). 33.13/4.91 thf('0', plain, (( n_pl ) = ( ^[X0:$i]: ( ap @ ( plus @ X0 ) ) )), 33.13/4.91 inference('simplify_rw_rule', [status(thm)], [def_n_pl])). 33.13/4.91 thf('1', plain, (( n_pl ) = ( ^[V_1:$i]: ( ap @ ( plus @ V_1 ) ) )), 33.13/4.91 define([status(thm)])).thf(def_n_is, axiom,(( n_is ) = (e_is @ nat))). 33.13/4.91 thf(def_nat, axiom,(( nat ) = 33.13/4.91 (d_Sep @ omega @ ( ^[X0:$i]: ( ( X0 ) != ( emptyset ) ) )))). 33.13/4.91 thf('2', plain, 33.13/4.91 (( nat ) = ( d_Sep @ omega @ ( ^[X0:$i]: ( ( X0 ) != ( emptyset ) ) ) )), 33.13/4.91 inference('simplify_rw_rule', [status(thm)], [def_nat])). 33.13/4.91 thf('3', plain, 33.13/4.91 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 33.13/4.91 define([status(thm)])). 33.13/4.91 thf('4', plain, (( n_is ) = ( e_is @ nat )), 33.13/4.91 inference('simplify_rw_rule', [status(thm)], [def_n_is, '3'])). 33.13/4.91 thf('5', plain, (( n_is ) = ( e_is @ nat )), define([status(thm)])). 33.13/4.91 thf(def_all_of, axiom,(( all_of ) = 33.13/4.91 (^[X0:( $i > $o ),X1:( $i > $o )]: 33.13/4.91 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) )))). 33.13/4.91 thf('6', plain, 33.13/4.91 (( all_of ) = 33.13/4.91 ( ^[X0:( $i > $o ),X1:( $i > $o )]: 33.13/4.91 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) ) )), 33.13/4.91 inference('simplify_rw_rule', [status(thm)], [def_all_of])). 33.13/4.91 thf('7', plain, 33.13/4.91 (( all_of ) = 33.13/4.91 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 33.13/4.91 ( ![X4:$i]: ( ( is_of @ X4 @ V_1 ) => ( V_2 @ X4 ) ) ) )), 33.13/4.91 define([status(thm)])). 33.13/4.91 thf(satz20e, conjecture, 33.13/4.91 (all_of @ 33.13/4.91 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 33.13/4.91 ( ^[X0:$i]: 33.13/4.91 ( all_of @ 33.13/4.91 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 33.13/4.91 ( ^[X1:$i]: 33.13/4.91 ( all_of @ 33.13/4.91 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 33.13/4.91 ( ^[X2:$i]: 33.13/4.91 ( ( n_is @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X2 @ X1 ) ) => 33.13/4.91 ( n_is @ X0 @ X1 ) ) ) ) ) ) ))). 33.13/4.91 thf(zf_stmt_0, conjecture, 33.13/4.91 (![X4:$i]: 33.13/4.91 ( ( is_of @ 33.13/4.91 X4 @ 33.13/4.91 ( ^[V_1:$i]: 33.13/4.91 ( in @ 33.13/4.91 V_1 @ 33.13/4.91 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) => 33.13/4.91 ( ![X6:$i]: 33.13/4.91 ( ( is_of @ 33.13/4.91 X6 @ 33.13/4.91 ( ^[V_3:$i]: 33.13/4.91 ( in @ 33.13/4.91 V_3 @ 33.13/4.91 ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 33.13/4.91 ( ![X8:$i]: 33.13/4.91 ( ( is_of @ 33.13/4.91 X8 @ 33.13/4.91 ( ^[V_5:$i]: 33.13/4.91 ( in @ 33.13/4.91 V_5 @ 33.13/4.91 ( d_Sep @ 33.13/4.91 omega @ ( ^[V_6:$i]: ( ( V_6 ) != ( emptyset ) ) ) ) ) ) ) => 33.13/4.91 ( ( e_is @ 33.13/4.91 ( d_Sep @ omega @ ( ^[V_7:$i]: ( ( V_7 ) != ( emptyset ) ) ) ) @ 33.13/4.91 ( ap @ ( plus @ X8 ) @ X4 ) @ ( ap @ ( plus @ X8 ) @ X6 ) ) => 33.13/4.91 ( e_is @ 33.13/4.91 ( d_Sep @ omega @ ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) @ 33.13/4.91 X4 @ X6 ) ) ) ) ) ) ))). 33.13/4.91 thf(zf_stmt_1, negated_conjecture, 33.13/4.91 (~( ![X4:$i]: 33.13/4.91 ( ( is_of @ 33.13/4.91 X4 @ 33.13/4.91 ( ^[V_1:$i]: 33.13/4.91 ( in @ 33.13/4.91 V_1 @ 33.13/4.91 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) => 33.13/4.91 ( ![X6:$i]: 33.13/4.91 ( ( is_of @ 33.13/4.91 X6 @ 33.13/4.91 ( ^[V_3:$i]: 33.13/4.91 ( in @ 33.13/4.91 V_3 @ 33.13/4.91 ( d_Sep @ 33.13/4.91 omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 33.13/4.91 ( ![X8:$i]: 33.13/4.91 ( ( is_of @ 33.13/4.91 X8 @ 33.13/4.91 ( ^[V_5:$i]: 33.13/4.91 ( in @ 33.13/4.91 V_5 @ 33.13/4.91 ( d_Sep @ 33.13/4.91 omega @ ( ^[V_6:$i]: ( ( V_6 ) != ( emptyset ) ) ) ) ) ) ) => 33.13/4.91 ( ( e_is @ 33.13/4.91 ( d_Sep @ 33.13/4.91 omega @ ( ^[V_7:$i]: ( ( V_7 ) != ( emptyset ) ) ) ) @ 33.13/4.91 ( ap @ ( plus @ X8 ) @ X4 ) @ ( ap @ ( plus @ X8 ) @ X6 ) ) => 33.13/4.91 ( e_is @ 33.13/4.91 ( d_Sep @ 33.13/4.91 omega @ ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) @ 33.13/4.91 X4 @ X6 ) ) ) ) ) ) ) )), 33.13/4.91 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 33.13/4.91 thf(zip_derived_cl13, plain, 33.13/4.91 (~ (((!!) @ (^[Y0 : $i]: 33.13/4.91 (((is_of @ Y0 @ 33.13/4.91 (^[Y1 : $i]: 33.13/4.91 (in @ Y1 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 33.13/4.91 (((!!) @ (^[Y1 : $i]: 33.13/4.91 (((is_of @ Y1 @ 33.13/4.91 (^[Y2 : $i]: 33.13/4.91 (in @ Y2 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y3 : $i]: (((Y3) != (emptyset)))))))) => 33.13/4.91 (((!!) @ (^[Y2 : $i]: 33.13/4.91 (((is_of @ Y2 @ 33.13/4.91 (^[Y3 : $i]: 33.13/4.91 (in @ Y3 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y4 : $i]: 33.13/4.91 (((Y4) != (emptyset)))))))) => 33.13/4.91 (((e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y3 : $i]: 33.13/4.91 (((Y3) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ Y2) @ Y0) @ 33.13/4.91 (ap @ (plus @ Y2) @ Y1)) => 33.13/4.91 (e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y3 : $i]: 33.13/4.91 (((Y3) != (emptyset))))) @ 33.13/4.91 Y0 @ Y1))))))))))))))))))), 33.13/4.91 inference('cnf', [status(esa)], [zf_stmt_1])). 33.13/4.91 thf(zip_derived_cl49, plain, 33.13/4.91 (~ (((is_of @ '#sk50' @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) => 33.13/4.91 (((!!) @ (^[Y0 : $i]: 33.13/4.91 (((is_of @ Y0 @ 33.13/4.91 (^[Y1 : $i]: 33.13/4.91 (in @ Y1 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 33.13/4.91 (((!!) @ (^[Y1 : $i]: 33.13/4.91 (((is_of @ Y1 @ 33.13/4.91 (^[Y2 : $i]: 33.13/4.91 (in @ Y2 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y3 : $i]: (((Y3) != (emptyset)))))))) => 33.13/4.91 (((e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ Y1) @ '#sk50') @ 33.13/4.91 (ap @ (plus @ Y1) @ Y0)) => (e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 33.13/4.91 '#sk50' @ Y0)))))))))))))))), 33.13/4.91 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl13])). 33.13/4.91 thf(zip_derived_cl51, plain, 33.13/4.91 (~ (((!!) @ (^[Y0 : $i]: 33.13/4.91 (((is_of @ Y0 @ 33.13/4.91 (^[Y1 : $i]: 33.13/4.91 (in @ Y1 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 33.13/4.91 (((!!) @ (^[Y1 : $i]: 33.13/4.91 (((is_of @ Y1 @ 33.13/4.91 (^[Y2 : $i]: 33.13/4.91 (in @ Y2 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y3 : $i]: (((Y3) != (emptyset)))))))) => 33.13/4.91 (((e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ Y1) @ '#sk50') @ 33.13/4.91 (ap @ (plus @ Y1) @ Y0)) => (e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 33.13/4.91 '#sk50' @ Y0)))))))))))))), 33.13/4.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 33.13/4.91 thf(zip_derived_cl52, plain, 33.13/4.91 (~ (((is_of @ '#sk51' @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) => 33.13/4.91 (((!!) @ (^[Y0 : $i]: 33.13/4.91 (((is_of @ Y0 @ 33.13/4.91 (^[Y1 : $i]: 33.13/4.91 (in @ Y1 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 33.13/4.91 (((e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ Y0) @ '#sk50') @ 33.13/4.91 (ap @ (plus @ Y0) @ '#sk51')) => (e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 33.13/4.91 '#sk50' @ '#sk51'))))))))))), 33.13/4.91 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl51])). 33.13/4.91 thf(zip_derived_cl54, plain, 33.13/4.91 (~ (((!!) @ (^[Y0 : $i]: 33.13/4.91 (((is_of @ Y0 @ 33.13/4.91 (^[Y1 : $i]: 33.13/4.91 (in @ Y1 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 33.13/4.91 (((e_is @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ Y0) @ '#sk50') @ 33.13/4.91 (ap @ (plus @ Y0) @ '#sk51')) => (e_is @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 33.13/4.91 '#sk50' @ '#sk51'))))))))), 33.13/4.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 33.13/4.91 thf(zip_derived_cl55, plain, 33.13/4.91 (~ (((is_of @ '#sk52' @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) => 33.13/4.91 (((e_is @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ '#sk52') @ '#sk50') @ 33.13/4.91 (ap @ (plus @ '#sk52') @ '#sk51')) => (e_is @ 33.13/4.91 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 33.13/4.91 '#sk50' @ '#sk51')))))), 33.13/4.91 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 33.13/4.91 thf(zip_derived_cl57, plain, 33.13/4.91 (~ (((e_is @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ '#sk52') @ '#sk50') @ 33.13/4.91 (ap @ (plus @ '#sk52') @ '#sk51')) => (e_is @ 33.13/4.91 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ '#sk50' @ 33.13/4.91 '#sk51')))), 33.13/4.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 33.13/4.91 thf(zip_derived_cl58, plain, 33.13/4.91 ( (e_is @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ '#sk52') @ '#sk50') @ (ap @ (plus @ '#sk52') @ '#sk51'))), 33.13/4.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 33.13/4.91 thf(satz8a, axiom, 33.13/4.91 (all_of @ 33.13/4.91 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 33.13/4.91 ( ^[X0:$i]: 33.13/4.91 ( all_of @ 33.13/4.91 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 33.13/4.91 ( ^[X1:$i]: 33.13/4.91 ( all_of @ 33.13/4.91 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 33.13/4.91 ( ^[X2:$i]: 33.13/4.91 ( ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X0 @ X2 ) ) => 33.13/4.91 ( n_is @ X1 @ X2 ) ) ) ) ) ) ))). 33.13/4.91 thf(zf_stmt_2, axiom, 33.13/4.91 (![X4:$i]: 33.13/4.91 ( ( is_of @ 33.13/4.91 X4 @ 33.13/4.91 ( ^[V_1:$i]: 33.13/4.91 ( in @ 33.13/4.91 V_1 @ 33.13/4.91 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) => 33.13/4.91 ( ![X6:$i]: 33.13/4.91 ( ( is_of @ 33.13/4.91 X6 @ 33.13/4.91 ( ^[V_3:$i]: 33.13/4.91 ( in @ 33.13/4.91 V_3 @ 33.13/4.91 ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 33.13/4.91 ( ![X8:$i]: 33.13/4.91 ( ( is_of @ 33.13/4.91 X8 @ 33.13/4.91 ( ^[V_5:$i]: 33.13/4.91 ( in @ 33.13/4.91 V_5 @ 33.13/4.91 ( d_Sep @ 33.13/4.91 omega @ ( ^[V_6:$i]: ( ( V_6 ) != ( emptyset ) ) ) ) ) ) ) => 33.13/4.91 ( ( e_is @ 33.13/4.91 ( d_Sep @ omega @ ( ^[V_7:$i]: ( ( V_7 ) != ( emptyset ) ) ) ) @ 33.13/4.91 ( ap @ ( plus @ X4 ) @ X6 ) @ ( ap @ ( plus @ X4 ) @ X8 ) ) => 33.13/4.91 ( e_is @ 33.13/4.91 ( d_Sep @ omega @ ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) @ 33.13/4.91 X6 @ X8 ) ) ) ) ) ) ))). 33.13/4.91 thf(zip_derived_cl10, plain, 33.13/4.91 ( (((!!) @ (^[Y0 : $i]: 33.13/4.91 (((is_of @ Y0 @ 33.13/4.91 (^[Y1 : $i]: 33.13/4.91 (in @ Y1 @ 33.13/4.91 (d_Sep @ omega @ (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 33.13/4.91 (((!!) @ (^[Y1 : $i]: 33.13/4.91 (((is_of @ Y1 @ 33.13/4.91 (^[Y2 : $i]: 33.13/4.91 (in @ Y2 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y3 : $i]: (((Y3) != (emptyset)))))))) => 33.13/4.91 (((!!) @ (^[Y2 : $i]: 33.13/4.91 (((is_of @ Y2 @ 33.13/4.91 (^[Y3 : $i]: 33.13/4.91 (in @ Y3 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y4 : $i]: 33.13/4.91 (((Y4) != (emptyset)))))))) => 33.13/4.91 (((e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y3 : $i]: 33.13/4.91 (((Y3) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ Y0) @ Y1) @ 33.13/4.91 (ap @ (plus @ Y0) @ Y2)) => 33.13/4.91 (e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y3 : $i]: 33.13/4.91 (((Y3) != (emptyset))))) @ 33.13/4.91 Y1 @ Y2))))))))))))))))))), 33.13/4.91 inference('cnf', [status(esa)], [zf_stmt_2])). 33.13/4.91 thf(zip_derived_cl108, plain, 33.13/4.91 (![X2 : $i]: 33.13/4.91 (((is_of @ X2 @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) => 33.13/4.91 (((!!) @ (^[Y0 : $i]: 33.13/4.91 (((is_of @ Y0 @ 33.13/4.91 (^[Y1 : $i]: 33.13/4.91 (in @ Y1 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 33.13/4.91 (((!!) @ (^[Y1 : $i]: 33.13/4.91 (((is_of @ Y1 @ 33.13/4.91 (^[Y2 : $i]: 33.13/4.91 (in @ Y2 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y3 : $i]: 33.13/4.91 (((Y3) != (emptyset)))))))) => 33.13/4.91 (((e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ X2) @ Y0) @ 33.13/4.91 (ap @ (plus @ X2) @ Y1)) => (e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 33.13/4.91 Y0 @ Y1)))))))))))))))), 33.13/4.91 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 33.13/4.91 thf(zip_derived_cl109, plain, 33.13/4.91 (![X2 : $i]: 33.13/4.91 (~ (is_of @ X2 @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 33.13/4.91 | (((!!) @ (^[Y0 : $i]: 33.13/4.91 (((is_of @ Y0 @ 33.13/4.91 (^[Y1 : $i]: 33.13/4.91 (in @ Y1 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 33.13/4.91 (((!!) @ (^[Y1 : $i]: 33.13/4.91 (((is_of @ Y1 @ 33.13/4.91 (^[Y2 : $i]: 33.13/4.91 (in @ Y2 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y3 : $i]: 33.13/4.91 (((Y3) != (emptyset)))))))) => 33.13/4.91 (((e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ X2) @ Y0) @ 33.13/4.91 (ap @ (plus @ X2) @ Y1)) => (e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 33.13/4.91 Y0 @ Y1))))))))))))))), 33.13/4.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 33.13/4.91 thf(zip_derived_cl110, plain, 33.13/4.91 (![X2 : $i, X4 : $i]: 33.13/4.91 ( (((is_of @ X4 @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) => 33.13/4.91 (((!!) @ (^[Y0 : $i]: 33.13/4.91 (((is_of @ Y0 @ 33.13/4.91 (^[Y1 : $i]: 33.13/4.91 (in @ Y1 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 33.13/4.91 (((e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ X2) @ X4) @ 33.13/4.91 (ap @ (plus @ X2) @ Y0)) => (e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 33.13/4.91 X4 @ Y0)))))))))) 33.13/4.91 | ~ (is_of @ X2 @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 33.13/4.91 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl109])). 33.13/4.91 thf(zip_derived_cl111, plain, 33.13/4.91 (![X2 : $i, X4 : $i]: 33.13/4.91 (~ (is_of @ X4 @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 33.13/4.91 | (((!!) @ (^[Y0 : $i]: 33.13/4.91 (((is_of @ Y0 @ 33.13/4.91 (^[Y1 : $i]: 33.13/4.91 (in @ Y1 @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 33.13/4.91 (((e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ X2) @ X4) @ 33.13/4.91 (ap @ (plus @ X2) @ Y0)) => (e_is @ 33.13/4.91 (d_Sep @ omega @ 33.13/4.91 (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 33.13/4.91 X4 @ Y0)))))))) 33.13/4.91 | ~ (is_of @ X2 @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 33.13/4.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl110])). 33.13/4.91 thf(zip_derived_cl112, plain, 33.13/4.91 (![X2 : $i, X4 : $i, X6 : $i]: 33.13/4.91 ( (((is_of @ X6 @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) => 33.13/4.91 (((e_is @ 33.13/4.91 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ X2) @ X4) @ (ap @ (plus @ X2) @ X6)) => (e_is @ 33.13/4.91 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ X4 @ 33.13/4.91 X6))))) 33.13/4.91 | ~ (is_of @ X2 @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 33.13/4.91 | ~ (is_of @ X4 @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 33.13/4.91 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl111])). 33.13/4.91 thf(zip_derived_cl113, plain, 33.13/4.91 (![X2 : $i, X4 : $i, X6 : $i]: 33.13/4.91 (~ (is_of @ X6 @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 33.13/4.91 | (((e_is @ 33.13/4.91 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ X2) @ X4) @ (ap @ (plus @ X2) @ X6)) => (e_is @ 33.13/4.91 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ X4 @ 33.13/4.91 X6))) 33.13/4.91 | ~ (is_of @ X4 @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 33.13/4.91 | ~ (is_of @ X2 @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 33.13/4.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl112])). 33.13/4.91 thf(zip_derived_cl114, plain, 33.13/4.91 (![X2 : $i, X4 : $i, X6 : $i]: 33.13/4.91 (~ (e_is @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 33.13/4.91 (ap @ (plus @ X2) @ X4) @ (ap @ (plus @ X2) @ X6)) 33.13/4.91 | (e_is @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 33.13/4.91 X4 @ X6) 33.13/4.91 | ~ (is_of @ X2 @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 33.13/4.91 | ~ (is_of @ X4 @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 33.13/4.91 | ~ (is_of @ X6 @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 33.13/4.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])). 33.13/4.91 thf(zip_derived_cl2075, plain, 33.13/4.91 ((~ (is_of @ '#sk51' @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 33.13/4.91 | ~ (is_of @ '#sk50' @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 33.13/4.91 | ~ (is_of @ '#sk52' @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ 33.13/4.91 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 33.13/4.91 | (e_is @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 33.13/4.91 '#sk50' @ '#sk51'))), 33.13/4.91 inference('sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl114])). 33.13/4.91 thf(zip_derived_cl53, plain, 33.13/4.91 ( (is_of @ '#sk51' @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))), 33.13/4.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 33.13/4.91 thf(zip_derived_cl50, plain, 33.13/4.91 ( (is_of @ '#sk50' @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))), 33.13/4.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 33.13/4.91 thf(zip_derived_cl56, plain, 33.13/4.91 ( (is_of @ '#sk52' @ 33.13/4.91 (^[Y0 : $i]: 33.13/4.91 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))), 33.13/4.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 33.13/4.91 thf(zip_derived_cl59, plain, 33.13/4.91 (~ (e_is @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 33.13/4.91 '#sk50' @ '#sk51')), 33.13/4.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 33.13/4.91 thf(zip_derived_cl2085, plain, ($false), 33.13/4.91 inference('demod', [status(thm)], 33.13/4.91 [zip_derived_cl2075, zip_derived_cl53, zip_derived_cl50, 33.13/4.91 zip_derived_cl56, zip_derived_cl59])). 33.13/4.91 33.13/4.91 % SZS output end Refutation 33.13/4.91 33.13/4.91 33.13/4.91 % Terminating... 33.52/5.04 % Runner terminated. 33.52/5.04 % Zipperpin 1.5 exiting 33.52/5.04 EOF