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.RP876npd3N true 0.15/0.36 % Computer : n005.cluster.edu 0.15/0.36 % Model : x86_64 x86_64 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.36 % Memory : 8042.1875MB 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.36 % CPULimit : 1200 0.15/0.36 % WCLimit : 120 0.15/0.36 % DateTime : Tue Jul 13 14:14:33 EDT 2021 0.15/0.36 % CPUTime : 0.15/0.36 % Running portfolio for 120 s 0.15/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.15/0.36 % Number of cores: 8 0.15/0.37 % Python version: Python 3.6.8 0.15/0.37 % Running in HO mode 0.48/0.64 % Total configuration time : 828 0.48/0.64 % Estimated wc time : 983 0.48/0.64 % Estimated cpu time (8 cpus) : 122.875 0.56/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.56/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.56/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.56/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.56/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.56/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.56/0.77 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.56/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 12.96/2.29 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 53s 28.05/4.22 % Solved by lams/30_sp5.sh. 28.05/4.22 % done 181 iterations in 3.381s 28.05/4.22 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 28.05/4.22 % SZS output start Refutation 28.05/4.22 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 28.05/4.22 thf(n_is_type, type, n_is: $i > $i > $o). 28.05/4.22 thf(ap_type, type, ap: $i > $i > $i). 28.05/4.22 thf('#sk50_type', type, '#sk50': $i). 28.05/4.22 thf(plus_type, type, plus: $i > $i). 28.05/4.22 thf('#sk51_type', type, '#sk51': $i). 28.05/4.22 thf(in_type, type, in: $i > $i > $o). 28.05/4.22 thf(nat_type, type, nat: $i). 28.05/4.22 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 28.05/4.22 thf(e_is_type, type, e_is: $i > $i > $i > $o). 28.05/4.22 thf(n_pl_type, type, n_pl: $i > $i > $i). 28.05/4.22 thf(omega_type, type, omega: $i). 28.05/4.22 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 28.05/4.22 thf('#sk52_type', type, '#sk52': $i). 28.05/4.22 thf(emptyset_type, type, emptyset: $i). 28.05/4.22 thf(def_n_pl, axiom,(( n_pl ) = (^[X0:$i]: ( ap @ ( plus @ X0 ) )))). 28.05/4.22 thf('0', plain, (( n_pl ) = ( ^[X0:$i]: ( ap @ ( plus @ X0 ) ) )), 28.05/4.22 inference('simplify_rw_rule', [status(thm)], [def_n_pl])). 28.05/4.22 thf('1', plain, (( n_pl ) = ( ^[V_1:$i]: ( ap @ ( plus @ V_1 ) ) )), 28.05/4.22 define([status(thm)])).thf(def_n_is, axiom,(( n_is ) = (e_is @ nat))). 28.05/4.22 thf(def_nat, axiom,(( nat ) = 28.05/4.22 (d_Sep @ omega @ ( ^[X0:$i]: ( ( X0 ) != ( emptyset ) ) )))). 28.05/4.22 thf('2', plain, 28.05/4.22 (( nat ) = ( d_Sep @ omega @ ( ^[X0:$i]: ( ( X0 ) != ( emptyset ) ) ) )), 28.05/4.22 inference('simplify_rw_rule', [status(thm)], [def_nat])). 28.05/4.22 thf('3', plain, 28.05/4.22 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 28.05/4.22 define([status(thm)])). 28.05/4.22 thf('4', plain, (( n_is ) = ( e_is @ nat )), 28.05/4.22 inference('simplify_rw_rule', [status(thm)], [def_n_is, '3'])). 28.05/4.22 thf('5', plain, (( n_is ) = ( e_is @ nat )), define([status(thm)])). 28.05/4.22 thf(def_all_of, axiom,(( all_of ) = 28.05/4.22 (^[X0:( $i > $o ),X1:( $i > $o )]: 28.05/4.22 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) )))). 28.05/4.22 thf('6', plain, 28.05/4.22 (( all_of ) = 28.05/4.22 ( ^[X0:( $i > $o ),X1:( $i > $o )]: 28.05/4.22 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) ) )), 28.05/4.22 inference('simplify_rw_rule', [status(thm)], [def_all_of])). 28.05/4.22 thf('7', plain, 28.05/4.22 (( all_of ) = 28.05/4.22 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 28.05/4.22 ( ![X4:$i]: ( ( is_of @ X4 @ V_1 ) => ( V_2 @ X4 ) ) ) )), 28.05/4.22 define([status(thm)])). 28.05/4.22 thf(satz20e, conjecture, 28.05/4.22 (all_of @ 28.05/4.22 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 28.05/4.22 ( ^[X0:$i]: 28.05/4.22 ( all_of @ 28.05/4.22 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 28.05/4.22 ( ^[X1:$i]: 28.05/4.22 ( all_of @ 28.05/4.22 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 28.05/4.22 ( ^[X2:$i]: 28.05/4.22 ( ( n_is @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X2 @ X1 ) ) => 28.05/4.22 ( n_is @ X0 @ X1 ) ) ) ) ) ) ))). 28.05/4.22 thf(zf_stmt_0, conjecture, 28.05/4.22 (![X4:$i]: 28.05/4.22 ( ( is_of @ 28.05/4.22 X4 @ 28.05/4.22 ( ^[V_1:$i]: 28.05/4.22 ( in @ 28.05/4.22 V_1 @ 28.05/4.22 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) => 28.05/4.22 ( ![X6:$i]: 28.05/4.22 ( ( is_of @ 28.05/4.22 X6 @ 28.05/4.22 ( ^[V_3:$i]: 28.05/4.22 ( in @ 28.05/4.22 V_3 @ 28.05/4.22 ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 28.05/4.22 ( ![X8:$i]: 28.05/4.22 ( ( is_of @ 28.05/4.22 X8 @ 28.05/4.22 ( ^[V_5:$i]: 28.05/4.22 ( in @ 28.05/4.22 V_5 @ 28.05/4.22 ( d_Sep @ 28.05/4.22 omega @ ( ^[V_6:$i]: ( ( V_6 ) != ( emptyset ) ) ) ) ) ) ) => 28.05/4.22 ( ( e_is @ 28.05/4.22 ( d_Sep @ omega @ ( ^[V_7:$i]: ( ( V_7 ) != ( emptyset ) ) ) ) @ 28.05/4.22 ( ap @ ( plus @ X8 ) @ X4 ) @ ( ap @ ( plus @ X8 ) @ X6 ) ) => 28.05/4.22 ( e_is @ 28.05/4.22 ( d_Sep @ omega @ ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) @ 28.05/4.22 X4 @ X6 ) ) ) ) ) ) ))). 28.05/4.22 thf(zf_stmt_1, negated_conjecture, 28.05/4.22 (~( ![X4:$i]: 28.05/4.22 ( ( is_of @ 28.05/4.22 X4 @ 28.05/4.22 ( ^[V_1:$i]: 28.05/4.22 ( in @ 28.05/4.22 V_1 @ 28.05/4.22 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) => 28.05/4.22 ( ![X6:$i]: 28.05/4.22 ( ( is_of @ 28.05/4.22 X6 @ 28.05/4.22 ( ^[V_3:$i]: 28.05/4.22 ( in @ 28.05/4.22 V_3 @ 28.05/4.22 ( d_Sep @ 28.05/4.22 omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 28.05/4.22 ( ![X8:$i]: 28.05/4.22 ( ( is_of @ 28.05/4.22 X8 @ 28.05/4.22 ( ^[V_5:$i]: 28.05/4.22 ( in @ 28.05/4.22 V_5 @ 28.05/4.22 ( d_Sep @ 28.05/4.22 omega @ ( ^[V_6:$i]: ( ( V_6 ) != ( emptyset ) ) ) ) ) ) ) => 28.05/4.22 ( ( e_is @ 28.05/4.22 ( d_Sep @ 28.05/4.22 omega @ ( ^[V_7:$i]: ( ( V_7 ) != ( emptyset ) ) ) ) @ 28.05/4.22 ( ap @ ( plus @ X8 ) @ X4 ) @ ( ap @ ( plus @ X8 ) @ X6 ) ) => 28.05/4.22 ( e_is @ 28.05/4.22 ( d_Sep @ 28.05/4.22 omega @ ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) @ 28.05/4.22 X4 @ X6 ) ) ) ) ) ) ) )), 28.05/4.22 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 28.05/4.22 thf(zip_derived_cl13, plain, 28.05/4.22 (~ (((!!) @ (^[Y0 : $i]: 28.05/4.22 (((is_of @ Y0 @ 28.05/4.22 (^[Y1 : $i]: 28.05/4.22 (in @ Y1 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 28.05/4.22 (((!!) @ (^[Y1 : $i]: 28.05/4.22 (((is_of @ Y1 @ 28.05/4.22 (^[Y2 : $i]: 28.05/4.22 (in @ Y2 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y3 : $i]: (((Y3) != (emptyset)))))))) => 28.05/4.22 (((!!) @ (^[Y2 : $i]: 28.05/4.22 (((is_of @ Y2 @ 28.05/4.22 (^[Y3 : $i]: 28.05/4.22 (in @ Y3 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y4 : $i]: 28.05/4.22 (((Y4) != (emptyset)))))))) => 28.05/4.22 (((e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y3 : $i]: 28.05/4.22 (((Y3) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ Y2) @ Y0) @ 28.05/4.22 (ap @ (plus @ Y2) @ Y1)) => 28.05/4.22 (e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y3 : $i]: 28.05/4.22 (((Y3) != (emptyset))))) @ 28.05/4.22 Y0 @ Y1))))))))))))))))))), 28.05/4.22 inference('cnf', [status(esa)], [zf_stmt_1])). 28.05/4.22 thf(zip_derived_cl49, plain, 28.05/4.22 (~ (((is_of @ '#sk50' @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) => 28.05/4.22 (((!!) @ (^[Y0 : $i]: 28.05/4.22 (((is_of @ Y0 @ 28.05/4.22 (^[Y1 : $i]: 28.05/4.22 (in @ Y1 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 28.05/4.22 (((!!) @ (^[Y1 : $i]: 28.05/4.22 (((is_of @ Y1 @ 28.05/4.22 (^[Y2 : $i]: 28.05/4.22 (in @ Y2 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y3 : $i]: (((Y3) != (emptyset)))))))) => 28.05/4.22 (((e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ Y1) @ '#sk50') @ 28.05/4.22 (ap @ (plus @ Y1) @ Y0)) => (e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 28.05/4.22 '#sk50' @ Y0)))))))))))))))), 28.05/4.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl13])). 28.05/4.22 thf(zip_derived_cl51, plain, 28.05/4.22 (~ (((!!) @ (^[Y0 : $i]: 28.05/4.22 (((is_of @ Y0 @ 28.05/4.22 (^[Y1 : $i]: 28.05/4.22 (in @ Y1 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 28.05/4.22 (((!!) @ (^[Y1 : $i]: 28.05/4.22 (((is_of @ Y1 @ 28.05/4.22 (^[Y2 : $i]: 28.05/4.22 (in @ Y2 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y3 : $i]: (((Y3) != (emptyset)))))))) => 28.05/4.22 (((e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ Y1) @ '#sk50') @ 28.05/4.22 (ap @ (plus @ Y1) @ Y0)) => (e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 28.05/4.22 '#sk50' @ Y0)))))))))))))), 28.05/4.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 28.05/4.22 thf(zip_derived_cl52, plain, 28.05/4.22 (~ (((is_of @ '#sk51' @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) => 28.05/4.22 (((!!) @ (^[Y0 : $i]: 28.05/4.22 (((is_of @ Y0 @ 28.05/4.22 (^[Y1 : $i]: 28.05/4.22 (in @ Y1 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 28.05/4.22 (((e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ Y0) @ '#sk50') @ 28.05/4.22 (ap @ (plus @ Y0) @ '#sk51')) => (e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 28.05/4.22 '#sk50' @ '#sk51'))))))))))), 28.05/4.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl51])). 28.05/4.22 thf(zip_derived_cl54, plain, 28.05/4.22 (~ (((!!) @ (^[Y0 : $i]: 28.05/4.22 (((is_of @ Y0 @ 28.05/4.22 (^[Y1 : $i]: 28.05/4.22 (in @ Y1 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 28.05/4.22 (((e_is @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ Y0) @ '#sk50') @ 28.05/4.22 (ap @ (plus @ Y0) @ '#sk51')) => (e_is @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 28.05/4.22 '#sk50' @ '#sk51'))))))))), 28.05/4.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 28.05/4.22 thf(zip_derived_cl55, plain, 28.05/4.22 (~ (((is_of @ '#sk52' @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) => 28.05/4.22 (((e_is @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ '#sk52') @ '#sk50') @ 28.05/4.22 (ap @ (plus @ '#sk52') @ '#sk51')) => (e_is @ 28.05/4.22 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 28.05/4.22 '#sk50' @ '#sk51')))))), 28.05/4.22 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 28.05/4.22 thf(zip_derived_cl57, plain, 28.05/4.22 (~ (((e_is @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ '#sk52') @ '#sk50') @ 28.05/4.22 (ap @ (plus @ '#sk52') @ '#sk51')) => (e_is @ 28.05/4.22 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ '#sk50' @ 28.05/4.22 '#sk51')))), 28.05/4.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 28.05/4.22 thf(zip_derived_cl58, plain, 28.05/4.22 ( (e_is @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ '#sk52') @ '#sk50') @ (ap @ (plus @ '#sk52') @ '#sk51'))), 28.05/4.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 28.05/4.22 thf(satz8a, axiom, 28.05/4.22 (all_of @ 28.05/4.22 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 28.05/4.22 ( ^[X0:$i]: 28.05/4.22 ( all_of @ 28.05/4.22 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 28.05/4.22 ( ^[X1:$i]: 28.05/4.22 ( all_of @ 28.05/4.22 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 28.05/4.22 ( ^[X2:$i]: 28.05/4.22 ( ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X0 @ X2 ) ) => 28.05/4.22 ( n_is @ X1 @ X2 ) ) ) ) ) ) ))). 28.05/4.22 thf(zf_stmt_2, axiom, 28.05/4.22 (![X4:$i]: 28.05/4.22 ( ( is_of @ 28.05/4.22 X4 @ 28.05/4.22 ( ^[V_1:$i]: 28.05/4.22 ( in @ 28.05/4.22 V_1 @ 28.05/4.22 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) => 28.05/4.22 ( ![X6:$i]: 28.05/4.22 ( ( is_of @ 28.05/4.22 X6 @ 28.05/4.22 ( ^[V_3:$i]: 28.05/4.22 ( in @ 28.05/4.22 V_3 @ 28.05/4.22 ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 28.05/4.22 ( ![X8:$i]: 28.05/4.22 ( ( is_of @ 28.05/4.22 X8 @ 28.05/4.22 ( ^[V_5:$i]: 28.05/4.22 ( in @ 28.05/4.22 V_5 @ 28.05/4.22 ( d_Sep @ 28.05/4.22 omega @ ( ^[V_6:$i]: ( ( V_6 ) != ( emptyset ) ) ) ) ) ) ) => 28.05/4.22 ( ( e_is @ 28.05/4.22 ( d_Sep @ omega @ ( ^[V_7:$i]: ( ( V_7 ) != ( emptyset ) ) ) ) @ 28.05/4.22 ( ap @ ( plus @ X4 ) @ X6 ) @ ( ap @ ( plus @ X4 ) @ X8 ) ) => 28.05/4.22 ( e_is @ 28.05/4.22 ( d_Sep @ omega @ ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) @ 28.05/4.22 X6 @ X8 ) ) ) ) ) ) ))). 28.05/4.22 thf(zip_derived_cl12, plain, 28.05/4.22 ( (((!!) @ (^[Y0 : $i]: 28.05/4.22 (((is_of @ Y0 @ 28.05/4.22 (^[Y1 : $i]: 28.05/4.22 (in @ Y1 @ 28.05/4.22 (d_Sep @ omega @ (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 28.05/4.22 (((!!) @ (^[Y1 : $i]: 28.05/4.22 (((is_of @ Y1 @ 28.05/4.22 (^[Y2 : $i]: 28.05/4.22 (in @ Y2 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y3 : $i]: (((Y3) != (emptyset)))))))) => 28.05/4.22 (((!!) @ (^[Y2 : $i]: 28.05/4.22 (((is_of @ Y2 @ 28.05/4.22 (^[Y3 : $i]: 28.05/4.22 (in @ Y3 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y4 : $i]: 28.05/4.22 (((Y4) != (emptyset)))))))) => 28.05/4.22 (((e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y3 : $i]: 28.05/4.22 (((Y3) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ Y0) @ Y1) @ 28.05/4.22 (ap @ (plus @ Y0) @ Y2)) => 28.05/4.22 (e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y3 : $i]: 28.05/4.22 (((Y3) != (emptyset))))) @ 28.05/4.22 Y1 @ Y2))))))))))))))))))), 28.05/4.22 inference('cnf', [status(esa)], [zf_stmt_2])). 28.05/4.22 thf(zip_derived_cl108, plain, 28.05/4.22 (![X2 : $i]: 28.05/4.22 (((is_of @ X2 @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) => 28.05/4.22 (((!!) @ (^[Y0 : $i]: 28.05/4.22 (((is_of @ Y0 @ 28.05/4.22 (^[Y1 : $i]: 28.05/4.22 (in @ Y1 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 28.05/4.22 (((!!) @ (^[Y1 : $i]: 28.05/4.22 (((is_of @ Y1 @ 28.05/4.22 (^[Y2 : $i]: 28.05/4.22 (in @ Y2 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y3 : $i]: 28.05/4.22 (((Y3) != (emptyset)))))))) => 28.05/4.22 (((e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ X2) @ Y0) @ 28.05/4.22 (ap @ (plus @ X2) @ Y1)) => (e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 28.05/4.22 Y0 @ Y1)))))))))))))))), 28.05/4.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 28.05/4.22 thf(zip_derived_cl109, plain, 28.05/4.22 (![X2 : $i]: 28.05/4.22 (~ (is_of @ X2 @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 28.05/4.22 | (((!!) @ (^[Y0 : $i]: 28.05/4.22 (((is_of @ Y0 @ 28.05/4.22 (^[Y1 : $i]: 28.05/4.22 (in @ Y1 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 28.05/4.22 (((!!) @ (^[Y1 : $i]: 28.05/4.22 (((is_of @ Y1 @ 28.05/4.22 (^[Y2 : $i]: 28.05/4.22 (in @ Y2 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y3 : $i]: 28.05/4.22 (((Y3) != (emptyset)))))))) => 28.05/4.22 (((e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ X2) @ Y0) @ 28.05/4.22 (ap @ (plus @ X2) @ Y1)) => (e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset))))) @ 28.05/4.22 Y0 @ Y1))))))))))))))), 28.05/4.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 28.05/4.22 thf(zip_derived_cl110, plain, 28.05/4.22 (![X2 : $i, X4 : $i]: 28.05/4.22 ( (((is_of @ X4 @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) => 28.05/4.22 (((!!) @ (^[Y0 : $i]: 28.05/4.22 (((is_of @ Y0 @ 28.05/4.22 (^[Y1 : $i]: 28.05/4.22 (in @ Y1 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 28.05/4.22 (((e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ X2) @ X4) @ 28.05/4.22 (ap @ (plus @ X2) @ Y0)) => (e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 28.05/4.22 X4 @ Y0)))))))))) 28.05/4.22 | ~ (is_of @ X2 @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 28.05/4.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl109])). 28.05/4.22 thf(zip_derived_cl111, plain, 28.05/4.22 (![X2 : $i, X4 : $i]: 28.05/4.22 (~ (is_of @ X4 @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 28.05/4.22 | (((!!) @ (^[Y0 : $i]: 28.05/4.22 (((is_of @ Y0 @ 28.05/4.22 (^[Y1 : $i]: 28.05/4.22 (in @ Y1 @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y2 : $i]: (((Y2) != (emptyset)))))))) => 28.05/4.22 (((e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ X2) @ X4) @ 28.05/4.22 (ap @ (plus @ X2) @ Y0)) => (e_is @ 28.05/4.22 (d_Sep @ omega @ 28.05/4.22 (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 28.05/4.22 X4 @ Y0)))))))) 28.05/4.22 | ~ (is_of @ X2 @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 28.05/4.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl110])). 28.05/4.22 thf(zip_derived_cl112, plain, 28.05/4.22 (![X2 : $i, X4 : $i, X6 : $i]: 28.05/4.22 ( (((is_of @ X6 @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) => 28.05/4.22 (((e_is @ 28.05/4.22 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ X2) @ X4) @ (ap @ (plus @ X2) @ X6)) => (e_is @ 28.05/4.22 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ X4 @ 28.05/4.22 X6))))) 28.05/4.22 | ~ (is_of @ X2 @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 28.05/4.22 | ~ (is_of @ X4 @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 28.05/4.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl111])). 28.05/4.22 thf(zip_derived_cl113, plain, 28.05/4.22 (![X2 : $i, X4 : $i, X6 : $i]: 28.05/4.22 (~ (is_of @ X6 @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 28.05/4.22 | (((e_is @ 28.05/4.22 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ X2) @ X4) @ (ap @ (plus @ X2) @ X6)) => (e_is @ 28.05/4.22 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ X4 @ 28.05/4.22 X6))) 28.05/4.22 | ~ (is_of @ X4 @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 28.05/4.22 | ~ (is_of @ X2 @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 28.05/4.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl112])). 28.05/4.22 thf(zip_derived_cl114, plain, 28.05/4.22 (![X2 : $i, X4 : $i, X6 : $i]: 28.05/4.22 (~ (e_is @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 28.05/4.22 (ap @ (plus @ X2) @ X4) @ (ap @ (plus @ X2) @ X6)) 28.05/4.22 | (e_is @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 28.05/4.22 X4 @ X6) 28.05/4.22 | ~ (is_of @ X2 @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 28.05/4.22 | ~ (is_of @ X4 @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 28.05/4.22 | ~ (is_of @ X6 @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 28.05/4.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])). 28.05/4.22 thf(zip_derived_cl2161, plain, 28.05/4.22 ((~ (is_of @ '#sk51' @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 28.05/4.22 | ~ (is_of @ '#sk50' @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 28.05/4.22 | ~ (is_of @ '#sk52' @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ 28.05/4.22 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 28.05/4.22 | (e_is @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 28.05/4.22 '#sk50' @ '#sk51'))), 28.05/4.22 inference('sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl114])). 28.05/4.22 thf(zip_derived_cl53, plain, 28.05/4.22 ( (is_of @ '#sk51' @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))), 28.05/4.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 28.05/4.22 thf(zip_derived_cl50, plain, 28.05/4.22 ( (is_of @ '#sk50' @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))), 28.05/4.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 28.05/4.22 thf(zip_derived_cl56, plain, 28.05/4.22 ( (is_of @ '#sk52' @ 28.05/4.22 (^[Y0 : $i]: 28.05/4.22 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))), 28.05/4.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 28.05/4.22 thf(zip_derived_cl59, plain, 28.05/4.22 (~ (e_is @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 28.05/4.22 '#sk50' @ '#sk51')), 28.05/4.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 28.05/4.22 thf(zip_derived_cl2174, plain, ($false), 28.05/4.22 inference('demod', [status(thm)], 28.05/4.22 [zip_derived_cl2161, zip_derived_cl53, zip_derived_cl50, 28.05/4.22 zip_derived_cl56, zip_derived_cl59])). 28.05/4.22 28.05/4.22 % SZS output end Refutation 28.05/4.22 28.05/4.22 28.05/4.22 % Terminating... 28.55/4.28 % Runner terminated. 28.55/4.28 % Zipperpin 1.5 exiting 28.55/4.28 EOF