0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.18 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.u844w4b4JK true 0.17/0.38 % Computer : n011.cluster.edu 0.17/0.38 % Model : x86_64 x86_64 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.17/0.38 % Memory : 8042.1875MB 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64 0.17/0.38 % CPULimit : 1440 0.17/0.38 % WCLimit : 180 0.17/0.38 % DateTime : Mon Jul 3 10:33:54 EDT 2023 0.17/0.38 % CPUTime : 0.17/0.38 % Running portfolio for 1440 s 0.17/0.38 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.17/0.38 % Number of cores: 8 0.17/0.38 % Python version: Python 3.6.8 0.17/0.39 % 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 0.53/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.53/0.75 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.53/0.75 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 129.70/17.47 % Solved by lams/40_c.s.sh. 129.70/17.47 % done 499 iterations in 16.712s 129.70/17.47 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 129.70/17.47 % SZS output start Refutation 129.70/17.47 thf(emptyset_type, type, emptyset: $i). 129.70/17.47 thf(n_2t_type, type, n_2t: $i). 129.70/17.47 thf(times_type, type, times: $i > $i). 129.70/17.47 thf(lessis_type, type, lessis: $i > $i > $o). 129.70/17.47 thf(ite_type, type, ite: $o > $i > $i > $i > $i). 129.70/17.47 thf(n_2_type, type, n_2: $i). 129.70/17.47 thf(d_Sigma_type, type, d_Sigma: $i > ($i > $i) > $i). 129.70/17.47 thf(omega_type, type, omega: $i). 129.70/17.47 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 129.70/17.47 thf(in_type, type, in: $i > $i > $o). 129.70/17.47 thf(pair1_type, type, pair1: $i > $i > $i > $i). 129.70/17.47 thf(prop1_type, type, prop1: $o > $i > $i > $i > $i > $o). 129.70/17.47 thf(d_1to_type, type, d_1to: $i > $i). 129.70/17.47 thf(den_type, type, den: $i > $i). 129.70/17.47 thf(n_1_type, type, n_1: $i). 129.70/17.47 thf(n_1t_type, type, n_1t: $i). 129.70/17.47 thf(ind_type, type, ind: $i > ($i > $o) > $i). 129.70/17.47 thf(sk__6_type, type, sk__6: $i). 129.70/17.47 thf(first1_type, type, first1: $i > $i > $i). 129.70/17.47 thf(n_fr_type, type, n_fr: $i > $i > $i). 129.70/17.47 thf(e_is_type, type, e_is: $i > $i > $i > $o). 129.70/17.47 thf(ap_type, type, ap: $i > $i > $i). 129.70/17.47 thf(nat_type, type, nat: $i). 129.70/17.47 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 129.70/17.47 thf(second1_type, type, second1: $i > $i > $i). 129.70/17.47 thf(outn_type, type, outn: $i > $i > $i). 129.70/17.47 thf(frac_type, type, frac: $i). 129.70/17.47 thf(n_ts_type, type, n_ts: $i > $i > $i). 129.70/17.47 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 129.70/17.47 thf(sk__5_type, type, sk__5: $i). 129.70/17.47 thf(n_eq_type, type, n_eq: $i > $i > $o). 129.70/17.47 thf(n_is_type, type, n_is: $i > $i > $o). 129.70/17.47 thf(ordsucc_type, type, ordsucc: $i > $i). 129.70/17.47 thf(n_pl_type, type, n_pl: $i > $i > $i). 129.70/17.47 thf(num_type, type, num: $i > $i). 129.70/17.47 thf(pair1type_type, type, pair1type: $i > $i). 129.70/17.47 thf(def_n_eq, axiom,(( n_eq ) = 129.70/17.47 (^[X0:$i,X1:$i]: 129.70/17.47 ( n_is @ 129.70/17.47 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 129.70/17.47 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) )))). 129.70/17.47 thf(def_den, axiom,(( den ) = (second1 @ nat))). 129.70/17.47 thf(def_second1, axiom,(( second1 ) = (^[X0:$i,X1:$i]: ( ap @ X1 @ n_2t )))). 129.70/17.47 thf(def_n_2t, axiom,(( n_2t ) = (outn @ n_2 @ n_2))). 129.70/17.47 thf(def_n_2, axiom,(( n_2 ) = (n_pl @ n_1 @ n_1))). 129.70/17.47 thf(def_n_1, axiom,(( n_1 ) = (ordsucc @ emptyset))). 129.70/17.47 thf('0', plain, (( n_1 ) = ( ordsucc @ emptyset )), 129.70/17.47 inference('simplify_rw_rule', [status(thm)], [def_n_1])). 129.70/17.47 thf('1', plain, (( n_1 ) = ( ordsucc @ emptyset )), define([status(thm)])). 129.70/17.47 thf('2', plain, (( n_2 ) = ( n_pl @ n_1 @ n_1 )), 129.70/17.47 inference('simplify_rw_rule', [status(thm)], [def_n_2, '1'])). 129.70/17.47 thf('3', plain, (( n_2 ) = ( n_pl @ n_1 @ n_1 )), define([status(thm)])). 129.70/17.47 thf('4', plain, (( n_2t ) = ( outn @ n_2 @ n_2 )), 129.70/17.47 inference('simplify_rw_rule', [status(thm)], [def_n_2t, '3', '1'])). 129.70/17.47 thf('5', plain, (( n_2t ) = ( outn @ n_2 @ n_2 )), define([status(thm)])). 129.70/17.47 thf('6', plain, (( second1 ) = ( ^[X0:$i,X1:$i]: ( ap @ X1 @ n_2t ) )), 129.70/17.47 inference('simplify_rw_rule', [status(thm)], [def_second1, '5', '3', '1'])). 129.70/17.47 thf('7', plain, (( second1 ) = ( ^[V_1:$i,V_2:$i]: ( ap @ V_2 @ n_2t ) )), 129.70/17.47 define([status(thm)])). 129.70/17.47 thf(def_nat, axiom,(( nat ) = 129.70/17.47 (d_Sep @ omega @ ( ^[X0:$i]: ( ( X0 ) != ( emptyset ) ) )))). 129.70/17.47 thf('8', plain, 129.70/17.47 (( nat ) = ( d_Sep @ omega @ ( ^[X0:$i]: ( ( X0 ) != ( emptyset ) ) ) )), 129.70/17.47 inference('simplify_rw_rule', [status(thm)], [def_nat])). 129.70/17.47 thf('9', plain, 129.70/17.47 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 129.70/17.47 define([status(thm)])). 129.70/17.47 thf('10', plain, (( den ) = ( second1 @ nat )), 129.70/17.47 inference('simplify_rw_rule', [status(thm)], [def_den, '7', '5', '9'])). 129.70/17.47 thf('11', plain, (( den ) = ( second1 @ nat )), define([status(thm)])). 129.70/17.47 thf(def_num, axiom,(( num ) = (first1 @ nat))). 129.70/17.47 thf(def_first1, axiom,(( first1 ) = (^[X0:$i,X1:$i]: ( ap @ X1 @ n_1t )))). 129.70/17.47 thf(def_n_1t, axiom,(( n_1t ) = (outn @ n_2 @ n_1))). 129.70/17.47 thf('12', plain, (( n_1t ) = ( outn @ n_2 @ n_1 )), 129.70/17.47 inference('simplify_rw_rule', [status(thm)], [def_n_1t, '3', '1'])). 129.70/17.47 thf('13', plain, (( n_1t ) = ( outn @ n_2 @ n_1 )), define([status(thm)])). 129.70/17.47 thf('14', plain, (( first1 ) = ( ^[X0:$i,X1:$i]: ( ap @ X1 @ n_1t ) )), 129.70/17.47 inference('simplify_rw_rule', [status(thm)], [def_first1, '13', '3', '1'])). 129.70/17.47 thf('15', plain, (( first1 ) = ( ^[V_1:$i,V_2:$i]: ( ap @ V_2 @ n_1t ) )), 129.70/17.47 define([status(thm)])). 129.70/17.47 thf('16', plain, (( num ) = ( first1 @ nat )), 129.70/17.47 inference('simplify_rw_rule', [status(thm)], [def_num, '15', '13', '9'])). 129.70/17.47 thf('17', plain, (( num ) = ( first1 @ nat )), define([status(thm)])). 129.70/17.47 thf(def_n_ts, axiom,(( n_ts ) = (^[X0:$i]: ( ap @ ( times @ X0 ) )))). 129.70/17.47 thf('18', plain, (( n_ts ) = ( ^[X0:$i]: ( ap @ ( times @ X0 ) ) )), 129.70/17.47 inference('simplify_rw_rule', [status(thm)], [def_n_ts])). 129.70/17.47 thf('19', plain, (( n_ts ) = ( ^[V_1:$i]: ( ap @ ( times @ V_1 ) ) )), 129.70/17.47 define([status(thm)])).thf(def_n_is, axiom,(( n_is ) = (e_is @ nat))). 129.70/17.47 thf(def_e_is, axiom,(( e_is ) = (^[X0:$i,X:$i,Y:$i]: ( ( X ) = ( Y ) )))). 129.70/17.47 thf('20', plain, (( e_is ) = ( ^[X0:$i,X:$i,Y:$i]: ( ( X ) = ( Y ) ) )), 129.70/17.47 inference('simplify_rw_rule', [status(thm)], [def_e_is])). 129.70/17.47 thf('21', plain, 129.70/17.47 (( e_is ) = ( ^[V_1:$i,V_2:$i,V_3:$i]: ( ( V_2 ) = ( V_3 ) ) )), 129.70/17.47 define([status(thm)])). 129.70/17.47 thf('22', plain, (( n_is ) = ( e_is @ nat )), 129.70/17.47 inference('simplify_rw_rule', [status(thm)], [def_n_is, '9', '21'])). 129.70/17.48 thf('23', plain, (( n_is ) = ( e_is @ nat )), define([status(thm)])). 129.70/17.48 thf('24', plain, 129.70/17.48 (( n_eq ) = 129.70/17.48 ( ^[X0:$i,X1:$i]: 129.70/17.48 ( n_is @ 129.70/17.48 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 129.70/17.48 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )), 129.70/17.48 inference('simplify_rw_rule', [status(thm)], 129.70/17.48 [def_n_eq, '11', '17', '7', '15', '5', '13', '3', '19', '1', 129.70/17.48 '23', '9', '21'])). 129.70/17.48 thf('25', plain, 129.70/17.48 (( n_eq ) = 129.70/17.48 ( ^[V_1:$i,V_2:$i]: 129.70/17.48 ( n_is @ 129.70/17.48 ( n_ts @ ( num @ V_1 ) @ ( den @ V_2 ) ) @ 129.70/17.48 ( n_ts @ ( num @ V_2 ) @ ( den @ V_1 ) ) ) )), 129.70/17.48 define([status(thm)])).thf(def_n_fr, axiom,(( n_fr ) = (pair1 @ nat))). 129.70/17.48 thf(def_pair1, axiom,(( pair1 ) = 129.70/17.48 (^[X0:$i,X1:$i,X2:$i]: 129.70/17.48 ( d_Sigma @ 129.70/17.48 ( d_1to @ n_2 ) @ 129.70/17.48 ( ^[X3:$i]: 129.70/17.48 ( ite @ ( e_is @ ( d_1to @ n_2 ) @ X3 @ n_1t ) @ X0 @ X1 @ X2 ) ) )))). 129.70/17.48 thf(def_d_1to, axiom,(( d_1to ) = 129.70/17.48 (^[X0:$i]: ( d_Sep @ nat @ ( ^[X1:$i]: ( lessis @ X1 @ X0 ) ) )))). 129.70/17.48 thf('26', plain, 129.70/17.48 (( d_1to ) = 129.70/17.48 ( ^[X0:$i]: ( d_Sep @ nat @ ( ^[X1:$i]: ( lessis @ X1 @ X0 ) ) ) )), 129.70/17.48 inference('simplify_rw_rule', [status(thm)], [def_d_1to, '9'])). 129.70/17.48 thf('27', plain, 129.70/17.48 (( d_1to ) = 129.70/17.48 ( ^[V_1:$i]: ( d_Sep @ nat @ ( ^[V_2:$i]: ( lessis @ V_2 @ V_1 ) ) ) )), 129.70/17.48 define([status(thm)])). 129.70/17.48 thf(def_ite, axiom,(( ite ) = 129.70/17.48 (^[X0:$o,X1:$i,X2:$i,X3:$i]: ( ind @ X1 @ ( prop1 @ X0 @ X1 @ X2 @ X3 ) )))). 129.70/17.48 thf('28', plain, 129.70/17.48 (( ite ) = 129.70/17.48 ( ^[X0:$o,X1:$i,X2:$i,X3:$i]: 129.70/17.48 ( ind @ X1 @ ( prop1 @ X0 @ X1 @ X2 @ X3 ) ) )), 129.70/17.48 inference('simplify_rw_rule', [status(thm)], [def_ite])). 129.70/17.48 thf('29', plain, 129.70/17.48 (( ite ) = 129.70/17.48 ( ^[V_1:$o,V_2:$i,V_3:$i,V_4:$i]: 129.70/17.48 ( ind @ V_2 @ ( prop1 @ V_1 @ V_2 @ V_3 @ V_4 ) ) )), 129.70/17.48 define([status(thm)])). 129.70/17.48 thf('30', plain, 129.70/17.48 (( pair1 ) = 129.70/17.48 ( ^[X0:$i,X1:$i,X2:$i]: 129.70/17.48 ( d_Sigma @ 129.70/17.48 ( d_1to @ n_2 ) @ 129.70/17.48 ( ^[X3:$i]: 129.70/17.48 ( ite @ ( e_is @ ( d_1to @ n_2 ) @ X3 @ n_1t ) @ X0 @ X1 @ X2 ) ) ) )), 129.70/17.48 inference('simplify_rw_rule', [status(thm)], 129.70/17.48 [def_pair1, '13', '3', '27', '1', '9', '29', '21'])). 129.70/17.48 thf('31', plain, 129.70/17.48 (( pair1 ) = 129.70/17.48 ( ^[V_1:$i,V_2:$i,V_3:$i]: 129.70/17.48 ( d_Sigma @ 129.70/17.48 ( d_1to @ n_2 ) @ 129.70/17.48 ( ^[V_4:$i]: 129.70/17.48 ( ite @ ( e_is @ ( d_1to @ n_2 ) @ V_4 @ n_1t ) @ V_1 @ V_2 @ V_3 ) ) ) )), 129.70/17.48 define([status(thm)])). 129.70/17.48 thf('32', plain, (( n_fr ) = ( pair1 @ nat )), 129.70/17.48 inference('simplify_rw_rule', [status(thm)], 129.70/17.48 [def_n_fr, '31', '13', '3', '27', '1', '9', '29', '21'])). 129.70/17.48 thf('33', plain, (( n_fr ) = ( pair1 @ nat )), define([status(thm)])). 129.70/17.48 thf(def_frac, axiom,(( frac ) = (pair1type @ nat))). 129.70/17.48 thf('34', plain, (( frac ) = ( pair1type @ nat )), 129.70/17.48 inference('simplify_rw_rule', [status(thm)], [def_frac, '9'])). 129.70/17.48 thf('35', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])). 129.70/17.48 thf(def_all_of, axiom,(( all_of ) = 129.70/17.48 (^[X0:( $i > $o ),X1:( $i > $o )]: 129.70/17.48 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) )))). 129.70/17.48 thf('36', plain, 129.70/17.48 (( all_of ) = 129.70/17.48 ( ^[X0:( $i > $o ),X1:( $i > $o )]: 129.70/17.48 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) ) )), 129.70/17.48 inference('simplify_rw_rule', [status(thm)], [def_all_of])). 129.70/17.48 thf('37', plain, 129.70/17.48 (( all_of ) = 129.70/17.48 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 129.70/17.48 ( ![X4:$i]: ( ( is_of @ X4 @ V_1 ) => ( V_2 @ X4 ) ) ) )), 129.70/17.48 define([status(thm)])). 129.70/17.48 thf(satz40a, conjecture, 129.70/17.48 (all_of @ 129.70/17.48 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 129.70/17.48 ( ^[X0:$i]: 129.70/17.48 ( all_of @ 129.70/17.48 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 129.70/17.48 ( ^[X1:$i]: 129.70/17.48 ( n_eq @ 129.70/17.48 ( n_fr @ 129.70/17.48 ( n_ts @ ( num @ X0 ) @ X1 ) @ ( n_ts @ ( den @ X0 ) @ X1 ) ) @ 129.70/17.48 X0 ) ) ) ))). 129.70/17.48 thf(zf_stmt_0, conjecture, 129.70/17.48 (![X4:$i]: 129.70/17.48 ( ( is_of @ 129.70/17.48 X4 @ 129.70/17.48 ( ^[V_1:$i]: 129.70/17.48 ( in @ 129.70/17.48 V_1 @ 129.70/17.48 ( pair1type @ 129.70/17.48 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) ) => 129.70/17.48 ( ![X6:$i]: 129.70/17.48 ( ( is_of @ 129.70/17.48 X6 @ 129.70/17.48 ( ^[V_3:$i]: 129.70/17.48 ( in @ 129.70/17.48 V_3 @ 129.70/17.48 ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 129.70/17.48 ( ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 ( d_Sigma @ 129.70/17.48 ( d_Sep @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ ( ^[V_5:$i]: ( ( V_5 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( ^[V_6:$i]: 129.70/17.48 ( lessis @ 129.70/17.48 V_6 @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) @ 129.70/17.48 ( ^[V_7:$i]: 129.70/17.48 ( ind @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( prop1 @ 129.70/17.48 ( ( V_7 ) = 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ ( ^[V_9:$i]: ( ( V_9 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) @ 129.70/17.48 X6 ) @ 129.70/17.48 ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) ) @ 129.70/17.48 X6 ) ) ) ) ) @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) = 129.70/17.48 ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) @ 129.70/17.48 ( ap @ 129.70/17.48 ( d_Sigma @ 129.70/17.48 ( d_Sep @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ ( ^[V_10:$i]: ( ( V_10 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( ^[V_11:$i]: 129.70/17.48 ( lessis @ 129.70/17.48 V_11 @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) @ 129.70/17.48 ( ^[V_12:$i]: 129.70/17.48 ( ind @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ ( ^[V_13:$i]: ( ( V_13 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( prop1 @ 129.70/17.48 ( ( V_12 ) = 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ ( ^[V_14:$i]: ( ( V_14 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) @ 129.70/17.48 X6 ) @ 129.70/17.48 ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) ) @ 129.70/17.48 X6 ) ) ) ) ) @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) ) ) ) ))). 129.70/17.48 thf(zf_stmt_1, negated_conjecture, 129.70/17.48 (~( ![X4:$i]: 129.70/17.48 ( ( is_of @ 129.70/17.48 X4 @ 129.70/17.48 ( ^[V_1:$i]: 129.70/17.48 ( in @ 129.70/17.48 V_1 @ 129.70/17.48 ( pair1type @ 129.70/17.48 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) ) => 129.70/17.48 ( ![X6:$i]: 129.70/17.48 ( ( is_of @ 129.70/17.48 X6 @ 129.70/17.48 ( ^[V_3:$i]: 129.70/17.48 ( in @ 129.70/17.48 V_3 @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 129.70/17.48 ( ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 ( d_Sigma @ 129.70/17.48 ( d_Sep @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ ( ^[V_5:$i]: ( ( V_5 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( ^[V_6:$i]: 129.70/17.48 ( lessis @ 129.70/17.48 V_6 @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) @ 129.70/17.48 ( ^[V_7:$i]: 129.70/17.48 ( ind @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ 129.70/17.48 ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( prop1 @ 129.70/17.48 ( ( V_7 ) = 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ 129.70/17.48 ( ^[V_9:$i]: ( ( V_9 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) @ 129.70/17.48 X6 ) @ 129.70/17.48 ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) ) @ 129.70/17.48 X6 ) ) ) ) ) @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) = 129.70/17.48 ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) @ 129.70/17.48 ( ap @ 129.70/17.48 ( d_Sigma @ 129.70/17.48 ( d_Sep @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ ( ^[V_10:$i]: ( ( V_10 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( ^[V_11:$i]: 129.70/17.48 ( lessis @ 129.70/17.48 V_11 @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) @ 129.70/17.48 ( ^[V_12:$i]: 129.70/17.48 ( ind @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ 129.70/17.48 ( ^[V_13:$i]: ( ( V_13 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( prop1 @ 129.70/17.48 ( ( V_12 ) = 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ 129.70/17.48 ( ^[V_14:$i]: ( ( V_14 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) @ 129.70/17.48 X6 ) @ 129.70/17.48 ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) ) @ 129.70/17.48 X6 ) ) ) ) ) @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) ) ) ) ) )), 129.70/17.48 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 129.70/17.48 thf(zip_derived_cl133, plain, 129.70/17.48 ( (is_of @ sk__6 @ 129.70/17.48 (^[Y0 : $i]: 129.70/17.48 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))), 129.70/17.48 inference('cnf', [status(esa)], [zf_stmt_1])). 129.70/17.48 thf(zip_derived_cl131, plain, 129.70/17.48 ( (is_of @ sk__5 @ 129.70/17.48 (^[Y0 : $i]: 129.70/17.48 (in @ Y0 @ 129.70/17.48 (pair1type @ 129.70/17.48 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 129.70/17.48 inference('cnf', [status(esa)], [zf_stmt_1])). 129.70/17.48 thf(zip_derived_cl132, plain, 129.70/17.48 (((ap @ 129.70/17.48 (times @ 129.70/17.48 (ap @ 129.70/17.48 (d_Sigma @ 129.70/17.48 (d_Sep @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 129.70/17.48 (^[Y0 : $i]: 129.70/17.48 (lessis @ Y0 @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 129.70/17.48 (^[Y0 : $i]: 129.70/17.48 (ind @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 129.70/17.48 (prop1 @ 129.70/17.48 (((Y0) = (outn @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (ordsucc @ emptyset)))) @ 129.70/17.48 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 129.70/17.48 (ap @ 129.70/17.48 (times @ 129.70/17.48 (ap @ sk__5 @ 129.70/17.48 (outn @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (ordsucc @ emptyset)))) @ 129.70/17.48 sk__6) @ 129.70/17.48 (ap @ 129.70/17.48 (times @ 129.70/17.48 (ap @ sk__5 @ 129.70/17.48 (outn @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 129.70/17.48 sk__6))))) @ 129.70/17.48 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (ordsucc @ emptyset)))) @ 129.70/17.48 (ap @ sk__5 @ 129.70/17.48 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) 129.70/17.48 != (ap @ 129.70/17.48 (times @ 129.70/17.48 (ap @ sk__5 @ 129.70/17.48 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (ordsucc @ emptyset)))) @ 129.70/17.48 (ap @ 129.70/17.48 (d_Sigma @ 129.70/17.48 (d_Sep @ 129.70/17.48 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 129.70/17.48 (^[Y0 : $i]: 129.70/17.48 (lessis @ Y0 @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 129.70/17.48 (^[Y0 : $i]: 129.70/17.48 (ind @ 129.70/17.48 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 129.70/17.48 (prop1 @ 129.70/17.48 (((Y0) = (outn @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (ordsucc @ emptyset)))) @ 129.70/17.48 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 129.70/17.48 (ap @ 129.70/17.48 (times @ 129.70/17.48 (ap @ sk__5 @ 129.70/17.48 (outn @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (ordsucc @ emptyset)))) @ 129.70/17.48 sk__6) @ 129.70/17.48 (ap @ 129.70/17.48 (times @ 129.70/17.48 (ap @ sk__5 @ 129.70/17.48 (outn @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 129.70/17.48 sk__6))))) @ 129.70/17.48 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))), 129.70/17.48 inference('cnf', [status(esa)], [zf_stmt_1])). 129.70/17.48 thf(satz40, axiom, 129.70/17.48 (all_of @ 129.70/17.48 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 129.70/17.48 ( ^[X0:$i]: 129.70/17.48 ( all_of @ 129.70/17.48 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 129.70/17.48 ( ^[X1:$i]: 129.70/17.48 ( n_eq @ 129.70/17.48 X0 @ 129.70/17.48 ( n_fr @ 129.70/17.48 ( n_ts @ ( num @ X0 ) @ X1 ) @ ( n_ts @ ( den @ X0 ) @ X1 ) ) ) ) ) ))). 129.70/17.48 thf(zf_stmt_2, axiom, 129.70/17.48 (![X4:$i]: 129.70/17.48 ( ( is_of @ 129.70/17.48 X4 @ 129.70/17.48 ( ^[V_1:$i]: 129.70/17.48 ( in @ 129.70/17.48 V_1 @ 129.70/17.48 ( pair1type @ 129.70/17.48 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) ) => 129.70/17.48 ( ![X6:$i]: 129.70/17.48 ( ( is_of @ 129.70/17.48 X6 @ 129.70/17.48 ( ^[V_3:$i]: 129.70/17.48 ( in @ 129.70/17.48 V_3 @ 129.70/17.48 ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 129.70/17.48 ( ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) @ 129.70/17.48 ( ap @ 129.70/17.48 ( d_Sigma @ 129.70/17.48 ( d_Sep @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ ( ^[V_5:$i]: ( ( V_5 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( ^[V_6:$i]: 129.70/17.48 ( lessis @ 129.70/17.48 V_6 @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) @ 129.70/17.48 ( ^[V_7:$i]: 129.70/17.48 ( ind @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( prop1 @ 129.70/17.48 ( ( V_7 ) = 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ ( ^[V_9:$i]: ( ( V_9 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) @ 129.70/17.48 X6 ) @ 129.70/17.48 ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) ) @ 129.70/17.48 X6 ) ) ) ) ) @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) = 129.70/17.48 ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 ( d_Sigma @ 129.70/17.48 ( d_Sep @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ ( ^[V_10:$i]: ( ( V_10 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( ^[V_11:$i]: 129.70/17.48 ( lessis @ 129.70/17.48 V_11 @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) @ 129.70/17.48 ( ^[V_12:$i]: 129.70/17.48 ( ind @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ ( ^[V_13:$i]: ( ( V_13 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( prop1 @ 129.70/17.48 ( ( V_12 ) = 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) @ 129.70/17.48 ( d_Sep @ 129.70/17.48 omega @ 129.70/17.48 ( ^[V_14:$i]: ( ( V_14 ) != ( emptyset ) ) ) ) @ 129.70/17.48 ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) @ 129.70/17.48 X6 ) @ 129.70/17.48 ( ap @ 129.70/17.48 ( times @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( n_pl @ 129.70/17.48 ( ordsucc @ emptyset ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) ) @ 129.70/17.48 X6 ) ) ) ) ) @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( ordsucc @ emptyset ) ) ) ) @ 129.70/17.48 ( ap @ 129.70/17.48 X4 @ 129.70/17.48 ( outn @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 129.70/17.48 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) ) ) ) ))). 129.70/17.48 thf(zip_derived_cl57, plain, 129.70/17.48 (![X0 : $i, X1 : $i]: 129.70/17.48 (~ (is_of @ X0 @ 129.70/17.48 (^[Y0 : $i]: 129.70/17.48 (in @ Y0 @ 129.70/17.48 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 129.70/17.48 | ((ap @ 129.70/17.48 (times @ 129.70/17.48 (ap @ X1 @ 129.70/17.48 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (ordsucc @ emptyset)))) @ 129.70/17.48 (ap @ 129.70/17.48 (d_Sigma @ 129.70/17.48 (d_Sep @ 129.70/17.48 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 129.70/17.48 (^[Y0 : $i]: 129.70/17.48 (lessis @ Y0 @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 129.70/17.48 (^[Y0 : $i]: 129.70/17.48 (ind @ 129.70/17.48 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 129.70/17.48 (prop1 @ 129.70/17.48 (((Y0) = (outn @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (ordsucc @ emptyset)))) @ 129.70/17.48 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 129.70/17.48 (ap @ 129.70/17.48 (times @ 129.70/17.48 (ap @ X1 @ 129.70/17.48 (outn @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (ordsucc @ emptyset)))) @ 129.70/17.48 X0) @ 129.70/17.48 (ap @ 129.70/17.48 (times @ 129.70/17.48 (ap @ X1 @ 129.70/17.48 (outn @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 129.70/17.48 X0))))) @ 129.70/17.48 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) 129.70/17.48 = (ap @ 129.70/17.48 (times @ 129.70/17.48 (ap @ 129.70/17.48 (d_Sigma @ 129.70/17.48 (d_Sep @ 129.70/17.48 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 129.70/17.48 (^[Y0 : $i]: 129.70/17.48 (lessis @ Y0 @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 129.70/17.48 (^[Y0 : $i]: 129.70/17.48 (ind @ 129.70/17.48 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 129.70/17.48 (prop1 @ 129.70/17.48 (((Y0) = (outn @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (ordsucc @ emptyset)))) @ 129.70/17.48 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 129.70/17.48 (ap @ 129.70/17.48 (times @ 129.70/17.48 (ap @ X1 @ 129.70/17.48 (outn @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ 129.70/17.48 (ordsucc @ emptyset)) @ 129.70/17.48 (ordsucc @ emptyset)))) @ 129.70/17.48 X0) @ 129.70/17.48 (ap @ 129.70/17.48 (times @ 129.70/17.48 (ap @ X1 @ 129.70/17.48 (outn @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ 129.70/17.48 (ordsucc @ emptyset)) @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ 129.70/17.48 (ordsucc @ emptyset))))) @ 129.70/17.48 X0))))) @ 129.70/17.48 (outn @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (ordsucc @ emptyset)))) @ 129.70/17.48 (ap @ X1 @ 129.70/17.48 (outn @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 129.70/17.48 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))) 129.70/17.48 | ~ (is_of @ X1 @ 129.70/17.48 (^[Y0 : $i]: 129.70/17.48 (in @ Y0 @ 129.70/17.48 (pair1type @ 129.70/17.48 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))))), 129.70/17.48 inference('cnf', [status(esa)], [zf_stmt_2])). 129.70/17.48 thf(zip_derived_cl8286, plain, ($false), 129.70/17.48 inference('eprover', [status(thm)], 129.70/17.48 [zip_derived_cl133, zip_derived_cl131, zip_derived_cl132, 129.70/17.48 zip_derived_cl57])). 129.70/17.48 129.70/17.48 % SZS output end Refutation 129.70/17.48 129.70/17.48 129.70/17.48 % Terminating... 129.98/17.60 % Runner terminated. 129.98/17.61 % Zipperpin 1.5 exiting 129.98/17.63 EOF