0.10/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.KH8aLjkR99 true 0.14/0.35 % Computer : n009.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1440 0.14/0.35 % WCLimit : 180 0.14/0.35 % DateTime : Thu Jul 4 09:49:39 EDT 2024 0.14/0.36 % CPUTime : 0.14/0.36 % Running portfolio for 1440 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 0.14/0.36 % Running in HO mode 0.52/0.73 % Total configuration time : 828 0.52/0.73 % Estimated wc time : 1656 0.52/0.73 % Estimated cpu time (8 cpus) : 207.0 0.53/0.93 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.53/1.05 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.53/1.07 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.53/1.08 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.53/1.11 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 1.85/1.22 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 1.85/1.23 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 1.93/1.26 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 68.97/17.56 % Solved by lams/40_c.s.sh. 68.97/17.56 % done 400 iterations in 16.522s 68.97/17.56 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 68.97/17.56 % SZS output start Refutation 68.97/17.56 thf(emptyset_type, type, emptyset: $i). 68.97/17.56 thf(n_2t_type, type, n_2t: $i). 68.97/17.56 thf(times_type, type, times: $i > $i). 68.97/17.56 thf(lessis_type, type, lessis: $i > $i > $o). 68.97/17.56 thf('#l_lift5770_type', type, '#l_lift5770': $i > $i > $o). 68.97/17.56 thf(ite_type, type, ite: $o > $i > $i > $i > $i). 68.97/17.56 thf('#l_lift5772_type', type, '#l_lift5772': $i > $i > $i > $i). 68.97/17.56 thf(n_2_type, type, n_2: $i). 68.97/17.56 thf(d_Sigma_type, type, d_Sigma: $i > ($i > $i) > $i). 68.97/17.56 thf(omega_type, type, omega: $i). 68.97/17.56 thf(d_Pi_type, type, d_Pi: $i > ($i > $i) > $i). 68.97/17.56 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 68.97/17.56 thf(in_type, type, in: $i > $i > $o). 68.97/17.56 thf(pair1_type, type, pair1: $i > $i > $i > $i). 68.97/17.56 thf(prop1_type, type, prop1: $o > $i > $i > $i > $i > $o). 68.97/17.56 thf(d_1to_type, type, d_1to: $i > $i). 68.97/17.56 thf(den_type, type, den: $i > $i). 68.97/17.56 thf(n_1_type, type, n_1: $i). 68.97/17.56 thf(n_1t_type, type, n_1t: $i). 68.97/17.56 thf(ind_type, type, ind: $i > ($i > $o) > $i). 68.97/17.56 thf(sk__6_type, type, sk__6: $i). 68.97/17.56 thf(first1_type, type, first1: $i > $i > $i). 68.97/17.56 thf('#l_lift5766_type', type, '#l_lift5766': $i > $o). 68.97/17.56 thf(n_fr_type, type, n_fr: $i > $i > $i). 68.97/17.56 thf(e_is_type, type, e_is: $i > $i > $i > $o). 68.97/17.56 thf(ap_type, type, ap: $i > $i > $i). 68.97/17.56 thf(nat_type, type, nat: $i). 68.97/17.56 thf(sk__2_type, type, sk__2: $i > $i > $i > $i). 68.97/17.56 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 68.97/17.56 thf('#l_lift5771_type', type, '#l_lift5771': $i > $o). 68.97/17.56 thf(second1_type, type, second1: $i > $i > $i). 68.97/17.56 thf(outn_type, type, outn: $i > $i > $i). 68.97/17.56 thf(frac_type, type, frac: $i). 68.97/17.56 thf(n_ts_type, type, n_ts: $i > $i > $i). 68.97/17.56 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 68.97/17.56 thf(sk__5_type, type, sk__5: $i). 68.97/17.56 thf(n_eq_type, type, n_eq: $i > $i > $o). 68.97/17.56 thf(n_is_type, type, n_is: $i > $i > $o). 68.97/17.56 thf(ordsucc_type, type, ordsucc: $i > $i). 68.97/17.56 thf(n_pl_type, type, n_pl: $i > $i > $i). 68.97/17.56 thf(num_type, type, num: $i > $i). 68.97/17.56 thf(pair1type_type, type, pair1type: $i > $i). 68.97/17.56 thf(def_n_eq, axiom,(( n_eq ) = 68.97/17.56 (^[X0:$i,X1:$i]: 68.97/17.56 ( n_is @ 68.97/17.56 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 68.97/17.56 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) )))). 68.97/17.56 thf(def_den, axiom,(( den ) = (second1 @ nat))). 68.97/17.56 thf(def_second1, axiom,(( second1 ) = (^[X0:$i,X1:$i]: ( ap @ X1 @ n_2t )))). 68.97/17.56 thf(def_n_2t, axiom,(( n_2t ) = (outn @ n_2 @ n_2))). 68.97/17.56 thf(def_n_2, axiom,(( n_2 ) = (n_pl @ n_1 @ n_1))). 68.97/17.56 thf(def_n_1, axiom,(( n_1 ) = (ordsucc @ emptyset))). 68.97/17.56 thf('0', plain, (( n_1 ) = ( ordsucc @ emptyset )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_n_1])). 68.97/17.56 thf('1', plain, (( n_1 ) = ( ordsucc @ emptyset )), define([status(thm)])). 68.97/17.56 thf('2', plain, (( n_2 ) = ( n_pl @ n_1 @ n_1 )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_n_2, '1'])). 68.97/17.56 thf('3', plain, (( n_2 ) = ( n_pl @ n_1 @ n_1 )), define([status(thm)])). 68.97/17.56 thf('4', plain, (( n_2t ) = ( outn @ n_2 @ n_2 )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_n_2t, '3', '1'])). 68.97/17.56 thf('5', plain, (( n_2t ) = ( outn @ n_2 @ n_2 )), define([status(thm)])). 68.97/17.56 thf('6', plain, (( second1 ) = ( ^[X0:$i,X1:$i]: ( ap @ X1 @ n_2t ) )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_second1, '5', '3', '1'])). 68.97/17.56 thf('7', plain, (( second1 ) = ( ^[V_1:$i,V_2:$i]: ( ap @ V_2 @ n_2t ) )), 68.97/17.56 define([status(thm)])). 68.97/17.56 thf(def_nat, axiom,(( nat ) = 68.97/17.56 (d_Sep @ omega @ ( ^[X0:$i]: ( ( X0 ) != ( emptyset ) ) )))). 68.97/17.56 thf('8', plain, 68.97/17.56 (( nat ) = ( d_Sep @ omega @ ( ^[X0:$i]: ( ( X0 ) != ( emptyset ) ) ) )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_nat])). 68.97/17.56 thf('9', plain, 68.97/17.56 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 68.97/17.56 define([status(thm)])). 68.97/17.56 thf('10', plain, (( den ) = ( second1 @ nat )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_den, '7', '5', '9'])). 68.97/17.56 thf('11', plain, (( den ) = ( second1 @ nat )), define([status(thm)])). 68.97/17.56 thf(def_num, axiom,(( num ) = (first1 @ nat))). 68.97/17.56 thf(def_first1, axiom,(( first1 ) = (^[X0:$i,X1:$i]: ( ap @ X1 @ n_1t )))). 68.97/17.56 thf(def_n_1t, axiom,(( n_1t ) = (outn @ n_2 @ n_1))). 68.97/17.56 thf('12', plain, (( n_1t ) = ( outn @ n_2 @ n_1 )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_n_1t, '3', '1'])). 68.97/17.56 thf('13', plain, (( n_1t ) = ( outn @ n_2 @ n_1 )), define([status(thm)])). 68.97/17.56 thf('14', plain, (( first1 ) = ( ^[X0:$i,X1:$i]: ( ap @ X1 @ n_1t ) )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_first1, '13', '3', '1'])). 68.97/17.56 thf('15', plain, (( first1 ) = ( ^[V_1:$i,V_2:$i]: ( ap @ V_2 @ n_1t ) )), 68.97/17.56 define([status(thm)])). 68.97/17.56 thf('16', plain, (( num ) = ( first1 @ nat )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_num, '15', '13', '9'])). 68.97/17.56 thf('17', plain, (( num ) = ( first1 @ nat )), define([status(thm)])). 68.97/17.56 thf(def_n_ts, axiom,(( n_ts ) = (^[X0:$i]: ( ap @ ( times @ X0 ) )))). 68.97/17.56 thf('18', plain, (( n_ts ) = ( ^[X0:$i]: ( ap @ ( times @ X0 ) ) )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_n_ts])). 68.97/17.56 thf('19', plain, (( n_ts ) = ( ^[V_1:$i]: ( ap @ ( times @ V_1 ) ) )), 68.97/17.56 define([status(thm)])).thf(def_n_is, axiom,(( n_is ) = (e_is @ nat))). 68.97/17.56 thf(def_e_is, axiom,(( e_is ) = (^[X0:$i,X:$i,Y:$i]: ( ( X ) = ( Y ) )))). 68.97/17.56 thf('20', plain, (( e_is ) = ( ^[X0:$i,X:$i,Y:$i]: ( ( X ) = ( Y ) ) )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_e_is])). 68.97/17.56 thf('21', plain, 68.97/17.56 (( e_is ) = ( ^[V_1:$i,V_2:$i,V_3:$i]: ( ( V_2 ) = ( V_3 ) ) )), 68.97/17.56 define([status(thm)])). 68.97/17.56 thf('22', plain, (( n_is ) = ( e_is @ nat )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_n_is, '9', '21'])). 68.97/17.56 thf('23', plain, (( n_is ) = ( e_is @ nat )), define([status(thm)])). 68.97/17.56 thf('24', plain, 68.97/17.56 (( n_eq ) = 68.97/17.56 ( ^[X0:$i,X1:$i]: 68.97/17.56 ( n_is @ 68.97/17.56 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 68.97/17.56 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], 68.97/17.56 [def_n_eq, '11', '17', '7', '15', '5', '13', '3', '19', '1', 68.97/17.56 '23', '9', '21'])). 68.97/17.56 thf('25', plain, 68.97/17.56 (( n_eq ) = 68.97/17.56 ( ^[V_1:$i,V_2:$i]: 68.97/17.56 ( n_is @ 68.97/17.56 ( n_ts @ ( num @ V_1 ) @ ( den @ V_2 ) ) @ 68.97/17.56 ( n_ts @ ( num @ V_2 ) @ ( den @ V_1 ) ) ) )), 68.97/17.56 define([status(thm)])).thf(def_n_fr, axiom,(( n_fr ) = (pair1 @ nat))). 68.97/17.56 thf(def_pair1, axiom,(( pair1 ) = 68.97/17.56 (^[X0:$i,X1:$i,X2:$i]: 68.97/17.56 ( d_Sigma @ 68.97/17.56 ( d_1to @ n_2 ) @ 68.97/17.56 ( ^[X3:$i]: 68.97/17.56 ( ite @ ( e_is @ ( d_1to @ n_2 ) @ X3 @ n_1t ) @ X0 @ X1 @ X2 ) ) )))). 68.97/17.56 thf(def_d_1to, axiom,(( d_1to ) = 68.97/17.56 (^[X0:$i]: ( d_Sep @ nat @ ( ^[X1:$i]: ( lessis @ X1 @ X0 ) ) )))). 68.97/17.56 thf('26', plain, 68.97/17.56 (( d_1to ) = 68.97/17.56 ( ^[X0:$i]: ( d_Sep @ nat @ ( ^[X1:$i]: ( lessis @ X1 @ X0 ) ) ) )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_d_1to, '9'])). 68.97/17.56 thf('27', plain, 68.97/17.56 (( d_1to ) = 68.97/17.56 ( ^[V_1:$i]: ( d_Sep @ nat @ ( ^[V_2:$i]: ( lessis @ V_2 @ V_1 ) ) ) )), 68.97/17.56 define([status(thm)])). 68.97/17.56 thf(def_ite, axiom,(( ite ) = 68.97/17.56 (^[X0:$o,X1:$i,X2:$i,X3:$i]: ( ind @ X1 @ ( prop1 @ X0 @ X1 @ X2 @ X3 ) )))). 68.97/17.56 thf('28', plain, 68.97/17.56 (( ite ) = 68.97/17.56 ( ^[X0:$o,X1:$i,X2:$i,X3:$i]: 68.97/17.56 ( ind @ X1 @ ( prop1 @ X0 @ X1 @ X2 @ X3 ) ) )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_ite])). 68.97/17.56 thf('29', plain, 68.97/17.56 (( ite ) = 68.97/17.56 ( ^[V_1:$o,V_2:$i,V_3:$i,V_4:$i]: 68.97/17.56 ( ind @ V_2 @ ( prop1 @ V_1 @ V_2 @ V_3 @ V_4 ) ) )), 68.97/17.56 define([status(thm)])). 68.97/17.56 thf('30', plain, 68.97/17.56 (( pair1 ) = 68.97/17.56 ( ^[X0:$i,X1:$i,X2:$i]: 68.97/17.56 ( d_Sigma @ 68.97/17.56 ( d_1to @ n_2 ) @ 68.97/17.56 ( ^[X3:$i]: 68.97/17.56 ( ite @ ( e_is @ ( d_1to @ n_2 ) @ X3 @ n_1t ) @ X0 @ X1 @ X2 ) ) ) )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], 68.97/17.56 [def_pair1, '13', '3', '27', '1', '9', '29', '21'])). 68.97/17.56 thf('31', plain, 68.97/17.56 (( pair1 ) = 68.97/17.56 ( ^[V_1:$i,V_2:$i,V_3:$i]: 68.97/17.56 ( d_Sigma @ 68.97/17.56 ( d_1to @ n_2 ) @ 68.97/17.56 ( ^[V_4:$i]: 68.97/17.56 ( ite @ ( e_is @ ( d_1to @ n_2 ) @ V_4 @ n_1t ) @ V_1 @ V_2 @ V_3 ) ) ) )), 68.97/17.56 define([status(thm)])). 68.97/17.56 thf('32', plain, (( n_fr ) = ( pair1 @ nat )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], 68.97/17.56 [def_n_fr, '31', '13', '3', '27', '1', '9', '29', '21'])). 68.97/17.56 thf('33', plain, (( n_fr ) = ( pair1 @ nat )), define([status(thm)])). 68.97/17.56 thf(def_frac, axiom,(( frac ) = (pair1type @ nat))). 68.97/17.56 thf('34', plain, (( frac ) = ( pair1type @ nat )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_frac, '9'])). 68.97/17.56 thf('35', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])). 68.97/17.56 thf(def_all_of, axiom,(( all_of ) = 68.97/17.56 (^[X0:( $i > $o ),X1:( $i > $o )]: 68.97/17.56 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) )))). 68.97/17.56 thf('36', plain, 68.97/17.56 (( all_of ) = 68.97/17.56 ( ^[X0:( $i > $o ),X1:( $i > $o )]: 68.97/17.56 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) ) )), 68.97/17.56 inference('simplify_rw_rule', [status(thm)], [def_all_of])). 68.97/17.56 thf('37', plain, 68.97/17.56 (( all_of ) = 68.97/17.56 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 68.97/17.56 ( ![X4:$i]: ( ( is_of @ X4 @ V_1 ) => ( V_2 @ X4 ) ) ) )), 68.97/17.56 define([status(thm)])). 68.97/17.56 thf(satz40a, conjecture, 68.97/17.56 (all_of @ 68.97/17.56 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 68.97/17.56 ( ^[X0:$i]: 68.97/17.56 ( all_of @ 68.97/17.56 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 68.97/17.56 ( ^[X1:$i]: 68.97/17.56 ( n_eq @ 68.97/17.56 ( n_fr @ 68.97/17.56 ( n_ts @ ( num @ X0 ) @ X1 ) @ ( n_ts @ ( den @ X0 ) @ X1 ) ) @ 68.97/17.56 X0 ) ) ) ))). 68.97/17.56 thf(zf_stmt_0, conjecture, 68.97/17.56 (![X4:$i]: 68.97/17.56 ( ( is_of @ 68.97/17.56 X4 @ 68.97/17.56 ( ^[V_1:$i]: 68.97/17.56 ( in @ 68.97/17.56 V_1 @ 68.97/17.56 ( pair1type @ 68.97/17.56 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) ) => 68.97/17.56 ( ![X6:$i]: 68.97/17.56 ( ( is_of @ 68.97/17.56 X6 @ 68.97/17.56 ( ^[V_3:$i]: 68.97/17.56 ( in @ 68.97/17.56 V_3 @ 68.97/17.56 ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 68.97/17.56 ( ( ap @ 68.97/17.56 ( times @ 68.97/17.56 ( ap @ 68.97/17.56 ( d_Sigma @ 68.97/17.56 ( d_Sep @ 68.97/17.56 ( d_Sep @ 68.97/17.56 omega @ ( ^[V_5:$i]: ( ( V_5 ) != ( emptyset ) ) ) ) @ 68.97/17.56 ( ^[V_6:$i]: 68.97/17.56 ( lessis @ 68.97/17.56 V_6 @ 68.97/17.56 ( n_pl @ 68.97/17.56 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) @ 68.97/17.56 ( ^[V_7:$i]: 68.97/17.56 ( ind @ 68.97/17.56 ( d_Sep @ 68.97/17.56 omega @ ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) @ 68.97/17.56 ( prop1 @ 68.97/17.56 ( ( V_7 ) = 68.97/17.56 ( outn @ 68.97/17.56 ( n_pl @ 68.97/17.56 ( ordsucc @ emptyset ) @ 68.97/17.56 ( ordsucc @ emptyset ) ) @ 68.97/17.56 ( ordsucc @ emptyset ) ) ) @ 68.97/17.56 ( d_Sep @ 68.97/17.56 omega @ ( ^[V_9:$i]: ( ( V_9 ) != ( emptyset ) ) ) ) @ 68.97/17.56 ( ap @ 68.97/17.56 ( times @ 68.97/17.56 ( ap @ 68.97/17.56 X4 @ 68.97/17.56 ( outn @ 68.97/17.56 ( n_pl @ 68.97/17.56 ( ordsucc @ emptyset ) @ 68.97/17.56 ( ordsucc @ emptyset ) ) @ 68.97/17.56 ( ordsucc @ emptyset ) ) ) ) @ 68.97/17.56 X6 ) @ 68.97/17.56 ( ap @ 68.97/17.56 ( times @ 68.97/17.56 ( ap @ 68.97/17.56 X4 @ 68.97/17.56 ( outn @ 68.97/17.56 ( n_pl @ 68.97/17.56 ( ordsucc @ emptyset ) @ 68.97/17.56 ( ordsucc @ emptyset ) ) @ 68.97/17.56 ( n_pl @ 68.97/17.56 ( ordsucc @ emptyset ) @ 68.97/17.56 ( ordsucc @ emptyset ) ) ) ) ) @ 68.97/17.56 X6 ) ) ) ) ) @ 68.97/17.56 ( outn @ 68.97/17.56 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 68.97/17.56 ( ordsucc @ emptyset ) ) ) ) @ 68.97/17.56 ( ap @ 68.97/17.56 X4 @ 68.97/17.56 ( outn @ 68.97/17.56 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 68.97/17.56 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) = 68.97/17.56 ( ap @ 68.97/17.56 ( times @ 68.97/17.56 ( ap @ 68.97/17.56 X4 @ 68.97/17.56 ( outn @ 68.97/17.56 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 68.97/17.56 ( ordsucc @ emptyset ) ) ) ) @ 68.97/17.56 ( ap @ 68.97/17.57 ( d_Sigma @ 68.97/17.57 ( d_Sep @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ ( ^[V_10:$i]: ( ( V_10 ) != ( emptyset ) ) ) ) @ 68.97/17.57 ( ^[V_11:$i]: 68.97/17.57 ( lessis @ 68.97/17.57 V_11 @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) @ 68.97/17.57 ( ^[V_12:$i]: 68.97/17.57 ( ind @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ ( ^[V_13:$i]: ( ( V_13 ) != ( emptyset ) ) ) ) @ 68.97/17.57 ( prop1 @ 68.97/17.57 ( ( V_12 ) = 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ ( ^[V_14:$i]: ( ( V_14 ) != ( emptyset ) ) ) ) @ 68.97/17.57 ( ap @ 68.97/17.57 ( times @ 68.97/17.57 ( ap @ 68.97/17.57 X4 @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) ) @ 68.97/17.57 X6 ) @ 68.97/17.57 ( ap @ 68.97/17.57 ( times @ 68.97/17.57 ( ap @ 68.97/17.57 X4 @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) ) ) @ 68.97/17.57 X6 ) ) ) ) ) @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) ) ) ) ))). 68.97/17.57 thf(zf_stmt_1, negated_conjecture, 68.97/17.57 (~( ![X4:$i]: 68.97/17.57 ( ( is_of @ 68.97/17.57 X4 @ 68.97/17.57 ( ^[V_1:$i]: 68.97/17.57 ( in @ 68.97/17.57 V_1 @ 68.97/17.57 ( pair1type @ 68.97/17.57 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) ) => 68.97/17.57 ( ![X6:$i]: 68.97/17.57 ( ( is_of @ 68.97/17.57 X6 @ 68.97/17.57 ( ^[V_3:$i]: 68.97/17.57 ( in @ 68.97/17.57 V_3 @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 68.97/17.57 ( ( ap @ 68.97/17.57 ( times @ 68.97/17.57 ( ap @ 68.97/17.57 ( d_Sigma @ 68.97/17.57 ( d_Sep @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ ( ^[V_5:$i]: ( ( V_5 ) != ( emptyset ) ) ) ) @ 68.97/17.57 ( ^[V_6:$i]: 68.97/17.57 ( lessis @ 68.97/17.57 V_6 @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) @ 68.97/17.57 ( ^[V_7:$i]: 68.97/17.57 ( ind @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ 68.97/17.57 ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) @ 68.97/17.57 ( prop1 @ 68.97/17.57 ( ( V_7 ) = 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ 68.97/17.57 ( ^[V_9:$i]: ( ( V_9 ) != ( emptyset ) ) ) ) @ 68.97/17.57 ( ap @ 68.97/17.57 ( times @ 68.97/17.57 ( ap @ 68.97/17.57 X4 @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) ) @ 68.97/17.57 X6 ) @ 68.97/17.57 ( ap @ 68.97/17.57 ( times @ 68.97/17.57 ( ap @ 68.97/17.57 X4 @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) ) ) @ 68.97/17.57 X6 ) ) ) ) ) @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) ) @ 68.97/17.57 ( ap @ 68.97/17.57 X4 @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) = 68.97/17.57 ( ap @ 68.97/17.57 ( times @ 68.97/17.57 ( ap @ 68.97/17.57 X4 @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) ) @ 68.97/17.57 ( ap @ 68.97/17.57 ( d_Sigma @ 68.97/17.57 ( d_Sep @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ ( ^[V_10:$i]: ( ( V_10 ) != ( emptyset ) ) ) ) @ 68.97/17.57 ( ^[V_11:$i]: 68.97/17.57 ( lessis @ 68.97/17.57 V_11 @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) @ 68.97/17.57 ( ^[V_12:$i]: 68.97/17.57 ( ind @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ 68.97/17.57 ( ^[V_13:$i]: ( ( V_13 ) != ( emptyset ) ) ) ) @ 68.97/17.57 ( prop1 @ 68.97/17.57 ( ( V_12 ) = 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ 68.97/17.57 ( ^[V_14:$i]: ( ( V_14 ) != ( emptyset ) ) ) ) @ 68.97/17.57 ( ap @ 68.97/17.57 ( times @ 68.97/17.57 ( ap @ 68.97/17.57 X4 @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) ) @ 68.97/17.57 X6 ) @ 68.97/17.57 ( ap @ 68.97/17.57 ( times @ 68.97/17.57 ( ap @ 68.97/17.57 X4 @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) ) ) @ 68.97/17.57 X6 ) ) ) ) ) @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) ) ) ) ) )), 68.97/17.57 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 68.97/17.57 thf(zip_derived_cl133, plain, 68.97/17.57 ( (is_of @ sk__6 @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))), 68.97/17.57 inference('cnf', [status(esa)], [zf_stmt_1])). 68.97/17.57 thf(e_fisi, axiom, 68.97/17.57 (![X0:$i,X1:$i]: 68.97/17.57 ( all_of @ 68.97/17.57 ( ^[X2:$i]: ( in @ X2 @ ( d_Pi @ X0 @ ( ^[X3:$i]: ( X1 ) ) ) ) ) @ 68.97/17.57 ( ^[X2:$i]: 68.97/17.57 ( all_of @ 68.97/17.57 ( ^[X3:$i]: ( in @ X3 @ ( d_Pi @ X0 @ ( ^[X4:$i]: ( X1 ) ) ) ) ) @ 68.97/17.57 ( ^[X3:$i]: 68.97/17.57 ( ( all_of @ 68.97/17.57 ( ^[X4:$i]: ( in @ X4 @ X0 ) ) @ 68.97/17.57 ( ^[X4:$i]: 68.97/17.57 ( e_is @ X1 @ ( ap @ X2 @ X4 ) @ ( ap @ X3 @ X4 ) ) ) ) => 68.97/17.57 ( e_is @ ( d_Pi @ X0 @ ( ^[X4:$i]: ( X1 ) ) ) @ X2 @ X3 ) ) ) ) ) ))). 68.97/17.57 thf(zf_stmt_2, axiom, 68.97/17.57 (![X4:$i,X6:$i,X8:$i]: 68.97/17.57 ( ( is_of @ 68.97/17.57 X8 @ 68.97/17.57 ( ^[V_1:$i]: ( in @ V_1 @ ( d_Pi @ X4 @ ( ^[V_2:$i]: ( X6 ) ) ) ) ) ) => 68.97/17.57 ( ![X10:$i]: 68.97/17.57 ( ( is_of @ 68.97/17.57 X10 @ 68.97/17.57 ( ^[V_3:$i]: ( in @ V_3 @ ( d_Pi @ X4 @ ( ^[V_4:$i]: ( X6 ) ) ) ) ) ) => 68.97/17.57 ( ( ![X12:$i]: 68.97/17.57 ( ( is_of @ X12 @ ( ^[V_5:$i]: ( in @ V_5 @ X4 ) ) ) => 68.97/17.57 ( ( ap @ X8 @ X12 ) = ( ap @ X10 @ X12 ) ) ) ) => 68.97/17.57 ( ( X8 ) = ( X10 ) ) ) ) ) ))). 68.97/17.57 thf(zip_derived_cl7, plain, 68.97/17.57 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 68.97/17.57 (~ (is_of @ X0 @ 68.97/17.57 (^[Y0 : $i]: (in @ Y0 @ (d_Pi @ X1 @ (^[Y1 : $i]: (X2)))))) 68.97/17.57 | ((X3) = (X0)) 68.97/17.57 | (is_of @ (sk__2 @ X0 @ X3 @ X1) @ (^[Y0 : $i]: (in @ Y0 @ X1))) 68.97/17.57 | ~ (is_of @ X3 @ 68.97/17.57 (^[Y0 : $i]: (in @ Y0 @ (d_Pi @ X1 @ (^[Y1 : $i]: (X2)))))))), 68.97/17.57 inference('cnf', [status(esa)], [zf_stmt_2])). 68.97/17.57 thf(zip_derived_cl5834, plain, 68.97/17.57 (![X1 : $i, X4 : $i]: (('#l_lift5770' @ X1 @ X4) = (in @ X4 @ X1))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(n_ax4, axiom, 68.97/17.57 (all_of @ 68.97/17.57 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 68.97/17.57 ( ^[X0:$i]: 68.97/17.57 ( all_of @ 68.97/17.57 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 68.97/17.57 ( ^[X1:$i]: 68.97/17.57 ( ( n_is @ ( ordsucc @ X0 ) @ ( ordsucc @ X1 ) ) => 68.97/17.57 ( n_is @ X0 @ X1 ) ) ) ) ))). 68.97/17.57 thf(zf_stmt_3, axiom, 68.97/17.57 (![X4:$i]: 68.97/17.57 ( ( is_of @ 68.97/17.57 X4 @ 68.97/17.57 ( ^[V_1:$i]: 68.97/17.57 ( in @ 68.97/17.57 V_1 @ 68.97/17.57 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) => 68.97/17.57 ( ![X6:$i]: 68.97/17.57 ( ( is_of @ 68.97/17.57 X6 @ 68.97/17.57 ( ^[V_3:$i]: 68.97/17.57 ( in @ 68.97/17.57 V_3 @ 68.97/17.57 ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 68.97/17.57 ( ( ( ordsucc @ X4 ) = ( ordsucc @ X6 ) ) => ( ( X4 ) = ( X6 ) ) ) ) ) ))). 68.97/17.57 thf(zip_derived_cl3, plain, 68.97/17.57 (![X0 : $i, X1 : $i]: 68.97/17.57 (~ (is_of @ X0 @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (in @ Y0 @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 68.97/17.57 | ((X1) = (X0)) 68.97/17.57 | ((ordsucc @ X1) != (ordsucc @ X0)) 68.97/17.57 | ~ (is_of @ X1 @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (in @ Y0 @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 68.97/17.57 inference('cnf', [status(esa)], [zf_stmt_3])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5957, plain, 68.97/17.57 ( (is_of @ sk__6 @ ('#l_lift5770' @ (d_Sep @ omega @ '#l_lift5766')))), 68.97/17.57 inference('lambda_lifting', [status(thm)], 68.97/17.57 [zip_derived_cl133, zip_derived_cl5834, zip_derived_cl5828])). 68.97/17.57 thf(zip_derived_cl131, plain, 68.97/17.57 ( (is_of @ sk__5 @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (in @ Y0 @ 68.97/17.57 (pair1type @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 68.97/17.57 inference('cnf', [status(esa)], [zf_stmt_1])). 68.97/17.57 thf(zip_derived_cl5834, plain, 68.97/17.57 (![X1 : $i, X4 : $i]: (('#l_lift5770' @ X1 @ X4) = (in @ X4 @ X1))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5955, plain, 68.97/17.57 ( (is_of @ sk__5 @ 68.97/17.57 ('#l_lift5770' @ (pair1type @ (d_Sep @ omega @ '#l_lift5766'))))), 68.97/17.57 inference('lambda_lifting', [status(thm)], 68.97/17.57 [zip_derived_cl131, zip_derived_cl5834, zip_derived_cl5828])). 68.97/17.57 thf(zip_derived_cl132, plain, 68.97/17.57 (((ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ 68.97/17.57 (d_Sigma @ 68.97/17.57 (d_Sep @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (lessis @ Y0 @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (ind @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (prop1 @ 68.97/17.57 (((Y0) = (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ sk__5 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 sk__6) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ sk__5 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 sk__6))))) @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (ap @ sk__5 @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) 68.97/17.57 != (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ sk__5 @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (ap @ 68.97/17.57 (d_Sigma @ 68.97/17.57 (d_Sep @ 68.97/17.57 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (lessis @ Y0 @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (ind @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (prop1 @ 68.97/17.57 (((Y0) = (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ sk__5 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 sk__6) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ sk__5 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 sk__6))))) @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))), 68.97/17.57 inference('cnf', [status(esa)], [zf_stmt_1])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(satz40, axiom, 68.97/17.57 (all_of @ 68.97/17.57 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 68.97/17.57 ( ^[X0:$i]: 68.97/17.57 ( all_of @ 68.97/17.57 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 68.97/17.57 ( ^[X1:$i]: 68.97/17.57 ( n_eq @ 68.97/17.57 X0 @ 68.97/17.57 ( n_fr @ 68.97/17.57 ( n_ts @ ( num @ X0 ) @ X1 ) @ ( n_ts @ ( den @ X0 ) @ X1 ) ) ) ) ) ))). 68.97/17.57 thf(zf_stmt_4, axiom, 68.97/17.57 (![X4:$i]: 68.97/17.57 ( ( is_of @ 68.97/17.57 X4 @ 68.97/17.57 ( ^[V_1:$i]: 68.97/17.57 ( in @ 68.97/17.57 V_1 @ 68.97/17.57 ( pair1type @ 68.97/17.57 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) ) => 68.97/17.57 ( ![X6:$i]: 68.97/17.57 ( ( is_of @ 68.97/17.57 X6 @ 68.97/17.57 ( ^[V_3:$i]: 68.97/17.57 ( in @ 68.97/17.57 V_3 @ 68.97/17.57 ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 68.97/17.57 ( ( ap @ 68.97/17.57 ( times @ 68.97/17.57 ( ap @ 68.97/17.57 X4 @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) ) @ 68.97/17.57 ( ap @ 68.97/17.57 ( d_Sigma @ 68.97/17.57 ( d_Sep @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ ( ^[V_5:$i]: ( ( V_5 ) != ( emptyset ) ) ) ) @ 68.97/17.57 ( ^[V_6:$i]: 68.97/17.57 ( lessis @ 68.97/17.57 V_6 @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) @ 68.97/17.57 ( ^[V_7:$i]: 68.97/17.57 ( ind @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) @ 68.97/17.57 ( prop1 @ 68.97/17.57 ( ( V_7 ) = 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ ( ^[V_9:$i]: ( ( V_9 ) != ( emptyset ) ) ) ) @ 68.97/17.57 ( ap @ 68.97/17.57 ( times @ 68.97/17.57 ( ap @ 68.97/17.57 X4 @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) ) @ 68.97/17.57 X6 ) @ 68.97/17.57 ( ap @ 68.97/17.57 ( times @ 68.97/17.57 ( ap @ 68.97/17.57 X4 @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) ) ) @ 68.97/17.57 X6 ) ) ) ) ) @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) = 68.97/17.57 ( ap @ 68.97/17.57 ( times @ 68.97/17.57 ( ap @ 68.97/17.57 ( d_Sigma @ 68.97/17.57 ( d_Sep @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ ( ^[V_10:$i]: ( ( V_10 ) != ( emptyset ) ) ) ) @ 68.97/17.57 ( ^[V_11:$i]: 68.97/17.57 ( lessis @ 68.97/17.57 V_11 @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) @ 68.97/17.57 ( ^[V_12:$i]: 68.97/17.57 ( ind @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ ( ^[V_13:$i]: ( ( V_13 ) != ( emptyset ) ) ) ) @ 68.97/17.57 ( prop1 @ 68.97/17.57 ( ( V_12 ) = 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) @ 68.97/17.57 ( d_Sep @ 68.97/17.57 omega @ 68.97/17.57 ( ^[V_14:$i]: ( ( V_14 ) != ( emptyset ) ) ) ) @ 68.97/17.57 ( ap @ 68.97/17.57 ( times @ 68.97/17.57 ( ap @ 68.97/17.57 X4 @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) ) @ 68.97/17.57 X6 ) @ 68.97/17.57 ( ap @ 68.97/17.57 ( times @ 68.97/17.57 ( ap @ 68.97/17.57 X4 @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( n_pl @ 68.97/17.57 ( ordsucc @ emptyset ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) ) ) @ 68.97/17.57 X6 ) ) ) ) ) @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( ordsucc @ emptyset ) ) ) ) @ 68.97/17.57 ( ap @ 68.97/17.57 X4 @ 68.97/17.57 ( outn @ 68.97/17.57 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ 68.97/17.57 ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ) ) ) ) ) ))). 68.97/17.57 thf(zip_derived_cl25, plain, 68.97/17.57 (![X0 : $i, X1 : $i]: 68.97/17.57 (~ (is_of @ X0 @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (in @ Y0 @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 68.97/17.57 | ((ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (ap @ 68.97/17.57 (d_Sigma @ 68.97/17.57 (d_Sep @ 68.97/17.57 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (lessis @ Y0 @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (ind @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (prop1 @ 68.97/17.57 (((Y0) = (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 X0) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 X0))))) @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) 68.97/17.57 = (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ 68.97/17.57 (d_Sigma @ 68.97/17.57 (d_Sep @ 68.97/17.57 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (lessis @ Y0 @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (ind @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (prop1 @ 68.97/17.57 (((Y0) = (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ 68.97/17.57 (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 X0) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ 68.97/17.57 (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ 68.97/17.57 (ordsucc @ emptyset))))) @ 68.97/17.57 X0))))) @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))) 68.97/17.57 | ~ (is_of @ X1 @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (in @ Y0 @ 68.97/17.57 (pair1type @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))))), 68.97/17.57 inference('cnf', [status(esa)], [zf_stmt_4])). 68.97/17.57 thf(zip_derived_cl5847, plain, 68.97/17.57 (![X2 : $i]: 68.97/17.57 (('#l_lift5771' @ X2) 68.97/17.57 = (lessis @ X2 @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl25, plain, 68.97/17.57 (![X0 : $i, X1 : $i]: 68.97/17.57 (~ (is_of @ X0 @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (in @ Y0 @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 68.97/17.57 | ((ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (ap @ 68.97/17.57 (d_Sigma @ 68.97/17.57 (d_Sep @ 68.97/17.57 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (lessis @ Y0 @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (ind @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (prop1 @ 68.97/17.57 (((Y0) = (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 X0) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 X0))))) @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) 68.97/17.57 = (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ 68.97/17.57 (d_Sigma @ 68.97/17.57 (d_Sep @ 68.97/17.57 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (lessis @ Y0 @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (ind @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (prop1 @ 68.97/17.57 (((Y0) = (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ 68.97/17.57 (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 X0) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ 68.97/17.57 (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ 68.97/17.57 (ordsucc @ emptyset))))) @ 68.97/17.57 X0))))) @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))) 68.97/17.57 | ~ (is_of @ X1 @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (in @ Y0 @ 68.97/17.57 (pair1type @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))))), 68.97/17.57 inference('cnf', [status(esa)], [zf_stmt_4])). 68.97/17.57 thf(zip_derived_cl5848, plain, 68.97/17.57 (![X0 : $i, X1 : $i, X3 : $i]: 68.97/17.57 (('#l_lift5772' @ X0 @ X1 @ X3) 68.97/17.57 = (ind @ (d_Sep @ omega @ '#l_lift5766') @ 68.97/17.57 (prop1 @ 68.97/17.57 (((X3) = (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (d_Sep @ omega @ '#l_lift5766') @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 X0) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 X0))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5847, plain, 68.97/17.57 (![X2 : $i]: 68.97/17.57 (('#l_lift5771' @ X2) 68.97/17.57 = (lessis @ X2 @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5848, plain, 68.97/17.57 (![X0 : $i, X1 : $i, X3 : $i]: 68.97/17.57 (('#l_lift5772' @ X0 @ X1 @ X3) 68.97/17.57 = (ind @ (d_Sep @ omega @ '#l_lift5766') @ 68.97/17.57 (prop1 @ 68.97/17.57 (((X3) = (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (d_Sep @ omega @ '#l_lift5766') @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 X0) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 X0))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5956, plain, 68.97/17.57 (((ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ 68.97/17.57 (d_Sigma @ 68.97/17.57 (d_Sep @ (d_Sep @ omega @ '#l_lift5766') @ '#l_lift5771') @ 68.97/17.57 ('#l_lift5772' @ sk__6 @ sk__5)) @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (ap @ sk__5 @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) 68.97/17.57 != (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ sk__5 @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (ap @ 68.97/17.57 (d_Sigma @ 68.97/17.57 (d_Sep @ (d_Sep @ omega @ '#l_lift5766') @ '#l_lift5771') @ 68.97/17.57 ('#l_lift5772' @ sk__6 @ sk__5)) @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))), 68.97/17.57 inference('lambda_lifting', [status(thm)], 68.97/17.57 [zip_derived_cl132, zip_derived_cl5828, zip_derived_cl5847, 68.97/17.57 zip_derived_cl5848, zip_derived_cl5828, zip_derived_cl5828, 68.97/17.57 zip_derived_cl5828, zip_derived_cl5847, zip_derived_cl5848, 68.97/17.57 zip_derived_cl5828, zip_derived_cl5828])). 68.97/17.57 thf(zip_derived_cl25, plain, 68.97/17.57 (![X0 : $i, X1 : $i]: 68.97/17.57 (~ (is_of @ X0 @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (in @ Y0 @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 68.97/17.57 | ((ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (ap @ 68.97/17.57 (d_Sigma @ 68.97/17.57 (d_Sep @ 68.97/17.57 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (lessis @ Y0 @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (ind @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (prop1 @ 68.97/17.57 (((Y0) = (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 X0) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 X0))))) @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) 68.97/17.57 = (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ 68.97/17.57 (d_Sigma @ 68.97/17.57 (d_Sep @ 68.97/17.57 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (lessis @ Y0 @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (ind @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (prop1 @ 68.97/17.57 (((Y0) = (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ 68.97/17.57 (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 X0) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ 68.97/17.57 (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ 68.97/17.57 (ordsucc @ emptyset))))) @ 68.97/17.57 X0))))) @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))) 68.97/17.57 | ~ (is_of @ X1 @ 68.97/17.57 (^[Y0 : $i]: 68.97/17.57 (in @ Y0 @ 68.97/17.57 (pair1type @ 68.97/17.57 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))))), 68.97/17.57 inference('cnf', [status(esa)], [zf_stmt_4])). 68.97/17.57 thf(zip_derived_cl5834, plain, 68.97/17.57 (![X1 : $i, X4 : $i]: (('#l_lift5770' @ X1 @ X4) = (in @ X4 @ X1))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5847, plain, 68.97/17.57 (![X2 : $i]: 68.97/17.57 (('#l_lift5771' @ X2) 68.97/17.57 = (lessis @ X2 @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5848, plain, 68.97/17.57 (![X0 : $i, X1 : $i, X3 : $i]: 68.97/17.57 (('#l_lift5772' @ X0 @ X1 @ X3) 68.97/17.57 = (ind @ (d_Sep @ omega @ '#l_lift5766') @ 68.97/17.57 (prop1 @ 68.97/17.57 (((X3) = (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (d_Sep @ omega @ '#l_lift5766') @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 X0) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 X0))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5834, plain, 68.97/17.57 (![X1 : $i, X4 : $i]: (('#l_lift5770' @ X1 @ X4) = (in @ X4 @ X1))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5828, plain, 68.97/17.57 (![X2 : $i]: (('#l_lift5766' @ X2) = (((X2) != (emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5847, plain, 68.97/17.57 (![X2 : $i]: 68.97/17.57 (('#l_lift5771' @ X2) 68.97/17.57 = (lessis @ X2 @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5848, plain, 68.97/17.57 (![X0 : $i, X1 : $i, X3 : $i]: 68.97/17.57 (('#l_lift5772' @ X0 @ X1 @ X3) 68.97/17.57 = (ind @ (d_Sep @ omega @ '#l_lift5766') @ 68.97/17.57 (prop1 @ 68.97/17.57 (((X3) = (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (d_Sep @ omega @ '#l_lift5766') @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 X0) @ 68.97/17.57 (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 68.97/17.57 X0))))), 68.97/17.57 define([status(thm)])). 68.97/17.57 thf(zip_derived_cl5849, plain, 68.97/17.57 (![X0 : $i, X1 : $i]: 68.97/17.57 (~ (is_of @ X0 @ ('#l_lift5770' @ (d_Sep @ omega @ '#l_lift5766'))) 68.97/17.57 | ((ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (ap @ 68.97/17.57 (d_Sigma @ 68.97/17.57 (d_Sep @ (d_Sep @ omega @ '#l_lift5766') @ '#l_lift5771') @ 68.97/17.57 ('#l_lift5772' @ X0 @ X1)) @ 68.97/17.57 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) 68.97/17.57 = (ap @ 68.97/17.57 (times @ 68.97/17.57 (ap @ 68.97/17.57 (d_Sigma @ 68.97/17.57 (d_Sep @ (d_Sep @ omega @ '#l_lift5766') @ '#l_lift5771') @ 68.97/17.57 ('#l_lift5772' @ X0 @ X1)) @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (ordsucc @ emptyset)))) @ 68.97/17.57 (ap @ X1 @ 68.97/17.57 (outn @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 68.97/17.57 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))) 68.97/17.57 | ~ (is_of @ X1 @ 68.97/17.57 ('#l_lift5770' @ (pair1type @ (d_Sep @ omega @ '#l_lift5766')))))), 68.97/17.57 inference('lambda_lifting', [status(thm)], 68.97/17.57 [zip_derived_cl25, zip_derived_cl5834, zip_derived_cl5828, 68.97/17.57 zip_derived_cl5828, zip_derived_cl5828, zip_derived_cl5828, 68.97/17.57 zip_derived_cl5828, zip_derived_cl5847, zip_derived_cl5848, 68.97/17.57 zip_derived_cl5828, zip_derived_cl5828, zip_derived_cl5834, 68.97/17.57 zip_derived_cl5828, zip_derived_cl5847, zip_derived_cl5848])). 68.97/17.57 thf(zip_derived_cl6020, plain, ($false), 68.97/17.57 inference('eprover', [status(thm)], 68.97/17.57 [zip_derived_cl5957, zip_derived_cl5955, zip_derived_cl5956, 68.97/17.57 zip_derived_cl5849])). 68.97/17.57 68.97/17.57 % SZS output end Refutation 68.97/17.57 68.97/17.57 68.97/17.57 % Terminating... 69.48/17.72 % Runner terminated. 69.48/17.73 % Zipperpin 1.5 exiting 69.48/17.75 EOF