0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.18 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.QaIlCvrrFX true 0.16/0.37 % Computer : n028.cluster.edu 0.16/0.37 % Model : x86_64 x86_64 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.37 % Memory : 8042.1875MB 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.37 % CPULimit : 1920 0.16/0.37 % WCLimit : 240 0.16/0.37 % DateTime : Wed Jul 30 10:07:34 EDT 2025 0.16/0.38 % CPUTime : 0.16/0.38 % Running portfolio for 1920 s 0.16/0.38 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.16/0.38 % Number of cores: 8 0.16/0.38 % Python version: Python 3.6.8 0.16/0.38 % Running in HO mode 0.51/0.66 % Total configuration time : 828 0.51/0.66 % Estimated wc time : 1656 0.51/0.66 % Estimated cpu time (8 cpus) : 207.0 0.52/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.52/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.52/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.52/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 47.62/6.68 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 238.87/30.94 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 317.81/41.09 % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s 481.18/61.99 % /export/starexec/sandbox2/solver/bin/lams/15_lifting3.sh running for 30s 555.20/71.42 % /export/starexec/sandbox2/solver/bin/lams/33_shallow_sine.sh running for 66s 557.37/71.79 % /export/starexec/sandbox2/solver/bin/lams/40_e_lift.sh running for 80s 632.31/81.29 % /export/starexec/sandbox2/solver/bin/lams/15_lifting1.sh running for 30s 638.43/82.20 % /export/starexec/sandbox2/solver/bin/lams/8_new_cnf.sh running for 16s 678.52/87.38 % /export/starexec/sandbox2/solver/bin/lams/10_e_short2.sh running for 20s 716.20/92.39 % /export/starexec/sandbox2/solver/bin/lams/8_add_var_l_av.sh running for 16s 718.32/92.71 % /export/starexec/sandbox2/solver/bin/lams/8_new_sh_or.sh running for 16s 761.48/98.39 % /export/starexec/sandbox2/solver/bin/lams/30_old_zip1.sh running for 36s 803.22/104.42 % Solved by lams/33_shallow_sine.sh. 803.22/104.42 % done 1384 iterations in 32.945s 803.22/104.42 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 803.22/104.42 % SZS output start Refutation 803.22/104.42 thf(rt_is_type, type, rt_is: $i > $i > $o). 803.22/104.42 thf(inf_type, type, inf: $i > $i > $o). 803.22/104.42 thf(rt_lessis_type, type, rt_lessis: $i > $i > $o). 803.22/104.42 thf(moref_type, type, moref: $i > $i > $o). 803.22/104.42 thf(d_not_type, type, d_not: $o > $o). 803.22/104.42 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 803.22/104.42 thf(in_type, type, in: $i > $i > $o). 803.22/104.42 thf(and3_type, type, and3: $o > $o > $o > $o). 803.22/104.42 thf(rt_more_type, type, rt_more: $i > $i > $o). 803.22/104.42 thf(e_is_type, type, e_is: $i > $i > $i > $o). 803.22/104.42 thf(sk__4_type, type, sk__4: $i). 803.22/104.42 thf(l_or_type, type, l_or: $o > $o > $o). 803.22/104.42 thf(rt_moreis_type, type, rt_moreis: $i > $i > $o). 803.22/104.42 thf(rat_type, type, rat: $i). 803.22/104.42 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 803.22/104.42 thf(sk__2_type, type, sk__2: $i). 803.22/104.42 thf(frac_type, type, frac: $i). 803.22/104.42 thf(imp_type, type, imp: $o > $o > $o). 803.22/104.42 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 803.22/104.42 thf(rt_less_type, type, rt_less: $i > $i > $o). 803.22/104.42 thf(n_eq_type, type, n_eq: $i > $i > $o). 803.22/104.42 thf(class_type, type, class: $i > $i). 803.22/104.42 thf(sk__3_type, type, sk__3: $i). 803.22/104.42 thf(ect_type, type, ect: $i > ($i > $i > $o) > $i). 803.22/104.42 thf(def_rt_moreis, axiom,(( rt_moreis ) = 803.22/104.42 (^[X0:$i,X1:$i]: ( l_or @ ( rt_more @ X0 @ X1 ) @ ( rt_is @ X0 @ X1 ) )))). 803.22/104.42 thf(def_rt_more, axiom,(( rt_more ) = 803.22/104.42 (^[X0:$i,X1:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[X2:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[X3:$i]: 803.22/104.42 ( and3 @ 803.22/104.42 ( inf @ X2 @ ( class @ X0 ) ) @ ( inf @ X3 @ ( class @ X1 ) ) @ 803.22/104.42 ( moref @ X2 @ X3 ) ) ) ) ) )))). 803.22/104.42 thf('0', plain, 803.22/104.42 (( rt_more ) = 803.22/104.42 ( ^[X0:$i,X1:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[X2:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[X3:$i]: 803.22/104.42 ( and3 @ 803.22/104.42 ( inf @ X2 @ ( class @ X0 ) ) @ 803.22/104.42 ( inf @ X3 @ ( class @ X1 ) ) @ ( moref @ X2 @ X3 ) ) ) ) ) ) )), 803.22/104.42 inference('simplify_rw_rule', [status(thm)], [def_rt_more])). 803.22/104.42 thf('1', plain, 803.22/104.42 (( rt_more ) = 803.22/104.42 ( ^[V_1:$i,V_2:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_3:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_4:$i]: 803.22/104.42 ( and3 @ 803.22/104.42 ( inf @ V_3 @ ( class @ V_1 ) ) @ 803.22/104.42 ( inf @ V_4 @ ( class @ V_2 ) ) @ ( moref @ V_3 @ V_4 ) ) ) ) ) ) )), 803.22/104.42 define([status(thm)])).thf(def_rt_is, axiom,(( rt_is ) = (e_is @ rat))). 803.22/104.42 thf(def_rat, axiom,(( rat ) = (ect @ frac @ n_eq))). 803.22/104.42 thf('2', plain, (( rat ) = ( ect @ frac @ n_eq )), 803.22/104.42 inference('simplify_rw_rule', [status(thm)], [def_rat])). 803.22/104.42 thf('3', plain, (( rat ) = ( ect @ frac @ n_eq )), define([status(thm)])). 803.22/104.42 thf('4', plain, (( rt_is ) = ( e_is @ rat )), 803.22/104.42 inference('simplify_rw_rule', [status(thm)], [def_rt_is, '3'])). 803.22/104.42 thf('5', plain, (( rt_is ) = ( e_is @ rat )), define([status(thm)])). 803.22/104.42 thf(def_l_or, axiom,(( l_or ) = (^[X0:$o]: ( imp @ ( d_not @ X0 ) )))). 803.22/104.42 thf('6', plain, (( l_or ) = ( ^[X0:$o]: ( imp @ ( d_not @ X0 ) ) )), 803.22/104.42 inference('simplify_rw_rule', [status(thm)], [def_l_or])). 803.22/104.42 thf('7', plain, (( l_or ) = ( ^[V_1:$o]: ( imp @ ( d_not @ V_1 ) ) )), 803.22/104.42 define([status(thm)])). 803.22/104.42 thf('8', plain, 803.22/104.42 (( rt_moreis ) = 803.22/104.42 ( ^[X0:$i,X1:$i]: ( l_or @ ( rt_more @ X0 @ X1 ) @ ( rt_is @ X0 @ X1 ) ) )), 803.22/104.42 inference('simplify_rw_rule', [status(thm)], 803.22/104.42 [def_rt_moreis, '1', '5', '3', '7'])). 803.22/104.42 thf('9', plain, 803.22/104.42 (( rt_moreis ) = 803.22/104.42 ( ^[V_1:$i,V_2:$i]: 803.22/104.42 ( l_or @ ( rt_more @ V_1 @ V_2 ) @ ( rt_is @ V_1 @ V_2 ) ) )), 803.22/104.42 define([status(thm)])). 803.22/104.42 thf(def_all_of, axiom,(( all_of ) = 803.22/104.42 (^[X0:( $i > $o ),X1:( $i > $o )]: 803.22/104.42 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) )))). 803.22/104.42 thf('10', plain, 803.22/104.42 (( all_of ) = 803.22/104.42 ( ^[X0:( $i > $o ),X1:( $i > $o )]: 803.22/104.42 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) ) )), 803.22/104.42 inference('simplify_rw_rule', [status(thm)], [def_all_of])). 803.22/104.42 thf('11', plain, 803.22/104.42 (( all_of ) = 803.22/104.42 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 803.22/104.42 ( ![X4:$i]: ( ( is_of @ X4 @ V_1 ) => ( V_2 @ X4 ) ) ) )), 803.22/104.42 define([status(thm)])). 803.22/104.42 thf(satz87c, conjecture, 803.22/104.42 (all_of @ 803.22/104.42 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 803.22/104.42 ( ^[X0:$i]: 803.22/104.42 ( all_of @ 803.22/104.42 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 803.22/104.42 ( ^[X1:$i]: 803.22/104.42 ( all_of @ 803.22/104.42 ( ^[X2:$i]: ( in @ X2 @ rat ) ) @ 803.22/104.42 ( ^[X2:$i]: 803.22/104.42 ( ( rt_moreis @ X0 @ X1 ) => 803.22/104.42 ( ( rt_more @ X1 @ X2 ) => ( rt_more @ X0 @ X2 ) ) ) ) ) ) ) ))). 803.22/104.42 thf(zf_stmt_0, conjecture, 803.22/104.42 (![X4:$i]: 803.22/104.42 ( ( is_of @ X4 @ ( ^[V_1:$i]: ( in @ V_1 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X6:$i]: 803.22/104.42 ( ( is_of @ X6 @ ( ^[V_2:$i]: ( in @ V_2 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X8:$i]: 803.22/104.42 ( ( is_of @ 803.22/104.42 X8 @ ( ^[V_3:$i]: ( in @ V_3 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ( imp @ 803.22/104.42 ( d_not @ 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_4:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_5:$i]: 803.22/104.42 ( and3 @ 803.22/104.42 ( inf @ V_4 @ ( class @ X4 ) ) @ 803.22/104.42 ( inf @ V_5 @ ( class @ X6 ) ) @ 803.22/104.42 ( moref @ V_4 @ V_5 ) ) ) ) ) ) ) @ 803.22/104.42 ( e_is @ ( ect @ frac @ n_eq ) @ X4 @ X6 ) ) => 803.22/104.42 ( ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_6:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_7:$i]: 803.22/104.42 ( and3 @ 803.22/104.42 ( inf @ V_6 @ ( class @ X6 ) ) @ 803.22/104.42 ( inf @ V_7 @ ( class @ X8 ) ) @ 803.22/104.42 ( moref @ V_6 @ V_7 ) ) ) ) ) ) => 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_8:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_9:$i]: 803.22/104.42 ( and3 @ 803.22/104.42 ( inf @ V_8 @ ( class @ X4 ) ) @ 803.22/104.42 ( inf @ V_9 @ ( class @ X8 ) ) @ 803.22/104.42 ( moref @ V_8 @ V_9 ) ) ) ) ) ) ) ) ) ) ) ) ))). 803.22/104.42 thf(zf_stmt_1, negated_conjecture, 803.22/104.42 (~( ![X4:$i]: 803.22/104.42 ( ( is_of @ X4 @ ( ^[V_1:$i]: ( in @ V_1 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X6:$i]: 803.22/104.42 ( ( is_of @ 803.22/104.42 X6 @ ( ^[V_2:$i]: ( in @ V_2 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X8:$i]: 803.22/104.42 ( ( is_of @ 803.22/104.42 X8 @ ( ^[V_3:$i]: ( in @ V_3 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ( imp @ 803.22/104.42 ( d_not @ 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_4:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_5:$i]: 803.22/104.42 ( and3 @ 803.22/104.42 ( inf @ V_4 @ ( class @ X4 ) ) @ 803.22/104.42 ( inf @ V_5 @ ( class @ X6 ) ) @ 803.22/104.42 ( moref @ V_4 @ V_5 ) ) ) ) ) ) ) @ 803.22/104.42 ( e_is @ ( ect @ frac @ n_eq ) @ X4 @ X6 ) ) => 803.22/104.42 ( ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_6:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_7:$i]: 803.22/104.42 ( and3 @ 803.22/104.42 ( inf @ V_6 @ ( class @ X6 ) ) @ 803.22/104.42 ( inf @ V_7 @ ( class @ X8 ) ) @ 803.22/104.42 ( moref @ V_6 @ V_7 ) ) ) ) ) ) => 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_8:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_9:$i]: 803.22/104.42 ( and3 @ 803.22/104.42 ( inf @ V_8 @ ( class @ X4 ) ) @ 803.22/104.42 ( inf @ V_9 @ ( class @ X8 ) ) @ 803.22/104.42 ( moref @ V_8 @ V_9 ) ) ) ) ) ) ) ) ) ) ) ) ) )), 803.22/104.42 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 803.22/104.42 thf(zip_derived_cl25, plain, 803.22/104.42 ( (is_of @ sk__3 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl20, plain, 803.22/104.42 ( (is_of @ sk__2 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(def_rt_lessis, axiom,(( rt_lessis ) = 803.22/104.42 (^[X0:$i,X1:$i]: ( l_or @ ( rt_less @ X0 @ X1 ) @ ( rt_is @ X0 @ X1 ) )))). 803.22/104.42 thf('12', plain, 803.22/104.42 (( rt_lessis ) = 803.22/104.42 ( ^[X0:$i,X1:$i]: ( l_or @ ( rt_less @ X0 @ X1 ) @ ( rt_is @ X0 @ X1 ) ) )), 803.22/104.42 inference('simplify_rw_rule', [status(thm)], 803.22/104.42 [def_rt_lessis, '5', '3', '7'])). 803.22/104.42 thf('13', plain, 803.22/104.42 (( rt_lessis ) = 803.22/104.42 ( ^[V_1:$i,V_2:$i]: 803.22/104.42 ( l_or @ ( rt_less @ V_1 @ V_2 ) @ ( rt_is @ V_1 @ V_2 ) ) )), 803.22/104.42 define([status(thm)])). 803.22/104.42 thf(satz81e, axiom, 803.22/104.42 (all_of @ 803.22/104.42 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 803.22/104.42 ( ^[X0:$i]: 803.22/104.42 ( all_of @ 803.22/104.42 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 803.22/104.42 ( ^[X1:$i]: 803.22/104.42 ( ( d_not @ ( rt_more @ X0 @ X1 ) ) => ( rt_lessis @ X0 @ X1 ) ) ) ) ))). 803.22/104.42 thf(zf_stmt_2, axiom, 803.22/104.42 (![X4:$i]: 803.22/104.42 ( ( is_of @ X4 @ ( ^[V_1:$i]: ( in @ V_1 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X6:$i]: 803.22/104.42 ( ( is_of @ X6 @ ( ^[V_2:$i]: ( in @ V_2 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ( d_not @ 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_3:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_4:$i]: 803.22/104.42 ( and3 @ 803.22/104.42 ( inf @ V_3 @ ( class @ X4 ) ) @ 803.22/104.42 ( inf @ V_4 @ ( class @ X6 ) ) @ ( moref @ V_3 @ V_4 ) ) ) ) ) ) ) => 803.22/104.42 ( imp @ 803.22/104.42 ( d_not @ ( rt_less @ X4 @ X6 ) ) @ 803.22/104.42 ( e_is @ ( ect @ frac @ n_eq ) @ X4 @ X6 ) ) ) ) ) ))). 803.22/104.42 thf(zip_derived_cl11, plain, 803.22/104.42 (![X0 : $i, X1 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | (imp @ (d_not @ (rt_less @ X1 @ X0)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ X1 @ X0)) 803.22/104.42 | ~ (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ X1)) @ 803.22/104.42 (inf @ Y1 @ (class @ X0)) @ (moref @ Y0 @ Y1))))))) 803.22/104.42 | ~ (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_2])). 803.22/104.42 thf(zip_derived_cl691, plain, 803.22/104.42 (![X0 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ X0)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__2)) @ (moref @ Y0 @ Y1))))))) 803.22/104.42 | (imp @ (d_not @ (rt_less @ X0 @ sk__2)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ X0 @ sk__2)))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl11])). 803.22/104.42 thf(zip_derived_cl7188, plain, 803.22/104.42 (( (imp @ (d_not @ (rt_less @ sk__3 @ sk__2)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__3 @ sk__2)) 803.22/104.42 | ~ (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__3)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__2)) @ (moref @ Y0 @ Y1))))))))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl691])). 803.22/104.42 thf(zip_derived_cl20, plain, 803.22/104.42 ( (is_of @ sk__2 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl21, plain, 803.22/104.42 ( (is_of @ sk__4 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl25, plain, 803.22/104.42 ( (is_of @ sk__3 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(satz87b, axiom, 803.22/104.42 (all_of @ 803.22/104.42 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 803.22/104.42 ( ^[X0:$i]: 803.22/104.42 ( all_of @ 803.22/104.42 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 803.22/104.42 ( ^[X1:$i]: 803.22/104.42 ( all_of @ 803.22/104.42 ( ^[X2:$i]: ( in @ X2 @ rat ) ) @ 803.22/104.42 ( ^[X2:$i]: 803.22/104.42 ( ( rt_less @ X0 @ X1 ) => 803.22/104.42 ( ( rt_lessis @ X1 @ X2 ) => ( rt_less @ X0 @ X2 ) ) ) ) ) ) ) ))). 803.22/104.42 thf(zf_stmt_3, axiom, 803.22/104.42 (![X4:$i]: 803.22/104.42 ( ( is_of @ X4 @ ( ^[V_1:$i]: ( in @ V_1 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X6:$i]: 803.22/104.42 ( ( is_of @ X6 @ ( ^[V_2:$i]: ( in @ V_2 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X8:$i]: 803.22/104.42 ( ( is_of @ 803.22/104.42 X8 @ ( ^[V_3:$i]: ( in @ V_3 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ( rt_less @ X4 @ X6 ) => 803.22/104.42 ( ( imp @ 803.22/104.42 ( d_not @ ( rt_less @ X6 @ X8 ) ) @ 803.22/104.42 ( e_is @ ( ect @ frac @ n_eq ) @ X6 @ X8 ) ) => 803.22/104.42 ( rt_less @ X4 @ X8 ) ) ) ) ) ) ) ))). 803.22/104.42 thf(zip_derived_cl4, plain, 803.22/104.42 (![X0 : $i, X1 : $i, X2 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (rt_less @ X1 @ X0) 803.22/104.42 | (rt_less @ X1 @ X2) 803.22/104.42 | ~ (imp @ (d_not @ (rt_less @ X0 @ X2)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ X0 @ X2)) 803.22/104.42 | ~ (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_3])). 803.22/104.42 thf(zip_derived_cl271, plain, 803.22/104.42 (![X0 : $i, X1 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (imp @ (d_not @ (rt_less @ sk__3 @ X1)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__3 @ X1)) 803.22/104.42 | (rt_less @ X0 @ X1) 803.22/104.42 | ~ (rt_less @ X0 @ sk__3))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl4])). 803.22/104.42 thf(zip_derived_cl901, plain, 803.22/104.42 (![X0 : $i]: 803.22/104.42 (~ (rt_less @ sk__4 @ sk__3) 803.22/104.42 | (rt_less @ sk__4 @ X0) 803.22/104.42 | ~ (imp @ (d_not @ (rt_less @ sk__3 @ X0)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__3 @ X0)) 803.22/104.42 | ~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl271])). 803.22/104.42 thf(zip_derived_cl25, plain, 803.22/104.42 ( (is_of @ sk__3 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl21, plain, 803.22/104.42 ( (is_of @ sk__4 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(satz82, axiom, 803.22/104.42 (all_of @ 803.22/104.42 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 803.22/104.42 ( ^[X0:$i]: 803.22/104.42 ( all_of @ 803.22/104.42 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 803.22/104.42 ( ^[X1:$i]: ( ( rt_more @ X0 @ X1 ) => ( rt_less @ X1 @ X0 ) ) ) ) ))). 803.22/104.42 thf(zf_stmt_4, axiom, 803.22/104.42 (![X4:$i]: 803.22/104.42 ( ( is_of @ X4 @ ( ^[V_1:$i]: ( in @ V_1 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X6:$i]: 803.22/104.42 ( ( is_of @ X6 @ ( ^[V_2:$i]: ( in @ V_2 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_3:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_4:$i]: 803.22/104.42 ( and3 @ 803.22/104.42 ( inf @ V_3 @ ( class @ X4 ) ) @ 803.22/104.42 ( inf @ V_4 @ ( class @ X6 ) ) @ ( moref @ V_3 @ V_4 ) ) ) ) ) ) => 803.22/104.42 ( rt_less @ X6 @ X4 ) ) ) ) ))). 803.22/104.42 thf(zip_derived_cl9, plain, 803.22/104.42 (![X0 : $i, X1 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | (rt_less @ X0 @ X1) 803.22/104.42 | ~ (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ X1)) @ 803.22/104.42 (inf @ Y1 @ (class @ X0)) @ (moref @ Y0 @ Y1)))))) 803.22/104.42 | ~ (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_4])). 803.22/104.42 thf(zip_derived_cl633, plain, 803.22/104.42 (![X0 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ X0)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__4)) @ (moref @ Y0 @ Y1)))))) 803.22/104.42 | (rt_less @ sk__4 @ X0))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl9])). 803.22/104.42 thf(zip_derived_cl640, plain, 803.22/104.42 (( (rt_less @ sk__4 @ sk__3) 803.22/104.42 | ~ (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__3)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__4)) @ (moref @ Y0 @ Y1)))))))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl633])). 803.22/104.42 thf(zip_derived_cl22, plain, 803.22/104.42 ( (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__3)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__4)) @ (moref @ Y0 @ Y1))))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl644, plain, ( (rt_less @ sk__4 @ sk__3)), 803.22/104.42 inference('demod', [status(thm)], [zip_derived_cl640, zip_derived_cl22])). 803.22/104.42 thf(zip_derived_cl906, plain, 803.22/104.42 (![X0 : $i]: 803.22/104.42 ( (rt_less @ sk__4 @ X0) 803.22/104.42 | ~ (imp @ (d_not @ (rt_less @ sk__3 @ X0)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__3 @ X0)) 803.22/104.42 | ~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('demod', [status(thm)], [zip_derived_cl901, zip_derived_cl644])). 803.22/104.42 thf(zip_derived_cl910, plain, 803.22/104.42 ((~ (imp @ (d_not @ (rt_less @ sk__3 @ sk__2)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__3 @ sk__2)) 803.22/104.42 | (rt_less @ sk__4 @ sk__2))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl906])). 803.22/104.42 thf(zip_derived_cl21, plain, 803.22/104.42 ( (is_of @ sk__4 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl20, plain, 803.22/104.42 ( (is_of @ sk__2 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(satz83, axiom, 803.22/104.42 (all_of @ 803.22/104.42 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 803.22/104.42 ( ^[X0:$i]: 803.22/104.42 ( all_of @ 803.22/104.42 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 803.22/104.42 ( ^[X1:$i]: ( ( rt_less @ X0 @ X1 ) => ( rt_more @ X1 @ X0 ) ) ) ) ))). 803.22/104.42 thf(zf_stmt_5, axiom, 803.22/104.42 (![X4:$i]: 803.22/104.42 ( ( is_of @ X4 @ ( ^[V_1:$i]: ( in @ V_1 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X6:$i]: 803.22/104.42 ( ( is_of @ X6 @ ( ^[V_2:$i]: ( in @ V_2 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ( rt_less @ X4 @ X6 ) => 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_3:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_4:$i]: 803.22/104.42 ( and3 @ 803.22/104.42 ( inf @ V_3 @ ( class @ X6 ) ) @ 803.22/104.42 ( inf @ V_4 @ ( class @ X4 ) ) @ ( moref @ V_3 @ V_4 ) ) ) ) ) ) ) ) ) ))). 803.22/104.42 thf(zip_derived_cl10, plain, 803.22/104.42 (![X0 : $i, X1 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ X0)) @ 803.22/104.42 (inf @ Y1 @ (class @ X1)) @ (moref @ Y0 @ Y1)))))) 803.22/104.42 | ~ (rt_less @ X1 @ X0) 803.22/104.42 | ~ (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_5])). 803.22/104.42 thf(zip_derived_cl306, plain, 803.22/104.42 (![X0 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (rt_less @ X0 @ sk__2) 803.22/104.42 | (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ X0)) @ (moref @ Y0 @ Y1)))))))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl10])). 803.22/104.42 thf(zip_derived_cl716, plain, 803.22/104.42 (( (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__4)) @ (moref @ Y0 @ Y1)))))) 803.22/104.42 | ~ (rt_less @ sk__4 @ sk__2))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl306])). 803.22/104.42 thf(zip_derived_cl23, plain, 803.22/104.42 (~ (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__4)) @ (moref @ Y0 @ Y1))))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl721, plain, (~ (rt_less @ sk__4 @ sk__2)), 803.22/104.42 inference('clc', [status(thm)], [zip_derived_cl716, zip_derived_cl23])). 803.22/104.42 thf(zip_derived_cl914, plain, 803.22/104.42 (~ (imp @ (d_not @ (rt_less @ sk__3 @ sk__2)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__3 @ sk__2))), 803.22/104.42 inference('demod', [status(thm)], [zip_derived_cl910, zip_derived_cl721])). 803.22/104.42 thf(zip_derived_cl7193, plain, 803.22/104.42 (~ (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__3)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__2)) @ (moref @ Y0 @ Y1)))))))), 803.22/104.42 inference('demod', [status(thm)], [zip_derived_cl7188, zip_derived_cl914])). 803.22/104.42 thf(zip_derived_cl20, plain, 803.22/104.42 ( (is_of @ sk__2 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl25, plain, 803.22/104.42 ( (is_of @ sk__3 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl10, plain, 803.22/104.42 (![X0 : $i, X1 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ X0)) @ 803.22/104.42 (inf @ Y1 @ (class @ X1)) @ (moref @ Y0 @ Y1)))))) 803.22/104.42 | ~ (rt_less @ X1 @ X0) 803.22/104.42 | ~ (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_5])). 803.22/104.42 thf(zip_derived_cl305, plain, 803.22/104.42 (![X0 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (rt_less @ X0 @ sk__3) 803.22/104.42 | (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__3)) @ 803.22/104.42 (inf @ Y1 @ (class @ X0)) @ (moref @ Y0 @ Y1)))))))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl10])). 803.22/104.42 thf(zip_derived_cl433, plain, 803.22/104.42 (( (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__3)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__2)) @ (moref @ Y0 @ Y1)))))) 803.22/104.42 | ~ (rt_less @ sk__2 @ sk__3))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl305])). 803.22/104.42 thf(zip_derived_cl24, plain, 803.22/104.42 ( (imp @ 803.22/104.42 (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1))))))) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__2 @ sk__3))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(satz81d, axiom, 803.22/104.42 (all_of @ 803.22/104.42 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 803.22/104.42 ( ^[X0:$i]: 803.22/104.42 ( all_of @ 803.22/104.42 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 803.22/104.42 ( ^[X1:$i]: 803.22/104.42 ( ( rt_lessis @ X0 @ X1 ) => ( d_not @ ( rt_more @ X0 @ X1 ) ) ) ) ) ))). 803.22/104.42 thf(zf_stmt_6, axiom, 803.22/104.42 (![X4:$i]: 803.22/104.42 ( ( is_of @ X4 @ ( ^[V_1:$i]: ( in @ V_1 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X6:$i]: 803.22/104.42 ( ( is_of @ X6 @ ( ^[V_2:$i]: ( in @ V_2 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ( imp @ 803.22/104.42 ( d_not @ ( rt_less @ X4 @ X6 ) ) @ 803.22/104.42 ( e_is @ ( ect @ frac @ n_eq ) @ X4 @ X6 ) ) => 803.22/104.42 ( d_not @ 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_3:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_4:$i]: 803.22/104.42 ( and3 @ 803.22/104.42 ( inf @ V_3 @ ( class @ X4 ) ) @ 803.22/104.42 ( inf @ V_4 @ ( class @ X6 ) ) @ ( moref @ V_3 @ V_4 ) ) ) ) ) ) ) ) ) ) ))). 803.22/104.42 thf(zip_derived_cl8, plain, 803.22/104.42 (![X0 : $i, X1 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ X1)) @ 803.22/104.42 (inf @ Y1 @ (class @ X0)) @ (moref @ Y0 @ Y1))))))) 803.22/104.42 | ~ (imp @ (d_not @ (rt_less @ X1 @ X0)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ X1 @ X0)) 803.22/104.42 | ~ (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_6])). 803.22/104.42 thf(zip_derived_cl559, plain, 803.22/104.42 ((((l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1)))))) 803.22/104.42 != (rt_less @ sk__2 @ sk__3)) 803.22/104.42 | ~ (is_of @ sk__3 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1))))))) 803.22/104.42 | ~ (is_of @ sk__2 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('ext_sup', [status(thm)], [zip_derived_cl24, zip_derived_cl8])). 803.22/104.42 thf(zip_derived_cl25, plain, 803.22/104.42 ( (is_of @ sk__3 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl20, plain, 803.22/104.42 ( (is_of @ sk__2 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl576, plain, 803.22/104.42 ((((l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1)))))) 803.22/104.42 != (rt_less @ sk__2 @ sk__3)) 803.22/104.42 | (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1))))))))), 803.22/104.42 inference('demod', [status(thm)], 803.22/104.42 [zip_derived_cl559, zip_derived_cl25, zip_derived_cl20])). 803.22/104.42 thf(zip_derived_cl577, plain, 803.22/104.42 ((((l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1)))))) 803.22/104.42 != (rt_less @ sk__2 @ sk__3)) 803.22/104.42 | (d_not @ (rt_less @ sk__2 @ sk__3)))), 803.22/104.42 inference('local_rewriting', [status(thm)], [zip_derived_cl576])). 803.22/104.42 thf(zip_derived_cl852, plain, 803.22/104.42 (( (d_not @ (rt_less @ sk__2 @ sk__3)) 803.22/104.42 | (rt_less @ sk__2 @ sk__3) 803.22/104.42 | (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1)))))))), 803.22/104.42 inference('cnf_otf', [status(thm)], [zip_derived_cl577])). 803.22/104.42 thf(zip_derived_cl854, plain, 803.22/104.42 (( (d_not @ ($false)) 803.22/104.42 | (rt_less @ sk__2 @ sk__3) 803.22/104.42 | (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1)))))))), 803.22/104.42 inference('local_rewriting', [status(thm)], [zip_derived_cl852])). 803.22/104.42 thf(zip_derived_cl20, plain, 803.22/104.42 ( (is_of @ sk__2 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl25, plain, 803.22/104.42 ( (is_of @ sk__3 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl9, plain, 803.22/104.42 (![X0 : $i, X1 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | (rt_less @ X0 @ X1) 803.22/104.42 | ~ (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ X1)) @ 803.22/104.42 (inf @ Y1 @ (class @ X0)) @ (moref @ Y0 @ Y1)))))) 803.22/104.42 | ~ (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_4])). 803.22/104.42 thf(zip_derived_cl634, plain, 803.22/104.42 (![X0 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ X0)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1)))))) 803.22/104.42 | (rt_less @ sk__3 @ X0))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl9])). 803.22/104.42 thf(zip_derived_cl711, plain, 803.22/104.42 (( (rt_less @ sk__3 @ sk__2) 803.22/104.42 | ~ (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1)))))))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl634])). 803.22/104.42 thf(zip_derived_cl916, plain, 803.22/104.42 (( (rt_less @ sk__2 @ sk__3) 803.22/104.42 | (d_not @ ($false)) 803.22/104.42 | (rt_less @ sk__3 @ sk__2))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl854, zip_derived_cl711])). 803.22/104.42 thf(zip_derived_cl20, plain, 803.22/104.42 ( (is_of @ sk__2 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl21, plain, 803.22/104.42 ( (is_of @ sk__4 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl25, plain, 803.22/104.42 ( (is_of @ sk__3 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(satz86, axiom, 803.22/104.42 (all_of @ 803.22/104.42 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 803.22/104.42 ( ^[X0:$i]: 803.22/104.42 ( all_of @ 803.22/104.42 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 803.22/104.42 ( ^[X1:$i]: 803.22/104.42 ( all_of @ 803.22/104.42 ( ^[X2:$i]: ( in @ X2 @ rat ) ) @ 803.22/104.42 ( ^[X2:$i]: 803.22/104.42 ( ( rt_less @ X0 @ X1 ) => 803.22/104.42 ( ( rt_less @ X1 @ X2 ) => ( rt_less @ X0 @ X2 ) ) ) ) ) ) ) ))). 803.22/104.42 thf(zf_stmt_7, axiom, 803.22/104.42 (![X4:$i]: 803.22/104.42 ( ( is_of @ X4 @ ( ^[V_1:$i]: ( in @ V_1 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X6:$i]: 803.22/104.42 ( ( is_of @ X6 @ ( ^[V_2:$i]: ( in @ V_2 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X8:$i]: 803.22/104.42 ( ( is_of @ 803.22/104.42 X8 @ ( ^[V_3:$i]: ( in @ V_3 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ( rt_less @ X4 @ X6 ) => 803.22/104.42 ( ( rt_less @ X6 @ X8 ) => ( rt_less @ X4 @ X8 ) ) ) ) ) ) ) ))). 803.22/104.42 thf(zip_derived_cl12, plain, 803.22/104.42 (![X0 : $i, X1 : $i, X2 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (rt_less @ X1 @ X0) 803.22/104.42 | (rt_less @ X1 @ X2) 803.22/104.42 | ~ (rt_less @ X0 @ X2) 803.22/104.42 | ~ (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_7])). 803.22/104.42 thf(zip_derived_cl491, plain, 803.22/104.42 (![X0 : $i, X1 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (rt_less @ sk__3 @ X1) 803.22/104.42 | (rt_less @ X0 @ X1) 803.22/104.42 | ~ (rt_less @ X0 @ sk__3))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl12])). 803.22/104.42 thf(zip_derived_cl543, plain, 803.22/104.42 (![X0 : $i]: 803.22/104.42 (~ (rt_less @ sk__4 @ sk__3) 803.22/104.42 | (rt_less @ sk__4 @ X0) 803.22/104.42 | ~ (rt_less @ sk__3 @ X0) 803.22/104.42 | ~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl491])). 803.22/104.42 thf(zip_derived_cl551, plain, 803.22/104.42 ((~ (rt_less @ sk__3 @ sk__2) 803.22/104.42 | (rt_less @ sk__4 @ sk__2) 803.22/104.42 | ~ (rt_less @ sk__4 @ sk__3))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl543])). 803.22/104.42 thf(zip_derived_cl644, plain, ( (rt_less @ sk__4 @ sk__3)), 803.22/104.42 inference('demod', [status(thm)], [zip_derived_cl640, zip_derived_cl22])). 803.22/104.42 thf(zip_derived_cl656, plain, 803.22/104.42 ((~ (rt_less @ sk__3 @ sk__2) | (rt_less @ sk__4 @ sk__2))), 803.22/104.42 inference('demod', [status(thm)], [zip_derived_cl551, zip_derived_cl644])). 803.22/104.42 thf(zip_derived_cl919, plain, 803.22/104.42 (( (d_not @ ($false)) 803.22/104.42 | (rt_less @ sk__2 @ sk__3) 803.22/104.42 | (rt_less @ sk__4 @ sk__2))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl916, zip_derived_cl656])). 803.22/104.42 thf(zip_derived_cl721, plain, (~ (rt_less @ sk__4 @ sk__2)), 803.22/104.42 inference('clc', [status(thm)], [zip_derived_cl716, zip_derived_cl23])). 803.22/104.42 thf(zip_derived_cl928, plain, 803.22/104.42 (( (rt_less @ sk__2 @ sk__3) | (d_not @ ($false)))), 803.22/104.42 inference('clc', [status(thm)], [zip_derived_cl919, zip_derived_cl721])). 803.22/104.42 thf(zip_derived_cl20, plain, 803.22/104.42 ( (is_of @ sk__2 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl25, plain, 803.22/104.42 ( (is_of @ sk__3 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(satz81c, axiom, 803.22/104.42 (all_of @ 803.22/104.42 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 803.22/104.42 ( ^[X0:$i]: 803.22/104.42 ( all_of @ 803.22/104.42 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 803.22/104.42 ( ^[X1:$i]: 803.22/104.42 ( ( rt_moreis @ X0 @ X1 ) => ( d_not @ ( rt_less @ X0 @ X1 ) ) ) ) ) ))). 803.22/104.42 thf(zf_stmt_8, axiom, 803.22/104.42 (![X4:$i]: 803.22/104.42 ( ( is_of @ X4 @ ( ^[V_1:$i]: ( in @ V_1 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X6:$i]: 803.22/104.42 ( ( is_of @ X6 @ ( ^[V_2:$i]: ( in @ V_2 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ( imp @ 803.22/104.42 ( d_not @ 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_3:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_4:$i]: 803.22/104.42 ( and3 @ 803.22/104.42 ( inf @ V_3 @ ( class @ X4 ) ) @ 803.22/104.42 ( inf @ V_4 @ ( class @ X6 ) ) @ 803.22/104.42 ( moref @ V_3 @ V_4 ) ) ) ) ) ) ) @ 803.22/104.42 ( e_is @ ( ect @ frac @ n_eq ) @ X4 @ X6 ) ) => 803.22/104.42 ( d_not @ ( rt_less @ X4 @ X6 ) ) ) ) ) ))). 803.22/104.42 thf(zip_derived_cl2, plain, 803.22/104.42 (![X0 : $i, X1 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | (d_not @ (rt_less @ X1 @ X0)) 803.22/104.42 | ~ (imp @ 803.22/104.42 (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ X1)) @ 803.22/104.42 (inf @ Y1 @ (class @ X0)) @ (moref @ Y0 @ Y1))))))) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ X1 @ X0)) 803.22/104.42 | ~ (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_8])). 803.22/104.42 thf(zip_derived_cl118, plain, 803.22/104.42 (![X0 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (imp @ 803.22/104.42 (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ X0)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1))))))) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ X0 @ sk__3)) 803.22/104.42 | (d_not @ (rt_less @ X0 @ sk__3)))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl2])). 803.22/104.42 thf(zip_derived_cl1738, plain, 803.22/104.42 (( (d_not @ (rt_less @ sk__2 @ sk__3)) 803.22/104.42 | ~ (imp @ 803.22/104.42 (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1))))))) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__2 @ sk__3)))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl118])). 803.22/104.42 thf(zip_derived_cl24, plain, 803.22/104.42 ( (imp @ 803.22/104.42 (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1))))))) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__2 @ sk__3))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl1743, plain, ( (d_not @ (rt_less @ sk__2 @ sk__3))), 803.22/104.42 inference('demod', [status(thm)], [zip_derived_cl1738, zip_derived_cl24])). 803.22/104.42 thf(zip_derived_cl1751, plain, (( (d_not @ ($true)) | (d_not @ ($false)))), 803.22/104.42 inference('sup+', [status(thm)], [zip_derived_cl928, zip_derived_cl1743])). 803.22/104.42 thf(zip_derived_cl20, plain, 803.22/104.42 ( (is_of @ sk__2 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl21, plain, 803.22/104.42 ( (is_of @ sk__4 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl11, plain, 803.22/104.42 (![X0 : $i, X1 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | (imp @ (d_not @ (rt_less @ X1 @ X0)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ X1 @ X0)) 803.22/104.42 | ~ (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ X1)) @ 803.22/104.42 (inf @ Y1 @ (class @ X0)) @ (moref @ Y0 @ Y1))))))) 803.22/104.42 | ~ (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_2])). 803.22/104.42 thf(zip_derived_cl689, plain, 803.22/104.42 (![X0 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ X0)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__4)) @ (moref @ Y0 @ Y1))))))) 803.22/104.42 | (imp @ (d_not @ (rt_less @ X0 @ sk__4)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ X0 @ sk__4)))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl11])). 803.22/104.42 thf(zip_derived_cl6753, plain, 803.22/104.42 (( (imp @ (d_not @ (rt_less @ sk__2 @ sk__4)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__2 @ sk__4)) 803.22/104.42 | ~ (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__4)) @ (moref @ Y0 @ Y1))))))))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl689])). 803.22/104.42 thf(zip_derived_cl23, plain, 803.22/104.42 (~ (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__4)) @ (moref @ Y0 @ Y1))))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl6758, plain, 803.22/104.42 (( (imp @ (d_not @ (rt_less @ sk__2 @ sk__4)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__2 @ sk__4)) 803.22/104.42 | ~ (d_not @ ($false)))), 803.22/104.42 inference('demod', [status(thm)], [zip_derived_cl6753, zip_derived_cl23])). 803.22/104.42 thf(zip_derived_cl6785, plain, 803.22/104.42 (( (d_not @ ($true)) 803.22/104.42 | (imp @ (d_not @ (rt_less @ sk__2 @ sk__4)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__2 @ sk__4)))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl1751, zip_derived_cl6758])). 803.22/104.42 thf(zip_derived_cl25, plain, 803.22/104.42 ( (is_of @ sk__3 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl20, plain, 803.22/104.42 ( (is_of @ sk__2 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl21, plain, 803.22/104.42 ( (is_of @ sk__4 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(satz87a, axiom, 803.22/104.42 (all_of @ 803.22/104.42 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 803.22/104.42 ( ^[X0:$i]: 803.22/104.42 ( all_of @ 803.22/104.42 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 803.22/104.42 ( ^[X1:$i]: 803.22/104.42 ( all_of @ 803.22/104.42 ( ^[X2:$i]: ( in @ X2 @ rat ) ) @ 803.22/104.42 ( ^[X2:$i]: 803.22/104.42 ( ( rt_lessis @ X0 @ X1 ) => 803.22/104.42 ( ( rt_less @ X1 @ X2 ) => ( rt_less @ X0 @ X2 ) ) ) ) ) ) ) ))). 803.22/104.42 thf(zf_stmt_9, axiom, 803.22/104.42 (![X4:$i]: 803.22/104.42 ( ( is_of @ X4 @ ( ^[V_1:$i]: ( in @ V_1 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X6:$i]: 803.22/104.42 ( ( is_of @ X6 @ ( ^[V_2:$i]: ( in @ V_2 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X8:$i]: 803.22/104.42 ( ( is_of @ 803.22/104.42 X8 @ ( ^[V_3:$i]: ( in @ V_3 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ( imp @ 803.22/104.42 ( d_not @ ( rt_less @ X4 @ X6 ) ) @ 803.22/104.42 ( e_is @ ( ect @ frac @ n_eq ) @ X4 @ X6 ) ) => 803.22/104.42 ( ( rt_less @ X6 @ X8 ) => ( rt_less @ X4 @ X8 ) ) ) ) ) ) ) ))). 803.22/104.42 thf(zip_derived_cl13, plain, 803.22/104.42 (![X0 : $i, X1 : $i, X2 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (imp @ (d_not @ (rt_less @ X1 @ X0)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ X1 @ X0)) 803.22/104.42 | (rt_less @ X1 @ X2) 803.22/104.42 | ~ (rt_less @ X0 @ X2) 803.22/104.42 | ~ (is_of @ X2 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_9])). 803.22/104.42 thf(zip_derived_cl760, plain, 803.22/104.42 (![X0 : $i, X1 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (rt_less @ sk__4 @ X1) 803.22/104.42 | (rt_less @ X0 @ X1) 803.22/104.42 | ~ (imp @ (d_not @ (rt_less @ X0 @ sk__4)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ X0 @ sk__4)))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl13])). 803.22/104.42 thf(zip_derived_cl1022, plain, 803.22/104.42 (![X0 : $i]: 803.22/104.42 (~ (imp @ (d_not @ (rt_less @ sk__2 @ sk__4)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__2 @ sk__4)) 803.22/104.42 | (rt_less @ sk__2 @ X0) 803.22/104.42 | ~ (rt_less @ sk__4 @ X0) 803.22/104.42 | ~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl760])). 803.22/104.42 thf(zip_derived_cl1095, plain, 803.22/104.42 ((~ (rt_less @ sk__4 @ sk__3) 803.22/104.42 | (rt_less @ sk__2 @ sk__3) 803.22/104.42 | ~ (imp @ (d_not @ (rt_less @ sk__2 @ sk__4)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__2 @ sk__4)))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl1022])). 803.22/104.42 thf(zip_derived_cl644, plain, ( (rt_less @ sk__4 @ sk__3)), 803.22/104.42 inference('demod', [status(thm)], [zip_derived_cl640, zip_derived_cl22])). 803.22/104.42 thf(zip_derived_cl1100, plain, 803.22/104.42 (( (rt_less @ sk__2 @ sk__3) 803.22/104.42 | ~ (imp @ (d_not @ (rt_less @ sk__2 @ sk__4)) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__2 @ sk__4)))), 803.22/104.42 inference('demod', [status(thm)], [zip_derived_cl1095, zip_derived_cl644])). 803.22/104.42 thf(zip_derived_cl6791, plain, 803.22/104.42 (( (d_not @ ($true)) | (rt_less @ sk__2 @ sk__3))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl6785, zip_derived_cl1100])). 803.22/104.42 thf(zip_derived_cl20, plain, 803.22/104.42 ( (is_of @ sk__2 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl25, plain, 803.22/104.42 ( (is_of @ sk__3 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(satz81j, axiom, 803.22/104.42 (all_of @ 803.22/104.42 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 803.22/104.42 ( ^[X0:$i]: 803.22/104.42 ( all_of @ 803.22/104.42 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 803.22/104.42 ( ^[X1:$i]: 803.22/104.42 ( ( d_not @ ( rt_moreis @ X0 @ X1 ) ) => ( rt_less @ X0 @ X1 ) ) ) ) ))). 803.22/104.42 thf(zf_stmt_10, axiom, 803.22/104.42 (![X4:$i]: 803.22/104.42 ( ( is_of @ X4 @ ( ^[V_1:$i]: ( in @ V_1 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ![X6:$i]: 803.22/104.42 ( ( is_of @ X6 @ ( ^[V_2:$i]: ( in @ V_2 @ ( ect @ frac @ n_eq ) ) ) ) => 803.22/104.42 ( ( d_not @ 803.22/104.42 ( imp @ 803.22/104.42 ( d_not @ 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_3:$i]: 803.22/104.42 ( l_some @ 803.22/104.42 frac @ 803.22/104.42 ( ^[V_4:$i]: 803.22/104.42 ( and3 @ 803.22/104.42 ( inf @ V_3 @ ( class @ X4 ) ) @ 803.22/104.42 ( inf @ V_4 @ ( class @ X6 ) ) @ 803.22/104.42 ( moref @ V_3 @ V_4 ) ) ) ) ) ) ) @ 803.22/104.42 ( e_is @ ( ect @ frac @ n_eq ) @ X4 @ X6 ) ) ) => 803.22/104.42 ( rt_less @ X4 @ X6 ) ) ) ) ))). 803.22/104.42 thf(zip_derived_cl3, plain, 803.22/104.42 (![X0 : $i, X1 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | (rt_less @ X1 @ X0) 803.22/104.42 | ~ (d_not @ 803.22/104.42 (imp @ 803.22/104.42 (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ X1)) @ 803.22/104.42 (inf @ Y1 @ (class @ X0)) @ (moref @ Y0 @ Y1))))))) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ X1 @ X0))) 803.22/104.42 | ~ (is_of @ X1 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_10])). 803.22/104.42 thf(zip_derived_cl168, plain, 803.22/104.42 (![X0 : $i]: 803.22/104.42 (~ (is_of @ X0 @ (^[Y0 : $i]: (in @ Y0 @ (ect @ frac @ n_eq)))) 803.22/104.42 | ~ (d_not @ 803.22/104.42 (imp @ 803.22/104.42 (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ X0)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1))))))) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ X0 @ sk__3))) 803.22/104.42 | (rt_less @ X0 @ sk__3))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl3])). 803.22/104.42 thf(zip_derived_cl2563, plain, 803.22/104.42 (( (rt_less @ sk__2 @ sk__3) 803.22/104.42 | ~ (d_not @ 803.22/104.42 (imp @ 803.22/104.42 (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1))))))) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__2 @ sk__3))))), 803.22/104.42 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl168])). 803.22/104.42 thf(zip_derived_cl24, plain, 803.22/104.42 ( (imp @ 803.22/104.42 (d_not @ 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__2)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__3)) @ (moref @ Y0 @ Y1))))))) @ 803.22/104.42 (e_is @ (ect @ frac @ n_eq) @ sk__2 @ sk__3))), 803.22/104.42 inference('cnf', [status(esa)], [zf_stmt_1])). 803.22/104.42 thf(zip_derived_cl2568, plain, 803.22/104.42 (( (rt_less @ sk__2 @ sk__3) | ~ (d_not @ ($true)))), 803.22/104.42 inference('demod', [status(thm)], [zip_derived_cl2563, zip_derived_cl24])). 803.22/104.42 thf(zip_derived_cl6800, plain, ( (rt_less @ sk__2 @ sk__3)), 803.22/104.42 inference('clc', [status(thm)], [zip_derived_cl6791, zip_derived_cl2568])). 803.22/104.42 thf(zip_derived_cl6801, plain, 803.22/104.42 ( (l_some @ frac @ 803.22/104.42 (^[Y0 : $i]: 803.22/104.42 (l_some @ frac @ 803.22/104.42 (^[Y1 : $i]: 803.22/104.42 (and3 @ (inf @ Y0 @ (class @ sk__3)) @ 803.22/104.42 (inf @ Y1 @ (class @ sk__2)) @ (moref @ Y0 @ Y1))))))), 803.22/104.42 inference('demod', [status(thm)], [zip_derived_cl433, zip_derived_cl6800])). 803.22/104.42 thf(zip_derived_cl1743, plain, ( (d_not @ (rt_less @ sk__2 @ sk__3))), 803.22/104.42 inference('demod', [status(thm)], [zip_derived_cl1738, zip_derived_cl24])). 803.22/104.42 thf(zip_derived_cl6800, plain, ( (rt_less @ sk__2 @ sk__3)), 803.22/104.42 inference('clc', [status(thm)], [zip_derived_cl6791, zip_derived_cl2568])). 803.22/104.42 thf(zip_derived_cl6810, plain, ( (d_not @ ($true))), 803.22/104.42 inference('demod', [status(thm)], 803.22/104.42 [zip_derived_cl1743, zip_derived_cl6800])). 803.22/104.42 thf(zip_derived_cl7760, plain, ($false), 803.22/104.42 inference('demod', [status(thm)], 803.22/104.42 [zip_derived_cl7193, zip_derived_cl6801, zip_derived_cl6810])). 803.22/104.42 803.22/104.42 % SZS output end Refutation 803.22/104.42 803.22/104.42 803.22/104.42 % Terminating... 803.40/104.55 % Runner terminated. 803.40/104.56 % Zipperpin 1.5 exiting 803.40/104.57 EOF