0.08/0.14 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.18 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.KNyqVf3rwa true 0.17/0.39 % Computer : n021.cluster.edu 0.17/0.39 % Model : x86_64 x86_64 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.17/0.39 % Memory : 8042.1875MB 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64 0.17/0.39 % CPULimit : 960 0.17/0.39 % WCLimit : 120 0.17/0.39 % DateTime : Tue Aug 9 07:52:35 EDT 2022 0.17/0.40 % CPUTime : 0.17/0.40 % Running portfolio for 960 s 0.17/0.40 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.17/0.40 % Number of cores: 8 0.25/0.40 % Python version: Python 3.6.8 0.25/0.40 % Running in HO mode 0.54/0.67 % Total configuration time : 828 0.54/0.67 % Estimated wc time : 1656 0.54/0.67 % Estimated cpu time (8 cpus) : 207.0 0.55/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.55/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 88.29/12.11 % Solved by lams/35_full_unif4.sh. 88.29/12.11 % done 682 iterations in 11.311s 88.29/12.11 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 88.29/12.11 % SZS output start Refutation 88.29/12.11 thf('#sk8899_type', type, '#sk8899': $i). 88.29/12.11 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 88.29/12.11 thf('#form7743_type', type, '#form7743': $i > $i > $o). 88.29/12.11 thf(n_is_type, type, n_is: $i > $i > $o). 88.29/12.11 thf('#sk8897_type', type, '#sk8897': $i). 88.29/12.11 thf(l_or_type, type, l_or: $o > $o > $o). 88.29/12.11 thf(in_type, type, in: $i > $i > $o). 88.29/12.11 thf(imp_type, type, imp: $o > $o > $o). 88.29/12.11 thf('#sk8898_type', type, '#sk8898': $i). 88.29/12.11 thf(lessis_type, type, lessis: $i > $i > $o). 88.29/12.11 thf(nat_type, type, nat: $i). 88.29/12.11 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 88.29/12.11 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 88.29/12.11 thf(e_is_type, type, e_is: $i > $i > $i > $o). 88.29/12.11 thf(non_type, type, non: $i > ($i > $o) > $i > $o). 88.29/12.11 thf(n_some_type, type, n_some: ($i > $o) > $o). 88.29/12.11 thf(n_pl_type, type, n_pl: $i > $i > $i). 88.29/12.11 thf(iii_type, type, iii: $i > $i > $o). 88.29/12.11 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 88.29/12.11 thf(d_not_type, type, d_not: $o > $o). 88.29/12.11 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 88.29/12.11 thf(def_d_29_ii, axiom,(( d_29_ii ) = 88.29/12.11 (^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X0 @ X1 ) )))). 88.29/12.11 thf(def_diffprop, axiom,(( diffprop ) = 88.29/12.11 (^[X0:$i,X1:$i,X2:$i]: ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) )))). 88.29/12.11 thf(def_n_is, axiom,(( n_is ) = (e_is @ nat))). 88.29/12.11 thf(def_e_is, axiom,(( e_is ) = (^[X0:$i,X:$i,Y:$i]: ( ( X ) = ( Y ) )))). 88.29/12.11 thf('0', plain, (( e_is ) = ( ^[X0:$i,X:$i,Y:$i]: ( ( X ) = ( Y ) ) )), 88.29/12.11 inference('simplify_rw_rule', [status(thm)], [def_e_is])). 88.29/12.11 thf('1', plain, 88.29/12.11 (( e_is ) = ( ^[V_1:$i,V_2:$i,V_3:$i]: ( ( V_2 ) = ( V_3 ) ) )), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf('2', plain, (( n_is ) = ( e_is @ nat )), 88.29/12.11 inference('simplify_rw_rule', [status(thm)], [def_n_is, '1'])). 88.29/12.11 thf('3', plain, (( n_is ) = ( e_is @ nat )), define([status(thm)])). 88.29/12.11 thf('4', plain, 88.29/12.11 (( diffprop ) = 88.29/12.11 ( ^[X0:$i,X1:$i,X2:$i]: ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) )), 88.29/12.11 inference('simplify_rw_rule', [status(thm)], [def_diffprop, '3', '1'])). 88.29/12.11 thf('5', plain, 88.29/12.11 (( diffprop ) = 88.29/12.11 ( ^[V_1:$i,V_2:$i,V_3:$i]: ( n_is @ V_1 @ ( n_pl @ V_2 @ V_3 ) ) )), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf(def_n_some, axiom,(( n_some ) = (l_some @ nat))). 88.29/12.11 thf(def_l_some, axiom,(( l_some ) = 88.29/12.11 (^[X0:$i,X1:( $i > $o )]: 88.29/12.11 ( d_not @ ( all_of @ ( ^[X2:$i]: ( in @ X2 @ X0 ) ) @ ( non @ X0 @ X1 ) ) )))). 88.29/12.11 thf(def_non, axiom,(( non ) = 88.29/12.11 (^[X0:$i,X1:( $i > $o ),X2:$i]: ( d_not @ ( X1 @ X2 ) )))). 88.29/12.11 thf(def_d_not, axiom,(( d_not ) = (^[X0:$o]: ( imp @ X0 @ $false )))). 88.29/12.11 thf(def_imp, axiom,(( imp ) = (^[X0:$o,X1:$o]: ( ( X0 ) => ( X1 ) )))). 88.29/12.11 thf('6', plain, (( imp ) = ( ^[X0:$o,X1:$o]: ( ( X0 ) => ( X1 ) ) )), 88.29/12.11 inference('simplify_rw_rule', [status(thm)], [def_imp])). 88.29/12.11 thf('7', plain, (( imp ) = ( ^[V_1:$o,V_2:$o]: ( ( V_1 ) => ( V_2 ) ) )), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf('8', plain, (( d_not ) = ( ^[X0:$o]: ( imp @ X0 @ $false ) )), 88.29/12.11 inference('simplify_rw_rule', [status(thm)], [def_d_not, '7'])). 88.29/12.11 thf('9', plain, (( d_not ) = ( ^[V_1:$o]: ( imp @ V_1 @ $false ) )), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf('10', plain, 88.29/12.11 (( non ) = ( ^[X0:$i,X1:( $i > $o ),X2:$i]: ( d_not @ ( X1 @ X2 ) ) )), 88.29/12.11 inference('simplify_rw_rule', [status(thm)], [def_non, '9', '7'])). 88.29/12.11 thf('11', plain, 88.29/12.11 (( non ) = 88.29/12.11 ( ^[V_1:$i,V_2:( $i > $o ),V_3:$i]: ( d_not @ ( V_2 @ V_3 ) ) )), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf(def_all_of, axiom,(( all_of ) = 88.29/12.11 (^[X0:( $i > $o ),X1:( $i > $o )]: 88.29/12.11 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) )))). 88.29/12.11 thf(def_is_of, axiom,(( is_of ) = (^[X0:$i,X1:( $i > $o )]: ( X1 @ X0 )))). 88.29/12.11 thf('12', plain, (( is_of ) = ( ^[X0:$i,X1:( $i > $o )]: ( X1 @ X0 ) )), 88.29/12.11 inference('simplify_rw_rule', [status(thm)], [def_is_of])). 88.29/12.11 thf('13', plain, (( is_of ) = ( ^[V_1:$i,V_2:( $i > $o )]: ( V_2 @ V_1 ) )), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf('14', plain, 88.29/12.11 (( all_of ) = 88.29/12.11 ( ^[X0:( $i > $o ),X1:( $i > $o )]: 88.29/12.11 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) ) )), 88.29/12.11 inference('simplify_rw_rule', [status(thm)], [def_all_of, '13'])). 88.29/12.11 thf('15', plain, 88.29/12.11 (( all_of ) = 88.29/12.11 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 88.29/12.11 ( ![X4:$i]: ( ( is_of @ X4 @ V_1 ) => ( V_2 @ X4 ) ) ) )), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf('16', plain, 88.29/12.11 (( l_some ) = 88.29/12.11 ( ^[X0:$i,X1:( $i > $o )]: 88.29/12.11 ( d_not @ 88.29/12.11 ( all_of @ ( ^[X2:$i]: ( in @ X2 @ X0 ) ) @ ( non @ X0 @ X1 ) ) ) )), 88.29/12.11 inference('simplify_rw_rule', [status(thm)], 88.29/12.11 [def_l_some, '11', '9', '7', '15', '13'])). 88.29/12.11 thf('17', plain, 88.29/12.11 (( l_some ) = 88.29/12.11 ( ^[V_1:$i,V_2:( $i > $o )]: 88.29/12.11 ( d_not @ 88.29/12.11 ( all_of @ ( ^[V_3:$i]: ( in @ V_3 @ V_1 ) ) @ ( non @ V_1 @ V_2 ) ) ) )), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf('18', plain, (( n_some ) = ( l_some @ nat )), 88.29/12.11 inference('simplify_rw_rule', [status(thm)], 88.29/12.11 [def_n_some, '17', '11', '9', '7', '15', '13'])). 88.29/12.11 thf('19', plain, (( n_some ) = ( l_some @ nat )), define([status(thm)])). 88.29/12.11 thf('20', plain, 88.29/12.11 (( d_29_ii ) = ( ^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 88.29/12.11 inference('simplify_rw_rule', [status(thm)], 88.29/12.11 [def_d_29_ii, '5', '19', '3', '1', '17', '11', '9', '7', '15', 88.29/12.11 '13'])). 88.29/12.11 thf('21', plain, 88.29/12.11 (( d_29_ii ) = 88.29/12.11 ( ^[V_1:$i,V_2:$i]: ( n_some @ ( diffprop @ V_1 @ V_2 ) ) )), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf(satz20a, axiom, 88.29/12.11 (all_of @ 88.29/12.11 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 88.29/12.11 ( ^[X0:$i]: 88.29/12.11 ( all_of @ 88.29/12.11 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 88.29/12.11 ( ^[X1:$i]: 88.29/12.11 ( all_of @ 88.29/12.11 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 88.29/12.11 ( ^[X2:$i]: 88.29/12.11 ( ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) => 88.29/12.11 ( d_29_ii @ X0 @ X1 ) ) ) ) ) ) ))). 88.29/12.11 thf(zf_stmt_0, axiom, 88.29/12.11 (![X4:$i]: 88.29/12.11 ( ( in @ X4 @ nat ) => 88.29/12.11 ( ![X6:$i]: 88.29/12.11 ( ( in @ X6 @ nat ) => 88.29/12.11 ( ![X8:$i]: 88.29/12.11 ( ( in @ X8 @ nat ) => 88.29/12.11 ( ( ~( ![X10:$i]: 88.29/12.11 ( ( in @ X10 @ nat ) => 88.29/12.11 ( ( n_pl @ X4 @ X8 ) != 88.29/12.11 ( n_pl @ ( n_pl @ X6 @ X8 ) @ X10 ) ) ) ) ) => 88.29/12.11 ( ~( ![X12:$i]: 88.29/12.11 ( ( in @ X12 @ nat ) => ( ( X4 ) != ( n_pl @ X6 @ X12 ) ) ) ) ) ) ) ) ) ) ))). 88.29/12.11 thf(zip_derived_cl130, plain, 88.29/12.11 ( (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ nat) => 88.29/12.11 (((((~) @ (((!!) @ (^[Y3 : $i]: 88.29/12.11 (( 88.29/12.11 (in @ 88.29/12.11 Y3 @ 88.29/12.11 nat) => 88.29/12.11 (( 88.29/12.11 (n_pl @ 88.29/12.11 Y0 @ 88.29/12.11 Y2) != 88.29/12.11 (n_pl @ 88.29/12.11 ( 88.29/12.11 n_pl @ 88.29/12.11 Y1 @ Y2) @ 88.29/12.11 Y3)))))))))) => 88.29/12.11 (((~) @ (((!!) @ (^[Y3 : $i]: 88.29/12.11 (( 88.29/12.11 (in @ 88.29/12.11 Y3 @ 88.29/12.11 nat) => 88.29/12.11 (( 88.29/12.11 (Y0) != 88.29/12.11 (n_pl @ 88.29/12.11 Y1 @ Y3)))))))))))))))))))))))))))), 88.29/12.11 inference('cnf', [status(esa)], [zf_stmt_0])). 88.29/12.11 thf(zip_derived_cl7002, plain, 88.29/12.11 (![X2 : $i]: 88.29/12.11 (((in @ X2 @ nat) => 88.29/12.11 (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((((~) @ (((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ 88.29/12.11 nat) => 88.29/12.11 (((n_pl @ X2 @ 88.29/12.11 Y1) != 88.29/12.11 (n_pl @ 88.29/12.11 (n_pl @ Y0 @ 88.29/12.11 Y1) @ 88.29/12.11 Y2)))))))))) => 88.29/12.11 (((~) @ (((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ 88.29/12.11 nat) => 88.29/12.11 (((X2) != 88.29/12.11 (n_pl @ Y0 @ 88.29/12.11 Y2))))))))))))))))))))))))), 88.29/12.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl130])). 88.29/12.11 thf(zip_derived_cl7003, plain, 88.29/12.11 (![X2 : $i]: 88.29/12.11 (~ (in @ X2 @ nat) 88.29/12.11 | (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((((~) @ (((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ 88.29/12.11 nat) => 88.29/12.11 (((n_pl @ 88.29/12.11 X2 @ Y1) != 88.29/12.11 (n_pl @ 88.29/12.11 (n_pl @ 88.29/12.11 Y0 @ Y1) @ 88.29/12.11 Y2)))))))))) => 88.29/12.11 (((~) @ (((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ 88.29/12.11 nat) => 88.29/12.11 (((X2) != 88.29/12.11 (n_pl @ 88.29/12.11 Y0 @ Y2)))))))))))))))))))))))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7002])). 88.29/12.11 thf(zip_derived_cl7004, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 ( (((in @ X4 @ nat) => 88.29/12.11 (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((((~) @ (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((n_pl @ X2 @ Y0) != 88.29/12.11 (n_pl @ 88.29/12.11 (n_pl @ X4 @ Y0) @ Y1)))))))))) => 88.29/12.11 (((~) @ (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((X2) != (n_pl @ X4 @ Y1))))))))))))))))))) 88.29/12.11 | ~ (in @ X2 @ nat))), 88.29/12.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7003])). 88.29/12.11 thf(zip_derived_cl7005, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 (~ (in @ X4 @ nat) 88.29/12.11 | (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((((~) @ (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((n_pl @ X2 @ Y0) != 88.29/12.11 (n_pl @ 88.29/12.11 (n_pl @ X4 @ Y0) @ Y1)))))))))) => 88.29/12.11 (((~) @ (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((X2) != (n_pl @ X4 @ Y1))))))))))))))))) 88.29/12.11 | ~ (in @ X2 @ nat))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7004])). 88.29/12.11 thf(zip_derived_cl7006, plain, 88.29/12.11 (![X2 : $i, X4 : $i, X6 : $i]: 88.29/12.11 ( (((in @ X6 @ nat) => 88.29/12.11 (((((~) @ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((n_pl @ X2 @ X6) != (n_pl @ 88.29/12.11 (n_pl @ X4 @ X6) @ Y0)))))))))) => 88.29/12.11 (((~) @ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((X2) != (n_pl @ X4 @ Y0)))))))))))))) 88.29/12.11 | ~ (in @ X2 @ nat) 88.29/12.11 | ~ (in @ X4 @ nat))), 88.29/12.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7005])). 88.29/12.11 thf(zip_derived_cl7007, plain, 88.29/12.11 (![X2 : $i, X4 : $i, X6 : $i]: 88.29/12.11 (~ (in @ X6 @ nat) 88.29/12.11 | (((((~) @ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((n_pl @ X2 @ X6) != (n_pl @ 88.29/12.11 (n_pl @ X4 @ X6) @ Y0)))))))))) => 88.29/12.11 (((~) @ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((X2) != (n_pl @ X4 @ Y0)))))))))))) 88.29/12.11 | ~ (in @ X4 @ nat) 88.29/12.11 | ~ (in @ X2 @ nat))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7006])). 88.29/12.11 thf(zip_derived_cl7008, plain, 88.29/12.11 (![X2 : $i, X4 : $i, X6 : $i]: 88.29/12.11 ( (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((n_pl @ X2 @ X6) != (n_pl @ (n_pl @ X4 @ X6) @ Y0)))))))) 88.29/12.11 | ~ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))) 88.29/12.11 | ~ (in @ X2 @ nat) 88.29/12.11 | ~ (in @ X4 @ nat) 88.29/12.11 | ~ (in @ X6 @ nat))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7007])). 88.29/12.11 thf(def_lessis, axiom,(( lessis ) = 88.29/12.11 (^[X0:$i,X1:$i]: ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) )))). 88.29/12.11 thf(def_iii, axiom,(( iii ) = 88.29/12.11 (^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X1 @ X0 ) )))). 88.29/12.11 thf('22', plain, 88.29/12.11 (( iii ) = ( ^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X1 @ X0 ) ) )), 88.29/12.11 inference('simplify_rw_rule', [status(thm)], 88.29/12.11 [def_iii, '5', '19', '3', '1', '17', '11', '9', '7', '15', '13'])). 88.29/12.11 thf('23', plain, 88.29/12.11 (( iii ) = ( ^[V_1:$i,V_2:$i]: ( n_some @ ( diffprop @ V_2 @ V_1 ) ) )), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf(def_l_or, axiom,(( l_or ) = (^[X0:$o]: ( imp @ ( d_not @ X0 ) )))). 88.29/12.11 thf('24', plain, (( l_or ) = ( ^[X0:$o]: ( imp @ ( d_not @ X0 ) ) )), 88.29/12.11 inference('simplify_rw_rule', [status(thm)], [def_l_or, '9', '7'])). 88.29/12.11 thf('25', plain, (( l_or ) = ( ^[V_1:$o]: ( imp @ ( d_not @ V_1 ) ) )), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf('26', plain, 88.29/12.11 (( lessis ) = 88.29/12.11 ( ^[X0:$i,X1:$i]: ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )), 88.29/12.11 inference('simplify_rw_rule', [status(thm)], 88.29/12.11 [def_lessis, '23', '5', '19', '3', '1', '17', '11', '25', '9', 88.29/12.11 '7', '15', '13'])). 88.29/12.11 thf('27', plain, 88.29/12.11 (( lessis ) = 88.29/12.11 ( ^[V_1:$i,V_2:$i]: 88.29/12.11 ( l_or @ ( iii @ V_1 @ V_2 ) @ ( n_is @ V_1 @ V_2 ) ) )), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf(satz19n, axiom, 88.29/12.11 (all_of @ 88.29/12.11 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 88.29/12.11 ( ^[X0:$i]: 88.29/12.11 ( all_of @ 88.29/12.11 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 88.29/12.11 ( ^[X1:$i]: 88.29/12.11 ( all_of @ 88.29/12.11 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 88.29/12.11 ( ^[X2:$i]: 88.29/12.11 ( ( lessis @ X0 @ X1 ) => 88.29/12.11 ( lessis @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) ) ) ) ) ) ))). 88.29/12.11 thf(zf_stmt_1, axiom, 88.29/12.11 (![X4:$i]: 88.29/12.11 ( ( in @ X4 @ nat ) => 88.29/12.11 ( ![X6:$i]: 88.29/12.11 ( ( in @ X6 @ nat ) => 88.29/12.11 ( ![X8:$i]: 88.29/12.11 ( ( in @ X8 @ nat ) => 88.29/12.11 ( ( ( ![X10:$i]: 88.29/12.11 ( ( in @ X10 @ nat ) => ( ( X6 ) != ( n_pl @ X4 @ X10 ) ) ) ) => 88.29/12.11 ( ( X4 ) = ( X6 ) ) ) => 88.29/12.11 ( ( ![X12:$i]: 88.29/12.11 ( ( in @ X12 @ nat ) => 88.29/12.11 ( ( n_pl @ X6 @ X8 ) != 88.29/12.11 ( n_pl @ ( n_pl @ X4 @ X8 ) @ X12 ) ) ) ) => 88.29/12.11 ( ( n_pl @ X4 @ X8 ) = ( n_pl @ X6 @ X8 ) ) ) ) ) ) ) ) ))). 88.29/12.11 thf(zip_derived_cl118, plain, 88.29/12.11 ( (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ nat) => 88.29/12.11 (((((((!!) @ (^[Y3 : $i]: 88.29/12.11 (((in @ Y3 @ 88.29/12.11 nat) => 88.29/12.11 (((Y1) != 88.29/12.11 (n_pl @ 88.29/12.11 Y0 @ Y3)))))))) => 88.29/12.11 (((Y0) = (Y1))))) => 88.29/12.11 (((((!!) @ (^[Y3 : $i]: 88.29/12.11 (((in @ Y3 @ 88.29/12.11 nat) => 88.29/12.11 (((n_pl @ 88.29/12.11 Y1 @ 88.29/12.11 Y2) != 88.29/12.11 (n_pl @ 88.29/12.11 ( 88.29/12.11 n_pl @ 88.29/12.11 Y0 @ Y2) @ 88.29/12.11 Y3)))))))) => 88.29/12.11 (((n_pl @ Y0 @ Y2) = 88.29/12.11 (n_pl @ Y1 @ Y2))))))))))))))))))))))), 88.29/12.11 inference('cnf', [status(esa)], [zf_stmt_1])). 88.29/12.11 thf(zip_derived_cl5747, plain, 88.29/12.11 (![X2 : $i]: 88.29/12.11 (((in @ X2 @ nat) => 88.29/12.11 (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((((((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ nat) => 88.29/12.11 (((Y0) != (n_pl @ 88.29/12.11 X2 @ Y2)))))))) => 88.29/12.11 (((X2) = (Y0))))) => 88.29/12.11 (((((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ nat) => 88.29/12.11 (((n_pl @ Y0 @ Y1) != 88.29/12.11 (n_pl @ 88.29/12.11 (n_pl @ X2 @ Y1) @ 88.29/12.11 Y2)))))))) => 88.29/12.11 (((n_pl @ X2 @ Y1) = (n_pl @ Y0 @ 88.29/12.11 Y1)))))))))))))))))))), 88.29/12.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl118])). 88.29/12.11 thf(zip_derived_cl5748, plain, 88.29/12.11 (![X2 : $i]: 88.29/12.11 (~ (in @ X2 @ nat) 88.29/12.11 | (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((((((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ nat) => 88.29/12.11 (((Y0) != (n_pl @ 88.29/12.11 X2 @ Y2)))))))) => 88.29/12.11 (((X2) = (Y0))))) => 88.29/12.11 (((((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ nat) => 88.29/12.11 (((n_pl @ Y0 @ 88.29/12.11 Y1) != (n_pl @ 88.29/12.11 (n_pl @ X2 @ Y1) @ 88.29/12.11 Y2)))))))) => 88.29/12.11 (((n_pl @ X2 @ Y1) = (n_pl @ Y0 @ 88.29/12.11 Y1))))))))))))))))))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5747])). 88.29/12.11 thf(zip_derived_cl5749, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 ( (((in @ X4 @ nat) => 88.29/12.11 (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((((((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((X4) != (n_pl @ X2 @ Y1)))))))) => 88.29/12.11 (((X2) = (X4))))) => 88.29/12.11 (((((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((n_pl @ X4 @ Y0) != (n_pl @ 88.29/12.11 (n_pl @ X2 @ Y0) @ Y1)))))))) => 88.29/12.11 (((n_pl @ X2 @ Y0) = (n_pl @ X4 @ Y0)))))))))))))) 88.29/12.11 | ~ (in @ X2 @ nat))), 88.29/12.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5748])). 88.29/12.11 thf(zip_derived_cl5750, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 (~ (in @ X4 @ nat) 88.29/12.11 | (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((((((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((X4) != (n_pl @ X2 @ Y1)))))))) => 88.29/12.11 (((X2) = (X4))))) => 88.29/12.11 (((((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((n_pl @ X4 @ Y0) != (n_pl @ 88.29/12.11 (n_pl @ X2 @ Y0) @ Y1)))))))) => 88.29/12.11 (((n_pl @ X2 @ Y0) = (n_pl @ X4 @ Y0)))))))))))) 88.29/12.11 | ~ (in @ X2 @ nat))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5749])). 88.29/12.11 thf(zip_derived_cl5751, plain, 88.29/12.11 (![X2 : $i, X4 : $i, X6 : $i]: 88.29/12.11 ( (((in @ X6 @ nat) => 88.29/12.11 (((((((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))) => 88.29/12.11 (((X2) = (X4))))) => 88.29/12.11 (((((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((n_pl @ X4 @ X6) != (n_pl @ 88.29/12.11 (n_pl @ X2 @ X6) @ Y0)))))))) => 88.29/12.11 (((n_pl @ X2 @ X6) = (n_pl @ X4 @ X6))))))))) 88.29/12.11 | ~ (in @ X2 @ nat) 88.29/12.11 | ~ (in @ X4 @ nat))), 88.29/12.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5750])). 88.29/12.11 thf(zip_derived_cl5752, plain, 88.29/12.11 (![X2 : $i, X4 : $i, X6 : $i]: 88.29/12.11 (~ (in @ X6 @ nat) 88.29/12.11 | (((((((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))) => 88.29/12.11 (((X2) = (X4))))) => 88.29/12.11 (((((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((n_pl @ X4 @ X6) != (n_pl @ 88.29/12.11 (n_pl @ X2 @ X6) @ Y0)))))))) => 88.29/12.11 (((n_pl @ X2 @ X6) = (n_pl @ X4 @ X6))))))) 88.29/12.11 | ~ (in @ X4 @ nat) 88.29/12.11 | ~ (in @ X2 @ nat))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5751])). 88.29/12.11 thf(zip_derived_cl5753, plain, 88.29/12.11 (![X2 : $i, X4 : $i, X6 : $i]: 88.29/12.11 (~ (((((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))) => 88.29/12.11 (((X2) = (X4))))) 88.29/12.11 | (((((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((n_pl @ X4 @ X6) != (n_pl @ (n_pl @ X2 @ X6) @ 88.29/12.11 Y0)))))))) => 88.29/12.11 (((n_pl @ X2 @ X6) = (n_pl @ X4 @ X6))))) 88.29/12.11 | ~ (in @ X2 @ nat) 88.29/12.11 | ~ (in @ X4 @ nat) 88.29/12.11 | ~ (in @ X6 @ nat))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5752])). 88.29/12.11 thf(zip_derived_cl5754, plain, 88.29/12.11 (![X2 : $i, X4 : $i, X6 : $i]: 88.29/12.11 ( (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))) 88.29/12.11 | ~ (in @ X6 @ nat) 88.29/12.11 | ~ (in @ X4 @ nat) 88.29/12.11 | ~ (in @ X2 @ nat) 88.29/12.11 | (((((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((n_pl @ X4 @ X6) != (n_pl @ (n_pl @ X2 @ X6) @ 88.29/12.11 Y0)))))))) => 88.29/12.11 (((n_pl @ X2 @ X6) = (n_pl @ X4 @ X6))))))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5753])). 88.29/12.11 thf(zip_derived_cl5756, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 (~ ('#form7743' @ X2 @ X4) 88.29/12.11 | (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf(satz10e, axiom, 88.29/12.11 (all_of @ 88.29/12.11 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 88.29/12.11 ( ^[X0:$i]: 88.29/12.11 ( all_of @ 88.29/12.11 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 88.29/12.11 ( ^[X1:$i]: 88.29/12.11 ( ( d_not @ ( d_29_ii @ X0 @ X1 ) ) => ( lessis @ X0 @ X1 ) ) ) ) ))). 88.29/12.11 thf(zf_stmt_2, axiom, 88.29/12.11 (![X4:$i]: 88.29/12.11 ( ( in @ X4 @ nat ) => 88.29/12.11 ( ![X6:$i]: 88.29/12.11 ( ( in @ X6 @ nat ) => 88.29/12.11 ( ( ![X8:$i]: 88.29/12.11 ( ( in @ X8 @ nat ) => ( ( X4 ) != ( n_pl @ X6 @ X8 ) ) ) ) => 88.29/12.11 ( ( ![X10:$i]: 88.29/12.11 ( ( in @ X10 @ nat ) => ( ( X6 ) != ( n_pl @ X4 @ X10 ) ) ) ) => 88.29/12.11 ( ( X4 ) = ( X6 ) ) ) ) ) ) ))). 88.29/12.11 thf(zip_derived_cl174, plain, 88.29/12.11 ( (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ nat) => 88.29/12.11 (((Y0) != (n_pl @ Y1 @ Y2)))))))) => 88.29/12.11 (((((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ nat) => 88.29/12.11 (((Y1) != (n_pl @ Y0 @ 88.29/12.11 Y2)))))))) => 88.29/12.11 (((Y0) = (Y1)))))))))))))))))), 88.29/12.11 inference('cnf', [status(esa)], [zf_stmt_2])). 88.29/12.11 thf(zip_derived_cl5665, plain, 88.29/12.11 (![X2 : $i]: 88.29/12.11 (((in @ X2 @ nat) => 88.29/12.11 (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((X2) != (n_pl @ Y0 @ Y1)))))))) => 88.29/12.11 (((((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((Y0) != (n_pl @ X2 @ Y1)))))))) => 88.29/12.11 (((X2) = (Y0))))))))))))))), 88.29/12.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl174])). 88.29/12.11 thf(zip_derived_cl5666, plain, 88.29/12.11 (![X2 : $i]: 88.29/12.11 (~ (in @ X2 @ nat) 88.29/12.11 | (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((X2) != (n_pl @ Y0 @ Y1)))))))) => 88.29/12.11 (((((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((Y0) != (n_pl @ X2 @ Y1)))))))) => 88.29/12.11 (((X2) = (Y0)))))))))))))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5665])). 88.29/12.11 thf(zip_derived_cl5667, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 ( (((in @ X4 @ nat) => 88.29/12.11 (((((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))) => 88.29/12.11 (((((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))) => 88.29/12.11 (((X2) = (X4))))))))) 88.29/12.11 | ~ (in @ X2 @ nat))), 88.29/12.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5666])). 88.29/12.11 thf(zip_derived_cl5668, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 (~ (in @ X4 @ nat) 88.29/12.11 | (((((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))) => 88.29/12.11 (((((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))) => 88.29/12.11 (((X2) = (X4))))))) 88.29/12.11 | ~ (in @ X2 @ nat))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5667])). 88.29/12.11 thf(zip_derived_cl5669, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 (~ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))) 88.29/12.11 | (((((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))) => 88.29/12.11 (((X2) = (X4))))) 88.29/12.11 | ~ (in @ X2 @ nat) 88.29/12.11 | ~ (in @ X4 @ nat))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5668])). 88.29/12.11 thf(zip_derived_cl5670, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 ( ('#form7743' @ X2 @ X4) 88.29/12.11 | ~ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf(zip_derived_cl7009, plain, 88.29/12.11 (![X2 : $i, X4 : $i, X6 : $i]: 88.29/12.11 ( ('#form7743' @ (n_pl @ X2 @ X6) @ (n_pl @ X4 @ X6)) 88.29/12.11 | ~ (in @ X6 @ nat) 88.29/12.11 | ~ (in @ X4 @ nat) 88.29/12.11 | ~ (in @ X2 @ nat) 88.29/12.11 | ~ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 88.29/12.11 inference('renaming', [status(thm)], 88.29/12.11 [zip_derived_cl7008, zip_derived_cl5756, zip_derived_cl5670])). 88.29/12.11 thf(zip_derived_cl5756, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 (~ ('#form7743' @ X2 @ X4) 88.29/12.11 | (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf(zip_derived_cl5670, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 ( ('#form7743' @ X2 @ X4) 88.29/12.11 | ~ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf(zip_derived_cl7010, plain, 88.29/12.11 (![X2 : $i, X4 : $i, X6 : $i]: 88.29/12.11 (~ ('#form7743' @ X2 @ X4) 88.29/12.11 | ~ (in @ X2 @ nat) 88.29/12.11 | ~ (in @ X4 @ nat) 88.29/12.11 | ~ (in @ X6 @ nat) 88.29/12.11 | ('#form7743' @ (n_pl @ X2 @ X6) @ (n_pl @ X4 @ X6)))), 88.29/12.11 inference('renaming', [status(thm)], 88.29/12.11 [zip_derived_cl7009, zip_derived_cl5756, zip_derived_cl5670])). 88.29/12.11 thf(satz6, axiom, 88.29/12.11 (all_of @ 88.29/12.11 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 88.29/12.11 ( ^[X0:$i]: 88.29/12.11 ( all_of @ 88.29/12.11 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 88.29/12.11 ( ^[X1:$i]: ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X1 @ X0 ) ) ) ) ))). 88.29/12.11 thf(zf_stmt_3, axiom, 88.29/12.11 (![X4:$i]: 88.29/12.11 ( ( in @ X4 @ nat ) => 88.29/12.11 ( ![X6:$i]: 88.29/12.11 ( ( in @ X6 @ nat ) => ( ( n_pl @ X4 @ X6 ) = ( n_pl @ X6 @ X4 ) ) ) ) ))). 88.29/12.11 thf(zip_derived_cl141, plain, 88.29/12.11 ( (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((n_pl @ Y0 @ Y1) = (n_pl @ Y1 @ Y0)))))))))))))), 88.29/12.11 inference('cnf', [status(esa)], [zf_stmt_3])). 88.29/12.11 thf(zip_derived_cl1073, plain, 88.29/12.11 (![X2 : $i]: 88.29/12.11 (((in @ X2 @ nat) => 88.29/12.11 (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((n_pl @ X2 @ Y0) = (n_pl @ Y0 @ X2))))))))))), 88.29/12.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl141])). 88.29/12.11 thf(zip_derived_cl1074, plain, 88.29/12.11 (![X2 : $i]: 88.29/12.11 (~ (in @ X2 @ nat) 88.29/12.11 | (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((n_pl @ X2 @ Y0) = (n_pl @ Y0 @ X2)))))))))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1073])). 88.29/12.11 thf(zip_derived_cl1075, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 ( (((in @ X4 @ nat) => (((n_pl @ X2 @ X4) = (n_pl @ X4 @ X2))))) 88.29/12.11 | ~ (in @ X2 @ nat))), 88.29/12.11 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1074])). 88.29/12.11 thf(zip_derived_cl1076, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 (~ (in @ X4 @ nat) 88.29/12.11 | (((n_pl @ X2 @ X4) = (n_pl @ X4 @ X2))) 88.29/12.11 | ~ (in @ X2 @ nat))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1075])). 88.29/12.11 thf(zip_derived_cl1077, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 (~ (in @ X4 @ nat) 88.29/12.11 | ((n_pl @ X2 @ X4) = (n_pl @ X4 @ X2)) 88.29/12.11 | ~ (in @ X2 @ nat))), 88.29/12.11 inference('simplify nested equalities', [status(thm)], 88.29/12.11 [zip_derived_cl1076])). 88.29/12.11 thf(zip_derived_cl1077, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 (~ (in @ X4 @ nat) 88.29/12.11 | ((n_pl @ X2 @ X4) = (n_pl @ X4 @ X2)) 88.29/12.11 | ~ (in @ X2 @ nat))), 88.29/12.11 inference('simplify nested equalities', [status(thm)], 88.29/12.11 [zip_derived_cl1076])). 88.29/12.11 thf(satz20d, conjecture, 88.29/12.11 (all_of @ 88.29/12.11 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 88.29/12.11 ( ^[X0:$i]: 88.29/12.11 ( all_of @ 88.29/12.11 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 88.29/12.11 ( ^[X1:$i]: 88.29/12.11 ( all_of @ 88.29/12.11 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 88.29/12.11 ( ^[X2:$i]: 88.29/12.11 ( ( d_29_ii @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X2 @ X1 ) ) => 88.29/12.11 ( d_29_ii @ X0 @ X1 ) ) ) ) ) ) ))). 88.29/12.11 thf(zf_stmt_4, conjecture, 88.29/12.11 (![X4:$i]: 88.29/12.11 ( ( in @ X4 @ nat ) => 88.29/12.11 ( ![X6:$i]: 88.29/12.11 ( ( in @ X6 @ nat ) => 88.29/12.11 ( ![X8:$i]: 88.29/12.11 ( ( in @ X8 @ nat ) => 88.29/12.11 ( ( ~( ![X10:$i]: 88.29/12.11 ( ( in @ X10 @ nat ) => 88.29/12.11 ( ( n_pl @ X8 @ X4 ) != 88.29/12.11 ( n_pl @ ( n_pl @ X8 @ X6 ) @ X10 ) ) ) ) ) => 88.29/12.11 ( ~( ![X12:$i]: 88.29/12.11 ( ( in @ X12 @ nat ) => ( ( X4 ) != ( n_pl @ X6 @ X12 ) ) ) ) ) ) ) ) ) ) ))). 88.29/12.11 thf(zf_stmt_5, negated_conjecture, 88.29/12.11 (~( ![X4:$i]: 88.29/12.11 ( ( in @ X4 @ nat ) => 88.29/12.11 ( ![X6:$i]: 88.29/12.11 ( ( in @ X6 @ nat ) => 88.29/12.11 ( ![X8:$i]: 88.29/12.11 ( ( in @ X8 @ nat ) => 88.29/12.11 ( ( ~( ![X10:$i]: 88.29/12.11 ( ( in @ X10 @ nat ) => 88.29/12.11 ( ( n_pl @ X8 @ X4 ) != 88.29/12.11 ( n_pl @ ( n_pl @ X8 @ X6 ) @ X10 ) ) ) ) ) => 88.29/12.11 ( ~( ![X12:$i]: 88.29/12.11 ( ( in @ X12 @ nat ) => 88.29/12.11 ( ( X4 ) != ( n_pl @ X6 @ X12 ) ) ) ) ) ) ) ) ) ) ) )), 88.29/12.11 inference('cnf.neg', [status(esa)], [zf_stmt_4])). 88.29/12.11 thf(zip_derived_cl180, plain, 88.29/12.11 (~ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ nat) => 88.29/12.11 (((((~) @ (((!!) @ ( 88.29/12.11 ^[Y3 : $i]: 88.29/12.11 (((in @ Y3 @ 88.29/12.11 nat) => 88.29/12.11 (((n_pl @ 88.29/12.11 Y2 @ 88.29/12.11 Y0) != 88.29/12.11 (n_pl @ 88.29/12.11 (n_pl @ 88.29/12.11 Y2 @ Y1) @ 88.29/12.11 Y3)))))))))) => 88.29/12.11 (((~) @ (((!!) @ ( 88.29/12.11 ^[Y3 : $i]: 88.29/12.11 (((in @ Y3 @ 88.29/12.11 nat) => 88.29/12.11 (((Y0) != 88.29/12.11 (n_pl @ 88.29/12.11 Y1 @ Y3)))))))))))))))))))))))))))), 88.29/12.11 inference('cnf', [status(esa)], [zf_stmt_5])). 88.29/12.11 thf(zip_derived_cl6896, plain, 88.29/12.11 (~ (((in @ '#sk8897' @ nat) => 88.29/12.11 (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((((~) @ (((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ 88.29/12.11 nat) => 88.29/12.11 (((n_pl @ Y1 @ 88.29/12.11 '#sk8897') != 88.29/12.11 (n_pl @ 88.29/12.11 (n_pl @ Y1 @ 88.29/12.11 Y0) @ 88.29/12.11 Y2)))))))))) => 88.29/12.11 (((~) @ (((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ 88.29/12.11 nat) => 88.29/12.11 ((('#sk8897') != 88.29/12.11 (n_pl @ Y0 @ 88.29/12.11 Y2))))))))))))))))))))))))), 88.29/12.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl180])). 88.29/12.11 thf(zip_derived_cl6898, plain, 88.29/12.11 (~ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((((~) @ (((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ nat) => 88.29/12.11 (((n_pl @ Y1 @ 88.29/12.11 '#sk8897') != 88.29/12.11 (n_pl @ 88.29/12.11 (n_pl @ Y1 @ Y0) @ 88.29/12.11 Y2)))))))))) => 88.29/12.11 (((~) @ (((!!) @ (^[Y2 : $i]: 88.29/12.11 (((in @ Y2 @ nat) => 88.29/12.11 ((('#sk8897') != 88.29/12.11 (n_pl @ Y0 @ Y2))))))))))))))))))))))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6896])). 88.29/12.11 thf(zip_derived_cl6899, plain, 88.29/12.11 (~ (((in @ '#sk8898' @ nat) => 88.29/12.11 (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((((~) @ (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((n_pl @ Y0 @ '#sk8897') != 88.29/12.11 (n_pl @ 88.29/12.11 (n_pl @ Y0 @ '#sk8898') @ 88.29/12.11 Y1)))))))))) => 88.29/12.11 (((~) @ (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 ((('#sk8897') != (n_pl @ 88.29/12.11 '#sk8898' @ Y1)))))))))))))))))))), 88.29/12.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6898])). 88.29/12.11 thf(zip_derived_cl6901, plain, 88.29/12.11 (~ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((((~) @ (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 (((n_pl @ Y0 @ '#sk8897') != 88.29/12.11 (n_pl @ 88.29/12.11 (n_pl @ Y0 @ '#sk8898') @ Y1)))))))))) => 88.29/12.11 (((~) @ (((!!) @ (^[Y1 : $i]: 88.29/12.11 (((in @ Y1 @ nat) => 88.29/12.11 ((('#sk8897') != (n_pl @ 88.29/12.11 '#sk8898' @ Y1)))))))))))))))))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6899])). 88.29/12.11 thf(zip_derived_cl6902, plain, 88.29/12.11 (~ (((in @ '#sk8899' @ nat) => 88.29/12.11 (((((~) @ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((n_pl @ '#sk8899' @ '#sk8897') != (n_pl @ 88.29/12.11 (n_pl @ '#sk8899' @ '#sk8898') @ Y0)))))))))) => 88.29/12.11 (((~) @ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 ((('#sk8897') != (n_pl @ '#sk8898' @ Y0))))))))))))))), 88.29/12.11 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6901])). 88.29/12.11 thf(zip_derived_cl6904, plain, 88.29/12.11 (~ (((((~) @ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((n_pl @ '#sk8899' @ '#sk8897') != (n_pl @ 88.29/12.11 (n_pl @ '#sk8899' @ '#sk8898') @ Y0)))))))))) => 88.29/12.11 (((~) @ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 ((('#sk8897') != (n_pl @ '#sk8898' @ Y0))))))))))))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6902])). 88.29/12.11 thf(zip_derived_cl6905, plain, 88.29/12.11 (~ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 (((n_pl @ '#sk8899' @ '#sk8897') != (n_pl @ 88.29/12.11 (n_pl @ '#sk8899' @ '#sk8898') @ Y0))))))))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6904])). 88.29/12.11 thf(zip_derived_cl5756, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 (~ ('#form7743' @ X2 @ X4) 88.29/12.11 | (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf(zip_derived_cl5670, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 ( ('#form7743' @ X2 @ X4) 88.29/12.11 | ~ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf(zip_derived_cl6907, plain, 88.29/12.11 (~ ('#form7743' @ (n_pl @ '#sk8899' @ '#sk8897') @ 88.29/12.11 (n_pl @ '#sk8899' @ '#sk8898'))), 88.29/12.11 inference('renaming', [status(thm)], 88.29/12.11 [zip_derived_cl6905, zip_derived_cl5756, zip_derived_cl5670])). 88.29/12.11 thf(zip_derived_cl7277, plain, 88.29/12.11 ((~ ('#form7743' @ (n_pl @ '#sk8897' @ '#sk8899') @ 88.29/12.11 (n_pl @ '#sk8899' @ '#sk8898')) 88.29/12.11 | ~ (in @ '#sk8897' @ nat) 88.29/12.11 | ~ (in @ '#sk8899' @ nat))), 88.29/12.11 inference('sup-', [status(thm)], [zip_derived_cl1077, zip_derived_cl6907])). 88.29/12.11 thf(zip_derived_cl6897, plain, ( (in @ '#sk8897' @ nat)), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6896])). 88.29/12.11 thf(zip_derived_cl6903, plain, ( (in @ '#sk8899' @ nat)), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6902])). 88.29/12.11 thf(zip_derived_cl7286, plain, 88.29/12.11 (~ ('#form7743' @ (n_pl @ '#sk8897' @ '#sk8899') @ 88.29/12.11 (n_pl @ '#sk8899' @ '#sk8898'))), 88.29/12.11 inference('demod', [status(thm)], 88.29/12.11 [zip_derived_cl7277, zip_derived_cl6897, zip_derived_cl6903])). 88.29/12.11 thf(zip_derived_cl7304, plain, 88.29/12.11 ((~ ('#form7743' @ (n_pl @ '#sk8897' @ '#sk8899') @ 88.29/12.11 (n_pl @ '#sk8898' @ '#sk8899')) 88.29/12.11 | ~ (in @ '#sk8898' @ nat) 88.29/12.11 | ~ (in @ '#sk8899' @ nat))), 88.29/12.11 inference('sup-', [status(thm)], [zip_derived_cl1077, zip_derived_cl7286])). 88.29/12.11 thf(zip_derived_cl6900, plain, ( (in @ '#sk8898' @ nat)), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6899])). 88.29/12.11 thf(zip_derived_cl6903, plain, ( (in @ '#sk8899' @ nat)), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6902])). 88.29/12.11 thf(zip_derived_cl7312, plain, 88.29/12.11 (~ ('#form7743' @ (n_pl @ '#sk8897' @ '#sk8899') @ 88.29/12.11 (n_pl @ '#sk8898' @ '#sk8899'))), 88.29/12.11 inference('demod', [status(thm)], 88.29/12.11 [zip_derived_cl7304, zip_derived_cl6900, zip_derived_cl6903])). 88.29/12.11 thf(zip_derived_cl7624, plain, 88.29/12.11 ((~ (in @ '#sk8899' @ nat) 88.29/12.11 | ~ (in @ '#sk8898' @ nat) 88.29/12.11 | ~ (in @ '#sk8897' @ nat) 88.29/12.11 | ~ ('#form7743' @ '#sk8897' @ '#sk8898'))), 88.29/12.11 inference('sup-', [status(thm)], [zip_derived_cl7010, zip_derived_cl7312])). 88.29/12.11 thf(zip_derived_cl6903, plain, ( (in @ '#sk8899' @ nat)), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6902])). 88.29/12.11 thf(zip_derived_cl6900, plain, ( (in @ '#sk8898' @ nat)), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6899])). 88.29/12.11 thf(zip_derived_cl6897, plain, ( (in @ '#sk8897' @ nat)), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6896])). 88.29/12.11 thf(zip_derived_cl6906, plain, 88.29/12.11 ( (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => 88.29/12.11 ((('#sk8897') != (n_pl @ '#sk8898' @ Y0))))))))), 88.29/12.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6904])). 88.29/12.11 thf(zip_derived_cl5756, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 (~ ('#form7743' @ X2 @ X4) 88.29/12.11 | (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf(zip_derived_cl5670, plain, 88.29/12.11 (![X2 : $i, X4 : $i]: 88.29/12.11 ( ('#form7743' @ X2 @ X4) 88.29/12.11 | ~ (((!!) @ (^[Y0 : $i]: 88.29/12.11 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 88.29/12.11 define([status(thm)])). 88.29/12.11 thf(zip_derived_cl6908, plain, ( ('#form7743' @ '#sk8897' @ '#sk8898')), 88.29/12.11 inference('renaming', [status(thm)], 88.29/12.11 [zip_derived_cl6906, zip_derived_cl5756, zip_derived_cl5670])). 88.29/12.11 thf(zip_derived_cl7649, plain, ($false), 88.29/12.11 inference('demod', [status(thm)], 88.29/12.11 [zip_derived_cl7624, zip_derived_cl6903, zip_derived_cl6900, 88.29/12.11 zip_derived_cl6897, zip_derived_cl6908])). 88.29/12.11 88.29/12.11 % SZS output end Refutation 88.29/12.11 88.29/12.11 88.29/12.11 % Terminating... 89.07/12.22 % Runner terminated. 89.07/12.22 % Zipperpin 1.5 exiting 89.07/12.22 EOF