0.03/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ecsNMrG7Gw true 0.12/0.34 % Computer : n011.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 960 0.12/0.34 % WCLimit : 120 0.12/0.34 % DateTime : Tue Aug 9 07:53:51 EDT 2022 0.12/0.34 % CPUTime : 0.12/0.34 % Running portfolio for 960 s 0.12/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.12/0.34 % Number of cores: 8 0.12/0.34 % Python version: Python 3.6.8 0.12/0.34 % Running in HO mode 0.48/0.62 % Total configuration time : 828 0.48/0.62 % Estimated wc time : 1656 0.48/0.62 % Estimated cpu time (8 cpus) : 207.0 0.50/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.50/0.71 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.50/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 131.55/17.19 % Solved by lams/35_full_unif4.sh. 131.55/17.19 % done 643 iterations in 16.425s 131.55/17.19 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 131.55/17.19 % SZS output start Refutation 131.55/17.19 thf(lessis_type, type, lessis: $i > $i > $o). 131.55/17.19 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 131.55/17.19 thf(d_not_type, type, d_not: $o > $o). 131.55/17.19 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 131.55/17.19 thf(in_type, type, in: $i > $i > $o). 131.55/17.19 thf(moreis_type, type, moreis: $i > $i > $o). 131.55/17.19 thf(e_is_type, type, e_is: $i > $i > $i > $o). 131.55/17.19 thf(nat_type, type, nat: $i). 131.55/17.19 thf(iii_type, type, iii: $i > $i > $o). 131.55/17.19 thf(l_or_type, type, l_or: $o > $o > $o). 131.55/17.19 thf('#form7812_type', type, '#form7812': $i > $i > $o). 131.55/17.19 thf('#sk8272_type', type, '#sk8272': $i). 131.55/17.19 thf(non_type, type, non: $i > ($i > $o) > $i > $o). 131.55/17.19 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 131.55/17.19 thf(imp_type, type, imp: $o > $o > $o). 131.55/17.19 thf('#sk8270_type', type, '#sk8270': $i). 131.55/17.19 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 131.55/17.19 thf('#sk8271_type', type, '#sk8271': $i). 131.55/17.19 thf(n_is_type, type, n_is: $i > $i > $o). 131.55/17.19 thf(n_some_type, type, n_some: ($i > $o) > $o). 131.55/17.19 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 131.55/17.19 thf(n_pl_type, type, n_pl: $i > $i > $i). 131.55/17.19 thf(def_d_29_ii, axiom,(( d_29_ii ) = 131.55/17.19 (^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X0 @ X1 ) )))). 131.55/17.19 thf(def_diffprop, axiom,(( diffprop ) = 131.55/17.19 (^[X0:$i,X1:$i,X2:$i]: ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) )))). 131.55/17.19 thf(def_n_is, axiom,(( n_is ) = (e_is @ nat))). 131.55/17.19 thf(def_e_is, axiom,(( e_is ) = (^[X0:$i,X:$i,Y:$i]: ( ( X ) = ( Y ) )))). 131.55/17.19 thf('0', plain, (( e_is ) = ( ^[X0:$i,X:$i,Y:$i]: ( ( X ) = ( Y ) ) )), 131.55/17.19 inference('simplify_rw_rule', [status(thm)], [def_e_is])). 131.55/17.19 thf('1', plain, 131.55/17.19 (( e_is ) = ( ^[V_1:$i,V_2:$i,V_3:$i]: ( ( V_2 ) = ( V_3 ) ) )), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf('2', plain, (( n_is ) = ( e_is @ nat )), 131.55/17.19 inference('simplify_rw_rule', [status(thm)], [def_n_is, '1'])). 131.55/17.19 thf('3', plain, (( n_is ) = ( e_is @ nat )), define([status(thm)])). 131.55/17.19 thf('4', plain, 131.55/17.19 (( diffprop ) = 131.55/17.19 ( ^[X0:$i,X1:$i,X2:$i]: ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) )), 131.55/17.19 inference('simplify_rw_rule', [status(thm)], [def_diffprop, '3', '1'])). 131.55/17.19 thf('5', plain, 131.55/17.19 (( diffprop ) = 131.55/17.19 ( ^[V_1:$i,V_2:$i,V_3:$i]: ( n_is @ V_1 @ ( n_pl @ V_2 @ V_3 ) ) )), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf(def_n_some, axiom,(( n_some ) = (l_some @ nat))). 131.55/17.19 thf(def_l_some, axiom,(( l_some ) = 131.55/17.19 (^[X0:$i,X1:( $i > $o )]: 131.55/17.19 ( d_not @ ( all_of @ ( ^[X2:$i]: ( in @ X2 @ X0 ) ) @ ( non @ X0 @ X1 ) ) )))). 131.55/17.19 thf(def_non, axiom,(( non ) = 131.55/17.19 (^[X0:$i,X1:( $i > $o ),X2:$i]: ( d_not @ ( X1 @ X2 ) )))). 131.55/17.19 thf(def_d_not, axiom,(( d_not ) = (^[X0:$o]: ( imp @ X0 @ $false )))). 131.55/17.19 thf(def_imp, axiom,(( imp ) = (^[X0:$o,X1:$o]: ( ( X0 ) => ( X1 ) )))). 131.55/17.19 thf('6', plain, (( imp ) = ( ^[X0:$o,X1:$o]: ( ( X0 ) => ( X1 ) ) )), 131.55/17.19 inference('simplify_rw_rule', [status(thm)], [def_imp])). 131.55/17.19 thf('7', plain, (( imp ) = ( ^[V_1:$o,V_2:$o]: ( ( V_1 ) => ( V_2 ) ) )), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf('8', plain, (( d_not ) = ( ^[X0:$o]: ( imp @ X0 @ $false ) )), 131.55/17.19 inference('simplify_rw_rule', [status(thm)], [def_d_not, '7'])). 131.55/17.19 thf('9', plain, (( d_not ) = ( ^[V_1:$o]: ( imp @ V_1 @ $false ) )), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf('10', plain, 131.55/17.19 (( non ) = ( ^[X0:$i,X1:( $i > $o ),X2:$i]: ( d_not @ ( X1 @ X2 ) ) )), 131.55/17.19 inference('simplify_rw_rule', [status(thm)], [def_non, '9', '7'])). 131.55/17.19 thf('11', plain, 131.55/17.19 (( non ) = 131.55/17.19 ( ^[V_1:$i,V_2:( $i > $o ),V_3:$i]: ( d_not @ ( V_2 @ V_3 ) ) )), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf(def_all_of, axiom,(( all_of ) = 131.55/17.19 (^[X0:( $i > $o ),X1:( $i > $o )]: 131.55/17.19 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) )))). 131.55/17.19 thf(def_is_of, axiom,(( is_of ) = (^[X0:$i,X1:( $i > $o )]: ( X1 @ X0 )))). 131.55/17.19 thf('12', plain, (( is_of ) = ( ^[X0:$i,X1:( $i > $o )]: ( X1 @ X0 ) )), 131.55/17.19 inference('simplify_rw_rule', [status(thm)], [def_is_of])). 131.55/17.19 thf('13', plain, (( is_of ) = ( ^[V_1:$i,V_2:( $i > $o )]: ( V_2 @ V_1 ) )), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf('14', plain, 131.55/17.19 (( all_of ) = 131.55/17.19 ( ^[X0:( $i > $o ),X1:( $i > $o )]: 131.55/17.19 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) ) )), 131.55/17.19 inference('simplify_rw_rule', [status(thm)], [def_all_of, '13'])). 131.55/17.19 thf('15', plain, 131.55/17.19 (( all_of ) = 131.55/17.19 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 131.55/17.19 ( ![X4:$i]: ( ( is_of @ X4 @ V_1 ) => ( V_2 @ X4 ) ) ) )), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf('16', plain, 131.55/17.19 (( l_some ) = 131.55/17.19 ( ^[X0:$i,X1:( $i > $o )]: 131.55/17.19 ( d_not @ 131.55/17.19 ( all_of @ ( ^[X2:$i]: ( in @ X2 @ X0 ) ) @ ( non @ X0 @ X1 ) ) ) )), 131.55/17.19 inference('simplify_rw_rule', [status(thm)], 131.55/17.19 [def_l_some, '11', '9', '7', '15', '13'])). 131.55/17.19 thf('17', plain, 131.55/17.19 (( l_some ) = 131.55/17.19 ( ^[V_1:$i,V_2:( $i > $o )]: 131.55/17.19 ( d_not @ 131.55/17.19 ( all_of @ ( ^[V_3:$i]: ( in @ V_3 @ V_1 ) ) @ ( non @ V_1 @ V_2 ) ) ) )), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf('18', plain, (( n_some ) = ( l_some @ nat )), 131.55/17.19 inference('simplify_rw_rule', [status(thm)], 131.55/17.19 [def_n_some, '17', '11', '9', '7', '15', '13'])). 131.55/17.19 thf('19', plain, (( n_some ) = ( l_some @ nat )), define([status(thm)])). 131.55/17.19 thf('20', plain, 131.55/17.19 (( d_29_ii ) = ( ^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 131.55/17.19 inference('simplify_rw_rule', [status(thm)], 131.55/17.19 [def_d_29_ii, '5', '19', '3', '1', '17', '11', '9', '7', '15', 131.55/17.19 '13'])). 131.55/17.19 thf('21', plain, 131.55/17.19 (( d_29_ii ) = 131.55/17.19 ( ^[V_1:$i,V_2:$i]: ( n_some @ ( diffprop @ V_1 @ V_2 ) ) )), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf(satz20a, axiom, 131.55/17.19 (all_of @ 131.55/17.19 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 131.55/17.19 ( ^[X0:$i]: 131.55/17.19 ( all_of @ 131.55/17.19 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 131.55/17.19 ( ^[X1:$i]: 131.55/17.19 ( all_of @ 131.55/17.19 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 131.55/17.19 ( ^[X2:$i]: 131.55/17.19 ( ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) => 131.55/17.19 ( d_29_ii @ X0 @ X1 ) ) ) ) ) ) ))). 131.55/17.19 thf(zf_stmt_0, axiom, 131.55/17.19 (![X4:$i]: 131.55/17.19 ( ( in @ X4 @ nat ) => 131.55/17.19 ( ![X6:$i]: 131.55/17.19 ( ( in @ X6 @ nat ) => 131.55/17.19 ( ![X8:$i]: 131.55/17.19 ( ( in @ X8 @ nat ) => 131.55/17.19 ( ( ~( ![X10:$i]: 131.55/17.19 ( ( in @ X10 @ nat ) => 131.55/17.19 ( ( n_pl @ X4 @ X8 ) != 131.55/17.19 ( n_pl @ ( n_pl @ X6 @ X8 ) @ X10 ) ) ) ) ) => 131.55/17.19 ( ~( ![X12:$i]: 131.55/17.19 ( ( in @ X12 @ nat ) => ( ( X4 ) != ( n_pl @ X6 @ X12 ) ) ) ) ) ) ) ) ) ) ))). 131.55/17.19 thf(zip_derived_cl130, plain, 131.55/17.19 ( (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((!!) @ (^[Y2 : $i]: 131.55/17.19 (((in @ Y2 @ nat) => 131.55/17.19 (((((~) @ (((!!) @ (^[Y3 : $i]: 131.55/17.19 (( 131.55/17.19 (in @ 131.55/17.19 Y3 @ 131.55/17.19 nat) => 131.55/17.19 (( 131.55/17.19 (n_pl @ 131.55/17.19 Y0 @ 131.55/17.19 Y2) != 131.55/17.19 (n_pl @ 131.55/17.19 ( 131.55/17.19 n_pl @ 131.55/17.19 Y1 @ Y2) @ 131.55/17.19 Y3)))))))))) => 131.55/17.19 (((~) @ (((!!) @ (^[Y3 : $i]: 131.55/17.19 (( 131.55/17.19 (in @ 131.55/17.19 Y3 @ 131.55/17.19 nat) => 131.55/17.19 (( 131.55/17.19 (Y0) != 131.55/17.19 (n_pl @ 131.55/17.19 Y1 @ Y3)))))))))))))))))))))))))))), 131.55/17.19 inference('cnf', [status(esa)], [zf_stmt_0])). 131.55/17.19 thf(zip_derived_cl6808, plain, 131.55/17.19 (![X2 : $i]: 131.55/17.19 (((in @ X2 @ nat) => 131.55/17.19 (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((((~) @ (((!!) @ (^[Y2 : $i]: 131.55/17.19 (((in @ Y2 @ 131.55/17.19 nat) => 131.55/17.19 (((n_pl @ X2 @ 131.55/17.19 Y1) != 131.55/17.19 (n_pl @ 131.55/17.19 (n_pl @ Y0 @ 131.55/17.19 Y1) @ 131.55/17.19 Y2)))))))))) => 131.55/17.19 (((~) @ (((!!) @ (^[Y2 : $i]: 131.55/17.19 (((in @ Y2 @ 131.55/17.19 nat) => 131.55/17.19 (((X2) != 131.55/17.19 (n_pl @ Y0 @ 131.55/17.19 Y2))))))))))))))))))))))))), 131.55/17.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl130])). 131.55/17.19 thf(zip_derived_cl6809, plain, 131.55/17.19 (![X2 : $i]: 131.55/17.19 (~ (in @ X2 @ nat) 131.55/17.19 | (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((((~) @ (((!!) @ (^[Y2 : $i]: 131.55/17.19 (((in @ Y2 @ 131.55/17.19 nat) => 131.55/17.19 (((n_pl @ 131.55/17.19 X2 @ Y1) != 131.55/17.19 (n_pl @ 131.55/17.19 (n_pl @ 131.55/17.19 Y0 @ Y1) @ 131.55/17.19 Y2)))))))))) => 131.55/17.19 (((~) @ (((!!) @ (^[Y2 : $i]: 131.55/17.19 (((in @ Y2 @ 131.55/17.19 nat) => 131.55/17.19 (((X2) != 131.55/17.19 (n_pl @ 131.55/17.19 Y0 @ Y2)))))))))))))))))))))))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6808])). 131.55/17.19 thf(zip_derived_cl6810, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 ( (((in @ X4 @ nat) => 131.55/17.19 (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((((~) @ (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((n_pl @ X2 @ Y0) != 131.55/17.19 (n_pl @ 131.55/17.19 (n_pl @ X4 @ Y0) @ Y1)))))))))) => 131.55/17.19 (((~) @ (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((X2) != (n_pl @ X4 @ Y1))))))))))))))))))) 131.55/17.19 | ~ (in @ X2 @ nat))), 131.55/17.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6809])). 131.55/17.19 thf(zip_derived_cl6811, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 (~ (in @ X4 @ nat) 131.55/17.19 | (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((((~) @ (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((n_pl @ X2 @ Y0) != 131.55/17.19 (n_pl @ 131.55/17.19 (n_pl @ X4 @ Y0) @ Y1)))))))))) => 131.55/17.19 (((~) @ (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((X2) != (n_pl @ X4 @ Y1))))))))))))))))) 131.55/17.19 | ~ (in @ X2 @ nat))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6810])). 131.55/17.19 thf(zip_derived_cl6812, plain, 131.55/17.19 (![X2 : $i, X4 : $i, X6 : $i]: 131.55/17.19 ( (((in @ X6 @ nat) => 131.55/17.19 (((((~) @ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((n_pl @ X2 @ X6) != (n_pl @ 131.55/17.19 (n_pl @ X4 @ X6) @ Y0)))))))))) => 131.55/17.19 (((~) @ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((X2) != (n_pl @ X4 @ Y0)))))))))))))) 131.55/17.19 | ~ (in @ X2 @ nat) 131.55/17.19 | ~ (in @ X4 @ nat))), 131.55/17.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6811])). 131.55/17.19 thf(zip_derived_cl6813, plain, 131.55/17.19 (![X2 : $i, X4 : $i, X6 : $i]: 131.55/17.19 (~ (in @ X6 @ nat) 131.55/17.19 | (((((~) @ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((n_pl @ X2 @ X6) != (n_pl @ 131.55/17.19 (n_pl @ X4 @ X6) @ Y0)))))))))) => 131.55/17.19 (((~) @ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((X2) != (n_pl @ X4 @ Y0)))))))))))) 131.55/17.19 | ~ (in @ X4 @ nat) 131.55/17.19 | ~ (in @ X2 @ nat))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6812])). 131.55/17.19 thf(zip_derived_cl6814, plain, 131.55/17.19 (![X2 : $i, X4 : $i, X6 : $i]: 131.55/17.19 ( (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((n_pl @ X2 @ X6) != (n_pl @ (n_pl @ X4 @ X6) @ Y0)))))))) 131.55/17.19 | ~ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))) 131.55/17.19 | ~ (in @ X2 @ nat) 131.55/17.19 | ~ (in @ X4 @ nat) 131.55/17.19 | ~ (in @ X6 @ nat))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6813])). 131.55/17.19 thf(def_moreis, axiom,(( moreis ) = 131.55/17.19 (^[X0:$i,X1:$i]: ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) )))). 131.55/17.19 thf(def_l_or, axiom,(( l_or ) = (^[X0:$o]: ( imp @ ( d_not @ X0 ) )))). 131.55/17.19 thf('22', plain, (( l_or ) = ( ^[X0:$o]: ( imp @ ( d_not @ X0 ) ) )), 131.55/17.19 inference('simplify_rw_rule', [status(thm)], [def_l_or, '9', '7'])). 131.55/17.19 thf('23', plain, (( l_or ) = ( ^[V_1:$o]: ( imp @ ( d_not @ V_1 ) ) )), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf('24', plain, 131.55/17.19 (( moreis ) = 131.55/17.19 ( ^[X0:$i,X1:$i]: ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )), 131.55/17.19 inference('simplify_rw_rule', [status(thm)], 131.55/17.19 [def_moreis, '21', '5', '19', '3', '1', '17', '11', '23', '9', 131.55/17.19 '7', '15', '13'])). 131.55/17.19 thf('25', plain, 131.55/17.19 (( moreis ) = 131.55/17.19 ( ^[V_1:$i,V_2:$i]: 131.55/17.19 ( l_or @ ( d_29_ii @ V_1 @ V_2 ) @ ( n_is @ V_1 @ V_2 ) ) )), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf(def_iii, axiom,(( iii ) = 131.55/17.19 (^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X1 @ X0 ) )))). 131.55/17.19 thf('26', plain, 131.55/17.19 (( iii ) = ( ^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X1 @ X0 ) ) )), 131.55/17.19 inference('simplify_rw_rule', [status(thm)], 131.55/17.19 [def_iii, '5', '19', '3', '1', '17', '11', '9', '7', '15', '13'])). 131.55/17.19 thf('27', plain, 131.55/17.19 (( iii ) = ( ^[V_1:$i,V_2:$i]: ( n_some @ ( diffprop @ V_2 @ V_1 ) ) )), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf(satz10c, axiom, 131.55/17.19 (all_of @ 131.55/17.19 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 131.55/17.19 ( ^[X0:$i]: 131.55/17.19 ( all_of @ 131.55/17.19 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 131.55/17.19 ( ^[X1:$i]: ( ( moreis @ X0 @ X1 ) => ( d_not @ ( iii @ X0 @ X1 ) ) ) ) ) ))). 131.55/17.19 thf(zf_stmt_1, axiom, 131.55/17.19 (![X4:$i]: 131.55/17.19 ( ( in @ X4 @ nat ) => 131.55/17.19 ( ![X6:$i]: 131.55/17.19 ( ( in @ X6 @ nat ) => 131.55/17.19 ( ( ( ![X8:$i]: 131.55/17.19 ( ( in @ X8 @ nat ) => ( ( X4 ) != ( n_pl @ X6 @ X8 ) ) ) ) => 131.55/17.19 ( ( X4 ) = ( X6 ) ) ) => 131.55/17.19 ( ![X10:$i]: 131.55/17.19 ( ( in @ X10 @ nat ) => ( ( X6 ) != ( n_pl @ X4 @ X10 ) ) ) ) ) ) ) ))). 131.55/17.19 thf(zip_derived_cl182, plain, 131.55/17.19 ( (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((((((!!) @ (^[Y2 : $i]: 131.55/17.19 (((in @ Y2 @ nat) => 131.55/17.19 (((Y0) != (n_pl @ Y1 @ 131.55/17.19 Y2)))))))) => 131.55/17.19 (((Y0) = (Y1))))) => 131.55/17.19 (((!!) @ (^[Y2 : $i]: 131.55/17.19 (((in @ Y2 @ nat) => 131.55/17.19 (((Y1) != (n_pl @ Y0 @ Y2))))))))))))))))))))), 131.55/17.19 inference('cnf', [status(esa)], [zf_stmt_1])). 131.55/17.19 thf(zip_derived_cl5728, plain, 131.55/17.19 (![X2 : $i]: 131.55/17.19 (((in @ X2 @ nat) => 131.55/17.19 (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((((((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((X2) != (n_pl @ Y0 @ Y1)))))))) => 131.55/17.19 (((X2) = (Y0))))) => 131.55/17.19 (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((Y0) != (n_pl @ X2 @ Y1)))))))))))))))))), 131.55/17.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl182])). 131.55/17.19 thf(zip_derived_cl5729, plain, 131.55/17.19 (![X2 : $i]: 131.55/17.19 (~ (in @ X2 @ nat) 131.55/17.19 | (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((((((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((X2) != (n_pl @ Y0 @ Y1)))))))) => 131.55/17.19 (((X2) = (Y0))))) => 131.55/17.19 (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((Y0) != (n_pl @ X2 @ Y1))))))))))))))))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5728])). 131.55/17.19 thf(zip_derived_cl5730, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 ( (((in @ X4 @ nat) => 131.55/17.19 (((((((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))) => 131.55/17.19 (((X2) = (X4))))) => 131.55/17.19 (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))))))) 131.55/17.19 | ~ (in @ X2 @ nat))), 131.55/17.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5729])). 131.55/17.19 thf(zip_derived_cl5731, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 (~ (in @ X4 @ nat) 131.55/17.19 | (((((((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))) => 131.55/17.19 (((X2) = (X4))))) => 131.55/17.19 (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))))) 131.55/17.19 | ~ (in @ X2 @ nat))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5730])). 131.55/17.19 thf(zip_derived_cl5732, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 (~ (((((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))) => 131.55/17.19 (((X2) = (X4))))) 131.55/17.19 | (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))) 131.55/17.19 | ~ (in @ X2 @ nat) 131.55/17.19 | ~ (in @ X4 @ nat))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5731])). 131.55/17.19 thf(zip_derived_cl5733, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 (~ ('#form7812' @ X2 @ X4) 131.55/17.19 | (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf(def_lessis, axiom,(( lessis ) = 131.55/17.19 (^[X0:$i,X1:$i]: ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) )))). 131.55/17.19 thf('28', plain, 131.55/17.19 (( lessis ) = 131.55/17.19 ( ^[X0:$i,X1:$i]: ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )), 131.55/17.19 inference('simplify_rw_rule', [status(thm)], 131.55/17.19 [def_lessis, '27', '5', '19', '3', '1', '17', '11', '23', '9', 131.55/17.19 '7', '15', '13'])). 131.55/17.19 thf('29', plain, 131.55/17.19 (( lessis ) = 131.55/17.19 ( ^[V_1:$i,V_2:$i]: 131.55/17.19 ( l_or @ ( iii @ V_1 @ V_2 ) @ ( n_is @ V_1 @ V_2 ) ) )), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf(satz10e, axiom, 131.55/17.19 (all_of @ 131.55/17.19 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 131.55/17.19 ( ^[X0:$i]: 131.55/17.19 ( all_of @ 131.55/17.19 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 131.55/17.19 ( ^[X1:$i]: 131.55/17.19 ( ( d_not @ ( d_29_ii @ X0 @ X1 ) ) => ( lessis @ X0 @ X1 ) ) ) ) ))). 131.55/17.19 thf(zf_stmt_2, axiom, 131.55/17.19 (![X4:$i]: 131.55/17.19 ( ( in @ X4 @ nat ) => 131.55/17.19 ( ![X6:$i]: 131.55/17.19 ( ( in @ X6 @ nat ) => 131.55/17.19 ( ( ![X8:$i]: 131.55/17.19 ( ( in @ X8 @ nat ) => ( ( X4 ) != ( n_pl @ X6 @ X8 ) ) ) ) => 131.55/17.19 ( ( ![X10:$i]: 131.55/17.19 ( ( in @ X10 @ nat ) => ( ( X6 ) != ( n_pl @ X4 @ X10 ) ) ) ) => 131.55/17.19 ( ( X4 ) = ( X6 ) ) ) ) ) ) ))). 131.55/17.19 thf(zip_derived_cl174, plain, 131.55/17.19 ( (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((((!!) @ (^[Y2 : $i]: 131.55/17.19 (((in @ Y2 @ nat) => 131.55/17.19 (((Y0) != (n_pl @ Y1 @ Y2)))))))) => 131.55/17.19 (((((!!) @ (^[Y2 : $i]: 131.55/17.19 (((in @ Y2 @ nat) => 131.55/17.19 (((Y1) != (n_pl @ Y0 @ 131.55/17.19 Y2)))))))) => 131.55/17.19 (((Y0) = (Y1)))))))))))))))))), 131.55/17.19 inference('cnf', [status(esa)], [zf_stmt_2])). 131.55/17.19 thf(zip_derived_cl5689, plain, 131.55/17.19 (![X2 : $i]: 131.55/17.19 (((in @ X2 @ nat) => 131.55/17.19 (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((X2) != (n_pl @ Y0 @ Y1)))))))) => 131.55/17.19 (((((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((Y0) != (n_pl @ X2 @ Y1)))))))) => 131.55/17.19 (((X2) = (Y0))))))))))))))), 131.55/17.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl174])). 131.55/17.19 thf(zip_derived_cl5690, plain, 131.55/17.19 (![X2 : $i]: 131.55/17.19 (~ (in @ X2 @ nat) 131.55/17.19 | (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((X2) != (n_pl @ Y0 @ Y1)))))))) => 131.55/17.19 (((((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((Y0) != (n_pl @ X2 @ Y1)))))))) => 131.55/17.19 (((X2) = (Y0)))))))))))))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5689])). 131.55/17.19 thf(zip_derived_cl5691, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 ( (((in @ X4 @ nat) => 131.55/17.19 (((((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))) => 131.55/17.19 (((((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))) => 131.55/17.19 (((X2) = (X4))))))))) 131.55/17.19 | ~ (in @ X2 @ nat))), 131.55/17.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5690])). 131.55/17.19 thf(zip_derived_cl5692, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 (~ (in @ X4 @ nat) 131.55/17.19 | (((((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))) => 131.55/17.19 (((((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))) => 131.55/17.19 (((X2) = (X4))))))) 131.55/17.19 | ~ (in @ X2 @ nat))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5691])). 131.55/17.19 thf(zip_derived_cl5693, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 (~ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))) 131.55/17.19 | (((((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))) => 131.55/17.19 (((X2) = (X4))))) 131.55/17.19 | ~ (in @ X2 @ nat) 131.55/17.19 | ~ (in @ X4 @ nat))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5692])). 131.55/17.19 thf(zip_derived_cl5694, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 ( ('#form7812' @ X2 @ X4) 131.55/17.19 | ~ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf(zip_derived_cl6815, plain, 131.55/17.19 (![X2 : $i, X4 : $i, X6 : $i]: 131.55/17.19 ( ('#form7812' @ (n_pl @ X2 @ X6) @ (n_pl @ X4 @ X6)) 131.55/17.19 | ~ (in @ X6 @ nat) 131.55/17.19 | ~ (in @ X4 @ nat) 131.55/17.19 | ~ (in @ X2 @ nat) 131.55/17.19 | ~ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 131.55/17.19 inference('renaming', [status(thm)], 131.55/17.19 [zip_derived_cl6814, zip_derived_cl5733, zip_derived_cl5694])). 131.55/17.19 thf(zip_derived_cl5733, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 (~ ('#form7812' @ X2 @ X4) 131.55/17.19 | (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf(zip_derived_cl5694, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 ( ('#form7812' @ X2 @ X4) 131.55/17.19 | ~ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf(zip_derived_cl6816, plain, 131.55/17.19 (![X2 : $i, X4 : $i, X6 : $i]: 131.55/17.19 (~ ('#form7812' @ X2 @ X4) 131.55/17.19 | ~ (in @ X2 @ nat) 131.55/17.19 | ~ (in @ X4 @ nat) 131.55/17.19 | ~ (in @ X6 @ nat) 131.55/17.19 | ('#form7812' @ (n_pl @ X2 @ X6) @ (n_pl @ X4 @ X6)))), 131.55/17.19 inference('renaming', [status(thm)], 131.55/17.19 [zip_derived_cl6815, zip_derived_cl5733, zip_derived_cl5694])). 131.55/17.19 thf(satz6, axiom, 131.55/17.19 (all_of @ 131.55/17.19 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 131.55/17.19 ( ^[X0:$i]: 131.55/17.19 ( all_of @ 131.55/17.19 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 131.55/17.19 ( ^[X1:$i]: ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X1 @ X0 ) ) ) ) ))). 131.55/17.19 thf(zf_stmt_3, axiom, 131.55/17.19 (![X4:$i]: 131.55/17.19 ( ( in @ X4 @ nat ) => 131.55/17.19 ( ![X6:$i]: 131.55/17.19 ( ( in @ X6 @ nat ) => ( ( n_pl @ X4 @ X6 ) = ( n_pl @ X6 @ X4 ) ) ) ) ))). 131.55/17.19 thf(zip_derived_cl141, plain, 131.55/17.19 ( (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((n_pl @ Y0 @ Y1) = (n_pl @ Y1 @ Y0)))))))))))))), 131.55/17.19 inference('cnf', [status(esa)], [zf_stmt_3])). 131.55/17.19 thf(zip_derived_cl1027, plain, 131.55/17.19 (![X2 : $i]: 131.55/17.19 (((in @ X2 @ nat) => 131.55/17.19 (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((n_pl @ X2 @ Y0) = (n_pl @ Y0 @ X2))))))))))), 131.55/17.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl141])). 131.55/17.19 thf(zip_derived_cl1028, plain, 131.55/17.19 (![X2 : $i]: 131.55/17.19 (~ (in @ X2 @ nat) 131.55/17.19 | (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((n_pl @ X2 @ Y0) = (n_pl @ Y0 @ X2)))))))))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1027])). 131.55/17.19 thf(zip_derived_cl1029, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 ( (((in @ X4 @ nat) => (((n_pl @ X2 @ X4) = (n_pl @ X4 @ X2))))) 131.55/17.19 | ~ (in @ X2 @ nat))), 131.55/17.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1028])). 131.55/17.19 thf(zip_derived_cl1030, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 (~ (in @ X4 @ nat) 131.55/17.19 | (((n_pl @ X2 @ X4) = (n_pl @ X4 @ X2))) 131.55/17.19 | ~ (in @ X2 @ nat))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1029])). 131.55/17.19 thf(zip_derived_cl1031, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 (~ (in @ X4 @ nat) 131.55/17.19 | ((n_pl @ X2 @ X4) = (n_pl @ X4 @ X2)) 131.55/17.19 | ~ (in @ X2 @ nat))), 131.55/17.19 inference('simplify nested equalities', [status(thm)], 131.55/17.19 [zip_derived_cl1030])). 131.55/17.19 thf(zip_derived_cl1031, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 (~ (in @ X4 @ nat) 131.55/17.19 | ((n_pl @ X2 @ X4) = (n_pl @ X4 @ X2)) 131.55/17.19 | ~ (in @ X2 @ nat))), 131.55/17.19 inference('simplify nested equalities', [status(thm)], 131.55/17.19 [zip_derived_cl1030])). 131.55/17.19 thf(satz20d, conjecture, 131.55/17.19 (all_of @ 131.55/17.19 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 131.55/17.19 ( ^[X0:$i]: 131.55/17.19 ( all_of @ 131.55/17.19 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 131.55/17.19 ( ^[X1:$i]: 131.55/17.19 ( all_of @ 131.55/17.19 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 131.55/17.19 ( ^[X2:$i]: 131.55/17.19 ( ( d_29_ii @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X2 @ X1 ) ) => 131.55/17.19 ( d_29_ii @ X0 @ X1 ) ) ) ) ) ) ))). 131.55/17.19 thf(zf_stmt_4, conjecture, 131.55/17.19 (![X4:$i]: 131.55/17.19 ( ( in @ X4 @ nat ) => 131.55/17.19 ( ![X6:$i]: 131.55/17.19 ( ( in @ X6 @ nat ) => 131.55/17.19 ( ![X8:$i]: 131.55/17.19 ( ( in @ X8 @ nat ) => 131.55/17.19 ( ( ~( ![X10:$i]: 131.55/17.19 ( ( in @ X10 @ nat ) => 131.55/17.19 ( ( n_pl @ X8 @ X4 ) != 131.55/17.19 ( n_pl @ ( n_pl @ X8 @ X6 ) @ X10 ) ) ) ) ) => 131.55/17.19 ( ~( ![X12:$i]: 131.55/17.19 ( ( in @ X12 @ nat ) => ( ( X4 ) != ( n_pl @ X6 @ X12 ) ) ) ) ) ) ) ) ) ) ))). 131.55/17.19 thf(zf_stmt_5, negated_conjecture, 131.55/17.19 (~( ![X4:$i]: 131.55/17.19 ( ( in @ X4 @ nat ) => 131.55/17.19 ( ![X6:$i]: 131.55/17.19 ( ( in @ X6 @ nat ) => 131.55/17.19 ( ![X8:$i]: 131.55/17.19 ( ( in @ X8 @ nat ) => 131.55/17.19 ( ( ~( ![X10:$i]: 131.55/17.19 ( ( in @ X10 @ nat ) => 131.55/17.19 ( ( n_pl @ X8 @ X4 ) != 131.55/17.19 ( n_pl @ ( n_pl @ X8 @ X6 ) @ X10 ) ) ) ) ) => 131.55/17.19 ( ~( ![X12:$i]: 131.55/17.19 ( ( in @ X12 @ nat ) => 131.55/17.19 ( ( X4 ) != ( n_pl @ X6 @ X12 ) ) ) ) ) ) ) ) ) ) ) )), 131.55/17.19 inference('cnf.neg', [status(esa)], [zf_stmt_4])). 131.55/17.19 thf(zip_derived_cl180, plain, 131.55/17.19 (~ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((!!) @ (^[Y2 : $i]: 131.55/17.19 (((in @ Y2 @ nat) => 131.55/17.19 (((((~) @ (((!!) @ ( 131.55/17.19 ^[Y3 : $i]: 131.55/17.19 (((in @ Y3 @ 131.55/17.19 nat) => 131.55/17.19 (((n_pl @ 131.55/17.19 Y2 @ 131.55/17.19 Y0) != 131.55/17.19 (n_pl @ 131.55/17.19 (n_pl @ 131.55/17.19 Y2 @ Y1) @ 131.55/17.19 Y3)))))))))) => 131.55/17.19 (((~) @ (((!!) @ ( 131.55/17.19 ^[Y3 : $i]: 131.55/17.19 (((in @ Y3 @ 131.55/17.19 nat) => 131.55/17.19 (((Y0) != 131.55/17.19 (n_pl @ 131.55/17.19 Y1 @ Y3)))))))))))))))))))))))))))), 131.55/17.19 inference('cnf', [status(esa)], [zf_stmt_5])). 131.55/17.19 thf(zip_derived_cl6301, plain, 131.55/17.19 (~ (((in @ '#sk8270' @ nat) => 131.55/17.19 (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((((~) @ (((!!) @ (^[Y2 : $i]: 131.55/17.19 (((in @ Y2 @ 131.55/17.19 nat) => 131.55/17.19 (((n_pl @ Y1 @ 131.55/17.19 '#sk8270') != 131.55/17.19 (n_pl @ 131.55/17.19 (n_pl @ Y1 @ 131.55/17.19 Y0) @ 131.55/17.19 Y2)))))))))) => 131.55/17.19 (((~) @ (((!!) @ (^[Y2 : $i]: 131.55/17.19 (((in @ Y2 @ 131.55/17.19 nat) => 131.55/17.19 ((('#sk8270') != 131.55/17.19 (n_pl @ Y0 @ 131.55/17.19 Y2))))))))))))))))))))))))), 131.55/17.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl180])). 131.55/17.19 thf(zip_derived_cl6303, plain, 131.55/17.19 (~ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((((~) @ (((!!) @ (^[Y2 : $i]: 131.55/17.19 (((in @ Y2 @ nat) => 131.55/17.19 (((n_pl @ Y1 @ 131.55/17.19 '#sk8270') != 131.55/17.19 (n_pl @ 131.55/17.19 (n_pl @ Y1 @ Y0) @ 131.55/17.19 Y2)))))))))) => 131.55/17.19 (((~) @ (((!!) @ (^[Y2 : $i]: 131.55/17.19 (((in @ Y2 @ nat) => 131.55/17.19 ((('#sk8270') != 131.55/17.19 (n_pl @ Y0 @ Y2))))))))))))))))))))))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6301])). 131.55/17.19 thf(zip_derived_cl6304, plain, 131.55/17.19 (~ (((in @ '#sk8271' @ nat) => 131.55/17.19 (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((((~) @ (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((n_pl @ Y0 @ '#sk8270') != 131.55/17.19 (n_pl @ 131.55/17.19 (n_pl @ Y0 @ '#sk8271') @ 131.55/17.19 Y1)))))))))) => 131.55/17.19 (((~) @ (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 ((('#sk8270') != (n_pl @ 131.55/17.19 '#sk8271' @ Y1)))))))))))))))))))), 131.55/17.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6303])). 131.55/17.19 thf(zip_derived_cl6306, plain, 131.55/17.19 (~ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((((~) @ (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 (((n_pl @ Y0 @ '#sk8270') != 131.55/17.19 (n_pl @ 131.55/17.19 (n_pl @ Y0 @ '#sk8271') @ Y1)))))))))) => 131.55/17.19 (((~) @ (((!!) @ (^[Y1 : $i]: 131.55/17.19 (((in @ Y1 @ nat) => 131.55/17.19 ((('#sk8270') != (n_pl @ 131.55/17.19 '#sk8271' @ Y1)))))))))))))))))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6304])). 131.55/17.19 thf(zip_derived_cl6307, plain, 131.55/17.19 (~ (((in @ '#sk8272' @ nat) => 131.55/17.19 (((((~) @ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((n_pl @ '#sk8272' @ '#sk8270') != (n_pl @ 131.55/17.19 (n_pl @ '#sk8272' @ '#sk8271') @ Y0)))))))))) => 131.55/17.19 (((~) @ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 ((('#sk8270') != (n_pl @ '#sk8271' @ Y0))))))))))))))), 131.55/17.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6306])). 131.55/17.19 thf(zip_derived_cl6309, plain, 131.55/17.19 (~ (((((~) @ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((n_pl @ '#sk8272' @ '#sk8270') != (n_pl @ 131.55/17.19 (n_pl @ '#sk8272' @ '#sk8271') @ Y0)))))))))) => 131.55/17.19 (((~) @ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 ((('#sk8270') != (n_pl @ '#sk8271' @ Y0))))))))))))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6307])). 131.55/17.19 thf(zip_derived_cl6310, plain, 131.55/17.19 (~ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 (((n_pl @ '#sk8272' @ '#sk8270') != (n_pl @ 131.55/17.19 (n_pl @ '#sk8272' @ '#sk8271') @ Y0))))))))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6309])). 131.55/17.19 thf(zip_derived_cl5733, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 (~ ('#form7812' @ X2 @ X4) 131.55/17.19 | (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf(zip_derived_cl5694, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 ( ('#form7812' @ X2 @ X4) 131.55/17.19 | ~ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf(zip_derived_cl6312, plain, 131.55/17.19 (~ ('#form7812' @ (n_pl @ '#sk8272' @ '#sk8270') @ 131.55/17.19 (n_pl @ '#sk8272' @ '#sk8271'))), 131.55/17.19 inference('renaming', [status(thm)], 131.55/17.19 [zip_derived_cl6310, zip_derived_cl5733, zip_derived_cl5694])). 131.55/17.19 thf(zip_derived_cl6710, plain, 131.55/17.19 ((~ ('#form7812' @ (n_pl @ '#sk8270' @ '#sk8272') @ 131.55/17.19 (n_pl @ '#sk8272' @ '#sk8271')) 131.55/17.19 | ~ (in @ '#sk8270' @ nat) 131.55/17.19 | ~ (in @ '#sk8272' @ nat))), 131.55/17.19 inference('sup-', [status(thm)], [zip_derived_cl1031, zip_derived_cl6312])). 131.55/17.19 thf(zip_derived_cl6302, plain, ( (in @ '#sk8270' @ nat)), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6301])). 131.55/17.19 thf(zip_derived_cl6308, plain, ( (in @ '#sk8272' @ nat)), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6307])). 131.55/17.19 thf(zip_derived_cl6718, plain, 131.55/17.19 (~ ('#form7812' @ (n_pl @ '#sk8270' @ '#sk8272') @ 131.55/17.19 (n_pl @ '#sk8272' @ '#sk8271'))), 131.55/17.19 inference('demod', [status(thm)], 131.55/17.19 [zip_derived_cl6710, zip_derived_cl6302, zip_derived_cl6308])). 131.55/17.19 thf(zip_derived_cl6736, plain, 131.55/17.19 ((~ ('#form7812' @ (n_pl @ '#sk8270' @ '#sk8272') @ 131.55/17.19 (n_pl @ '#sk8271' @ '#sk8272')) 131.55/17.19 | ~ (in @ '#sk8271' @ nat) 131.55/17.19 | ~ (in @ '#sk8272' @ nat))), 131.55/17.19 inference('sup-', [status(thm)], [zip_derived_cl1031, zip_derived_cl6718])). 131.55/17.19 thf(zip_derived_cl6305, plain, ( (in @ '#sk8271' @ nat)), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6304])). 131.55/17.19 thf(zip_derived_cl6308, plain, ( (in @ '#sk8272' @ nat)), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6307])). 131.55/17.19 thf(zip_derived_cl6744, plain, 131.55/17.19 (~ ('#form7812' @ (n_pl @ '#sk8270' @ '#sk8272') @ 131.55/17.19 (n_pl @ '#sk8271' @ '#sk8272'))), 131.55/17.19 inference('demod', [status(thm)], 131.55/17.19 [zip_derived_cl6736, zip_derived_cl6305, zip_derived_cl6308])). 131.55/17.19 thf(zip_derived_cl7240, plain, 131.55/17.19 ((~ (in @ '#sk8272' @ nat) 131.55/17.19 | ~ (in @ '#sk8271' @ nat) 131.55/17.19 | ~ (in @ '#sk8270' @ nat) 131.55/17.19 | ~ ('#form7812' @ '#sk8270' @ '#sk8271'))), 131.55/17.19 inference('sup-', [status(thm)], [zip_derived_cl6816, zip_derived_cl6744])). 131.55/17.19 thf(zip_derived_cl6308, plain, ( (in @ '#sk8272' @ nat)), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6307])). 131.55/17.19 thf(zip_derived_cl6305, plain, ( (in @ '#sk8271' @ nat)), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6304])). 131.55/17.19 thf(zip_derived_cl6302, plain, ( (in @ '#sk8270' @ nat)), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6301])). 131.55/17.19 thf(zip_derived_cl6311, plain, 131.55/17.19 ( (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => 131.55/17.19 ((('#sk8270') != (n_pl @ '#sk8271' @ Y0))))))))), 131.55/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6309])). 131.55/17.19 thf(zip_derived_cl5733, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 (~ ('#form7812' @ X2 @ X4) 131.55/17.19 | (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf(zip_derived_cl5694, plain, 131.55/17.19 (![X2 : $i, X4 : $i]: 131.55/17.19 ( ('#form7812' @ X2 @ X4) 131.55/17.19 | ~ (((!!) @ (^[Y0 : $i]: 131.55/17.19 (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))), 131.55/17.19 define([status(thm)])). 131.55/17.19 thf(zip_derived_cl6313, plain, ( ('#form7812' @ '#sk8270' @ '#sk8271')), 131.55/17.19 inference('renaming', [status(thm)], 131.55/17.19 [zip_derived_cl6311, zip_derived_cl5733, zip_derived_cl5694])). 131.55/17.19 thf(zip_derived_cl7249, plain, ($false), 131.55/17.19 inference('demod', [status(thm)], 131.55/17.19 [zip_derived_cl7240, zip_derived_cl6308, zip_derived_cl6305, 131.55/17.19 zip_derived_cl6302, zip_derived_cl6313])). 131.55/17.19 131.55/17.19 % SZS output end Refutation 131.55/17.19 131.55/17.19 131.55/17.19 % Terminating... 132.26/17.28 % Runner terminated. 132.26/17.29 % Zipperpin 1.5 exiting 132.26/17.30 EOF