0.05/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.uNhB2GjCRb true 0.13/0.34 % Computer : n007.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1200 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Jul 13 10:55:49 EDT 2021 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 120 s 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.34 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.49/0.64 % Total configuration time : 828 0.49/0.64 % Estimated wc time : 983 0.49/0.64 % Estimated cpu time (8 cpus) : 122.875 0.51/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 47s 0.51/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 47s 0.51/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 47s 0.51/0.73 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 18s 0.51/0.73 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 41s 0.51/0.73 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 53s 0.51/0.73 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.51/0.74 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 35s 77.33/10.42 % Solved by lams/40_c.s.sh. 77.33/10.42 % running E: timeout 32 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.uNhB2GjCRb/e_inputd05cac --cpu-limit=30 --auto-schedule -s -p 77.33/10.42 % done 504 iterations in 9.638s 77.33/10.42 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 77.33/10.42 % SZS output start Refutation 77.33/10.42 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 77.33/10.42 thf(n_is_type, type, n_is: $i > $i > $o). 77.33/10.42 thf(ap_type, type, ap: $i > $i > $i). 77.33/10.42 thf(n_1_type, type, n_1: $i). 77.33/10.42 thf(plus_type, type, plus: $i > $i). 77.33/10.42 thf(nis_type, type, nis: $i > $i > $o). 77.33/10.42 thf(in_type, type, in: $i > $i > $o). 77.33/10.42 thf(sk__4_type, type, sk__4: $i). 77.33/10.42 thf(imp_type, type, imp: $o > $o > $o). 77.33/10.42 thf(nat_type, type, nat: $i). 77.33/10.42 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 77.33/10.42 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 77.33/10.42 thf(e_is_type, type, e_is: $i > $i > $i > $o). 77.33/10.42 thf(n_some_type, type, n_some: ($i > $o) > $o). 77.33/10.42 thf(ordsucc_type, type, ordsucc: $i > $i). 77.33/10.42 thf(n_pl_type, type, n_pl: $i > $i > $i). 77.33/10.42 thf(omega_type, type, omega: $i). 77.33/10.42 thf('#l_lift4287_type', type, '#l_lift4287': $i > $o). 77.33/10.42 thf(sk__2_type, type, sk__2: $i). 77.33/10.42 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 77.33/10.42 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 77.33/10.42 thf(d_not_type, type, d_not: $o > $o). 77.33/10.42 thf(emptyset_type, type, emptyset: $i). 77.33/10.42 thf(sk__3_type, type, sk__3: $i). 77.33/10.42 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 77.33/10.42 thf(def_d_29_ii, axiom,(( d_29_ii ) = 77.33/10.42 (^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X0 @ X1 ) )))). 77.33/10.42 thf(def_n_some, axiom,(( n_some ) = (l_some @ nat))). 77.33/10.42 thf(def_nat, axiom,(( nat ) = 77.33/10.42 (d_Sep @ omega @ ( ^[X0:$i]: ( ( X0 ) != ( emptyset ) ) )))). 77.33/10.42 thf('0', plain, 77.33/10.42 (( nat ) = ( d_Sep @ omega @ ( ^[X0:$i]: ( ( X0 ) != ( emptyset ) ) ) )), 77.33/10.42 inference('simplify_rw_rule', [status(thm)], [def_nat])). 77.33/10.42 thf('1', plain, 77.33/10.42 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 77.33/10.42 define([status(thm)])). 77.33/10.42 thf('2', plain, (( n_some ) = ( l_some @ nat )), 77.33/10.42 inference('simplify_rw_rule', [status(thm)], [def_n_some, '1'])). 77.33/10.43 thf('3', plain, (( n_some ) = ( l_some @ nat )), define([status(thm)])). 77.33/10.43 thf('4', plain, 77.33/10.43 (( d_29_ii ) = ( ^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 77.33/10.43 inference('simplify_rw_rule', [status(thm)], [def_d_29_ii, '3', '1'])). 77.33/10.43 thf('5', plain, 77.33/10.43 (( d_29_ii ) = 77.33/10.43 ( ^[V_1:$i,V_2:$i]: ( n_some @ ( diffprop @ V_1 @ V_2 ) ) )), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(def_n_pl, axiom,(( n_pl ) = (^[X0:$i]: ( ap @ ( plus @ X0 ) )))). 77.33/10.43 thf('6', plain, (( n_pl ) = ( ^[X0:$i]: ( ap @ ( plus @ X0 ) ) )), 77.33/10.43 inference('simplify_rw_rule', [status(thm)], [def_n_pl])). 77.33/10.43 thf('7', plain, (( n_pl ) = ( ^[V_1:$i]: ( ap @ ( plus @ V_1 ) ) )), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(def_all_of, axiom,(( all_of ) = 77.33/10.43 (^[X0:( $i > $o ),X1:( $i > $o )]: 77.33/10.43 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) )))). 77.33/10.43 thf(def_is_of, axiom,(( is_of ) = (^[X0:$i,X1:( $i > $o )]: ( X1 @ X0 )))). 77.33/10.43 thf('8', plain, (( is_of ) = ( ^[X0:$i,X1:( $i > $o )]: ( X1 @ X0 ) )), 77.33/10.43 inference('simplify_rw_rule', [status(thm)], [def_is_of])). 77.33/10.43 thf('9', plain, (( is_of ) = ( ^[V_1:$i,V_2:( $i > $o )]: ( V_2 @ V_1 ) )), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf('10', plain, 77.33/10.43 (( all_of ) = 77.33/10.43 ( ^[X0:( $i > $o ),X1:( $i > $o )]: 77.33/10.43 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) ) )), 77.33/10.43 inference('simplify_rw_rule', [status(thm)], [def_all_of, '9'])). 77.33/10.43 thf('11', plain, 77.33/10.43 (( all_of ) = 77.33/10.43 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 77.33/10.43 ( ![X4:$i]: ( ( is_of @ X4 @ V_1 ) => ( V_2 @ X4 ) ) ) )), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(satz19d, conjecture, 77.33/10.43 (all_of @ 77.33/10.43 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 77.33/10.43 ( ^[X0:$i]: 77.33/10.43 ( all_of @ 77.33/10.43 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 77.33/10.43 ( ^[X1:$i]: 77.33/10.43 ( all_of @ 77.33/10.43 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 77.33/10.43 ( ^[X2:$i]: 77.33/10.43 ( ( d_29_ii @ X0 @ X1 ) => 77.33/10.43 ( d_29_ii @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X2 @ X1 ) ) ) ) ) ) ) ))). 77.33/10.43 thf(zf_stmt_0, conjecture, 77.33/10.43 (![X4:$i]: 77.33/10.43 ( ( in @ 77.33/10.43 X4 @ ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) ) ) => 77.33/10.43 ( ![X6:$i]: 77.33/10.43 ( ( in @ 77.33/10.43 X6 @ 77.33/10.43 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) => 77.33/10.43 ( ![X8:$i]: 77.33/10.43 ( ( in @ 77.33/10.43 X8 @ 77.33/10.43 ( d_Sep @ omega @ ( ^[V_3:$i]: ( ( V_3 ) != ( emptyset ) ) ) ) ) => 77.33/10.43 ( ( l_some @ 77.33/10.43 ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) @ 77.33/10.43 ( diffprop @ X4 @ X6 ) ) => 77.33/10.43 ( l_some @ 77.33/10.43 ( d_Sep @ omega @ ( ^[V_5:$i]: ( ( V_5 ) != ( emptyset ) ) ) ) @ 77.33/10.43 ( diffprop @ 77.33/10.43 ( ap @ ( plus @ X8 ) @ X4 ) @ ( ap @ ( plus @ X8 ) @ X6 ) ) ) ) ) ) ) ) ))). 77.33/10.43 thf(zf_stmt_1, negated_conjecture, 77.33/10.43 (~( ![X4:$i]: 77.33/10.43 ( ( in @ 77.33/10.43 X4 @ ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) ) ) => 77.33/10.43 ( ![X6:$i]: 77.33/10.43 ( ( in @ 77.33/10.43 X6 @ 77.33/10.43 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) => 77.33/10.43 ( ![X8:$i]: 77.33/10.43 ( ( in @ 77.33/10.43 X8 @ 77.33/10.43 ( d_Sep @ 77.33/10.43 omega @ ( ^[V_3:$i]: ( ( V_3 ) != ( emptyset ) ) ) ) ) => 77.33/10.43 ( ( l_some @ 77.33/10.43 ( d_Sep @ 77.33/10.43 omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) @ 77.33/10.43 ( diffprop @ X4 @ X6 ) ) => 77.33/10.43 ( l_some @ 77.33/10.43 ( d_Sep @ 77.33/10.43 omega @ ( ^[V_5:$i]: ( ( V_5 ) != ( emptyset ) ) ) ) @ 77.33/10.43 ( diffprop @ 77.33/10.43 ( ap @ ( plus @ X8 ) @ X4 ) @ 77.33/10.43 ( ap @ ( plus @ X8 ) @ X6 ) ) ) ) ) ) ) ) ) )), 77.33/10.43 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 77.33/10.43 thf(zip_derived_cl78, plain, 77.33/10.43 ( (l_some @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 77.33/10.43 (diffprop @ sk__2 @ sk__3))), 77.33/10.43 inference('cnf', [status(esa)], [zf_stmt_1])). 77.33/10.43 thf(def_n_1, axiom,(( n_1 ) = (ordsucc @ emptyset))). 77.33/10.43 thf('12', plain, (( n_1 ) = ( ordsucc @ emptyset )), 77.33/10.43 inference('simplify_rw_rule', [status(thm)], [def_n_1])). 77.33/10.43 thf('13', plain, (( n_1 ) = ( ordsucc @ emptyset )), define([status(thm)])). 77.33/10.43 thf(def_nis, axiom,(( nis ) = 77.33/10.43 (^[X0:$i,X1:$i]: ( d_not @ ( n_is @ X0 @ X1 ) )))). 77.33/10.43 thf(def_n_is, axiom,(( n_is ) = (e_is @ nat))). 77.33/10.43 thf(def_e_is, axiom,(( e_is ) = (^[X0:$i,X:$i,Y:$i]: ( ( X ) = ( Y ) )))). 77.33/10.43 thf('14', plain, (( e_is ) = ( ^[X0:$i,X:$i,Y:$i]: ( ( X ) = ( Y ) ) )), 77.33/10.43 inference('simplify_rw_rule', [status(thm)], [def_e_is])). 77.33/10.43 thf('15', plain, 77.33/10.43 (( e_is ) = ( ^[V_1:$i,V_2:$i,V_3:$i]: ( ( V_2 ) = ( V_3 ) ) )), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf('16', plain, (( n_is ) = ( e_is @ nat )), 77.33/10.43 inference('simplify_rw_rule', [status(thm)], [def_n_is, '1', '15'])). 77.33/10.43 thf('17', plain, (( n_is ) = ( e_is @ nat )), define([status(thm)])). 77.33/10.43 thf(def_d_not, axiom,(( d_not ) = (^[X0:$o]: ( imp @ X0 @ $false )))). 77.33/10.43 thf(def_imp, axiom,(( imp ) = (^[X0:$o,X1:$o]: ( ( X0 ) => ( X1 ) )))). 77.33/10.43 thf('18', plain, (( imp ) = ( ^[X0:$o,X1:$o]: ( ( X0 ) => ( X1 ) ) )), 77.33/10.43 inference('simplify_rw_rule', [status(thm)], [def_imp])). 77.33/10.43 thf('19', plain, (( imp ) = ( ^[V_1:$o,V_2:$o]: ( ( V_1 ) => ( V_2 ) ) )), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf('20', plain, (( d_not ) = ( ^[X0:$o]: ( imp @ X0 @ $false ) )), 77.33/10.43 inference('simplify_rw_rule', [status(thm)], [def_d_not, '19'])). 77.33/10.43 thf('21', plain, (( d_not ) = ( ^[V_1:$o]: ( imp @ V_1 @ $false ) )), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf('22', plain, 77.33/10.43 (( nis ) = ( ^[X0:$i,X1:$i]: ( d_not @ ( n_is @ X0 @ X1 ) ) )), 77.33/10.43 inference('simplify_rw_rule', [status(thm)], 77.33/10.43 [def_nis, '17', '1', '15', '21', '19'])). 77.33/10.43 thf('23', plain, 77.33/10.43 (( nis ) = ( ^[V_1:$i,V_2:$i]: ( d_not @ ( n_is @ V_1 @ V_2 ) ) )), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(n_ax3, axiom, 77.33/10.43 (all_of @ 77.33/10.43 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 77.33/10.43 ( ^[X0:$i]: ( nis @ ( ordsucc @ X0 ) @ n_1 ) ))). 77.33/10.43 thf(zf_stmt_2, axiom, 77.33/10.43 (![X4:$i]: 77.33/10.43 ( ( in @ 77.33/10.43 X4 @ ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) ) ) => 77.33/10.43 ( ( ordsucc @ X4 ) != ( ordsucc @ emptyset ) ) ))). 77.33/10.43 thf(zip_derived_cl3, plain, 77.33/10.43 (![X0 : $i]: 77.33/10.43 (((ordsucc @ X0) != (ordsucc @ emptyset)) 77.33/10.43 | ~ (in @ X0 @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))), 77.33/10.43 inference('cnf', [status(esa)], [zf_stmt_2])). 77.33/10.43 thf(zip_derived_cl4931, plain, 77.33/10.43 (![X1 : $i]: (('#l_lift4287' @ X1) = (((X1) != (emptyset))))), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(zip_derived_cl4995, plain, 77.33/10.43 ( (l_some @ (d_Sep @ omega @ '#l_lift4287') @ (diffprop @ sk__2 @ sk__3))), 77.33/10.43 inference('lambda_lifting', [status(thm)], 77.33/10.43 [zip_derived_cl78, zip_derived_cl4931])). 77.33/10.43 thf(satz19a, axiom, 77.33/10.43 (all_of @ 77.33/10.43 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 77.33/10.43 ( ^[X0:$i]: 77.33/10.43 ( all_of @ 77.33/10.43 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 77.33/10.43 ( ^[X1:$i]: 77.33/10.43 ( all_of @ 77.33/10.43 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 77.33/10.43 ( ^[X2:$i]: 77.33/10.43 ( ( d_29_ii @ X0 @ X1 ) => 77.33/10.43 ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) ) ) ) ) ) ))). 77.33/10.43 thf(zf_stmt_3, axiom, 77.33/10.43 (![X4:$i]: 77.33/10.43 ( ( in @ 77.33/10.43 X4 @ ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) ) ) => 77.33/10.43 ( ![X6:$i]: 77.33/10.43 ( ( in @ 77.33/10.43 X6 @ 77.33/10.43 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) => 77.33/10.43 ( ![X8:$i]: 77.33/10.43 ( ( in @ 77.33/10.43 X8 @ 77.33/10.43 ( d_Sep @ omega @ ( ^[V_3:$i]: ( ( V_3 ) != ( emptyset ) ) ) ) ) => 77.33/10.43 ( ( l_some @ 77.33/10.43 ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) @ 77.33/10.43 ( diffprop @ X4 @ X6 ) ) => 77.33/10.43 ( l_some @ 77.33/10.43 ( d_Sep @ omega @ ( ^[V_5:$i]: ( ( V_5 ) != ( emptyset ) ) ) ) @ 77.33/10.43 ( diffprop @ 77.33/10.43 ( ap @ ( plus @ X4 ) @ X8 ) @ ( ap @ ( plus @ X6 ) @ X8 ) ) ) ) ) ) ) ) ))). 77.33/10.43 thf(zip_derived_cl19, plain, 77.33/10.43 (![X0 : $i, X1 : $i, X2 : $i]: 77.33/10.43 (~ (in @ X0 @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))) 77.33/10.43 | ~ (l_some @ 77.33/10.43 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 77.33/10.43 (diffprop @ X1 @ X0)) 77.33/10.43 | (l_some @ 77.33/10.43 (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 77.33/10.43 (diffprop @ (ap @ (plus @ X1) @ X2) @ (ap @ (plus @ X0) @ X2))) 77.33/10.43 | ~ (in @ X2 @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))) 77.33/10.43 | ~ (in @ X1 @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))), 77.33/10.43 inference('cnf', [status(esa)], [zf_stmt_3])). 77.33/10.43 thf(zip_derived_cl4931, plain, 77.33/10.43 (![X1 : $i]: (('#l_lift4287' @ X1) = (((X1) != (emptyset))))), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(zip_derived_cl4931, plain, 77.33/10.43 (![X1 : $i]: (('#l_lift4287' @ X1) = (((X1) != (emptyset))))), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(zip_derived_cl4931, plain, 77.33/10.43 (![X1 : $i]: (('#l_lift4287' @ X1) = (((X1) != (emptyset))))), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(zip_derived_cl4931, plain, 77.33/10.43 (![X1 : $i]: (('#l_lift4287' @ X1) = (((X1) != (emptyset))))), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(zip_derived_cl4931, plain, 77.33/10.43 (![X1 : $i]: (('#l_lift4287' @ X1) = (((X1) != (emptyset))))), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(zip_derived_cl4937, plain, 77.33/10.43 (![X0 : $i, X1 : $i, X2 : $i]: 77.33/10.43 (~ (in @ X0 @ (d_Sep @ omega @ '#l_lift4287')) 77.33/10.43 | ~ (l_some @ (d_Sep @ omega @ '#l_lift4287') @ (diffprop @ X1 @ X0)) 77.33/10.43 | (l_some @ (d_Sep @ omega @ '#l_lift4287') @ 77.33/10.43 (diffprop @ (ap @ (plus @ X1) @ X2) @ (ap @ (plus @ X0) @ X2))) 77.33/10.43 | ~ (in @ X2 @ (d_Sep @ omega @ '#l_lift4287')) 77.33/10.43 | ~ (in @ X1 @ (d_Sep @ omega @ '#l_lift4287')))), 77.33/10.43 inference('lambda_lifting', [status(thm)], 77.33/10.43 [zip_derived_cl19, zip_derived_cl4931, zip_derived_cl4931, 77.33/10.43 zip_derived_cl4931, zip_derived_cl4931, zip_derived_cl4931])). 77.33/10.43 thf(zip_derived_cl75, plain, 77.33/10.43 ( (in @ sk__2 @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))))), 77.33/10.43 inference('cnf', [status(esa)], [zf_stmt_1])). 77.33/10.43 thf(zip_derived_cl4931, plain, 77.33/10.43 (![X1 : $i]: (('#l_lift4287' @ X1) = (((X1) != (emptyset))))), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(zip_derived_cl4992, plain, 77.33/10.43 ( (in @ sk__2 @ (d_Sep @ omega @ '#l_lift4287'))), 77.33/10.43 inference('lambda_lifting', [status(thm)], 77.33/10.43 [zip_derived_cl75, zip_derived_cl4931])). 77.33/10.43 thf(zip_derived_cl79, plain, 77.33/10.43 ( (in @ sk__3 @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))))), 77.33/10.43 inference('cnf', [status(esa)], [zf_stmt_1])). 77.33/10.43 thf(zip_derived_cl4931, plain, 77.33/10.43 (![X1 : $i]: (('#l_lift4287' @ X1) = (((X1) != (emptyset))))), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(zip_derived_cl4996, plain, 77.33/10.43 ( (in @ sk__3 @ (d_Sep @ omega @ '#l_lift4287'))), 77.33/10.43 inference('lambda_lifting', [status(thm)], 77.33/10.43 [zip_derived_cl79, zip_derived_cl4931])). 77.33/10.43 thf(zip_derived_cl77, plain, 77.33/10.43 (~ (l_some @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))) @ 77.33/10.43 (diffprop @ (ap @ (plus @ sk__4) @ sk__2) @ 77.33/10.43 (ap @ (plus @ sk__4) @ sk__3)))), 77.33/10.43 inference('cnf', [status(esa)], [zf_stmt_1])). 77.33/10.43 thf(zip_derived_cl4931, plain, 77.33/10.43 (![X1 : $i]: (('#l_lift4287' @ X1) = (((X1) != (emptyset))))), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(zip_derived_cl4994, plain, 77.33/10.43 (~ (l_some @ (d_Sep @ omega @ '#l_lift4287') @ 77.33/10.43 (diffprop @ (ap @ (plus @ sk__4) @ sk__2) @ 77.33/10.43 (ap @ (plus @ sk__4) @ sk__3)))), 77.33/10.43 inference('lambda_lifting', [status(thm)], 77.33/10.43 [zip_derived_cl77, zip_derived_cl4931])). 77.33/10.43 thf(zip_derived_cl76, plain, 77.33/10.43 ( (in @ sk__4 @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset))))))), 77.33/10.43 inference('cnf', [status(esa)], [zf_stmt_1])). 77.33/10.43 thf(zip_derived_cl4931, plain, 77.33/10.43 (![X1 : $i]: (('#l_lift4287' @ X1) = (((X1) != (emptyset))))), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(zip_derived_cl4993, plain, 77.33/10.43 ( (in @ sk__4 @ (d_Sep @ omega @ '#l_lift4287'))), 77.33/10.43 inference('lambda_lifting', [status(thm)], 77.33/10.43 [zip_derived_cl76, zip_derived_cl4931])). 77.33/10.43 thf(satz6, axiom, 77.33/10.43 (all_of @ 77.33/10.43 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 77.33/10.43 ( ^[X0:$i]: 77.33/10.43 ( all_of @ 77.33/10.43 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 77.33/10.43 ( ^[X1:$i]: ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X1 @ X0 ) ) ) ) ))). 77.33/10.43 thf(zf_stmt_4, axiom, 77.33/10.43 (![X4:$i]: 77.33/10.43 ( ( in @ 77.33/10.43 X4 @ ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) ) ) => 77.33/10.43 ( ![X6:$i]: 77.33/10.43 ( ( in @ 77.33/10.43 X6 @ 77.33/10.43 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) => 77.33/10.43 ( ( ap @ ( plus @ X4 ) @ X6 ) = ( ap @ ( plus @ X6 ) @ X4 ) ) ) ) ))). 77.33/10.43 thf(zip_derived_cl21, plain, 77.33/10.43 (![X0 : $i, X1 : $i]: 77.33/10.43 (~ (in @ X0 @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))) 77.33/10.43 | ((ap @ (plus @ X1) @ X0) = (ap @ (plus @ X0) @ X1)) 77.33/10.43 | ~ (in @ X1 @ (d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))), 77.33/10.43 inference('cnf', [status(esa)], [zf_stmt_4])). 77.33/10.43 thf(zip_derived_cl4931, plain, 77.33/10.43 (![X1 : $i]: (('#l_lift4287' @ X1) = (((X1) != (emptyset))))), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(zip_derived_cl4931, plain, 77.33/10.43 (![X1 : $i]: (('#l_lift4287' @ X1) = (((X1) != (emptyset))))), 77.33/10.43 define([status(thm)])). 77.33/10.43 thf(zip_derived_cl4939, plain, 77.33/10.43 (![X0 : $i, X1 : $i]: 77.33/10.43 (~ (in @ X0 @ (d_Sep @ omega @ '#l_lift4287')) 77.33/10.43 | ((ap @ (plus @ X1) @ X0) = (ap @ (plus @ X0) @ X1)) 77.33/10.43 | ~ (in @ X1 @ (d_Sep @ omega @ '#l_lift4287')))), 77.33/10.43 inference('lambda_lifting', [status(thm)], 77.33/10.43 [zip_derived_cl21, zip_derived_cl4931, zip_derived_cl4931])). 77.33/10.43 thf(zip_derived_cl5016, plain, ($false), 77.33/10.43 inference('eprover', [status(thm)], 77.33/10.43 [zip_derived_cl4995, zip_derived_cl4937, zip_derived_cl4992, 77.33/10.43 zip_derived_cl4996, zip_derived_cl4994, zip_derived_cl4993, 77.33/10.43 zip_derived_cl4939])). 77.33/10.43 77.33/10.43 % SZS output end Refutation 77.33/10.43 77.33/10.43 77.33/10.43 % Terminating... 77.75/10.50 % Runner terminated. 77.81/10.51 % Zipperpin 1.5 exiting 77.81/10.51 EOF