0.02/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.s9YQGDghzq true 0.12/0.34 % Computer : n023.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 : 1440 0.12/0.34 % WCLimit : 180 0.12/0.34 % DateTime : Thu Jul 4 09:57:54 EDT 2024 0.12/0.34 % CPUTime : 0.12/0.34 % Running portfolio for 1440 s 0.12/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.12/0.34 % Number of cores: 8 0.12/0.34 % Python version: Python 3.6.8 0.12/0.35 % Running in HO mode 0.47/0.60 % Total configuration time : 828 0.47/0.60 % Estimated wc time : 1656 0.47/0.60 % Estimated cpu time (8 cpus) : 207.0 0.51/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.51/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.51/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.51/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.51/0.84 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.51/0.84 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.51/0.84 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.51/0.84 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 112.33/17.15 % Solved by lams/40_c.s.sh. 112.33/17.15 % done 593 iterations in 16.382s 112.33/17.15 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 112.33/17.15 % SZS output start Refutation 112.33/17.15 thf(emptyset_type, type, emptyset: $i). 112.33/17.15 thf(lessis_type, type, lessis: $i > $i > $o). 112.33/17.15 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 112.33/17.15 thf(nis_type, type, nis: $i > $i > $o). 112.33/17.15 thf(omega_type, type, omega: $i). 112.33/17.15 thf(d_not_type, type, d_not: $o > $o). 112.33/17.15 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 112.33/17.15 thf(in_type, type, in: $i > $i > $o). 112.33/17.15 thf(n_1_type, type, n_1: $i). 112.33/17.15 thf(sk__5_type, type, sk__5: $i). 112.33/17.15 thf('#l_lift4105_type', type, '#l_lift4105': $i > $o). 112.33/17.15 thf(ap_type, type, ap: $i > $i > $i). 112.33/17.15 thf(nat_type, type, nat: $i). 112.33/17.15 thf(iii_type, type, iii: $i > $i > $o). 112.33/17.15 thf(l_or_type, type, l_or: $o > $o > $o). 112.33/17.15 thf(sk__4_type, type, sk__4: $i). 112.33/17.15 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 112.33/17.15 thf(imp_type, type, imp: $o > $o > $o). 112.33/17.15 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 112.33/17.15 thf('#l_lift4104_type', type, '#l_lift4104': $i > $o). 112.33/17.15 thf(plus_type, type, plus: $i > $i). 112.33/17.15 thf(n_is_type, type, n_is: $i > $i > $o). 112.33/17.15 thf(sk__2_type, type, sk__2: $i). 112.33/17.15 thf(n_some_type, type, n_some: ($i > $o) > $o). 112.33/17.15 thf(ordsucc_type, type, ordsucc: $i > $i). 112.33/17.15 thf(n_pl_type, type, n_pl: $i > $i > $i). 112.33/17.15 thf(sk__3_type, type, sk__3: $i). 112.33/17.15 thf(def_lessis, axiom,(( lessis ) = 112.33/17.15 (^[X0:$i,X1:$i]: ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) )))). 112.33/17.15 thf(def_iii, axiom,(( iii ) = 112.33/17.15 (^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X1 @ X0 ) )))). 112.33/17.15 thf('0', plain, 112.33/17.15 (( iii ) = ( ^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X1 @ X0 ) ) )), 112.33/17.15 inference('simplify_rw_rule', [status(thm)], [def_iii])). 112.33/17.15 thf('1', plain, 112.33/17.15 (( iii ) = ( ^[V_1:$i,V_2:$i]: ( n_some @ ( diffprop @ V_2 @ V_1 ) ) )), 112.33/17.15 define([status(thm)])). 112.33/17.15 thf(def_l_or, axiom,(( l_or ) = (^[X0:$o]: ( imp @ ( d_not @ X0 ) )))). 112.33/17.15 thf(def_d_not, axiom,(( d_not ) = (^[X0:$o]: ( imp @ X0 @ $false )))). 112.33/17.15 thf(def_imp, axiom,(( imp ) = (^[X0:$o,X1:$o]: ( ( X0 ) => ( X1 ) )))). 112.33/17.15 thf('2', plain, (( imp ) = ( ^[X0:$o,X1:$o]: ( ( X0 ) => ( X1 ) ) )), 112.33/17.15 inference('simplify_rw_rule', [status(thm)], [def_imp])). 112.33/17.15 thf('3', plain, (( imp ) = ( ^[V_1:$o,V_2:$o]: ( ( V_1 ) => ( V_2 ) ) )), 112.33/17.15 define([status(thm)])). 112.33/17.15 thf('4', plain, (( d_not ) = ( ^[X0:$o]: ( imp @ X0 @ $false ) )), 112.33/17.15 inference('simplify_rw_rule', [status(thm)], [def_d_not, '3'])). 112.33/17.15 thf('5', plain, (( d_not ) = ( ^[V_1:$o]: ( imp @ V_1 @ $false ) )), 112.33/17.15 define([status(thm)])). 112.33/17.15 thf('6', plain, (( l_or ) = ( ^[X0:$o]: ( imp @ ( d_not @ X0 ) ) )), 112.33/17.15 inference('simplify_rw_rule', [status(thm)], [def_l_or, '5', '3'])). 112.33/17.15 thf('7', plain, (( l_or ) = ( ^[V_1:$o]: ( imp @ ( d_not @ V_1 ) ) )), 112.33/17.15 define([status(thm)])). 112.33/17.15 thf('8', plain, 112.33/17.15 (( lessis ) = 112.33/17.15 ( ^[X0:$i,X1:$i]: ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )), 112.33/17.15 inference('simplify_rw_rule', [status(thm)], 112.33/17.15 [def_lessis, '1', '7', '5', '3'])). 112.33/17.15 thf('9', plain, 112.33/17.15 (( lessis ) = 112.33/17.15 ( ^[V_1:$i,V_2:$i]: 112.33/17.15 ( l_or @ ( iii @ V_1 @ V_2 ) @ ( n_is @ V_1 @ V_2 ) ) )), 112.33/17.15 define([status(thm)])). 112.33/17.15 thf(def_n_pl, axiom,(( n_pl ) = (^[X0:$i]: ( ap @ ( plus @ X0 ) )))). 112.33/17.15 thf('10', plain, (( n_pl ) = ( ^[X0:$i]: ( ap @ ( plus @ X0 ) ) )), 112.33/17.15 inference('simplify_rw_rule', [status(thm)], [def_n_pl])). 112.33/17.15 thf('11', plain, (( n_pl ) = ( ^[V_1:$i]: ( ap @ ( plus @ V_1 ) ) )), 112.33/17.15 define([status(thm)])). 112.33/17.15 thf(def_nat, axiom,(( nat ) = 112.33/17.15 (d_Sep @ omega @ ( ^[X0:$i]: ( ( X0 ) != ( emptyset ) ) )))). 112.33/17.15 thf('12', plain, 112.33/17.15 (( nat ) = ( d_Sep @ omega @ ( ^[X0:$i]: ( ( X0 ) != ( emptyset ) ) ) )), 112.33/17.15 inference('simplify_rw_rule', [status(thm)], [def_nat])). 112.33/17.15 thf('13', plain, 112.33/17.15 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 112.33/17.15 define([status(thm)])). 112.33/17.15 thf(def_all_of, axiom,(( all_of ) = 112.33/17.15 (^[X0:( $i > $o ),X1:( $i > $o )]: 112.33/17.15 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) )))). 112.33/17.15 thf('14', plain, 112.33/17.15 (( all_of ) = 112.33/17.15 ( ^[X0:( $i > $o ),X1:( $i > $o )]: 112.33/17.15 ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) ) )), 112.33/17.15 inference('simplify_rw_rule', [status(thm)], [def_all_of])). 112.33/17.15 thf('15', plain, 112.33/17.15 (( all_of ) = 112.33/17.15 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 112.33/17.15 ( ![X4:$i]: ( ( is_of @ X4 @ V_1 ) => ( V_2 @ X4 ) ) ) )), 112.33/17.15 define([status(thm)])). 112.33/17.15 thf(satz22d, conjecture, 112.33/17.15 (all_of @ 112.33/17.15 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 112.33/17.15 ( ^[X0:$i]: 112.33/17.15 ( all_of @ 112.33/17.15 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 112.33/17.15 ( ^[X1:$i]: 112.33/17.15 ( all_of @ 112.33/17.15 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 112.33/17.15 ( ^[X2:$i]: 112.33/17.15 ( all_of @ 112.33/17.15 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @ 112.33/17.15 ( ^[X3:$i]: 112.33/17.15 ( ( iii @ X0 @ X1 ) => 112.33/17.15 ( ( lessis @ X2 @ X3 ) => 112.33/17.15 ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 112.33/17.15 thf(zf_stmt_0, conjecture, 112.33/17.15 (![X4:$i]: 112.33/17.15 ( ( is_of @ 112.33/17.15 X4 @ 112.33/17.15 ( ^[V_1:$i]: 112.33/17.15 ( in @ 112.33/17.15 V_1 @ 112.33/17.15 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.15 ( ![X6:$i]: 112.33/17.15 ( ( is_of @ 112.33/17.15 X6 @ 112.33/17.15 ( ^[V_3:$i]: 112.33/17.15 ( in @ 112.33/17.15 V_3 @ 112.33/17.15 ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.15 ( ![X8:$i]: 112.33/17.15 ( ( is_of @ 112.33/17.15 X8 @ 112.33/17.15 ( ^[V_5:$i]: 112.33/17.15 ( in @ 112.33/17.15 V_5 @ 112.33/17.15 ( d_Sep @ 112.33/17.15 omega @ ( ^[V_6:$i]: ( ( V_6 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.15 ( ![X10:$i]: 112.33/17.15 ( ( is_of @ 112.33/17.15 X10 @ 112.33/17.15 ( ^[V_7:$i]: 112.33/17.15 ( in @ 112.33/17.15 V_7 @ 112.33/17.15 ( d_Sep @ 112.33/17.15 omega @ ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.15 ( ( n_some @ ( diffprop @ X6 @ X4 ) ) => 112.33/17.15 ( ( ( ~( n_some @ ( diffprop @ X10 @ X8 ) ) ) => 112.33/17.15 ( n_is @ X8 @ X10 ) ) => 112.33/17.15 ( n_some @ 112.33/17.15 ( diffprop @ 112.33/17.15 ( ap @ ( plus @ X6 ) @ X10 ) @ 112.33/17.15 ( ap @ ( plus @ X4 ) @ X8 ) ) ) ) ) ) ) ) ) ) ) ))). 112.33/17.15 thf(zf_stmt_1, negated_conjecture, 112.33/17.15 (~( ![X4:$i]: 112.33/17.15 ( ( is_of @ 112.33/17.15 X4 @ 112.33/17.15 ( ^[V_1:$i]: 112.33/17.15 ( in @ 112.33/17.15 V_1 @ 112.33/17.15 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.15 ( ![X6:$i]: 112.33/17.15 ( ( is_of @ 112.33/17.15 X6 @ 112.33/17.15 ( ^[V_3:$i]: 112.33/17.15 ( in @ 112.33/17.15 V_3 @ 112.33/17.15 ( d_Sep @ 112.33/17.15 omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.15 ( ![X8:$i]: 112.33/17.15 ( ( is_of @ 112.33/17.15 X8 @ 112.33/17.15 ( ^[V_5:$i]: 112.33/17.15 ( in @ 112.33/17.15 V_5 @ 112.33/17.15 ( d_Sep @ 112.33/17.15 omega @ ( ^[V_6:$i]: ( ( V_6 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.15 ( ![X10:$i]: 112.33/17.15 ( ( is_of @ 112.33/17.15 X10 @ 112.33/17.15 ( ^[V_7:$i]: 112.33/17.15 ( in @ 112.33/17.15 V_7 @ 112.33/17.15 ( d_Sep @ 112.33/17.15 omega @ 112.33/17.15 ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.15 ( ( n_some @ ( diffprop @ X6 @ X4 ) ) => 112.33/17.15 ( ( ( ~( n_some @ ( diffprop @ X10 @ X8 ) ) ) => 112.33/17.15 ( n_is @ X8 @ X10 ) ) => 112.33/17.15 ( n_some @ 112.33/17.15 ( diffprop @ 112.33/17.15 ( ap @ ( plus @ X6 ) @ X10 ) @ 112.33/17.15 ( ap @ ( plus @ X4 ) @ X8 ) ) ) ) ) ) ) ) ) ) ) ) )), 112.33/17.15 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 112.33/17.15 thf(zip_derived_cl80, plain, 112.33/17.15 (( (n_is @ sk__4 @ sk__5) | (n_some @ (diffprop @ sk__5 @ sk__4)))), 112.33/17.15 inference('cnf', [status(esa)], [zf_stmt_1])). 112.33/17.15 thf(zip_derived_cl81, plain, 112.33/17.15 ( (is_of @ sk__5 @ 112.33/17.15 (^[Y0 : $i]: 112.33/17.15 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))), 112.33/17.15 inference('cnf', [status(esa)], [zf_stmt_1])). 112.33/17.15 thf(def_nis, axiom,(( nis ) = 112.33/17.15 (^[X0:$i,X1:$i]: ( d_not @ ( n_is @ X0 @ X1 ) )))). 112.33/17.15 thf('16', plain, 112.33/17.15 (( nis ) = ( ^[X0:$i,X1:$i]: ( d_not @ ( n_is @ X0 @ X1 ) ) )), 112.33/17.16 inference('simplify_rw_rule', [status(thm)], [def_nis, '5', '3'])). 112.33/17.16 thf('17', plain, 112.33/17.16 (( nis ) = ( ^[V_1:$i,V_2:$i]: ( d_not @ ( n_is @ V_1 @ V_2 ) ) )), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(n_ax3, axiom, 112.33/17.16 (all_of @ 112.33/17.16 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 112.33/17.16 ( ^[X0:$i]: ( nis @ ( ordsucc @ X0 ) @ n_1 ) ))). 112.33/17.16 thf(zf_stmt_2, axiom, 112.33/17.16 (![X4:$i]: 112.33/17.16 ( ( is_of @ 112.33/17.16 X4 @ 112.33/17.16 ( ^[V_1:$i]: 112.33/17.16 ( in @ 112.33/17.16 V_1 @ 112.33/17.16 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.16 ( ~( n_is @ ( ordsucc @ X4 ) @ n_1 ) ) ))). 112.33/17.16 thf(zip_derived_cl0, plain, 112.33/17.16 (![X0 : $i]: 112.33/17.16 (~ (n_is @ (ordsucc @ X0) @ n_1) 112.33/17.16 | ~ (is_of @ X0 @ 112.33/17.16 (^[Y0 : $i]: 112.33/17.16 (in @ Y0 @ 112.33/17.16 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 112.33/17.16 inference('cnf', [status(esa)], [zf_stmt_2])). 112.33/17.16 thf(zip_derived_cl7090, plain, 112.33/17.16 (![X2 : $i]: 112.33/17.16 (('#l_lift4105' @ X2) = (in @ X2 @ (d_Sep @ omega @ '#l_lift4104')))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl0, plain, 112.33/17.16 (![X0 : $i]: 112.33/17.16 (~ (n_is @ (ordsucc @ X0) @ n_1) 112.33/17.16 | ~ (is_of @ X0 @ 112.33/17.16 (^[Y0 : $i]: 112.33/17.16 (in @ Y0 @ 112.33/17.16 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 112.33/17.16 inference('cnf', [status(esa)], [zf_stmt_2])). 112.33/17.16 thf(zip_derived_cl7089, plain, 112.33/17.16 (![X1 : $i]: (('#l_lift4104' @ X1) = (((X1) != (emptyset))))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7163, plain, ( (is_of @ sk__5 @ '#l_lift4105')), 112.33/17.16 inference('lambda_lifting', [status(thm)], 112.33/17.16 [zip_derived_cl81, zip_derived_cl7090, zip_derived_cl7089])). 112.33/17.16 thf(zip_derived_cl82, plain, 112.33/17.16 ( (is_of @ sk__3 @ 112.33/17.16 (^[Y0 : $i]: 112.33/17.16 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))), 112.33/17.16 inference('cnf', [status(esa)], [zf_stmt_1])). 112.33/17.16 thf(zip_derived_cl7090, plain, 112.33/17.16 (![X2 : $i]: 112.33/17.16 (('#l_lift4105' @ X2) = (in @ X2 @ (d_Sep @ omega @ '#l_lift4104')))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7089, plain, 112.33/17.16 (![X1 : $i]: (('#l_lift4104' @ X1) = (((X1) != (emptyset))))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7164, plain, ( (is_of @ sk__3 @ '#l_lift4105')), 112.33/17.16 inference('lambda_lifting', [status(thm)], 112.33/17.16 [zip_derived_cl82, zip_derived_cl7090, zip_derived_cl7089])). 112.33/17.16 thf(zip_derived_cl76, plain, 112.33/17.16 ( (is_of @ sk__2 @ 112.33/17.16 (^[Y0 : $i]: 112.33/17.16 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))), 112.33/17.16 inference('cnf', [status(esa)], [zf_stmt_1])). 112.33/17.16 thf(zip_derived_cl7090, plain, 112.33/17.16 (![X2 : $i]: 112.33/17.16 (('#l_lift4105' @ X2) = (in @ X2 @ (d_Sep @ omega @ '#l_lift4104')))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7089, plain, 112.33/17.16 (![X1 : $i]: (('#l_lift4104' @ X1) = (((X1) != (emptyset))))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7161, plain, ( (is_of @ sk__2 @ '#l_lift4105')), 112.33/17.16 inference('lambda_lifting', [status(thm)], 112.33/17.16 [zip_derived_cl76, zip_derived_cl7090, zip_derived_cl7089])). 112.33/17.16 thf(zip_derived_cl77, plain, 112.33/17.16 ( (is_of @ sk__4 @ 112.33/17.16 (^[Y0 : $i]: 112.33/17.16 (in @ Y0 @ (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset))))))))), 112.33/17.16 inference('cnf', [status(esa)], [zf_stmt_1])). 112.33/17.16 thf(zip_derived_cl7090, plain, 112.33/17.16 (![X2 : $i]: 112.33/17.16 (('#l_lift4105' @ X2) = (in @ X2 @ (d_Sep @ omega @ '#l_lift4104')))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7089, plain, 112.33/17.16 (![X1 : $i]: (('#l_lift4104' @ X1) = (((X1) != (emptyset))))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7162, plain, ( (is_of @ sk__4 @ '#l_lift4105')), 112.33/17.16 inference('lambda_lifting', [status(thm)], 112.33/17.16 [zip_derived_cl77, zip_derived_cl7090, zip_derived_cl7089])). 112.33/17.16 thf(zip_derived_cl78, plain, ( (n_some @ (diffprop @ sk__3 @ sk__2))), 112.33/17.16 inference('cnf', [status(esa)], [zf_stmt_1])). 112.33/17.16 thf(zip_derived_cl79, plain, 112.33/17.16 (~ (n_some @ 112.33/17.16 (diffprop @ (ap @ (plus @ sk__3) @ sk__5) @ 112.33/17.16 (ap @ (plus @ sk__2) @ sk__4)))), 112.33/17.16 inference('cnf', [status(esa)], [zf_stmt_1])). 112.33/17.16 thf(satz22c, axiom, 112.33/17.16 (all_of @ 112.33/17.16 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 112.33/17.16 ( ^[X0:$i]: 112.33/17.16 ( all_of @ 112.33/17.16 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 112.33/17.16 ( ^[X1:$i]: 112.33/17.16 ( all_of @ 112.33/17.16 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 112.33/17.16 ( ^[X2:$i]: 112.33/17.16 ( all_of @ 112.33/17.16 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @ 112.33/17.16 ( ^[X3:$i]: 112.33/17.16 ( ( lessis @ X0 @ X1 ) => 112.33/17.16 ( ( iii @ X2 @ X3 ) => 112.33/17.16 ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 112.33/17.16 thf(zf_stmt_3, axiom, 112.33/17.16 (![X4:$i]: 112.33/17.16 ( ( is_of @ 112.33/17.16 X4 @ 112.33/17.16 ( ^[V_1:$i]: 112.33/17.16 ( in @ 112.33/17.16 V_1 @ 112.33/17.16 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.16 ( ![X6:$i]: 112.33/17.16 ( ( is_of @ 112.33/17.16 X6 @ 112.33/17.16 ( ^[V_3:$i]: 112.33/17.16 ( in @ 112.33/17.16 V_3 @ 112.33/17.16 ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.16 ( ![X8:$i]: 112.33/17.16 ( ( is_of @ 112.33/17.16 X8 @ 112.33/17.16 ( ^[V_5:$i]: 112.33/17.16 ( in @ 112.33/17.16 V_5 @ 112.33/17.16 ( d_Sep @ 112.33/17.16 omega @ ( ^[V_6:$i]: ( ( V_6 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.16 ( ![X10:$i]: 112.33/17.16 ( ( is_of @ 112.33/17.16 X10 @ 112.33/17.16 ( ^[V_7:$i]: 112.33/17.16 ( in @ 112.33/17.16 V_7 @ 112.33/17.16 ( d_Sep @ 112.33/17.16 omega @ ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.16 ( ( ( ~( n_some @ ( diffprop @ X6 @ X4 ) ) ) => 112.33/17.16 ( n_is @ X4 @ X6 ) ) => 112.33/17.16 ( ( n_some @ ( diffprop @ X10 @ X8 ) ) => 112.33/17.16 ( n_some @ 112.33/17.16 ( diffprop @ 112.33/17.16 ( ap @ ( plus @ X6 ) @ X10 ) @ 112.33/17.16 ( ap @ ( plus @ X4 ) @ X8 ) ) ) ) ) ) ) ) ) ) ) ))). 112.33/17.16 thf(zip_derived_cl41, plain, 112.33/17.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 112.33/17.16 (~ (is_of @ X0 @ 112.33/17.16 (^[Y0 : $i]: 112.33/17.16 (in @ Y0 @ 112.33/17.16 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 112.33/17.16 | ~ (is_of @ X1 @ 112.33/17.16 (^[Y0 : $i]: 112.33/17.16 (in @ Y0 @ 112.33/17.16 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 112.33/17.16 | ~ (n_some @ (diffprop @ X1 @ X2)) 112.33/17.16 | (n_some @ 112.33/17.16 (diffprop @ (ap @ (plus @ X0) @ X1) @ (ap @ (plus @ X3) @ X2))) 112.33/17.16 | ~ (n_some @ (diffprop @ X0 @ X3)) 112.33/17.16 | ~ (is_of @ X2 @ 112.33/17.16 (^[Y0 : $i]: 112.33/17.16 (in @ Y0 @ 112.33/17.16 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 112.33/17.16 | ~ (is_of @ X3 @ 112.33/17.16 (^[Y0 : $i]: 112.33/17.16 (in @ Y0 @ 112.33/17.16 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 112.33/17.16 inference('cnf', [status(esa)], [zf_stmt_3])). 112.33/17.16 thf(zip_derived_cl7090, plain, 112.33/17.16 (![X2 : $i]: 112.33/17.16 (('#l_lift4105' @ X2) = (in @ X2 @ (d_Sep @ omega @ '#l_lift4104')))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7089, plain, 112.33/17.16 (![X1 : $i]: (('#l_lift4104' @ X1) = (((X1) != (emptyset))))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7090, plain, 112.33/17.16 (![X2 : $i]: 112.33/17.16 (('#l_lift4105' @ X2) = (in @ X2 @ (d_Sep @ omega @ '#l_lift4104')))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7089, plain, 112.33/17.16 (![X1 : $i]: (('#l_lift4104' @ X1) = (((X1) != (emptyset))))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7090, plain, 112.33/17.16 (![X2 : $i]: 112.33/17.16 (('#l_lift4105' @ X2) = (in @ X2 @ (d_Sep @ omega @ '#l_lift4104')))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7089, plain, 112.33/17.16 (![X1 : $i]: (('#l_lift4104' @ X1) = (((X1) != (emptyset))))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7090, plain, 112.33/17.16 (![X2 : $i]: 112.33/17.16 (('#l_lift4105' @ X2) = (in @ X2 @ (d_Sep @ omega @ '#l_lift4104')))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7089, plain, 112.33/17.16 (![X1 : $i]: (('#l_lift4104' @ X1) = (((X1) != (emptyset))))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7130, plain, 112.33/17.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 112.33/17.16 (~ (is_of @ X0 @ '#l_lift4105') 112.33/17.16 | ~ (is_of @ X1 @ '#l_lift4105') 112.33/17.16 | ~ (n_some @ (diffprop @ X1 @ X2)) 112.33/17.16 | (n_some @ 112.33/17.16 (diffprop @ (ap @ (plus @ X0) @ X1) @ (ap @ (plus @ X3) @ X2))) 112.33/17.16 | ~ (n_some @ (diffprop @ X0 @ X3)) 112.33/17.16 | ~ (is_of @ X2 @ '#l_lift4105') 112.33/17.16 | ~ (is_of @ X3 @ '#l_lift4105'))), 112.33/17.16 inference('lambda_lifting', [status(thm)], 112.33/17.16 [zip_derived_cl41, zip_derived_cl7090, zip_derived_cl7089, 112.33/17.16 zip_derived_cl7090, zip_derived_cl7089, zip_derived_cl7090, 112.33/17.16 zip_derived_cl7089, zip_derived_cl7090, zip_derived_cl7089])). 112.33/17.16 thf(satz19k, axiom, 112.33/17.16 (all_of @ 112.33/17.16 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 112.33/17.16 ( ^[X0:$i]: 112.33/17.16 ( all_of @ 112.33/17.16 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 112.33/17.16 ( ^[X1:$i]: 112.33/17.16 ( all_of @ 112.33/17.16 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 112.33/17.16 ( ^[X2:$i]: 112.33/17.16 ( all_of @ 112.33/17.16 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @ 112.33/17.16 ( ^[X3:$i]: 112.33/17.16 ( ( n_is @ X0 @ X1 ) => 112.33/17.16 ( ( iii @ X2 @ X3 ) => 112.33/17.16 ( iii @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ))). 112.33/17.16 thf(zf_stmt_4, axiom, 112.33/17.16 (![X4:$i]: 112.33/17.16 ( ( is_of @ 112.33/17.16 X4 @ 112.33/17.16 ( ^[V_1:$i]: 112.33/17.16 ( in @ 112.33/17.16 V_1 @ 112.33/17.16 ( d_Sep @ omega @ ( ^[V_2:$i]: ( ( V_2 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.16 ( ![X6:$i]: 112.33/17.16 ( ( is_of @ 112.33/17.16 X6 @ 112.33/17.16 ( ^[V_3:$i]: 112.33/17.16 ( in @ 112.33/17.16 V_3 @ 112.33/17.16 ( d_Sep @ omega @ ( ^[V_4:$i]: ( ( V_4 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.16 ( ![X8:$i]: 112.33/17.16 ( ( is_of @ 112.33/17.16 X8 @ 112.33/17.16 ( ^[V_5:$i]: 112.33/17.16 ( in @ 112.33/17.16 V_5 @ 112.33/17.16 ( d_Sep @ 112.33/17.16 omega @ ( ^[V_6:$i]: ( ( V_6 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.16 ( ![X10:$i]: 112.33/17.16 ( ( is_of @ 112.33/17.16 X10 @ 112.33/17.16 ( ^[V_7:$i]: 112.33/17.16 ( in @ 112.33/17.16 V_7 @ 112.33/17.16 ( d_Sep @ 112.33/17.16 omega @ ( ^[V_8:$i]: ( ( V_8 ) != ( emptyset ) ) ) ) ) ) ) => 112.33/17.16 ( ( n_is @ X4 @ X6 ) => 112.33/17.16 ( ( n_some @ ( diffprop @ X10 @ X8 ) ) => 112.33/17.16 ( n_some @ 112.33/17.16 ( diffprop @ 112.33/17.16 ( ap @ ( plus @ X10 ) @ X6 ) @ 112.33/17.16 ( ap @ ( plus @ X8 ) @ X4 ) ) ) ) ) ) ) ) ) ) ) ))). 112.33/17.16 thf(zip_derived_cl23, plain, 112.33/17.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 112.33/17.16 (~ (is_of @ X0 @ 112.33/17.16 (^[Y0 : $i]: 112.33/17.16 (in @ Y0 @ 112.33/17.16 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 112.33/17.16 | ~ (is_of @ X1 @ 112.33/17.16 (^[Y0 : $i]: 112.33/17.16 (in @ Y0 @ 112.33/17.16 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 112.33/17.16 | ~ (n_some @ (diffprop @ X1 @ X2)) 112.33/17.16 | (n_some @ 112.33/17.16 (diffprop @ (ap @ (plus @ X1) @ X0) @ (ap @ (plus @ X2) @ X3))) 112.33/17.16 | ~ (n_is @ X3 @ X0) 112.33/17.16 | ~ (is_of @ X2 @ 112.33/17.16 (^[Y0 : $i]: 112.33/17.16 (in @ Y0 @ 112.33/17.16 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))) 112.33/17.16 | ~ (is_of @ X3 @ 112.33/17.16 (^[Y0 : $i]: 112.33/17.16 (in @ Y0 @ 112.33/17.16 (d_Sep @ omega @ (^[Y1 : $i]: (((Y1) != (emptyset)))))))))), 112.33/17.16 inference('cnf', [status(esa)], [zf_stmt_4])). 112.33/17.16 thf(zip_derived_cl7090, plain, 112.33/17.16 (![X2 : $i]: 112.33/17.16 (('#l_lift4105' @ X2) = (in @ X2 @ (d_Sep @ omega @ '#l_lift4104')))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7089, plain, 112.33/17.16 (![X1 : $i]: (('#l_lift4104' @ X1) = (((X1) != (emptyset))))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7090, plain, 112.33/17.16 (![X2 : $i]: 112.33/17.16 (('#l_lift4105' @ X2) = (in @ X2 @ (d_Sep @ omega @ '#l_lift4104')))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7089, plain, 112.33/17.16 (![X1 : $i]: (('#l_lift4104' @ X1) = (((X1) != (emptyset))))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7090, plain, 112.33/17.16 (![X2 : $i]: 112.33/17.16 (('#l_lift4105' @ X2) = (in @ X2 @ (d_Sep @ omega @ '#l_lift4104')))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7089, plain, 112.33/17.16 (![X1 : $i]: (('#l_lift4104' @ X1) = (((X1) != (emptyset))))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7090, plain, 112.33/17.16 (![X2 : $i]: 112.33/17.16 (('#l_lift4105' @ X2) = (in @ X2 @ (d_Sep @ omega @ '#l_lift4104')))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7089, plain, 112.33/17.16 (![X1 : $i]: (('#l_lift4104' @ X1) = (((X1) != (emptyset))))), 112.33/17.16 define([status(thm)])). 112.33/17.16 thf(zip_derived_cl7111, plain, 112.33/17.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 112.33/17.16 (~ (is_of @ X0 @ '#l_lift4105') 112.33/17.16 | ~ (is_of @ X1 @ '#l_lift4105') 112.33/17.16 | ~ (n_some @ (diffprop @ X1 @ X2)) 112.33/17.16 | (n_some @ 112.33/17.16 (diffprop @ (ap @ (plus @ X1) @ X0) @ (ap @ (plus @ X2) @ X3))) 112.33/17.16 | ~ (n_is @ X3 @ X0) 112.33/17.16 | ~ (is_of @ X2 @ '#l_lift4105') 112.33/17.16 | ~ (is_of @ X3 @ '#l_lift4105'))), 112.33/17.16 inference('lambda_lifting', [status(thm)], 112.33/17.16 [zip_derived_cl23, zip_derived_cl7090, zip_derived_cl7089, 112.33/17.16 zip_derived_cl7090, zip_derived_cl7089, zip_derived_cl7090, 112.33/17.16 zip_derived_cl7089, zip_derived_cl7090, zip_derived_cl7089])). 112.33/17.16 thf(zip_derived_cl7200, plain, ($false), 112.33/17.16 inference('eprover', [status(thm)], 112.33/17.16 [zip_derived_cl80, zip_derived_cl7163, zip_derived_cl7164, 112.33/17.16 zip_derived_cl7161, zip_derived_cl7162, zip_derived_cl78, 112.33/17.16 zip_derived_cl79, zip_derived_cl7130, zip_derived_cl7111])). 112.33/17.16 112.33/17.16 % SZS output end Refutation 112.33/17.16 112.33/17.16 112.33/17.16 % Terminating... 112.80/17.36 % Runner terminated. 112.80/17.37 % Zipperpin 1.5 exiting 112.80/17.39 EOF