%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM726^4 : TPTP v9.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.FvQRhoBJQA true
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:48:08 PM UTC 2025
% Result : Theorem 5.19s 1.31s
% Output : Refutation 5.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM726^4 : TPTP v9.2.0. Released v7.1.0.
% 0.03/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.FvQRhoBJQA true
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 16:45:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.36 % 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
% 0.54/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.54/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.56/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.56/0.77 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.56/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.56/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.56/0.83 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 5.19/1.31 % Solved by lams/30_b.l.sh.
% 5.19/1.31 % done 0 iterations in 0.432s
% 5.19/1.31 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 5.19/1.31 % SZS output start Refutation
% 5.19/1.31 thf(n_1_type, type, n_1: $i).
% 5.19/1.31 thf(nat_type, type, nat: $i).
% 5.19/1.31 thf(lessis_type, type, lessis: $i > $i > $o).
% 5.19/1.31 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 5.19/1.31 thf(in_type, type, in: $i > $i > $o).
% 5.19/1.31 thf('#sk12_type', type, '#sk12': $i).
% 5.19/1.31 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 5.19/1.31 thf(n_2_type, type, n_2: $i).
% 5.19/1.31 thf(d_Sigma_type, type, d_Sigma: $i > ($i > $i) > $i).
% 5.19/1.31 thf(ap_type, type, ap: $i > $i > $i).
% 5.19/1.31 thf(union_type, type, union: $i > $i).
% 5.19/1.31 thf(emptyset_type, type, emptyset: $i).
% 5.19/1.31 thf(n_is_type, type, n_is: $i > $i > $o).
% 5.19/1.31 thf(n_1t_type, type, n_1t: $i).
% 5.19/1.31 thf(frac_type, type, frac: $i).
% 5.19/1.31 thf(d_Pi_type, type, d_Pi: $i > ($i > $i) > $i).
% 5.19/1.31 thf(n_2t_type, type, n_2t: $i).
% 5.19/1.31 thf(n_ts_type, type, n_ts: $i > $i > $i).
% 5.19/1.31 thf(n_eq_type, type, n_eq: $i > $i > $o).
% 5.19/1.31 thf(pair1type_type, type, pair1type: $i > $i).
% 5.19/1.31 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 5.19/1.31 thf(num_type, type, num: $i > $i).
% 5.19/1.31 thf(d_1to_type, type, d_1to: $i > $i).
% 5.19/1.31 thf(ordsucc_type, type, ordsucc: $i > $i).
% 5.19/1.31 thf(outn_type, type, outn: $i > $i > $i).
% 5.19/1.31 thf(first1_type, type, first1: $i > $i > $i).
% 5.19/1.31 thf('#sk13_type', type, '#sk13': $i).
% 5.19/1.31 thf(den_type, type, den: $i > $i).
% 5.19/1.31 thf(power_type, type, power: $i > $i).
% 5.19/1.31 thf(second1_type, type, second1: $i > $i > $i).
% 5.19/1.31 thf(e_is_type, type, e_is: $i > $i > $i > $o).
% 5.19/1.31 thf(out_type, type, out: $i > ($i > $o) > $i > $i).
% 5.19/1.31 thf(n_pl_type, type, n_pl: $i > $i > $i).
% 5.19/1.31 thf(satz38, conjecture,
% 5.19/1.31 (all_of @
% 5.19/1.31 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 5.19/1.31 ( ^[X0:$i]:
% 5.19/1.31 ( all_of @
% 5.19/1.31 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 5.19/1.31 ( ^[X1:$i]: ( ( n_eq @ X0 @ X1 ) => ( n_eq @ X1 @ X0 ) ) ) ) ))).
% 5.19/1.31 thf(zf_stmt_0, negated_conjecture,
% 5.19/1.31 (~( all_of @
% 5.19/1.31 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 5.19/1.31 ( ^[X0:$i]:
% 5.19/1.31 ( all_of @
% 5.19/1.31 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 5.19/1.31 ( ^[X1:$i]: ( ( n_eq @ X0 @ X1 ) => ( n_eq @ X1 @ X0 ) ) ) ) ) )),
% 5.19/1.31 inference('cnf.neg', [status(esa)], [satz38])).
% 5.19/1.31 thf(zip_derived_cl152, plain,
% 5.19/1.31 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 5.19/1.31 (^[Y1 : $i]: (((n_eq @ Y0 @ Y1) => (n_eq @ Y1 @ Y0)))))))),
% 5.19/1.31 inference('cnf', [status(esa)], [zf_stmt_0])).
% 5.19/1.31 thf(def_d_Pi, axiom,(( d_Pi @ (X0)@ (X1)) =
% 5.19/1.31 ((d_Sep @ (power @ (d_Sigma @ X0 @ (^[Y0 : $i]: (union @ (X1 @ Y0))))) @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (((!!) @ (^[Y1 : $i]:
% 5.19/1.31 (((in @ Y1 @ X0) => (in @ (ap @ Y0 @ Y1) @ (X1 @ Y1)))))))))))).
% 5.19/1.31 thf('0', plain,
% 5.19/1.31 (![X1:( $i > $i ),X0:$i]:
% 5.19/1.31 ( ( d_Pi @ X0 @ X1 ) =
% 5.19/1.31 ( d_Sep @
% 5.19/1.31 ( power @ ( d_Sigma @ X0 @ ( ^[V_1:$i]: ( union @ ( X1 @ V_1 ) ) ) ) ) @
% 5.19/1.31 ( ^[V_2:$i]:
% 5.19/1.31 ( ![X5:$i]:
% 5.19/1.31 ( ( in @ X5 @ X0 ) => ( in @ ( ap @ V_2 @ X5 ) @ ( X1 @ X5 ) ) ) ) ) ) )),
% 5.19/1.31 define([status(thm)])).
% 5.19/1.31 thf(def_n_1, axiom,(( n_1 ) = ((ordsucc @ emptyset)))).
% 5.19/1.31 thf('1', plain, (( n_1 ) = ( ordsucc @ emptyset )), define([status(thm)])).
% 5.19/1.31 thf(def_d_1to, axiom,(( d_1to @ (X0)) =
% 5.19/1.31 ((d_Sep @ nat @ (^[Y0 : $i]: (lessis @ Y0 @ X0)))))).
% 5.19/1.31 thf('2', plain,
% 5.19/1.31 (![X0:$i]:
% 5.19/1.31 ( ( d_1to @ X0 ) =
% 5.19/1.31 ( d_Sep @ nat @ ( ^[V_1:$i]: ( lessis @ V_1 @ X0 ) ) ) )),
% 5.19/1.31 define([status(thm)])).
% 5.19/1.31 thf(def_n_2, axiom,(( n_2 ) = ((n_pl @ n_1 @ n_1)))).
% 5.19/1.31 thf('3', plain, (( n_2 ) = ( n_pl @ n_1 @ n_1 )), define([status(thm)])).
% 5.19/1.31 thf(def_pair1type, axiom,(( pair1type @ (X0)) =
% 5.19/1.31 ((d_Pi @ (d_1to @ n_2) @ (^[Y0 : $i]: (X0)))))).
% 5.19/1.31 thf('4', plain,
% 5.19/1.31 (![X0:$i]:
% 5.19/1.31 ( ( pair1type @ X0 ) =
% 5.19/1.31 ( d_Pi @ ( d_1to @ n_2 ) @ ( ^[V_1:$i]: ( X0 ) ) ) )),
% 5.19/1.31 define([status(thm)])).
% 5.19/1.31 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))).
% 5.19/1.31 thf('5', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])).
% 5.19/1.31 thf(zip_derived_cl173, plain,
% 5.19/1.31 (~ (all_of @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (in @ Y0 @
% 5.19/1.31 (d_Sep @
% 5.19/1.31 (power @
% 5.19/1.31 (d_Sigma @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (lessis @ Y1 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 5.19/1.31 (^[Y1 : $i]: (union @ nat)))) @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (((!!) @ (^[Y2 : $i]:
% 5.19/1.31 (((in @ Y2 @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y3 : $i]:
% 5.19/1.31 (lessis @ Y3 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset)))))) =>
% 5.19/1.31 (in @ (ap @ Y1 @ Y2) @ nat)))))))))) @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (all_of @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (in @ Y1 @
% 5.19/1.31 (d_Sep @
% 5.19/1.31 (power @
% 5.19/1.31 (d_Sigma @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y2 : $i]:
% 5.19/1.31 (lessis @ Y2 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 5.19/1.31 (^[Y2 : $i]: (union @ nat)))) @
% 5.19/1.31 (^[Y2 : $i]:
% 5.19/1.31 (((!!) @ (^[Y3 : $i]:
% 5.19/1.31 (((in @ Y3 @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y4 : $i]:
% 5.19/1.31 (lessis @ Y4 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset)))))) =>
% 5.19/1.31 (in @ (ap @ Y2 @ Y3) @ nat)))))))))) @
% 5.19/1.31 (^[Y1 : $i]: (((n_eq @ Y0 @ Y1) => (n_eq @ Y1 @ Y0)))))))),
% 5.19/1.31 inference('rw', [status(thm)],
% 5.19/1.31 [zip_derived_cl152, '0', '1', '2', '3', '4', '5'])).
% 5.19/1.31 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 5.19/1.31 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 5.19/1.31 thf('6', plain,
% 5.19/1.31 (![X0:( $i > $o ),X1:( $i > $o )]:
% 5.19/1.31 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 5.19/1.31 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 5.19/1.31 inference('rw.lit', [status(esa)], [def_all_of])).
% 5.19/1.31 thf(zip_derived_cl174, plain,
% 5.19/1.31 (~ (((!!) @ (^[Y0 : $i]:
% 5.19/1.31 (((is_of @ Y0 @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (in @ Y1 @
% 5.19/1.31 (d_Sep @
% 5.19/1.31 (power @
% 5.19/1.31 (d_Sigma @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y2 : $i]:
% 5.19/1.31 (lessis @ Y2 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset))))) @
% 5.19/1.31 (^[Y2 : $i]: (union @ nat)))) @
% 5.19/1.31 (^[Y2 : $i]:
% 5.19/1.31 (((!!) @ (^[Y3 : $i]:
% 5.19/1.31 (((in @ Y3 @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y4 : $i]:
% 5.19/1.31 (lessis @ Y4 @
% 5.19/1.31 (n_pl @
% 5.19/1.31 (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset)))))) =>
% 5.19/1.31 (in @ (ap @ Y2 @ Y3) @ nat))))))))))) =>
% 5.19/1.31 ((^[Y1 : $i]:
% 5.19/1.31 (all_of @
% 5.19/1.31 (^[Y2 : $i]:
% 5.19/1.31 (in @ Y2 @
% 5.19/1.31 (d_Sep @
% 5.19/1.31 (power @
% 5.19/1.31 (d_Sigma @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y3 : $i]:
% 5.19/1.31 (lessis @ Y3 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset))))) @
% 5.19/1.31 (^[Y3 : $i]: (union @ nat)))) @
% 5.19/1.31 (^[Y3 : $i]:
% 5.19/1.31 (((!!) @ (^[Y4 : $i]:
% 5.19/1.31 (((in @ Y4 @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y5 : $i]:
% 5.19/1.31 (lessis @ Y5 @
% 5.19/1.31 (n_pl @
% 5.19/1.31 (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset)))))) =>
% 5.19/1.31 (in @ (ap @ Y3 @ Y4) @ nat)))))))))) @
% 5.19/1.31 (^[Y2 : $i]:
% 5.19/1.31 (((n_eq @ Y1 @ Y2) => (n_eq @ Y2 @ Y1)))))) @
% 5.19/1.31 Y0))))))),
% 5.19/1.31 inference('rw_clause', [status(thm)], [zip_derived_cl173, '6'])).
% 5.19/1.31 thf(zip_derived_cl175, plain,
% 5.19/1.31 (~ (((!!) @ (^[Y0 : $i]:
% 5.19/1.31 (((is_of @ Y0 @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (in @ Y1 @
% 5.19/1.31 (d_Sep @
% 5.19/1.31 (power @
% 5.19/1.31 (d_Sigma @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y2 : $i]:
% 5.19/1.31 (lessis @ Y2 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset))))) @
% 5.19/1.31 (^[Y2 : $i]: (union @ nat)))) @
% 5.19/1.31 (^[Y2 : $i]:
% 5.19/1.31 (((!!) @ (^[Y3 : $i]:
% 5.19/1.31 (((in @ Y3 @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y4 : $i]:
% 5.19/1.31 (lessis @ Y4 @
% 5.19/1.31 (n_pl @
% 5.19/1.31 (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset)))))) =>
% 5.19/1.31 (in @ (ap @ Y2 @ Y3) @ nat))))))))))) =>
% 5.19/1.31 (all_of @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (in @ Y1 @
% 5.19/1.31 (d_Sep @
% 5.19/1.31 (power @
% 5.19/1.31 (d_Sigma @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y2 : $i]:
% 5.19/1.31 (lessis @ Y2 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset))))) @
% 5.19/1.31 (^[Y2 : $i]: (union @ nat)))) @
% 5.19/1.31 (^[Y2 : $i]:
% 5.19/1.31 (((!!) @ (^[Y3 : $i]:
% 5.19/1.31 (((in @ Y3 @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y4 : $i]:
% 5.19/1.31 (lessis @ Y4 @
% 5.19/1.31 (n_pl @
% 5.19/1.31 (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset)))))) =>
% 5.19/1.31 (in @ (ap @ Y2 @ Y3) @ nat)))))))))) @
% 5.19/1.31 (^[Y1 : $i]: (((n_eq @ Y0 @ Y1) => (n_eq @ Y1 @ Y0))))))))))),
% 5.19/1.31 inference('ho_norm', [status(thm)], [zip_derived_cl174])).
% 5.19/1.31 thf(zip_derived_cl176, plain,
% 5.19/1.31 (~ (((is_of @ '#sk12' @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (in @ Y0 @
% 5.19/1.31 (d_Sep @
% 5.19/1.31 (power @
% 5.19/1.31 (d_Sigma @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (lessis @ Y1 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 5.19/1.31 (^[Y1 : $i]: (union @ nat)))) @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (((!!) @ (^[Y2 : $i]:
% 5.19/1.31 (((in @ Y2 @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y3 : $i]:
% 5.19/1.31 (lessis @ Y3 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset)))))) =>
% 5.19/1.31 (in @ (ap @ Y1 @ Y2) @ nat))))))))))) =>
% 5.19/1.31 (all_of @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (in @ Y0 @
% 5.19/1.31 (d_Sep @
% 5.19/1.31 (power @
% 5.19/1.31 (d_Sigma @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (lessis @ Y1 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 5.19/1.31 (^[Y1 : $i]: (union @ nat)))) @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (((!!) @ (^[Y2 : $i]:
% 5.19/1.31 (((in @ Y2 @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y3 : $i]:
% 5.19/1.31 (lessis @ Y3 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset)))))) =>
% 5.19/1.31 (in @ (ap @ Y1 @ Y2) @ nat)))))))))) @
% 5.19/1.31 (^[Y0 : $i]: (((n_eq @ '#sk12' @ Y0) => (n_eq @ Y0 @ '#sk12')))))))),
% 5.19/1.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl175])).
% 5.19/1.31 thf(zip_derived_cl178, plain,
% 5.19/1.31 (~ (all_of @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (in @ Y0 @
% 5.19/1.31 (d_Sep @
% 5.19/1.31 (power @
% 5.19/1.31 (d_Sigma @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (lessis @ Y1 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 5.19/1.31 (^[Y1 : $i]: (union @ nat)))) @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (((!!) @ (^[Y2 : $i]:
% 5.19/1.31 (((in @ Y2 @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y3 : $i]:
% 5.19/1.31 (lessis @ Y3 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset)))))) =>
% 5.19/1.31 (in @ (ap @ Y1 @ Y2) @ nat)))))))))) @
% 5.19/1.31 (^[Y0 : $i]: (((n_eq @ '#sk12' @ Y0) => (n_eq @ Y0 @ '#sk12')))))),
% 5.19/1.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl176])).
% 5.19/1.31 thf(zip_derived_cl179, plain,
% 5.19/1.31 (~ (((!!) @ (^[Y0 : $i]:
% 5.19/1.31 (((is_of @ Y0 @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (in @ Y1 @
% 5.19/1.31 (d_Sep @
% 5.19/1.31 (power @
% 5.19/1.31 (d_Sigma @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y2 : $i]:
% 5.19/1.31 (lessis @ Y2 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset))))) @
% 5.19/1.31 (^[Y2 : $i]: (union @ nat)))) @
% 5.19/1.31 (^[Y2 : $i]:
% 5.19/1.31 (((!!) @ (^[Y3 : $i]:
% 5.19/1.31 (((in @ Y3 @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y4 : $i]:
% 5.19/1.31 (lessis @ Y4 @
% 5.19/1.31 (n_pl @
% 5.19/1.31 (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset)))))) =>
% 5.19/1.31 (in @ (ap @ Y2 @ Y3) @ nat))))))))))) =>
% 5.19/1.31 ((^[Y1 : $i]:
% 5.19/1.31 (((n_eq @ '#sk12' @ Y1) => (n_eq @ Y1 @ '#sk12')))) @
% 5.19/1.31 Y0))))))),
% 5.19/1.31 inference('rw_clause', [status(thm)], [zip_derived_cl178, '6'])).
% 5.19/1.31 thf(zip_derived_cl180, plain,
% 5.19/1.31 (~ (((!!) @ (^[Y0 : $i]:
% 5.19/1.31 (((is_of @ Y0 @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (in @ Y1 @
% 5.19/1.31 (d_Sep @
% 5.19/1.31 (power @
% 5.19/1.31 (d_Sigma @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y2 : $i]:
% 5.19/1.31 (lessis @ Y2 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset))))) @
% 5.19/1.31 (^[Y2 : $i]: (union @ nat)))) @
% 5.19/1.31 (^[Y2 : $i]:
% 5.19/1.31 (((!!) @ (^[Y3 : $i]:
% 5.19/1.31 (((in @ Y3 @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y4 : $i]:
% 5.19/1.31 (lessis @ Y4 @
% 5.19/1.31 (n_pl @
% 5.19/1.31 (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset)))))) =>
% 5.19/1.31 (in @ (ap @ Y2 @ Y3) @ nat))))))))))) =>
% 5.19/1.31 (((n_eq @ '#sk12' @ Y0) => (n_eq @ Y0 @ '#sk12'))))))))),
% 5.19/1.31 inference('ho_norm', [status(thm)], [zip_derived_cl179])).
% 5.19/1.31 thf(zip_derived_cl181, plain,
% 5.19/1.31 (~ (((is_of @ '#sk13' @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (in @ Y0 @
% 5.19/1.31 (d_Sep @
% 5.19/1.31 (power @
% 5.19/1.31 (d_Sigma @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (lessis @ Y1 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 5.19/1.31 (^[Y1 : $i]: (union @ nat)))) @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (((!!) @ (^[Y2 : $i]:
% 5.19/1.31 (((in @ Y2 @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y3 : $i]:
% 5.19/1.31 (lessis @ Y3 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset)))))) =>
% 5.19/1.31 (in @ (ap @ Y1 @ Y2) @ nat))))))))))) =>
% 5.19/1.31 (((n_eq @ '#sk12' @ '#sk13') => (n_eq @ '#sk13' @ '#sk12')))))),
% 5.19/1.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl180])).
% 5.19/1.31 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))).
% 5.19/1.31 thf('7', plain,
% 5.19/1.31 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )),
% 5.19/1.31 define([status(thm)])).
% 5.19/1.31 thf(def_n_is, axiom,(( n_is @ (X0)@ (X1)) = ((e_is @ nat @ X0 @ X1)))).
% 5.19/1.31 thf('8', plain,
% 5.19/1.31 (![X1:$i,X0:$i]: ( ( n_is @ X0 @ X1 ) = ( e_is @ nat @ X0 @ X1 ) )),
% 5.19/1.31 define([status(thm)])).
% 5.19/1.31 thf(def_outn, axiom,(( outn @ (X0)@ (X1)) =
% 5.19/1.31 ((out @ nat @ (^[Y0 : $i]: (lessis @ Y0 @ X0)) @ X1)))).
% 5.19/1.31 thf('9', plain,
% 5.19/1.31 (![X1:$i,X0:$i]:
% 5.19/1.31 ( ( outn @ X0 @ X1 ) =
% 5.19/1.31 ( out @ nat @ ( ^[V_1:$i]: ( lessis @ V_1 @ X0 ) ) @ X1 ) )),
% 5.19/1.31 define([status(thm)])).
% 5.19/1.31 thf(def_n_1t, axiom,(( n_1t ) = ((outn @ n_2 @ n_1)))).
% 5.19/1.31 thf('10', plain, (( n_1t ) = ( outn @ n_2 @ n_1 )), define([status(thm)])).
% 5.19/1.31 thf(def_n_2t, axiom,(( n_2t ) = ((outn @ n_2 @ n_2)))).
% 5.19/1.31 thf('11', plain, (( n_2t ) = ( outn @ n_2 @ n_2 )), define([status(thm)])).
% 5.19/1.31 thf(def_first1, axiom,(( first1 @ (X1)@ (X0)) = ((ap @ X0 @ n_1t)))).
% 5.19/1.31 thf('12', plain,
% 5.19/1.31 (![X1:$i,X0:$i]: ( ( first1 @ X1 @ X0 ) = ( ap @ X0 @ n_1t ) )),
% 5.19/1.31 define([status(thm)])).
% 5.19/1.31 thf(def_second1, axiom,(( second1 @ (X1)@ (X0)) = ((ap @ X0 @ n_2t)))).
% 5.19/1.31 thf('13', plain,
% 5.19/1.31 (![X1:$i,X0:$i]: ( ( second1 @ X1 @ X0 ) = ( ap @ X0 @ n_2t ) )),
% 5.19/1.31 define([status(thm)])).
% 5.19/1.31 thf(def_num, axiom,(( num @ (X0)) = ((first1 @ nat @ X0)))).
% 5.19/1.31 thf('14', plain, (![X0:$i]: ( ( num @ X0 ) = ( first1 @ nat @ X0 ) )),
% 5.19/1.31 define([status(thm)])).
% 5.19/1.31 thf(def_den, axiom,(( den @ (X0)) = ((second1 @ nat @ X0)))).
% 5.19/1.31 thf('15', plain, (![X0:$i]: ( ( den @ X0 ) = ( second1 @ nat @ X0 ) )),
% 5.19/1.31 define([status(thm)])).
% 5.19/1.31 thf(def_n_eq, axiom,(( n_eq @ (X0)@ (X1)) =
% 5.19/1.31 ((n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 5.19/1.31 (n_ts @ (num @ X1) @ (den @ X0)))))).
% 5.19/1.31 thf('16', plain,
% 5.19/1.31 (![X1:$i,X0:$i]:
% 5.19/1.31 ( ( n_eq @ X0 @ X1 ) =
% 5.19/1.31 ( n_is @
% 5.19/1.31 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 5.19/1.31 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )),
% 5.19/1.31 define([status(thm)])).
% 5.19/1.31 thf(zip_derived_cl182, plain,
% 5.19/1.31 (~ (((is_of @ '#sk13' @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (in @ Y0 @
% 5.19/1.31 (d_Sep @
% 5.19/1.31 (power @
% 5.19/1.31 (d_Sigma @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (lessis @ Y1 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 5.19/1.31 (^[Y1 : $i]: (union @ nat)))) @
% 5.19/1.31 (^[Y1 : $i]:
% 5.19/1.31 (((!!) @ (^[Y2 : $i]:
% 5.19/1.31 (((in @ Y2 @
% 5.19/1.31 (d_Sep @ nat @
% 5.19/1.31 (^[Y3 : $i]:
% 5.19/1.31 (lessis @ Y3 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @
% 5.19/1.31 (ordsucc @ emptyset)))))) =>
% 5.19/1.31 (in @ (ap @ Y1 @ Y2) @ nat))))))))))) =>
% 5.19/1.31 (((((n_ts @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) =
% 5.19/1.31 (n_ts @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))) =>
% 5.19/1.31 (((n_ts @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) =
% 5.19/1.31 (n_ts @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))))))))),
% 5.19/1.31 inference('rw', [status(thm)],
% 5.19/1.31 [zip_derived_cl181, '7', '7', '8', '8', '1', '9', '9', '3',
% 5.19/1.31 '10', '11', '12', '12', '13', '13', '14', '14', '15', '15',
% 5.19/1.31 '16', '16'])).
% 5.19/1.31 thf(zip_derived_cl184, plain,
% 5.19/1.31 (~ (((((n_ts @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) =
% 5.19/1.31 (n_ts @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))) =>
% 5.19/1.31 (((n_ts @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) =
% 5.19/1.31 (n_ts @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))))))),
% 5.19/1.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl182])).
% 5.19/1.31 thf(zip_derived_cl185, plain,
% 5.19/1.31 ( (((n_ts @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) =
% 5.19/1.31 (n_ts @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))))),
% 5.19/1.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl184])).
% 5.19/1.31 thf(zip_derived_cl187, plain,
% 5.19/1.31 (((n_ts @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))
% 5.19/1.31 = (n_ts @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))),
% 5.19/1.31 inference('simplify nested equalities', [status(thm)],
% 5.19/1.31 [zip_derived_cl185])).
% 5.19/1.31 thf(zip_derived_cl186, plain,
% 5.19/1.31 (~ (((n_ts @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) =
% 5.19/1.31 (n_ts @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))))),
% 5.19/1.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl184])).
% 5.19/1.31 thf(zip_derived_cl188, plain,
% 5.19/1.31 (((n_ts @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))
% 5.19/1.31 != (n_ts @
% 5.19/1.31 (ap @ '#sk12' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (ordsucc @ emptyset))) @
% 5.19/1.31 (ap @ '#sk13' @
% 5.19/1.31 (out @ nat @
% 5.19/1.31 (^[Y0 : $i]:
% 5.19/1.31 (lessis @ Y0 @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 5.19/1.31 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))),
% 5.19/1.31 inference('simplify nested equalities', [status(thm)],
% 5.19/1.31 [zip_derived_cl186])).
% 5.19/1.31 thf(zip_derived_cl825, plain, ($false),
% 5.19/1.31 inference('simplify_reflect-', [status(thm)],
% 5.19/1.31 [zip_derived_cl187, zip_derived_cl188])).
% 5.19/1.31
% 5.19/1.31 % SZS output end Refutation
% 5.19/1.31
% 5.19/1.31
% 5.19/1.31 % Terminating...
% 5.70/1.39 % Runner terminated.
% 5.70/1.40 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------