%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM642^4 : 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.iWv5LidZrw true
% Computer : n003.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 04:47:46 PM UTC 2025
% Result : Theorem 5.83s 1.38s
% Output : Refutation 5.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM642^4 : TPTP v9.2.0. Released v7.1.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.iWv5LidZrw true
% 0.13/0.34 % Computer : n003.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 : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 16:36:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.34 % Running in HO mode
% 0.52/0.64 % Total configuration time : 828
% 0.52/0.64 % Estimated wc time : 1656
% 0.52/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.54/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.54/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.54/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.54/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.54/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.54/0.77 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 5.83/1.38 % Solved by lams/40_b.comb.sh.
% 5.83/1.38 % done 79 iterations in 0.566s
% 5.83/1.38 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 5.83/1.38 % SZS output start Refutation
% 5.83/1.38 thf('#sk3_type', type, '#sk3': $i).
% 5.83/1.38 thf(nat_type, type, nat: $i).
% 5.83/1.38 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 5.83/1.38 thf(in_type, type, in: $i > $i > $o).
% 5.83/1.38 thf('#sk2_type', type, '#sk2': $i).
% 5.83/1.38 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 5.83/1.38 thf(ap_type, type, ap: $i > $i > $i).
% 5.83/1.38 thf(emptyset_type, type, emptyset: $i).
% 5.83/1.38 thf(d_Sing_type, type, d_Sing: $i > $i).
% 5.83/1.38 thf(n_is_type, type, n_is: $i > $i > $o).
% 5.83/1.38 thf(omega_type, type, omega: $i).
% 5.83/1.38 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 5.83/1.38 thf(binunion_type, type, binunion: $i > $i > $i).
% 5.83/1.38 thf(ordsucc_type, type, ordsucc: $i > $i).
% 5.83/1.38 thf(plus_type, type, plus: $i > $i).
% 5.83/1.38 thf(e_is_type, type, e_is: $i > $i > $i > $o).
% 5.83/1.38 thf(n_pl_type, type, n_pl: $i > $i > $i).
% 5.83/1.38 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 5.83/1.38 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 5.83/1.38 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 5.83/1.38 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 5.83/1.38 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 5.83/1.38 thf(satz4d, axiom,
% 5.83/1.38 (all_of @
% 5.83/1.38 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 5.83/1.38 ( ^[X0:$i]:
% 5.83/1.38 ( all_of @
% 5.83/1.38 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 5.83/1.38 ( ^[X1:$i]:
% 5.83/1.38 ( n_is @
% 5.83/1.38 ( n_pl @ ( ordsucc @ X0 ) @ X1 ) @
% 5.83/1.38 ( ordsucc @ ( n_pl @ X0 @ X1 ) ) ) ) ) ))).
% 5.83/1.38 thf(zip_derived_cl81, plain,
% 5.83/1.38 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 5.83/1.38 (^[Y0 : $i]:
% 5.83/1.38 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 5.83/1.38 (^[Y1 : $i]:
% 5.83/1.38 (n_is @ (n_pl @ (ordsucc @ Y0) @ Y1) @
% 5.83/1.38 (ordsucc @ (n_pl @ Y0 @ Y1)))))))),
% 5.83/1.38 inference('cnf', [status(esa)], [satz4d])).
% 5.83/1.38 thf(zip_derived_cl82, plain,
% 5.83/1.38 ( (all_of @ ((('#C') @ in @ nat)) @
% 5.83/1.38 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ ('#S') @
% 5.83/1.38 ((('#B') @ ((('#B') @ n_is)) @
% 5.83/1.38 ((('#B') @ n_pl @ ordsucc)))))) @
% 5.83/1.38 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl)))))))),
% 5.83/1.38 inference('lams2combs', [status(thm)], [zip_derived_cl81])).
% 5.83/1.38 thf(def_nat, axiom,(( nat ) =
% 5.83/1.38 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))).
% 5.83/1.38 thf('0', plain,
% 5.83/1.38 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
% 5.83/1.38 define([status(thm)])).
% 5.83/1.38 thf(zip_derived_cl174, plain,
% 5.83/1.38 ( (all_of @
% 5.83/1.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 5.83/1.38 ((('#B') @ (all_of @
% 5.83/1.38 ((('#C') @ in @
% 5.83/1.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ ('#S') @
% 5.83/1.38 ((('#B') @ ((('#B') @ n_is)) @
% 5.83/1.38 ((('#B') @ n_pl @ ordsucc)))))) @
% 5.83/1.38 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl)))))))),
% 5.83/1.38 inference('rw', [status(thm)], [zip_derived_cl82, '0'])).
% 5.83/1.38 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 5.83/1.38 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 5.83/1.38 thf('1', plain,
% 5.83/1.38 (![X0:( $i > $o ),X1:( $i > $o )]:
% 5.83/1.38 ( ( all_of @ X0 @ X1 ) <=>
% 5.83/1.38 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 5.83/1.38 inference('rw.lit', [status(esa)], [def_all_of])).
% 5.83/1.38 thf(zip_derived_cl175, plain,
% 5.83/1.38 ( (((!!) @ (^[Y0 : $i]:
% 5.83/1.38 (((is_of @ Y0 @
% 5.83/1.38 ((('#C') @ in @
% 5.83/1.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 5.83/1.38 ((('#B') @ (all_of @
% 5.83/1.38 ((('#C') @ in @
% 5.83/1.38 (d_Sep @ omega @
% 5.83/1.38 ((('#C') @ (!=) @ emptyset)))))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ ('#S') @
% 5.83/1.38 ((('#B') @ ((('#B') @ n_is)) @
% 5.83/1.38 ((('#B') @ n_pl @ ordsucc)))))) @
% 5.83/1.38 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl)))) @
% 5.83/1.38 Y0)))))))),
% 5.83/1.38 inference('rw_clause', [status(thm)], [zip_derived_cl174, '1'])).
% 5.83/1.38 thf(zip_derived_cl176, plain,
% 5.83/1.38 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 5.83/1.38 ((('#C') @ is_of @
% 5.83/1.38 ((('#C') @ in @
% 5.83/1.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 5.83/1.38 ((('#B') @ (all_of @
% 5.83/1.38 ((('#C') @ in @
% 5.83/1.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ ('#S') @
% 5.83/1.38 ((('#B') @ ((('#B') @ n_is)) @
% 5.83/1.38 ((('#B') @ n_pl @ ordsucc)))))) @
% 5.83/1.38 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl))))))))))),
% 5.83/1.38 inference('comb-normalize', [status(thm)], [zip_derived_cl175])).
% 5.83/1.38 thf(zip_derived_cl177, plain,
% 5.83/1.38 (![X2 : $i]:
% 5.83/1.38 (((is_of @ X2 @
% 5.83/1.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 5.83/1.38 (all_of @
% 5.83/1.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ n_is @ (n_pl @ (ordsucc @ X2)))) @
% 5.83/1.38 ((('#B') @ ordsucc @ (n_pl @ X2))))))))),
% 5.83/1.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl176])).
% 5.83/1.38 thf(def_is_of, axiom,(( is_of @ (X1)@ (X0)) = ((X0 @ X1)))).
% 5.83/1.38 thf('2', plain,
% 5.83/1.38 (![X0:( $i > $o ),X1:$i]: ( ( is_of @ X1 @ X0 ) = ( X0 @ X1 ) )),
% 5.83/1.38 define([status(thm)])).
% 5.83/1.38 thf(def_ordsucc, axiom,(( ordsucc @ (X0)) =
% 5.83/1.38 ((binunion @ X0 @ (d_Sing @ X0))))).
% 5.83/1.38 thf('3', plain,
% 5.83/1.38 (![X0:$i]: ( ( ordsucc @ X0 ) = ( binunion @ X0 @ ( d_Sing @ X0 ) ) )),
% 5.83/1.38 define([status(thm)])).
% 5.83/1.38 thf(zip_derived_cl178, plain,
% 5.83/1.38 (![X2 : $i]:
% 5.83/1.38 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 5.83/1.38 (all_of @
% 5.83/1.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ n_is @
% 5.83/1.38 (n_pl @ (binunion @ X2 @ (d_Sing @ X2))))) @
% 5.83/1.38 ((('#B') @ ordsucc @ (n_pl @ X2))))))))),
% 5.83/1.38 inference('rw', [status(thm)], [zip_derived_cl177, '2', '3'])).
% 5.83/1.38 thf(zip_derived_cl179, plain,
% 5.83/1.38 (![X2 : $i]:
% 5.83/1.38 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 5.83/1.38 | (all_of @
% 5.83/1.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ n_is @
% 5.83/1.38 (n_pl @ (binunion @ X2 @ (d_Sing @ X2))))) @
% 5.83/1.38 ((('#B') @ ordsucc @ (n_pl @ X2)))))))),
% 5.83/1.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl178])).
% 5.83/1.38 thf(zip_derived_cl180, plain,
% 5.83/1.38 (![X0 : $i]:
% 5.83/1.38 ( (((!!) @ (^[Y0 : $i]:
% 5.83/1.38 (((is_of @ Y0 @
% 5.83/1.38 ((('#C') @ in @
% 5.83/1.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 5.83/1.38 ((('#S') @ ((('#B') @ n_is @
% 5.83/1.38 (n_pl @ (binunion @ X0 @ (d_Sing @ X0))))) @
% 5.83/1.38 ((('#B') @ ordsucc @ (n_pl @ X0))) @ Y0)))))))
% 5.83/1.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 5.83/1.38 inference('rw_clause', [status(thm)], [zip_derived_cl179, '1'])).
% 5.83/1.38 thf(zip_derived_cl181, plain,
% 5.83/1.38 (![X0 : $i]:
% 5.83/1.38 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 5.83/1.38 ((('#C') @ is_of @
% 5.83/1.38 ((('#C') @ in @
% 5.83/1.38 (d_Sep @ omega @
% 5.83/1.38 ((('#C') @ (!=) @ emptyset))))))))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ n_is @
% 5.83/1.38 (n_pl @ (binunion @ X0 @ (d_Sing @ X0))))) @
% 5.83/1.38 ((('#B') @ ordsucc @ (n_pl @ X0)))))))))
% 5.83/1.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 5.83/1.38 inference('comb-normalize', [status(thm)], [zip_derived_cl180])).
% 5.83/1.38 thf(zip_derived_cl182, plain,
% 5.83/1.38 (![X0 : $i, X2 : $i]:
% 5.83/1.38 ( (((is_of @ X2 @
% 5.83/1.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 5.83/1.38 (n_is @ (n_pl @ (binunion @ X0 @ (d_Sing @ X0)) @ X2) @
% 5.83/1.38 (ordsucc @ (n_pl @ X0 @ X2)))))
% 5.83/1.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 5.83/1.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl181])).
% 5.83/1.38 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))).
% 5.83/1.38 thf('4', plain,
% 5.83/1.38 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )),
% 5.83/1.38 define([status(thm)])).
% 5.83/1.38 thf(def_n_is, axiom,(( n_is @ (X0)@ (X1)) = ((e_is @ nat @ X0 @ X1)))).
% 5.83/1.38 thf('5', plain,
% 5.83/1.38 (![X1:$i,X0:$i]: ( ( n_is @ X0 @ X1 ) = ( e_is @ nat @ X0 @ X1 ) )),
% 5.83/1.38 define([status(thm)])).
% 5.83/1.38 thf(def_n_pl, axiom,(( n_pl @ (X0)@ (X1)) = ((ap @ (plus @ X0) @ X1)))).
% 5.83/1.38 thf('6', plain,
% 5.83/1.38 (![X1:$i,X0:$i]: ( ( n_pl @ X0 @ X1 ) = ( ap @ ( plus @ X0 ) @ X1 ) )),
% 5.83/1.38 define([status(thm)])).
% 5.83/1.38 thf(zip_derived_cl183, plain,
% 5.83/1.38 (![X0 : $i, X2 : $i]:
% 5.83/1.38 ( (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 5.83/1.38 (((ap @ (plus @ (binunion @ X0 @ (d_Sing @ X0))) @ X2) =
% 5.83/1.38 (binunion @ (ap @ (plus @ X0) @ X2) @
% 5.83/1.38 (d_Sing @ (ap @ (plus @ X0) @ X2)))))))
% 5.83/1.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 5.83/1.38 inference('rw', [status(thm)],
% 5.83/1.38 [zip_derived_cl182, '2', '3', '4', '0', '5', '6', '6'])).
% 5.83/1.38 thf(zip_derived_cl184, plain,
% 5.83/1.38 (![X0 : $i, X2 : $i]:
% 5.83/1.38 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 5.83/1.38 | (((ap @ (plus @ (binunion @ X0 @ (d_Sing @ X0))) @ X2) =
% 5.83/1.38 (binunion @ (ap @ (plus @ X0) @ X2) @
% 5.83/1.38 (d_Sing @ (ap @ (plus @ X0) @ X2)))))
% 5.83/1.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 5.83/1.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl183])).
% 5.83/1.38 thf(zip_derived_cl185, plain,
% 5.83/1.38 (![X0 : $i, X2 : $i]:
% 5.83/1.38 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 5.83/1.38 | ((ap @ (plus @ (binunion @ X0 @ (d_Sing @ X0))) @ X2)
% 5.83/1.38 = (binunion @ (ap @ (plus @ X0) @ X2) @
% 5.83/1.38 (d_Sing @ (ap @ (plus @ X0) @ X2))))
% 5.83/1.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 5.83/1.38 inference('simplify nested equalities', [status(thm)],
% 5.83/1.38 [zip_derived_cl184])).
% 5.83/1.38 thf(satz4h, conjecture,
% 5.83/1.38 (all_of @
% 5.83/1.38 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 5.83/1.38 ( ^[X0:$i]:
% 5.83/1.38 ( all_of @
% 5.83/1.38 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 5.83/1.38 ( ^[X1:$i]:
% 5.83/1.38 ( n_is @
% 5.83/1.38 ( ordsucc @ ( n_pl @ X0 @ X1 ) ) @
% 5.83/1.38 ( n_pl @ ( ordsucc @ X0 ) @ X1 ) ) ) ) ))).
% 5.83/1.38 thf(zf_stmt_0, negated_conjecture,
% 5.83/1.38 (~( all_of @
% 5.83/1.38 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 5.83/1.38 ( ^[X0:$i]:
% 5.83/1.38 ( all_of @
% 5.83/1.38 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 5.83/1.38 ( ^[X1:$i]:
% 5.83/1.38 ( n_is @
% 5.83/1.38 ( ordsucc @ ( n_pl @ X0 @ X1 ) ) @
% 5.83/1.38 ( n_pl @ ( ordsucc @ X0 ) @ X1 ) ) ) ) ) )),
% 5.83/1.38 inference('cnf.neg', [status(esa)], [satz4h])).
% 5.83/1.38 thf(zip_derived_cl89, plain,
% 5.83/1.38 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 5.83/1.38 (^[Y0 : $i]:
% 5.83/1.38 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 5.83/1.38 (^[Y1 : $i]:
% 5.83/1.38 (n_is @ (ordsucc @ (n_pl @ Y0 @ Y1)) @
% 5.83/1.38 (n_pl @ (ordsucc @ Y0) @ Y1))))))),
% 5.83/1.38 inference('cnf', [status(esa)], [zf_stmt_0])).
% 5.83/1.38 thf(zip_derived_cl90, plain,
% 5.83/1.38 (~ (all_of @ ((('#C') @ in @ nat)) @
% 5.83/1.38 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ ('#S') @
% 5.83/1.38 ((('#B') @ ((('#B') @ n_is)) @
% 5.83/1.38 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl)))))) @
% 5.83/1.38 ((('#B') @ n_pl @ ordsucc)))))))),
% 5.83/1.38 inference('lams2combs', [status(thm)], [zip_derived_cl89])).
% 5.83/1.38 thf(zip_derived_cl160, plain,
% 5.83/1.38 (~ (all_of @
% 5.83/1.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 5.83/1.38 ((('#B') @ (all_of @
% 5.83/1.38 ((('#C') @ in @
% 5.83/1.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ ('#S') @
% 5.83/1.38 ((('#B') @ ((('#B') @ n_is)) @
% 5.83/1.38 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl)))))) @
% 5.83/1.38 ((('#B') @ n_pl @ ordsucc)))))))),
% 5.83/1.38 inference('rw', [status(thm)], [zip_derived_cl90, '0'])).
% 5.83/1.38 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 5.83/1.38 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 5.83/1.38 thf('7', plain,
% 5.83/1.38 (![X0:( $i > $o ),X1:( $i > $o )]:
% 5.83/1.38 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 5.83/1.38 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 5.83/1.38 inference('rw.lit', [status(esa)], [def_all_of])).
% 5.83/1.38 thf(zip_derived_cl161, plain,
% 5.83/1.38 (~ (((!!) @ (^[Y0 : $i]:
% 5.83/1.38 (((is_of @ Y0 @
% 5.83/1.38 ((('#C') @ in @
% 5.83/1.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 5.83/1.38 ((('#B') @ (all_of @
% 5.83/1.38 ((('#C') @ in @
% 5.83/1.38 (d_Sep @ omega @
% 5.83/1.38 ((('#C') @ (!=) @ emptyset)))))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ ('#S') @
% 5.83/1.38 ((('#B') @ ((('#B') @ n_is)) @
% 5.83/1.38 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl)))))) @
% 5.83/1.38 ((('#B') @ n_pl @ ordsucc)))) @
% 5.83/1.38 Y0)))))))),
% 5.83/1.38 inference('rw_clause', [status(thm)], [zip_derived_cl160, '7'])).
% 5.83/1.38 thf(zip_derived_cl162, plain,
% 5.83/1.38 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 5.83/1.38 ((('#C') @ is_of @
% 5.83/1.38 ((('#C') @ in @
% 5.83/1.38 (d_Sep @ omega @
% 5.83/1.38 ((('#C') @ (!=) @ emptyset))))))))) @
% 5.83/1.38 ((('#B') @ (all_of @
% 5.83/1.38 ((('#C') @ in @
% 5.83/1.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ ('#S') @
% 5.83/1.38 ((('#B') @ ((('#B') @ n_is)) @
% 5.83/1.38 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl)))))) @
% 5.83/1.38 ((('#B') @ n_pl @ ordsucc))))))))))),
% 5.83/1.38 inference('comb-normalize', [status(thm)], [zip_derived_cl161])).
% 5.83/1.38 thf(zip_derived_cl163, plain,
% 5.83/1.38 (~ (((is_of @ '#sk2' @
% 5.83/1.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 5.83/1.38 (all_of @
% 5.83/1.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ n_is @ ((('#B') @ ordsucc @ (n_pl @ '#sk2'))))) @
% 5.83/1.38 (n_pl @ (ordsucc @ '#sk2')))))))),
% 5.83/1.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl162])).
% 5.83/1.38 thf(zip_derived_cl164, plain,
% 5.83/1.38 (~ (((in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 5.83/1.38 (all_of @
% 5.83/1.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ n_is @ ((('#B') @ ordsucc @ (n_pl @ '#sk2'))))) @
% 5.83/1.38 (n_pl @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))))))))),
% 5.83/1.38 inference('rw', [status(thm)], [zip_derived_cl163, '2', '3'])).
% 5.83/1.38 thf(zip_derived_cl166, plain,
% 5.83/1.38 (~ (all_of @
% 5.83/1.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ n_is @ ((('#B') @ ordsucc @ (n_pl @ '#sk2'))))) @
% 5.83/1.38 (n_pl @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))))))),
% 5.83/1.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])).
% 5.83/1.38 thf(zip_derived_cl167, plain,
% 5.83/1.38 (~ (((!!) @ (^[Y0 : $i]:
% 5.83/1.38 (((is_of @ Y0 @
% 5.83/1.38 ((('#C') @ in @
% 5.83/1.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 5.83/1.38 ((('#S') @ ((('#B') @ n_is @
% 5.83/1.38 ((('#B') @ ordsucc @ (n_pl @ '#sk2'))))) @
% 5.83/1.38 (n_pl @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))) @ Y0)))))))),
% 5.83/1.38 inference('rw_clause', [status(thm)], [zip_derived_cl166, '7'])).
% 5.83/1.38 thf(zip_derived_cl168, plain,
% 5.83/1.38 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 5.83/1.38 ((('#C') @ is_of @
% 5.83/1.38 ((('#C') @ in @
% 5.83/1.38 (d_Sep @ omega @
% 5.83/1.38 ((('#C') @ (!=) @ emptyset))))))))) @
% 5.83/1.38 ((('#S') @ ((('#B') @ n_is @
% 5.83/1.38 ((('#B') @ ordsucc @ (n_pl @ '#sk2'))))) @
% 5.83/1.38 (n_pl @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')))))))))),
% 5.83/1.38 inference('comb-normalize', [status(thm)], [zip_derived_cl167])).
% 5.83/1.38 thf(zip_derived_cl169, plain,
% 5.83/1.38 (~ (((is_of @ '#sk3' @
% 5.83/1.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 5.83/1.38 (n_is @ (ordsucc @ (n_pl @ '#sk2' @ '#sk3')) @
% 5.83/1.38 (n_pl @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')) @ '#sk3'))))),
% 5.83/1.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl168])).
% 5.83/1.38 thf(zip_derived_cl170, plain,
% 5.83/1.38 (~ (((in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 5.83/1.38 (((binunion @ (ap @ (plus @ '#sk2') @ '#sk3') @
% 5.83/1.38 (d_Sing @ (ap @ (plus @ '#sk2') @ '#sk3'))) = (ap @
% 5.83/1.38 (plus @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))) @ '#sk3')))))),
% 5.83/1.38 inference('rw', [status(thm)],
% 5.83/1.38 [zip_derived_cl169, '2', '3', '4', '0', '5', '6', '6'])).
% 5.83/1.38 thf(zip_derived_cl172, plain,
% 5.83/1.38 (~ (((binunion @ (ap @ (plus @ '#sk2') @ '#sk3') @
% 5.83/1.38 (d_Sing @ (ap @ (plus @ '#sk2') @ '#sk3'))) = (ap @
% 5.83/1.38 (plus @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))) @ '#sk3')))),
% 5.83/1.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl170])).
% 5.83/1.38 thf(zip_derived_cl173, plain,
% 5.83/1.38 (((binunion @ (ap @ (plus @ '#sk2') @ '#sk3') @
% 5.83/1.38 (d_Sing @ (ap @ (plus @ '#sk2') @ '#sk3')))
% 5.83/1.38 != (ap @ (plus @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))) @ '#sk3'))),
% 5.83/1.38 inference('simplify nested equalities', [status(thm)],
% 5.83/1.38 [zip_derived_cl172])).
% 5.83/1.38 thf(zip_derived_cl840, plain,
% 5.83/1.38 ((((ap @ (plus @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))) @ '#sk3')
% 5.83/1.38 != (ap @ (plus @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))) @ '#sk3'))
% 5.83/1.38 | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 5.83/1.38 | ~ (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 5.83/1.38 inference('sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl173])).
% 5.83/1.38 thf(zip_derived_cl165, plain,
% 5.83/1.38 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 5.83/1.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])).
% 5.83/1.38 thf(zip_derived_cl171, plain,
% 5.83/1.38 ( (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 5.83/1.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl170])).
% 5.83/1.38 thf(zip_derived_cl885, plain,
% 5.83/1.38 (((ap @ (plus @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))) @ '#sk3')
% 5.83/1.38 != (ap @ (plus @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))) @ '#sk3'))),
% 5.83/1.38 inference('demod', [status(thm)],
% 5.83/1.38 [zip_derived_cl840, zip_derived_cl165, zip_derived_cl171])).
% 5.83/1.38 thf(zip_derived_cl886, plain, ($false),
% 5.83/1.38 inference('simplify', [status(thm)], [zip_derived_cl885])).
% 5.83/1.38
% 5.83/1.38 % SZS output end Refutation
% 5.83/1.38
% 5.83/1.38
% 5.83/1.38 % Terminating...
% 6.31/1.49 % Runner terminated.
% 6.31/1.50 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------