TSTP Solution File: NUM640^4 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM640^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.rV0mQbAFbh true
% Computer : n004.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 Aug 31 12:42:59 EDT 2023
% Result : Theorem 8.34s 1.66s
% Output : Refutation 8.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM640^4 : TPTP v8.1.2. Released v7.1.0.
% 0.13/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.rV0mQbAFbh true
% 0.13/0.34 % Computer : n004.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 : Fri Aug 25 16:06:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.21/0.62 % Total configuration time : 828
% 0.21/0.62 % Estimated wc time : 1656
% 0.21/0.62 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 8.34/1.66 % Solved by lams/40_b.comb.sh.
% 8.34/1.66 % done 141 iterations in 0.864s
% 8.34/1.66 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 8.34/1.66 % SZS output start Refutation
% 8.34/1.66 thf(nat_type, type, nat: $i).
% 8.34/1.66 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 8.34/1.66 thf(in_type, type, in: $i > $i > $o).
% 8.34/1.66 thf('#sk3_type', type, '#sk3': $i).
% 8.34/1.66 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 8.34/1.66 thf(ap_type, type, ap: $i > $i > $i).
% 8.34/1.66 thf(emptyset_type, type, emptyset: $i).
% 8.34/1.66 thf(d_Sing_type, type, d_Sing: $i > $i).
% 8.34/1.66 thf(n_is_type, type, n_is: $i > $i > $o).
% 8.34/1.66 thf(omega_type, type, omega: $i).
% 8.34/1.66 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 8.34/1.66 thf(binunion_type, type, binunion: $i > $i > $i).
% 8.34/1.66 thf(ordsucc_type, type, ordsucc: $i > $i).
% 8.34/1.66 thf(plus_type, type, plus: $i > $i).
% 8.34/1.66 thf('#sk2_type', type, '#sk2': $i).
% 8.34/1.66 thf(e_is_type, type, e_is: $i > $i > $i > $o).
% 8.34/1.66 thf(n_pl_type, type, n_pl: $i > $i > $i).
% 8.34/1.66 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 8.34/1.66 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 8.34/1.66 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 8.34/1.66 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 8.34/1.66 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 8.34/1.66 thf(satz4b, axiom,
% 8.34/1.66 (all_of @
% 8.34/1.66 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 8.34/1.66 ( ^[X0:$i]:
% 8.34/1.66 ( all_of @
% 8.34/1.66 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 8.34/1.66 ( ^[X1:$i]:
% 8.34/1.66 ( n_is @
% 8.34/1.66 ( n_pl @ X0 @ ( ordsucc @ X1 ) ) @
% 8.34/1.66 ( ordsucc @ ( n_pl @ X0 @ X1 ) ) ) ) ) ))).
% 8.34/1.66 thf(zip_derived_cl77, plain,
% 8.34/1.66 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 8.34/1.66 (^[Y0 : $i]:
% 8.34/1.66 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 8.34/1.66 (^[Y1 : $i]:
% 8.34/1.66 (n_is @ (n_pl @ Y0 @ (ordsucc @ Y1)) @
% 8.34/1.66 (ordsucc @ (n_pl @ Y0 @ Y1)))))))),
% 8.34/1.66 inference('cnf', [status(esa)], [satz4b])).
% 8.34/1.66 thf(zip_derived_cl78, plain,
% 8.34/1.66 ( (all_of @ ((('#C') @ in @ nat)) @
% 8.34/1.66 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ ('#S') @
% 8.34/1.66 ((('#B') @ ((('#B') @ n_is)) @
% 8.34/1.66 ((('#C') @ ((('#B') @ ('#B') @ n_pl)) @ ordsucc)))))) @
% 8.34/1.66 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl)))))))),
% 8.34/1.66 inference('lams2combs', [status(thm)], [zip_derived_cl77])).
% 8.34/1.66 thf(def_nat, axiom,(( nat ) =
% 8.34/1.66 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))).
% 8.34/1.66 thf('0', plain,
% 8.34/1.66 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
% 8.34/1.66 define([status(thm)])).
% 8.34/1.66 thf(zip_derived_cl239, plain,
% 8.34/1.66 ( (all_of @
% 8.34/1.66 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 8.34/1.66 ((('#B') @ (all_of @
% 8.34/1.66 ((('#C') @ in @
% 8.34/1.66 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ ('#S') @
% 8.34/1.66 ((('#B') @ ((('#B') @ n_is)) @
% 8.34/1.66 ((('#C') @ ((('#B') @ ('#B') @ n_pl)) @ ordsucc)))))) @
% 8.34/1.66 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl)))))))),
% 8.34/1.66 inference('rw', [status(thm)], [zip_derived_cl78, '0'])).
% 8.34/1.66 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 8.34/1.66 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 8.34/1.66 thf('1', plain,
% 8.34/1.66 (![X0:( $i > $o ),X1:( $i > $o )]:
% 8.34/1.66 ( ( all_of @ X0 @ X1 ) <=>
% 8.34/1.66 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 8.34/1.66 inference('rw.lit', [status(esa)], [def_all_of])).
% 8.34/1.66 thf(zip_derived_cl240, plain,
% 8.34/1.66 ( (((!!) @ (^[Y0 : $i]:
% 8.34/1.66 (((is_of @ Y0 @
% 8.34/1.66 ((('#C') @ in @
% 8.34/1.66 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 8.34/1.66 ((('#B') @ (all_of @
% 8.34/1.66 ((('#C') @ in @
% 8.34/1.66 (d_Sep @ omega @
% 8.34/1.66 ((('#C') @ (!=) @ emptyset)))))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ ('#S') @
% 8.34/1.66 ((('#B') @ ((('#B') @ n_is)) @
% 8.34/1.66 ((('#C') @ ((('#B') @ ('#B') @ n_pl)) @
% 8.34/1.66 ordsucc)))))) @
% 8.34/1.66 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl)))) @
% 8.34/1.66 Y0)))))))),
% 8.34/1.66 inference('rw_clause', [status(thm)], [zip_derived_cl239, '1'])).
% 8.34/1.66 thf(zip_derived_cl241, plain,
% 8.34/1.66 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 8.34/1.66 ((('#C') @ is_of @
% 8.34/1.66 ((('#C') @ in @
% 8.34/1.66 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 8.34/1.66 ((('#B') @ (all_of @
% 8.34/1.66 ((('#C') @ in @
% 8.34/1.66 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ ('#S') @
% 8.34/1.66 ((('#B') @ ((('#B') @ n_is)) @
% 8.34/1.66 ((('#C') @ ((('#B') @ ('#B') @ n_pl)) @
% 8.34/1.66 ordsucc)))))) @
% 8.34/1.66 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl))))))))))),
% 8.34/1.66 inference('comb-normalize', [status(thm)], [zip_derived_cl240])).
% 8.34/1.66 thf(zip_derived_cl242, plain,
% 8.34/1.66 (![X2 : $i]:
% 8.34/1.66 (((is_of @ X2 @
% 8.34/1.66 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 8.34/1.66 (all_of @
% 8.34/1.66 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ n_is @ ((('#B') @ (n_pl @ X2) @ ordsucc)))) @
% 8.34/1.66 ((('#B') @ ordsucc @ (n_pl @ X2))))))))),
% 8.34/1.66 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl241])).
% 8.34/1.66 thf(def_is_of, axiom,(( is_of @ (X1)@ (X0)) = ((X0 @ X1)))).
% 8.34/1.66 thf('2', plain,
% 8.34/1.66 (![X0:( $i > $o ),X1:$i]: ( ( is_of @ X1 @ X0 ) = ( X0 @ X1 ) )),
% 8.34/1.66 define([status(thm)])).
% 8.34/1.66 thf(zip_derived_cl243, plain,
% 8.34/1.66 (![X2 : $i]:
% 8.34/1.66 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 8.34/1.66 (all_of @
% 8.34/1.66 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ n_is @ ((('#B') @ (n_pl @ X2) @ ordsucc)))) @
% 8.34/1.66 ((('#B') @ ordsucc @ (n_pl @ X2))))))))),
% 8.34/1.66 inference('rw', [status(thm)], [zip_derived_cl242, '2'])).
% 8.34/1.66 thf(zip_derived_cl244, plain,
% 8.34/1.66 (![X2 : $i]:
% 8.34/1.66 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 8.34/1.66 | (all_of @
% 8.34/1.66 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ n_is @ ((('#B') @ (n_pl @ X2) @ ordsucc)))) @
% 8.34/1.66 ((('#B') @ ordsucc @ (n_pl @ X2)))))))),
% 8.34/1.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl243])).
% 8.34/1.66 thf(zip_derived_cl245, plain,
% 8.34/1.66 (![X0 : $i]:
% 8.34/1.66 ( (((!!) @ (^[Y0 : $i]:
% 8.34/1.66 (((is_of @ Y0 @
% 8.34/1.66 ((('#C') @ in @
% 8.34/1.66 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 8.34/1.66 ((('#S') @ ((('#B') @ n_is @
% 8.34/1.66 ((('#B') @ (n_pl @ X0) @ ordsucc)))) @
% 8.34/1.66 ((('#B') @ ordsucc @ (n_pl @ X0))) @ Y0)))))))
% 8.34/1.66 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 8.34/1.66 inference('rw_clause', [status(thm)], [zip_derived_cl244, '1'])).
% 8.34/1.66 thf(zip_derived_cl246, plain,
% 8.34/1.66 (![X0 : $i]:
% 8.34/1.66 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 8.34/1.66 ((('#C') @ is_of @
% 8.34/1.66 ((('#C') @ in @
% 8.34/1.66 (d_Sep @ omega @
% 8.34/1.66 ((('#C') @ (!=) @ emptyset))))))))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ n_is @
% 8.34/1.66 ((('#B') @ (n_pl @ X0) @ ordsucc)))) @
% 8.34/1.66 ((('#B') @ ordsucc @ (n_pl @ X0)))))))))
% 8.34/1.66 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 8.34/1.66 inference('comb-normalize', [status(thm)], [zip_derived_cl245])).
% 8.34/1.66 thf(zip_derived_cl247, plain,
% 8.34/1.66 (![X0 : $i, X2 : $i]:
% 8.34/1.66 ( (((is_of @ X2 @
% 8.34/1.66 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 8.34/1.66 (n_is @ (n_pl @ X0 @ (ordsucc @ X2)) @
% 8.34/1.66 (ordsucc @ (n_pl @ X0 @ X2)))))
% 8.34/1.66 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 8.34/1.66 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl246])).
% 8.34/1.66 thf(def_ordsucc, axiom,(( ordsucc @ (X0)) =
% 8.34/1.66 ((binunion @ X0 @ (d_Sing @ X0))))).
% 8.34/1.66 thf('3', plain,
% 8.34/1.66 (![X0:$i]: ( ( ordsucc @ X0 ) = ( binunion @ X0 @ ( d_Sing @ X0 ) ) )),
% 8.34/1.66 define([status(thm)])).
% 8.34/1.66 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))).
% 8.34/1.66 thf('4', plain,
% 8.34/1.66 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )),
% 8.34/1.66 define([status(thm)])).
% 8.34/1.66 thf(def_n_is, axiom,(( n_is @ (X0)@ (X1)) = ((e_is @ nat @ X0 @ X1)))).
% 8.34/1.66 thf('5', plain,
% 8.34/1.66 (![X1:$i,X0:$i]: ( ( n_is @ X0 @ X1 ) = ( e_is @ nat @ X0 @ X1 ) )),
% 8.34/1.66 define([status(thm)])).
% 8.34/1.66 thf(def_n_pl, axiom,(( n_pl @ (X0)@ (X1)) = ((ap @ (plus @ X0) @ X1)))).
% 8.34/1.66 thf('6', plain,
% 8.34/1.66 (![X1:$i,X0:$i]: ( ( n_pl @ X0 @ X1 ) = ( ap @ ( plus @ X0 ) @ X1 ) )),
% 8.34/1.66 define([status(thm)])).
% 8.34/1.66 thf(zip_derived_cl248, plain,
% 8.34/1.66 (![X0 : $i, X2 : $i]:
% 8.34/1.66 ( (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 8.34/1.66 (((ap @ (plus @ X0) @ (binunion @ X2 @ (d_Sing @ X2))) =
% 8.34/1.66 (binunion @ (ap @ (plus @ X0) @ X2) @
% 8.34/1.66 (d_Sing @ (ap @ (plus @ X0) @ X2)))))))
% 8.34/1.66 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 8.34/1.66 inference('rw', [status(thm)],
% 8.34/1.66 [zip_derived_cl247, '2', '3', '3', '4', '0', '5', '6', '6'])).
% 8.34/1.66 thf(zip_derived_cl249, plain,
% 8.34/1.66 (![X0 : $i, X2 : $i]:
% 8.34/1.66 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 8.34/1.66 | (((ap @ (plus @ X0) @ (binunion @ X2 @ (d_Sing @ X2))) =
% 8.34/1.66 (binunion @ (ap @ (plus @ X0) @ X2) @
% 8.34/1.66 (d_Sing @ (ap @ (plus @ X0) @ X2)))))
% 8.34/1.66 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 8.34/1.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl248])).
% 8.34/1.66 thf(zip_derived_cl250, plain,
% 8.34/1.66 (![X0 : $i, X2 : $i]:
% 8.34/1.66 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 8.34/1.66 | ((ap @ (plus @ X0) @ (binunion @ X2 @ (d_Sing @ X2)))
% 8.34/1.66 = (binunion @ (ap @ (plus @ X0) @ X2) @
% 8.34/1.66 (d_Sing @ (ap @ (plus @ X0) @ X2))))
% 8.34/1.66 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 8.34/1.66 inference('simplify nested equalities', [status(thm)],
% 8.34/1.66 [zip_derived_cl249])).
% 8.34/1.66 thf(satz4f, conjecture,
% 8.34/1.66 (all_of @
% 8.34/1.66 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 8.34/1.66 ( ^[X0:$i]:
% 8.34/1.66 ( all_of @
% 8.34/1.66 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 8.34/1.66 ( ^[X1:$i]:
% 8.34/1.66 ( n_is @
% 8.34/1.66 ( ordsucc @ ( n_pl @ X0 @ X1 ) ) @
% 8.34/1.66 ( n_pl @ X0 @ ( ordsucc @ X1 ) ) ) ) ) ))).
% 8.34/1.66 thf(zf_stmt_0, negated_conjecture,
% 8.34/1.66 (~( all_of @
% 8.34/1.66 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 8.34/1.66 ( ^[X0:$i]:
% 8.34/1.66 ( all_of @
% 8.34/1.66 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 8.34/1.66 ( ^[X1:$i]:
% 8.34/1.66 ( n_is @
% 8.34/1.66 ( ordsucc @ ( n_pl @ X0 @ X1 ) ) @
% 8.34/1.66 ( n_pl @ X0 @ ( ordsucc @ X1 ) ) ) ) ) ) )),
% 8.34/1.66 inference('cnf.neg', [status(esa)], [satz4f])).
% 8.34/1.66 thf(zip_derived_cl85, plain,
% 8.34/1.66 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 8.34/1.66 (^[Y0 : $i]:
% 8.34/1.66 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 8.34/1.66 (^[Y1 : $i]:
% 8.34/1.66 (n_is @ (ordsucc @ (n_pl @ Y0 @ Y1)) @
% 8.34/1.66 (n_pl @ Y0 @ (ordsucc @ Y1)))))))),
% 8.34/1.66 inference('cnf', [status(esa)], [zf_stmt_0])).
% 8.34/1.66 thf(zip_derived_cl86, plain,
% 8.34/1.66 (~ (all_of @ ((('#C') @ in @ nat)) @
% 8.34/1.66 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ ('#S') @
% 8.34/1.66 ((('#B') @ ((('#B') @ n_is)) @
% 8.34/1.66 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl)))))) @
% 8.34/1.66 ((('#C') @ ((('#B') @ ('#B') @ n_pl)) @ ordsucc)))))))),
% 8.34/1.66 inference('lams2combs', [status(thm)], [zip_derived_cl85])).
% 8.34/1.66 thf(zip_derived_cl149, plain,
% 8.34/1.66 (~ (all_of @
% 8.34/1.66 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 8.34/1.66 ((('#B') @ (all_of @
% 8.34/1.66 ((('#C') @ in @
% 8.34/1.66 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ ('#S') @
% 8.34/1.66 ((('#B') @ ((('#B') @ n_is)) @
% 8.34/1.66 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl)))))) @
% 8.34/1.66 ((('#C') @ ((('#B') @ ('#B') @ n_pl)) @ ordsucc)))))))),
% 8.34/1.66 inference('rw', [status(thm)], [zip_derived_cl86, '0'])).
% 8.34/1.66 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 8.34/1.66 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 8.34/1.66 thf('7', plain,
% 8.34/1.66 (![X0:( $i > $o ),X1:( $i > $o )]:
% 8.34/1.66 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 8.34/1.66 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 8.34/1.66 inference('rw.lit', [status(esa)], [def_all_of])).
% 8.34/1.66 thf(zip_derived_cl150, plain,
% 8.34/1.66 (~ (((!!) @ (^[Y0 : $i]:
% 8.34/1.66 (((is_of @ Y0 @
% 8.34/1.66 ((('#C') @ in @
% 8.34/1.66 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 8.34/1.66 ((('#B') @ (all_of @
% 8.34/1.66 ((('#C') @ in @
% 8.34/1.66 (d_Sep @ omega @
% 8.34/1.66 ((('#C') @ (!=) @ emptyset)))))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ ('#S') @
% 8.34/1.66 ((('#B') @ ((('#B') @ n_is)) @
% 8.34/1.66 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl)))))) @
% 8.34/1.66 ((('#C') @ ((('#B') @ ('#B') @ n_pl)) @ ordsucc)))) @
% 8.34/1.66 Y0)))))))),
% 8.34/1.66 inference('rw_clause', [status(thm)], [zip_derived_cl149, '7'])).
% 8.34/1.66 thf(zip_derived_cl151, plain,
% 8.34/1.66 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 8.34/1.66 ((('#C') @ is_of @
% 8.34/1.66 ((('#C') @ in @
% 8.34/1.66 (d_Sep @ omega @
% 8.34/1.66 ((('#C') @ (!=) @ emptyset))))))))) @
% 8.34/1.66 ((('#B') @ (all_of @
% 8.34/1.66 ((('#C') @ in @
% 8.34/1.66 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ ('#S') @
% 8.34/1.66 ((('#B') @ ((('#B') @ n_is)) @
% 8.34/1.66 ((('#B') @ ((('#B') @ ordsucc)) @ n_pl)))))) @
% 8.34/1.66 ((('#C') @ ((('#B') @ ('#B') @ n_pl)) @ ordsucc))))))))))),
% 8.34/1.66 inference('comb-normalize', [status(thm)], [zip_derived_cl150])).
% 8.34/1.66 thf(zip_derived_cl152, plain,
% 8.34/1.66 (~ (((is_of @ '#sk2' @
% 8.34/1.66 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 8.34/1.66 (all_of @
% 8.34/1.66 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ n_is @ ((('#B') @ ordsucc @ (n_pl @ '#sk2'))))) @
% 8.34/1.66 ((('#B') @ (n_pl @ '#sk2') @ ordsucc)))))))),
% 8.34/1.66 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl151])).
% 8.34/1.66 thf(zip_derived_cl153, plain,
% 8.34/1.66 (~ (((in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 8.34/1.66 (all_of @
% 8.34/1.66 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ n_is @ ((('#B') @ ordsucc @ (n_pl @ '#sk2'))))) @
% 8.34/1.66 ((('#B') @ (n_pl @ '#sk2') @ ordsucc)))))))),
% 8.34/1.66 inference('rw', [status(thm)], [zip_derived_cl152, '2'])).
% 8.34/1.66 thf(zip_derived_cl155, plain,
% 8.34/1.66 (~ (all_of @
% 8.34/1.66 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ n_is @ ((('#B') @ ordsucc @ (n_pl @ '#sk2'))))) @
% 8.34/1.66 ((('#B') @ (n_pl @ '#sk2') @ ordsucc)))))),
% 8.34/1.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl153])).
% 8.34/1.66 thf(zip_derived_cl156, plain,
% 8.34/1.66 (~ (((!!) @ (^[Y0 : $i]:
% 8.34/1.66 (((is_of @ Y0 @
% 8.34/1.66 ((('#C') @ in @
% 8.34/1.66 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 8.34/1.66 ((('#S') @ ((('#B') @ n_is @
% 8.34/1.66 ((('#B') @ ordsucc @ (n_pl @ '#sk2'))))) @
% 8.34/1.66 ((('#B') @ (n_pl @ '#sk2') @ ordsucc)) @ Y0)))))))),
% 8.34/1.66 inference('rw_clause', [status(thm)], [zip_derived_cl155, '7'])).
% 8.34/1.66 thf(zip_derived_cl157, plain,
% 8.34/1.66 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 8.34/1.66 ((('#C') @ is_of @
% 8.34/1.66 ((('#C') @ in @
% 8.34/1.66 (d_Sep @ omega @
% 8.34/1.66 ((('#C') @ (!=) @ emptyset))))))))) @
% 8.34/1.66 ((('#S') @ ((('#B') @ n_is @
% 8.34/1.66 ((('#B') @ ordsucc @ (n_pl @ '#sk2'))))) @
% 8.34/1.66 ((('#B') @ (n_pl @ '#sk2') @ ordsucc))))))))),
% 8.34/1.66 inference('comb-normalize', [status(thm)], [zip_derived_cl156])).
% 8.34/1.66 thf(zip_derived_cl158, plain,
% 8.34/1.66 (~ (((is_of @ '#sk3' @
% 8.34/1.66 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 8.34/1.66 (n_is @ (ordsucc @ (n_pl @ '#sk2' @ '#sk3')) @
% 8.34/1.66 (n_pl @ '#sk2' @ (ordsucc @ '#sk3')))))),
% 8.34/1.66 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl157])).
% 8.34/1.66 thf(zip_derived_cl159, plain,
% 8.34/1.66 (~ (((in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 8.34/1.66 (((binunion @ (ap @ (plus @ '#sk2') @ '#sk3') @
% 8.34/1.66 (d_Sing @ (ap @ (plus @ '#sk2') @ '#sk3'))) = (ap @
% 8.34/1.66 (plus @ '#sk2') @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')))))))),
% 8.34/1.66 inference('rw', [status(thm)],
% 8.34/1.66 [zip_derived_cl158, '2', '3', '3', '4', '0', '5', '6', '6'])).
% 8.34/1.66 thf(zip_derived_cl161, plain,
% 8.34/1.66 (~ (((binunion @ (ap @ (plus @ '#sk2') @ '#sk3') @
% 8.34/1.66 (d_Sing @ (ap @ (plus @ '#sk2') @ '#sk3'))) = (ap @
% 8.34/1.66 (plus @ '#sk2') @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')))))),
% 8.34/1.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])).
% 8.34/1.66 thf(zip_derived_cl162, plain,
% 8.34/1.66 (((binunion @ (ap @ (plus @ '#sk2') @ '#sk3') @
% 8.34/1.66 (d_Sing @ (ap @ (plus @ '#sk2') @ '#sk3')))
% 8.34/1.66 != (ap @ (plus @ '#sk2') @ (binunion @ '#sk3' @ (d_Sing @ '#sk3'))))),
% 8.34/1.66 inference('simplify nested equalities', [status(thm)],
% 8.34/1.66 [zip_derived_cl161])).
% 8.34/1.66 thf(zip_derived_cl1609, plain,
% 8.34/1.66 ((((ap @ (plus @ '#sk2') @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')))
% 8.34/1.66 != (ap @ (plus @ '#sk2') @ (binunion @ '#sk3' @ (d_Sing @ '#sk3'))))
% 8.34/1.66 | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 8.34/1.66 | ~ (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 8.34/1.66 inference('sup-', [status(thm)], [zip_derived_cl250, zip_derived_cl162])).
% 8.34/1.66 thf(zip_derived_cl154, plain,
% 8.34/1.66 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 8.34/1.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl153])).
% 8.34/1.66 thf(zip_derived_cl160, plain,
% 8.34/1.66 ( (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 8.34/1.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])).
% 8.34/1.66 thf(zip_derived_cl1669, plain,
% 8.34/1.66 (((ap @ (plus @ '#sk2') @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')))
% 8.34/1.66 != (ap @ (plus @ '#sk2') @ (binunion @ '#sk3' @ (d_Sing @ '#sk3'))))),
% 8.34/1.66 inference('demod', [status(thm)],
% 8.34/1.66 [zip_derived_cl1609, zip_derived_cl154, zip_derived_cl160])).
% 8.34/1.66 thf(zip_derived_cl1670, plain, ($false),
% 8.34/1.66 inference('simplify', [status(thm)], [zip_derived_cl1669])).
% 8.34/1.66
% 8.34/1.66 % SZS output end Refutation
% 8.34/1.66
% 8.34/1.66
% 8.34/1.66 % Terminating...
% 8.63/1.75 % Runner terminated.
% 8.63/1.76 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------