%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : PHI002^2 : TPTP v9.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.xMra3f8LlS true
% Computer : n023.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 04:49:03 PM UTC 2025
% Result : Theorem 0.59s 0.94s
% Output : Refutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PHI002^2 : TPTP v9.2.0. Released v6.1.0.
% 0.03/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.xMra3f8LlS true
% 0.13/0.34 % Computer : n023.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 16:56:53 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
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.56/0.68 % Total configuration time : 828
% 0.56/0.68 % Estimated wc time : 1656
% 0.56/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.56/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.56/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.57/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.57/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.57/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.57/0.81 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 0.59/0.87 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 0.59/0.94 % Solved by lams/40_b.comb.sh.
% 0.59/0.94 % done 18 iterations in 0.121s
% 0.59/0.94 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.59/0.94 % SZS output start Refutation
% 0.59/0.94 thf(mu_type, type, mu: $tType).
% 0.59/0.94 thf(mdia_type, type, mdia: ($i > $o) > $i > $o).
% 0.59/0.94 thf(mexists_ind_type, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.59/0.94 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.59/0.94 thf(rel_type, type, rel: $i > $i > $o).
% 0.59/0.94 thf(positive_type, type, positive: (mu > $i > $o) > $i > $o).
% 0.59/0.94 thf(mnot_type, type, mnot: ($i > $o) > $i > $o).
% 0.59/0.94 thf(mforall_ind_type, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.59/0.94 thf(mbox_generic_type, type, mbox_generic: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.59/0.94 thf('#sk4_type', type, '#sk4': $i > (mu > $i > $o) > (mu > $i > $o) > mu).
% 0.59/0.94 thf(mdia_generic_type, type, mdia_generic: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.59/0.94 thf('#sk3_type', type, '#sk3': $i > (mu > $i > $o) > (mu > $i > $o) > $i).
% 0.59/0.94 thf(mequiv_type, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.59/0.94 thf(mforall_indset_type, type, mforall_indset: ((mu > $i > $o) > $i > $o) >
% 0.59/0.94 $i > $o).
% 0.59/0.94 thf(mvalid_type, type, mvalid: ($i > $o) > $o).
% 0.59/0.94 thf('#sk1_type', type, '#sk1': $i).
% 0.59/0.94 thf(mbox_type, type, mbox: ($i > $o) > $i > $o).
% 0.59/0.94 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.59/0.94 thf('#sk2_type', type, '#sk2': mu > $i > $o).
% 0.59/0.94 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 0.59/0.94 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 0.59/0.94 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 0.59/0.94 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 0.59/0.94 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 0.59/0.94 thf(axA1, axiom,
% 0.59/0.94 (mvalid @
% 0.59/0.94 ( mforall_indset @
% 0.59/0.94 ( ^[Phi:( mu > $i > $o )]:
% 0.59/0.94 ( mequiv @
% 0.59/0.94 ( positive @ ( ^[X:mu]: ( mnot @ ( Phi @ X ) ) ) ) @
% 0.59/0.94 ( mnot @ ( positive @ Phi ) ) ) ) ))).
% 0.59/0.94 thf(zip_derived_cl0, plain,
% 0.59/0.94 ( (mvalid @
% 0.59/0.94 (mforall_indset @
% 0.59/0.94 (^[Y0 : mu > $i > $o]:
% 0.59/0.94 (mequiv @ (positive @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))) @
% 0.59/0.94 (mnot @ (positive @ Y0))))))),
% 0.59/0.94 inference('cnf', [status(esa)], [axA1])).
% 0.59/0.94 thf(zip_derived_cl1, plain,
% 0.59/0.94 ( (mvalid @
% 0.59/0.94 (mforall_indset @
% 0.59/0.94 ((('#S') @ ((('#B') @ mequiv @
% 0.59/0.94 ((('#B') @ positive @ ((('#B') @ mnot)))))) @
% 0.59/0.94 ((('#B') @ mnot @ positive))))))),
% 0.59/0.94 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 0.59/0.94 thf(mvalid, axiom, (mvalid @ X0) =>
% 0.59/0.94 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) = ($true))).
% 0.59/0.94 thf('0', plain,
% 0.59/0.94 (![X0:( $i > $o )]: ( ( mvalid @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 ) ) )),
% 0.59/0.94 inference('rw.lit', [status(esa)], [mvalid])).
% 0.59/0.94 thf(zip_derived_cl23, plain,
% 0.59/0.94 ( (((!!) @ (^[Y0 : $i]:
% 0.59/0.94 (mforall_indset @
% 0.59/0.94 ((('#S') @ ((('#B') @ mequiv @
% 0.59/0.94 ((('#B') @ positive @ ((('#B') @ mnot)))))) @
% 0.59/0.94 ((('#B') @ mnot @ positive)))) @
% 0.59/0.94 Y0))))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl1, '0'])).
% 0.59/0.94 thf(zip_derived_cl24, plain,
% 0.59/0.94 ( (((!!) @ (mforall_indset @
% 0.59/0.94 ((('#S') @ ((('#B') @ mequiv @
% 0.59/0.94 ((('#B') @ positive @ ((('#B') @ mnot)))))) @
% 0.59/0.94 ((('#B') @ mnot @ positive)))))))),
% 0.59/0.94 inference('comb-normalize', [status(thm)], [zip_derived_cl23])).
% 0.59/0.94 thf(zip_derived_cl25, plain,
% 0.59/0.94 (![X2 : $i]:
% 0.59/0.94 (mforall_indset @
% 0.59/0.94 ((('#S') @ ((('#B') @ mequiv @
% 0.59/0.94 ((('#B') @ positive @ ((('#B') @ mnot)))))) @
% 0.59/0.94 ((('#B') @ mnot @ positive)))) @
% 0.59/0.94 X2)),
% 0.59/0.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl24])).
% 0.59/0.94 thf(mforall_indset, axiom, (mforall_indset @ X0 @ X1) =>
% 0.59/0.94 ((((!!) @ (^[Y0 : mu > $i > $o]: (X0 @ Y0 @ X1)))) = ($true))).
% 0.59/0.94 thf('1', plain,
% 0.59/0.94 (![X0:( ( mu > $i > $o ) > $i > $o ),X1:$i]:
% 0.59/0.94 ( ( mforall_indset @ X0 @ X1 ) <=>
% 0.59/0.94 ( ![X6:( mu > $i > $o )]: ( X0 @ X6 @ X1 ) ) )),
% 0.59/0.94 inference('rw.lit', [status(esa)], [mforall_indset])).
% 0.59/0.94 thf(zip_derived_cl26, plain,
% 0.59/0.94 (![X0 : $i]:
% 0.59/0.94 (((!!) @ (^[Y0 : mu > $i > $o]:
% 0.59/0.94 ((('#S') @ ((('#B') @ mequiv @
% 0.59/0.94 ((('#B') @ positive @ ((('#B') @ mnot)))))) @
% 0.59/0.94 ((('#B') @ mnot @ positive)) @ Y0 @ X0)))))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl25, '1'])).
% 0.59/0.94 thf(zip_derived_cl27, plain,
% 0.59/0.94 (![X0 : $i]:
% 0.59/0.94 (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mequiv @
% 0.59/0.94 ((('#B') @ positive @
% 0.59/0.94 ((('#B') @ mnot)))))) @
% 0.59/0.94 ((('#B') @ mnot @ positive)))) @
% 0.59/0.94 X0))))),
% 0.59/0.94 inference('comb-normalize', [status(thm)], [zip_derived_cl26])).
% 0.59/0.94 thf(zip_derived_cl28, plain,
% 0.59/0.94 (![X0 : $i, X2 : mu > $i > $o]:
% 0.59/0.94 (mequiv @ (positive @ ((('#B') @ mnot @ X2))) @
% 0.59/0.94 (mnot @ (positive @ X2)) @ X0)),
% 0.59/0.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl27])).
% 0.59/0.94 thf(mequiv, axiom, (mequiv @ X0 @ X1 @ X2) => ((X0 @ X2) = (X1 @ X2))).
% 0.59/0.94 thf('2', plain,
% 0.59/0.94 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 0.59/0.94 ( ( mequiv @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) <=> ( X1 @ X2 ) ) )),
% 0.59/0.94 inference('rw.lit', [status(esa)], [mequiv])).
% 0.59/0.94 thf(zip_derived_cl29, plain,
% 0.59/0.94 (![X0 : mu > $i > $o, X1 : $i]:
% 0.59/0.94 ((positive @ ((('#B') @ mnot @ X0)) @ X1)
% 0.59/0.94 = (mnot @ (positive @ X0) @ X1))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl28, '2'])).
% 0.59/0.94 thf(zip_derived_cl56, plain,
% 0.59/0.94 (![X0 : mu > $i > $o, X1 : $i]:
% 0.59/0.94 (~ (positive @ ((('#B') @ mnot @ X0)) @ X1)
% 0.59/0.94 | (mnot @ (positive @ X0) @ X1))),
% 0.59/0.94 inference('eq_elim', [status(thm)], [zip_derived_cl29])).
% 0.59/0.94 thf(mnot, axiom, (mnot @ X0 @ X1) => ((X0 @ X1) != ($true))).
% 0.59/0.94 thf('3', plain,
% 0.59/0.94 (![X0:( $i > $o ),X1:$i]: ( ( mnot @ X0 @ X1 ) <=> ( ~( X0 @ X1 ) ) )),
% 0.59/0.94 inference('rw.lit', [status(esa)], [mnot])).
% 0.59/0.94 thf(zip_derived_cl64, plain,
% 0.59/0.94 (![X0 : $i, X1 : mu > $i > $o]:
% 0.59/0.94 (~ (positive @ X1 @ X0) | ~ (positive @ ((('#B') @ mnot @ X1)) @ X0))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl56, '3'])).
% 0.59/0.94 thf(axA2, axiom,
% 0.59/0.94 (mvalid @
% 0.59/0.94 ( mforall_indset @
% 0.59/0.94 ( ^[Phi:( mu > $i > $o )]:
% 0.59/0.94 ( mforall_indset @
% 0.59/0.94 ( ^[Psi:( mu > $i > $o )]:
% 0.59/0.94 ( mimplies @
% 0.59/0.94 ( mand @
% 0.59/0.94 ( positive @ Phi ) @
% 0.59/0.94 ( mbox @
% 0.59/0.94 ( mforall_ind @
% 0.59/0.94 ( ^[X:mu]: ( mimplies @ ( Phi @ X ) @ ( Psi @ X ) ) ) ) ) ) @
% 0.59/0.94 ( positive @ Psi ) ) ) ) ) ))).
% 0.59/0.94 thf(zip_derived_cl2, plain,
% 0.59/0.94 ( (mvalid @
% 0.59/0.94 (mforall_indset @
% 0.59/0.94 (^[Y0 : mu > $i > $o]:
% 0.59/0.94 (mforall_indset @
% 0.59/0.94 (^[Y1 : mu > $i > $o]:
% 0.59/0.94 (mimplies @
% 0.59/0.94 (mand @ (positive @ Y0) @
% 0.59/0.94 (mbox @
% 0.59/0.94 (mforall_ind @
% 0.59/0.94 (^[Y2 : mu]: (mimplies @ (Y0 @ Y2) @ (Y1 @ Y2)))))) @
% 0.59/0.94 (positive @ Y1)))))))),
% 0.59/0.94 inference('cnf', [status(esa)], [axA2])).
% 0.59/0.94 thf(zip_derived_cl3, plain,
% 0.59/0.94 ( (mvalid @
% 0.59/0.94 (mforall_indset @
% 0.59/0.94 ((('#B') @ mforall_indset @
% 0.59/0.94 ((('#C') @ ((('#B') @ ('#S') @
% 0.59/0.94 ((('#B') @ ((('#B') @ mimplies)) @
% 0.59/0.94 ((('#S') @ ((('#B') @ ('#B') @
% 0.59/0.94 ((('#B') @ mand @ positive)))) @
% 0.59/0.94 ((('#B') @ ((('#B') @ mbox)) @
% 0.59/0.94 ((('#B') @ ((('#B') @ mforall_ind)) @
% 0.59/0.94 ((('#B') @ ('#S') @ ((('#B') @ mimplies)))))))))))))) @
% 0.59/0.94 positive))))))),
% 0.59/0.94 inference('lams2combs', [status(thm)], [zip_derived_cl2])).
% 0.59/0.94 thf(zip_derived_cl30, plain,
% 0.59/0.94 ( (((!!) @ (^[Y0 : $i]:
% 0.59/0.94 (mforall_indset @
% 0.59/0.94 ((('#B') @ mforall_indset @
% 0.59/0.94 ((('#C') @ ((('#B') @ ('#S') @
% 0.59/0.94 ((('#B') @ ((('#B') @ mimplies)) @
% 0.59/0.94 ((('#S') @ ((('#B') @ ('#B') @
% 0.59/0.94 ((('#B') @ mand @ positive)))) @
% 0.59/0.94 ((('#B') @ ((('#B') @ mbox)) @
% 0.59/0.94 ((('#B') @ ((('#B') @ mforall_ind)) @
% 0.59/0.94 ((('#B') @ ('#S') @
% 0.59/0.94 ((('#B') @ mimplies)))))))))))))) @
% 0.59/0.94 positive)))) @
% 0.59/0.94 Y0))))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl3, '0'])).
% 0.59/0.94 thf(zip_derived_cl31, plain,
% 0.59/0.94 ( (((!!) @ (mforall_indset @
% 0.59/0.94 ((('#B') @ mforall_indset @
% 0.59/0.94 ((('#C') @ ((('#B') @ ('#S') @
% 0.59/0.94 ((('#B') @ ((('#B') @ mimplies)) @
% 0.59/0.94 ((('#S') @ ((('#B') @ ('#B') @
% 0.59/0.94 ((('#B') @ mand @ positive)))) @
% 0.59/0.94 ((('#B') @ ((('#B') @ mbox)) @
% 0.59/0.94 ((('#B') @ ((('#B') @ mforall_ind)) @
% 0.59/0.94 ((('#B') @ ('#S') @
% 0.59/0.94 ((('#B') @ mimplies)))))))))))))) @
% 0.59/0.94 positive)))))))),
% 0.59/0.94 inference('comb-normalize', [status(thm)], [zip_derived_cl30])).
% 0.59/0.94 thf(zip_derived_cl32, plain,
% 0.59/0.94 (![X2 : $i]:
% 0.59/0.94 (mforall_indset @
% 0.59/0.94 ((('#B') @ mforall_indset @
% 0.59/0.94 ((('#C') @ ((('#B') @ ('#S') @
% 0.59/0.94 ((('#B') @ ((('#B') @ mimplies)) @
% 0.59/0.94 ((('#S') @ ((('#B') @ ('#B') @
% 0.59/0.94 ((('#B') @ mand @ positive)))) @
% 0.59/0.94 ((('#B') @ ((('#B') @ mbox)) @
% 0.59/0.94 ((('#B') @ ((('#B') @ mforall_ind)) @
% 0.59/0.94 ((('#B') @ ('#S') @ ((('#B') @ mimplies)))))))))))))) @
% 0.59/0.94 positive)))) @
% 0.59/0.94 X2)),
% 0.59/0.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl31])).
% 0.59/0.94 thf(zip_derived_cl33, plain,
% 0.59/0.94 (![X0 : $i]:
% 0.59/0.94 (((!!) @ (^[Y0 : mu > $i > $o]:
% 0.59/0.94 ((('#B') @ mforall_indset @
% 0.59/0.94 ((('#C') @ ((('#B') @ ('#S') @
% 0.59/0.94 ((('#B') @ ((('#B') @ mimplies)) @
% 0.59/0.94 ((('#S') @ ((('#B') @ ('#B') @
% 0.59/0.94 ((('#B') @ mand @ positive)))) @
% 0.59/0.94 ((('#B') @ ((('#B') @ mbox)) @
% 0.59/0.94 ((('#B') @ ((('#B') @ mforall_ind)) @
% 0.59/0.94 ((('#B') @ ('#S') @
% 0.59/0.94 ((('#B') @ mimplies)))))))))))))) @
% 0.59/0.94 positive)) @
% 0.59/0.94 Y0 @ X0)))))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl32, '1'])).
% 0.59/0.94 thf(zip_derived_cl34, plain,
% 0.59/0.94 (![X0 : $i]:
% 0.59/0.94 (((!!) @ ((('#C') @ ((('#B') @ mforall_indset @
% 0.59/0.94 ((('#C') @ ((('#B') @ ('#S') @
% 0.59/0.94 ((('#B') @ ((('#B') @ mimplies)) @
% 0.59/0.94 ((('#S') @ ((('#B') @ ('#B') @
% 0.59/0.94 ((('#B') @ mand @
% 0.59/0.94 positive)))) @
% 0.59/0.94 ((('#B') @ ((('#B') @ mbox)) @
% 0.59/0.94 ((('#B') @ ((('#B') @ mforall_ind)) @
% 0.59/0.94 ((('#B') @ ('#S') @
% 0.59/0.94 ((('#B') @ mimplies)))))))))))))) @
% 0.59/0.94 positive)))) @
% 0.59/0.94 X0))))),
% 0.59/0.94 inference('comb-normalize', [status(thm)], [zip_derived_cl33])).
% 0.59/0.94 thf(zip_derived_cl35, plain,
% 0.59/0.94 (![X0 : $i, X2 : mu > $i > $o]:
% 0.59/0.94 (mforall_indset @
% 0.59/0.94 ((('#S') @ ((('#B') @ mimplies @
% 0.59/0.94 ((('#B') @ (mand @ (positive @ X2)) @
% 0.59/0.94 ((('#B') @ mbox @
% 0.59/0.94 ((('#B') @ mforall_ind @
% 0.59/0.94 ((('#S') @ ((('#B') @ mimplies @ X2)))))))))))) @
% 0.59/0.94 positive)) @
% 0.59/0.94 X0)),
% 0.59/0.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])).
% 0.59/0.94 thf(zip_derived_cl36, plain,
% 0.59/0.94 (![X0 : mu > $i > $o, X1 : $i]:
% 0.59/0.94 (((!!) @ (^[Y0 : mu > $i > $o]:
% 0.59/0.94 ((('#S') @ ((('#B') @ mimplies @
% 0.59/0.94 ((('#B') @ (mand @ (positive @ X0)) @
% 0.59/0.94 ((('#B') @ mbox @
% 0.59/0.94 ((('#B') @ mforall_ind @
% 0.59/0.94 ((('#S') @ ((('#B') @ mimplies @ X0)))))))))))) @
% 0.59/0.94 positive @ Y0 @ X1)))))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl35, '1'])).
% 0.59/0.94 thf(zip_derived_cl37, plain,
% 0.59/0.94 (![X0 : mu > $i > $o, X1 : $i]:
% 0.59/0.94 (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @
% 0.59/0.94 ((('#B') @ (mand @ (positive @ X0)) @
% 0.59/0.94 ((('#B') @ mbox @
% 0.59/0.94 ((('#B') @ mforall_ind @
% 0.59/0.94 ((('#S') @ ((('#B') @ mimplies @
% 0.59/0.94 X0)))))))))))) @
% 0.59/0.94 positive)) @
% 0.59/0.94 X1))))),
% 0.59/0.94 inference('comb-normalize', [status(thm)], [zip_derived_cl36])).
% 0.59/0.94 thf(zip_derived_cl38, plain,
% 0.59/0.94 (![X0 : mu > $i > $o, X1 : $i, X3 : mu > $i > $o]:
% 0.59/0.94 (mimplies @
% 0.59/0.94 (mand @ (positive @ X0) @
% 0.59/0.94 (mbox @
% 0.59/0.94 (mforall_ind @ ((('#S') @ ((('#B') @ mimplies @ X0)) @ X3))))) @
% 0.59/0.94 (positive @ X3) @ X1)),
% 0.59/0.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])).
% 0.59/0.94 thf(mimplies, axiom, (mimplies @ X0 @ X1 @ X2) =>
% 0.59/0.94 ((((X0 @ X2) => (X1 @ X2))) = ($true))).
% 0.59/0.94 thf('4', plain,
% 0.59/0.94 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 0.59/0.94 ( ( mimplies @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) => ( X1 @ X2 ) ) )),
% 0.59/0.94 inference('rw.lit', [status(esa)], [mimplies])).
% 0.59/0.94 thf(zip_derived_cl39, plain,
% 0.59/0.94 (![X0 : mu > $i > $o, X1 : $i, X2 : mu > $i > $o]:
% 0.59/0.94 (((mand @ (positive @ X2) @
% 0.59/0.94 (mbox @
% 0.59/0.94 (mforall_ind @ ((('#S') @ ((('#B') @ mimplies @ X2)) @ X0)))) @
% 0.59/0.94 X1) => (positive @ X0 @ X1)))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl38, '4'])).
% 0.59/0.94 thf(zip_derived_cl40, plain,
% 0.59/0.94 (![X0 : mu > $i > $o, X1 : $i, X2 : mu > $i > $o]:
% 0.59/0.94 (~ (mand @ (positive @ X2) @
% 0.59/0.94 (mbox @
% 0.59/0.94 (mforall_ind @ ((('#S') @ ((('#B') @ mimplies @ X2)) @ X0)))) @
% 0.59/0.94 X1)
% 0.59/0.94 | (positive @ X0 @ X1))),
% 0.59/0.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])).
% 0.59/0.94 thf(mand, axiom, ~ (mand @ X0 @ X1 @ X2) =>
% 0.59/0.94 ((((X0 @ X2) & (X1 @ X2))) != ($true))).
% 0.59/0.94 thf('5', plain,
% 0.59/0.94 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 0.59/0.94 ( ( ~( mand @ X0 @ X1 @ X2 ) ) <=> ( ~( ( X0 @ X2 ) & ( X1 @ X2 ) ) ) )),
% 0.59/0.94 inference('rw.lit', [status(esa)], [mand])).
% 0.59/0.94 thf(zip_derived_cl41, plain,
% 0.59/0.94 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 0.59/0.94 (~ (((positive @ X2 @ X0) & (mbox @
% 0.59/0.94 (mforall_ind @ ((('#S') @ ((('#B') @ mimplies @ X2)) @ X1))) @
% 0.59/0.94 X0)))
% 0.59/0.94 | (positive @ X1 @ X0))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl40, '5'])).
% 0.59/0.94 thf(mbox, axiom,(( mbox @ (X0)@ (X1)) = ((mbox_generic @ rel @ X0 @ X1)))).
% 0.59/0.94 thf('6', plain,
% 0.59/0.94 (![X1:$i,X0:( $i > $o )]:
% 0.59/0.94 ( ( mbox @ X0 @ X1 ) = ( mbox_generic @ rel @ X0 @ X1 ) )),
% 0.59/0.94 define([status(thm)])).
% 0.59/0.94 thf(zip_derived_cl42, plain,
% 0.59/0.94 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 0.59/0.94 (~ (((positive @ X2 @ X0) & (mbox_generic @ rel @
% 0.59/0.94 (mforall_ind @ ((('#S') @ ((('#B') @ mimplies @ X2)) @ X1))) @
% 0.59/0.94 X0)))
% 0.59/0.94 | (positive @ X1 @ X0))),
% 0.59/0.94 inference('rw', [status(thm)], [zip_derived_cl41, '6'])).
% 0.59/0.94 thf(zip_derived_cl43, plain,
% 0.59/0.94 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 0.59/0.94 (~ (positive @ X2 @ X0)
% 0.59/0.94 | ~ (mbox_generic @ rel @
% 0.59/0.94 (mforall_ind @ ((('#S') @ ((('#B') @ mimplies @ X2)) @ X1))) @
% 0.59/0.94 X0)
% 0.59/0.94 | (positive @ X1 @ X0))),
% 0.59/0.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl42])).
% 0.59/0.94 thf(mbox_generic, axiom, ~ (mbox_generic @ X0 @ X1 @ X2) =>
% 0.59/0.94 ((((!!) @ (^[Y0 : $i]: (((((~) @ (X0 @ X2 @ Y0))) | (X1 @ Y0)))))) !=
% 0.59/0.94 ($true))).
% 0.59/0.94 thf('7', plain,
% 0.59/0.94 (![X0:( $i > $i > $o ),X1:( $i > $o ),X2:$i]:
% 0.59/0.94 ( ( ~( mbox_generic @ X0 @ X1 @ X2 ) ) <=>
% 0.59/0.94 ( ~( ![X7:$i]: ( ( ~( X0 @ X2 @ X7 ) ) | ( X1 @ X7 ) ) ) ) )),
% 0.59/0.94 inference('rw.lit', [status(esa)], [mbox_generic])).
% 0.59/0.94 thf(zip_derived_cl44, plain,
% 0.59/0.94 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 0.59/0.94 (~ (((!!) @ (^[Y0 : $i]:
% 0.59/0.94 (((((~) @ (rel @ X0 @ Y0))) | (mforall_ind @
% 0.59/0.94 ((('#S') @ ((('#B') @ mimplies @ X2)) @ X1)) @ Y0))))))
% 0.59/0.94 | (positive @ X1 @ X0)
% 0.59/0.94 | ~ (positive @ X2 @ X0))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl43, '7'])).
% 0.59/0.94 thf(zip_derived_cl45, plain,
% 0.59/0.94 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 0.59/0.94 (~ (((!!) @ ((('#S') @ ((('#B') @ (|) @ ((('#B') @ (~) @ (rel @ X0))))) @
% 0.59/0.94 (mforall_ind @
% 0.59/0.94 ((('#S') @ ((('#B') @ mimplies @ X2)) @ X1)))))))
% 0.59/0.94 | (positive @ X1 @ X0)
% 0.59/0.94 | ~ (positive @ X2 @ X0))),
% 0.59/0.94 inference('comb-normalize', [status(thm)], [zip_derived_cl44])).
% 0.59/0.94 thf(zip_derived_cl46, plain,
% 0.59/0.94 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 0.59/0.94 (~ (((((~) @ (rel @ X0 @ ('#sk3' @ X0 @ X1 @ X2)))) | (mforall_ind @
% 0.59/0.94 ((('#S') @ ((('#B') @ mimplies @ X2)) @ X1)) @
% 0.59/0.94 ('#sk3' @ X0 @ X1 @ X2))))
% 0.59/0.94 | ~ (positive @ X2 @ X0)
% 0.59/0.94 | (positive @ X1 @ X0))),
% 0.59/0.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl45])).
% 0.59/0.94 thf(zip_derived_cl47, plain,
% 0.59/0.94 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 0.59/0.94 ( (rel @ X0 @ ('#sk3' @ X0 @ X1 @ X2))
% 0.59/0.94 | (positive @ X1 @ X0)
% 0.59/0.94 | ~ (positive @ X2 @ X0))),
% 0.59/0.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])).
% 0.59/0.94 thf(thmT1, conjecture,
% 0.59/0.94 (mvalid @
% 0.59/0.94 ( mforall_indset @
% 0.59/0.94 ( ^[Phi:( mu > $i > $o )]:
% 0.59/0.94 ( mimplies @
% 0.59/0.94 ( positive @ Phi ) @
% 0.59/0.94 ( mdia @ ( mexists_ind @ ( ^[X:mu]: ( Phi @ X ) ) ) ) ) ) ))).
% 0.59/0.94 thf(zf_stmt_0, negated_conjecture,
% 0.59/0.94 (~( mvalid @
% 0.59/0.94 ( mforall_indset @
% 0.59/0.94 ( ^[Phi:( mu > $i > $o )]:
% 0.59/0.94 ( mimplies @
% 0.59/0.94 ( positive @ Phi ) @
% 0.59/0.94 ( mdia @ ( mexists_ind @ ( ^[X:mu]: ( Phi @ X ) ) ) ) ) ) ) )),
% 0.59/0.94 inference('cnf.neg', [status(esa)], [thmT1])).
% 0.59/0.94 thf(zip_derived_cl4, plain,
% 0.59/0.94 (~ (mvalid @
% 0.59/0.94 (mforall_indset @
% 0.59/0.94 (^[Y0 : mu > $i > $o]:
% 0.59/0.94 (mimplies @ (positive @ Y0) @
% 0.59/0.94 (mdia @ (mexists_ind @ (^[Y1 : mu]: (Y0 @ Y1))))))))),
% 0.59/0.94 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.59/0.94 thf(zip_derived_cl5, plain,
% 0.59/0.94 (~ (mvalid @
% 0.59/0.94 (mforall_indset @
% 0.59/0.94 ((('#S') @ ((('#B') @ mimplies @ positive)) @
% 0.59/0.94 ((('#B') @ mdia @ mexists_ind))))))),
% 0.59/0.94 inference('lams2combs', [status(thm)], [zip_derived_cl4])).
% 0.59/0.94 thf(mvalid, axiom, ~ (mvalid @ X0) =>
% 0.59/0.94 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) != ($true))).
% 0.59/0.94 thf('8', plain,
% 0.59/0.94 (![X0:( $i > $o )]:
% 0.59/0.94 ( ( ~( mvalid @ X0 ) ) <=> ( ~( ![X5:$i]: ( X0 @ X5 ) ) ) )),
% 0.59/0.94 inference('rw.lit', [status(esa)], [mvalid])).
% 0.59/0.94 thf(zip_derived_cl6, plain,
% 0.59/0.94 (~ (((!!) @ (^[Y0 : $i]:
% 0.59/0.94 (mforall_indset @
% 0.59/0.94 ((('#S') @ ((('#B') @ mimplies @ positive)) @
% 0.59/0.94 ((('#B') @ mdia @ mexists_ind)))) @
% 0.59/0.94 Y0))))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl5, '8'])).
% 0.59/0.94 thf(zip_derived_cl7, plain,
% 0.59/0.94 (~ (((!!) @ (mforall_indset @
% 0.59/0.94 ((('#S') @ ((('#B') @ mimplies @ positive)) @
% 0.59/0.94 ((('#B') @ mdia @ mexists_ind)))))))),
% 0.59/0.94 inference('comb-normalize', [status(thm)], [zip_derived_cl6])).
% 0.59/0.94 thf(zip_derived_cl8, plain,
% 0.59/0.94 (~ (mforall_indset @
% 0.59/0.94 ((('#S') @ ((('#B') @ mimplies @ positive)) @
% 0.59/0.94 ((('#B') @ mdia @ mexists_ind)))) @
% 0.59/0.94 '#sk1')),
% 0.59/0.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl7])).
% 0.59/0.94 thf(mforall_indset, axiom, ~ (mforall_indset @ X0 @ X1) =>
% 0.59/0.94 ((((!!) @ (^[Y0 : mu > $i > $o]: (X0 @ Y0 @ X1)))) != ($true))).
% 0.59/0.94 thf('9', plain,
% 0.59/0.94 (![X0:( ( mu > $i > $o ) > $i > $o ),X1:$i]:
% 0.59/0.94 ( ( ~( mforall_indset @ X0 @ X1 ) ) <=>
% 0.59/0.94 ( ~( ![X6:( mu > $i > $o )]: ( X0 @ X6 @ X1 ) ) ) )),
% 0.59/0.94 inference('rw.lit', [status(esa)], [mforall_indset])).
% 0.59/0.94 thf(zip_derived_cl9, plain,
% 0.59/0.94 (~ (((!!) @ (^[Y0 : mu > $i > $o]:
% 0.59/0.94 ((('#S') @ ((('#B') @ mimplies @ positive)) @
% 0.59/0.94 ((('#B') @ mdia @ mexists_ind)) @ Y0 @ '#sk1')))))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl8, '9'])).
% 0.59/0.94 thf(zip_derived_cl10, plain,
% 0.59/0.94 (~ (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @ positive)) @
% 0.59/0.94 ((('#B') @ mdia @ mexists_ind)))) @
% 0.59/0.94 '#sk1'))))),
% 0.59/0.94 inference('comb-normalize', [status(thm)], [zip_derived_cl9])).
% 0.59/0.94 thf(zip_derived_cl11, plain,
% 0.59/0.94 (~ (mimplies @ (positive @ '#sk2') @ (mdia @ (mexists_ind @ '#sk2')) @
% 0.59/0.94 '#sk1')),
% 0.59/0.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl10])).
% 0.59/0.94 thf(mimplies, axiom, ~ (mimplies @ X0 @ X1 @ X2) =>
% 0.59/0.94 ((((X0 @ X2) => (X1 @ X2))) != ($true))).
% 0.59/0.94 thf('10', plain,
% 0.59/0.94 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 0.59/0.94 ( ( ~( mimplies @ X0 @ X1 @ X2 ) ) <=>
% 0.59/0.94 ( ~( ( X0 @ X2 ) => ( X1 @ X2 ) ) ) )),
% 0.59/0.94 inference('rw.lit', [status(esa)], [mimplies])).
% 0.59/0.94 thf(zip_derived_cl12, plain,
% 0.59/0.94 (~ (((positive @ '#sk2' @ '#sk1') => (mdia @ (mexists_ind @ '#sk2') @
% 0.59/0.94 '#sk1')))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl11, '10'])).
% 0.59/0.94 thf(mdia, axiom,(( mdia @ (X0)@ (X1)) = ((mdia_generic @ rel @ X0 @ X1)))).
% 0.59/0.94 thf('11', plain,
% 0.59/0.94 (![X1:$i,X0:( $i > $o )]:
% 0.59/0.94 ( ( mdia @ X0 @ X1 ) = ( mdia_generic @ rel @ X0 @ X1 ) )),
% 0.59/0.94 define([status(thm)])).
% 0.59/0.94 thf(zip_derived_cl13, plain,
% 0.59/0.94 (~ (((positive @ '#sk2' @ '#sk1') => (mdia_generic @ rel @
% 0.59/0.94 (mexists_ind @ '#sk2') @ '#sk1')))),
% 0.59/0.94 inference('rw', [status(thm)], [zip_derived_cl12, '11'])).
% 0.59/0.94 thf(zip_derived_cl15, plain,
% 0.59/0.94 (~ (mdia_generic @ rel @ (mexists_ind @ '#sk2') @ '#sk1')),
% 0.59/0.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])).
% 0.59/0.94 thf(mdia_generic, axiom, ~ (mdia_generic @ X0 @ X1 @ X2) =>
% 0.59/0.94 ((((??) @ (^[Y0 : $i]: (((X0 @ X2 @ Y0) & (X1 @ Y0)))))) != ($true))).
% 0.59/0.94 thf('12', plain,
% 0.59/0.94 (![X0:( $i > $i > $o ),X1:( $i > $o ),X2:$i]:
% 0.59/0.94 ( ( ~( mdia_generic @ X0 @ X1 @ X2 ) ) <=>
% 0.59/0.94 ( ~( ?[X7:$i]: ( ( X0 @ X2 @ X7 ) & ( X1 @ X7 ) ) ) ) )),
% 0.59/0.94 inference('rw.lit', [status(esa)], [mdia_generic])).
% 0.59/0.94 thf(zip_derived_cl16, plain,
% 0.59/0.94 (~ (((??) @ (^[Y0 : $i]:
% 0.59/0.94 (((rel @ '#sk1' @ Y0) & (mexists_ind @ '#sk2' @ Y0))))))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl15, '12'])).
% 0.59/0.94 thf(zip_derived_cl17, plain,
% 0.59/0.94 (~ (((??) @ ((('#S') @ ((('#B') @ (&) @ (rel @ '#sk1'))) @
% 0.59/0.94 (mexists_ind @ '#sk2')))))),
% 0.59/0.94 inference('comb-normalize', [status(thm)], [zip_derived_cl16])).
% 0.59/0.94 thf(zip_derived_cl18, plain,
% 0.59/0.94 (![X2 : $i]: ~ (((rel @ '#sk1' @ X2) & (mexists_ind @ '#sk2' @ X2)))),
% 0.59/0.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])).
% 0.59/0.94 thf(zip_derived_cl19, plain,
% 0.59/0.94 (![X2 : $i]: (~ (rel @ '#sk1' @ X2) | ~ (mexists_ind @ '#sk2' @ X2))),
% 0.59/0.94 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])).
% 0.59/0.94 thf(mexists_ind, axiom, ~ (mexists_ind @ X0 @ X1) =>
% 0.59/0.94 ((((??) @ (^[Y0 : mu]: (X0 @ Y0 @ X1)))) != ($true))).
% 0.59/0.94 thf('13', plain,
% 0.59/0.94 (![X0:( mu > $i > $o ),X1:$i]:
% 0.59/0.94 ( ( ~( mexists_ind @ X0 @ X1 ) ) <=> ( ~( ?[X6:mu]: ( X0 @ X6 @ X1 ) ) ) )),
% 0.59/0.94 inference('rw.lit', [status(esa)], [mexists_ind])).
% 0.59/0.94 thf(zip_derived_cl20, plain,
% 0.59/0.94 (![X0 : $i]:
% 0.59/0.94 (~ (((??) @ (^[Y0 : mu]: ('#sk2' @ Y0 @ X0)))) | ~ (rel @ '#sk1' @ X0))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl19, '13'])).
% 0.59/0.94 thf(zip_derived_cl21, plain,
% 0.59/0.94 (![X0 : $i]:
% 0.59/0.94 (~ (((??) @ ((('#C') @ '#sk2' @ X0)))) | ~ (rel @ '#sk1' @ X0))),
% 0.59/0.94 inference('comb-normalize', [status(thm)], [zip_derived_cl20])).
% 0.59/0.94 thf(zip_derived_cl22, plain,
% 0.59/0.94 (![X0 : $i, X2 : mu]: (~ ('#sk2' @ X2 @ X0) | ~ (rel @ '#sk1' @ X0))),
% 0.59/0.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])).
% 0.59/0.94 thf(zip_derived_cl62, plain,
% 0.59/0.94 (![X0 : mu > $i > $o, X1 : mu > $i > $o, X2 : mu]:
% 0.59/0.94 (~ (positive @ X0 @ '#sk1')
% 0.59/0.94 | (positive @ X1 @ '#sk1')
% 0.59/0.94 | ~ ('#sk2' @ X2 @ ('#sk3' @ '#sk1' @ X1 @ X0)))),
% 0.59/0.94 inference('sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl22])).
% 0.59/0.94 thf(zip_derived_cl48, plain,
% 0.59/0.94 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 0.59/0.94 (~ (mforall_ind @ ((('#S') @ ((('#B') @ mimplies @ X2)) @ X1)) @
% 0.59/0.94 ('#sk3' @ X0 @ X1 @ X2))
% 0.59/0.94 | (positive @ X1 @ X0)
% 0.59/0.94 | ~ (positive @ X2 @ X0))),
% 0.59/0.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])).
% 0.59/0.94 thf(mforall_ind, axiom, ~ (mforall_ind @ X0 @ X1) =>
% 0.59/0.94 ((((!!) @ (^[Y0 : mu]: (X0 @ Y0 @ X1)))) != ($true))).
% 0.59/0.94 thf('14', plain,
% 0.59/0.94 (![X0:( mu > $i > $o ),X1:$i]:
% 0.59/0.94 ( ( ~( mforall_ind @ X0 @ X1 ) ) <=> ( ~( ![X6:mu]: ( X0 @ X6 @ X1 ) ) ) )),
% 0.59/0.94 inference('rw.lit', [status(esa)], [mforall_ind])).
% 0.59/0.94 thf(zip_derived_cl49, plain,
% 0.59/0.94 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 0.59/0.94 (~ (((!!) @ (^[Y0 : mu]:
% 0.59/0.94 ((('#S') @ ((('#B') @ mimplies @ X1)) @ X2 @ Y0 @
% 0.59/0.94 ('#sk3' @ X0 @ X2 @ X1))))))
% 0.59/0.94 | ~ (positive @ X1 @ X0)
% 0.59/0.94 | (positive @ X2 @ X0))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl48, '14'])).
% 0.59/0.94 thf(zip_derived_cl50, plain,
% 0.59/0.94 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 0.59/0.94 (~ (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @ X1)) @ X2)) @
% 0.59/0.94 ('#sk3' @ X0 @ X2 @ X1)))))
% 0.59/0.94 | ~ (positive @ X1 @ X0)
% 0.59/0.94 | (positive @ X2 @ X0))),
% 0.59/0.94 inference('comb-normalize', [status(thm)], [zip_derived_cl49])).
% 0.59/0.94 thf(zip_derived_cl51, plain,
% 0.59/0.94 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 0.59/0.94 (~ (mimplies @ (X1 @ ('#sk4' @ X0 @ X1 @ X2)) @
% 0.59/0.94 (X2 @ ('#sk4' @ X0 @ X1 @ X2)) @ ('#sk3' @ X0 @ X2 @ X1))
% 0.59/0.94 | (positive @ X2 @ X0)
% 0.59/0.94 | ~ (positive @ X1 @ X0))),
% 0.59/0.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl50])).
% 0.59/0.94 thf(zip_derived_cl52, plain,
% 0.59/0.94 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 0.59/0.94 (~ (((X1 @ ('#sk4' @ X0 @ X1 @ X2) @ ('#sk3' @ X0 @ X2 @ X1)) =>
% 0.59/0.94 (X2 @ ('#sk4' @ X0 @ X1 @ X2) @ ('#sk3' @ X0 @ X2 @ X1))))
% 0.59/0.94 | ~ (positive @ X1 @ X0)
% 0.59/0.94 | (positive @ X2 @ X0))),
% 0.59/0.94 inference('rw_clause', [status(thm)], [zip_derived_cl51, '10'])).
% 0.59/0.94 thf(zip_derived_cl53, plain,
% 0.59/0.94 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 0.59/0.94 ( (X1 @ ('#sk4' @ X0 @ X1 @ X2) @ ('#sk3' @ X0 @ X2 @ X1))
% 0.59/0.94 | (positive @ X2 @ X0)
% 0.59/0.94 | ~ (positive @ X1 @ X0))),
% 0.59/0.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
% 0.59/0.94 thf(zip_derived_cl156, plain,
% 0.59/0.94 (![X0 : mu > $i > $o]:
% 0.59/0.94 ( (positive @ X0 @ '#sk1')
% 0.59/0.94 | ~ (positive @ '#sk2' @ '#sk1')
% 0.59/0.94 | ~ (positive @ '#sk2' @ '#sk1')
% 0.59/0.94 | (positive @ X0 @ '#sk1'))),
% 0.59/0.94 inference('sup+', [status(thm)], [zip_derived_cl62, zip_derived_cl53])).
% 0.59/0.94 thf(zip_derived_cl14, plain, ( (positive @ '#sk2' @ '#sk1')),
% 0.59/0.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])).
% 0.59/0.94 thf(zip_derived_cl14, plain, ( (positive @ '#sk2' @ '#sk1')),
% 0.59/0.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])).
% 0.59/0.94 thf(zip_derived_cl184, plain,
% 0.59/0.94 (![X0 : mu > $i > $o]:
% 0.59/0.94 ( (positive @ X0 @ '#sk1') | (positive @ X0 @ '#sk1'))),
% 0.59/0.94 inference('demod', [status(thm)],
% 0.59/0.94 [zip_derived_cl156, zip_derived_cl14, zip_derived_cl14])).
% 0.59/0.94 thf(zip_derived_cl185, plain,
% 0.59/0.94 (![X0 : mu > $i > $o]: (positive @ X0 @ '#sk1')),
% 0.59/0.94 inference('simplify', [status(thm)], [zip_derived_cl184])).
% 0.59/0.94 thf(zip_derived_cl202, plain,
% 0.59/0.94 (![X0 : mu > $i > $o]: ~ (positive @ ((('#B') @ mnot @ X0)) @ '#sk1')),
% 0.59/0.94 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl185])).
% 0.59/0.94 thf(zip_derived_cl185, plain,
% 0.59/0.94 (![X0 : mu > $i > $o]: (positive @ X0 @ '#sk1')),
% 0.59/0.94 inference('simplify', [status(thm)], [zip_derived_cl184])).
% 0.59/0.94 thf(zip_derived_cl205, plain, ($false),
% 0.59/0.94 inference('demod', [status(thm)], [zip_derived_cl202, zip_derived_cl185])).
% 0.59/0.94
% 0.59/0.94 % SZS output end Refutation
% 0.59/0.94
% 0.59/0.94
% 0.59/0.94 % Terminating...
% 0.59/0.99 % Runner terminated.
% 0.59/1.01 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------