%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM636^3 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.UlO3hOgXZm true
% Computer : n014.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 04:47:44 PM UTC 2025
% Result : Theorem 1.74s 1.29s
% Output : Refutation 1.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.21 % Problem : NUM636^3 : TPTP v9.2.0. Released v3.7.0.
% 0.11/0.22 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.UlO3hOgXZm true
% 0.11/0.48 % Computer : n014.cluster.edu
% 0.11/0.48 % Model : x86_64 x86_64
% 0.11/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.48 % Memory : 8042.1875MB
% 0.11/0.48 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.48 % CPULimit : 300
% 0.11/0.48 % WCLimit : 300
% 0.11/0.48 % DateTime : Wed Oct 1 16:51:23 EDT 2025
% 0.17/0.48 % CPUTime :
% 0.17/0.48 % Running portfolio for 300 s
% 0.17/0.48 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % Number of cores: 8
% 0.17/0.49 % Python version: Python 3.6.8
% 0.17/0.50 % Running in HO mode
% 0.30/0.85 % Total configuration time : 828
% 0.30/0.85 % Estimated wc time : 1656
% 0.30/0.85 % Estimated cpu time (8 cpus) : 207.0
% 0.31/0.98 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 1.45/1.09 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.45/1.09 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.45/1.10 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.45/1.11 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.45/1.11 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.45/1.13 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.45/1.13 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.74/1.29 % Solved by lams/40_b.comb.sh.
% 1.74/1.29 % done 18 iterations in 0.113s
% 1.74/1.29 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.74/1.29 % SZS output start Refutation
% 1.74/1.29 thf(one_type, type, one: $i).
% 1.74/1.29 thf(m_type, type, m: $i > $o).
% 1.74/1.29 thf('#sk2_type', type, '#sk2': ($i > $o) > $i).
% 1.74/1.29 thf(succ_type, type, succ: $i > $i).
% 1.74/1.29 thf('#sk1_type', type, '#sk1': $i).
% 1.74/1.29 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 1.74/1.29 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 1.74/1.29 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 1.74/1.29 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 1.74/1.29 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 1.74/1.29 thf(induction, axiom,
% 1.74/1.29 (![M:( $i > $o )]:
% 1.74/1.29 ( ( ( ![X:$i]: ( ( M @ X ) => ( M @ ( succ @ X ) ) ) ) & ( M @ one ) ) =>
% 1.74/1.29 ( ![Y:$i]: ( M @ Y ) ) ))).
% 1.74/1.29 thf(zip_derived_cl4, plain,
% 1.74/1.29 ( (((!!) @ (^[Y0 : $i > $o]:
% 1.74/1.29 (((((((!!) @ (^[Y1 : $i]:
% 1.74/1.29 (((Y0 @ Y1) => (Y0 @ (succ @ Y1))))))) &
% 1.74/1.29 (Y0 @ one))) =>
% 1.74/1.29 (((!!) @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 1.74/1.29 inference('cnf', [status(esa)], [induction])).
% 1.74/1.29 thf(zip_derived_cl5, plain,
% 1.74/1.29 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 1.74/1.29 ((('#S') @ ((('#B') @ (&) @
% 1.74/1.29 ((('#B') @ (!!) @
% 1.74/1.29 ((('#S') @ ((('#B') @ ('#S') @
% 1.74/1.29 ((('#B') @ (=>))))) @
% 1.74/1.29 ((('#C') @ ('#B') @ succ)))))))) @
% 1.74/1.29 ((('#C') @ ('#I') @ one)))))) @
% 1.74/1.29 (!!)))))),
% 1.74/1.29 inference('lams2combs', [status(thm)], [zip_derived_cl4])).
% 1.74/1.29 thf(zip_derived_cl24, plain,
% 1.74/1.29 (![X2 : $i > $o]:
% 1.74/1.29 (((((((!!) @ ((('#S') @ ((('#B') @ (=>) @ X2)) @
% 1.74/1.29 ((('#B') @ X2 @ succ)))))) &
% 1.74/1.29 (X2 @ one))) =>
% 1.74/1.29 (((!!) @ X2))))),
% 1.74/1.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])).
% 1.74/1.29 thf(zip_derived_cl25, plain,
% 1.74/1.29 (![X2 : $i > $o]:
% 1.74/1.29 (~ (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ X2)) @
% 1.74/1.29 ((('#B') @ X2 @ succ)))))) &
% 1.74/1.29 (X2 @ one)))
% 1.74/1.29 | (((!!) @ X2)))),
% 1.74/1.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])).
% 1.74/1.29 thf(zip_derived_cl26, plain,
% 1.74/1.29 (![X2 : $i > $o]:
% 1.74/1.29 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ X2)) @ ((('#B') @ X2 @ succ))))))
% 1.74/1.29 | ~ (X2 @ one)
% 1.74/1.29 | (((!!) @ X2)))),
% 1.74/1.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl25])).
% 1.74/1.29 thf(zip_derived_cl27, plain,
% 1.74/1.29 (![X2 : $i > $o]:
% 1.74/1.29 (~ (((X2 @ ('#sk2' @ X2)) => (X2 @ (succ @ ('#sk2' @ X2)))))
% 1.74/1.29 | (((!!) @ X2))
% 1.74/1.29 | ~ (X2 @ one))),
% 1.74/1.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl26])).
% 1.74/1.29 thf(zip_derived_cl29, plain,
% 1.74/1.29 (![X2 : $i > $o]:
% 1.74/1.29 (~ (X2 @ (succ @ ('#sk2' @ X2))) | ~ (X2 @ one) | (((!!) @ X2)))),
% 1.74/1.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])).
% 1.74/1.29 thf(zip_derived_cl31, plain,
% 1.74/1.29 (![X2 : $i > $o, X4 : $i]:
% 1.74/1.29 ( (X2 @ X4) | ~ (X2 @ one) | ~ (X2 @ (succ @ ('#sk2' @ X2))))),
% 1.74/1.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])).
% 1.74/1.29 thf(zip_derived_cl108, plain,
% 1.74/1.29 (![X0 : $i]:
% 1.74/1.29 ( ((^[Y0 : $i]: (((X0) != (Y0)))) @ X0)
% 1.74/1.29 | ~ ((^[Y0 : $i]: (((X0) != (Y0)))) @ one)
% 1.74/1.29 | ~ ((^[Y0 : $i]: (((X0) != (Y0)))) @
% 1.74/1.29 (succ @ ('#sk2' @ (^[Y0 : $i]: (((X0) != (Y0))))))))),
% 1.74/1.29 inference('elim_leibniz_eq_+', [status(thm)], [zip_derived_cl31])).
% 1.74/1.29 thf(zip_derived_cl148, plain,
% 1.74/1.29 (![X0 : $i]:
% 1.74/1.29 ( (((X0) != (X0)))
% 1.74/1.29 | ~ (((X0) != (one)))
% 1.74/1.29 | ~ (((X0) != (succ @ ('#sk2' @ ((($i) != (X0))))))))),
% 1.74/1.29 inference('comb-normalize', [status(thm)], [zip_derived_cl108])).
% 1.74/1.29 thf(zip_derived_cl149, plain,
% 1.74/1.29 (![X0 : $i]:
% 1.74/1.29 (~ (((X0) != (one)))
% 1.74/1.29 | ~ (((X0) != (succ @ ('#sk2' @ ((($i) != (X0))))))))),
% 1.74/1.29 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl148])).
% 1.74/1.29 thf(zip_derived_cl150, plain,
% 1.74/1.29 (![X0 : $i]:
% 1.74/1.29 (((X0) = (one)) | ((X0) = (succ @ ('#sk2' @ ((($i) != (X0)))))))),
% 1.74/1.29 inference('simplify nested equalities', [status(thm)],
% 1.74/1.29 [zip_derived_cl149])).
% 1.74/1.29 thf(m_is_all, conjecture, (![X:$i]: ( m @ X ))).
% 1.74/1.29 thf(zf_stmt_0, negated_conjecture, (~( ![X:$i]: ( m @ X ) )),
% 1.74/1.29 inference('cnf.neg', [status(esa)], [m_is_all])).
% 1.74/1.29 thf(zip_derived_cl9, plain, (~ (((!!) @ (^[Y0 : $i]: (m @ Y0))))),
% 1.74/1.29 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.74/1.29 thf(zip_derived_cl10, plain, (~ (((!!) @ m))),
% 1.74/1.29 inference('lams2combs', [status(thm)], [zip_derived_cl9])).
% 1.74/1.29 thf(zip_derived_cl11, plain, (~ (m @ '#sk1')),
% 1.74/1.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl10])).
% 1.74/1.29 thf(m_defn, axiom, ~ (m @ X0) => ((succ @ X0) = (X0))).
% 1.74/1.29 thf('0', plain,
% 1.74/1.29 (![X0:$i]: ( ( ~( m @ X0 ) ) <=> ( ( succ @ X0 ) = ( X0 ) ) )),
% 1.74/1.29 inference('rw.lit', [status(esa)], [m_defn])).
% 1.74/1.29 thf(zip_derived_cl12, plain, (((succ @ '#sk1') = ('#sk1'))),
% 1.74/1.29 inference('rw_clause', [status(thm)], [zip_derived_cl11, '0'])).
% 1.74/1.29 thf(succ_injective, axiom,
% 1.74/1.29 (![X:$i,Y:$i]: ( ( ( succ @ X ) = ( succ @ Y ) ) => ( ( X ) = ( Y ) ) ))).
% 1.74/1.29 thf(zip_derived_cl2, plain,
% 1.74/1.29 ( (((!!) @ (^[Y0 : $i]:
% 1.74/1.29 (((!!) @ (^[Y1 : $i]:
% 1.74/1.29 (((((succ @ Y0) = (succ @ Y1))) =>
% 1.74/1.29 (((Y0) = (Y1)))))))))))),
% 1.74/1.29 inference('cnf', [status(esa)], [succ_injective])).
% 1.74/1.29 thf(zip_derived_cl3, plain,
% 1.74/1.29 ( (((!!) @ ((('#B') @ (!!) @
% 1.74/1.29 ((('#S') @ ((('#B') @ ('#S') @
% 1.74/1.29 ((('#B') @ ((('#B') @ (=>))) @
% 1.74/1.29 ((('#C') @ ((('#B') @ ('#B') @
% 1.74/1.29 ((('#B') @ (=) @ succ)))) @
% 1.74/1.29 succ)))))) @
% 1.74/1.29 (=)))))))),
% 1.74/1.29 inference('lams2combs', [status(thm)], [zip_derived_cl2])).
% 1.74/1.29 thf(zip_derived_cl20, plain,
% 1.74/1.29 (![X2 : $i]:
% 1.74/1.29 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 1.74/1.29 ((('#B') @ ((($i) = (succ @ X2))) @ succ)))) @
% 1.74/1.29 ((($i) = (X2)))))))),
% 1.74/1.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])).
% 1.74/1.29 thf(zip_derived_cl21, plain,
% 1.74/1.29 (![X2 : $i, X4 : $i]:
% 1.74/1.29 (((((succ @ X2) = (succ @ X4))) => (((X2) = (X4)))))),
% 1.74/1.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])).
% 1.74/1.29 thf(zip_derived_cl22, plain,
% 1.74/1.29 (![X2 : $i, X4 : $i]:
% 1.74/1.29 (~ (((succ @ X2) = (succ @ X4))) | (((X2) = (X4))))),
% 1.74/1.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])).
% 1.74/1.29 thf(zip_derived_cl23, plain,
% 1.74/1.29 (![X2 : $i, X4 : $i]: (((succ @ X2) != (succ @ X4)) | ((X2) = (X4)))),
% 1.74/1.29 inference('simplify nested equalities', [status(thm)], [zip_derived_cl22])).
% 1.74/1.29 thf(zip_derived_cl68, plain,
% 1.74/1.29 (![X0 : $i]: ((('#sk1') != (succ @ X0)) | (('#sk1') = (X0)))),
% 1.74/1.29 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl23])).
% 1.74/1.29 thf(zip_derived_cl165, plain,
% 1.74/1.29 (![X0 : $i]:
% 1.74/1.29 ((('#sk1') != (X0))
% 1.74/1.29 | ((X0) = (one))
% 1.74/1.29 | (('#sk1') = ('#sk2' @ ((($i) != (X0))))))),
% 1.74/1.29 inference('sup-', [status(thm)], [zip_derived_cl150, zip_derived_cl68])).
% 1.74/1.29 thf(zip_derived_cl28, plain,
% 1.74/1.29 (![X2 : $i > $o]: ( (X2 @ ('#sk2' @ X2)) | ~ (X2 @ one) | (((!!) @ X2)))),
% 1.74/1.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])).
% 1.74/1.29 thf(zip_derived_cl30, plain,
% 1.74/1.29 (![X2 : $i > $o, X4 : $i]:
% 1.74/1.29 ( (X2 @ X4) | ~ (X2 @ one) | (X2 @ ('#sk2' @ X2)))),
% 1.74/1.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])).
% 1.74/1.29 thf(zip_derived_cl32, plain,
% 1.74/1.29 (![X0 : $i > $o]: ( (X0 @ ('#sk2' @ X0)) | ~ (X0 @ one))),
% 1.74/1.29 inference('condensation', [status(thm)], [zip_derived_cl30])).
% 1.74/1.29 thf(zip_derived_cl253, plain,
% 1.74/1.29 (![X0 : $i]:
% 1.74/1.29 ( (((X0) != ('#sk1')))
% 1.74/1.29 | ((X0) = (one))
% 1.74/1.29 | (('#sk1') != (X0))
% 1.74/1.29 | ~ (((X0) != (one))))),
% 1.74/1.29 inference('sup+', [status(thm)], [zip_derived_cl165, zip_derived_cl32])).
% 1.74/1.29 thf(zip_derived_cl260, plain,
% 1.74/1.29 (![X0 : $i]:
% 1.74/1.29 (((X0) != ('#sk1'))
% 1.74/1.29 | ((X0) = (one))
% 1.74/1.29 | (('#sk1') != (X0))
% 1.74/1.29 | ((X0) = (one)))),
% 1.74/1.29 inference('simplify nested equalities', [status(thm)],
% 1.74/1.29 [zip_derived_cl253])).
% 1.74/1.29 thf(zip_derived_cl261, plain,
% 1.74/1.29 (![X0 : $i]: (((X0) = (one)) | ((X0) != ('#sk1')))),
% 1.74/1.29 inference('simplify', [status(thm)], [zip_derived_cl260])).
% 1.74/1.29 thf(zip_derived_cl275, plain, ((('#sk1') = (one))),
% 1.74/1.29 inference('eq_res', [status(thm)], [zip_derived_cl261])).
% 1.74/1.29 thf(zip_derived_cl12, plain, (((succ @ '#sk1') = ('#sk1'))),
% 1.74/1.29 inference('rw_clause', [status(thm)], [zip_derived_cl11, '0'])).
% 1.74/1.29 thf(one_is_first, axiom, (![X:$i]: ( ( succ @ X ) != ( one ) ))).
% 1.74/1.29 thf(zip_derived_cl0, plain,
% 1.74/1.29 ( (((!!) @ (^[Y0 : $i]: (((succ @ Y0) != (one))))))),
% 1.74/1.29 inference('cnf', [status(esa)], [one_is_first])).
% 1.74/1.29 thf(zip_derived_cl1, plain,
% 1.74/1.29 ( (((!!) @ ((('#C') @ ((('#B') @ (!=) @ succ)) @ one))))),
% 1.74/1.29 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 1.74/1.29 thf(zip_derived_cl14, plain, (![X2 : $i]: (((succ @ X2) != (one)))),
% 1.74/1.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])).
% 1.74/1.29 thf(zip_derived_cl15, plain, (![X2 : $i]: ((succ @ X2) != (one))),
% 1.74/1.29 inference('simplify nested equalities', [status(thm)], [zip_derived_cl14])).
% 1.74/1.29 thf(zip_derived_cl33, plain, ((('#sk1') != (one))),
% 1.74/1.29 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl15])).
% 1.74/1.29 thf(zip_derived_cl276, plain, ($false),
% 1.74/1.29 inference('simplify_reflect-', [status(thm)],
% 1.74/1.29 [zip_derived_cl275, zip_derived_cl33])).
% 1.74/1.29
% 1.74/1.29 % SZS output end Refutation
% 1.74/1.29
% 1.74/1.29
% 1.74/1.29 % Terminating...
% 1.92/1.45 % Runner terminated.
% 1.92/1.47 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------