TSTP Solution File: GEG009^1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GEG009^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.jebFCDDjPn true
% Computer : n021.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 : Wed Aug 30 22:42:14 EDT 2023
% Result : Theorem 21.27s 3.40s
% Output : Refutation 21.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GEG009^1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.jebFCDDjPn true
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 01:00:13 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.37 % Python version: Python 3.6.8
% 0.14/0.37 % Running in HO mode
% 0.22/0.68 % Total configuration time : 828
% 0.22/0.68 % Estimated wc time : 1656
% 0.22/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.31/0.81 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.31/0.82 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 21.27/3.40 % Solved by lams/30_b.l.sh.
% 21.27/3.40 % done 651 iterations in 2.530s
% 21.27/3.40 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 21.27/3.40 % SZS output start Refutation
% 21.27/3.40 thf(reg_type, type, reg: $tType).
% 21.27/3.40 thf('#form54_type', type, '#form54': reg > $o).
% 21.27/3.40 thf(mbox_type, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 21.27/3.40 thf(paris_type, type, paris: reg).
% 21.27/3.40 thf(ntpp_type, type, ntpp: reg > reg > $o).
% 21.27/3.40 thf(a_type, type, a: $i > $i > $o).
% 21.27/3.40 thf('#sk4_type', type, '#sk4': reg > reg).
% 21.27/3.40 thf(pp_type, type, pp: reg > reg > $o).
% 21.27/3.40 thf('#form8_type', type, '#form8': reg > $o).
% 21.27/3.40 thf(fool_type, type, fool: $i > $i > $o).
% 21.27/3.40 thf(eq_type, type, eq: reg > reg > $o).
% 21.27/3.40 thf(france_type, type, france: reg).
% 21.27/3.40 thf(mnot_type, type, mnot: ($i > $o) > $i > $o).
% 21.27/3.40 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 21.27/3.40 thf('#sk21_type', type, '#sk21': ($i > $o) > $i > $i).
% 21.27/3.40 thf(ec_type, type, ec: reg > reg > $o).
% 21.27/3.40 thf('#sk11_type', type, '#sk11': reg > reg).
% 21.27/3.40 thf('#sk53_type', type, '#sk53': $i).
% 21.27/3.40 thf(o_type, type, o: reg > reg > $o).
% 21.27/3.40 thf(c_type, type, c: reg > reg > $o).
% 21.27/3.40 thf(p_type, type, p: reg > reg > $o).
% 21.27/3.40 thf('#sk52_type', type, '#sk52': $i).
% 21.27/3.40 thf(spain_type, type, spain: reg).
% 21.27/3.40 thf('#sk7_type', type, '#sk7': reg > reg).
% 21.27/3.40 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 21.27/3.40 thf(mforall_prop_type, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 21.27/3.40 thf(mvalid_type, type, mvalid: ($i > $o) > $o).
% 21.27/3.40 thf(con, conjecture,
% 21.27/3.40 (mvalid @
% 21.27/3.40 ( mbox @
% 21.27/3.40 a @
% 21.27/3.40 ( ^[X:$i]:
% 21.27/3.40 ( ?[Z:reg]: ( ( ~( o @ Z @ paris ) ) & ( ~( eq @ Z @ spain ) ) ) ) ) ))).
% 21.27/3.40 thf(zf_stmt_0, negated_conjecture,
% 21.27/3.40 (~( mvalid @
% 21.27/3.40 ( mbox @
% 21.27/3.40 a @
% 21.27/3.40 ( ^[X:$i]:
% 21.27/3.40 ( ?[Z:reg]: ( ( ~( o @ Z @ paris ) ) & ( ~( eq @ Z @ spain ) ) ) ) ) ) )),
% 21.27/3.40 inference('cnf.neg', [status(esa)], [con])).
% 21.27/3.40 thf(zip_derived_cl8, plain,
% 21.27/3.40 (~ (mvalid @
% 21.27/3.40 (mbox @ a @
% 21.27/3.40 (^[Y0 : $i]:
% 21.27/3.40 (((??) @ (^[Y1 : reg]:
% 21.27/3.40 (((((~) @ (o @ Y1 @ paris))) &
% 21.27/3.40 (((~) @ (eq @ Y1 @ spain)))))))))))),
% 21.27/3.40 inference('cnf', [status(esa)], [zf_stmt_0])).
% 21.27/3.40 thf(mvalid, axiom, ~ (mvalid @ X0) =>
% 21.27/3.40 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) != ($true))).
% 21.27/3.40 thf('0', plain,
% 21.27/3.40 (![X0:( $i > $o )]:
% 21.27/3.40 ( ( ~( mvalid @ X0 ) ) <=> ( ~( ![X5:$i]: ( X0 @ X5 ) ) ) )),
% 21.27/3.40 inference('rw.lit', [status(esa)], [mvalid])).
% 21.27/3.40 thf(zip_derived_cl168, plain,
% 21.27/3.40 (~ (((!!) @ (^[Y0 : $i]:
% 21.27/3.40 (mbox @ a @
% 21.27/3.40 (^[Y1 : $i]:
% 21.27/3.40 (((??) @ (^[Y2 : reg]:
% 21.27/3.40 (((((~) @ (o @ Y2 @ paris))) &
% 21.27/3.40 (((~) @ (eq @ Y2 @ spain))))))))) @
% 21.27/3.40 Y0))))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl8, '0'])).
% 21.27/3.40 thf(zip_derived_cl169, plain,
% 21.27/3.40 (~ (mbox @ a @
% 21.27/3.40 (^[Y0 : $i]:
% 21.27/3.40 (((??) @ (^[Y1 : reg]:
% 21.27/3.40 (((((~) @ (o @ Y1 @ paris))) &
% 21.27/3.40 (((~) @ (eq @ Y1 @ spain))))))))) @
% 21.27/3.40 '#sk52')),
% 21.27/3.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl168])).
% 21.27/3.40 thf(mbox, axiom, ~ (mbox @ X0 @ X1 @ X2) =>
% 21.27/3.40 ((((!!) @ (^[Y0 : $i]: (((((~) @ (X0 @ X2 @ Y0))) | (X1 @ Y0)))))) !=
% 21.27/3.40 ($true))).
% 21.27/3.40 thf('1', plain,
% 21.27/3.40 (![X0:( $i > $i > $o ),X1:( $i > $o ),X2:$i]:
% 21.27/3.40 ( ( ~( mbox @ X0 @ X1 @ X2 ) ) <=>
% 21.27/3.40 ( ~( ![X7:$i]: ( ( ~( X0 @ X2 @ X7 ) ) | ( X1 @ X7 ) ) ) ) )),
% 21.27/3.40 inference('rw.lit', [status(esa)], [mbox])).
% 21.27/3.40 thf(zip_derived_cl170, plain,
% 21.27/3.40 (~ (((!!) @ (^[Y0 : $i]:
% 21.27/3.40 (((((~) @ (a @ '#sk52' @ Y0))) |
% 21.27/3.40 ((^[Y1 : $i]:
% 21.27/3.40 (((??) @ (^[Y2 : reg]:
% 21.27/3.40 (((((~) @ (o @ Y2 @ paris))) &
% 21.27/3.40 (((~) @ (eq @ Y2 @ spain))))))))) @
% 21.27/3.40 Y0))))))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl169, '1'])).
% 21.27/3.40 thf(zip_derived_cl171, plain,
% 21.27/3.40 (~ (((!!) @ (^[Y0 : $i]:
% 21.27/3.40 (((((~) @ (a @ '#sk52' @ Y0))) |
% 21.27/3.40 (((??) @ (^[Y1 : reg]:
% 21.27/3.40 (((((~) @ (o @ Y1 @ paris))) &
% 21.27/3.40 (((~) @ (eq @ Y1 @ spain)))))))))))))),
% 21.27/3.40 inference('ho_norm', [status(thm)], [zip_derived_cl170])).
% 21.27/3.40 thf(zip_derived_cl172, plain,
% 21.27/3.40 (~ (((((~) @ (a @ '#sk52' @ '#sk53'))) |
% 21.27/3.40 (((??) @ (^[Y0 : reg]:
% 21.27/3.40 (((((~) @ (o @ Y0 @ paris))) &
% 21.27/3.40 (((~) @ (eq @ Y0 @ spain))))))))))),
% 21.27/3.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl171])).
% 21.27/3.40 thf(zip_derived_cl174, plain,
% 21.27/3.40 (~ (((??) @ (^[Y0 : reg]:
% 21.27/3.40 (((((~) @ (o @ Y0 @ paris))) & (((~) @ (eq @ Y0 @ spain))))))))),
% 21.27/3.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl172])).
% 21.27/3.40 thf(zip_derived_cl175, plain,
% 21.27/3.40 (![X2 : reg]:
% 21.27/3.40 ~ (((((~) @ (o @ X2 @ paris))) & (((~) @ (eq @ X2 @ spain)))))),
% 21.27/3.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl174])).
% 21.27/3.40 thf(zip_derived_cl176, plain,
% 21.27/3.40 (![X2 : reg]: ( (o @ X2 @ paris) | (eq @ X2 @ spain))),
% 21.27/3.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl175])).
% 21.27/3.40 thf(o, axiom, (o @ X0 @ X1) =>
% 21.27/3.40 ((((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ X1)))))) = ($true))).
% 21.27/3.40 thf('2', plain,
% 21.27/3.40 (![X0:reg,X1:reg]:
% 21.27/3.40 ( ( o @ X0 @ X1 ) <=>
% 21.27/3.40 ( ?[X6:reg]: ( ( p @ X6 @ X0 ) & ( p @ X6 @ X1 ) ) ) )),
% 21.27/3.40 inference('rw.lit', [status(esa)], [o])).
% 21.27/3.40 thf(zip_derived_cl177, plain,
% 21.27/3.40 (![X0 : reg]:
% 21.27/3.40 ( (((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ paris))))))
% 21.27/3.40 | (eq @ X0 @ spain))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl176, '2'])).
% 21.27/3.40 thf(eq, axiom, (eq @ X0 @ X1) =>
% 21.27/3.40 ((((p @ X1 @ X0) & (p @ X0 @ X1))) = ($true))).
% 21.27/3.40 thf('3', plain,
% 21.27/3.40 (![X0:reg,X1:reg]:
% 21.27/3.40 ( ( eq @ X0 @ X1 ) <=> ( ( p @ X0 @ X1 ) & ( p @ X1 @ X0 ) ) )),
% 21.27/3.40 inference('rw.lit', [status(esa)], [eq])).
% 21.27/3.40 thf(zip_derived_cl178, plain,
% 21.27/3.40 (![X0 : reg]:
% 21.27/3.40 ( (((p @ spain @ X0) & (p @ X0 @ spain)))
% 21.27/3.40 | (((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ paris)))))))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl177, '3'])).
% 21.27/3.40 thf(zip_derived_cl179, plain,
% 21.27/3.40 (![X0 : reg]:
% 21.27/3.40 ( (p @ spain @ X0)
% 21.27/3.40 | (((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ paris)))))))),
% 21.27/3.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl178])).
% 21.27/3.40 thf(zip_derived_cl181, plain,
% 21.27/3.40 (![X0 : reg]:
% 21.27/3.40 (~ ('#form54' @ X0)
% 21.27/3.40 | (((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ paris)))))))),
% 21.27/3.40 define([status(thm)])).
% 21.27/3.40 thf(zip_derived_cl182, plain,
% 21.27/3.40 (![X0 : reg]:
% 21.27/3.40 ( (((p @ ('#sk11' @ X0) @ X0) & (p @ ('#sk11' @ X0) @ paris)))
% 21.27/3.40 | ~ ('#form54' @ X0))),
% 21.27/3.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl181])).
% 21.27/3.40 thf(zip_derived_cl186, plain,
% 21.27/3.40 (![X0 : reg]: ( (p @ ('#sk11' @ X0) @ X0) | ~ ('#form54' @ X0))),
% 21.27/3.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl182])).
% 21.27/3.40 thf(p, axiom, (p @ X0 @ X1) =>
% 21.27/3.40 ((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ X1)))))) = ($true))).
% 21.27/3.40 thf('4', plain,
% 21.27/3.40 (![X0:reg,X1:reg]:
% 21.27/3.40 ( ( p @ X0 @ X1 ) <=>
% 21.27/3.40 ( ![X6:reg]: ( ( c @ X6 @ X0 ) => ( c @ X6 @ X1 ) ) ) )),
% 21.27/3.40 inference('rw.lit', [status(esa)], [p])).
% 21.27/3.40 thf(zip_derived_cl190, plain,
% 21.27/3.40 (![X0 : reg]:
% 21.27/3.40 ( (((!!) @ (^[Y0 : reg]:
% 21.27/3.40 (((c @ Y0 @ ('#sk11' @ X0)) => (c @ Y0 @ X0))))))
% 21.27/3.40 | ~ ('#form54' @ X0))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl186, '4'])).
% 21.27/3.40 thf(zip_derived_cl194, plain,
% 21.27/3.40 (![X0 : reg, X2 : reg]:
% 21.27/3.40 ( (((c @ X2 @ ('#sk11' @ X0)) => (c @ X2 @ X0))) | ~ ('#form54' @ X0))),
% 21.27/3.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl190])).
% 21.27/3.40 thf(zip_derived_cl197, plain,
% 21.27/3.40 (![X0 : reg, X2 : reg]:
% 21.27/3.40 (~ (c @ X2 @ ('#sk11' @ X0)) | (c @ X2 @ X0) | ~ ('#form54' @ X0))),
% 21.27/3.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl194])).
% 21.27/3.40 thf(zip_derived_cl187, plain,
% 21.27/3.40 (![X0 : reg]: ( (p @ ('#sk11' @ X0) @ paris) | ~ ('#form54' @ X0))),
% 21.27/3.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl182])).
% 21.27/3.40 thf(zip_derived_cl191, plain,
% 21.27/3.40 (![X0 : reg]:
% 21.27/3.40 ( (((!!) @ (^[Y0 : reg]:
% 21.27/3.40 (((c @ Y0 @ ('#sk11' @ X0)) => (c @ Y0 @ paris))))))
% 21.27/3.40 | ~ ('#form54' @ X0))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl187, '4'])).
% 21.27/3.40 thf(zip_derived_cl195, plain,
% 21.27/3.40 (![X0 : reg, X2 : reg]:
% 21.27/3.40 ( (((c @ X2 @ ('#sk11' @ X0)) => (c @ X2 @ paris)))
% 21.27/3.40 | ~ ('#form54' @ X0))),
% 21.27/3.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl191])).
% 21.27/3.40 thf(zip_derived_cl198, plain,
% 21.27/3.40 (![X0 : reg, X2 : reg]:
% 21.27/3.40 (~ (c @ X2 @ ('#sk11' @ X0)) | (c @ X2 @ paris) | ~ ('#form54' @ X0))),
% 21.27/3.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl195])).
% 21.27/3.40 thf(c_reflexive, axiom, (![X:reg]: ( c @ X @ X ))).
% 21.27/3.40 thf(zip_derived_cl0, plain, ( (((!!) @ (^[Y0 : reg]: (c @ Y0 @ Y0))))),
% 21.27/3.40 inference('cnf', [status(esa)], [c_reflexive])).
% 21.27/3.40 thf(zip_derived_cl9, plain, (![X2 : reg]: (c @ X2 @ X2)),
% 21.27/3.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])).
% 21.27/3.40 thf(zip_derived_cl2642, plain,
% 21.27/3.40 (![X0 : reg]: (~ ('#form54' @ X0) | (c @ ('#sk11' @ X0) @ paris))),
% 21.27/3.40 inference('sup+', [status(thm)], [zip_derived_cl198, zip_derived_cl9])).
% 21.27/3.40 thf(c_symmetric, axiom, (![X:reg,Y:reg]: ( ( c @ X @ Y ) => ( c @ Y @ X ) ))).
% 21.27/3.40 thf(zip_derived_cl1, plain,
% 21.27/3.40 ( (((!!) @ (^[Y0 : reg]:
% 21.27/3.40 (((!!) @ (^[Y1 : reg]: (((c @ Y0 @ Y1) => (c @ Y1 @ Y0)))))))))),
% 21.27/3.40 inference('cnf', [status(esa)], [c_symmetric])).
% 21.27/3.40 thf(zip_derived_cl147, plain,
% 21.27/3.40 (![X2 : reg]:
% 21.27/3.40 (((!!) @ (^[Y0 : reg]: (((c @ X2 @ Y0) => (c @ Y0 @ X2))))))),
% 21.27/3.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])).
% 21.27/3.40 thf(zip_derived_cl148, plain,
% 21.27/3.40 (![X2 : reg, X4 : reg]: (((c @ X2 @ X4) => (c @ X4 @ X2)))),
% 21.27/3.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl147])).
% 21.27/3.40 thf(zip_derived_cl149, plain,
% 21.27/3.40 (![X2 : reg, X4 : reg]: (~ (c @ X2 @ X4) | (c @ X4 @ X2))),
% 21.27/3.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl148])).
% 21.27/3.40 thf(zip_derived_cl4458, plain,
% 21.27/3.40 (![X0 : reg]: (~ ('#form54' @ X0) | (c @ paris @ ('#sk11' @ X0)))),
% 21.27/3.40 inference('sup-', [status(thm)], [zip_derived_cl2642, zip_derived_cl149])).
% 21.27/3.40 thf(zip_derived_cl5975, plain,
% 21.27/3.40 (![X0 : reg]:
% 21.27/3.40 (~ ('#form54' @ X0) | (c @ paris @ X0) | ~ ('#form54' @ X0))),
% 21.27/3.40 inference('sup+', [status(thm)], [zip_derived_cl197, zip_derived_cl4458])).
% 21.27/3.40 thf(zip_derived_cl5995, plain,
% 21.27/3.40 (![X0 : reg]: ( (c @ paris @ X0) | ~ ('#form54' @ X0))),
% 21.27/3.40 inference('simplify', [status(thm)], [zip_derived_cl5975])).
% 21.27/3.40 thf(ax3, axiom,
% 21.27/3.40 (mvalid @ ( mbox @ a @ ( ^[X:$i]: ( ntpp @ paris @ france ) ) ))).
% 21.27/3.40 thf(zip_derived_cl7, plain,
% 21.27/3.40 ( (mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france))))),
% 21.27/3.40 inference('cnf', [status(esa)], [ax3])).
% 21.27/3.40 thf(mvalid, axiom, (mvalid @ X0) =>
% 21.27/3.40 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) = ($true))).
% 21.27/3.40 thf('5', plain,
% 21.27/3.40 (![X0:( $i > $o )]: ( ( mvalid @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 ) ) )),
% 21.27/3.40 inference('rw.lit', [status(esa)], [mvalid])).
% 21.27/3.40 thf(zip_derived_cl83, plain,
% 21.27/3.40 ( (((!!) @ (^[Y0 : $i]:
% 21.27/3.40 (mbox @ a @ (^[Y1 : $i]: (ntpp @ paris @ france)) @ Y0))))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl7, '5'])).
% 21.27/3.40 thf(zip_derived_cl84, plain,
% 21.27/3.40 (![X2 : $i]: (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)) @ X2)),
% 21.27/3.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl83])).
% 21.27/3.40 thf(mbox, axiom, (mbox @ X0 @ X1 @ X2) =>
% 21.27/3.40 ((((!!) @ (^[Y0 : $i]: (((((~) @ (X0 @ X2 @ Y0))) | (X1 @ Y0)))))) =
% 21.27/3.40 ($true))).
% 21.27/3.40 thf('6', plain,
% 21.27/3.40 (![X0:( $i > $i > $o ),X1:( $i > $o ),X2:$i]:
% 21.27/3.40 ( ( mbox @ X0 @ X1 @ X2 ) <=>
% 21.27/3.40 ( ![X7:$i]: ( ( ~( X0 @ X2 @ X7 ) ) | ( X1 @ X7 ) ) ) )),
% 21.27/3.40 inference('rw.lit', [status(esa)], [mbox])).
% 21.27/3.40 thf(zip_derived_cl85, plain,
% 21.27/3.40 (![X0 : $i]:
% 21.27/3.40 (((!!) @ (^[Y0 : $i]:
% 21.27/3.40 (((((~) @ (a @ X0 @ Y0))) |
% 21.27/3.40 ((^[Y1 : $i]: (ntpp @ paris @ france)) @ Y0))))))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl84, '6'])).
% 21.27/3.40 thf(zip_derived_cl86, plain,
% 21.27/3.40 (![X0 : $i]:
% 21.27/3.40 (((!!) @ (^[Y0 : $i]:
% 21.27/3.40 (((((~) @ (a @ X0 @ Y0))) | (ntpp @ paris @ france))))))),
% 21.27/3.40 inference('ho_norm', [status(thm)], [zip_derived_cl85])).
% 21.27/3.40 thf(zip_derived_cl87, plain,
% 21.27/3.40 (![X0 : $i, X2 : $i]:
% 21.27/3.40 (((((~) @ (a @ X0 @ X2))) | (ntpp @ paris @ france)))),
% 21.27/3.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl86])).
% 21.27/3.40 thf(zip_derived_cl88, plain,
% 21.27/3.40 (![X0 : $i, X2 : $i]: (~ (a @ X0 @ X2) | (ntpp @ paris @ france))),
% 21.27/3.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl87])).
% 21.27/3.40 thf(ntpp, axiom, (ntpp @ X0 @ X1) =>
% 21.27/3.40 ((((((~) @ (((??) @ (^[Y0 : reg]: (((ec @ Y0 @ X0) & (ec @ Y0 @ X1)))))))) &
% 21.27/3.40 (pp @ X0 @ X1)))
% 21.27/3.40 = ($true))).
% 21.27/3.40 thf('7', plain,
% 21.27/3.40 (![X0:reg,X1:reg]:
% 21.27/3.40 ( ( ntpp @ X0 @ X1 ) <=>
% 21.27/3.40 ( ( pp @ X0 @ X1 ) &
% 21.27/3.40 ( ~( ?[X6:reg]: ( ( ec @ X6 @ X0 ) & ( ec @ X6 @ X1 ) ) ) ) ) )),
% 21.27/3.40 inference('rw.lit', [status(esa)], [ntpp])).
% 21.27/3.40 thf(zip_derived_cl89, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i]:
% 21.27/3.40 ( (((((~) @ (((??) @ (^[Y0 : reg]:
% 21.27/3.40 (((ec @ Y0 @ paris) & (ec @ Y0 @ france)))))))) &
% 21.27/3.40 (pp @ paris @ france)))
% 21.27/3.40 | ~ (a @ X1 @ X0))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl88, '7'])).
% 21.27/3.40 thf(zip_derived_cl91, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i]: ( (pp @ paris @ france) | ~ (a @ X1 @ X0))),
% 21.27/3.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl89])).
% 21.27/3.40 thf(pp, axiom, (pp @ X0 @ X1) =>
% 21.27/3.40 ((((((~) @ (p @ X1 @ X0))) & (p @ X0 @ X1))) = ($true))).
% 21.27/3.40 thf('8', plain,
% 21.27/3.40 (![X0:reg,X1:reg]:
% 21.27/3.40 ( ( pp @ X0 @ X1 ) <=> ( ( p @ X0 @ X1 ) & ( ~( p @ X1 @ X0 ) ) ) )),
% 21.27/3.40 inference('rw.lit', [status(esa)], [pp])).
% 21.27/3.40 thf(zip_derived_cl93, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i]:
% 21.27/3.40 ( (((((~) @ (p @ france @ paris))) & (p @ paris @ france)))
% 21.27/3.40 | ~ (a @ X1 @ X0))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl91, '8'])).
% 21.27/3.40 thf(zip_derived_cl96, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i]: ( (p @ paris @ france) | ~ (a @ X1 @ X0))),
% 21.27/3.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])).
% 21.27/3.40 thf(zip_derived_cl99, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i]:
% 21.27/3.40 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ paris) => (c @ Y0 @ france))))))
% 21.27/3.40 | ~ (a @ X1 @ X0))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl96, '4'])).
% 21.27/3.40 thf(zip_derived_cl102, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i, X3 : reg]:
% 21.27/3.40 ( (((c @ X3 @ paris) => (c @ X3 @ france))) | ~ (a @ X1 @ X0))),
% 21.27/3.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl99])).
% 21.27/3.40 thf(zip_derived_cl106, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i, X3 : reg]:
% 21.27/3.40 (~ (c @ X3 @ paris) | (c @ X3 @ france) | ~ (a @ X1 @ X0))),
% 21.27/3.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])).
% 21.27/3.40 thf(zip_derived_cl173, plain, ( (a @ '#sk52' @ '#sk53')),
% 21.27/3.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl172])).
% 21.27/3.40 thf(zip_derived_cl666, plain,
% 21.27/3.40 (![X0 : reg]: ( (c @ X0 @ france) | ~ (c @ X0 @ paris))),
% 21.27/3.40 inference('sup+', [status(thm)], [zip_derived_cl106, zip_derived_cl173])).
% 21.27/3.40 thf(zip_derived_cl149, plain,
% 21.27/3.40 (![X2 : reg, X4 : reg]: (~ (c @ X2 @ X4) | (c @ X4 @ X2))),
% 21.27/3.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl148])).
% 21.27/3.40 thf(zip_derived_cl873, plain,
% 21.27/3.40 (![X0 : reg]: ( (c @ X0 @ france) | ~ (c @ paris @ X0))),
% 21.27/3.40 inference('sup+', [status(thm)], [zip_derived_cl666, zip_derived_cl149])).
% 21.27/3.40 thf(t_axiom_for_fool, axiom,
% 21.27/3.40 (mvalid @
% 21.27/3.40 ( mforall_prop @
% 21.27/3.40 ( ^[A:( $i > $o )]: ( mimplies @ ( mbox @ fool @ A ) @ A ) ) ))).
% 21.27/3.40 thf(zip_derived_cl2, plain,
% 21.27/3.40 ( (mvalid @
% 21.27/3.40 (mforall_prop @
% 21.27/3.40 (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0))))),
% 21.27/3.40 inference('cnf', [status(esa)], [t_axiom_for_fool])).
% 21.27/3.40 thf(zip_derived_cl134, plain,
% 21.27/3.40 ( (((!!) @ (^[Y0 : $i]:
% 21.27/3.40 (mforall_prop @
% 21.27/3.40 (^[Y1 : $i > $o]: (mimplies @ (mbox @ fool @ Y1) @ Y1)) @
% 21.27/3.40 Y0))))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl2, '5'])).
% 21.27/3.40 thf(zip_derived_cl135, plain,
% 21.27/3.40 (![X2 : $i]:
% 21.27/3.40 (mforall_prop @
% 21.27/3.40 (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0)) @ X2)),
% 21.27/3.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl134])).
% 21.27/3.40 thf(mforall_prop, axiom, (mforall_prop @ X0 @ X1) =>
% 21.27/3.40 ((((!!) @ (^[Y0 : $i > $o]: (X0 @ Y0 @ X1)))) = ($true))).
% 21.27/3.40 thf('9', plain,
% 21.27/3.40 (![X0:( ( $i > $o ) > $i > $o ),X1:$i]:
% 21.27/3.40 ( ( mforall_prop @ X0 @ X1 ) <=> ( ![X6:( $i > $o )]: ( X0 @ X6 @ X1 ) ) )),
% 21.27/3.40 inference('rw.lit', [status(esa)], [mforall_prop])).
% 21.27/3.40 thf(zip_derived_cl136, plain,
% 21.27/3.40 (![X0 : $i]:
% 21.27/3.40 (((!!) @ (^[Y0 : $i > $o]:
% 21.27/3.40 ((^[Y1 : $i > $o]: (mimplies @ (mbox @ fool @ Y1) @ Y1)) @
% 21.27/3.40 Y0 @ X0))))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl135, '9'])).
% 21.27/3.40 thf(zip_derived_cl137, plain,
% 21.27/3.40 (![X0 : $i]:
% 21.27/3.40 (((!!) @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0 @ X0))))),
% 21.27/3.40 inference('ho_norm', [status(thm)], [zip_derived_cl136])).
% 21.27/3.40 thf(zip_derived_cl138, plain,
% 21.27/3.40 (![X0 : $i, X2 : $i > $o]: (mimplies @ (mbox @ fool @ X2) @ X2 @ X0)),
% 21.27/3.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl137])).
% 21.27/3.40 thf(mimplies, axiom,(( mimplies @ (X0)@ (X1)@ (X2)) =
% 21.27/3.40 ((mor @ (mnot @ X0) @ X1 @ X2)))).
% 21.27/3.40 thf('10', plain,
% 21.27/3.40 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]:
% 21.27/3.40 ( ( mimplies @ X0 @ X1 @ X2 ) = ( mor @ ( mnot @ X0 ) @ X1 @ X2 ) )),
% 21.27/3.40 define([status(thm)])).
% 21.27/3.40 thf(zip_derived_cl139, plain,
% 21.27/3.40 (![X0 : $i, X2 : $i > $o]: (mor @ (mnot @ (mbox @ fool @ X2)) @ X2 @ X0)),
% 21.27/3.40 inference('rw', [status(thm)], [zip_derived_cl138, '10'])).
% 21.27/3.40 thf(mor, axiom, (mor @ X0 @ X1 @ X2) =>
% 21.27/3.40 ((((X1 @ X2) | (X0 @ X2))) = ($true))).
% 21.27/3.40 thf('11', plain,
% 21.27/3.40 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 21.27/3.40 ( ( mor @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) | ( X1 @ X2 ) ) )),
% 21.27/3.40 inference('rw.lit', [status(esa)], [mor])).
% 21.27/3.40 thf(zip_derived_cl140, plain,
% 21.27/3.40 (![X0 : $i > $o, X1 : $i]:
% 21.27/3.40 (((X0 @ X1) | (mnot @ (mbox @ fool @ X0) @ X1)))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl139, '11'])).
% 21.27/3.40 thf(zip_derived_cl141, plain,
% 21.27/3.40 (![X0 : $i > $o, X1 : $i]:
% 21.27/3.40 ( (X0 @ X1) | (mnot @ (mbox @ fool @ X0) @ X1))),
% 21.27/3.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl140])).
% 21.27/3.40 thf(mnot, axiom, (mnot @ X0 @ X1) => ((X0 @ X1) != ($true))).
% 21.27/3.40 thf('12', plain,
% 21.27/3.40 (![X0:( $i > $o ),X1:$i]: ( ( mnot @ X0 @ X1 ) <=> ( ~( X0 @ X1 ) ) )),
% 21.27/3.40 inference('rw.lit', [status(esa)], [mnot])).
% 21.27/3.40 thf(zip_derived_cl142, plain,
% 21.27/3.40 (![X0 : $i > $o, X1 : $i]: (~ (mbox @ fool @ X0 @ X1) | (X0 @ X1))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl141, '12'])).
% 21.27/3.40 thf(zip_derived_cl143, plain,
% 21.27/3.40 (![X0 : $i > $o, X1 : $i]:
% 21.27/3.40 (~ (((!!) @ (^[Y0 : $i]: (((((~) @ (fool @ X1 @ Y0))) | (X0 @ Y0))))))
% 21.27/3.40 | (X0 @ X1))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl142, '1'])).
% 21.27/3.40 thf(zip_derived_cl144, plain,
% 21.27/3.40 (![X0 : $i > $o, X1 : $i]:
% 21.27/3.40 (~ (((((~) @ (fool @ X1 @ ('#sk21' @ X0 @ X1)))) | (X0 @
% 21.27/3.40 ('#sk21' @ X0 @ X1))))
% 21.27/3.40 | (X0 @ X1))),
% 21.27/3.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl143])).
% 21.27/3.40 thf(zip_derived_cl146, plain,
% 21.27/3.40 (![X0 : $i > $o, X1 : $i]: (~ (X0 @ ('#sk21' @ X0 @ X1)) | (X0 @ X1))),
% 21.27/3.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl144])).
% 21.27/3.40 thf(zip_derived_cl280, plain,
% 21.27/3.40 (![X0 : $i]:
% 21.27/3.40 (~ ((^[Y0 : $i]: (((X0) != (Y0)))) @
% 21.27/3.40 ('#sk21' @ (^[Y0 : $i]: (((X0) != (Y0)))) @ X0))
% 21.27/3.40 | ((^[Y0 : $i]: (((X0) != (Y0)))) @ X0))),
% 21.27/3.40 inference('elim_leibniz_eq_+', [status(thm)], [zip_derived_cl146])).
% 21.27/3.40 thf(zip_derived_cl290, plain,
% 21.27/3.40 (![X0 : $i]:
% 21.27/3.40 (~ (((X0) != ('#sk21' @ ((($i) != (X0))) @ X0))) | (((X0) != (X0))))),
% 21.27/3.40 inference('ho_norm', [status(thm)], [zip_derived_cl280])).
% 21.27/3.40 thf(zip_derived_cl291, plain,
% 21.27/3.40 (![X0 : $i]: ~ (((X0) != ('#sk21' @ ((($i) != (X0))) @ X0)))),
% 21.27/3.40 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl290])).
% 21.27/3.40 thf(zip_derived_cl292, plain,
% 21.27/3.40 (![X0 : $i]: ((X0) = ('#sk21' @ ((($i) != (X0))) @ X0))),
% 21.27/3.40 inference('simplify nested equalities', [status(thm)],
% 21.27/3.40 [zip_derived_cl291])).
% 21.27/3.40 thf(zip_derived_cl145, plain,
% 21.27/3.40 (![X0 : $i > $o, X1 : $i]:
% 21.27/3.40 ( (fool @ X1 @ ('#sk21' @ X0 @ X1)) | (X0 @ X1))),
% 21.27/3.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl144])).
% 21.27/3.40 thf(zip_derived_cl948, plain,
% 21.27/3.40 (![X0 : $i]: ( (fool @ X0 @ X0) | (((X0) != (X0))))),
% 21.27/3.40 inference('sup+', [status(thm)], [zip_derived_cl292, zip_derived_cl145])).
% 21.27/3.40 thf(zip_derived_cl970, plain, (![X0 : $i]: (fool @ X0 @ X0)),
% 21.27/3.40 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl948])).
% 21.27/3.40 thf(ax2, axiom,
% 21.27/3.40 (mvalid @ ( mbox @ fool @ ( ^[X:$i]: ( ec @ spain @ france ) ) ))).
% 21.27/3.40 thf(zip_derived_cl6, plain,
% 21.27/3.40 ( (mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france))))),
% 21.27/3.40 inference('cnf', [status(esa)], [ax2])).
% 21.27/3.40 thf(zip_derived_cl60, plain,
% 21.27/3.40 ( (((!!) @ (^[Y0 : $i]:
% 21.27/3.40 (mbox @ fool @ (^[Y1 : $i]: (ec @ spain @ france)) @ Y0))))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl6, '5'])).
% 21.27/3.40 thf(zip_derived_cl61, plain,
% 21.27/3.40 (![X2 : $i]: (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france)) @ X2)),
% 21.27/3.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl60])).
% 21.27/3.40 thf(zip_derived_cl62, plain,
% 21.27/3.40 (![X0 : $i]:
% 21.27/3.40 (((!!) @ (^[Y0 : $i]:
% 21.27/3.40 (((((~) @ (fool @ X0 @ Y0))) |
% 21.27/3.40 ((^[Y1 : $i]: (ec @ spain @ france)) @ Y0))))))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl61, '6'])).
% 21.27/3.40 thf(zip_derived_cl63, plain,
% 21.27/3.40 (![X0 : $i]:
% 21.27/3.40 (((!!) @ (^[Y0 : $i]:
% 21.27/3.40 (((((~) @ (fool @ X0 @ Y0))) | (ec @ spain @ france))))))),
% 21.27/3.40 inference('ho_norm', [status(thm)], [zip_derived_cl62])).
% 21.27/3.40 thf(zip_derived_cl64, plain,
% 21.27/3.40 (![X0 : $i, X2 : $i]:
% 21.27/3.40 (((((~) @ (fool @ X0 @ X2))) | (ec @ spain @ france)))),
% 21.27/3.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])).
% 21.27/3.40 thf(zip_derived_cl65, plain,
% 21.27/3.40 (![X0 : $i, X2 : $i]: (~ (fool @ X0 @ X2) | (ec @ spain @ france))),
% 21.27/3.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl64])).
% 21.27/3.40 thf(ec, axiom, (ec @ X0 @ X1) =>
% 21.27/3.40 ((((((~) @ (o @ X0 @ X1))) & (c @ X0 @ X1))) = ($true))).
% 21.27/3.40 thf('13', plain,
% 21.27/3.40 (![X0:reg,X1:reg]:
% 21.27/3.40 ( ( ec @ X0 @ X1 ) <=> ( ( c @ X0 @ X1 ) & ( ~( o @ X0 @ X1 ) ) ) )),
% 21.27/3.40 inference('rw.lit', [status(esa)], [ec])).
% 21.27/3.40 thf(zip_derived_cl66, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i]:
% 21.27/3.40 ( (((((~) @ (o @ spain @ france))) & (c @ spain @ france)))
% 21.27/3.40 | ~ (fool @ X1 @ X0))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl65, '13'])).
% 21.27/3.40 thf(zip_derived_cl67, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i]: (~ (o @ spain @ france) | ~ (fool @ X1 @ X0))),
% 21.27/3.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl66])).
% 21.27/3.40 thf(o, axiom, ~ (o @ X0 @ X1) =>
% 21.27/3.40 ((((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ X1)))))) != ($true))).
% 21.27/3.40 thf('14', plain,
% 21.27/3.40 (![X0:reg,X1:reg]:
% 21.27/3.40 ( ( ~( o @ X0 @ X1 ) ) <=>
% 21.27/3.40 ( ~( ?[X6:reg]: ( ( p @ X6 @ X0 ) & ( p @ X6 @ X1 ) ) ) ) )),
% 21.27/3.40 inference('rw.lit', [status(esa)], [o])).
% 21.27/3.40 thf(zip_derived_cl69, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i]:
% 21.27/3.40 (~ (((??) @ (^[Y0 : reg]: (((p @ Y0 @ spain) & (p @ Y0 @ france))))))
% 21.27/3.40 | ~ (fool @ X1 @ X0))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl67, '14'])).
% 21.27/3.40 thf(zip_derived_cl70, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i, X3 : reg]:
% 21.27/3.40 (~ (((p @ X3 @ spain) & (p @ X3 @ france))) | ~ (fool @ X1 @ X0))),
% 21.27/3.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl69])).
% 21.27/3.40 thf(zip_derived_cl71, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i, X3 : reg]:
% 21.27/3.40 (~ (p @ X3 @ spain) | ~ (p @ X3 @ france) | ~ (fool @ X1 @ X0))),
% 21.27/3.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl70])).
% 21.27/3.40 thf(p, axiom, ~ (p @ X0 @ X1) =>
% 21.27/3.40 ((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ X1)))))) != ($true))).
% 21.27/3.40 thf('15', plain,
% 21.27/3.40 (![X0:reg,X1:reg]:
% 21.27/3.40 ( ( ~( p @ X0 @ X1 ) ) <=>
% 21.27/3.40 ( ~( ![X6:reg]: ( ( c @ X6 @ X0 ) => ( c @ X6 @ X1 ) ) ) ) )),
% 21.27/3.40 inference('rw.lit', [status(esa)], [p])).
% 21.27/3.40 thf(zip_derived_cl72, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i, X2 : reg]:
% 21.27/3.40 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain))))))
% 21.27/3.40 | ~ (fool @ X1 @ X0)
% 21.27/3.40 | ~ (p @ X2 @ france))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl71, '15'])).
% 21.27/3.40 thf(zip_derived_cl73, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i, X2 : reg]:
% 21.27/3.40 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ france))))))
% 21.27/3.40 | ~ (fool @ X1 @ X0)
% 21.27/3.40 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl72, '15'])).
% 21.27/3.40 thf(zip_derived_cl74, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i, X2 : reg]:
% 21.27/3.40 (~ (((c @ ('#sk7' @ X2) @ X2) => (c @ ('#sk7' @ X2) @ france)))
% 21.27/3.40 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain))))))
% 21.27/3.40 | ~ (fool @ X1 @ X0))),
% 21.27/3.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl73])).
% 21.27/3.40 thf(zip_derived_cl76, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i, X2 : reg]:
% 21.27/3.40 (~ (c @ ('#sk7' @ X2) @ france)
% 21.27/3.40 | ~ (fool @ X1 @ X0)
% 21.27/3.40 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 21.27/3.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])).
% 21.27/3.40 thf(zip_derived_cl75, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i, X2 : reg]:
% 21.27/3.40 ( (c @ ('#sk7' @ X2) @ X2)
% 21.27/3.40 | ~ (fool @ X1 @ X0)
% 21.27/3.40 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 21.27/3.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])).
% 21.27/3.40 thf(zip_derived_cl77, plain,
% 21.27/3.40 (![X2 : reg]:
% 21.27/3.40 ( ('#form8' @ X2)
% 21.27/3.40 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 21.27/3.40 define([status(thm)])).
% 21.27/3.40 thf(zip_derived_cl80, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i, X2 : reg]:
% 21.27/3.40 (~ ('#form8' @ X2)
% 21.27/3.40 | ~ (fool @ X1 @ X0)
% 21.27/3.40 | ~ (c @ ('#sk7' @ X2) @ france))),
% 21.27/3.40 inference('renaming', [status(thm)], [zip_derived_cl76, zip_derived_cl77])).
% 21.27/3.40 thf(zip_derived_cl1163, plain,
% 21.27/3.40 (![X1 : reg]: (~ (c @ ('#sk7' @ X1) @ france) | ~ ('#form8' @ X1))),
% 21.27/3.40 inference('sup-', [status(thm)], [zip_derived_cl970, zip_derived_cl80])).
% 21.27/3.40 thf(zip_derived_cl4315, plain,
% 21.27/3.40 (![X0 : reg]: (~ (c @ paris @ ('#sk7' @ X0)) | ~ ('#form8' @ X0))),
% 21.27/3.40 inference('sup-', [status(thm)], [zip_derived_cl873, zip_derived_cl1163])).
% 21.27/3.40 thf(zip_derived_cl6069, plain,
% 21.27/3.40 (![X0 : reg]: (~ ('#form54' @ ('#sk7' @ X0)) | ~ ('#form8' @ X0))),
% 21.27/3.40 inference('sup-', [status(thm)], [zip_derived_cl5995, zip_derived_cl4315])).
% 21.27/3.40 thf(zip_derived_cl179, plain,
% 21.27/3.40 (![X0 : reg]:
% 21.27/3.40 ( (p @ spain @ X0)
% 21.27/3.40 | (((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ paris)))))))),
% 21.27/3.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl178])).
% 21.27/3.40 thf(zip_derived_cl181, plain,
% 21.27/3.40 (![X0 : reg]:
% 21.27/3.40 (~ ('#form54' @ X0)
% 21.27/3.40 | (((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ paris)))))))),
% 21.27/3.40 define([status(thm)])).
% 21.27/3.40 thf(zip_derived_cl183, plain,
% 21.27/3.40 (![X0 : reg]: ( ('#form54' @ X0) | (p @ spain @ X0))),
% 21.27/3.40 inference('renaming', [status(thm)],
% 21.27/3.40 [zip_derived_cl179, zip_derived_cl181])).
% 21.27/3.40 thf(zip_derived_cl185, plain,
% 21.27/3.40 (![X0 : reg]:
% 21.27/3.40 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ spain) => (c @ Y0 @ X0))))))
% 21.27/3.40 | ('#form54' @ X0))),
% 21.27/3.40 inference('rw_clause', [status(thm)], [zip_derived_cl183, '4'])).
% 21.27/3.40 thf(zip_derived_cl189, plain,
% 21.27/3.40 (![X0 : reg, X2 : reg]:
% 21.27/3.40 ( (((c @ X2 @ spain) => (c @ X2 @ X0))) | ('#form54' @ X0))),
% 21.27/3.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl185])).
% 21.27/3.40 thf(zip_derived_cl193, plain,
% 21.27/3.40 (![X0 : reg, X2 : reg]:
% 21.27/3.40 (~ (c @ X2 @ spain) | (c @ X2 @ X0) | ('#form54' @ X0))),
% 21.27/3.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl189])).
% 21.27/3.40 thf(zip_derived_cl1163, plain,
% 21.27/3.40 (![X1 : reg]: (~ (c @ ('#sk7' @ X1) @ france) | ~ ('#form8' @ X1))),
% 21.27/3.40 inference('sup-', [status(thm)], [zip_derived_cl970, zip_derived_cl80])).
% 21.27/3.40 thf(zip_derived_cl149, plain,
% 21.27/3.40 (![X2 : reg, X4 : reg]: (~ (c @ X2 @ X4) | (c @ X4 @ X2))),
% 21.27/3.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl148])).
% 21.27/3.40 thf(zip_derived_cl1184, plain,
% 21.27/3.40 (![X0 : reg]: (~ ('#form8' @ X0) | ~ (c @ france @ ('#sk7' @ X0)))),
% 21.27/3.40 inference('sup+', [status(thm)], [zip_derived_cl1163, zip_derived_cl149])).
% 21.27/3.40 thf(zip_derived_cl1911, plain,
% 21.27/3.40 (![X0 : reg]:
% 21.27/3.40 ( ('#form54' @ ('#sk7' @ X0))
% 21.27/3.40 | ~ (c @ france @ spain)
% 21.27/3.40 | ~ ('#form8' @ X0))),
% 21.27/3.40 inference('sup-', [status(thm)], [zip_derived_cl193, zip_derived_cl1184])).
% 21.27/3.40 thf(zip_derived_cl970, plain, (![X0 : $i]: (fool @ X0 @ X0)),
% 21.27/3.40 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl948])).
% 21.27/3.40 thf(zip_derived_cl68, plain,
% 21.27/3.40 (![X0 : $i, X1 : $i]: ( (c @ spain @ france) | ~ (fool @ X1 @ X0))),
% 21.27/3.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl66])).
% 21.27/3.40 thf(zip_derived_cl1165, plain, ( (c @ spain @ france)),
% 21.27/3.40 inference('sup-', [status(thm)], [zip_derived_cl970, zip_derived_cl68])).
% 21.27/3.40 thf(zip_derived_cl149, plain,
% 21.27/3.40 (![X2 : reg, X4 : reg]: (~ (c @ X2 @ X4) | (c @ X4 @ X2))),
% 21.27/3.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl148])).
% 21.27/3.40 thf(zip_derived_cl1480, plain, ( (c @ france @ spain)),
% 21.27/3.40 inference('sup-', [status(thm)], [zip_derived_cl1165, zip_derived_cl149])).
% 21.27/3.40 thf(zip_derived_cl1918, plain,
% 21.27/3.40 (![X0 : reg]: ( ('#form54' @ ('#sk7' @ X0)) | ~ ('#form8' @ X0))),
% 21.27/3.40 inference('demod', [status(thm)],
% 21.27/3.40 [zip_derived_cl1911, zip_derived_cl1480])).
% 21.27/3.40 thf(zip_derived_cl6240, plain, (![X0 : reg]: ~ ('#form8' @ X0)),
% 21.27/3.40 inference('clc', [status(thm)], [zip_derived_cl6069, zip_derived_cl1918])).
% 21.27/3.40 thf(zip_derived_cl77, plain,
% 21.27/3.40 (![X2 : reg]:
% 21.27/3.40 ( ('#form8' @ X2)
% 21.27/3.40 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 21.27/3.40 define([status(thm)])).
% 21.27/3.40 thf(zip_derived_cl78, plain,
% 21.27/3.40 (![X2 : reg]:
% 21.27/3.40 (~ (((c @ ('#sk4' @ X2) @ X2) => (c @ ('#sk4' @ X2) @ spain)))
% 21.27/3.40 | ('#form8' @ X2))),
% 21.27/3.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl77])).
% 21.27/3.40 thf(zip_derived_cl82, plain,
% 21.27/3.40 (![X2 : reg]: (~ (c @ ('#sk4' @ X2) @ spain) | ('#form8' @ X2))),
% 21.27/3.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])).
% 21.27/3.40 thf(zip_derived_cl81, plain,
% 21.27/3.40 (![X2 : reg]: ( (c @ ('#sk4' @ X2) @ X2) | ('#form8' @ X2))),
% 21.27/3.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])).
% 21.27/3.40 thf(zip_derived_cl536, plain, (( ('#form8' @ spain) | ('#form8' @ spain))),
% 21.27/3.40 inference('sup+', [status(thm)], [zip_derived_cl82, zip_derived_cl81])).
% 21.27/3.40 thf(zip_derived_cl550, plain, ( ('#form8' @ spain)),
% 21.27/3.40 inference('simplify', [status(thm)], [zip_derived_cl536])).
% 21.27/3.40 thf(zip_derived_cl6248, plain, ($false),
% 21.27/3.40 inference('sup+', [status(thm)], [zip_derived_cl6240, zip_derived_cl550])).
% 21.27/3.40
% 21.27/3.40 % SZS output end Refutation
% 21.27/3.40
% 21.27/3.40
% 21.27/3.40 % Terminating...
% 22.69/3.66 % Runner terminated.
% 22.69/3.68 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------