%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO683-1 : TPTP v9.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.xHLvnnOdJD true
% Computer : n024.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 05:08:08 PM UTC 2025
% Result : Unsatisfiable 0.58s 0.89s
% Output : Refutation 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO683-1 : TPTP v9.2.0. Released v7.3.0.
% 0.04/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.xHLvnnOdJD true
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 17:59:53 EDT 2025
% 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 FO mode
% 0.55/0.64 % Total configuration time : 435
% 0.55/0.64 % Estimated wc time : 1092
% 0.55/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.57/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.58/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.58/0.89 % Solved by fo/fo4.sh.
% 0.58/0.89 % done 92 iterations in 0.096s
% 0.58/0.89 % SZS status Unsatisfiable for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.58/0.89 % SZS output start Refutation
% 0.58/0.89 thf(suc_type, type, suc: $i > $i).
% 0.58/0.89 thf(z_type, type, z: $i).
% 0.58/0.89 thf(f_type, type, f: $i > $i).
% 0.58/0.89 thf(0_type, type, 0: $i).
% 0.58/0.89 thf(E_type, type, E: $i > $i > $o).
% 0.58/0.89 thf(LE_type, type, LE: $i > $i > $o).
% 0.58/0.89 thf(s_type, type, s: $i > $i).
% 0.58/0.89 thf(iLEQ_type, type, iLEQ: $i > $i > $o).
% 0.58/0.89 thf(clause_287, axiom, (~( LE @ ( f @ z ) @ 0 ))).
% 0.58/0.89 thf(zip_derived_cl8, plain, (~ (LE @ (f @ z) @ 0)),
% 0.58/0.89 inference('cnf', [status(esa)], [clause_287])).
% 0.58/0.89 thf(clause_547, axiom,
% 0.58/0.89 (( ~( LE @ ( f @ ( suc @ B_309 ) ) @ ( s @ 0 ) ) ) |
% 0.58/0.89 ( E @ 0 @ ( f @ ( suc @ B_309 ) ) ) | ( LE @ ( f @ B_309 ) @ 0 ))).
% 0.58/0.89 thf(zip_derived_cl9, plain,
% 0.58/0.89 (![X0 : $i]:
% 0.58/0.89 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 0.58/0.89 | (E @ 0 @ (f @ (suc @ X0)))
% 0.58/0.89 | (LE @ (f @ X0) @ 0))),
% 0.58/0.89 inference('cnf', [status(esa)], [clause_547])).
% 0.58/0.89 thf(clause_222, axiom,
% 0.58/0.89 (( ~( LE @ ( f @ ( suc @ B_291 ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 0.58/0.89 ( E @ ( s @ 0 ) @ ( f @ ( suc @ B_291 ) ) ) |
% 0.58/0.89 ( LE @ ( f @ B_291 ) @ ( s @ 0 ) ))).
% 0.58/0.89 thf(zip_derived_cl13, plain,
% 0.58/0.89 (![X0 : $i]:
% 0.58/0.89 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 0.58/0.89 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.58/0.89 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.58/0.89 inference('cnf', [status(esa)], [clause_222])).
% 0.58/0.89 thf(clause_476, axiom,
% 0.58/0.89 (( ~( LE @ ( f @ ( suc @ B_247 ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 0.58/0.89 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_247 ) ) ) |
% 0.58/0.89 ( LE @ ( f @ B_247 ) @ ( s @ ( s @ 0 ) ) ))).
% 0.58/0.89 thf(zip_derived_cl5, plain,
% 0.58/0.89 (![X0 : $i]:
% 0.58/0.89 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0))))
% 0.58/0.89 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.58/0.89 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.58/0.89 inference('cnf', [status(esa)], [clause_476])).
% 0.58/0.89 thf(clause_443, axiom,
% 0.58/0.89 (( ~( LE @ ( f @ ( suc @ B_158 ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 0.58/0.89 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_158 ) ) ) |
% 0.58/0.89 ( LE @ ( f @ B_158 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 0.58/0.89 thf(zip_derived_cl7, plain,
% 0.58/0.89 (![X0 : $i]:
% 0.58/0.89 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ (s @ 0)))))
% 0.58/0.89 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.58/0.89 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.58/0.89 inference('cnf', [status(esa)], [clause_443])).
% 0.58/0.89 thf(clause_451, axiom, (LE @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 0.58/0.89 thf(zip_derived_cl2, plain,
% 0.58/0.89 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 0.58/0.89 inference('cnf', [status(esa)], [clause_451])).
% 0.58/0.89 thf(zip_derived_cl32, plain,
% 0.58/0.89 (![X0 : $i]:
% 0.58/0.89 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.58/0.89 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.58/0.89 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.58/0.89 thf(clause_560, axiom,
% 0.58/0.89 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_159 ) ) ) ) |
% 0.58/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_162 ) ) ) |
% 0.58/0.89 ( ~( iLEQ @ ( suc @ B_160 ) @ ( suc @ B_161 ) ) ) |
% 0.58/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_162 ) ) ) ) |
% 0.58/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_159 ) ) ) |
% 0.58/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_161 ) ) ) |
% 0.58/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_160 ) ) ) |
% 0.58/0.89 ( ~( iLEQ @ ( suc @ B_159 ) @ ( suc @ B_160 ) ) ) |
% 0.58/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 0.58/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_161 ) ) ) ) |
% 0.58/0.89 ( ~( iLEQ @ ( suc @ B_161 ) @ ( suc @ B_162 ) ) ) |
% 0.58/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_160 ) ) ) ) |
% 0.58/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.58/0.89 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_159 ) ) ))).
% 0.58/0.89 thf(zip_derived_cl4, plain,
% 0.58/0.89 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.58/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X3))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X4))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X3)))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X3) @ (suc @ X1))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X4)))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X4) @ (suc @ X0)))),
% 0.58/0.89 inference('cnf', [status(esa)], [clause_560])).
% 0.58/0.89 thf(zip_derived_cl18, plain,
% 0.58/0.89 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.89 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X3)))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X3))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 0.58/0.89 inference('eq_fact', [status(thm)], [zip_derived_cl4])).
% 0.58/0.89 thf(zip_derived_cl22, plain,
% 0.58/0.89 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.89 (~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X3))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X3)))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0)))),
% 0.58/0.89 inference('simplify', [status(thm)], [zip_derived_cl18])).
% 0.58/0.89 thf(zip_derived_cl99, plain,
% 0.58/0.89 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.89 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0)))),
% 0.58/0.89 inference('eq_fact', [status(thm)], [zip_derived_cl22])).
% 0.58/0.89 thf(zip_derived_cl102, plain,
% 0.58/0.89 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.89 (~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0)))),
% 0.58/0.89 inference('simplify', [status(thm)], [zip_derived_cl99])).
% 0.58/0.89 thf(zip_derived_cl140, plain,
% 0.58/0.89 (![X0 : $i, X1 : $i]:
% 0.58/0.89 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.58/0.89 inference('eq_fact', [status(thm)], [zip_derived_cl102])).
% 0.58/0.89 thf(zip_derived_cl142, plain,
% 0.58/0.89 (![X0 : $i, X1 : $i]:
% 0.58/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0)))),
% 0.58/0.89 inference('simplify', [status(thm)], [zip_derived_cl140])).
% 0.58/0.89 thf(clause_59, axiom,
% 0.58/0.89 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 0.58/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.58/0.89 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 0.58/0.89 thf(zip_derived_cl12, plain,
% 0.58/0.89 (![X0 : $i]:
% 0.58/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.58/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.58/0.89 inference('cnf', [status(esa)], [clause_59])).
% 0.58/0.89 thf(zip_derived_cl144, plain,
% 0.58/0.89 (![X0 : $i, X1 : $i]:
% 0.58/0.89 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 0.58/0.89 inference('clc', [status(thm)], [zip_derived_cl142, zip_derived_cl12])).
% 0.58/0.89 thf(zip_derived_cl148, plain,
% 0.58/0.89 (![X0 : $i]:
% 0.58/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.58/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.58/0.89 inference('eq_fact', [status(thm)], [zip_derived_cl144])).
% 0.58/0.89 thf(zip_derived_cl149, plain,
% 0.58/0.89 (![X0 : $i]:
% 0.58/0.89 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 0.58/0.89 inference('simplify', [status(thm)], [zip_derived_cl148])).
% 0.58/0.89 thf(zip_derived_cl12, plain,
% 0.58/0.89 (![X0 : $i]:
% 0.58/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.58/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.58/0.89 inference('cnf', [status(esa)], [clause_59])).
% 0.58/0.89 thf(zip_derived_cl150, plain,
% 0.58/0.89 (![X0 : $i]:
% 0.58/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 0.58/0.89 inference('clc', [status(thm)], [zip_derived_cl149, zip_derived_cl12])).
% 0.58/0.89 thf(zip_derived_cl152, plain,
% 0.58/0.89 (![X0 : $i]:
% 0.58/0.89 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.58/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 0.58/0.89 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl150])).
% 0.58/0.89 thf(clause_539, axiom,
% 0.58/0.89 (( ~( LE @ ( f @ B_158 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 0.58/0.89 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_158 ) ) |
% 0.58/0.89 ( LE @ ( f @ B_158 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 0.58/0.89 thf(zip_derived_cl11, plain,
% 0.58/0.89 (![X0 : $i]:
% 0.58/0.89 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 0.58/0.89 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.58/0.89 inference('cnf', [status(esa)], [clause_539])).
% 0.58/0.89 thf(zip_derived_cl2, plain,
% 0.58/0.89 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 0.58/0.89 inference('cnf', [status(esa)], [clause_451])).
% 0.58/0.89 thf(zip_derived_cl26, plain,
% 0.58/0.89 (![X0 : $i]:
% 0.58/0.89 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.58/0.89 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.58/0.89 inference('demod', [status(thm)], [zip_derived_cl11, zip_derived_cl2])).
% 0.58/0.89 thf(zip_derived_cl154, plain,
% 0.58/0.90 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 0.58/0.90 inference('clc', [status(thm)], [zip_derived_cl152, zip_derived_cl26])).
% 0.58/0.90 thf(zip_derived_cl155, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.58/0.90 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.58/0.90 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl154])).
% 0.58/0.90 thf(clause_563, axiom,
% 0.58/0.90 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_249 ) ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_250 ) ) ) |
% 0.58/0.90 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_248 ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_248 ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_251 ) ) ) ) |
% 0.58/0.90 ( ~( iLEQ @ ( suc @ B_249 ) @ ( suc @ B_250 ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_251 ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_248 ) ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_250 ) ) ) ) |
% 0.58/0.90 ( ~( iLEQ @ ( suc @ B_248 ) @ ( suc @ B_249 ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_249 ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 0.58/0.90 ( ~( iLEQ @ ( suc @ B_250 ) @ ( suc @ B_251 ) ) ))).
% 0.58/0.90 thf(zip_derived_cl10, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.58/0.90 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X3))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X4)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X4))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X3)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X4)))),
% 0.58/0.90 inference('cnf', [status(esa)], [clause_563])).
% 0.58/0.90 thf(zip_derived_cl68, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.90 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X3)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X3))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X1)))),
% 0.58/0.90 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 0.58/0.90 thf(zip_derived_cl72, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.90 (~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X3))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X3)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0)))),
% 0.58/0.90 inference('simplify', [status(thm)], [zip_derived_cl68])).
% 0.58/0.90 thf(zip_derived_cl190, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.90 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 0.58/0.90 inference('eq_fact', [status(thm)], [zip_derived_cl72])).
% 0.58/0.90 thf(zip_derived_cl193, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.90 (~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.58/0.90 inference('simplify', [status(thm)], [zip_derived_cl190])).
% 0.58/0.90 thf(zip_derived_cl197, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i]:
% 0.58/0.90 (~ (iLEQ @ (suc @ X1) @ (suc @ X1))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.58/0.90 inference('eq_fact', [status(thm)], [zip_derived_cl193])).
% 0.58/0.90 thf(zip_derived_cl199, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i]:
% 0.58/0.90 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X1)))),
% 0.58/0.90 inference('simplify', [status(thm)], [zip_derived_cl197])).
% 0.58/0.90 thf(clause_29, axiom,
% 0.58/0.90 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.58/0.90 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 0.58/0.90 thf(zip_derived_cl3, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.58/0.90 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.58/0.90 inference('cnf', [status(esa)], [clause_29])).
% 0.58/0.90 thf(zip_derived_cl201, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i]:
% 0.58/0.90 (~ (iLEQ @ (suc @ X1) @ (suc @ X1))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 0.58/0.90 inference('clc', [status(thm)], [zip_derived_cl199, zip_derived_cl3])).
% 0.58/0.90 thf(zip_derived_cl3, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.58/0.90 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.58/0.90 inference('cnf', [status(esa)], [clause_29])).
% 0.58/0.90 thf(zip_derived_cl202, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i]:
% 0.58/0.90 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 0.58/0.90 inference('clc', [status(thm)], [zip_derived_cl201, zip_derived_cl3])).
% 0.58/0.90 thf(zip_derived_cl206, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 0.58/0.90 inference('eq_fact', [status(thm)], [zip_derived_cl202])).
% 0.58/0.90 thf(zip_derived_cl207, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 0.58/0.90 inference('simplify', [status(thm)], [zip_derived_cl206])).
% 0.58/0.90 thf(zip_derived_cl3, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.58/0.90 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.58/0.90 inference('cnf', [status(esa)], [clause_29])).
% 0.58/0.90 thf(zip_derived_cl208, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 0.58/0.90 inference('clc', [status(thm)], [zip_derived_cl207, zip_derived_cl3])).
% 0.58/0.90 thf(zip_derived_cl210, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 ( (LE @ (f @ X0) @ (s @ (s @ 0))) | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 0.58/0.90 inference('sup-', [status(thm)], [zip_derived_cl155, zip_derived_cl208])).
% 0.58/0.90 thf(clause_97, axiom,
% 0.58/0.90 (( ~( LE @ ( f @ B_247 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 0.58/0.90 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_247 ) ) |
% 0.58/0.90 ( LE @ ( f @ B_247 ) @ ( s @ ( s @ 0 ) ) ))).
% 0.58/0.90 thf(zip_derived_cl6, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.58/0.90 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.58/0.90 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.58/0.90 inference('cnf', [status(esa)], [clause_97])).
% 0.58/0.90 thf(zip_derived_cl154, plain,
% 0.58/0.90 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 0.58/0.90 inference('clc', [status(thm)], [zip_derived_cl152, zip_derived_cl26])).
% 0.58/0.90 thf(zip_derived_cl156, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.58/0.90 inference('demod', [status(thm)], [zip_derived_cl6, zip_derived_cl154])).
% 0.58/0.90 thf(zip_derived_cl212, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 0.58/0.90 inference('clc', [status(thm)], [zip_derived_cl210, zip_derived_cl156])).
% 0.58/0.90 thf(zip_derived_cl213, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 0.58/0.90 inference('demod', [status(thm)], [zip_derived_cl13, zip_derived_cl212])).
% 0.58/0.90 thf(clause_151, axiom,
% 0.58/0.90 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_294 ) ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ 0 ) @ ( f @ B_295 ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_295 ) ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_292 ) ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ 0 ) @ ( f @ B_294 ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ 0 ) @ ( f @ B_292 ) ) ) |
% 0.58/0.90 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_292 ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ 0 ) @ ( f @ B_293 ) ) ) |
% 0.58/0.90 ( ~( iLEQ @ ( suc @ B_294 ) @ ( suc @ B_295 ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_293 ) ) ) ) |
% 0.58/0.90 ( ~( iLEQ @ ( suc @ B_293 ) @ ( suc @ B_294 ) ) ) |
% 0.58/0.90 ( ~( iLEQ @ ( suc @ B_292 ) @ ( suc @ B_293 ) ) ))).
% 0.58/0.90 thf(zip_derived_cl17, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.58/0.90 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X1))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X2))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X4))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X3))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X4)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X4) @ (suc @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X2) @ (suc @ X4)))),
% 0.58/0.90 inference('cnf', [status(esa)], [clause_151])).
% 0.58/0.90 thf(zip_derived_cl60, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.90 (~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X3))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X1))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X2))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 0.58/0.90 inference('eq_fact', [status(thm)], [zip_derived_cl17])).
% 0.58/0.90 thf(zip_derived_cl64, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.90 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X2))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X1))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X3))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1)))),
% 0.58/0.90 inference('simplify', [status(thm)], [zip_derived_cl60])).
% 0.58/0.90 thf(zip_derived_cl116, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.90 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X2))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X1))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X1))))),
% 0.58/0.90 inference('eq_fact', [status(thm)], [zip_derived_cl64])).
% 0.58/0.90 thf(zip_derived_cl119, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.90 (~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X1))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X2))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0)))),
% 0.58/0.90 inference('simplify', [status(thm)], [zip_derived_cl116])).
% 0.58/0.90 thf(zip_derived_cl121, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i]:
% 0.58/0.90 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X1))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X1))))),
% 0.58/0.90 inference('eq_fact', [status(thm)], [zip_derived_cl119])).
% 0.58/0.90 thf(zip_derived_cl123, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i]:
% 0.58/0.90 (~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X1))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.58/0.90 inference('simplify', [status(thm)], [zip_derived_cl121])).
% 0.58/0.90 thf(clause_398, axiom,
% 0.58/0.90 (( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 0.58/0.90 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.58/0.90 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 0.58/0.90 thf(zip_derived_cl1, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (E @ (s @ 0) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.58/0.90 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.58/0.90 inference('cnf', [status(esa)], [clause_398])).
% 0.58/0.90 thf(zip_derived_cl124, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i]:
% 0.58/0.90 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X1))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X1))))),
% 0.58/0.90 inference('clc', [status(thm)], [zip_derived_cl123, zip_derived_cl1])).
% 0.58/0.90 thf(zip_derived_cl125, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 0.58/0.90 inference('eq_fact', [status(thm)], [zip_derived_cl124])).
% 0.58/0.90 thf(zip_derived_cl126, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (E @ (s @ 0) @ (f @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 0.58/0.90 inference('simplify', [status(thm)], [zip_derived_cl125])).
% 0.58/0.90 thf(zip_derived_cl1, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (E @ (s @ 0) @ (f @ X0))
% 0.58/0.90 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.58/0.90 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.58/0.90 inference('cnf', [status(esa)], [clause_398])).
% 0.58/0.90 thf(zip_derived_cl127, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (E @ (s @ 0) @ (f @ (suc @ X0))) | ~ (E @ (s @ 0) @ (f @ X0)))),
% 0.58/0.90 inference('clc', [status(thm)], [zip_derived_cl126, zip_derived_cl1])).
% 0.58/0.90 thf(zip_derived_cl217, plain,
% 0.58/0.90 (![X0 : $i]: ( (LE @ (f @ X0) @ (s @ 0)) | ~ (E @ (s @ 0) @ (f @ X0)))),
% 0.58/0.90 inference('sup-', [status(thm)], [zip_derived_cl213, zip_derived_cl127])).
% 0.58/0.90 thf(clause_44, axiom,
% 0.58/0.90 (( ~( LE @ ( f @ B_291 ) @ ( s @ ( s @ 0 ) ) ) ) |
% 0.58/0.90 ( E @ ( s @ 0 ) @ ( f @ B_291 ) ) | ( LE @ ( f @ B_291 ) @ ( s @ 0 ) ))).
% 0.58/0.90 thf(zip_derived_cl14, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.58/0.90 | (E @ (s @ 0) @ (f @ X0))
% 0.58/0.90 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.58/0.90 inference('cnf', [status(esa)], [clause_44])).
% 0.58/0.90 thf(zip_derived_cl212, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 0.58/0.90 inference('clc', [status(thm)], [zip_derived_cl210, zip_derived_cl156])).
% 0.58/0.90 thf(zip_derived_cl214, plain,
% 0.58/0.90 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 0.58/0.90 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl212])).
% 0.58/0.90 thf(zip_derived_cl218, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 0.58/0.90 inference('clc', [status(thm)], [zip_derived_cl217, zip_derived_cl214])).
% 0.58/0.90 thf(zip_derived_cl219, plain,
% 0.58/0.90 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 0.58/0.90 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl218])).
% 0.58/0.90 thf(clause_442, axiom,
% 0.58/0.90 (( ~( E @ 0 @ ( f @ ( suc @ B_310 ) ) ) ) |
% 0.58/0.90 ( ~( E @ 0 @ ( f @ ( suc @ B_311 ) ) ) ) |
% 0.58/0.90 ( ~( E @ 0 @ ( f @ B_311 ) ) ) |
% 0.58/0.90 ( ~( E @ 0 @ ( f @ ( suc @ B_313 ) ) ) ) |
% 0.58/0.90 ( ~( E @ 0 @ ( f @ B_310 ) ) ) | ( ~( E @ 0 @ ( f @ B_312 ) ) ) |
% 0.58/0.90 ( ~( E @ 0 @ ( f @ ( suc @ B_312 ) ) ) ) |
% 0.58/0.90 ( ~( E @ 0 @ ( f @ B_313 ) ) ) |
% 0.58/0.90 ( ~( iLEQ @ ( suc @ B_311 ) @ ( suc @ B_312 ) ) ) |
% 0.58/0.90 ( ~( iLEQ @ ( suc @ B_310 ) @ ( suc @ B_311 ) ) ) |
% 0.58/0.90 ( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_310 ) ) ) |
% 0.58/0.90 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.58/0.90 ( ~( iLEQ @ ( suc @ B_312 ) @ ( suc @ B_313 ) ) ) |
% 0.58/0.90 ( ~( E @ 0 @ ( f @ A_4 ) ) ))).
% 0.58/0.90 thf(zip_derived_cl15, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.58/0.90 (~ (E @ 0 @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X1))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X3))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X2))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X3))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X4) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X4)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X4)))),
% 0.58/0.90 inference('cnf', [status(esa)], [clause_442])).
% 0.58/0.90 thf(zip_derived_cl52, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.90 (~ (E @ 0 @ (f @ X1))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X2))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X3))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 0.58/0.90 inference('eq_fact', [status(thm)], [zip_derived_cl15])).
% 0.58/0.90 thf(zip_derived_cl56, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.90 (~ (E @ 0 @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X3))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X2))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X1)))),
% 0.58/0.90 inference('simplify', [status(thm)], [zip_derived_cl52])).
% 0.58/0.90 thf(zip_derived_cl77, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.90 (~ (E @ 0 @ (f @ X1))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X2))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X2))))),
% 0.58/0.90 inference('eq_fact', [status(thm)], [zip_derived_cl56])).
% 0.58/0.90 thf(zip_derived_cl80, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.90 (~ (E @ 0 @ (f @ (suc @ X2)))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X2))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X1)))),
% 0.58/0.90 inference('simplify', [status(thm)], [zip_derived_cl77])).
% 0.58/0.90 thf(zip_derived_cl82, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i]:
% 0.58/0.90 (~ (E @ 0 @ (f @ X1))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X0)))),
% 0.58/0.90 inference('eq_fact', [status(thm)], [zip_derived_cl80])).
% 0.58/0.90 thf(zip_derived_cl84, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i]:
% 0.58/0.90 (~ (E @ 0 @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X1)))),
% 0.58/0.90 inference('simplify', [status(thm)], [zip_derived_cl82])).
% 0.58/0.90 thf(clause_469, axiom,
% 0.58/0.90 (( ~( E @ 0 @ ( f @ A_4 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.58/0.90 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 0.58/0.90 thf(zip_derived_cl0, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (E @ 0 @ (f @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.58/0.90 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.58/0.90 inference('cnf', [status(esa)], [clause_469])).
% 0.58/0.90 thf(zip_derived_cl86, plain,
% 0.58/0.90 (![X0 : $i, X1 : $i]:
% 0.58/0.90 (~ (E @ 0 @ (f @ X1))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 0.58/0.90 inference('clc', [status(thm)], [zip_derived_cl84, zip_derived_cl0])).
% 0.58/0.90 thf(zip_derived_cl87, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (E @ 0 @ (f @ (suc @ X0)))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X0))
% 0.58/0.90 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X0)))),
% 0.58/0.90 inference('eq_fact', [status(thm)], [zip_derived_cl86])).
% 0.58/0.90 thf(zip_derived_cl88, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 0.58/0.90 inference('simplify', [status(thm)], [zip_derived_cl87])).
% 0.58/0.90 thf(zip_derived_cl0, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (E @ 0 @ (f @ X0))
% 0.58/0.90 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.58/0.90 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.58/0.90 inference('cnf', [status(esa)], [clause_469])).
% 0.58/0.90 thf(zip_derived_cl89, plain,
% 0.58/0.90 (![X0 : $i]: (~ (E @ 0 @ (f @ (suc @ X0))) | ~ (E @ 0 @ (f @ X0)))),
% 0.58/0.90 inference('clc', [status(thm)], [zip_derived_cl88, zip_derived_cl0])).
% 0.58/0.90 thf(zip_derived_cl222, plain,
% 0.58/0.90 (![X0 : $i]: ( (LE @ (f @ X0) @ 0) | ~ (E @ 0 @ (f @ X0)))),
% 0.58/0.90 inference('sup-', [status(thm)], [zip_derived_cl219, zip_derived_cl89])).
% 0.58/0.90 thf(clause_89, axiom,
% 0.58/0.90 (( ~( LE @ ( f @ B_309 ) @ ( s @ 0 ) ) ) | ( E @ 0 @ ( f @ B_309 ) ) |
% 0.58/0.90 ( LE @ ( f @ B_309 ) @ 0 ))).
% 0.58/0.90 thf(zip_derived_cl16, plain,
% 0.58/0.90 (![X0 : $i]:
% 0.58/0.90 (~ (LE @ (f @ X0) @ (s @ 0))
% 0.58/0.90 | (E @ 0 @ (f @ X0))
% 0.58/0.90 | (LE @ (f @ X0) @ 0))),
% 0.58/0.90 inference('cnf', [status(esa)], [clause_89])).
% 0.58/0.90 thf(zip_derived_cl218, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 0.58/0.90 inference('clc', [status(thm)], [zip_derived_cl217, zip_derived_cl214])).
% 0.58/0.90 thf(zip_derived_cl220, plain,
% 0.58/0.90 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 0.58/0.90 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl218])).
% 0.58/0.90 thf(zip_derived_cl223, plain, (![X0 : $i]: (LE @ (f @ X0) @ 0)),
% 0.58/0.90 inference('clc', [status(thm)], [zip_derived_cl222, zip_derived_cl220])).
% 0.58/0.90 thf(zip_derived_cl224, plain, ($false),
% 0.58/0.90 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl223])).
% 0.58/0.90
% 0.58/0.90 % SZS output end Refutation
% 0.58/0.90
% 0.58/0.90
% 0.58/0.90 % Terminating...
% 0.60/0.96 % Runner terminated.
% 0.60/0.97 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------