TSTP Solution File: SYO656-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO656-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.UX9owG9VKW true
% Computer : n029.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 : Fri Sep 1 05:52:26 EDT 2023
% Result : Unsatisfiable 1.32s 1.09s
% Output : Refutation 1.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO656-1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.UX9owG9VKW true
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 04:46:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.22/0.63 % Total configuration time : 435
% 0.22/0.63 % Estimated wc time : 1092
% 0.22/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.21/0.84 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 1.32/1.09 % Solved by fo/fo7.sh.
% 1.32/1.09 % done 63 iterations in 0.297s
% 1.32/1.09 % SZS status Unsatisfiable for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.32/1.09 % SZS output start Refutation
% 1.32/1.09 thf(z_type, type, z: $i).
% 1.32/1.09 thf(suc_type, type, suc: $i > $i).
% 1.32/1.09 thf(f_type, type, f: $i > $i).
% 1.32/1.09 thf(LE_type, type, LE: $i > $i > $o).
% 1.32/1.09 thf(0_type, type, 0: $i).
% 1.32/1.09 thf(E_type, type, E: $i > $i > $o).
% 1.32/1.09 thf(s_type, type, s: $i > $i).
% 1.32/1.09 thf(iLEQ_type, type, iLEQ: $i > $i > $o).
% 1.32/1.09 thf(clause_854, axiom,
% 1.32/1.09 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.32/1.09 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ A_1 ) ) ) | ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 1.32/1.09 thf(zip_derived_cl69, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.32/1.09 inference('cnf', [status(esa)], [clause_854])).
% 1.32/1.09 thf(clause_1005, axiom,
% 1.32/1.09 (( ~( LE @ ( f @ B_23 ) @ ( s @ 0 ) ) ) | ( E @ 0 @ ( f @ B_23 ) ) |
% 1.32/1.09 ( LE @ ( f @ B_23 ) @ 0 ))).
% 1.32/1.09 thf(zip_derived_cl62, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 (~ (LE @ (f @ X0) @ (s @ 0))
% 1.32/1.09 | (E @ 0 @ (f @ X0))
% 1.32/1.09 | (LE @ (f @ X0) @ 0))),
% 1.32/1.09 inference('cnf', [status(esa)], [clause_1005])).
% 1.32/1.09 thf(clause_1153, axiom, (LE @ ( f @ A ) @ ( s @ 0 ))).
% 1.32/1.09 thf(zip_derived_cl64, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 1.32/1.09 inference('cnf', [status(esa)], [clause_1153])).
% 1.32/1.09 thf(zip_derived_cl71, plain,
% 1.32/1.09 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 1.32/1.09 inference('demod', [status(thm)], [zip_derived_cl62, zip_derived_cl64])).
% 1.32/1.09 thf(clause_613, axiom, (~( LE @ ( f @ z ) @ 0 ))).
% 1.32/1.09 thf(zip_derived_cl12, plain, (~ (LE @ (f @ z) @ 0)),
% 1.32/1.09 inference('cnf', [status(esa)], [clause_613])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(clause_1201, axiom,
% 1.32/1.09 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_28 ) ) ) ) ) |
% 1.32/1.09 ( ~( iLEQ @ ( suc @ B_25 ) @ ( suc @ B_26 ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ B_25 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ B_27 ) ) ) ) |
% 1.32/1.09 ( ~( iLEQ @ ( suc @ B_24 ) @ ( suc @ B_25 ) ) ) |
% 1.32/1.09 ( ~( E @ ( f @ B_24 ) @ ( f @ ( suc @ B_24 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_24 ) ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.32/1.09 ( ~( E @ ( f @ B_26 ) @ ( f @ ( suc @ B_26 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_25 ) ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ A_1 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ B_26 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ B_28 ) ) ) |
% 1.32/1.09 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_24 ) ) ) |
% 1.32/1.09 ( ~( E @ ( f @ B_27 ) @ ( f @ ( suc @ B_27 ) ) ) ) |
% 1.32/1.09 ( ~( iLEQ @ ( suc @ B_26 ) @ ( suc @ B_27 ) ) ) |
% 1.32/1.09 ( ~( E @ ( f @ B_25 ) @ ( f @ ( suc @ B_25 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_27 ) ) ) ) ) |
% 1.32/1.09 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ B_26 ) ) ) |
% 1.32/1.09 ( ~( E @ ( f @ B_28 ) @ ( f @ ( suc @ B_28 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ B_24 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_24 ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ B_28 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_27 ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_26 ) ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ B_25 ) ) ) |
% 1.32/1.09 ( ~( iLEQ @ ( suc @ B_27 ) @ ( suc @ B_28 ) ) ))).
% 1.32/1.09 thf(zip_derived_cl35, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.32/1.09 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X4) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ (f @ X4) @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X4))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X5)))
% 1.32/1.09 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X5))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X5))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X5) @ (suc @ X4))
% 1.32/1.09 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X3))))
% 1.32/1.09 | ~ (E @ (f @ X5) @ (f @ (suc @ X5)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0)))),
% 1.32/1.09 inference('cnf', [status(esa)], [clause_1201])).
% 1.32/1.09 thf(zip_derived_cl73, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X3))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.32/1.09 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X3) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 1.32/1.09 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X4))))
% 1.32/1.09 | ~ (E @ (f @ X4) @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X4) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl35])).
% 1.32/1.09 thf(clause_73, axiom,
% 1.32/1.09 (( ~( LE @ ( f @ ( suc @ ( suc @ B_23 ) ) ) @ ( s @ 0 ) ) ) |
% 1.32/1.09 ( E @ 0 @ ( f @ ( suc @ ( suc @ B_23 ) ) ) ) | ( LE @ ( f @ B_23 ) @ 0 ))).
% 1.32/1.09 thf(zip_derived_cl14, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 1.32/1.09 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | (LE @ (f @ X0) @ 0))),
% 1.32/1.09 inference('cnf', [status(esa)], [clause_73])).
% 1.32/1.09 thf(zip_derived_cl64, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 1.32/1.09 inference('cnf', [status(esa)], [clause_1153])).
% 1.32/1.09 thf(zip_derived_cl77, plain,
% 1.32/1.09 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 1.32/1.09 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl64])).
% 1.32/1.09 thf(zip_derived_cl12, plain, (~ (LE @ (f @ z) @ 0)),
% 1.32/1.09 inference('cnf', [status(esa)], [clause_613])).
% 1.32/1.09 thf(zip_derived_cl78, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl12])).
% 1.32/1.09 thf(clause_968, axiom,
% 1.32/1.09 (( ~( LE @ ( f @ ( suc @ B_23 ) ) @ ( s @ 0 ) ) ) |
% 1.32/1.09 ( E @ 0 @ ( f @ ( suc @ B_23 ) ) ) | ( LE @ ( f @ B_23 ) @ 0 ))).
% 1.32/1.09 thf(zip_derived_cl45, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 1.32/1.09 | (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | (LE @ (f @ X0) @ 0))),
% 1.32/1.09 inference('cnf', [status(esa)], [clause_968])).
% 1.32/1.09 thf(zip_derived_cl64, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 1.32/1.09 inference('cnf', [status(esa)], [clause_1153])).
% 1.32/1.09 thf(zip_derived_cl74, plain,
% 1.32/1.09 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 1.32/1.09 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl64])).
% 1.32/1.09 thf(zip_derived_cl12, plain, (~ (LE @ (f @ z) @ 0)),
% 1.32/1.09 inference('cnf', [status(esa)], [clause_613])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl95, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X3))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.32/1.09 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X3) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.32/1.09 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X4))))
% 1.32/1.09 | ~ (E @ (f @ X4) @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X4) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl73, zip_derived_cl78, zip_derived_cl75])).
% 1.32/1.09 thf(clause_181, axiom,
% 1.32/1.09 (( ~( E @ 0 @ ( f @ A_1 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.32/1.09 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 1.32/1.09 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 1.32/1.09 thf(zip_derived_cl9, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 (~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.32/1.09 inference('cnf', [status(esa)], [clause_181])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(clause_1185, axiom,
% 1.32/1.09 (( ~( iLEQ @ ( suc @ B_25 ) @ ( suc @ B_26 ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ B_25 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ B_27 ) ) ) ) |
% 1.32/1.09 ( ~( iLEQ @ ( suc @ B_24 ) @ ( suc @ B_25 ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ A_1 ) ) ) ) | ( ~( E @ 0 @ ( f @ A_1 ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ B_26 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_28 ) ) ) |
% 1.32/1.09 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_24 ) ) ) |
% 1.32/1.09 ( ~( iLEQ @ ( suc @ B_26 ) @ ( suc @ B_27 ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ B_26 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ B_24 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ B_24 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ B_28 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ B_27 ) ) ) | ( ~( E @ 0 @ ( f @ B_25 ) ) ) |
% 1.32/1.09 ( ~( iLEQ @ ( suc @ B_27 ) @ ( suc @ B_28 ) ) ) |
% 1.32/1.09 ( E @ ( f @ B_24 ) @ ( f @ ( suc @ B_24 ) ) ) |
% 1.32/1.09 ( E @ ( f @ B_26 ) @ ( f @ ( suc @ B_26 ) ) ) |
% 1.32/1.09 ( E @ ( f @ B_27 ) @ ( f @ ( suc @ B_27 ) ) ) |
% 1.32/1.09 ( E @ ( f @ B_25 ) @ ( f @ ( suc @ B_25 ) ) ) |
% 1.32/1.09 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 1.32/1.09 ( E @ ( f @ B_28 ) @ ( f @ ( suc @ B_28 ) ) ))).
% 1.32/1.09 thf(zip_derived_cl5, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X5))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X4) @ (suc @ X3))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X5)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ X5))
% 1.32/1.09 | (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | (E @ (f @ X4) @ (f @ (suc @ X4)))
% 1.32/1.09 | (E @ (f @ X5) @ (f @ (suc @ X5))))),
% 1.32/1.09 inference('cnf', [status(esa)], [clause_1185])).
% 1.32/1.09 thf(zip_derived_cl101, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.32/1.09 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | (E @ (f @ X4) @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X4) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ X3)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl5])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl104, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.32/1.09 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | (E @ (f @ X4) @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X4) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ X3)))),
% 1.32/1.09 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl75])).
% 1.32/1.09 thf(zip_derived_cl106, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ X3))
% 1.32/1.09 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ X3) @ (f @ (suc @ X3))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl104])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl109, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ X3))
% 1.32/1.09 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ X3) @ (f @ (suc @ X3))))),
% 1.32/1.09 inference('demod', [status(thm)], [zip_derived_cl106, zip_derived_cl75])).
% 1.32/1.09 thf(zip_derived_cl110, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.32/1.09 ( (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X0)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl109])).
% 1.32/1.09 thf(zip_derived_cl112, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 1.32/1.09 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ X2) @ (f @ (suc @ X2))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl110])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl115, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 1.32/1.09 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ X2) @ (f @ (suc @ X2))))),
% 1.32/1.09 inference('demod', [status(thm)], [zip_derived_cl112, zip_derived_cl75])).
% 1.32/1.09 thf(zip_derived_cl116, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.32/1.09 ( (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X0)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl115])).
% 1.32/1.09 thf(zip_derived_cl118, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl116])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl121, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 1.32/1.09 inference('demod', [status(thm)], [zip_derived_cl118, zip_derived_cl75])).
% 1.32/1.09 thf(zip_derived_cl122, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i]:
% 1.32/1.09 ( (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X0)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl121])).
% 1.32/1.09 thf(zip_derived_cl129, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.32/1.09 inference('eq_fact', [status(thm)], [zip_derived_cl122])).
% 1.32/1.09 thf(zip_derived_cl132, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl129])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl133, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl132, zip_derived_cl72, zip_derived_cl75])).
% 1.32/1.09 thf(zip_derived_cl141, plain,
% 1.32/1.09 ((~ (E @ 0 @ (f @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z))))),
% 1.32/1.09 inference('eq_fact', [status(thm)], [zip_derived_cl133])).
% 1.32/1.09 thf(zip_derived_cl142, plain,
% 1.32/1.09 (( (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ z)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl141])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl143, plain,
% 1.32/1.09 (( (E @ (f @ z) @ (f @ (suc @ z))) | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl142, zip_derived_cl75, zip_derived_cl72])).
% 1.32/1.09 thf(zip_derived_cl147, plain,
% 1.32/1.09 (( (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ z))
% 1.32/1.09 | (E @ (f @ z) @ (f @ (suc @ z))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl143])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl149, plain,
% 1.32/1.09 (( (E @ (f @ z) @ (f @ (suc @ z))) | (E @ (f @ z) @ (f @ (suc @ z))))),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl147, zip_derived_cl75, zip_derived_cl72])).
% 1.32/1.09 thf(zip_derived_cl150, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl149])).
% 1.32/1.09 thf(zip_derived_cl153, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X3))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.32/1.09 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X3) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.32/1.09 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X4))))
% 1.32/1.09 | ~ (E @ (f @ X4) @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X4) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 1.32/1.09 inference('demod', [status(thm)], [zip_derived_cl95, zip_derived_cl150])).
% 1.32/1.09 thf(zip_derived_cl211, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.32/1.09 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X3) @ (suc @ z))
% 1.32/1.09 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X3))))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X3))
% 1.32/1.09 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl153])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl78, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl150, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl149])).
% 1.32/1.09 thf(zip_derived_cl214, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.32/1.09 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X3) @ (suc @ z))
% 1.32/1.09 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X3))))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X3))
% 1.32/1.09 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0)))),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl211, zip_derived_cl75, zip_derived_cl78,
% 1.32/1.09 zip_derived_cl150])).
% 1.32/1.09 thf(zip_derived_cl216, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.32/1.09 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl214])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl150, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl149])).
% 1.32/1.09 thf(zip_derived_cl78, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl219, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.32/1.09 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1)))),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl216, zip_derived_cl75, zip_derived_cl150,
% 1.32/1.09 zip_derived_cl78])).
% 1.32/1.09 thf(zip_derived_cl221, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl219])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl150, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl149])).
% 1.32/1.09 thf(zip_derived_cl78, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl224, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl221, zip_derived_cl75, zip_derived_cl150,
% 1.32/1.09 zip_derived_cl78])).
% 1.32/1.09 thf(zip_derived_cl231, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 (~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ z))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 1.32/1.09 inference('eq_fact', [status(thm)], [zip_derived_cl224])).
% 1.32/1.09 thf(zip_derived_cl235, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl231])).
% 1.32/1.09 thf(zip_derived_cl150, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl149])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl78, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl236, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0)))),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl235, zip_derived_cl150, zip_derived_cl75,
% 1.32/1.09 zip_derived_cl72, zip_derived_cl78])).
% 1.32/1.09 thf(zip_derived_cl69, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.32/1.09 inference('cnf', [status(esa)], [clause_854])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(clause_741, axiom,
% 1.32/1.09 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_28 ) ) ) ) ) |
% 1.32/1.09 ( ~( iLEQ @ ( suc @ B_25 ) @ ( suc @ B_26 ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ B_25 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ B_27 ) ) ) ) |
% 1.32/1.09 ( ~( iLEQ @ ( suc @ B_24 ) @ ( suc @ B_25 ) ) ) |
% 1.32/1.09 ( ~( E @ ( f @ B_24 ) @ ( f @ ( suc @ B_24 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_24 ) ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_25 ) ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ A_1 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ B_26 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ B_28 ) ) ) |
% 1.32/1.09 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_24 ) ) ) |
% 1.32/1.09 ( ~( E @ ( f @ B_27 ) @ ( f @ ( suc @ B_27 ) ) ) ) |
% 1.32/1.09 ( ~( iLEQ @ ( suc @ B_26 ) @ ( suc @ B_27 ) ) ) |
% 1.32/1.09 ( ~( E @ ( f @ B_25 ) @ ( f @ ( suc @ B_25 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_27 ) ) ) ) ) |
% 1.32/1.09 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ B_26 ) ) ) |
% 1.32/1.09 ( ~( E @ ( f @ B_28 ) @ ( f @ ( suc @ B_28 ) ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ B_24 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_24 ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ ( suc @ B_28 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_27 ) ) ) |
% 1.32/1.09 ( ~( E @ 0 @ ( f @ B_25 ) ) ) |
% 1.32/1.09 ( ~( iLEQ @ ( suc @ B_27 ) @ ( suc @ B_28 ) ) ) |
% 1.32/1.09 ( E @ ( f @ B_26 ) @ ( f @ ( suc @ B_26 ) ) ))).
% 1.32/1.09 thf(zip_derived_cl10, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.32/1.09 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X4) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ (f @ X4) @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X4))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X5)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X5))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X5))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X5) @ (suc @ X4))
% 1.32/1.09 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X3))))
% 1.32/1.09 | ~ (E @ (f @ X5) @ (f @ (suc @ X5)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 1.32/1.09 | (E @ (f @ X2) @ (f @ (suc @ X2))))),
% 1.32/1.09 inference('cnf', [status(esa)], [clause_741])).
% 1.32/1.09 thf(zip_derived_cl80, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.32/1.09 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.32/1.09 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X3))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X4))))
% 1.32/1.09 | ~ (E @ (f @ X4) @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X4) @ (suc @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1)))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl10])).
% 1.32/1.09 thf(zip_derived_cl78, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl83, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.32/1.09 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.32/1.09 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X3))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X4))))
% 1.32/1.09 | ~ (E @ (f @ X4) @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X4) @ (suc @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1)))))),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl80, zip_derived_cl78, zip_derived_cl75])).
% 1.32/1.09 thf(zip_derived_cl150, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl149])).
% 1.32/1.09 thf(zip_derived_cl152, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.32/1.09 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.32/1.09 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X4))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X3))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X4))))
% 1.32/1.09 | ~ (E @ (f @ X4) @ (f @ (suc @ X4)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X4) @ (suc @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1)))))),
% 1.32/1.09 inference('demod', [status(thm)], [zip_derived_cl83, zip_derived_cl150])).
% 1.32/1.09 thf(zip_derived_cl158, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.32/1.09 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X3) @ (suc @ z))
% 1.32/1.09 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X3))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X3))
% 1.32/1.09 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.32/1.09 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl152])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl78, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl150, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl149])).
% 1.32/1.09 thf(zip_derived_cl161, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.32/1.09 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X3) @ (suc @ z))
% 1.32/1.09 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X3))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X3))
% 1.32/1.09 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X3))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.32/1.09 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl158, zip_derived_cl75, zip_derived_cl78,
% 1.32/1.09 zip_derived_cl150])).
% 1.32/1.09 thf(zip_derived_cl163, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.32/1.09 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.32/1.09 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl161])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl150, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl149])).
% 1.32/1.09 thf(zip_derived_cl78, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl166, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.32/1.09 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.32/1.09 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X2) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X0)))),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl163, zip_derived_cl75, zip_derived_cl150,
% 1.32/1.09 zip_derived_cl78])).
% 1.32/1.09 thf(zip_derived_cl168, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl166])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl150, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl149])).
% 1.32/1.09 thf(zip_derived_cl78, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl171, plain,
% 1.32/1.09 (![X0 : $i, X1 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 1.32/1.09 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X1))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl168, zip_derived_cl75, zip_derived_cl150,
% 1.32/1.09 zip_derived_cl78])).
% 1.32/1.09 thf(zip_derived_cl177, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X0)))),
% 1.32/1.09 inference('eq_fact', [status(thm)], [zip_derived_cl171])).
% 1.32/1.09 thf(zip_derived_cl181, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ z))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl177])).
% 1.32/1.09 thf(zip_derived_cl150, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl149])).
% 1.32/1.09 thf(zip_derived_cl78, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl184, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl181, zip_derived_cl150, zip_derived_cl78,
% 1.32/1.09 zip_derived_cl75, zip_derived_cl72])).
% 1.32/1.09 thf(zip_derived_cl190, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 (~ (E @ 0 @ (f @ z))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 1.32/1.09 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X0)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl69, zip_derived_cl184])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl150, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl149])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl78, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl198, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X0)))),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl190, zip_derived_cl72, zip_derived_cl150,
% 1.32/1.09 zip_derived_cl75, zip_derived_cl78])).
% 1.32/1.09 thf(zip_derived_cl242, plain,
% 1.32/1.09 (![X0 : $i]:
% 1.32/1.09 (~ (E @ 0 @ (f @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ X0) @ (suc @ z)))),
% 1.32/1.09 inference('clc', [status(thm)], [zip_derived_cl236, zip_derived_cl198])).
% 1.32/1.09 thf(zip_derived_cl246, plain,
% 1.32/1.09 ((~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ z)))),
% 1.32/1.09 inference('eq_fact', [status(thm)], [zip_derived_cl242])).
% 1.32/1.09 thf(zip_derived_cl248, plain,
% 1.32/1.09 ((~ (E @ 0 @ (f @ z))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 1.32/1.09 | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl246])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl78, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl249, plain, (~ (iLEQ @ (suc @ z) @ (suc @ z))),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl248, zip_derived_cl72, zip_derived_cl75,
% 1.32/1.09 zip_derived_cl78])).
% 1.32/1.09 thf(zip_derived_cl265, plain,
% 1.32/1.09 ((~ (E @ 0 @ (f @ z))
% 1.32/1.09 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ z)))
% 1.32/1.09 | ~ (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl69, zip_derived_cl249])).
% 1.32/1.09 thf(zip_derived_cl72, plain, ( (E @ 0 @ (f @ z))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl150, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 1.32/1.09 inference('simplify', [status(thm)], [zip_derived_cl149])).
% 1.32/1.09 thf(zip_derived_cl75, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl78, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 1.32/1.09 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl12])).
% 1.32/1.09 thf(zip_derived_cl267, plain, ($false),
% 1.32/1.09 inference('demod', [status(thm)],
% 1.32/1.09 [zip_derived_cl265, zip_derived_cl72, zip_derived_cl150,
% 1.32/1.09 zip_derived_cl75, zip_derived_cl78])).
% 1.32/1.09
% 1.32/1.09 % SZS output end Refutation
% 1.32/1.09
% 1.32/1.09
% 1.32/1.09 % Terminating...
% 1.64/1.14 % Runner terminated.
% 1.64/1.16 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------