TSTP Solution File: SYO670-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO670-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.wZNEHLMCNz true
% Computer : n008.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 05:52:30 EDT 2023
% Result : Unsatisfiable 1.36s 1.27s
% Output : Refutation 1.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO670-1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.wZNEHLMCNz true
% 0.14/0.35 % Computer : n008.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 03:48:32 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.22/0.65 % Total configuration time : 435
% 0.22/0.65 % Estimated wc time : 1092
% 0.22/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.80/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.80/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.80/0.77 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.80/0.77 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.80/0.78 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.36/0.83 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 1.36/1.27 % Solved by fo/fo5.sh.
% 1.36/1.27 % done 351 iterations in 0.459s
% 1.36/1.27 % SZS status Unsatisfiable for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.36/1.27 % SZS output start Refutation
% 1.36/1.27 thf(f_type, type, f: $i > $i).
% 1.36/1.27 thf(0_type, type, 0: $i).
% 1.36/1.27 thf(suc_type, type, suc: $i > $i).
% 1.36/1.27 thf(s_type, type, s: $i > $i).
% 1.36/1.27 thf(E_type, type, E: $i > $i > $o).
% 1.36/1.27 thf(iLEQ_type, type, iLEQ: $i > $i > $o).
% 1.36/1.27 thf(LE_type, type, LE: $i > $i > $o).
% 1.36/1.27 thf(z_type, type, z: $i).
% 1.36/1.27 thf(clause_575, axiom, (~( LE @ ( f @ z ) @ 0 ))).
% 1.36/1.27 thf(zip_derived_cl64, plain, (~ (LE @ (f @ z) @ 0)),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_575])).
% 1.36/1.27 thf(clause_803, axiom,
% 1.36/1.27 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ B_10 ) ) ) ) @ ( s @ 0 ) ) ) |
% 1.36/1.27 ( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_10 ) ) ) ) ) |
% 1.36/1.27 ( LE @ ( f @ B_10 ) @ 0 ))).
% 1.36/1.27 thf(zip_derived_cl30, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0))
% 1.36/1.27 | (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (LE @ (f @ X0) @ 0))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_803])).
% 1.36/1.27 thf(clause_1042, axiom,
% 1.36/1.27 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ B_7 ) ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 1.36/1.27 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_7 ) ) ) ) ) |
% 1.36/1.27 ( LE @ ( f @ B_7 ) @ ( s @ 0 ) ))).
% 1.36/1.27 thf(zip_derived_cl54, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ 0)))
% 1.36/1.27 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_1042])).
% 1.36/1.27 thf(clause_330, axiom,
% 1.36/1.27 (( ~( LE @
% 1.36/1.27 ( f @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 1.36/1.27 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) ) |
% 1.36/1.27 ( LE @ ( f @ B_3 ) @ ( s @ ( s @ 0 ) ) ))).
% 1.36/1.27 thf(zip_derived_cl37, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ (s @ 0))))
% 1.36/1.27 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_330])).
% 1.36/1.27 thf(clause_1161, axiom, (LE @ ( f @ A ) @ ( s @ ( s @ ( s @ 0 ) ) ))).
% 1.36/1.27 thf(zip_derived_cl44, plain,
% 1.36/1.27 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_1161])).
% 1.36/1.27 thf(zip_derived_cl104, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl44])).
% 1.36/1.27 thf(clause_481, axiom,
% 1.36/1.27 (( ~( LE @
% 1.36/1.27 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) ) @
% 1.36/1.27 ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 1.36/1.27 ( E @
% 1.36/1.27 ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) ) ) |
% 1.36/1.27 ( LE @ ( f @ B_3 ) @ ( s @ ( s @ 0 ) ) ))).
% 1.36/1.27 thf(zip_derived_cl63, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @
% 1.36/1.27 (s @ (s @ (s @ 0))))
% 1.36/1.27 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_481])).
% 1.36/1.27 thf(zip_derived_cl44, plain,
% 1.36/1.27 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_1161])).
% 1.36/1.27 thf(zip_derived_cl121, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl63, zip_derived_cl44])).
% 1.36/1.27 thf(clause_539, axiom,
% 1.36/1.27 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 1.36/1.27 ( ~( E @
% 1.36/1.27 ( s @ ( s @ 0 ) ) @
% 1.36/1.27 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_4 ) ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ B_4 ) @ ( f @ ( suc @ B_4 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( ~( E @
% 1.36/1.27 ( s @ ( s @ 0 ) ) @
% 1.36/1.27 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ B_4 ) @ ( f @ ( suc @ ( suc @ B_4 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ B_4 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_4 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_4 ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_4 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_4 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_4 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_4 ) ) ))).
% 1.36/1.27 thf(zip_derived_cl75, plain,
% 1.36/1.27 (![X0 : $i, X1 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 1.36/1.27 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 1.36/1.27 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X1)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_539])).
% 1.36/1.27 thf(zip_derived_cl384, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 1.36/1.27 inference('eq_fact', [status(thm)], [zip_derived_cl75])).
% 1.36/1.27 thf(zip_derived_cl385, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 1.36/1.27 inference('simplify', [status(thm)], [zip_derived_cl384])).
% 1.36/1.27 thf(zip_derived_cl465, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.27 inference('sup-', [status(thm)], [zip_derived_cl121, zip_derived_cl385])).
% 1.36/1.27 thf(zip_derived_cl578, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('sup-', [status(thm)], [zip_derived_cl104, zip_derived_cl465])).
% 1.36/1.27 thf(zip_derived_cl581, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('simplify', [status(thm)], [zip_derived_cl578])).
% 1.36/1.27 thf(clause_893, axiom,
% 1.36/1.27 (( ~( LE @ ( f @ B_3 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 1.36/1.27 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_3 ) ) |
% 1.36/1.27 ( LE @ ( f @ B_3 ) @ ( s @ ( s @ 0 ) ) ))).
% 1.36/1.27 thf(zip_derived_cl33, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 1.36/1.27 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_893])).
% 1.36/1.27 thf(zip_derived_cl44, plain,
% 1.36/1.27 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_1161])).
% 1.36/1.27 thf(zip_derived_cl77, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl582, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl581, zip_derived_cl77])).
% 1.36/1.27 thf(zip_derived_cl104, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl44])).
% 1.36/1.27 thf(clause_597, axiom,
% 1.36/1.27 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ B_4 ) @ ( f @ ( suc @ B_4 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ B_4 ) @ ( f @ ( suc @ ( suc @ B_4 ) ) ) ) ) |
% 1.36/1.27 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_4 ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_4 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_4 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_4 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_4 ) ) ) |
% 1.36/1.27 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.36/1.27 ( E @ ( f @ B_4 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_4 ) ) ) ) ))).
% 1.36/1.27 thf(zip_derived_cl29, plain,
% 1.36/1.27 (![X0 : $i, X1 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1))))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_597])).
% 1.36/1.27 thf(zip_derived_cl364, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 1.36/1.27 inference('eq_fact', [status(thm)], [zip_derived_cl29])).
% 1.36/1.27 thf(zip_derived_cl365, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.27 inference('simplify', [status(thm)], [zip_derived_cl364])).
% 1.36/1.27 thf(clause_372, axiom,
% 1.36/1.27 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.36/1.27 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.36/1.27 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 1.36/1.27 thf(zip_derived_cl56, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_372])).
% 1.36/1.27 thf(clause_983, axiom,
% 1.36/1.27 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 1.36/1.27 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 1.36/1.27 thf(zip_derived_cl51, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_983])).
% 1.36/1.27 thf(clause_90, axiom,
% 1.36/1.27 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 1.36/1.27 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 1.36/1.27 thf(zip_derived_cl5, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_90])).
% 1.36/1.27 thf(zip_derived_cl136, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl51, zip_derived_cl5])).
% 1.36/1.27 thf(zip_derived_cl198, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl56, zip_derived_cl136])).
% 1.36/1.27 thf(clause_292, axiom,
% 1.36/1.27 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_4 ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_4 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_4 ) ) ) |
% 1.36/1.27 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 1.36/1.27 ( E @ ( f @ B_4 ) @ ( f @ ( suc @ B_4 ) ) ))).
% 1.36/1.27 thf(zip_derived_cl32, plain,
% 1.36/1.27 (![X0 : $i, X1 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_292])).
% 1.36/1.27 thf(zip_derived_cl174, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 1.36/1.27 inference('eq_fact', [status(thm)], [zip_derived_cl32])).
% 1.36/1.27 thf(zip_derived_cl175, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('simplify', [status(thm)], [zip_derived_cl174])).
% 1.36/1.27 thf(zip_derived_cl5, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_90])).
% 1.36/1.27 thf(zip_derived_cl182, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl175, zip_derived_cl5])).
% 1.36/1.27 thf(zip_derived_cl199, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl198, zip_derived_cl182])).
% 1.36/1.27 thf(zip_derived_cl410, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl365, zip_derived_cl199])).
% 1.36/1.27 thf(zip_derived_cl182, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl175, zip_derived_cl5])).
% 1.36/1.27 thf(zip_derived_cl411, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl410, zip_derived_cl182])).
% 1.36/1.27 thf(clause_280, axiom,
% 1.36/1.27 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ B_4 ) @ ( f @ ( suc @ B_4 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_4 ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_4 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_4 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_4 ) ) ) |
% 1.36/1.27 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( E @ ( f @ B_4 ) @ ( f @ ( suc @ ( suc @ B_4 ) ) ) ))).
% 1.36/1.27 thf(zip_derived_cl71, plain,
% 1.36/1.27 (![X0 : $i, X1 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1)))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_280])).
% 1.36/1.27 thf(zip_derived_cl271, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 1.36/1.27 inference('eq_fact', [status(thm)], [zip_derived_cl71])).
% 1.36/1.27 thf(zip_derived_cl272, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('simplify', [status(thm)], [zip_derived_cl271])).
% 1.36/1.27 thf(zip_derived_cl136, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl51, zip_derived_cl5])).
% 1.36/1.27 thf(zip_derived_cl279, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl272, zip_derived_cl136])).
% 1.36/1.27 thf(zip_derived_cl182, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl175, zip_derived_cl5])).
% 1.36/1.27 thf(zip_derived_cl280, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl279, zip_derived_cl182])).
% 1.36/1.27 thf(zip_derived_cl412, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl411, zip_derived_cl280])).
% 1.36/1.27 thf(zip_derived_cl415, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.27 inference('sup-', [status(thm)], [zip_derived_cl104, zip_derived_cl412])).
% 1.36/1.27 thf(clause_577, axiom,
% 1.36/1.27 (( ~( LE @ ( f @ ( suc @ B_3 ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 1.36/1.27 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_3 ) ) ) |
% 1.36/1.27 ( LE @ ( f @ B_3 ) @ ( s @ ( s @ 0 ) ) ))).
% 1.36/1.27 thf(zip_derived_cl17, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0))))
% 1.36/1.27 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_577])).
% 1.36/1.27 thf(zip_derived_cl44, plain,
% 1.36/1.27 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_1161])).
% 1.36/1.27 thf(zip_derived_cl83, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl418, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl415, zip_derived_cl83])).
% 1.36/1.27 thf(zip_derived_cl77, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl419, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl418, zip_derived_cl77])).
% 1.36/1.27 thf(clause_1165, axiom,
% 1.36/1.27 (( ~( LE @ ( f @ ( suc @ ( suc @ B_3 ) ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 1.36/1.27 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_3 ) ) ) ) |
% 1.36/1.27 ( LE @ ( f @ B_3 ) @ ( s @ ( s @ 0 ) ) ))).
% 1.36/1.27 thf(zip_derived_cl48, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0))))
% 1.36/1.27 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_1165])).
% 1.36/1.27 thf(zip_derived_cl44, plain,
% 1.36/1.27 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_1161])).
% 1.36/1.27 thf(zip_derived_cl91, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl420, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl419, zip_derived_cl91])).
% 1.36/1.27 thf(zip_derived_cl583, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl582, zip_derived_cl420])).
% 1.36/1.27 thf(zip_derived_cl91, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl584, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl583, zip_derived_cl91])).
% 1.36/1.27 thf(zip_derived_cl104, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl121, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl63, zip_derived_cl44])).
% 1.36/1.27 thf(clause_471, axiom,
% 1.36/1.27 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( ~( E @
% 1.36/1.27 ( s @ ( s @ 0 ) ) @
% 1.36/1.27 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.36/1.27 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 1.36/1.27 thf(zip_derived_cl49, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_471])).
% 1.36/1.27 thf(zip_derived_cl244, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 1.36/1.27 inference('sup-', [status(thm)], [zip_derived_cl121, zip_derived_cl49])).
% 1.36/1.27 thf(zip_derived_cl315, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('sup-', [status(thm)], [zip_derived_cl104, zip_derived_cl244])).
% 1.36/1.27 thf(zip_derived_cl318, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('simplify', [status(thm)], [zip_derived_cl315])).
% 1.36/1.27 thf(zip_derived_cl91, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl319, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl318, zip_derived_cl91])).
% 1.36/1.27 thf(zip_derived_cl77, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl320, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl319, zip_derived_cl77])).
% 1.36/1.27 thf(zip_derived_cl83, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl182, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl175, zip_derived_cl5])).
% 1.36/1.27 thf(zip_derived_cl184, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('sup-', [status(thm)], [zip_derived_cl83, zip_derived_cl182])).
% 1.36/1.27 thf(zip_derived_cl77, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl188, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl184, zip_derived_cl77])).
% 1.36/1.27 thf(zip_derived_cl321, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl320, zip_derived_cl188])).
% 1.36/1.27 thf(zip_derived_cl83, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl322, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl321, zip_derived_cl83])).
% 1.36/1.27 thf(zip_derived_cl91, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl280, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl279, zip_derived_cl182])).
% 1.36/1.27 thf(zip_derived_cl284, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('sup-', [status(thm)], [zip_derived_cl91, zip_derived_cl280])).
% 1.36/1.27 thf(zip_derived_cl77, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl286, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl284, zip_derived_cl77])).
% 1.36/1.27 thf(zip_derived_cl83, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl287, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl286, zip_derived_cl83])).
% 1.36/1.27 thf(zip_derived_cl323, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl322, zip_derived_cl287])).
% 1.36/1.27 thf(zip_derived_cl104, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl199, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl198, zip_derived_cl182])).
% 1.36/1.27 thf(zip_derived_cl202, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 1.36/1.27 inference('sup-', [status(thm)], [zip_derived_cl104, zip_derived_cl199])).
% 1.36/1.27 thf(zip_derived_cl91, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl220, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl202, zip_derived_cl91])).
% 1.36/1.27 thf(zip_derived_cl77, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl221, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl220, zip_derived_cl77])).
% 1.36/1.27 thf(zip_derived_cl83, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl222, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl221, zip_derived_cl83])).
% 1.36/1.27 thf(zip_derived_cl324, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (iLEQ @ (suc @ X0) @ (suc @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl323, zip_derived_cl222])).
% 1.36/1.27 thf(zip_derived_cl585, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl584, zip_derived_cl324])).
% 1.36/1.27 thf(zip_derived_cl188, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl184, zip_derived_cl77])).
% 1.36/1.27 thf(zip_derived_cl586, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl585, zip_derived_cl188])).
% 1.36/1.27 thf(zip_derived_cl287, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl286, zip_derived_cl83])).
% 1.36/1.27 thf(zip_derived_cl587, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl586, zip_derived_cl287])).
% 1.36/1.27 thf(zip_derived_cl83, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl44])).
% 1.36/1.27 thf(zip_derived_cl588, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl587, zip_derived_cl83])).
% 1.36/1.27 thf(zip_derived_cl593, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl588])).
% 1.36/1.27 thf(clause_787, axiom,
% 1.36/1.27 (( ~( LE @
% 1.36/1.27 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_7 ) ) ) ) ) @
% 1.36/1.27 ( s @ ( s @ 0 ) ) ) ) |
% 1.36/1.27 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_7 ) ) ) ) ) ) |
% 1.36/1.27 ( LE @ ( f @ B_7 ) @ ( s @ 0 ) ))).
% 1.36/1.27 thf(zip_derived_cl4, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ (s @ 0)))
% 1.36/1.27 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_787])).
% 1.36/1.27 thf(zip_derived_cl588, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl587, zip_derived_cl83])).
% 1.36/1.27 thf(zip_derived_cl589, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl588])).
% 1.36/1.27 thf(clause_783, axiom,
% 1.36/1.27 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 1.36/1.27 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 1.36/1.27 thf(zip_derived_cl66, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_783])).
% 1.36/1.27 thf(zip_derived_cl626, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('sup-', [status(thm)], [zip_derived_cl589, zip_derived_cl66])).
% 1.36/1.27 thf(zip_derived_cl749, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('sup-', [status(thm)], [zip_derived_cl593, zip_derived_cl626])).
% 1.36/1.27 thf(zip_derived_cl750, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('simplify', [status(thm)], [zip_derived_cl749])).
% 1.36/1.27 thf(zip_derived_cl593, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl588])).
% 1.36/1.27 thf(zip_derived_cl589, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl588])).
% 1.36/1.27 thf(clause_360, axiom,
% 1.36/1.27 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ B_8 ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_8 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ B_8 ) @ ( f @ ( suc @ ( suc @ B_8 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_8 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_8 ) ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ B_8 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_8 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ B_8 ) @ ( f @ ( suc @ B_8 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_8 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 1.36/1.27 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_8 ) ) ))).
% 1.36/1.27 thf(zip_derived_cl14, plain,
% 1.36/1.27 (![X0 : $i, X1 : $i]:
% 1.36/1.27 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X1))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.27 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 1.36/1.27 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_360])).
% 1.36/1.27 thf(zip_derived_cl277, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('eq_fact', [status(thm)], [zip_derived_cl14])).
% 1.36/1.27 thf(zip_derived_cl278, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('simplify', [status(thm)], [zip_derived_cl277])).
% 1.36/1.27 thf(zip_derived_cl627, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('sup-', [status(thm)], [zip_derived_cl589, zip_derived_cl278])).
% 1.36/1.27 thf(zip_derived_cl718, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('sup-', [status(thm)], [zip_derived_cl593, zip_derived_cl627])).
% 1.36/1.27 thf(zip_derived_cl719, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('simplify', [status(thm)], [zip_derived_cl718])).
% 1.36/1.27 thf(clause_1064, axiom,
% 1.36/1.27 (( ~( LE @ ( f @ B_7 ) @ ( s @ ( s @ 0 ) ) ) ) |
% 1.36/1.27 ( E @ ( s @ 0 ) @ ( f @ B_7 ) ) | ( LE @ ( f @ B_7 ) @ ( s @ 0 ) ))).
% 1.36/1.27 thf(zip_derived_cl15, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.36/1.27 | (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_1064])).
% 1.36/1.27 thf(zip_derived_cl588, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl587, zip_derived_cl83])).
% 1.36/1.27 thf(zip_derived_cl591, plain,
% 1.36/1.27 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl588])).
% 1.36/1.27 thf(zip_derived_cl720, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl719, zip_derived_cl591])).
% 1.36/1.27 thf(clause_758, axiom,
% 1.36/1.27 (( ~( LE @ ( f @ ( suc @ ( suc @ B_7 ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 1.36/1.27 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_7 ) ) ) ) |
% 1.36/1.27 ( LE @ ( f @ B_7 ) @ ( s @ 0 ) ))).
% 1.36/1.27 thf(zip_derived_cl46, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 1.36/1.27 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_758])).
% 1.36/1.27 thf(zip_derived_cl588, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl587, zip_derived_cl83])).
% 1.36/1.27 thf(zip_derived_cl592, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl588])).
% 1.36/1.27 thf(clause_560, axiom,
% 1.36/1.27 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ B_8 ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_8 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_8 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ B_8 ) @ ( f @ ( suc @ B_8 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 1.36/1.27 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_8 ) ) ) |
% 1.36/1.27 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.27 ( E @ ( f @ B_8 ) @ ( f @ ( suc @ ( suc @ B_8 ) ) ) ))).
% 1.36/1.27 thf(zip_derived_cl68, plain,
% 1.36/1.27 (![X0 : $i, X1 : $i]:
% 1.36/1.27 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X1))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1)))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_560])).
% 1.36/1.27 thf(zip_derived_cl245, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('eq_fact', [status(thm)], [zip_derived_cl68])).
% 1.36/1.27 thf(zip_derived_cl246, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('simplify', [status(thm)], [zip_derived_cl245])).
% 1.36/1.27 thf(clause_34, axiom,
% 1.36/1.27 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ B_8 ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_8 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 1.36/1.27 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_8 ) ) ) |
% 1.36/1.27 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 1.36/1.27 ( E @ ( f @ B_8 ) @ ( f @ ( suc @ B_8 ) ) ))).
% 1.36/1.27 thf(zip_derived_cl35, plain,
% 1.36/1.27 (![X0 : $i, X1 : $i]:
% 1.36/1.27 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X1))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_34])).
% 1.36/1.27 thf(zip_derived_cl134, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 1.36/1.27 inference('eq_fact', [status(thm)], [zip_derived_cl35])).
% 1.36/1.27 thf(zip_derived_cl135, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('simplify', [status(thm)], [zip_derived_cl134])).
% 1.36/1.27 thf(clause_172, axiom,
% 1.36/1.27 (( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.27 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 1.36/1.27 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 1.36/1.27 thf(zip_derived_cl25, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_172])).
% 1.36/1.27 thf(zip_derived_cl143, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl135, zip_derived_cl25])).
% 1.36/1.27 thf(zip_derived_cl247, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl246, zip_derived_cl143])).
% 1.36/1.27 thf(clause_276, axiom,
% 1.36/1.27 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 1.36/1.27 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.27 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 1.36/1.27 thf(zip_derived_cl13, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_276])).
% 1.36/1.27 thf(zip_derived_cl25, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_172])).
% 1.36/1.27 thf(zip_derived_cl133, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl13, zip_derived_cl25])).
% 1.36/1.27 thf(zip_derived_cl248, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl247, zip_derived_cl133])).
% 1.36/1.27 thf(zip_derived_cl614, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('sup-', [status(thm)], [zip_derived_cl592, zip_derived_cl248])).
% 1.36/1.27 thf(zip_derived_cl591, plain,
% 1.36/1.27 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl588])).
% 1.36/1.27 thf(zip_derived_cl631, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl614, zip_derived_cl591])).
% 1.36/1.27 thf(clause_49, axiom,
% 1.36/1.27 (( ~( LE @ ( f @ ( suc @ B_7 ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 1.36/1.27 ( E @ ( s @ 0 ) @ ( f @ ( suc @ B_7 ) ) ) |
% 1.36/1.27 ( LE @ ( f @ B_7 ) @ ( s @ 0 ) ))).
% 1.36/1.27 thf(zip_derived_cl8, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 1.36/1.27 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_49])).
% 1.36/1.27 thf(zip_derived_cl588, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl587, zip_derived_cl83])).
% 1.36/1.27 thf(zip_derived_cl590, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl588])).
% 1.36/1.27 thf(zip_derived_cl632, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl631, zip_derived_cl590])).
% 1.36/1.27 thf(zip_derived_cl721, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl720, zip_derived_cl632])).
% 1.36/1.27 thf(zip_derived_cl590, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl588])).
% 1.36/1.27 thf(zip_derived_cl143, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl135, zip_derived_cl25])).
% 1.36/1.27 thf(zip_derived_cl600, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.36/1.27 inference('sup-', [status(thm)], [zip_derived_cl590, zip_derived_cl143])).
% 1.36/1.27 thf(zip_derived_cl591, plain,
% 1.36/1.27 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl588])).
% 1.36/1.27 thf(zip_derived_cl606, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl600, zip_derived_cl591])).
% 1.36/1.27 thf(zip_derived_cl722, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl721, zip_derived_cl606])).
% 1.36/1.27 thf(zip_derived_cl590, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl588])).
% 1.36/1.27 thf(zip_derived_cl723, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('clc', [status(thm)], [zip_derived_cl722, zip_derived_cl590])).
% 1.36/1.27 thf(zip_derived_cl593, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.27 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl588])).
% 1.36/1.27 thf(clause_766, axiom,
% 1.36/1.27 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ B_8 ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_8 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ B_8 ) @ ( f @ ( suc @ ( suc @ B_8 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_8 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ B_8 ) @ ( f @ ( suc @ B_8 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_8 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.27 ( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 1.36/1.27 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_8 ) ) ) |
% 1.36/1.27 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 1.36/1.27 ( E @ ( f @ B_8 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_8 ) ) ) ) ))).
% 1.36/1.27 thf(zip_derived_cl47, plain,
% 1.36/1.27 (![X0 : $i, X1 : $i]:
% 1.36/1.27 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X1))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 1.36/1.27 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.27 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1))))))),
% 1.36/1.27 inference('cnf', [status(esa)], [clause_766])).
% 1.36/1.27 thf(zip_derived_cl357, plain,
% 1.36/1.27 (![X0 : $i]:
% 1.36/1.27 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.27 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.27 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.28 inference('eq_fact', [status(thm)], [zip_derived_cl47])).
% 1.36/1.28 thf(zip_derived_cl358, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.28 inference('simplify', [status(thm)], [zip_derived_cl357])).
% 1.36/1.28 thf(zip_derived_cl248, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl247, zip_derived_cl133])).
% 1.36/1.28 thf(zip_derived_cl392, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl358, zip_derived_cl248])).
% 1.36/1.28 thf(clause_1155, axiom,
% 1.36/1.28 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 1.36/1.28 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 1.36/1.28 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 1.36/1.28 thf(zip_derived_cl34, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.28 inference('cnf', [status(esa)], [clause_1155])).
% 1.36/1.28 thf(zip_derived_cl133, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl13, zip_derived_cl25])).
% 1.36/1.28 thf(zip_derived_cl178, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl34, zip_derived_cl133])).
% 1.36/1.28 thf(zip_derived_cl143, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl135, zip_derived_cl25])).
% 1.36/1.28 thf(zip_derived_cl179, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl178, zip_derived_cl143])).
% 1.36/1.28 thf(zip_derived_cl393, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl392, zip_derived_cl179])).
% 1.36/1.28 thf(zip_derived_cl143, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl135, zip_derived_cl25])).
% 1.36/1.28 thf(zip_derived_cl394, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl393, zip_derived_cl143])).
% 1.36/1.28 thf(zip_derived_cl622, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.28 inference('sup-', [status(thm)], [zip_derived_cl593, zip_derived_cl394])).
% 1.36/1.28 thf(zip_derived_cl590, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl588])).
% 1.36/1.28 thf(zip_derived_cl654, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl622, zip_derived_cl590])).
% 1.36/1.28 thf(zip_derived_cl591, plain,
% 1.36/1.28 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl588])).
% 1.36/1.28 thf(zip_derived_cl655, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl654, zip_derived_cl591])).
% 1.36/1.28 thf(zip_derived_cl592, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl588])).
% 1.36/1.28 thf(zip_derived_cl656, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl655, zip_derived_cl592])).
% 1.36/1.28 thf(zip_derived_cl724, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl723, zip_derived_cl656])).
% 1.36/1.28 thf(zip_derived_cl592, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl588])).
% 1.36/1.28 thf(zip_derived_cl725, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (iLEQ @ (suc @ X0) @ (suc @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl724, zip_derived_cl592])).
% 1.36/1.28 thf(zip_derived_cl751, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl750, zip_derived_cl725])).
% 1.36/1.28 thf(zip_derived_cl248, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl247, zip_derived_cl133])).
% 1.36/1.28 thf(zip_derived_cl752, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ (s @ 0) @ (f @ X0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.28 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl751, zip_derived_cl248])).
% 1.36/1.28 thf(zip_derived_cl591, plain,
% 1.36/1.28 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl588])).
% 1.36/1.28 thf(zip_derived_cl753, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl752, zip_derived_cl591])).
% 1.36/1.28 thf(zip_derived_cl590, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl588])).
% 1.36/1.28 thf(zip_derived_cl754, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl753, zip_derived_cl590])).
% 1.36/1.28 thf(zip_derived_cl606, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl600, zip_derived_cl591])).
% 1.36/1.28 thf(zip_derived_cl755, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl754, zip_derived_cl606])).
% 1.36/1.28 thf(zip_derived_cl656, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl655, zip_derived_cl592])).
% 1.36/1.28 thf(zip_derived_cl756, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl755, zip_derived_cl656])).
% 1.36/1.28 thf(zip_derived_cl592, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl588])).
% 1.36/1.28 thf(zip_derived_cl757, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl756, zip_derived_cl592])).
% 1.36/1.28 thf(zip_derived_cl760, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))) | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl30, zip_derived_cl757])).
% 1.36/1.28 thf(clause_72, axiom,
% 1.36/1.28 (( ~( E @ 0 @ ( f @ ( suc @ B_11 ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_11 ) ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_11 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ B_11 ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ B_11 ) @ ( f @ ( suc @ ( suc @ B_11 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ A_3 ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_11 ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ B_11 ) @ ( f @ ( suc @ B_11 ) ) ) ) |
% 1.36/1.28 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 1.36/1.28 ( E @ ( f @ B_11 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_11 ) ) ) ) ))).
% 1.36/1.28 thf(zip_derived_cl74, plain,
% 1.36/1.28 (![X0 : $i, X1 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X1)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X1))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.36/1.28 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.28 inference('cnf', [status(esa)], [clause_72])).
% 1.36/1.28 thf(zip_derived_cl326, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 1.36/1.28 inference('eq_fact', [status(thm)], [zip_derived_cl74])).
% 1.36/1.28 thf(zip_derived_cl327, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.28 inference('simplify', [status(thm)], [zip_derived_cl326])).
% 1.36/1.28 thf(clause_410, axiom,
% 1.36/1.28 (( ~( E @ 0 @ ( f @ ( suc @ B_11 ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_11 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ B_11 ) ) ) | ( ~( E @ 0 @ ( f @ A_3 ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_11 ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ B_11 ) @ ( f @ ( suc @ B_11 ) ) ) ) |
% 1.36/1.28 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( E @ ( f @ B_11 ) @ ( f @ ( suc @ ( suc @ B_11 ) ) ) ))).
% 1.36/1.28 thf(zip_derived_cl36, plain,
% 1.36/1.28 (![X0 : $i, X1 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X1))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.36/1.28 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.28 inference('cnf', [status(esa)], [clause_410])).
% 1.36/1.28 thf(zip_derived_cl205, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 1.36/1.28 inference('eq_fact', [status(thm)], [zip_derived_cl36])).
% 1.36/1.28 thf(zip_derived_cl206, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.28 inference('simplify', [status(thm)], [zip_derived_cl205])).
% 1.36/1.28 thf(clause_555, axiom,
% 1.36/1.28 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ A_3 ) ) ) |
% 1.36/1.28 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 1.36/1.28 thf(zip_derived_cl20, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.28 inference('cnf', [status(esa)], [clause_555])).
% 1.36/1.28 thf(clause_244, axiom,
% 1.36/1.28 (( ~( E @ 0 @ ( f @ A_3 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 1.36/1.28 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 1.36/1.28 thf(zip_derived_cl27, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.28 inference('cnf', [status(esa)], [clause_244])).
% 1.36/1.28 thf(zip_derived_cl130, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl20, zip_derived_cl27])).
% 1.36/1.28 thf(zip_derived_cl218, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl206, zip_derived_cl130])).
% 1.36/1.28 thf(clause_986, axiom,
% 1.36/1.28 (( ~( E @ 0 @ ( f @ ( suc @ B_11 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_11 ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ A_3 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_11 ) ) ) |
% 1.36/1.28 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 1.36/1.28 ( E @ ( f @ B_11 ) @ ( f @ ( suc @ B_11 ) ) ))).
% 1.36/1.28 thf(zip_derived_cl52, plain,
% 1.36/1.28 (![X0 : $i, X1 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X1))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.36/1.28 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.36/1.28 inference('cnf', [status(esa)], [clause_986])).
% 1.36/1.28 thf(zip_derived_cl131, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0)))),
% 1.36/1.28 inference('eq_fact', [status(thm)], [zip_derived_cl52])).
% 1.36/1.28 thf(zip_derived_cl132, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.36/1.28 inference('simplify', [status(thm)], [zip_derived_cl131])).
% 1.36/1.28 thf(zip_derived_cl27, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.28 inference('cnf', [status(esa)], [clause_244])).
% 1.36/1.28 thf(zip_derived_cl142, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl132, zip_derived_cl27])).
% 1.36/1.28 thf(zip_derived_cl219, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl218, zip_derived_cl142])).
% 1.36/1.28 thf(zip_derived_cl334, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl327, zip_derived_cl219])).
% 1.36/1.28 thf(zip_derived_cl142, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl132, zip_derived_cl27])).
% 1.36/1.28 thf(zip_derived_cl335, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl334, zip_derived_cl142])).
% 1.36/1.28 thf(clause_384, axiom,
% 1.36/1.28 (( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ A_3 ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 1.36/1.28 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 1.36/1.28 thf(zip_derived_cl58, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.28 inference('cnf', [status(esa)], [clause_384])).
% 1.36/1.28 thf(zip_derived_cl130, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl20, zip_derived_cl27])).
% 1.36/1.28 thf(zip_derived_cl176, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl58, zip_derived_cl130])).
% 1.36/1.28 thf(zip_derived_cl142, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl132, zip_derived_cl27])).
% 1.36/1.28 thf(zip_derived_cl177, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl176, zip_derived_cl142])).
% 1.36/1.28 thf(zip_derived_cl336, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl335, zip_derived_cl177])).
% 1.36/1.28 thf(zip_derived_cl784, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ 0)
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.28 inference('sup-', [status(thm)], [zip_derived_cl760, zip_derived_cl336])).
% 1.36/1.28 thf(clause_66, axiom,
% 1.36/1.28 (( ~( LE @ ( f @ B_10 ) @ ( s @ 0 ) ) ) | ( E @ 0 @ ( f @ B_10 ) ) |
% 1.36/1.28 ( LE @ ( f @ B_10 ) @ 0 ))).
% 1.36/1.28 thf(zip_derived_cl55, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (LE @ (f @ X0) @ (s @ 0))
% 1.36/1.28 | (E @ 0 @ (f @ X0))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('cnf', [status(esa)], [clause_66])).
% 1.36/1.28 thf(zip_derived_cl757, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl756, zip_derived_cl592])).
% 1.36/1.28 thf(zip_derived_cl762, plain,
% 1.36/1.28 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl55, zip_derived_cl757])).
% 1.36/1.28 thf(zip_derived_cl825, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl784, zip_derived_cl762])).
% 1.36/1.28 thf(clause_1033, axiom,
% 1.36/1.28 (( ~( LE @ ( f @ ( suc @ B_10 ) ) @ ( s @ 0 ) ) ) |
% 1.36/1.28 ( E @ 0 @ ( f @ ( suc @ B_10 ) ) ) | ( LE @ ( f @ B_10 ) @ 0 ))).
% 1.36/1.28 thf(zip_derived_cl50, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 1.36/1.28 | (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('cnf', [status(esa)], [clause_1033])).
% 1.36/1.28 thf(zip_derived_cl757, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl756, zip_derived_cl592])).
% 1.36/1.28 thf(zip_derived_cl761, plain,
% 1.36/1.28 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl50, zip_derived_cl757])).
% 1.36/1.28 thf(zip_derived_cl826, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ 0)
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl825, zip_derived_cl761])).
% 1.36/1.28 thf(clause_23, axiom,
% 1.36/1.28 (( ~( LE @ ( f @ ( suc @ ( suc @ B_10 ) ) ) @ ( s @ 0 ) ) ) |
% 1.36/1.28 ( E @ 0 @ ( f @ ( suc @ ( suc @ B_10 ) ) ) ) | ( LE @ ( f @ B_10 ) @ 0 ))).
% 1.36/1.28 thf(zip_derived_cl12, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 1.36/1.28 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('cnf', [status(esa)], [clause_23])).
% 1.36/1.28 thf(zip_derived_cl757, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl756, zip_derived_cl592])).
% 1.36/1.28 thf(zip_derived_cl759, plain,
% 1.36/1.28 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl12, zip_derived_cl757])).
% 1.36/1.28 thf(zip_derived_cl827, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl826, zip_derived_cl759])).
% 1.36/1.28 thf(clause_909, axiom,
% 1.36/1.28 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_10 ) ) ) ) ) @ ( s @ 0 ) ) ) |
% 1.36/1.28 ( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_10 ) ) ) ) ) ) |
% 1.36/1.28 ( LE @ ( f @ B_10 ) @ 0 ))).
% 1.36/1.28 thf(zip_derived_cl1, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0))
% 1.36/1.28 | (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('cnf', [status(esa)], [clause_909])).
% 1.36/1.28 thf(zip_derived_cl757, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl756, zip_derived_cl592])).
% 1.36/1.28 thf(zip_derived_cl758, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl757])).
% 1.36/1.28 thf(clause_352, axiom,
% 1.36/1.28 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ A_3 ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 1.36/1.28 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 1.36/1.28 thf(zip_derived_cl9, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.28 inference('cnf', [status(esa)], [clause_352])).
% 1.36/1.28 thf(zip_derived_cl787, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ 0)
% 1.36/1.28 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.28 inference('sup-', [status(thm)], [zip_derived_cl758, zip_derived_cl9])).
% 1.36/1.28 thf(zip_derived_cl913, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ 0)
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('sup-', [status(thm)], [zip_derived_cl827, zip_derived_cl787])).
% 1.36/1.28 thf(zip_derived_cl919, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('simplify', [status(thm)], [zip_derived_cl913])).
% 1.36/1.28 thf(zip_derived_cl827, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl826, zip_derived_cl759])).
% 1.36/1.28 thf(zip_derived_cl758, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl757])).
% 1.36/1.28 thf(clause_1, axiom,
% 1.36/1.28 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ B_11 ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_11 ) ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_11 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ B_11 ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ B_11 ) @ ( f @ ( suc @ ( suc @ B_11 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ A_3 ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_11 ) ) ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.36/1.28 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_11 ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ B_11 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_11 ) ) ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ B_11 ) @ ( f @ ( suc @ B_11 ) ) ) ) |
% 1.36/1.28 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ))).
% 1.36/1.28 thf(zip_derived_cl24, plain,
% 1.36/1.28 (![X0 : $i, X1 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X1)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X1))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.36/1.28 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 1.36/1.28 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.28 inference('cnf', [status(esa)], [clause_1])).
% 1.36/1.28 thf(zip_derived_cl332, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 1.36/1.28 inference('eq_fact', [status(thm)], [zip_derived_cl24])).
% 1.36/1.28 thf(zip_derived_cl333, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 1.36/1.28 inference('simplify', [status(thm)], [zip_derived_cl332])).
% 1.36/1.28 thf(zip_derived_cl789, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ 0)
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.28 inference('sup-', [status(thm)], [zip_derived_cl758, zip_derived_cl333])).
% 1.36/1.28 thf(zip_derived_cl882, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ 0)
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('sup-', [status(thm)], [zip_derived_cl827, zip_derived_cl789])).
% 1.36/1.28 thf(zip_derived_cl887, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('simplify', [status(thm)], [zip_derived_cl882])).
% 1.36/1.28 thf(zip_derived_cl142, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl132, zip_derived_cl27])).
% 1.36/1.28 thf(zip_derived_cl889, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ 0)
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl887, zip_derived_cl142])).
% 1.36/1.28 thf(zip_derived_cl219, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl218, zip_derived_cl142])).
% 1.36/1.28 thf(zip_derived_cl890, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl889, zip_derived_cl219])).
% 1.36/1.28 thf(zip_derived_cl761, plain,
% 1.36/1.28 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl50, zip_derived_cl757])).
% 1.36/1.28 thf(zip_derived_cl891, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ 0)
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl890, zip_derived_cl761])).
% 1.36/1.28 thf(zip_derived_cl760, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))) | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl30, zip_derived_cl757])).
% 1.36/1.28 thf(zip_derived_cl892, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl891, zip_derived_cl760])).
% 1.36/1.28 thf(zip_derived_cl759, plain,
% 1.36/1.28 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl12, zip_derived_cl757])).
% 1.36/1.28 thf(zip_derived_cl893, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ 0)
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl892, zip_derived_cl759])).
% 1.36/1.28 thf(zip_derived_cl762, plain,
% 1.36/1.28 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl55, zip_derived_cl757])).
% 1.36/1.28 thf(zip_derived_cl894, plain,
% 1.36/1.28 (![X0 : $i]: (~ (iLEQ @ (suc @ X0) @ (suc @ X0)) | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl893, zip_derived_cl762])).
% 1.36/1.28 thf(zip_derived_cl920, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ 0)
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl919, zip_derived_cl894])).
% 1.36/1.28 thf(zip_derived_cl219, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl218, zip_derived_cl142])).
% 1.36/1.28 thf(zip_derived_cl921, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl920, zip_derived_cl219])).
% 1.36/1.28 thf(zip_derived_cl142, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0)))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl132, zip_derived_cl27])).
% 1.36/1.28 thf(zip_derived_cl922, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ 0)
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl921, zip_derived_cl142])).
% 1.36/1.28 thf(zip_derived_cl760, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))) | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl30, zip_derived_cl757])).
% 1.36/1.28 thf(zip_derived_cl923, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ (suc @ X0)))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl922, zip_derived_cl760])).
% 1.36/1.28 thf(zip_derived_cl761, plain,
% 1.36/1.28 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl50, zip_derived_cl757])).
% 1.36/1.28 thf(zip_derived_cl924, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 ( (LE @ (f @ X0) @ 0)
% 1.36/1.28 | ~ (E @ 0 @ (f @ X0))
% 1.36/1.28 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl923, zip_derived_cl761])).
% 1.36/1.28 thf(zip_derived_cl762, plain,
% 1.36/1.28 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl55, zip_derived_cl757])).
% 1.36/1.28 thf(zip_derived_cl925, plain,
% 1.36/1.28 (![X0 : $i]:
% 1.36/1.28 (~ (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl924, zip_derived_cl762])).
% 1.36/1.28 thf(zip_derived_cl759, plain,
% 1.36/1.28 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl12, zip_derived_cl757])).
% 1.36/1.28 thf(zip_derived_cl926, plain, (![X0 : $i]: (LE @ (f @ X0) @ 0)),
% 1.36/1.28 inference('clc', [status(thm)], [zip_derived_cl925, zip_derived_cl759])).
% 1.36/1.28 thf(zip_derived_cl927, plain, ($false),
% 1.36/1.28 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl926])).
% 1.36/1.28
% 1.36/1.28 % SZS output end Refutation
% 1.36/1.28
% 1.36/1.28
% 1.36/1.28 % Terminating...
% 1.99/1.39 % Runner terminated.
% 1.99/1.39 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------