TSTP Solution File: SYO676-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO676-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.DOXh5TaojX true
% Computer : n004.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 05:52:31 EDT 2023
% Result : Unsatisfiable 0.56s 1.07s
% Output : Refutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO676-1 : TPTP v8.1.2. Released v7.3.0.
% 0.14/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.DOXh5TaojX true
% 0.14/0.35 % Computer : n004.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 06:33:53 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.21/0.67 % Total configuration time : 435
% 0.21/0.67 % Estimated wc time : 1092
% 0.21/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.55/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.55/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.55/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.55/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.55/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.55/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 0.56/1.07 % Solved by fo/fo1_lcnf.sh.
% 0.56/1.07 % done 153 iterations in 0.217s
% 0.56/1.07 % SZS status Unsatisfiable for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.56/1.07 % SZS output start Refutation
% 0.56/1.07 thf(suc_type, type, suc: $i > $i).
% 0.56/1.07 thf(0_type, type, 0: $i).
% 0.56/1.07 thf(f_type, type, f: $i > $i).
% 0.56/1.07 thf(z_type, type, z: $i).
% 0.56/1.07 thf(E_type, type, E: $i > $i > $o).
% 0.56/1.07 thf(LE_type, type, LE: $i > $i > $o).
% 0.56/1.07 thf(s_type, type, s: $i > $i).
% 0.56/1.07 thf(clause_64, axiom, (~( LE @ ( f @ z ) @ 0 ))).
% 0.56/1.07 thf(zip_derived_cl20, plain, (~ (LE @ (f @ z) @ 0)),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_64])).
% 0.56/1.07 thf(clause_38, axiom,
% 0.56/1.07 (( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ A_4 ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl13, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ X0)))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_38])).
% 0.56/1.07 thf(zip_derived_cl143, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ X0))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl13])).
% 0.56/1.07 thf(clause_52, axiom,
% 0.56/1.07 (( ~( E @ 0 @ ( f @ A_4 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ))).
% 0.56/1.07 thf(zip_derived_cl8, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ 0 @ (f @ X0)))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ (suc @ X0))))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ X0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_52])).
% 0.56/1.07 thf(zip_derived_cl48, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ 0 @ (f @ X0))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl8])).
% 0.56/1.07 thf(zip_derived_cl144, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ X0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl143, zip_derived_cl48])).
% 0.56/1.07 thf(clause_31, axiom,
% 0.56/1.07 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ A_4 ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl1, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ 0 @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ X0)))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_31])).
% 0.56/1.07 thf(zip_derived_cl60, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ X0))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1])).
% 0.56/1.07 thf(zip_derived_cl48, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ 0 @ (f @ X0))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl8])).
% 0.56/1.07 thf(zip_derived_cl61, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ X0))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl60, zip_derived_cl48])).
% 0.56/1.07 thf(zip_derived_cl145, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ X0))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl144, zip_derived_cl61])).
% 0.56/1.07 thf(clause_87, axiom,
% 0.56/1.07 (( ~( LE @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B_2 ) ) ) ) ) ) @
% 0.56/1.07 ( s @ 0 ) ) ) |
% 0.56/1.07 ( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B_2 ) ) ) ) ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B_2 ) @ 0 ))).
% 0.56/1.07 thf(zip_derived_cl9, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @
% 0.56/1.07 (s @ 0)))) |
% 0.56/1.07 (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (LE @ (f @ X0) @ 0)))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_87])).
% 0.56/1.07 thf(zip_derived_cl68, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @ (s @ 0))
% 0.56/1.07 | (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 0.56/1.07 | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl9])).
% 0.56/1.07 thf(clause_29, axiom,
% 0.56/1.07 (( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl0, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ X0)))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_29])).
% 0.56/1.07 thf(zip_derived_cl49, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl0])).
% 0.56/1.07 thf(clause_96, axiom,
% 0.56/1.07 (( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl29, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ X0)))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_96])).
% 0.56/1.07 thf(zip_derived_cl161, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])).
% 0.56/1.07 thf(clause_104, axiom,
% 0.56/1.07 (( ~( LE @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B_1 ) ) ) ) ) ) @
% 0.56/1.07 ( s @ ( s @ 0 ) ) ) ) |
% 0.56/1.07 ( E @
% 0.56/1.07 ( s @ 0 ) @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B_1 ) ) ) ) ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B_1 ) @ ( s @ 0 ) ))).
% 0.56/1.07 thf(zip_derived_cl17, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @
% 0.56/1.07 (s @ (s @ 0))))) |
% 0.56/1.07 (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ 0))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_104])).
% 0.56/1.07 thf(zip_derived_cl84, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @
% 0.56/1.07 (s @ (s @ 0)))
% 0.56/1.07 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl17])).
% 0.56/1.07 thf(clause_95, axiom,
% 0.56/1.07 (( ~( LE @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_0 ) ) ) ) ) @
% 0.56/1.07 ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 0.56/1.07 ( E @
% 0.56/1.07 ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_0 ) ) ) ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B_0 ) @ ( s @ ( s @ 0 ) ) ))).
% 0.56/1.07 thf(zip_derived_cl25, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @
% 0.56/1.07 (s @ (s @ (s @ 0)))))) |
% 0.56/1.07 (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_95])).
% 0.56/1.07 thf(zip_derived_cl90, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @
% 0.56/1.07 (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl25])).
% 0.56/1.07 thf(clause_27, axiom,
% 0.56/1.07 (( ~( LE @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) @
% 0.56/1.07 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 0.56/1.07 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl10, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @
% 0.56/1.07 (s @ (s @ (s @ (s @ 0))))))) |
% 0.56/1.07 (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0))))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_27])).
% 0.56/1.07 thf(clause_100, axiom, (LE @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl6, plain,
% 0.56/1.07 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_100])).
% 0.56/1.07 thf(zip_derived_cl91, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ ($true))) |
% 0.56/1.07 (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0))))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl6])).
% 0.56/1.07 thf(zip_derived_cl92, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((LE @ (f @ X0) @ (s @ (s @ (s @ 0)))) | (E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl91])).
% 0.56/1.07 thf(zip_derived_cl93, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl92])).
% 0.56/1.07 thf(clause_16, axiom,
% 0.56/1.07 (( ~( LE @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) @
% 0.56/1.07 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 0.56/1.07 ( E @
% 0.56/1.07 ( s @ ( s @ ( s @ 0 ) ) ) @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl2, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @
% 0.56/1.07 (s @ (s @ (s @ (s @ 0))))))) |
% 0.56/1.07 (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_16])).
% 0.56/1.07 thf(zip_derived_cl6, plain,
% 0.56/1.07 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_100])).
% 0.56/1.07 thf(zip_derived_cl78, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ ($true))) |
% 0.56/1.07 (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl6])).
% 0.56/1.07 thf(zip_derived_cl79, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ X0)))))) | (LE @ (f @ X0) @
% 0.56/1.07 (s @ (s @ (s @ 0))))))),
% 0.56/1.07 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl78])).
% 0.56/1.07 thf(zip_derived_cl80, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl79])).
% 0.56/1.07 thf(clause_35, axiom,
% 0.56/1.07 (( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @
% 0.56/1.07 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.56/1.07 ( ~( E @
% 0.56/1.07 ( s @ ( s @ ( s @ 0 ) ) ) @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl4, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_35])).
% 0.56/1.07 thf(zip_derived_cl100, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])).
% 0.56/1.07 thf(zip_derived_cl101, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl100])).
% 0.56/1.07 thf(zip_derived_cl221, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl101])).
% 0.56/1.07 thf(zip_derived_cl226, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('simplify', [status(thm)], [zip_derived_cl221])).
% 0.56/1.07 thf(clause_105, axiom,
% 0.56/1.07 (( ~( LE @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 0.56/1.07 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl41, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ (s @ 0))))))) |
% 0.56/1.07 (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_105])).
% 0.56/1.07 thf(zip_derived_cl6, plain,
% 0.56/1.07 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_100])).
% 0.56/1.07 thf(zip_derived_cl72, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ ($true))) | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl41, zip_derived_cl6])).
% 0.56/1.07 thf(zip_derived_cl73, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((LE @ (f @ X0) @ (s @ (s @ (s @ 0)))) | (E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ (suc @ X0)))))),
% 0.56/1.07 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl72])).
% 0.56/1.07 thf(zip_derived_cl74, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl73])).
% 0.56/1.07 thf(zip_derived_cl252, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl226, zip_derived_cl74])).
% 0.56/1.07 thf(zip_derived_cl93, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl92])).
% 0.56/1.07 thf(clause_11, axiom,
% 0.56/1.07 (( ~( E @
% 0.56/1.07 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl11, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_11])).
% 0.56/1.07 thf(zip_derived_cl149, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl11])).
% 0.56/1.07 thf(clause_102, axiom,
% 0.56/1.07 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl36, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_102])).
% 0.56/1.07 thf(zip_derived_cl118, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl36])).
% 0.56/1.07 thf(clause_8, axiom,
% 0.56/1.07 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ))).
% 0.56/1.07 thf(zip_derived_cl45, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ X0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_8])).
% 0.56/1.07 thf(zip_derived_cl65, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl45])).
% 0.56/1.07 thf(zip_derived_cl119, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl118, zip_derived_cl65])).
% 0.56/1.07 thf(zip_derived_cl150, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl149, zip_derived_cl119])).
% 0.56/1.07 thf(zip_derived_cl65, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl45])).
% 0.56/1.07 thf(zip_derived_cl151, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl150, zip_derived_cl65])).
% 0.56/1.07 thf(zip_derived_cl153, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl151])).
% 0.56/1.07 thf(clause_121, axiom,
% 0.56/1.07 (( ~( LE @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 0.56/1.07 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B ) ) |
% 0.56/1.07 ( LE @ ( f @ B ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl19, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))) |
% 0.56/1.07 (E @ (s @ (s @ (s @ 0))) @ (f @ X0)) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_121])).
% 0.56/1.07 thf(zip_derived_cl6, plain,
% 0.56/1.07 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_100])).
% 0.56/1.07 thf(zip_derived_cl62, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ ($true))) | (E @ (s @ (s @ (s @ 0))) @ (f @ X0)) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl6])).
% 0.56/1.07 thf(zip_derived_cl63, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((LE @ (f @ X0) @ (s @ (s @ (s @ 0)))) | (E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ X0))))),
% 0.56/1.07 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl62])).
% 0.56/1.07 thf(zip_derived_cl64, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl63])).
% 0.56/1.07 thf(zip_derived_cl182, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl153, zip_derived_cl64])).
% 0.56/1.07 thf(zip_derived_cl74, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl73])).
% 0.56/1.07 thf(zip_derived_cl183, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl182, zip_derived_cl74])).
% 0.56/1.07 thf(clause_6, axiom,
% 0.56/1.07 (( ~( LE @
% 0.56/1.07 ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 0.56/1.07 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl35, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ (s @ 0))))))) |
% 0.56/1.07 (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_6])).
% 0.56/1.07 thf(zip_derived_cl6, plain,
% 0.56/1.07 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_100])).
% 0.56/1.07 thf(zip_derived_cl85, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ ($true))) |
% 0.56/1.07 (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl35, zip_derived_cl6])).
% 0.56/1.07 thf(zip_derived_cl86, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((LE @ (f @ X0) @ (s @ (s @ (s @ 0)))) | (E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl85])).
% 0.56/1.07 thf(zip_derived_cl87, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl86])).
% 0.56/1.07 thf(zip_derived_cl184, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl183, zip_derived_cl87])).
% 0.56/1.07 thf(zip_derived_cl253, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl252, zip_derived_cl184])).
% 0.56/1.07 thf(zip_derived_cl74, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl73])).
% 0.56/1.07 thf(zip_derived_cl65, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl45])).
% 0.56/1.07 thf(zip_derived_cl76, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl65])).
% 0.56/1.07 thf(zip_derived_cl64, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl63])).
% 0.56/1.07 thf(zip_derived_cl77, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl76, zip_derived_cl64])).
% 0.56/1.07 thf(zip_derived_cl254, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl253, zip_derived_cl77])).
% 0.56/1.07 thf(zip_derived_cl64, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl63])).
% 0.56/1.07 thf(zip_derived_cl255, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl254, zip_derived_cl64])).
% 0.56/1.07 thf(zip_derived_cl87, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl86])).
% 0.56/1.07 thf(zip_derived_cl119, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl118, zip_derived_cl65])).
% 0.56/1.07 thf(zip_derived_cl123, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl87, zip_derived_cl119])).
% 0.56/1.07 thf(zip_derived_cl64, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl63])).
% 0.56/1.07 thf(zip_derived_cl126, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl123, zip_derived_cl64])).
% 0.56/1.07 thf(zip_derived_cl74, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl73])).
% 0.56/1.07 thf(zip_derived_cl127, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl126, zip_derived_cl74])).
% 0.56/1.07 thf(zip_derived_cl256, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl255, zip_derived_cl127])).
% 0.56/1.07 thf(zip_derived_cl87, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl86])).
% 0.56/1.07 thf(zip_derived_cl257, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl256, zip_derived_cl87])).
% 0.56/1.07 thf(zip_derived_cl80, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl79])).
% 0.56/1.07 thf(clause_4, axiom,
% 0.56/1.07 (( ~( LE @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ) @
% 0.56/1.07 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 0.56/1.07 ( E @
% 0.56/1.07 ( s @ ( s @ ( s @ 0 ) ) ) @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl26, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @
% 0.56/1.07 (s @ (s @ (s @ (s @ 0))))))) |
% 0.56/1.07 (E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_4])).
% 0.56/1.07 thf(zip_derived_cl6, plain,
% 0.56/1.07 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_100])).
% 0.56/1.07 thf(zip_derived_cl110, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ ($true))) |
% 0.56/1.07 (E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl6])).
% 0.56/1.07 thf(zip_derived_cl111, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((LE @ (f @ X0) @ (s @ (s @ (s @ 0)))) | (E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))))),
% 0.56/1.07 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl110])).
% 0.56/1.07 thf(zip_derived_cl112, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl111])).
% 0.56/1.07 thf(clause_40, axiom,
% 0.56/1.07 (( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @
% 0.56/1.07 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @
% 0.56/1.07 ( s @ ( s @ ( s @ 0 ) ) ) @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.56/1.07 ( ~( E @
% 0.56/1.07 ( s @ ( s @ ( s @ 0 ) ) ) @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl32, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_40])).
% 0.56/1.07 thf(zip_derived_cl175, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl32])).
% 0.56/1.07 thf(zip_derived_cl181, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl112, zip_derived_cl175])).
% 0.56/1.07 thf(zip_derived_cl282, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl181])).
% 0.56/1.07 thf(zip_derived_cl288, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('simplify', [status(thm)], [zip_derived_cl282])).
% 0.56/1.07 thf(zip_derived_cl303, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl257, zip_derived_cl288])).
% 0.56/1.07 thf(zip_derived_cl312, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('simplify', [status(thm)], [zip_derived_cl303])).
% 0.56/1.07 thf(zip_derived_cl151, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl150, zip_derived_cl65])).
% 0.56/1.07 thf(zip_derived_cl317, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl312, zip_derived_cl151])).
% 0.56/1.07 thf(zip_derived_cl74, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl73])).
% 0.56/1.07 thf(zip_derived_cl318, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl317, zip_derived_cl74])).
% 0.56/1.07 thf(zip_derived_cl93, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl92])).
% 0.56/1.07 thf(zip_derived_cl319, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl318, zip_derived_cl93])).
% 0.56/1.07 thf(zip_derived_cl77, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl76, zip_derived_cl64])).
% 0.56/1.07 thf(zip_derived_cl320, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl319, zip_derived_cl77])).
% 0.56/1.07 thf(zip_derived_cl64, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl63])).
% 0.56/1.07 thf(zip_derived_cl321, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl320, zip_derived_cl64])).
% 0.56/1.07 thf(zip_derived_cl127, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl126, zip_derived_cl74])).
% 0.56/1.07 thf(zip_derived_cl322, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl321, zip_derived_cl127])).
% 0.56/1.07 thf(zip_derived_cl87, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl86])).
% 0.56/1.07 thf(zip_derived_cl323, plain,
% 0.56/1.07 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl322, zip_derived_cl87])).
% 0.56/1.07 thf(zip_derived_cl328, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl90, zip_derived_cl323])).
% 0.56/1.07 thf(clause_42, axiom,
% 0.56/1.07 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.56/1.07 ( ~( E @
% 0.56/1.07 ( s @ ( s @ 0 ) ) @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl22, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @ (f @ X0)))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_42])).
% 0.56/1.07 thf(zip_derived_cl171, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl22])).
% 0.56/1.07 thf(clause_3, axiom,
% 0.56/1.07 (( ~( LE @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B_0 ) ) ) ) ) ) @
% 0.56/1.07 ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 0.56/1.07 ( E @
% 0.56/1.07 ( s @ ( s @ 0 ) ) @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B_0 ) ) ) ) ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B_0 ) @ ( s @ ( s @ 0 ) ) ))).
% 0.56/1.07 thf(zip_derived_cl14, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @
% 0.56/1.07 (s @ (s @ (s @ 0)))))) |
% 0.56/1.07 (E @ (s @ (s @ 0)) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_3])).
% 0.56/1.07 thf(zip_derived_cl107, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @
% 0.56/1.07 (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ 0)) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl14])).
% 0.56/1.07 thf(zip_derived_cl323, plain,
% 0.56/1.07 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl322, zip_derived_cl87])).
% 0.56/1.07 thf(zip_derived_cl329, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ (s @ 0)) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl323])).
% 0.56/1.07 thf(clause_85, axiom,
% 0.56/1.07 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @
% 0.56/1.07 ( s @ ( s @ 0 ) ) @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.56/1.07 ( ~( E @
% 0.56/1.07 ( s @ ( s @ 0 ) ) @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl12, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @ (f @ X0)))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0)))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_85])).
% 0.56/1.07 thf(zip_derived_cl170, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl12])).
% 0.56/1.07 thf(zip_derived_cl335, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl329, zip_derived_cl170])).
% 0.56/1.07 thf(zip_derived_cl345, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl171, zip_derived_cl335])).
% 0.56/1.07 thf(zip_derived_cl348, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('simplify', [status(thm)], [zip_derived_cl345])).
% 0.56/1.07 thf(zip_derived_cl354, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl328, zip_derived_cl348])).
% 0.56/1.07 thf(zip_derived_cl358, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('simplify', [status(thm)], [zip_derived_cl354])).
% 0.56/1.07 thf(clause_86, axiom,
% 0.56/1.07 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ))).
% 0.56/1.07 thf(zip_derived_cl40, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (s @ (s @ 0)) @ (f @ X0)))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ X0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_86])).
% 0.56/1.07 thf(zip_derived_cl57, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])).
% 0.56/1.07 thf(zip_derived_cl359, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl358, zip_derived_cl57])).
% 0.56/1.07 thf(clause_81, axiom,
% 0.56/1.07 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl34, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @ (f @ X0)))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_81])).
% 0.56/1.07 thf(zip_derived_cl116, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])).
% 0.56/1.07 thf(zip_derived_cl57, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])).
% 0.56/1.07 thf(zip_derived_cl117, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl116, zip_derived_cl57])).
% 0.56/1.07 thf(zip_derived_cl360, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl359, zip_derived_cl117])).
% 0.56/1.07 thf(clause_46, axiom,
% 0.56/1.07 (( ~( LE @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ B_0 ) ) ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 0.56/1.07 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_0 ) ) ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B_0 ) @ ( s @ ( s @ 0 ) ) ))).
% 0.56/1.07 thf(zip_derived_cl37, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @
% 0.56/1.07 (s @ (s @ (s @ 0)))))) |
% 0.56/1.07 (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0))))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_46])).
% 0.56/1.07 thf(zip_derived_cl83, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl37])).
% 0.56/1.07 thf(zip_derived_cl323, plain,
% 0.56/1.07 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl322, zip_derived_cl87])).
% 0.56/1.07 thf(zip_derived_cl327, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl83, zip_derived_cl323])).
% 0.56/1.07 thf(zip_derived_cl361, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl360, zip_derived_cl327])).
% 0.56/1.07 thf(clause_62, axiom,
% 0.56/1.07 (( ~( LE @ ( f @ ( suc @ B_0 ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 0.56/1.07 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_0 ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B_0 ) @ ( s @ ( s @ 0 ) ) ))).
% 0.56/1.07 thf(zip_derived_cl28, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0)))))) |
% 0.56/1.07 (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_62])).
% 0.56/1.07 thf(zip_derived_cl58, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl28])).
% 0.56/1.07 thf(zip_derived_cl323, plain,
% 0.56/1.07 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl322, zip_derived_cl87])).
% 0.56/1.07 thf(zip_derived_cl325, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl58, zip_derived_cl323])).
% 0.56/1.07 thf(zip_derived_cl362, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl361, zip_derived_cl325])).
% 0.56/1.07 thf(clause_98, axiom,
% 0.56/1.07 (( ~( LE @ ( f @ B_0 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 0.56/1.07 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_0 ) ) |
% 0.56/1.07 ( LE @ ( f @ B_0 ) @ ( s @ ( s @ 0 ) ) ))).
% 0.56/1.07 thf(zip_derived_cl43, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))) |
% 0.56/1.07 (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_98])).
% 0.56/1.07 thf(zip_derived_cl55, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])).
% 0.56/1.07 thf(zip_derived_cl323, plain,
% 0.56/1.07 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl322, zip_derived_cl87])).
% 0.56/1.07 thf(zip_derived_cl324, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl55, zip_derived_cl323])).
% 0.56/1.07 thf(zip_derived_cl363, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl362, zip_derived_cl324])).
% 0.56/1.07 thf(clause_60, axiom,
% 0.56/1.07 (( ~( LE @ ( f @ ( suc @ ( suc @ B_0 ) ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 0.56/1.07 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_0 ) ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B_0 ) @ ( s @ ( s @ 0 ) ) ))).
% 0.56/1.07 thf(zip_derived_cl44, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0)))))) |
% 0.56/1.07 (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ (s @ 0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_60])).
% 0.56/1.07 thf(zip_derived_cl69, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0))))
% 0.56/1.07 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])).
% 0.56/1.07 thf(zip_derived_cl323, plain,
% 0.56/1.07 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl322, zip_derived_cl87])).
% 0.56/1.07 thf(zip_derived_cl326, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl323])).
% 0.56/1.07 thf(zip_derived_cl364, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl363, zip_derived_cl326])).
% 0.56/1.07 thf(clause_45, axiom,
% 0.56/1.07 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl24, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @ (f @ X0)))) |
% 0.56/1.07 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_45])).
% 0.56/1.07 thf(zip_derived_cl146, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl24])).
% 0.56/1.07 thf(zip_derived_cl117, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl116, zip_derived_cl57])).
% 0.56/1.07 thf(zip_derived_cl147, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl146, zip_derived_cl117])).
% 0.56/1.07 thf(zip_derived_cl57, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])).
% 0.56/1.07 thf(zip_derived_cl148, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl147, zip_derived_cl57])).
% 0.56/1.07 thf(zip_derived_cl367, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('s_sup+', [status(thm)], [zip_derived_cl364, zip_derived_cl148])).
% 0.56/1.07 thf(zip_derived_cl325, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl58, zip_derived_cl323])).
% 0.56/1.07 thf(zip_derived_cl371, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl367, zip_derived_cl325])).
% 0.56/1.07 thf(zip_derived_cl327, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl83, zip_derived_cl323])).
% 0.56/1.07 thf(zip_derived_cl372, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl371, zip_derived_cl327])).
% 0.56/1.07 thf(zip_derived_cl326, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl323])).
% 0.56/1.07 thf(zip_derived_cl373, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl372, zip_derived_cl326])).
% 0.56/1.07 thf(zip_derived_cl324, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl55, zip_derived_cl323])).
% 0.56/1.07 thf(zip_derived_cl374, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl373, zip_derived_cl324])).
% 0.56/1.07 thf(zip_derived_cl380, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl84, zip_derived_cl374])).
% 0.56/1.07 thf(clause_41, axiom,
% 0.56/1.07 (( ~( E @
% 0.56/1.07 ( s @ 0 ) @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl31, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (s @ 0) @
% 0.56/1.07 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ X0)))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_41])).
% 0.56/1.07 thf(zip_derived_cl174, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])).
% 0.56/1.07 thf(zip_derived_cl386, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ 0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl380, zip_derived_cl174])).
% 0.56/1.07 thf(zip_derived_cl393, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl161, zip_derived_cl386])).
% 0.56/1.07 thf(zip_derived_cl396, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ 0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('simplify', [status(thm)], [zip_derived_cl393])).
% 0.56/1.07 thf(zip_derived_cl404, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl396])).
% 0.56/1.07 thf(zip_derived_cl407, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('simplify', [status(thm)], [zip_derived_cl404])).
% 0.56/1.07 thf(clause_125, axiom,
% 0.56/1.07 (( ~( LE @
% 0.56/1.07 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_1 ) ) ) ) ) @
% 0.56/1.07 ( s @ ( s @ 0 ) ) ) ) |
% 0.56/1.07 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_1 ) ) ) ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B_1 ) @ ( s @ 0 ) ))).
% 0.56/1.07 thf(zip_derived_cl38, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @
% 0.56/1.07 (s @ (s @ 0))))) |
% 0.56/1.07 (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ 0))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_125])).
% 0.56/1.07 thf(zip_derived_cl70, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ (s @ 0)))
% 0.56/1.07 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl38])).
% 0.56/1.07 thf(zip_derived_cl374, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl373, zip_derived_cl324])).
% 0.56/1.07 thf(zip_derived_cl379, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl374])).
% 0.56/1.07 thf(zip_derived_cl409, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl407, zip_derived_cl379])).
% 0.56/1.07 thf(clause_91, axiom,
% 0.56/1.07 (( ~( LE @ ( f @ ( suc @ ( suc @ B_1 ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 0.56/1.07 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_1 ) ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B_1 ) @ ( s @ 0 ) ))).
% 0.56/1.07 thf(zip_derived_cl30, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0))))) |
% 0.56/1.07 (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ 0))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_91])).
% 0.56/1.07 thf(zip_derived_cl56, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 0.56/1.07 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])).
% 0.56/1.07 thf(zip_derived_cl374, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl373, zip_derived_cl324])).
% 0.56/1.07 thf(zip_derived_cl377, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl56, zip_derived_cl374])).
% 0.56/1.07 thf(zip_derived_cl410, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ 0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl409, zip_derived_cl377])).
% 0.56/1.07 thf(clause_56, axiom,
% 0.56/1.07 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ B_1 ) ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 0.56/1.07 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_1 ) ) ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B_1 ) @ ( s @ 0 ) ))).
% 0.56/1.07 thf(zip_derived_cl23, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ 0))))) |
% 0.56/1.07 (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0))))) |
% 0.56/1.07 (LE @ (f @ X0) @ (s @ 0))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_56])).
% 0.56/1.07 thf(zip_derived_cl67, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ 0)))
% 0.56/1.07 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl23])).
% 0.56/1.07 thf(zip_derived_cl374, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl373, zip_derived_cl324])).
% 0.56/1.07 thf(zip_derived_cl378, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl67, zip_derived_cl374])).
% 0.56/1.07 thf(zip_derived_cl411, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl410, zip_derived_cl378])).
% 0.56/1.07 thf(clause_58, axiom,
% 0.56/1.07 (( ~( LE @ ( f @ B_1 ) @ ( s @ ( s @ 0 ) ) ) ) |
% 0.56/1.07 ( E @ ( s @ 0 ) @ ( f @ B_1 ) ) | ( LE @ ( f @ B_1 ) @ ( s @ 0 ) ))).
% 0.56/1.07 thf(zip_derived_cl42, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ X0) @ (s @ (s @ 0))))) |
% 0.56/1.07 (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_58])).
% 0.56/1.07 thf(zip_derived_cl50, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.56/1.07 | (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl42])).
% 0.56/1.07 thf(zip_derived_cl374, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl373, zip_derived_cl324])).
% 0.56/1.07 thf(zip_derived_cl375, plain,
% 0.56/1.07 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl50, zip_derived_cl374])).
% 0.56/1.07 thf(zip_derived_cl412, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ 0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl411, zip_derived_cl375])).
% 0.56/1.07 thf(clause_84, axiom,
% 0.56/1.07 (( ~( LE @ ( f @ ( suc @ B_1 ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 0.56/1.07 ( E @ ( s @ 0 ) @ ( f @ ( suc @ B_1 ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B_1 ) @ ( s @ 0 ) ))).
% 0.56/1.07 thf(zip_derived_cl3, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0))))) |
% 0.56/1.07 (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_84])).
% 0.56/1.07 thf(zip_derived_cl53, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 0.56/1.07 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3])).
% 0.56/1.07 thf(zip_derived_cl374, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl373, zip_derived_cl324])).
% 0.56/1.07 thf(zip_derived_cl376, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl374])).
% 0.56/1.07 thf(zip_derived_cl413, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl412, zip_derived_cl376])).
% 0.56/1.07 thf(clause_109, axiom,
% 0.56/1.07 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl39, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ X0)))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_109])).
% 0.56/1.07 thf(zip_derived_cl108, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])).
% 0.56/1.07 thf(clause_50, axiom,
% 0.56/1.07 (( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 0.56/1.07 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ))).
% 0.56/1.07 thf(zip_derived_cl16, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (s @ 0) @ (f @ X0)))) |
% 0.56/1.07 (((~) @ (E @ (s @ 0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ X0)))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_50])).
% 0.56/1.07 thf(zip_derived_cl51, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl16])).
% 0.56/1.07 thf(zip_derived_cl109, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl108, zip_derived_cl51])).
% 0.56/1.07 thf(zip_derived_cl415, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ 0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('s_sup+', [status(thm)], [zip_derived_cl413, zip_derived_cl109])).
% 0.56/1.07 thf(zip_derived_cl51, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl16])).
% 0.56/1.07 thf(zip_derived_cl422, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl415, zip_derived_cl51])).
% 0.56/1.07 thf(zip_derived_cl377, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl56, zip_derived_cl374])).
% 0.56/1.07 thf(zip_derived_cl423, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ (s @ 0))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.56/1.07 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl422, zip_derived_cl377])).
% 0.56/1.07 thf(zip_derived_cl375, plain,
% 0.56/1.07 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl50, zip_derived_cl374])).
% 0.56/1.07 thf(zip_derived_cl424, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl423, zip_derived_cl375])).
% 0.56/1.07 thf(zip_derived_cl376, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl374])).
% 0.56/1.07 thf(zip_derived_cl425, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl424, zip_derived_cl376])).
% 0.56/1.07 thf(zip_derived_cl431, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 0.56/1.07 | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl425])).
% 0.56/1.07 thf(clause_10, axiom,
% 0.56/1.07 (( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ A_4 ) ) ) |
% 0.56/1.07 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ))).
% 0.56/1.07 thf(zip_derived_cl21, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ X0)))) |
% 0.56/1.07 (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_10])).
% 0.56/1.07 thf(zip_derived_cl158, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ X0))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl21])).
% 0.56/1.07 thf(clause_130, axiom,
% 0.56/1.07 (( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.56/1.07 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 0.56/1.07 ( ~( E @ 0 @ ( f @ A_4 ) ) ))).
% 0.56/1.07 thf(zip_derived_cl7, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ (suc @ X0))))) |
% 0.56/1.07 (((~) @ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (((~) @ (E @ 0 @ (f @ X0))))))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_130])).
% 0.56/1.07 thf(zip_derived_cl142, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ X0)))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])).
% 0.56/1.07 thf(zip_derived_cl159, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ 0 @ (f @ X0))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ X0)))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl158, zip_derived_cl142])).
% 0.56/1.07 thf(zip_derived_cl160, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ X0)))),
% 0.56/1.07 inference('simplify', [status(thm)], [zip_derived_cl159])).
% 0.56/1.07 thf(zip_derived_cl438, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ 0)
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ X0)))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl431, zip_derived_cl160])).
% 0.56/1.07 thf(zip_derived_cl443, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ 0 @ (f @ X0))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (LE @ (f @ X0) @ 0)
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ X0)))),
% 0.56/1.07 inference('s_sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl438])).
% 0.56/1.07 thf(zip_derived_cl446, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | (LE @ (f @ X0) @ 0)
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ X0)))),
% 0.56/1.07 inference('simplify', [status(thm)], [zip_derived_cl443])).
% 0.56/1.07 thf(zip_derived_cl61, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ X0))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl60, zip_derived_cl48])).
% 0.56/1.07 thf(zip_derived_cl449, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ 0 @ (f @ X0))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (LE @ (f @ X0) @ 0)
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl446, zip_derived_cl61])).
% 0.56/1.07 thf(clause_22, axiom,
% 0.56/1.07 (( ~( LE @ ( f @ B_2 ) @ ( s @ 0 ) ) ) | ( E @ 0 @ ( f @ B_2 ) ) |
% 0.56/1.07 ( LE @ ( f @ B_2 ) @ 0 ))).
% 0.56/1.07 thf(zip_derived_cl18, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ X0) @ (s @ 0)))) | (E @ 0 @ (f @ X0)) |
% 0.56/1.07 (LE @ (f @ X0) @ 0)))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_22])).
% 0.56/1.07 thf(zip_derived_cl46, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ X0) @ (s @ 0))
% 0.56/1.07 | (E @ 0 @ (f @ X0))
% 0.56/1.07 | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl18])).
% 0.56/1.07 thf(zip_derived_cl425, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl424, zip_derived_cl376])).
% 0.56/1.07 thf(zip_derived_cl426, plain,
% 0.56/1.07 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl425])).
% 0.56/1.07 thf(zip_derived_cl450, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | (LE @ (f @ X0) @ 0)
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl449, zip_derived_cl426])).
% 0.56/1.07 thf(clause_20, axiom,
% 0.56/1.07 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_2 ) ) ) ) ) @ ( s @ 0 ) ) ) |
% 0.56/1.07 ( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_2 ) ) ) ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B_2 ) @ 0 ))).
% 0.56/1.07 thf(zip_derived_cl33, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0)))) |
% 0.56/1.07 (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))) |
% 0.56/1.07 (LE @ (f @ X0) @ 0)))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_20])).
% 0.56/1.07 thf(zip_derived_cl59, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0))
% 0.56/1.07 | (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl33])).
% 0.56/1.07 thf(zip_derived_cl425, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl424, zip_derived_cl376])).
% 0.56/1.07 thf(zip_derived_cl430, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 0.56/1.07 | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl425])).
% 0.56/1.07 thf(zip_derived_cl451, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (LE @ (f @ X0) @ 0)
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl450, zip_derived_cl430])).
% 0.56/1.07 thf(clause_74, axiom,
% 0.56/1.07 (( ~( LE @ ( f @ ( suc @ B_2 ) ) @ ( s @ 0 ) ) ) |
% 0.56/1.07 ( E @ 0 @ ( f @ ( suc @ B_2 ) ) ) | ( LE @ ( f @ B_2 ) @ 0 ))).
% 0.56/1.07 thf(zip_derived_cl5, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ X0)) @ (s @ 0)))) |
% 0.56/1.07 (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0)))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_74])).
% 0.56/1.07 thf(zip_derived_cl47, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 0.56/1.07 | (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl5])).
% 0.56/1.07 thf(zip_derived_cl425, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl424, zip_derived_cl376])).
% 0.56/1.07 thf(zip_derived_cl427, plain,
% 0.56/1.07 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl425])).
% 0.56/1.07 thf(zip_derived_cl452, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.56/1.07 | (LE @ (f @ X0) @ 0)
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl451, zip_derived_cl427])).
% 0.56/1.07 thf(clause_63, axiom,
% 0.56/1.07 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ B_2 ) ) ) ) @ ( s @ 0 ) ) ) |
% 0.56/1.07 ( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_2 ) ) ) ) ) |
% 0.56/1.07 ( LE @ ( f @ B_2 ) @ 0 ))).
% 0.56/1.07 thf(zip_derived_cl15, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0)))) |
% 0.56/1.07 (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))) | (LE @ (f @ X0) @ 0)))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_63])).
% 0.56/1.07 thf(zip_derived_cl54, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0))
% 0.56/1.07 | (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 0.56/1.07 | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl15])).
% 0.56/1.07 thf(zip_derived_cl425, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl424, zip_derived_cl376])).
% 0.56/1.07 thf(zip_derived_cl429, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))) | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl425])).
% 0.56/1.07 thf(zip_derived_cl453, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ 0)
% 0.56/1.07 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl452, zip_derived_cl429])).
% 0.56/1.07 thf(clause_128, axiom,
% 0.56/1.07 (( ~( LE @ ( f @ ( suc @ ( suc @ B_2 ) ) ) @ ( s @ 0 ) ) ) |
% 0.56/1.07 ( E @ 0 @ ( f @ ( suc @ ( suc @ B_2 ) ) ) ) | ( LE @ ( f @ B_2 ) @ 0 ))).
% 0.56/1.07 thf(zip_derived_cl27, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (((((~) @ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0)))) |
% 0.56/1.07 (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0)))),
% 0.56/1.07 inference('cnf', [status(esa)], [clause_128])).
% 0.56/1.07 thf(zip_derived_cl52, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 0.56/1.07 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.56/1.07 | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl27])).
% 0.56/1.07 thf(zip_derived_cl425, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl424, zip_derived_cl376])).
% 0.56/1.07 thf(zip_derived_cl428, plain,
% 0.56/1.07 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl425])).
% 0.56/1.07 thf(zip_derived_cl454, plain,
% 0.56/1.07 (![X0 : $i]: (~ (E @ (f @ X0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl453, zip_derived_cl428])).
% 0.56/1.07 thf(zip_derived_cl48, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 (~ (E @ 0 @ (f @ X0))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.56/1.07 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl8])).
% 0.56/1.07 thf(zip_derived_cl455, plain,
% 0.56/1.07 (![X0 : $i]:
% 0.56/1.07 ( (LE @ (f @ X0) @ 0)
% 0.56/1.07 | ~ (E @ 0 @ (f @ X0))
% 0.56/1.07 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 0.56/1.07 inference('s_sup+', [status(thm)], [zip_derived_cl454, zip_derived_cl48])).
% 0.56/1.07 thf(zip_derived_cl426, plain,
% 0.56/1.07 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl425])).
% 0.56/1.07 thf(zip_derived_cl461, plain,
% 0.56/1.07 (![X0 : $i]: (~ (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl455, zip_derived_cl426])).
% 0.56/1.07 thf(zip_derived_cl427, plain,
% 0.56/1.07 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl425])).
% 0.56/1.07 thf(zip_derived_cl462, plain, (![X0 : $i]: (LE @ (f @ X0) @ 0)),
% 0.56/1.07 inference('clc', [status(thm)], [zip_derived_cl461, zip_derived_cl427])).
% 0.56/1.07 thf(zip_derived_cl463, plain, ($false),
% 0.56/1.07 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl462])).
% 0.56/1.07
% 0.56/1.07 % SZS output end Refutation
% 0.56/1.07
% 0.56/1.07
% 0.56/1.07 % Terminating...
% 0.59/1.16 % Runner terminated.
% 0.59/1.17 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------