TSTP Solution File: SYO687-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO687-1 : 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.3imMHXR9Fa true
% Computer : n028.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 05:52:34 EDT 2023
% Result : Unsatisfiable 7.90s 1.77s
% Output : Refutation 7.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO687-1 : TPTP v8.1.2. Released v7.3.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.3imMHXR9Fa true
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 07:22:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.34 % Number of cores: 8
% 0.19/0.35 % Python version: Python 3.6.8
% 0.19/0.35 % Running in FO mode
% 0.19/0.65 % Total configuration time : 435
% 0.19/0.65 % Estimated wc time : 1092
% 0.19/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.19/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.19/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.19/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.19/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.19/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.19/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.19/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.19/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 0.19/0.81 % /export/starexec/sandbox2/solver/bin/fo/fo17_bce.sh running for 50s
% 0.19/0.81 % /export/starexec/sandbox2/solver/bin/fo/fo8.sh running for 50s
% 7.90/1.77 % Solved by fo/fo5.sh.
% 7.90/1.77 % done 696 iterations in 0.922s
% 7.90/1.77 % SZS status Unsatisfiable for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 7.90/1.77 % SZS output start Refutation
% 7.90/1.77 thf(f_type, type, f: $i > $i).
% 7.90/1.77 thf(0_type, type, 0: $i).
% 7.90/1.77 thf(s_type, type, s: $i > $i).
% 7.90/1.77 thf(LE_type, type, LE: $i > $i > $o).
% 7.90/1.77 thf(z_type, type, z: $i).
% 7.90/1.77 thf(E_type, type, E: $i > $i > $o).
% 7.90/1.77 thf(suc_type, type, suc: $i > $i).
% 7.90/1.77 thf(iLEQ_type, type, iLEQ: $i > $i > $o).
% 7.90/1.77 thf(clause_1188, axiom, (~( LE @ ( f @ z ) @ 0 ))).
% 7.90/1.77 thf(zip_derived_cl67, plain, (~ (LE @ (f @ z) @ 0)),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1188])).
% 7.90/1.77 thf(clause_1860, axiom,
% 7.90/1.77 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ B_23 ) ) ) ) @ ( s @ 0 ) ) ) |
% 7.90/1.77 ( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_23 ) ) ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_23 ) @ 0 ))).
% 7.90/1.77 thf(zip_derived_cl89, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0))
% 7.90/1.77 | (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1860])).
% 7.90/1.77 thf(clause_1248, axiom,
% 7.90/1.77 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ B_20 ) ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 7.90/1.77 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_20 ) ) ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_20 ) @ ( s @ 0 ) ))).
% 7.90/1.77 thf(zip_derived_cl108, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ 0)))
% 7.90/1.77 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1248])).
% 7.90/1.77 thf(clause_953, axiom,
% 7.90/1.77 (( ~( LE @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ B_16 ) ) ) ) @
% 7.90/1.77 ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 7.90/1.77 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_16 ) ) ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_16 ) @ ( s @ ( s @ 0 ) ) ))).
% 7.90/1.77 thf(zip_derived_cl57, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_953])).
% 7.90/1.77 thf(clause_1301, axiom,
% 7.90/1.77 (( ~( LE @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ B_11 ) ) ) ) @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 7.90/1.77 ( E @
% 7.90/1.77 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_11 ) ) ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_11 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl107, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1301])).
% 7.90/1.77 thf(clause_2369, axiom,
% 7.90/1.77 (( ~( LE @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) ) |
% 7.90/1.77 ( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_5 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl48, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @
% 7.90/1.77 (s @ (s @ (s @ (s @ (s @ 0))))))
% 7.90/1.77 | (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2369])).
% 7.90/1.77 thf(clause_683, axiom,
% 7.90/1.77 (LE @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl17, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_683])).
% 7.90/1.77 thf(zip_derived_cl167, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl17])).
% 7.90/1.77 thf(clause_2053, axiom,
% 7.90/1.77 (( ~( LE @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) ) @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) ) |
% 7.90/1.77 ( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_5 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl14, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @
% 7.90/1.77 (s @ (s @ (s @ (s @ (s @ 0))))))
% 7.90/1.77 | (E @ (s @ (s @ (s @ (s @ 0)))) @
% 7.90/1.77 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2053])).
% 7.90/1.77 thf(zip_derived_cl17, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_683])).
% 7.90/1.77 thf(zip_derived_cl191, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @
% 7.90/1.77 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl17])).
% 7.90/1.77 thf(clause_1769, axiom,
% 7.90/1.77 (( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 7.90/1.77 thf(zip_derived_cl34, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @
% 7.90/1.77 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1769])).
% 7.90/1.77 thf(zip_derived_cl427, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl191, zip_derived_cl34])).
% 7.90/1.77 thf(zip_derived_cl1081, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl167, zip_derived_cl427])).
% 7.90/1.77 thf(zip_derived_cl1083, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl1081])).
% 7.90/1.77 thf(zip_derived_cl167, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl191, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @
% 7.90/1.77 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl17])).
% 7.90/1.77 thf(clause_2443, axiom,
% 7.90/1.77 (( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_6 ) ) ) |
% 7.90/1.77 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_6 ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_6 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ B_6 ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl35, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @
% 7.90/1.77 (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @
% 7.90/1.77 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2443])).
% 7.90/1.77 thf(zip_derived_cl646, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @
% 7.90/1.77 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl35])).
% 7.90/1.77 thf(zip_derived_cl647, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @
% 7.90/1.77 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl646])).
% 7.90/1.77 thf(zip_derived_cl710, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl191, zip_derived_cl647])).
% 7.90/1.77 thf(zip_derived_cl714, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl167, zip_derived_cl710])).
% 7.90/1.77 thf(zip_derived_cl716, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl714])).
% 7.90/1.77 thf(clause_475, axiom,
% 7.90/1.77 (( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_6 ) ) ) |
% 7.90/1.77 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_6 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_6 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 7.90/1.77 ( E @ ( f @ B_6 ) @ ( f @ ( suc @ B_6 ) ) ))).
% 7.90/1.77 thf(zip_derived_cl52, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 7.90/1.77 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_475])).
% 7.90/1.77 thf(zip_derived_cl309, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl52])).
% 7.90/1.77 thf(zip_derived_cl310, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl309])).
% 7.90/1.77 thf(clause_1522, axiom,
% 7.90/1.77 (( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 7.90/1.77 thf(zip_derived_cl21, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1522])).
% 7.90/1.77 thf(zip_derived_cl317, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl310, zip_derived_cl21])).
% 7.90/1.77 thf(zip_derived_cl717, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl716, zip_derived_cl317])).
% 7.90/1.77 thf(clause_1143, axiom,
% 7.90/1.77 (( ~( LE @
% 7.90/1.77 ( f @ ( suc @ ( suc @ B_5 ) ) ) @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) ) |
% 7.90/1.77 ( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ B_5 ) ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_5 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl33, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ (s @ (s @ 0))))))
% 7.90/1.77 | (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1143])).
% 7.90/1.77 thf(zip_derived_cl17, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_683])).
% 7.90/1.77 thf(zip_derived_cl148, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl718, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl717, zip_derived_cl148])).
% 7.90/1.77 thf(clause_1366, axiom,
% 7.90/1.77 (( ~( LE @ ( f @ B_5 ) @ ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) ) |
% 7.90/1.77 ( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_5 ) ) |
% 7.90/1.77 ( LE @ ( f @ B_5 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl101, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))
% 7.90/1.77 | (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1366])).
% 7.90/1.77 thf(zip_derived_cl17, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_683])).
% 7.90/1.77 thf(zip_derived_cl129, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl719, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl718, zip_derived_cl129])).
% 7.90/1.77 thf(clause_2214, axiom,
% 7.90/1.77 (( ~( LE @
% 7.90/1.77 ( f @ ( suc @ B_5 ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) ) |
% 7.90/1.77 ( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_5 ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_5 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl88, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ (s @ (s @ 0))))))
% 7.90/1.77 | (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2214])).
% 7.90/1.77 thf(zip_derived_cl17, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_683])).
% 7.90/1.77 thf(zip_derived_cl132, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl88, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl720, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl719, zip_derived_cl132])).
% 7.90/1.77 thf(zip_derived_cl148, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl17])).
% 7.90/1.77 thf(clause_1682, axiom,
% 7.90/1.77 (( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_6 ) ) ) |
% 7.90/1.77 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_6 ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_6 ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ B_6 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl29, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1682])).
% 7.90/1.77 thf(zip_derived_cl561, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl29])).
% 7.90/1.77 thf(zip_derived_cl562, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl561])).
% 7.90/1.77 thf(clause_1081, axiom,
% 7.90/1.77 (( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 7.90/1.77 thf(zip_derived_cl74, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1081])).
% 7.90/1.77 thf(zip_derived_cl21, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1522])).
% 7.90/1.77 thf(zip_derived_cl202, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl74, zip_derived_cl21])).
% 7.90/1.77 thf(zip_derived_cl570, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl562, zip_derived_cl202])).
% 7.90/1.77 thf(zip_derived_cl317, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl310, zip_derived_cl21])).
% 7.90/1.77 thf(zip_derived_cl571, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl570, zip_derived_cl317])).
% 7.90/1.77 thf(zip_derived_cl573, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl148, zip_derived_cl571])).
% 7.90/1.77 thf(zip_derived_cl129, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl577, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl573, zip_derived_cl129])).
% 7.90/1.77 thf(zip_derived_cl132, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl88, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl578, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl577, zip_derived_cl132])).
% 7.90/1.77 thf(zip_derived_cl721, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl720, zip_derived_cl578])).
% 7.90/1.77 thf(zip_derived_cl578, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl577, zip_derived_cl132])).
% 7.90/1.77 thf(zip_derived_cl167, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl17])).
% 7.90/1.77 thf(clause_1841, axiom,
% 7.90/1.77 (( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_6 ) ) ) |
% 7.90/1.77 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_6 ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_6 ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ B_6 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl0, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1841])).
% 7.90/1.77 thf(zip_derived_cl127, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl0])).
% 7.90/1.77 thf(zip_derived_cl128, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl127])).
% 7.90/1.77 thf(zip_derived_cl171, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl167, zip_derived_cl128])).
% 7.90/1.77 thf(zip_derived_cl129, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl185, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl171, zip_derived_cl129])).
% 7.90/1.77 thf(zip_derived_cl148, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl186, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl185, zip_derived_cl148])).
% 7.90/1.77 thf(zip_derived_cl132, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl88, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl187, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl186, zip_derived_cl132])).
% 7.90/1.77 thf(zip_derived_cl581, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl578, zip_derived_cl187])).
% 7.90/1.77 thf(zip_derived_cl585, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl581])).
% 7.90/1.77 thf(zip_derived_cl167, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl17])).
% 7.90/1.77 thf(clause_1981, axiom,
% 7.90/1.77 (( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 7.90/1.77 thf(zip_derived_cl119, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1981])).
% 7.90/1.77 thf(zip_derived_cl202, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl74, zip_derived_cl21])).
% 7.90/1.77 thf(zip_derived_cl385, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl119, zip_derived_cl202])).
% 7.90/1.77 thf(zip_derived_cl317, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl310, zip_derived_cl21])).
% 7.90/1.77 thf(zip_derived_cl386, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl385, zip_derived_cl317])).
% 7.90/1.77 thf(zip_derived_cl390, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl167, zip_derived_cl386])).
% 7.90/1.77 thf(zip_derived_cl129, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl401, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl390, zip_derived_cl129])).
% 7.90/1.77 thf(zip_derived_cl148, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl402, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl401, zip_derived_cl148])).
% 7.90/1.77 thf(zip_derived_cl132, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl88, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl403, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl402, zip_derived_cl132])).
% 7.90/1.77 thf(zip_derived_cl587, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl585, zip_derived_cl403])).
% 7.90/1.77 thf(zip_derived_cl132, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl88, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl317, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl310, zip_derived_cl21])).
% 7.90/1.77 thf(zip_derived_cl320, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl317])).
% 7.90/1.77 thf(zip_derived_cl129, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl323, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl320, zip_derived_cl129])).
% 7.90/1.77 thf(zip_derived_cl588, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl587, zip_derived_cl323])).
% 7.90/1.77 thf(zip_derived_cl722, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl721, zip_derived_cl588])).
% 7.90/1.77 thf(zip_derived_cl1084, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1083, zip_derived_cl722])).
% 7.90/1.77 thf(zip_derived_cl588, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl587, zip_derived_cl323])).
% 7.90/1.77 thf(zip_derived_cl1085, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1084, zip_derived_cl588])).
% 7.90/1.77 thf(zip_derived_cl129, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl1086, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1085, zip_derived_cl129])).
% 7.90/1.77 thf(zip_derived_cl148, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl1087, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1086, zip_derived_cl148])).
% 7.90/1.77 thf(zip_derived_cl323, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl320, zip_derived_cl129])).
% 7.90/1.77 thf(zip_derived_cl1088, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1087, zip_derived_cl323])).
% 7.90/1.77 thf(zip_derived_cl578, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl577, zip_derived_cl132])).
% 7.90/1.77 thf(zip_derived_cl1089, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1088, zip_derived_cl578])).
% 7.90/1.77 thf(zip_derived_cl132, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl88, zip_derived_cl17])).
% 7.90/1.77 thf(zip_derived_cl1090, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1089, zip_derived_cl132])).
% 7.90/1.77 thf(zip_derived_cl1094, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl1090])).
% 7.90/1.77 thf(clause_1067, axiom,
% 7.90/1.77 (( ~( LE @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_11 ) ) ) ) ) @
% 7.90/1.77 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 7.90/1.77 ( E @
% 7.90/1.77 ( s @ ( s @ ( s @ 0 ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_11 ) ) ) ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_11 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl113, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @
% 7.90/1.77 (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (E @ (s @ (s @ (s @ 0))) @
% 7.90/1.77 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1067])).
% 7.90/1.77 thf(zip_derived_cl1090, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1089, zip_derived_cl132])).
% 7.90/1.77 thf(zip_derived_cl1095, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl113, zip_derived_cl1090])).
% 7.90/1.77 thf(clause_1710, axiom,
% 7.90/1.77 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ 0 ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 7.90/1.77 thf(zip_derived_cl36, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @
% 7.90/1.77 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1710])).
% 7.90/1.77 thf(zip_derived_cl1158, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1095, zip_derived_cl36])).
% 7.90/1.77 thf(zip_derived_cl1446, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1094, zip_derived_cl1158])).
% 7.90/1.77 thf(zip_derived_cl1449, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl1446])).
% 7.90/1.77 thf(zip_derived_cl1094, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl1090])).
% 7.90/1.77 thf(zip_derived_cl1095, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl113, zip_derived_cl1090])).
% 7.90/1.77 thf(clause_2273, axiom,
% 7.90/1.77 (( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_12 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_12 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_12 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_12 ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ 0 ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ B_12 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_12 ) @ ( f @ ( suc @ ( suc @ B_12 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ 0 ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_12 ) ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ 0 ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_12 ) @ ( f @ ( suc @ B_12 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_12 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_12 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl6, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @
% 7.90/1.77 (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @
% 7.90/1.77 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2273])).
% 7.90/1.77 thf(zip_derived_cl260, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @
% 7.90/1.77 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 7.90/1.77 thf(zip_derived_cl261, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @
% 7.90/1.77 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl260])).
% 7.90/1.77 thf(zip_derived_cl1159, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1095, zip_derived_cl261])).
% 7.90/1.77 thf(zip_derived_cl1282, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1094, zip_derived_cl1159])).
% 7.90/1.77 thf(zip_derived_cl1285, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl1282])).
% 7.90/1.77 thf(clause_623, axiom,
% 7.90/1.77 (( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_12 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_12 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_12 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 7.90/1.77 ( E @ ( f @ B_12 ) @ ( f @ ( suc @ B_12 ) ) ))).
% 7.90/1.77 thf(zip_derived_cl123, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_623])).
% 7.90/1.77 thf(zip_derived_cl244, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl123])).
% 7.90/1.77 thf(zip_derived_cl245, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl244])).
% 7.90/1.77 thf(clause_380, axiom,
% 7.90/1.77 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 7.90/1.77 thf(zip_derived_cl31, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_380])).
% 7.90/1.77 thf(zip_derived_cl262, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl245, zip_derived_cl31])).
% 7.90/1.77 thf(zip_derived_cl1286, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1285, zip_derived_cl262])).
% 7.90/1.77 thf(clause_1185, axiom,
% 7.90/1.77 (( ~( LE @ ( f @ B_11 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 7.90/1.77 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_11 ) ) |
% 7.90/1.77 ( LE @ ( f @ B_11 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl106, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1185])).
% 7.90/1.77 thf(zip_derived_cl1090, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1089, zip_derived_cl132])).
% 7.90/1.77 thf(zip_derived_cl1093, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl106, zip_derived_cl1090])).
% 7.90/1.77 thf(zip_derived_cl1287, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1286, zip_derived_cl1093])).
% 7.90/1.77 thf(clause_682, axiom,
% 7.90/1.77 (( ~( LE @
% 7.90/1.77 ( f @ ( suc @ ( suc @ B_11 ) ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 7.90/1.77 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_11 ) ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_11 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl2, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_682])).
% 7.90/1.77 thf(zip_derived_cl1090, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1089, zip_derived_cl132])).
% 7.90/1.77 thf(zip_derived_cl1091, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl1090])).
% 7.90/1.77 thf(zip_derived_cl1288, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1287, zip_derived_cl1091])).
% 7.90/1.77 thf(zip_derived_cl1091, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl1090])).
% 7.90/1.77 thf(clause_1232, axiom,
% 7.90/1.77 (( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_12 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_12 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_12 ) @ ( f @ ( suc @ B_12 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_12 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_12 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ B_12 ) @ ( f @ ( suc @ ( suc @ B_12 ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl72, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1)))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1232])).
% 7.90/1.77 thf(zip_derived_cl468, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl72])).
% 7.90/1.77 thf(zip_derived_cl469, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl468])).
% 7.90/1.77 thf(clause_222, axiom,
% 7.90/1.77 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 7.90/1.77 thf(zip_derived_cl79, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_222])).
% 7.90/1.77 thf(zip_derived_cl31, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_380])).
% 7.90/1.77 thf(zip_derived_cl196, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl79, zip_derived_cl31])).
% 7.90/1.77 thf(zip_derived_cl476, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl469, zip_derived_cl196])).
% 7.90/1.77 thf(zip_derived_cl262, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl245, zip_derived_cl31])).
% 7.90/1.77 thf(zip_derived_cl477, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl476, zip_derived_cl262])).
% 7.90/1.77 thf(zip_derived_cl1130, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1091, zip_derived_cl477])).
% 7.90/1.77 thf(clause_1340, axiom,
% 7.90/1.77 (( ~( LE @ ( f @ ( suc @ B_11 ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 7.90/1.77 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_11 ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_11 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl105, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ (s @ 0)))))
% 7.90/1.77 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1340])).
% 7.90/1.77 thf(zip_derived_cl1090, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1089, zip_derived_cl132])).
% 7.90/1.77 thf(zip_derived_cl1092, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl105, zip_derived_cl1090])).
% 7.90/1.77 thf(zip_derived_cl1169, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1130, zip_derived_cl1092])).
% 7.90/1.77 thf(zip_derived_cl1093, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl106, zip_derived_cl1090])).
% 7.90/1.77 thf(zip_derived_cl1170, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1169, zip_derived_cl1093])).
% 7.90/1.77 thf(zip_derived_cl1289, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1288, zip_derived_cl1170])).
% 7.90/1.77 thf(zip_derived_cl1092, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl105, zip_derived_cl1090])).
% 7.90/1.77 thf(zip_derived_cl1290, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1289, zip_derived_cl1092])).
% 7.90/1.77 thf(zip_derived_cl1094, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl1090])).
% 7.90/1.77 thf(clause_818, axiom,
% 7.90/1.77 (( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_12 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_12 ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ 0 ) ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ B_12 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_12 ) @ ( f @ ( suc @ ( suc @ B_12 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_12 ) @ ( f @ ( suc @ B_12 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_12 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_12 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ B_12 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_12 ) ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl60, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_818])).
% 7.90/1.77 thf(zip_derived_cl732, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl60])).
% 7.90/1.77 thf(zip_derived_cl733, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl732])).
% 7.90/1.77 thf(clause_971, axiom,
% 7.90/1.77 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 7.90/1.77 thf(zip_derived_cl97, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_971])).
% 7.90/1.77 thf(zip_derived_cl196, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl79, zip_derived_cl31])).
% 7.90/1.77 thf(zip_derived_cl353, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl97, zip_derived_cl196])).
% 7.90/1.77 thf(zip_derived_cl262, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl245, zip_derived_cl31])).
% 7.90/1.77 thf(zip_derived_cl354, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl353, zip_derived_cl262])).
% 7.90/1.77 thf(zip_derived_cl760, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl733, zip_derived_cl354])).
% 7.90/1.77 thf(zip_derived_cl262, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl245, zip_derived_cl31])).
% 7.90/1.77 thf(zip_derived_cl761, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl760, zip_derived_cl262])).
% 7.90/1.77 thf(zip_derived_cl477, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl476, zip_derived_cl262])).
% 7.90/1.77 thf(zip_derived_cl762, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl761, zip_derived_cl477])).
% 7.90/1.77 thf(zip_derived_cl1144, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1094, zip_derived_cl762])).
% 7.90/1.77 thf(zip_derived_cl1093, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl106, zip_derived_cl1090])).
% 7.90/1.77 thf(zip_derived_cl1201, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1144, zip_derived_cl1093])).
% 7.90/1.77 thf(zip_derived_cl1091, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl1090])).
% 7.90/1.77 thf(zip_derived_cl1202, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1201, zip_derived_cl1091])).
% 7.90/1.77 thf(zip_derived_cl1092, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl105, zip_derived_cl1090])).
% 7.90/1.77 thf(zip_derived_cl1203, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1202, zip_derived_cl1092])).
% 7.90/1.77 thf(zip_derived_cl1291, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1290, zip_derived_cl1203])).
% 7.90/1.77 thf(zip_derived_cl1450, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1449, zip_derived_cl1291])).
% 7.90/1.77 thf(zip_derived_cl477, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl476, zip_derived_cl262])).
% 7.90/1.77 thf(zip_derived_cl1451, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1450, zip_derived_cl477])).
% 7.90/1.77 thf(zip_derived_cl262, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl245, zip_derived_cl31])).
% 7.90/1.77 thf(zip_derived_cl1452, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1451, zip_derived_cl262])).
% 7.90/1.77 thf(zip_derived_cl1092, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl105, zip_derived_cl1090])).
% 7.90/1.77 thf(zip_derived_cl1453, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1452, zip_derived_cl1092])).
% 7.90/1.77 thf(zip_derived_cl1091, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl1090])).
% 7.90/1.77 thf(zip_derived_cl1454, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1453, zip_derived_cl1091])).
% 7.90/1.77 thf(zip_derived_cl1093, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl106, zip_derived_cl1090])).
% 7.90/1.77 thf(zip_derived_cl1455, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1454, zip_derived_cl1093])).
% 7.90/1.77 thf(zip_derived_cl1203, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1202, zip_derived_cl1092])).
% 7.90/1.77 thf(zip_derived_cl1456, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1455, zip_derived_cl1203])).
% 7.90/1.77 thf(zip_derived_cl1459, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl57, zip_derived_cl1456])).
% 7.90/1.77 thf(clause_1556, axiom,
% 7.90/1.77 (( ~( LE @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_16 ) ) ) ) ) @
% 7.90/1.77 ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 7.90/1.77 ( E @
% 7.90/1.77 ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_16 ) ) ) ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_16 ) @ ( s @ ( s @ 0 ) ) ))).
% 7.90/1.77 thf(zip_derived_cl37, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @
% 7.90/1.77 (s @ (s @ (s @ 0))))
% 7.90/1.77 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1556])).
% 7.90/1.77 thf(zip_derived_cl1456, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1455, zip_derived_cl1203])).
% 7.90/1.77 thf(zip_derived_cl1458, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl1456])).
% 7.90/1.77 thf(clause_1424, axiom,
% 7.90/1.77 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ 0 ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 7.90/1.77 thf(zip_derived_cl25, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1424])).
% 7.90/1.77 thf(zip_derived_cl1498, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1458, zip_derived_cl25])).
% 7.90/1.77 thf(zip_derived_cl1642, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1459, zip_derived_cl1498])).
% 7.90/1.77 thf(zip_derived_cl1645, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl1642])).
% 7.90/1.77 thf(zip_derived_cl1459, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl57, zip_derived_cl1456])).
% 7.90/1.77 thf(zip_derived_cl1458, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl1456])).
% 7.90/1.77 thf(clause_920, axiom,
% 7.90/1.77 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_17 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ 0 ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_17 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_17 ) ) ) |
% 7.90/1.77 ( ~( E @
% 7.90/1.77 ( s @ ( s @ 0 ) ) @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_17 ) ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_17 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl75, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_920])).
% 7.90/1.77 thf(zip_derived_cl734, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl75])).
% 7.90/1.77 thf(zip_derived_cl735, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl734])).
% 7.90/1.77 thf(zip_derived_cl1499, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1458, zip_derived_cl735])).
% 7.90/1.77 thf(zip_derived_cl1580, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1459, zip_derived_cl1499])).
% 7.90/1.77 thf(zip_derived_cl1583, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl1580])).
% 7.90/1.77 thf(clause_1204, axiom,
% 7.90/1.77 (( ~( LE @ ( f @ ( suc @ ( suc @ B_16 ) ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 7.90/1.77 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_16 ) ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_16 ) @ ( s @ ( s @ 0 ) ) ))).
% 7.90/1.77 thf(zip_derived_cl110, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1204])).
% 7.90/1.77 thf(zip_derived_cl1456, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1455, zip_derived_cl1203])).
% 7.90/1.77 thf(zip_derived_cl1460, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl110, zip_derived_cl1456])).
% 7.90/1.77 thf(zip_derived_cl1584, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1583, zip_derived_cl1460])).
% 7.90/1.77 thf(clause_1064, axiom,
% 7.90/1.77 (( ~( LE @ ( f @ ( suc @ B_16 ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 7.90/1.77 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_16 ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_16 ) @ ( s @ ( s @ 0 ) ) ))).
% 7.90/1.77 thf(zip_derived_cl124, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1064])).
% 7.90/1.77 thf(zip_derived_cl1456, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1455, zip_derived_cl1203])).
% 7.90/1.77 thf(zip_derived_cl1461, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl124, zip_derived_cl1456])).
% 7.90/1.77 thf(zip_derived_cl1585, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1584, zip_derived_cl1461])).
% 7.90/1.77 thf(clause_1473, axiom,
% 7.90/1.77 (( ~( LE @ ( f @ B_16 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 7.90/1.77 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_16 ) ) |
% 7.90/1.77 ( LE @ ( f @ B_16 ) @ ( s @ ( s @ 0 ) ) ))).
% 7.90/1.77 thf(zip_derived_cl8, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 7.90/1.77 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1473])).
% 7.90/1.77 thf(zip_derived_cl1456, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1455, zip_derived_cl1203])).
% 7.90/1.77 thf(zip_derived_cl1457, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl1456])).
% 7.90/1.77 thf(zip_derived_cl1586, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1585, zip_derived_cl1457])).
% 7.90/1.77 thf(zip_derived_cl1460, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl110, zip_derived_cl1456])).
% 7.90/1.77 thf(clause_2159, axiom,
% 7.90/1.77 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_17 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 7.90/1.77 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_17 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ B_17 ) @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl92, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2159])).
% 7.90/1.77 thf(zip_derived_cl428, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl92])).
% 7.90/1.77 thf(zip_derived_cl429, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl428])).
% 7.90/1.77 thf(clause_2489, axiom,
% 7.90/1.77 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 7.90/1.77 thf(zip_derived_cl116, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2489])).
% 7.90/1.77 thf(clause_1701, axiom,
% 7.90/1.77 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 7.90/1.77 thf(zip_derived_cl27, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1701])).
% 7.90/1.77 thf(zip_derived_cl190, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl116, zip_derived_cl27])).
% 7.90/1.77 thf(zip_derived_cl433, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl429, zip_derived_cl190])).
% 7.90/1.77 thf(clause_1405, axiom,
% 7.90/1.77 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_17 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_17 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 7.90/1.77 ( E @ ( f @ B_17 ) @ ( f @ ( suc @ B_17 ) ) ))).
% 7.90/1.77 thf(zip_derived_cl28, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 7.90/1.77 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1405])).
% 7.90/1.77 thf(zip_derived_cl200, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl28])).
% 7.90/1.77 thf(zip_derived_cl201, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl200])).
% 7.90/1.77 thf(zip_derived_cl27, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1701])).
% 7.90/1.77 thf(zip_derived_cl214, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl201, zip_derived_cl27])).
% 7.90/1.77 thf(zip_derived_cl434, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl433, zip_derived_cl214])).
% 7.90/1.77 thf(zip_derived_cl1483, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1460, zip_derived_cl434])).
% 7.90/1.77 thf(zip_derived_cl1457, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl1456])).
% 7.90/1.77 thf(zip_derived_cl1502, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1483, zip_derived_cl1457])).
% 7.90/1.77 thf(zip_derived_cl1461, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl124, zip_derived_cl1456])).
% 7.90/1.77 thf(zip_derived_cl1503, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1502, zip_derived_cl1461])).
% 7.90/1.77 thf(zip_derived_cl1587, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1586, zip_derived_cl1503])).
% 7.90/1.77 thf(zip_derived_cl1459, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl57, zip_derived_cl1456])).
% 7.90/1.77 thf(clause_351, axiom,
% 7.90/1.77 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_17 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 7.90/1.77 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_17 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_17 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ B_17 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_17 ) ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl73, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_351])).
% 7.90/1.77 thf(zip_derived_cl689, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl73])).
% 7.90/1.77 thf(zip_derived_cl690, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl689])).
% 7.90/1.77 thf(zip_derived_cl434, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl433, zip_derived_cl214])).
% 7.90/1.77 thf(zip_derived_cl703, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl690, zip_derived_cl434])).
% 7.90/1.77 thf(zip_derived_cl214, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl201, zip_derived_cl27])).
% 7.90/1.77 thf(zip_derived_cl704, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl703, zip_derived_cl214])).
% 7.90/1.77 thf(clause_2054, axiom,
% 7.90/1.77 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 7.90/1.77 thf(zip_derived_cl11, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2054])).
% 7.90/1.77 thf(zip_derived_cl190, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl116, zip_derived_cl27])).
% 7.90/1.77 thf(zip_derived_cl311, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl11, zip_derived_cl190])).
% 7.90/1.77 thf(zip_derived_cl214, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl201, zip_derived_cl27])).
% 7.90/1.77 thf(zip_derived_cl312, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl311, zip_derived_cl214])).
% 7.90/1.77 thf(zip_derived_cl705, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl704, zip_derived_cl312])).
% 7.90/1.77 thf(zip_derived_cl1489, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1459, zip_derived_cl705])).
% 7.90/1.77 thf(zip_derived_cl1461, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl124, zip_derived_cl1456])).
% 7.90/1.77 thf(zip_derived_cl1525, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1489, zip_derived_cl1461])).
% 7.90/1.77 thf(zip_derived_cl1460, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl110, zip_derived_cl1456])).
% 7.90/1.77 thf(zip_derived_cl1526, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1525, zip_derived_cl1460])).
% 7.90/1.77 thf(zip_derived_cl1457, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl1456])).
% 7.90/1.77 thf(zip_derived_cl1527, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1526, zip_derived_cl1457])).
% 7.90/1.77 thf(zip_derived_cl1588, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1587, zip_derived_cl1527])).
% 7.90/1.77 thf(zip_derived_cl1461, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl124, zip_derived_cl1456])).
% 7.90/1.77 thf(zip_derived_cl214, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl201, zip_derived_cl27])).
% 7.90/1.77 thf(zip_derived_cl1469, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1461, zip_derived_cl214])).
% 7.90/1.77 thf(zip_derived_cl1457, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl1456])).
% 7.90/1.77 thf(zip_derived_cl1476, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1469, zip_derived_cl1457])).
% 7.90/1.77 thf(zip_derived_cl1589, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1588, zip_derived_cl1476])).
% 7.90/1.77 thf(zip_derived_cl1646, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1645, zip_derived_cl1589])).
% 7.90/1.77 thf(zip_derived_cl1461, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl124, zip_derived_cl1456])).
% 7.90/1.77 thf(zip_derived_cl1647, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1646, zip_derived_cl1461])).
% 7.90/1.77 thf(zip_derived_cl1457, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl1456])).
% 7.90/1.77 thf(zip_derived_cl1648, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1647, zip_derived_cl1457])).
% 7.90/1.77 thf(zip_derived_cl1503, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1502, zip_derived_cl1461])).
% 7.90/1.77 thf(zip_derived_cl1649, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1648, zip_derived_cl1503])).
% 7.90/1.77 thf(zip_derived_cl1527, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1526, zip_derived_cl1457])).
% 7.90/1.77 thf(zip_derived_cl1650, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1649, zip_derived_cl1527])).
% 7.90/1.77 thf(zip_derived_cl1460, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl110, zip_derived_cl1456])).
% 7.90/1.77 thf(zip_derived_cl1651, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1650, zip_derived_cl1460])).
% 7.90/1.77 thf(zip_derived_cl1476, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1469, zip_derived_cl1457])).
% 7.90/1.77 thf(zip_derived_cl1652, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1651, zip_derived_cl1476])).
% 7.90/1.77 thf(zip_derived_cl1657, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl108, zip_derived_cl1652])).
% 7.90/1.77 thf(clause_2498, axiom,
% 7.90/1.77 (( ~( LE @
% 7.90/1.77 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_20 ) ) ) ) ) @
% 7.90/1.77 ( s @ ( s @ 0 ) ) ) ) |
% 7.90/1.77 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_20 ) ) ) ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_20 ) @ ( s @ 0 ) ))).
% 7.90/1.77 thf(zip_derived_cl54, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ (s @ 0)))
% 7.90/1.77 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2498])).
% 7.90/1.77 thf(zip_derived_cl1652, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1651, zip_derived_cl1476])).
% 7.90/1.77 thf(zip_derived_cl1654, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl1652])).
% 7.90/1.77 thf(clause_1310, axiom,
% 7.90/1.77 (( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 7.90/1.77 thf(zip_derived_cl38, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1310])).
% 7.90/1.77 thf(zip_derived_cl1686, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1654, zip_derived_cl38])).
% 7.90/1.77 thf(zip_derived_cl1835, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1657, zip_derived_cl1686])).
% 7.90/1.77 thf(zip_derived_cl1838, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl1835])).
% 7.90/1.77 thf(zip_derived_cl1657, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl108, zip_derived_cl1652])).
% 7.90/1.77 thf(zip_derived_cl1654, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl1652])).
% 7.90/1.77 thf(clause_216, axiom,
% 7.90/1.77 (( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_21 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_21 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_21 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ B_21 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_21 ) ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_21 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_21 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_21 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_21 ) @ ( f @ ( suc @ B_21 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_21 ) @ ( f @ ( suc @ ( suc @ B_21 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl102, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X1))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_216])).
% 7.90/1.77 thf(zip_derived_cl691, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl102])).
% 7.90/1.77 thf(zip_derived_cl692, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl691])).
% 7.90/1.77 thf(zip_derived_cl1687, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1654, zip_derived_cl692])).
% 7.90/1.77 thf(zip_derived_cl1766, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1657, zip_derived_cl1687])).
% 7.90/1.77 thf(zip_derived_cl1769, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl1766])).
% 7.90/1.77 thf(clause_2189, axiom,
% 7.90/1.77 (( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_21 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_21 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_21 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ B_21 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_21 ) @ ( f @ ( suc @ B_21 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ B_21 ) @ ( f @ ( suc @ ( suc @ B_21 ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl61, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X1))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1)))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2189])).
% 7.90/1.77 thf(zip_derived_cl392, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl61])).
% 7.90/1.77 thf(zip_derived_cl393, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl392])).
% 7.90/1.77 thf(clause_1403, axiom,
% 7.90/1.77 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 7.90/1.77 thf(zip_derived_cl76, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1403])).
% 7.90/1.77 thf(clause_2348, axiom,
% 7.90/1.77 (( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 7.90/1.77 thf(zip_derived_cl26, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2348])).
% 7.90/1.77 thf(zip_derived_cl155, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl76, zip_derived_cl26])).
% 7.90/1.77 thf(zip_derived_cl399, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl393, zip_derived_cl155])).
% 7.90/1.77 thf(clause_1073, axiom,
% 7.90/1.77 (( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_21 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_21 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ B_21 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) |
% 7.90/1.77 ( E @ ( f @ B_21 ) @ ( f @ ( suc @ B_21 ) ) ))).
% 7.90/1.77 thf(zip_derived_cl55, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X1))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1073])).
% 7.90/1.77 thf(zip_derived_cl188, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl55])).
% 7.90/1.77 thf(zip_derived_cl189, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl188])).
% 7.90/1.77 thf(zip_derived_cl26, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2348])).
% 7.90/1.77 thf(zip_derived_cl213, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl189, zip_derived_cl26])).
% 7.90/1.77 thf(zip_derived_cl400, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl399, zip_derived_cl213])).
% 7.90/1.77 thf(zip_derived_cl1770, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1769, zip_derived_cl400])).
% 7.90/1.77 thf(clause_1408, axiom,
% 7.90/1.77 (( ~( LE @ ( f @ ( suc @ ( suc @ B_20 ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 7.90/1.77 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_20 ) ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_20 ) @ ( s @ 0 ) ))).
% 7.90/1.77 thf(zip_derived_cl94, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 7.90/1.77 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1408])).
% 7.90/1.77 thf(zip_derived_cl1652, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1651, zip_derived_cl1476])).
% 7.90/1.77 thf(zip_derived_cl1656, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl1652])).
% 7.90/1.77 thf(zip_derived_cl1771, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1770, zip_derived_cl1656])).
% 7.90/1.77 thf(clause_2107, axiom,
% 7.90/1.77 (( ~( LE @ ( f @ B_20 ) @ ( s @ ( s @ 0 ) ) ) ) |
% 7.90/1.77 ( E @ ( s @ 0 ) @ ( f @ B_20 ) ) | ( LE @ ( f @ B_20 ) @ ( s @ 0 ) ))).
% 7.90/1.77 thf(zip_derived_cl5, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 7.90/1.77 | (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2107])).
% 7.90/1.77 thf(zip_derived_cl1652, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1651, zip_derived_cl1476])).
% 7.90/1.77 thf(zip_derived_cl1653, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1652])).
% 7.90/1.77 thf(zip_derived_cl1772, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1771, zip_derived_cl1653])).
% 7.90/1.77 thf(zip_derived_cl1657, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl108, zip_derived_cl1652])).
% 7.90/1.77 thf(clause_2472, axiom,
% 7.90/1.77 (( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_21 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_21 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_21 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ B_21 ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_21 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_21 ) @ ( f @ ( suc @ B_21 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_21 ) @ ( f @ ( suc @ ( suc @ B_21 ) ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ B_21 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_21 ) ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl22, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X1))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2472])).
% 7.90/1.77 thf(zip_derived_cl568, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl22])).
% 7.90/1.77 thf(zip_derived_cl569, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl568])).
% 7.90/1.77 thf(clause_1605, axiom,
% 7.90/1.77 (( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 7.90/1.77 thf(zip_derived_cl58, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1605])).
% 7.90/1.77 thf(zip_derived_cl213, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl189, zip_derived_cl26])).
% 7.90/1.77 thf(zip_derived_cl246, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl58, zip_derived_cl213])).
% 7.90/1.77 thf(zip_derived_cl155, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl76, zip_derived_cl26])).
% 7.90/1.77 thf(zip_derived_cl247, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl246, zip_derived_cl155])).
% 7.90/1.77 thf(zip_derived_cl661, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl569, zip_derived_cl247])).
% 7.90/1.77 thf(zip_derived_cl400, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl399, zip_derived_cl213])).
% 7.90/1.77 thf(zip_derived_cl662, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl661, zip_derived_cl400])).
% 7.90/1.77 thf(zip_derived_cl213, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl189, zip_derived_cl26])).
% 7.90/1.77 thf(zip_derived_cl663, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl662, zip_derived_cl213])).
% 7.90/1.77 thf(zip_derived_cl1677, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1657, zip_derived_cl663])).
% 7.90/1.77 thf(zip_derived_cl1656, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl1652])).
% 7.90/1.77 thf(zip_derived_cl1722, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1677, zip_derived_cl1656])).
% 7.90/1.77 thf(zip_derived_cl1653, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1652])).
% 7.90/1.77 thf(zip_derived_cl1723, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1722, zip_derived_cl1653])).
% 7.90/1.77 thf(clause_415, axiom,
% 7.90/1.77 (( ~( LE @ ( f @ ( suc @ B_20 ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 7.90/1.77 ( E @ ( s @ 0 ) @ ( f @ ( suc @ B_20 ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_20 ) @ ( s @ 0 ) ))).
% 7.90/1.77 thf(zip_derived_cl87, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 7.90/1.77 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_415])).
% 7.90/1.77 thf(zip_derived_cl1652, plain,
% 7.90/1.77 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1651, zip_derived_cl1476])).
% 7.90/1.77 thf(zip_derived_cl1655, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl87, zip_derived_cl1652])).
% 7.90/1.77 thf(zip_derived_cl1724, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1723, zip_derived_cl1655])).
% 7.90/1.77 thf(zip_derived_cl1773, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1772, zip_derived_cl1724])).
% 7.90/1.77 thf(zip_derived_cl1655, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl87, zip_derived_cl1652])).
% 7.90/1.77 thf(zip_derived_cl213, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl189, zip_derived_cl26])).
% 7.90/1.77 thf(zip_derived_cl1667, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1655, zip_derived_cl213])).
% 7.90/1.77 thf(zip_derived_cl1653, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1652])).
% 7.90/1.77 thf(zip_derived_cl1688, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1667, zip_derived_cl1653])).
% 7.90/1.77 thf(zip_derived_cl1774, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1773, zip_derived_cl1688])).
% 7.90/1.77 thf(zip_derived_cl1655, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl87, zip_derived_cl1652])).
% 7.90/1.77 thf(zip_derived_cl1775, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1774, zip_derived_cl1655])).
% 7.90/1.77 thf(zip_derived_cl1839, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1838, zip_derived_cl1775])).
% 7.90/1.77 thf(zip_derived_cl213, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl189, zip_derived_cl26])).
% 7.90/1.77 thf(zip_derived_cl1840, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1839, zip_derived_cl213])).
% 7.90/1.77 thf(zip_derived_cl1653, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1652])).
% 7.90/1.77 thf(zip_derived_cl1841, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1840, zip_derived_cl1653])).
% 7.90/1.77 thf(zip_derived_cl1656, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl1652])).
% 7.90/1.77 thf(zip_derived_cl1842, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1841, zip_derived_cl1656])).
% 7.90/1.77 thf(zip_derived_cl1656, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl1652])).
% 7.90/1.77 thf(zip_derived_cl400, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl399, zip_derived_cl213])).
% 7.90/1.77 thf(zip_derived_cl1670, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ X0))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1656, zip_derived_cl400])).
% 7.90/1.77 thf(zip_derived_cl1653, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl1652])).
% 7.90/1.77 thf(zip_derived_cl1696, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1670, zip_derived_cl1653])).
% 7.90/1.77 thf(zip_derived_cl1655, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl87, zip_derived_cl1652])).
% 7.90/1.77 thf(zip_derived_cl1697, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1696, zip_derived_cl1655])).
% 7.90/1.77 thf(zip_derived_cl1843, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1842, zip_derived_cl1697])).
% 7.90/1.77 thf(zip_derived_cl1724, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1723, zip_derived_cl1655])).
% 7.90/1.77 thf(zip_derived_cl1844, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1843, zip_derived_cl1724])).
% 7.90/1.77 thf(zip_derived_cl1655, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl87, zip_derived_cl1652])).
% 7.90/1.77 thf(zip_derived_cl1845, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1844, zip_derived_cl1655])).
% 7.90/1.77 thf(zip_derived_cl1849, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl1845])).
% 7.90/1.77 thf(clause_565, axiom,
% 7.90/1.77 (( ~( E @ ( f @ B_24 ) @ ( f @ ( suc @ B_24 ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_24 ) ) ) ) ) |
% 7.90/1.77 ( ~( iLEQ @ ( suc @ A_5 ) @ ( suc @ B_24 ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ A_5 ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_5 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_24 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_24 ) @ ( f @ ( suc @ ( suc @ B_24 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ B_24 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_24 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_5 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ B_24 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_24 ) ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl56, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X1))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_565])).
% 7.90/1.77 thf(zip_derived_cl621, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl56])).
% 7.90/1.77 thf(zip_derived_cl622, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl621])).
% 7.90/1.77 thf(clause_1659, axiom,
% 7.90/1.77 (( ~( E @ 0 @ ( f @ A_5 ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_5 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_5 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_5 ) @ ( suc @ A_5 ) ))).
% 7.90/1.77 thf(zip_derived_cl10, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1659])).
% 7.90/1.77 thf(clause_1912, axiom,
% 7.90/1.77 (( ~( iLEQ @ ( suc @ A_5 ) @ ( suc @ B_24 ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ A_5 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ B_24 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_24 ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) |
% 7.90/1.77 ( E @ ( f @ B_24 ) @ ( f @ ( suc @ B_24 ) ) ))).
% 7.90/1.77 thf(zip_derived_cl18, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X1))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1912])).
% 7.90/1.77 thf(zip_derived_cl153, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl18])).
% 7.90/1.77 thf(zip_derived_cl154, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl153])).
% 7.90/1.77 thf(clause_231, axiom,
% 7.90/1.77 (( ~( E @ 0 @ ( f @ A_5 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_5 ) @ ( suc @ A_5 ) ))).
% 7.90/1.77 thf(zip_derived_cl30, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_231])).
% 7.90/1.77 thf(zip_derived_cl162, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl154, zip_derived_cl30])).
% 7.90/1.77 thf(zip_derived_cl238, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl10, zip_derived_cl162])).
% 7.90/1.77 thf(clause_2224, axiom,
% 7.90/1.77 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ A_5 ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_5 ) @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_5 ) @ ( suc @ A_5 ) ))).
% 7.90/1.77 thf(zip_derived_cl90, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2224])).
% 7.90/1.77 thf(zip_derived_cl30, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_231])).
% 7.90/1.77 thf(zip_derived_cl147, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl90, zip_derived_cl30])).
% 7.90/1.77 thf(zip_derived_cl239, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl238, zip_derived_cl147])).
% 7.90/1.77 thf(zip_derived_cl651, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl622, zip_derived_cl239])).
% 7.90/1.77 thf(clause_1697, axiom,
% 7.90/1.77 (( ~( E @ ( f @ B_24 ) @ ( f @ ( suc @ B_24 ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_24 ) ) ) ) ) |
% 7.90/1.77 ( ~( iLEQ @ ( suc @ A_5 ) @ ( suc @ B_24 ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ A_5 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ B_24 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_24 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ A_5 ) @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( E @ ( f @ B_24 ) @ ( f @ ( suc @ ( suc @ B_24 ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl62, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X1))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1697])).
% 7.90/1.77 thf(zip_derived_cl355, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl62])).
% 7.90/1.77 thf(zip_derived_cl356, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl355])).
% 7.90/1.77 thf(zip_derived_cl147, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl90, zip_derived_cl30])).
% 7.90/1.77 thf(zip_derived_cl372, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl356, zip_derived_cl147])).
% 7.90/1.77 thf(zip_derived_cl162, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl154, zip_derived_cl30])).
% 7.90/1.77 thf(zip_derived_cl373, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl372, zip_derived_cl162])).
% 7.90/1.77 thf(zip_derived_cl652, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl651, zip_derived_cl373])).
% 7.90/1.77 thf(zip_derived_cl162, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl154, zip_derived_cl30])).
% 7.90/1.77 thf(zip_derived_cl653, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl652, zip_derived_cl162])).
% 7.90/1.77 thf(zip_derived_cl1874, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ 0)
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1849, zip_derived_cl653])).
% 7.90/1.77 thf(clause_161, axiom,
% 7.90/1.77 (( ~( LE @ ( f @ ( suc @ ( suc @ B_23 ) ) ) @ ( s @ 0 ) ) ) |
% 7.90/1.77 ( E @ 0 @ ( f @ ( suc @ ( suc @ B_23 ) ) ) ) | ( LE @ ( f @ B_23 ) @ 0 ))).
% 7.90/1.77 thf(zip_derived_cl12, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 7.90/1.77 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_161])).
% 7.90/1.77 thf(zip_derived_cl1845, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1844, zip_derived_cl1655])).
% 7.90/1.77 thf(zip_derived_cl1847, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl12, zip_derived_cl1845])).
% 7.90/1.77 thf(zip_derived_cl1916, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1874, zip_derived_cl1847])).
% 7.90/1.77 thf(clause_1953, axiom,
% 7.90/1.77 (( ~( LE @ ( f @ B_23 ) @ ( s @ 0 ) ) ) | ( E @ 0 @ ( f @ B_23 ) ) |
% 7.90/1.77 ( LE @ ( f @ B_23 ) @ 0 ))).
% 7.90/1.77 thf(zip_derived_cl82, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ X0) @ (s @ 0))
% 7.90/1.77 | (E @ 0 @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1953])).
% 7.90/1.77 thf(zip_derived_cl1845, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1844, zip_derived_cl1655])).
% 7.90/1.77 thf(zip_derived_cl1848, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl82, zip_derived_cl1845])).
% 7.90/1.77 thf(zip_derived_cl1917, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ 0)
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1916, zip_derived_cl1848])).
% 7.90/1.77 thf(clause_1896, axiom,
% 7.90/1.77 (( ~( LE @ ( f @ ( suc @ B_23 ) ) @ ( s @ 0 ) ) ) |
% 7.90/1.77 ( E @ 0 @ ( f @ ( suc @ B_23 ) ) ) | ( LE @ ( f @ B_23 ) @ 0 ))).
% 7.90/1.77 thf(zip_derived_cl7, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 7.90/1.77 | (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_1896])).
% 7.90/1.77 thf(zip_derived_cl1845, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1844, zip_derived_cl1655])).
% 7.90/1.77 thf(zip_derived_cl1846, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl1845])).
% 7.90/1.77 thf(zip_derived_cl1918, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1917, zip_derived_cl1846])).
% 7.90/1.77 thf(clause_734, axiom,
% 7.90/1.77 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_23 ) ) ) ) ) @ ( s @ 0 ) ) ) |
% 7.90/1.77 ( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_23 ) ) ) ) ) ) |
% 7.90/1.77 ( LE @ ( f @ B_23 ) @ 0 ))).
% 7.90/1.77 thf(zip_derived_cl103, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0))
% 7.90/1.77 | (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_734])).
% 7.90/1.77 thf(zip_derived_cl1845, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1844, zip_derived_cl1655])).
% 7.90/1.77 thf(zip_derived_cl1850, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl103, zip_derived_cl1845])).
% 7.90/1.77 thf(clause_2293, axiom,
% 7.90/1.77 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_5 ) ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_24 ) @ ( f @ ( suc @ B_24 ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_24 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_24 ) ) ) ) ) ) ) |
% 7.90/1.77 ( ~( iLEQ @ ( suc @ A_5 ) @ ( suc @ B_24 ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ A_5 ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_5 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_24 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_24 ) @ ( f @ ( suc @ ( suc @ B_24 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ B_24 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_24 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ B_24 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_24 ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_5 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ))).
% 7.90/1.77 thf(zip_derived_cl81, plain,
% 7.90/1.77 (![X0 : $i, X1 : $i]:
% 7.90/1.77 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 7.90/1.77 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X1))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2293])).
% 7.90/1.77 thf(zip_derived_cl670, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('eq_fact', [status(thm)], [zip_derived_cl81])).
% 7.90/1.77 thf(zip_derived_cl671, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl670])).
% 7.90/1.77 thf(zip_derived_cl1887, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ 0)
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1850, zip_derived_cl671])).
% 7.90/1.77 thf(zip_derived_cl2001, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ 0)
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1918, zip_derived_cl1887])).
% 7.90/1.77 thf(zip_derived_cl2009, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl2001])).
% 7.90/1.77 thf(zip_derived_cl373, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl372, zip_derived_cl162])).
% 7.90/1.77 thf(zip_derived_cl2010, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ 0)
% 7.90/1.77 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl2009, zip_derived_cl373])).
% 7.90/1.77 thf(zip_derived_cl1918, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1917, zip_derived_cl1846])).
% 7.90/1.77 thf(zip_derived_cl1850, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl103, zip_derived_cl1845])).
% 7.90/1.77 thf(clause_2289, axiom,
% 7.90/1.77 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_5 ) ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ A_5 ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_5 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_5 ) ) ) ) ) ) |
% 7.90/1.77 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 7.90/1.77 ( iLEQ @ ( suc @ A_5 ) @ ( suc @ A_5 ) ))).
% 7.90/1.77 thf(zip_derived_cl117, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('cnf', [status(esa)], [clause_2289])).
% 7.90/1.77 thf(zip_derived_cl1886, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ 0)
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0)))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1850, zip_derived_cl117])).
% 7.90/1.77 thf(zip_derived_cl1967, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ 0)
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1918, zip_derived_cl1886])).
% 7.90/1.77 thf(zip_derived_cl1975, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('simplify', [status(thm)], [zip_derived_cl1967])).
% 7.90/1.77 thf(zip_derived_cl373, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl372, zip_derived_cl162])).
% 7.90/1.77 thf(zip_derived_cl1976, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ 0)
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1975, zip_derived_cl373])).
% 7.90/1.77 thf(zip_derived_cl1848, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl82, zip_derived_cl1845])).
% 7.90/1.77 thf(zip_derived_cl1977, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1976, zip_derived_cl1848])).
% 7.90/1.77 thf(zip_derived_cl1846, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl1845])).
% 7.90/1.77 thf(zip_derived_cl162, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl154, zip_derived_cl30])).
% 7.90/1.77 thf(zip_derived_cl1859, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ 0)
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('sup-', [status(thm)], [zip_derived_cl1846, zip_derived_cl162])).
% 7.90/1.77 thf(zip_derived_cl1848, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl82, zip_derived_cl1845])).
% 7.90/1.77 thf(zip_derived_cl1869, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ (f @ X0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1859, zip_derived_cl1848])).
% 7.90/1.77 thf(zip_derived_cl1978, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ 0)
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1977, zip_derived_cl1869])).
% 7.90/1.77 thf(zip_derived_cl1849, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl1845])).
% 7.90/1.77 thf(zip_derived_cl1979, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1978, zip_derived_cl1849])).
% 7.90/1.77 thf(zip_derived_cl1847, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl12, zip_derived_cl1845])).
% 7.90/1.77 thf(zip_derived_cl1980, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ 0)
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1979, zip_derived_cl1847])).
% 7.90/1.77 thf(zip_derived_cl1846, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl1845])).
% 7.90/1.77 thf(zip_derived_cl1981, plain,
% 7.90/1.77 (![X0 : $i]: ( (iLEQ @ (suc @ X0) @ (suc @ X0)) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl1980, zip_derived_cl1846])).
% 7.90/1.77 thf(zip_derived_cl2011, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl2010, zip_derived_cl1981])).
% 7.90/1.77 thf(zip_derived_cl162, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl154, zip_derived_cl30])).
% 7.90/1.77 thf(zip_derived_cl2012, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ 0)
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ X0)))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl2011, zip_derived_cl162])).
% 7.90/1.77 thf(zip_derived_cl1847, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl12, zip_derived_cl1845])).
% 7.90/1.77 thf(zip_derived_cl2013, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 (~ (E @ 0 @ (f @ X0))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl2012, zip_derived_cl1847])).
% 7.90/1.77 thf(zip_derived_cl1848, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl82, zip_derived_cl1845])).
% 7.90/1.77 thf(zip_derived_cl2014, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (LE @ (f @ X0) @ 0)
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 7.90/1.77 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl2013, zip_derived_cl1848])).
% 7.90/1.77 thf(zip_derived_cl1849, plain,
% 7.90/1.77 (![X0 : $i]:
% 7.90/1.77 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl1845])).
% 7.90/1.77 thf(zip_derived_cl2015, plain,
% 7.90/1.77 (![X0 : $i]: (~ (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl2014, zip_derived_cl1849])).
% 7.90/1.77 thf(zip_derived_cl1846, plain,
% 7.90/1.77 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl1845])).
% 7.90/1.77 thf(zip_derived_cl2016, plain, (![X0 : $i]: (LE @ (f @ X0) @ 0)),
% 7.90/1.77 inference('clc', [status(thm)], [zip_derived_cl2015, zip_derived_cl1846])).
% 7.90/1.77 thf(zip_derived_cl2017, plain, ($false),
% 7.90/1.77 inference('demod', [status(thm)], [zip_derived_cl67, zip_derived_cl2016])).
% 7.90/1.77
% 7.90/1.77 % SZS output end Refutation
% 7.90/1.77
% 7.90/1.77
% 7.90/1.77 % Terminating...
% 8.55/1.85 % Runner terminated.
% 8.55/1.86 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------