TSTP Solution File: SYO660-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO660-1 : 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.lTi1viHT5b true
% Computer : n020.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 05:52:27 EDT 2023
% Result : Unsatisfiable 6.15s 1.54s
% Output : Refutation 6.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO660-1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.lTi1viHT5b true
% 0.13/0.34 % Computer : n020.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
% 0.13/0.35 % DateTime : Sat Aug 26 06:11:00 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.21/0.61 % Total configuration time : 435
% 0.21/0.61 % Estimated wc time : 1092
% 0.21/0.61 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.21/0.87 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 6.15/1.54 % Solved by fo/fo3_bce.sh.
% 6.15/1.54 % BCE start: 74
% 6.15/1.54 % BCE eliminated: 0
% 6.15/1.54 % PE start: 74
% 6.15/1.54 logic: neq
% 6.15/1.54 % PE eliminated: 40
% 6.15/1.54 % done 229 iterations in 0.733s
% 6.15/1.54 % SZS status Unsatisfiable for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 6.15/1.54 % SZS output start Refutation
% 6.15/1.54 thf(0_type, type, 0: $i).
% 6.15/1.54 thf(iLEQ_type, type, iLEQ: $i > $i > $o).
% 6.15/1.54 thf(f_type, type, f: $i > $i).
% 6.15/1.54 thf(suc_type, type, suc: $i > $i).
% 6.15/1.54 thf(z_type, type, z: $i).
% 6.15/1.54 thf(LE_type, type, LE: $i > $i > $o).
% 6.15/1.54 thf(E_type, type, E: $i > $i > $o).
% 6.15/1.54 thf(s_type, type, s: $i > $i).
% 6.15/1.54 thf(clause_1502, axiom, (~( LE @ ( f @ z ) @ 0 ))).
% 6.15/1.54 thf(zip_derived_cl2, plain, (~ (LE @ (f @ z) @ 0)),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1502])).
% 6.15/1.54 thf(clause_1962, axiom,
% 6.15/1.54 (( ~( LE @ ( f @ B_5 ) @ ( s @ 0 ) ) ) | ( E @ 0 @ ( f @ B_5 ) ) |
% 6.15/1.54 ( LE @ ( f @ B_5 ) @ 0 ))).
% 6.15/1.54 thf(zip_derived_cl3, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | (E @ 0 @ (f @ X0))
% 6.15/1.54 | (LE @ (f @ X0) @ 0))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1962])).
% 6.15/1.54 thf(clause_2165, axiom,
% 6.15/1.54 (( ~( LE @ ( f @ ( suc @ B_5 ) ) @ ( s @ 0 ) ) ) |
% 6.15/1.54 ( E @ 0 @ ( f @ ( suc @ B_5 ) ) ) | ( LE @ ( f @ B_5 ) @ 0 ))).
% 6.15/1.54 thf(zip_derived_cl23, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 6.15/1.54 | (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | (LE @ (f @ X0) @ 0))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_2165])).
% 6.15/1.54 thf(clause_2540, axiom,
% 6.15/1.54 (( ~( LE @ ( f @ ( suc @ ( suc @ B_5 ) ) ) @ ( s @ 0 ) ) ) |
% 6.15/1.54 ( E @ 0 @ ( f @ ( suc @ ( suc @ B_5 ) ) ) ) | ( LE @ ( f @ B_5 ) @ 0 ))).
% 6.15/1.54 thf(zip_derived_cl4, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 6.15/1.54 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (LE @ (f @ X0) @ 0))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_2540])).
% 6.15/1.54 thf(clause_2700, axiom,
% 6.15/1.54 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) @ ( s @ 0 ) ) ) |
% 6.15/1.54 ( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) ) |
% 6.15/1.54 ( LE @ ( f @ B_5 ) @ 0 ))).
% 6.15/1.54 thf(zip_derived_cl27, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0))
% 6.15/1.54 | (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (LE @ (f @ X0) @ 0))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_2700])).
% 6.15/1.54 thf(clause_514, axiom,
% 6.15/1.54 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) ) @ ( s @ 0 ) ) ) |
% 6.15/1.54 ( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) ) ) |
% 6.15/1.54 ( LE @ ( f @ B_5 ) @ 0 ))).
% 6.15/1.54 thf(zip_derived_cl41, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0))
% 6.15/1.54 | (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | (LE @ (f @ X0) @ 0))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_514])).
% 6.15/1.54 thf(clause_2196, axiom,
% 6.15/1.54 (( ~( E @ 0 @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ A_2 ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 6.15/1.54 thf(zip_derived_cl42, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_2196])).
% 6.15/1.54 thf(clause_1574, axiom,
% 6.15/1.54 (( ~( E @ 0 @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ A_2 ) ) ) |
% 6.15/1.54 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_6 ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ B_6 ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ B_6 ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ B_6 ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ))).
% 6.15/1.54 thf(zip_derived_cl32, plain,
% 6.15/1.54 (![X0 : $i, X1 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X1)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X1))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1))))))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1574])).
% 6.15/1.54 thf(zip_derived_cl297, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('dp-resolution', [status(thm)],
% 6.15/1.54 [zip_derived_cl42, zip_derived_cl32])).
% 6.15/1.54 thf(zip_derived_cl627, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl297])).
% 6.15/1.54 thf(clause_70, axiom,
% 6.15/1.54 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ A_2 ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 6.15/1.54 thf(zip_derived_cl40, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_70])).
% 6.15/1.54 thf(clause_1325, axiom,
% 6.15/1.54 (( ~( E @ 0 @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ A_2 ) ) ) |
% 6.15/1.54 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_6 ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ B_6 ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ B_6 ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ B_6 ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ))).
% 6.15/1.54 thf(zip_derived_cl67, plain,
% 6.15/1.54 (![X0 : $i, X1 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X1))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1)))))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1325])).
% 6.15/1.54 thf(zip_derived_cl271, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('dp-resolution', [status(thm)],
% 6.15/1.54 [zip_derived_cl40, zip_derived_cl67])).
% 6.15/1.54 thf(zip_derived_cl595, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl271])).
% 6.15/1.54 thf(clause_1634, axiom,
% 6.15/1.54 (( ~( E @ 0 @ ( f @ A_2 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 6.15/1.54 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 6.15/1.54 thf(zip_derived_cl69, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1634])).
% 6.15/1.54 thf(clause_997, axiom,
% 6.15/1.54 (( ~( E @ 0 @ ( f @ ( suc @ A_2 ) ) ) ) | ( ~( E @ 0 @ ( f @ A_2 ) ) ) |
% 6.15/1.54 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_6 ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ B_6 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ B_6 ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 6.15/1.54 ( E @ ( f @ B_6 ) @ ( f @ ( suc @ B_6 ) ) ))).
% 6.15/1.54 thf(zip_derived_cl52, plain,
% 6.15/1.54 (![X0 : $i, X1 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X1))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_997])).
% 6.15/1.54 thf(zip_derived_cl461, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('dp-resolution', [status(thm)],
% 6.15/1.54 [zip_derived_cl69, zip_derived_cl52])).
% 6.15/1.54 thf(zip_derived_cl580, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl461])).
% 6.15/1.54 thf(zip_derived_cl596, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl595, zip_derived_cl580])).
% 6.15/1.54 thf(zip_derived_cl628, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl627, zip_derived_cl596])).
% 6.15/1.54 thf(zip_derived_cl580, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl461])).
% 6.15/1.54 thf(zip_derived_cl629, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl628, zip_derived_cl580])).
% 6.15/1.54 thf(clause_2932, axiom,
% 6.15/1.54 (( ~( E @ 0 @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ A_2 ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 6.15/1.54 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 6.15/1.54 thf(zip_derived_cl11, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_2932])).
% 6.15/1.54 thf(clause_1151, axiom,
% 6.15/1.54 (( ~( E @ 0 @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ A_2 ) ) ) |
% 6.15/1.54 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_6 ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ B_6 ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ B_6 ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ B_6 ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ) ))).
% 6.15/1.54 thf(zip_derived_cl35, plain,
% 6.15/1.54 (![X0 : $i, X1 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X1)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X1))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ (suc @ X1)))))))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1151])).
% 6.15/1.54 thf(zip_derived_cl149, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('dp-resolution', [status(thm)],
% 6.15/1.54 [zip_derived_cl11, zip_derived_cl35])).
% 6.15/1.54 thf(zip_derived_cl625, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl149])).
% 6.15/1.54 thf(clause_249, axiom,
% 6.15/1.54 (( ~( E @ 0 @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ A_2 ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 6.15/1.54 thf(zip_derived_cl53, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_249])).
% 6.15/1.54 thf(clause_165, axiom,
% 6.15/1.54 (( ~( E @ 0 @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ A_2 ) ) ) |
% 6.15/1.54 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_6 ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ B_6 ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ B_6 ) ) ) ) |
% 6.15/1.54 ( ~( E @ 0 @ ( f @ ( suc @ B_6 ) ) ) ))).
% 6.15/1.54 thf(zip_derived_cl48, plain,
% 6.15/1.54 (![X0 : $i, X1 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X1)))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X1)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X1))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X1))))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_165])).
% 6.15/1.54 thf(zip_derived_cl357, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('dp-resolution', [status(thm)],
% 6.15/1.54 [zip_derived_cl53, zip_derived_cl48])).
% 6.15/1.54 thf(zip_derived_cl658, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl357])).
% 6.15/1.54 thf(zip_derived_cl660, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('sup-', [status(thm)], [zip_derived_cl625, zip_derived_cl658])).
% 6.15/1.54 thf(zip_derived_cl661, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl660])).
% 6.15/1.54 thf(zip_derived_cl746, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))),
% 6.15/1.54 inference('sup-', [status(thm)], [zip_derived_cl629, zip_derived_cl661])).
% 6.15/1.54 thf(zip_derived_cl750, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl746])).
% 6.15/1.54 thf(zip_derived_cl596, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl595, zip_derived_cl580])).
% 6.15/1.54 thf(zip_derived_cl752, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl750, zip_derived_cl596])).
% 6.15/1.54 thf(zip_derived_cl580, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl461])).
% 6.15/1.54 thf(zip_derived_cl753, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl752, zip_derived_cl580])).
% 6.15/1.54 thf(clause_1204, axiom,
% 6.15/1.54 (( ~( LE @
% 6.15/1.54 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) ) ) @
% 6.15/1.54 ( s @ 0 ) ) ) |
% 6.15/1.54 ( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) ) ) ) |
% 6.15/1.54 ( LE @ ( f @ B_5 ) @ 0 ))).
% 6.15/1.54 thf(zip_derived_cl58, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @ (s @ 0))
% 6.15/1.54 | (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | (LE @ (f @ X0) @ 0))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1204])).
% 6.15/1.54 thf(zip_derived_cl757, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | (LE @ (f @ X0) @ 0)
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @ (s @ 0)))),
% 6.15/1.54 inference('sup+', [status(thm)], [zip_derived_cl753, zip_derived_cl58])).
% 6.15/1.54 thf(zip_derived_cl776, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ 0)
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @ (s @ 0))
% 6.15/1.54 | (LE @ (f @ X0) @ 0)
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 6.15/1.54 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl757])).
% 6.15/1.54 thf(zip_derived_cl778, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0))
% 6.15/1.54 | (LE @ (f @ X0) @ 0))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl776])).
% 6.15/1.54 thf(zip_derived_cl791, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ 0)
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0))
% 6.15/1.54 | (LE @ (f @ X0) @ 0)
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @ (s @ 0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0)))),
% 6.15/1.54 inference('sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl778])).
% 6.15/1.54 thf(zip_derived_cl792, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0))
% 6.15/1.54 | (LE @ (f @ X0) @ 0))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl791])).
% 6.15/1.54 thf(zip_derived_cl802, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ 0)
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 6.15/1.54 | (LE @ (f @ X0) @ 0)
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @ (s @ 0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0)))),
% 6.15/1.54 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl792])).
% 6.15/1.54 thf(zip_derived_cl807, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 6.15/1.54 | (LE @ (f @ X0) @ 0))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl802])).
% 6.15/1.54 thf(zip_derived_cl817, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ 0)
% 6.15/1.54 | ~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 6.15/1.54 | (LE @ (f @ X0) @ 0)
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @ (s @ 0))
% 6.15/1.54 | ~ (E @ 0 @ (f @ X0)))),
% 6.15/1.54 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl807])).
% 6.15/1.54 thf(zip_derived_cl821, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ 0 @ (f @ X0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 6.15/1.54 | (LE @ (f @ X0) @ 0))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl817])).
% 6.15/1.54 thf(zip_derived_cl846, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ 0)
% 6.15/1.54 | ~ (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | (LE @ (f @ X0) @ 0)
% 6.15/1.54 | ~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @ (s @ 0)))),
% 6.15/1.54 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl821])).
% 6.15/1.54 thf(zip_derived_cl852, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 6.15/1.54 | ~ (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | (LE @ (f @ X0) @ 0))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl846])).
% 6.15/1.54 thf(clause_410, axiom,
% 6.15/1.54 (( ~( LE @
% 6.15/1.54 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_2 ) ) ) ) ) @
% 6.15/1.54 ( s @ ( s @ 0 ) ) ) ) |
% 6.15/1.54 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_2 ) ) ) ) ) ) |
% 6.15/1.54 ( LE @ ( f @ B_2 ) @ ( s @ 0 ) ))).
% 6.15/1.54 thf(zip_derived_cl34, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ (s @ 0)))
% 6.15/1.54 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_410])).
% 6.15/1.54 thf(clause_1215, axiom, (LE @ ( f @ A ) @ ( s @ ( s @ 0 ) ))).
% 6.15/1.54 thf(zip_derived_cl72, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1215])).
% 6.15/1.54 thf(zip_derived_cl578, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl72])).
% 6.15/1.54 thf(clause_1276, axiom,
% 6.15/1.54 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ B_2 ) ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 6.15/1.54 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_2 ) ) ) ) ) |
% 6.15/1.54 ( LE @ ( f @ B_2 ) @ ( s @ 0 ) ))).
% 6.15/1.54 thf(zip_derived_cl28, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ 0)))
% 6.15/1.54 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1276])).
% 6.15/1.54 thf(zip_derived_cl72, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1215])).
% 6.15/1.54 thf(zip_derived_cl577, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl28, zip_derived_cl72])).
% 6.15/1.54 thf(zip_derived_cl578, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl72])).
% 6.15/1.54 thf(clause_664, axiom,
% 6.15/1.54 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ A_1 ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 6.15/1.54 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 6.15/1.54 thf(zip_derived_cl38, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_664])).
% 6.15/1.54 thf(clause_2717, axiom,
% 6.15/1.54 (( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_3 ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ A_1 ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_3 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_3 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ B_3 ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_3 ) @ ( f @ ( suc @ B_3 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_3 ) @ ( f @ ( suc @ ( suc @ B_3 ) ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ B_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) ) ))).
% 6.15/1.54 thf(zip_derived_cl63, plain,
% 6.15/1.54 (![X0 : $i, X1 : $i]:
% 6.15/1.54 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X1))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ (suc @ X1)))))))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_2717])).
% 6.15/1.54 thf(zip_derived_cl218, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('dp-resolution', [status(thm)],
% 6.15/1.54 [zip_derived_cl38, zip_derived_cl63])).
% 6.15/1.54 thf(zip_derived_cl665, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl218])).
% 6.15/1.54 thf(zip_derived_cl670, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('sup-', [status(thm)], [zip_derived_cl578, zip_derived_cl665])).
% 6.15/1.54 thf(zip_derived_cl1116, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('sup-', [status(thm)], [zip_derived_cl577, zip_derived_cl670])).
% 6.15/1.54 thf(zip_derived_cl1117, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl1116])).
% 6.15/1.54 thf(clause_1397, axiom,
% 6.15/1.54 (( ~( E @ ( s @ 0 ) @ ( f @ A_1 ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 6.15/1.54 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 6.15/1.54 thf(zip_derived_cl5, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1397])).
% 6.15/1.54 thf(clause_2550, axiom,
% 6.15/1.54 (( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_3 ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ A_1 ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_3 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ B_3 ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 6.15/1.54 ( E @ ( f @ B_3 ) @ ( f @ ( suc @ B_3 ) ) ))).
% 6.15/1.54 thf(zip_derived_cl66, plain,
% 6.15/1.54 (![X0 : $i, X1 : $i]:
% 6.15/1.54 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X1))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_2550])).
% 6.15/1.54 thf(zip_derived_cl120, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 6.15/1.54 inference('dp-resolution', [status(thm)],
% 6.15/1.54 [zip_derived_cl5, zip_derived_cl66])).
% 6.15/1.54 thf(zip_derived_cl584, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl120])).
% 6.15/1.54 thf(zip_derived_cl1161, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1117, zip_derived_cl584])).
% 6.15/1.54 thf(clause_2336, axiom,
% 6.15/1.54 (( ~( LE @ ( f @ ( suc @ ( suc @ B_2 ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 6.15/1.54 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_2 ) ) ) ) |
% 6.15/1.54 ( LE @ ( f @ B_2 ) @ ( s @ 0 ) ))).
% 6.15/1.54 thf(zip_derived_cl39, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 6.15/1.54 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_2336])).
% 6.15/1.54 thf(zip_derived_cl72, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1215])).
% 6.15/1.54 thf(zip_derived_cl576, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl72])).
% 6.15/1.54 thf(zip_derived_cl1162, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1161, zip_derived_cl576])).
% 6.15/1.54 thf(zip_derived_cl576, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl72])).
% 6.15/1.54 thf(clause_307, axiom,
% 6.15/1.54 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ A_1 ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 6.15/1.54 thf(zip_derived_cl70, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_307])).
% 6.15/1.54 thf(clause_720, axiom,
% 6.15/1.54 (( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_3 ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ A_1 ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_3 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_3 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ B_3 ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_3 ) @ ( f @ ( suc @ B_3 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ B_3 ) @ ( f @ ( suc @ ( suc @ B_3 ) ) ) ))).
% 6.15/1.54 thf(zip_derived_cl68, plain,
% 6.15/1.54 (![X0 : $i, X1 : $i]:
% 6.15/1.54 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X1))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1)))))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_720])).
% 6.15/1.54 thf(zip_derived_cl522, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('dp-resolution', [status(thm)],
% 6.15/1.54 [zip_derived_cl70, zip_derived_cl68])).
% 6.15/1.54 thf(zip_derived_cl607, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl522])).
% 6.15/1.54 thf(zip_derived_cl584, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl120])).
% 6.15/1.54 thf(zip_derived_cl608, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl607, zip_derived_cl584])).
% 6.15/1.54 thf(zip_derived_cl612, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('sup-', [status(thm)], [zip_derived_cl576, zip_derived_cl608])).
% 6.15/1.54 thf(clause_1847, axiom,
% 6.15/1.54 (( ~( LE @ ( f @ ( suc @ B_2 ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 6.15/1.54 ( E @ ( s @ 0 ) @ ( f @ ( suc @ B_2 ) ) ) |
% 6.15/1.54 ( LE @ ( f @ B_2 ) @ ( s @ 0 ) ))).
% 6.15/1.54 thf(zip_derived_cl0, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 6.15/1.54 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1847])).
% 6.15/1.54 thf(zip_derived_cl72, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1215])).
% 6.15/1.54 thf(zip_derived_cl575, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl72])).
% 6.15/1.54 thf(zip_derived_cl623, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl612, zip_derived_cl575])).
% 6.15/1.54 thf(clause_934, axiom,
% 6.15/1.54 (( ~( LE @ ( f @ B_2 ) @ ( s @ ( s @ 0 ) ) ) ) |
% 6.15/1.54 ( E @ ( s @ 0 ) @ ( f @ B_2 ) ) | ( LE @ ( f @ B_2 ) @ ( s @ 0 ) ))).
% 6.15/1.54 thf(zip_derived_cl60, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 6.15/1.54 | (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_934])).
% 6.15/1.54 thf(zip_derived_cl72, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1215])).
% 6.15/1.54 thf(zip_derived_cl574, plain,
% 6.15/1.54 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl72])).
% 6.15/1.54 thf(zip_derived_cl624, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl623, zip_derived_cl574])).
% 6.15/1.54 thf(zip_derived_cl1163, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1162, zip_derived_cl624])).
% 6.15/1.54 thf(zip_derived_cl574, plain,
% 6.15/1.54 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl72])).
% 6.15/1.54 thf(zip_derived_cl1164, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1163, zip_derived_cl574])).
% 6.15/1.54 thf(zip_derived_cl575, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl72])).
% 6.15/1.54 thf(zip_derived_cl1165, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0)))))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1164, zip_derived_cl575])).
% 6.15/1.54 thf(zip_derived_cl577, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl28, zip_derived_cl72])).
% 6.15/1.54 thf(clause_2795, axiom,
% 6.15/1.54 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ A_1 ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 6.15/1.54 thf(zip_derived_cl64, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_2795])).
% 6.15/1.54 thf(clause_2494, axiom,
% 6.15/1.54 (( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_3 ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ A_1 ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_3 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_3 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ B_3 ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_3 ) @ ( f @ ( suc @ B_3 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_3 ) @ ( f @ ( suc @ ( suc @ B_3 ) ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( E @ ( f @ B_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) ))).
% 6.15/1.54 thf(zip_derived_cl54, plain,
% 6.15/1.54 (![X0 : $i, X1 : $i]:
% 6.15/1.54 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X1))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1))))))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_2494])).
% 6.15/1.54 thf(zip_derived_cl412, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('dp-resolution', [status(thm)],
% 6.15/1.54 [zip_derived_cl64, zip_derived_cl54])).
% 6.15/1.54 thf(zip_derived_cl632, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl412])).
% 6.15/1.54 thf(zip_derived_cl608, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl607, zip_derived_cl584])).
% 6.15/1.54 thf(zip_derived_cl633, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl632, zip_derived_cl608])).
% 6.15/1.54 thf(zip_derived_cl584, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl120])).
% 6.15/1.54 thf(zip_derived_cl634, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl633, zip_derived_cl584])).
% 6.15/1.54 thf(zip_derived_cl640, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('sup-', [status(thm)], [zip_derived_cl577, zip_derived_cl634])).
% 6.15/1.54 thf(zip_derived_cl575, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl72])).
% 6.15/1.54 thf(zip_derived_cl687, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl640, zip_derived_cl575])).
% 6.15/1.54 thf(zip_derived_cl576, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl72])).
% 6.15/1.54 thf(zip_derived_cl688, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl687, zip_derived_cl576])).
% 6.15/1.54 thf(zip_derived_cl574, plain,
% 6.15/1.54 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl72])).
% 6.15/1.54 thf(zip_derived_cl689, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl688, zip_derived_cl574])).
% 6.15/1.54 thf(zip_derived_cl1166, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1165, zip_derived_cl689])).
% 6.15/1.54 thf(clause_1595, axiom,
% 6.15/1.54 (( ~( LE @
% 6.15/1.54 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B_2 ) ) ) ) ) ) @
% 6.15/1.54 ( s @ ( s @ 0 ) ) ) ) |
% 6.15/1.54 ( E @
% 6.15/1.54 ( s @ 0 ) @
% 6.15/1.54 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B_2 ) ) ) ) ) ) ) |
% 6.15/1.54 ( LE @ ( f @ B_2 ) @ ( s @ 0 ) ))).
% 6.15/1.54 thf(zip_derived_cl56, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))) @
% 6.15/1.54 (s @ (s @ 0)))
% 6.15/1.54 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1595])).
% 6.15/1.54 thf(zip_derived_cl72, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_1215])).
% 6.15/1.54 thf(zip_derived_cl579, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl56, zip_derived_cl72])).
% 6.15/1.54 thf(clause_2367, axiom,
% 6.15/1.54 (( ~( E @
% 6.15/1.54 ( s @ 0 ) @
% 6.15/1.54 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ A_1 ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 6.15/1.54 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 6.15/1.54 thf(zip_derived_cl73, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_2367])).
% 6.15/1.54 thf(clause_2034, axiom,
% 6.15/1.54 (( ~( E @
% 6.15/1.54 ( s @ 0 ) @
% 6.15/1.54 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_3 ) ) ) |
% 6.15/1.54 ( ~( E @
% 6.15/1.54 ( s @ 0 ) @
% 6.15/1.54 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ A_1 ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_3 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_3 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ B_3 ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_3 ) @ ( f @ ( suc @ B_3 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 6.15/1.54 ( ~( E @ ( f @ B_3 ) @ ( f @ ( suc @ ( suc @ B_3 ) ) ) ) ))).
% 6.15/1.54 thf(zip_derived_cl6, plain,
% 6.15/1.54 (![X0 : $i, X1 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X1)))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X1))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1)))))),
% 6.15/1.54 inference('cnf', [status(esa)], [clause_2034])).
% 6.15/1.54 thf(zip_derived_cl525, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))),
% 6.15/1.54 inference('dp-resolution', [status(thm)],
% 6.15/1.54 [zip_derived_cl73, zip_derived_cl6])).
% 6.15/1.54 thf(zip_derived_cl672, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl525])).
% 6.15/1.54 thf(zip_derived_cl675, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('sup-', [status(thm)], [zip_derived_cl579, zip_derived_cl672])).
% 6.15/1.54 thf(zip_derived_cl1177, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('sup-', [status(thm)], [zip_derived_cl1166, zip_derived_cl675])).
% 6.15/1.54 thf(zip_derived_cl1179, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl1177])).
% 6.15/1.54 thf(zip_derived_cl1198, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 6.15/1.54 inference('sup-', [status(thm)], [zip_derived_cl578, zip_derived_cl1179])).
% 6.15/1.54 thf(zip_derived_cl1200, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl1198])).
% 6.15/1.54 thf(zip_derived_cl577, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl28, zip_derived_cl72])).
% 6.15/1.54 thf(zip_derived_cl1201, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1200, zip_derived_cl577])).
% 6.15/1.54 thf(zip_derived_cl576, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl72])).
% 6.15/1.54 thf(zip_derived_cl1202, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1201, zip_derived_cl576])).
% 6.15/1.54 thf(zip_derived_cl584, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('simplify', [status(thm)], [zip_derived_cl120])).
% 6.15/1.54 thf(zip_derived_cl1203, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ X0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1202, zip_derived_cl584])).
% 6.15/1.54 thf(zip_derived_cl574, plain,
% 6.15/1.54 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl72])).
% 6.15/1.54 thf(zip_derived_cl1204, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1203, zip_derived_cl574])).
% 6.15/1.54 thf(zip_derived_cl624, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl623, zip_derived_cl574])).
% 6.15/1.54 thf(zip_derived_cl1205, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (LE @ (f @ X0) @ (s @ 0))
% 6.15/1.54 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1204, zip_derived_cl624])).
% 6.15/1.54 thf(zip_derived_cl689, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 6.15/1.54 | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl688, zip_derived_cl574])).
% 6.15/1.54 thf(zip_derived_cl1206, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 (~ (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1205, zip_derived_cl689])).
% 6.15/1.54 thf(zip_derived_cl575, plain,
% 6.15/1.54 (![X0 : $i]:
% 6.15/1.54 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl72])).
% 6.15/1.54 thf(zip_derived_cl1207, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1206, zip_derived_cl575])).
% 6.15/1.54 thf(zip_derived_cl1207, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1206, zip_derived_cl575])).
% 6.15/1.54 thf(zip_derived_cl1207, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1206, zip_derived_cl575])).
% 6.15/1.54 thf(zip_derived_cl1207, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1206, zip_derived_cl575])).
% 6.15/1.54 thf(zip_derived_cl1207, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1206, zip_derived_cl575])).
% 6.15/1.54 thf(zip_derived_cl1207, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 6.15/1.54 inference('clc', [status(thm)], [zip_derived_cl1206, zip_derived_cl575])).
% 6.15/1.54 thf(zip_derived_cl1225, plain, (![X0 : $i]: (LE @ (f @ X0) @ 0)),
% 6.15/1.54 inference('demod', [status(thm)],
% 6.15/1.54 [zip_derived_cl852, zip_derived_cl1207, zip_derived_cl1207,
% 6.15/1.54 zip_derived_cl1207, zip_derived_cl1207, zip_derived_cl1207,
% 6.15/1.54 zip_derived_cl1207])).
% 6.15/1.54 thf(zip_derived_cl1235, plain, ($false),
% 6.15/1.54 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl1225])).
% 6.15/1.54
% 6.15/1.54 % SZS output end Refutation
% 6.15/1.54
% 6.15/1.54
% 6.15/1.54 % Terminating...
% 7.76/1.81 % Runner terminated.
% 7.76/1.83 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------