TSTP Solution File: SYO679-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO679-1 : 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.8LxDubzre9 true
% Computer : n023.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 05:52:32 EDT 2023
% Result : Unsatisfiable 5.33s 1.36s
% Output : Refutation 5.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO679-1 : TPTP v8.1.2. Released v7.3.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.8LxDubzre9 true
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 06:12:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.46/0.62 % Total configuration time : 435
% 0.46/0.62 % Estimated wc time : 1092
% 0.46/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.54/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.54/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.56/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 0.56/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo17_bce.sh running for 50s
% 0.56/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo8.sh running for 50s
% 5.33/1.36 % Solved by fo/fo5.sh.
% 5.33/1.36 % done 425 iterations in 0.554s
% 5.33/1.36 % SZS status Unsatisfiable for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 5.33/1.36 % SZS output start Refutation
% 5.33/1.36 thf(f_type, type, f: $i > $i).
% 5.33/1.36 thf(0_type, type, 0: $i).
% 5.33/1.36 thf(suc_type, type, suc: $i > $i).
% 5.33/1.36 thf(s_type, type, s: $i > $i).
% 5.33/1.36 thf(E_type, type, E: $i > $i > $o).
% 5.33/1.36 thf(iLEQ_type, type, iLEQ: $i > $i > $o).
% 5.33/1.36 thf(LE_type, type, LE: $i > $i > $o).
% 5.33/1.36 thf(z_type, type, z: $i).
% 5.33/1.36 thf(clause_876, axiom, (~( LE @ ( f @ z ) @ 0 ))).
% 5.33/1.36 thf(zip_derived_cl69, plain, (~ (LE @ (f @ z) @ 0)),
% 5.33/1.36 inference('cnf', [status(esa)], [clause_876])).
% 5.33/1.36 thf(clause_476, axiom,
% 5.33/1.36 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ B_16 ) ) ) ) @ ( s @ 0 ) ) ) |
% 5.33/1.36 ( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_16 ) ) ) ) ) |
% 5.33/1.36 ( LE @ ( f @ B_16 ) @ 0 ))).
% 5.33/1.36 thf(zip_derived_cl25, plain,
% 5.33/1.36 (![X0 : $i]:
% 5.33/1.36 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0))
% 5.33/1.36 | (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.33/1.36 | (LE @ (f @ X0) @ 0))),
% 5.33/1.36 inference('cnf', [status(esa)], [clause_476])).
% 5.58/1.36 thf(clause_1604, axiom,
% 5.58/1.36 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ B_13 ) ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 5.58/1.36 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_13 ) ) ) ) ) |
% 5.58/1.36 ( LE @ ( f @ B_13 ) @ ( s @ 0 ) ))).
% 5.58/1.36 thf(zip_derived_cl78, plain,
% 5.58/1.36 (![X0 : $i]:
% 5.58/1.36 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ 0)))
% 5.58/1.36 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.36 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.36 inference('cnf', [status(esa)], [clause_1604])).
% 5.58/1.36 thf(clause_1386, axiom,
% 5.58/1.36 (( ~( LE @
% 5.58/1.36 ( f @ ( suc @ ( suc @ ( suc @ B_9 ) ) ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 5.58/1.36 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_9 ) ) ) ) ) |
% 5.58/1.36 ( LE @ ( f @ B_9 ) @ ( s @ ( s @ 0 ) ) ))).
% 5.58/1.36 thf(zip_derived_cl14, plain,
% 5.58/1.36 (![X0 : $i]:
% 5.58/1.36 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ (s @ 0))))
% 5.58/1.36 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.36 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.36 inference('cnf', [status(esa)], [clause_1386])).
% 5.58/1.36 thf(clause_47, axiom,
% 5.58/1.36 (( ~( LE @
% 5.58/1.36 ( f @ ( suc @ ( suc @ ( suc @ B_4 ) ) ) ) @
% 5.58/1.36 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 5.58/1.36 ( E @
% 5.58/1.36 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_4 ) ) ) ) ) |
% 5.58/1.36 ( LE @ ( f @ B_4 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 5.58/1.36 thf(zip_derived_cl92, plain,
% 5.58/1.36 (![X0 : $i]:
% 5.58/1.36 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ (s @ (s @ 0)))))
% 5.58/1.36 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.36 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.36 inference('cnf', [status(esa)], [clause_47])).
% 5.58/1.36 thf(clause_1318, axiom, (LE @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 5.58/1.36 thf(zip_derived_cl20, plain,
% 5.58/1.36 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 5.58/1.36 inference('cnf', [status(esa)], [clause_1318])).
% 5.58/1.36 thf(zip_derived_cl123, plain,
% 5.58/1.36 (![X0 : $i]:
% 5.58/1.36 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.36 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.36 inference('demod', [status(thm)], [zip_derived_cl92, zip_derived_cl20])).
% 5.58/1.36 thf(clause_350, axiom,
% 5.58/1.36 (( ~( LE @
% 5.58/1.36 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_4 ) ) ) ) ) @
% 5.58/1.36 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 5.58/1.36 ( E @
% 5.58/1.36 ( s @ ( s @ ( s @ 0 ) ) ) @
% 5.58/1.36 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_4 ) ) ) ) ) ) |
% 5.58/1.36 ( LE @ ( f @ B_4 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 5.58/1.36 thf(zip_derived_cl46, plain,
% 5.58/1.36 (![X0 : $i]:
% 5.58/1.36 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @
% 5.58/1.36 (s @ (s @ (s @ (s @ 0)))))
% 5.58/1.36 | (E @ (s @ (s @ (s @ 0))) @
% 5.58/1.36 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.36 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.36 inference('cnf', [status(esa)], [clause_350])).
% 5.58/1.36 thf(zip_derived_cl20, plain,
% 5.58/1.36 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 5.58/1.36 inference('cnf', [status(esa)], [clause_1318])).
% 5.58/1.36 thf(zip_derived_cl126, plain,
% 5.58/1.36 (![X0 : $i]:
% 5.58/1.36 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.36 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.36 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl20])).
% 5.58/1.37 thf(clause_1356, axiom,
% 5.58/1.37 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_5 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_5 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_5 ) @ ( f @ ( suc @ B_5 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_5 ) ) ) |
% 5.58/1.37 ( ~( E @
% 5.58/1.37 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @
% 5.58/1.37 ( s @ ( s @ ( s @ 0 ) ) ) @
% 5.58/1.37 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_5 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @
% 5.58/1.37 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_5 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( ~( E @
% 5.58/1.37 ( s @ ( s @ ( s @ 0 ) ) ) @
% 5.58/1.37 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_5 ) @ ( f @ ( suc @ ( suc @ B_5 ) ) ) ) ))).
% 5.58/1.37 thf(zip_derived_cl84, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @
% 5.58/1.37 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @
% 5.58/1.37 (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1356])).
% 5.58/1.37 thf(zip_derived_cl444, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @
% 5.58/1.37 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl84])).
% 5.58/1.37 thf(zip_derived_cl445, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @
% 5.58/1.37 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl444])).
% 5.58/1.37 thf(zip_derived_cl481, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl126, zip_derived_cl445])).
% 5.58/1.37 thf(zip_derived_cl485, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl123, zip_derived_cl481])).
% 5.58/1.37 thf(zip_derived_cl487, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl485])).
% 5.58/1.37 thf(clause_1086, axiom,
% 5.58/1.37 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_5 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_5 ) @ ( f @ ( suc @ B_5 ) ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_5 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_5 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_5 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ B_5 ) @ ( f @ ( suc @ ( suc @ B_5 ) ) ) ))).
% 5.58/1.37 thf(zip_derived_cl100, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 5.58/1.37 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1086])).
% 5.58/1.37 thf(zip_derived_cl317, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl100])).
% 5.58/1.37 thf(zip_derived_cl318, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl317])).
% 5.58/1.37 thf(clause_531, axiom,
% 5.58/1.37 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 5.58/1.37 thf(zip_derived_cl58, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_531])).
% 5.58/1.37 thf(clause_685, axiom,
% 5.58/1.37 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 5.58/1.37 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 5.58/1.37 thf(zip_derived_cl31, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_685])).
% 5.58/1.37 thf(zip_derived_cl140, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl58, zip_derived_cl31])).
% 5.58/1.37 thf(zip_derived_cl327, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl318, zip_derived_cl140])).
% 5.58/1.37 thf(clause_508, axiom,
% 5.58/1.37 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_5 ) ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_5 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_5 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 5.58/1.37 ( E @ ( f @ B_5 ) @ ( f @ ( suc @ B_5 ) ) ))).
% 5.58/1.37 thf(zip_derived_cl40, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 5.58/1.37 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_508])).
% 5.58/1.37 thf(zip_derived_cl161, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl40])).
% 5.58/1.37 thf(zip_derived_cl162, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl161])).
% 5.58/1.37 thf(zip_derived_cl31, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_685])).
% 5.58/1.37 thf(zip_derived_cl166, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl162, zip_derived_cl31])).
% 5.58/1.37 thf(zip_derived_cl328, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl327, zip_derived_cl166])).
% 5.58/1.37 thf(zip_derived_cl488, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl487, zip_derived_cl328])).
% 5.58/1.37 thf(zip_derived_cl123, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl92, zip_derived_cl20])).
% 5.58/1.37 thf(clause_309, axiom,
% 5.58/1.37 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_5 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_5 ) @ ( f @ ( suc @ B_5 ) ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_5 ) ) ) |
% 5.58/1.37 ( ~( E @
% 5.58/1.37 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_5 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @
% 5.58/1.37 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_5 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_5 ) @ ( f @ ( suc @ ( suc @ B_5 ) ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ B_5 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) ))).
% 5.58/1.37 thf(zip_derived_cl62, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_309])).
% 5.58/1.37 thf(zip_derived_cl415, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl62])).
% 5.58/1.37 thf(zip_derived_cl416, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl415])).
% 5.58/1.37 thf(clause_1562, axiom,
% 5.58/1.37 (( ~( E @
% 5.58/1.37 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 5.58/1.37 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 5.58/1.37 thf(zip_derived_cl35, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1562])).
% 5.58/1.37 thf(zip_derived_cl140, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl58, zip_derived_cl31])).
% 5.58/1.37 thf(zip_derived_cl184, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl140])).
% 5.58/1.37 thf(zip_derived_cl166, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl162, zip_derived_cl31])).
% 5.58/1.37 thf(zip_derived_cl185, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl184, zip_derived_cl166])).
% 5.58/1.37 thf(zip_derived_cl420, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl416, zip_derived_cl185])).
% 5.58/1.37 thf(zip_derived_cl328, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl327, zip_derived_cl166])).
% 5.58/1.37 thf(zip_derived_cl421, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl420, zip_derived_cl328])).
% 5.58/1.37 thf(zip_derived_cl166, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl162, zip_derived_cl31])).
% 5.58/1.37 thf(zip_derived_cl422, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl421, zip_derived_cl166])).
% 5.58/1.37 thf(zip_derived_cl426, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl123, zip_derived_cl422])).
% 5.58/1.37 thf(clause_624, axiom,
% 5.58/1.37 (( ~( LE @ ( f @ B_4 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 5.58/1.37 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_4 ) ) |
% 5.58/1.37 ( LE @ ( f @ B_4 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 5.58/1.37 thf(zip_derived_cl17, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 5.58/1.37 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_624])).
% 5.58/1.37 thf(zip_derived_cl20, plain,
% 5.58/1.37 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1318])).
% 5.58/1.37 thf(zip_derived_cl104, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl428, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl426, zip_derived_cl104])).
% 5.58/1.37 thf(clause_129, axiom,
% 5.58/1.37 (( ~( LE @ ( f @ ( suc @ B_4 ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 5.58/1.37 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_4 ) ) ) |
% 5.58/1.37 ( LE @ ( f @ B_4 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 5.58/1.37 thf(zip_derived_cl74, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ (s @ 0)))))
% 5.58/1.37 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_129])).
% 5.58/1.37 thf(zip_derived_cl20, plain,
% 5.58/1.37 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1318])).
% 5.58/1.37 thf(zip_derived_cl106, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl74, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl429, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl428, zip_derived_cl106])).
% 5.58/1.37 thf(clause_1620, axiom,
% 5.58/1.37 (( ~( LE @
% 5.58/1.37 ( f @ ( suc @ ( suc @ B_4 ) ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 5.58/1.37 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_4 ) ) ) ) |
% 5.58/1.37 ( LE @ ( f @ B_4 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 5.58/1.37 thf(zip_derived_cl71, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ (s @ 0)))))
% 5.58/1.37 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1620])).
% 5.58/1.37 thf(zip_derived_cl20, plain,
% 5.58/1.37 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1318])).
% 5.58/1.37 thf(zip_derived_cl115, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl71, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl430, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl429, zip_derived_cl115])).
% 5.58/1.37 thf(zip_derived_cl489, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl488, zip_derived_cl430])).
% 5.58/1.37 thf(zip_derived_cl106, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl74, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl490, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl489, zip_derived_cl106])).
% 5.58/1.37 thf(zip_derived_cl123, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl92, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl126, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl46, zip_derived_cl20])).
% 5.58/1.37 thf(clause_1274, axiom,
% 5.58/1.37 (( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @
% 5.58/1.37 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.58/1.37 ( ~( E @
% 5.58/1.37 ( s @ ( s @ ( s @ 0 ) ) ) @
% 5.58/1.37 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) ) |
% 5.58/1.37 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 5.58/1.37 thf(zip_derived_cl13, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @
% 5.58/1.37 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1274])).
% 5.58/1.37 thf(zip_derived_cl224, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl126, zip_derived_cl13])).
% 5.58/1.37 thf(zip_derived_cl284, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl123, zip_derived_cl224])).
% 5.58/1.37 thf(zip_derived_cl286, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl284])).
% 5.58/1.37 thf(zip_derived_cl106, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl74, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl287, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl286, zip_derived_cl106])).
% 5.58/1.37 thf(zip_derived_cl123, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl92, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl185, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl184, zip_derived_cl166])).
% 5.58/1.37 thf(zip_derived_cl189, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl123, zip_derived_cl185])).
% 5.58/1.37 thf(zip_derived_cl106, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl74, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl206, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl189, zip_derived_cl106])).
% 5.58/1.37 thf(zip_derived_cl104, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl207, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl206, zip_derived_cl104])).
% 5.58/1.37 thf(zip_derived_cl115, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl71, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl208, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl207, zip_derived_cl115])).
% 5.58/1.37 thf(zip_derived_cl288, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl287, zip_derived_cl208])).
% 5.58/1.37 thf(zip_derived_cl106, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl74, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl166, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl162, zip_derived_cl31])).
% 5.58/1.37 thf(zip_derived_cl167, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl166])).
% 5.58/1.37 thf(zip_derived_cl104, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl172, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl167, zip_derived_cl104])).
% 5.58/1.37 thf(zip_derived_cl289, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl288, zip_derived_cl172])).
% 5.58/1.37 thf(zip_derived_cl104, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl290, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl289, zip_derived_cl104])).
% 5.58/1.37 thf(zip_derived_cl115, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl71, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl140, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl58, zip_derived_cl31])).
% 5.58/1.37 thf(zip_derived_cl143, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl115, zip_derived_cl140])).
% 5.58/1.37 thf(zip_derived_cl106, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl74, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl146, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl143, zip_derived_cl106])).
% 5.58/1.37 thf(zip_derived_cl104, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl147, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl146, zip_derived_cl104])).
% 5.58/1.37 thf(zip_derived_cl291, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl290, zip_derived_cl147])).
% 5.58/1.37 thf(zip_derived_cl115, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl71, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl292, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl291, zip_derived_cl115])).
% 5.58/1.37 thf(zip_derived_cl491, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl490, zip_derived_cl292])).
% 5.58/1.37 thf(zip_derived_cl115, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl71, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl492, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl491, zip_derived_cl115])).
% 5.58/1.37 thf(zip_derived_cl104, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl20])).
% 5.58/1.37 thf(zip_derived_cl493, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl492, zip_derived_cl104])).
% 5.58/1.37 thf(zip_derived_cl172, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl167, zip_derived_cl104])).
% 5.58/1.37 thf(zip_derived_cl494, plain,
% 5.58/1.37 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl493, zip_derived_cl172])).
% 5.58/1.37 thf(zip_derived_cl496, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl494])).
% 5.58/1.37 thf(clause_1037, axiom,
% 5.58/1.37 (( ~( LE @
% 5.58/1.37 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_9 ) ) ) ) ) @
% 5.58/1.37 ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 5.58/1.37 ( E @
% 5.58/1.37 ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_9 ) ) ) ) ) ) |
% 5.58/1.37 ( LE @ ( f @ B_9 ) @ ( s @ ( s @ 0 ) ) ))).
% 5.58/1.37 thf(zip_derived_cl49, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @
% 5.58/1.37 (s @ (s @ (s @ 0))))
% 5.58/1.37 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1037])).
% 5.58/1.37 thf(zip_derived_cl494, plain,
% 5.58/1.37 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl493, zip_derived_cl172])).
% 5.58/1.37 thf(zip_derived_cl499, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl49, zip_derived_cl494])).
% 5.58/1.37 thf(clause_957, axiom,
% 5.58/1.37 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( ~( E @
% 5.58/1.37 ( s @ ( s @ 0 ) ) @
% 5.58/1.37 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 5.58/1.37 thf(zip_derived_cl7, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_957])).
% 5.58/1.37 thf(zip_derived_cl537, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl499, zip_derived_cl7])).
% 5.58/1.37 thf(zip_derived_cl627, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl496, zip_derived_cl537])).
% 5.58/1.37 thf(zip_derived_cl629, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl627])).
% 5.58/1.37 thf(zip_derived_cl496, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl494])).
% 5.58/1.37 thf(zip_derived_cl499, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl49, zip_derived_cl494])).
% 5.58/1.37 thf(clause_883, axiom,
% 5.58/1.37 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_10 ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_10 ) @ ( f @ ( suc @ ( suc @ B_10 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_10 ) @ ( f @ ( suc @ B_10 ) ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_10 ) ) ) |
% 5.58/1.37 ( ~( E @
% 5.58/1.37 ( s @ ( s @ 0 ) ) @
% 5.58/1.37 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @
% 5.58/1.37 ( s @ ( s @ 0 ) ) @
% 5.58/1.37 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_10 ) ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_10 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_10 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_10 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_10 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_10 ) ) ) ) ))).
% 5.58/1.37 thf(zip_derived_cl21, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1)))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_883])).
% 5.58/1.37 thf(zip_derived_cl325, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl21])).
% 5.58/1.37 thf(zip_derived_cl326, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl325])).
% 5.58/1.37 thf(zip_derived_cl539, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl499, zip_derived_cl326])).
% 5.58/1.37 thf(zip_derived_cl615, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl496, zip_derived_cl539])).
% 5.58/1.37 thf(zip_derived_cl617, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl615])).
% 5.58/1.37 thf(clause_154, axiom,
% 5.58/1.37 (( ~( LE @ ( f @ ( suc @ ( suc @ B_9 ) ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 5.58/1.37 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_9 ) ) ) ) |
% 5.58/1.37 ( LE @ ( f @ B_9 ) @ ( s @ ( s @ 0 ) ) ))).
% 5.58/1.37 thf(zip_derived_cl19, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_154])).
% 5.58/1.37 thf(zip_derived_cl494, plain,
% 5.58/1.37 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl493, zip_derived_cl172])).
% 5.58/1.37 thf(zip_derived_cl497, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl494])).
% 5.58/1.37 thf(zip_derived_cl618, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl617, zip_derived_cl497])).
% 5.58/1.37 thf(zip_derived_cl497, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl494])).
% 5.58/1.37 thf(clause_1664, axiom,
% 5.58/1.37 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_10 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_10 ) @ ( f @ ( suc @ B_10 ) ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_10 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_10 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_10 ) ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ B_10 ) @ ( f @ ( suc @ ( suc @ B_10 ) ) ) ))).
% 5.58/1.37 thf(zip_derived_cl32, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1664])).
% 5.58/1.37 thf(zip_derived_cl249, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl32])).
% 5.58/1.37 thf(zip_derived_cl250, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl249])).
% 5.58/1.37 thf(clause_768, axiom,
% 5.58/1.37 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 5.58/1.37 thf(zip_derived_cl59, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_768])).
% 5.58/1.37 thf(clause_920, axiom,
% 5.58/1.37 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 5.58/1.37 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 5.58/1.37 thf(zip_derived_cl43, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_920])).
% 5.58/1.37 thf(zip_derived_cl132, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl59, zip_derived_cl43])).
% 5.58/1.37 thf(zip_derived_cl262, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl250, zip_derived_cl132])).
% 5.58/1.37 thf(clause_356, axiom,
% 5.58/1.37 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_10 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_10 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_10 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 5.58/1.37 ( E @ ( f @ B_10 ) @ ( f @ ( suc @ B_10 ) ) ))).
% 5.58/1.37 thf(zip_derived_cl52, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 5.58/1.37 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_356])).
% 5.58/1.37 thf(zip_derived_cl135, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl52])).
% 5.58/1.37 thf(zip_derived_cl136, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl135])).
% 5.58/1.37 thf(zip_derived_cl43, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_920])).
% 5.58/1.37 thf(zip_derived_cl137, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl136, zip_derived_cl43])).
% 5.58/1.37 thf(zip_derived_cl263, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl262, zip_derived_cl137])).
% 5.58/1.37 thf(zip_derived_cl513, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl263])).
% 5.58/1.37 thf(clause_812, axiom,
% 5.58/1.37 (( ~( LE @ ( f @ B_9 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 5.58/1.37 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_9 ) ) |
% 5.58/1.37 ( LE @ ( f @ B_9 ) @ ( s @ ( s @ 0 ) ) ))).
% 5.58/1.37 thf(zip_derived_cl6, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_812])).
% 5.58/1.37 thf(zip_derived_cl494, plain,
% 5.58/1.37 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl493, zip_derived_cl172])).
% 5.58/1.37 thf(zip_derived_cl495, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl6, zip_derived_cl494])).
% 5.58/1.37 thf(zip_derived_cl531, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl513, zip_derived_cl495])).
% 5.58/1.37 thf(clause_933, axiom,
% 5.58/1.37 (( ~( LE @ ( f @ ( suc @ B_9 ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 5.58/1.37 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_9 ) ) ) |
% 5.58/1.37 ( LE @ ( f @ B_9 ) @ ( s @ ( s @ 0 ) ) ))).
% 5.58/1.37 thf(zip_derived_cl27, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0))))
% 5.58/1.37 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_933])).
% 5.58/1.37 thf(zip_derived_cl494, plain,
% 5.58/1.37 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl493, zip_derived_cl172])).
% 5.58/1.37 thf(zip_derived_cl498, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl27, zip_derived_cl494])).
% 5.58/1.37 thf(zip_derived_cl532, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl531, zip_derived_cl498])).
% 5.58/1.37 thf(zip_derived_cl619, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl618, zip_derived_cl532])).
% 5.58/1.37 thf(zip_derived_cl496, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl494])).
% 5.58/1.37 thf(clause_1357, axiom,
% 5.58/1.37 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_10 ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_10 ) @ ( f @ ( suc @ ( suc @ B_10 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_10 ) @ ( f @ ( suc @ B_10 ) ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_10 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_10 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_10 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_10 ) ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ B_10 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_10 ) ) ) ) ))).
% 5.58/1.37 thf(zip_derived_cl88, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1))))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1357])).
% 5.58/1.37 thf(zip_derived_cl399, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl88])).
% 5.58/1.37 thf(zip_derived_cl400, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl399])).
% 5.58/1.37 thf(zip_derived_cl263, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl262, zip_derived_cl137])).
% 5.58/1.37 thf(zip_derived_cl417, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl400, zip_derived_cl263])).
% 5.58/1.37 thf(zip_derived_cl137, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl136, zip_derived_cl43])).
% 5.58/1.37 thf(zip_derived_cl418, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl417, zip_derived_cl137])).
% 5.58/1.37 thf(clause_952, axiom,
% 5.58/1.37 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 5.58/1.37 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 5.58/1.37 thf(zip_derived_cl83, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_952])).
% 5.58/1.37 thf(zip_derived_cl132, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl59, zip_derived_cl43])).
% 5.58/1.37 thf(zip_derived_cl182, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl83, zip_derived_cl132])).
% 5.58/1.37 thf(zip_derived_cl137, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl136, zip_derived_cl43])).
% 5.58/1.37 thf(zip_derived_cl183, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl182, zip_derived_cl137])).
% 5.58/1.37 thf(zip_derived_cl419, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl418, zip_derived_cl183])).
% 5.58/1.37 thf(zip_derived_cl520, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl496, zip_derived_cl419])).
% 5.58/1.37 thf(zip_derived_cl498, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl27, zip_derived_cl494])).
% 5.58/1.37 thf(zip_derived_cl561, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl520, zip_derived_cl498])).
% 5.58/1.37 thf(zip_derived_cl497, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl494])).
% 5.58/1.37 thf(zip_derived_cl562, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl561, zip_derived_cl497])).
% 5.58/1.37 thf(zip_derived_cl495, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl6, zip_derived_cl494])).
% 5.58/1.37 thf(zip_derived_cl563, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl562, zip_derived_cl495])).
% 5.58/1.37 thf(zip_derived_cl620, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl619, zip_derived_cl563])).
% 5.58/1.37 thf(zip_derived_cl498, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl27, zip_derived_cl494])).
% 5.58/1.37 thf(zip_derived_cl621, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl620, zip_derived_cl498])).
% 5.58/1.37 thf(zip_derived_cl498, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl27, zip_derived_cl494])).
% 5.58/1.37 thf(zip_derived_cl137, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl136, zip_derived_cl43])).
% 5.58/1.37 thf(zip_derived_cl506, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl498, zip_derived_cl137])).
% 5.58/1.37 thf(zip_derived_cl495, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl6, zip_derived_cl494])).
% 5.58/1.37 thf(zip_derived_cl524, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl506, zip_derived_cl495])).
% 5.58/1.37 thf(zip_derived_cl622, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl621, zip_derived_cl524])).
% 5.58/1.37 thf(zip_derived_cl495, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl6, zip_derived_cl494])).
% 5.58/1.37 thf(zip_derived_cl623, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (iLEQ @ (suc @ X0) @ (suc @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl622, zip_derived_cl495])).
% 5.58/1.37 thf(zip_derived_cl630, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl629, zip_derived_cl623])).
% 5.58/1.37 thf(zip_derived_cl263, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl262, zip_derived_cl137])).
% 5.58/1.37 thf(zip_derived_cl631, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl630, zip_derived_cl263])).
% 5.58/1.37 thf(zip_derived_cl137, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl136, zip_derived_cl43])).
% 5.58/1.37 thf(zip_derived_cl632, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl631, zip_derived_cl137])).
% 5.58/1.37 thf(zip_derived_cl498, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl27, zip_derived_cl494])).
% 5.58/1.37 thf(zip_derived_cl633, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl632, zip_derived_cl498])).
% 5.58/1.37 thf(zip_derived_cl495, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl6, zip_derived_cl494])).
% 5.58/1.37 thf(zip_derived_cl634, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl633, zip_derived_cl495])).
% 5.58/1.37 thf(zip_derived_cl563, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl562, zip_derived_cl495])).
% 5.58/1.37 thf(zip_derived_cl635, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl634, zip_derived_cl563])).
% 5.58/1.37 thf(zip_derived_cl497, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl494])).
% 5.58/1.37 thf(zip_derived_cl636, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl635, zip_derived_cl497])).
% 5.58/1.37 thf(zip_derived_cl640, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl78, zip_derived_cl636])).
% 5.58/1.37 thf(clause_725, axiom,
% 5.58/1.37 (( ~( LE @
% 5.58/1.37 ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_13 ) ) ) ) ) @
% 5.58/1.37 ( s @ ( s @ 0 ) ) ) ) |
% 5.58/1.37 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_13 ) ) ) ) ) ) |
% 5.58/1.37 ( LE @ ( f @ B_13 ) @ ( s @ 0 ) ))).
% 5.58/1.37 thf(zip_derived_cl3, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ (s @ 0)))
% 5.58/1.37 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_725])).
% 5.58/1.37 thf(zip_derived_cl636, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl635, zip_derived_cl497])).
% 5.58/1.37 thf(zip_derived_cl637, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl636])).
% 5.58/1.37 thf(clause_1725, axiom,
% 5.58/1.37 (( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 5.58/1.37 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 5.58/1.37 thf(zip_derived_cl38, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1725])).
% 5.58/1.37 thf(zip_derived_cl649, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl637, zip_derived_cl38])).
% 5.58/1.37 thf(zip_derived_cl823, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl640, zip_derived_cl649])).
% 5.58/1.37 thf(zip_derived_cl824, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl823])).
% 5.58/1.37 thf(zip_derived_cl640, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl78, zip_derived_cl636])).
% 5.58/1.37 thf(zip_derived_cl637, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl3, zip_derived_cl636])).
% 5.58/1.37 thf(clause_158, axiom,
% 5.58/1.37 (( ~( E @ ( f @ B_14 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_14 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_14 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_14 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_14 ) ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ B_14 ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_14 ) @ ( f @ ( suc @ B_14 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_14 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_14 ) @ ( f @ ( suc @ ( suc @ B_14 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_14 ) ) ))).
% 5.58/1.37 thf(zip_derived_cl61, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_158])).
% 5.58/1.37 thf(zip_derived_cl401, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl61])).
% 5.58/1.37 thf(zip_derived_cl402, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl401])).
% 5.58/1.37 thf(zip_derived_cl651, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl637, zip_derived_cl402])).
% 5.58/1.37 thf(zip_derived_cl790, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl640, zip_derived_cl651])).
% 5.58/1.37 thf(zip_derived_cl791, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl790])).
% 5.58/1.37 thf(clause_484, axiom,
% 5.58/1.37 (( ~( LE @ ( f @ ( suc @ ( suc @ B_13 ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 5.58/1.37 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_13 ) ) ) ) |
% 5.58/1.37 ( LE @ ( f @ B_13 ) @ ( s @ 0 ) ))).
% 5.58/1.37 thf(zip_derived_cl87, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 5.58/1.37 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_484])).
% 5.58/1.37 thf(zip_derived_cl636, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl635, zip_derived_cl497])).
% 5.58/1.37 thf(zip_derived_cl641, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl87, zip_derived_cl636])).
% 5.58/1.37 thf(zip_derived_cl792, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl791, zip_derived_cl641])).
% 5.58/1.37 thf(clause_363, axiom,
% 5.58/1.37 (( ~( LE @ ( f @ ( suc @ B_13 ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 5.58/1.37 ( E @ ( s @ 0 ) @ ( f @ ( suc @ B_13 ) ) ) |
% 5.58/1.37 ( LE @ ( f @ B_13 ) @ ( s @ 0 ) ))).
% 5.58/1.37 thf(zip_derived_cl64, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 5.58/1.37 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_363])).
% 5.58/1.37 thf(zip_derived_cl636, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl635, zip_derived_cl497])).
% 5.58/1.37 thf(zip_derived_cl639, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl636])).
% 5.58/1.37 thf(zip_derived_cl793, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl792, zip_derived_cl639])).
% 5.58/1.37 thf(zip_derived_cl641, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl87, zip_derived_cl636])).
% 5.58/1.37 thf(clause_152, axiom,
% 5.58/1.37 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_14 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_14 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ B_14 ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_14 ) @ ( f @ ( suc @ B_14 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_14 ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ B_14 ) @ ( f @ ( suc @ ( suc @ B_14 ) ) ) ))).
% 5.58/1.37 thf(zip_derived_cl16, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_152])).
% 5.58/1.37 thf(zip_derived_cl247, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl16])).
% 5.58/1.37 thf(zip_derived_cl248, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl247])).
% 5.58/1.37 thf(clause_1310, axiom,
% 5.58/1.37 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_14 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ B_14 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_14 ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 5.58/1.37 ( E @ ( f @ B_14 ) @ ( f @ ( suc @ B_14 ) ) ))).
% 5.58/1.37 thf(zip_derived_cl15, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1310])).
% 5.58/1.37 thf(zip_derived_cl130, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl15])).
% 5.58/1.37 thf(zip_derived_cl131, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl130])).
% 5.58/1.37 thf(clause_1330, axiom,
% 5.58/1.37 (( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 5.58/1.37 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 5.58/1.37 thf(zip_derived_cl29, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1330])).
% 5.58/1.37 thf(zip_derived_cl134, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl131, zip_derived_cl29])).
% 5.58/1.37 thf(zip_derived_cl260, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl248, zip_derived_cl134])).
% 5.58/1.37 thf(clause_625, axiom,
% 5.58/1.37 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 5.58/1.37 thf(zip_derived_cl81, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_625])).
% 5.58/1.37 thf(zip_derived_cl29, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1330])).
% 5.58/1.37 thf(zip_derived_cl129, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl81, zip_derived_cl29])).
% 5.58/1.37 thf(zip_derived_cl261, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl260, zip_derived_cl129])).
% 5.58/1.37 thf(zip_derived_cl671, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl641, zip_derived_cl261])).
% 5.58/1.37 thf(clause_141, axiom,
% 5.58/1.37 (( ~( LE @ ( f @ B_13 ) @ ( s @ ( s @ 0 ) ) ) ) |
% 5.58/1.37 ( E @ ( s @ 0 ) @ ( f @ B_13 ) ) | ( LE @ ( f @ B_13 ) @ ( s @ 0 ) ))).
% 5.58/1.37 thf(zip_derived_cl9, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.58/1.37 | (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_141])).
% 5.58/1.37 thf(zip_derived_cl636, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl635, zip_derived_cl497])).
% 5.58/1.37 thf(zip_derived_cl638, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl636])).
% 5.58/1.37 thf(zip_derived_cl684, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl671, zip_derived_cl638])).
% 5.58/1.37 thf(zip_derived_cl639, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl636])).
% 5.58/1.37 thf(zip_derived_cl685, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl684, zip_derived_cl639])).
% 5.58/1.37 thf(zip_derived_cl794, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl793, zip_derived_cl685])).
% 5.58/1.37 thf(zip_derived_cl639, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl636])).
% 5.58/1.37 thf(zip_derived_cl134, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl131, zip_derived_cl29])).
% 5.58/1.37 thf(zip_derived_cl659, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl639, zip_derived_cl134])).
% 5.58/1.37 thf(zip_derived_cl638, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl636])).
% 5.58/1.37 thf(zip_derived_cl663, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl659, zip_derived_cl638])).
% 5.58/1.37 thf(zip_derived_cl795, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl794, zip_derived_cl663])).
% 5.58/1.37 thf(zip_derived_cl640, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl78, zip_derived_cl636])).
% 5.58/1.37 thf(clause_1237, axiom,
% 5.58/1.37 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_14 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_14 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ B_14 ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_14 ) @ ( f @ ( suc @ B_14 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_14 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_14 ) @ ( f @ ( suc @ ( suc @ B_14 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_14 ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ B_14 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_14 ) ) ) ) ))).
% 5.58/1.37 thf(zip_derived_cl10, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1237])).
% 5.58/1.37 thf(zip_derived_cl225, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 5.58/1.37 thf(zip_derived_cl226, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl225])).
% 5.58/1.37 thf(zip_derived_cl134, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl131, zip_derived_cl29])).
% 5.58/1.37 thf(zip_derived_cl229, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl226, zip_derived_cl134])).
% 5.58/1.37 thf(clause_8, axiom,
% 5.58/1.37 (( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 5.58/1.37 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 5.58/1.37 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 5.58/1.37 thf(zip_derived_cl73, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_8])).
% 5.58/1.37 thf(zip_derived_cl129, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl81, zip_derived_cl29])).
% 5.58/1.37 thf(zip_derived_cl163, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl73, zip_derived_cl129])).
% 5.58/1.37 thf(zip_derived_cl134, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl131, zip_derived_cl29])).
% 5.58/1.37 thf(zip_derived_cl164, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl163, zip_derived_cl134])).
% 5.58/1.37 thf(zip_derived_cl230, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl229, zip_derived_cl164])).
% 5.58/1.37 thf(zip_derived_cl682, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl640, zip_derived_cl230])).
% 5.58/1.37 thf(zip_derived_cl641, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl87, zip_derived_cl636])).
% 5.58/1.37 thf(zip_derived_cl717, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl682, zip_derived_cl641])).
% 5.58/1.37 thf(zip_derived_cl639, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl636])).
% 5.58/1.37 thf(zip_derived_cl718, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl717, zip_derived_cl639])).
% 5.58/1.37 thf(zip_derived_cl685, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl684, zip_derived_cl639])).
% 5.58/1.37 thf(zip_derived_cl719, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl718, zip_derived_cl685])).
% 5.58/1.37 thf(zip_derived_cl638, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl636])).
% 5.58/1.37 thf(zip_derived_cl720, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl719, zip_derived_cl638])).
% 5.58/1.37 thf(zip_derived_cl796, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl795, zip_derived_cl720])).
% 5.58/1.37 thf(zip_derived_cl638, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl636])).
% 5.58/1.37 thf(zip_derived_cl797, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (iLEQ @ (suc @ X0) @ (suc @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl796, zip_derived_cl638])).
% 5.58/1.37 thf(zip_derived_cl825, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl824, zip_derived_cl797])).
% 5.58/1.37 thf(zip_derived_cl261, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl260, zip_derived_cl129])).
% 5.58/1.37 thf(zip_derived_cl826, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl825, zip_derived_cl261])).
% 5.58/1.37 thf(zip_derived_cl641, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl87, zip_derived_cl636])).
% 5.58/1.37 thf(zip_derived_cl827, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl826, zip_derived_cl641])).
% 5.58/1.37 thf(zip_derived_cl639, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl636])).
% 5.58/1.37 thf(zip_derived_cl828, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl827, zip_derived_cl639])).
% 5.58/1.37 thf(zip_derived_cl720, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl719, zip_derived_cl638])).
% 5.58/1.37 thf(zip_derived_cl829, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl828, zip_derived_cl720])).
% 5.58/1.37 thf(zip_derived_cl663, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl659, zip_derived_cl638])).
% 5.58/1.37 thf(zip_derived_cl830, plain,
% 5.58/1.37 (![X0 : $i]: (~ (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl829, zip_derived_cl663])).
% 5.58/1.37 thf(zip_derived_cl638, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl636])).
% 5.58/1.37 thf(zip_derived_cl831, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl830, zip_derived_cl638])).
% 5.58/1.37 thf(zip_derived_cl833, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl25, zip_derived_cl831])).
% 5.58/1.37 thf(clause_781, axiom,
% 5.58/1.37 (( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ B_17 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_17 ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ B_17 ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_17 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ A_4 ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ B_17 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_17 ) ) ) ) ))).
% 5.58/1.37 thf(zip_derived_cl56, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X1))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X1)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1))))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_781])).
% 5.58/1.37 thf(zip_derived_cl369, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl56])).
% 5.58/1.37 thf(zip_derived_cl370, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl369])).
% 5.58/1.37 thf(clause_112, axiom,
% 5.58/1.37 (( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ A_4 ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 5.58/1.37 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 5.58/1.37 thf(zip_derived_cl94, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_112])).
% 5.58/1.37 thf(clause_17, axiom,
% 5.58/1.37 (( ~( E @ 0 @ ( f @ ( suc @ B_17 ) ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_17 ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ B_17 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ A_4 ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) |
% 5.58/1.37 ( E @ ( f @ B_17 ) @ ( f @ ( suc @ B_17 ) ) ))).
% 5.58/1.37 thf(zip_derived_cl2, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X1))
% 5.58/1.37 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_17])).
% 5.58/1.37 thf(zip_derived_cl121, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl2])).
% 5.58/1.37 thf(zip_derived_cl122, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl121])).
% 5.58/1.37 thf(clause_1728, axiom,
% 5.58/1.37 (( ~( E @ 0 @ ( f @ A_4 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) |
% 5.58/1.37 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 5.58/1.37 thf(zip_derived_cl82, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1728])).
% 5.58/1.37 thf(zip_derived_cl133, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl122, zip_derived_cl82])).
% 5.58/1.37 thf(zip_derived_cl154, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl94, zip_derived_cl133])).
% 5.58/1.37 thf(clause_1373, axiom,
% 5.58/1.37 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ A_4 ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 5.58/1.37 thf(zip_derived_cl33, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1373])).
% 5.58/1.37 thf(zip_derived_cl82, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1728])).
% 5.58/1.37 thf(zip_derived_cl120, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl33, zip_derived_cl82])).
% 5.58/1.37 thf(zip_derived_cl155, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl154, zip_derived_cl120])).
% 5.58/1.37 thf(zip_derived_cl380, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl370, zip_derived_cl155])).
% 5.58/1.37 thf(zip_derived_cl133, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl122, zip_derived_cl82])).
% 5.58/1.37 thf(zip_derived_cl381, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl380, zip_derived_cl133])).
% 5.58/1.37 thf(clause_1217, axiom,
% 5.58/1.37 (( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ B_17 ) ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_17 ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ B_17 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ A_4 ) ) ) |
% 5.58/1.37 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( E @ ( f @ B_17 ) @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ))).
% 5.58/1.37 thf(zip_derived_cl47, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X1))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1)))))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1217])).
% 5.58/1.37 thf(zip_derived_cl218, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl47])).
% 5.58/1.37 thf(zip_derived_cl219, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl218])).
% 5.58/1.37 thf(zip_derived_cl120, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl33, zip_derived_cl82])).
% 5.58/1.37 thf(zip_derived_cl227, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl219, zip_derived_cl120])).
% 5.58/1.37 thf(zip_derived_cl133, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl122, zip_derived_cl82])).
% 5.58/1.37 thf(zip_derived_cl228, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl227, zip_derived_cl133])).
% 5.58/1.37 thf(zip_derived_cl382, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl381, zip_derived_cl228])).
% 5.58/1.37 thf(zip_derived_cl856, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0)
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl833, zip_derived_cl382])).
% 5.58/1.37 thf(clause_246, axiom,
% 5.58/1.37 (( ~( LE @ ( f @ ( suc @ ( suc @ B_16 ) ) ) @ ( s @ 0 ) ) ) |
% 5.58/1.37 ( E @ 0 @ ( f @ ( suc @ ( suc @ B_16 ) ) ) ) | ( LE @ ( f @ B_16 ) @ 0 ))).
% 5.58/1.37 thf(zip_derived_cl99, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 5.58/1.37 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_246])).
% 5.58/1.37 thf(zip_derived_cl831, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl830, zip_derived_cl638])).
% 5.58/1.37 thf(zip_derived_cl836, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl99, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl904, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl856, zip_derived_cl836])).
% 5.58/1.37 thf(clause_1657, axiom,
% 5.58/1.37 (( ~( LE @ ( f @ B_16 ) @ ( s @ 0 ) ) ) | ( E @ 0 @ ( f @ B_16 ) ) |
% 5.58/1.37 ( LE @ ( f @ B_16 ) @ 0 ))).
% 5.58/1.37 thf(zip_derived_cl4, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (LE @ (f @ X0) @ (s @ 0))
% 5.58/1.37 | (E @ 0 @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1657])).
% 5.58/1.37 thf(zip_derived_cl831, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl830, zip_derived_cl638])).
% 5.58/1.37 thf(zip_derived_cl832, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl905, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0)
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl904, zip_derived_cl832])).
% 5.58/1.37 thf(clause_35, axiom,
% 5.58/1.37 (( ~( LE @ ( f @ ( suc @ B_16 ) ) @ ( s @ 0 ) ) ) |
% 5.58/1.37 ( E @ 0 @ ( f @ ( suc @ B_16 ) ) ) | ( LE @ ( f @ B_16 ) @ 0 ))).
% 5.58/1.37 thf(zip_derived_cl42, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 5.58/1.37 | (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_35])).
% 5.58/1.37 thf(zip_derived_cl831, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl830, zip_derived_cl638])).
% 5.58/1.37 thf(zip_derived_cl834, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl42, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl906, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl905, zip_derived_cl834])).
% 5.58/1.37 thf(clause_1079, axiom,
% 5.58/1.37 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_16 ) ) ) ) ) @ ( s @ 0 ) ) ) |
% 5.58/1.37 ( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_16 ) ) ) ) ) ) |
% 5.58/1.37 ( LE @ ( f @ B_16 ) @ 0 ))).
% 5.58/1.37 thf(zip_derived_cl79, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (LE @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))) @ (s @ 0))
% 5.58/1.37 | (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_1079])).
% 5.58/1.37 thf(zip_derived_cl831, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl830, zip_derived_cl638])).
% 5.58/1.37 thf(zip_derived_cl835, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl79, zip_derived_cl831])).
% 5.58/1.37 thf(clause_440, axiom,
% 5.58/1.37 (( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ A_4 ) ) ) | ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 5.58/1.37 thf(zip_derived_cl66, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_440])).
% 5.58/1.37 thf(zip_derived_cl863, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0)
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl835, zip_derived_cl66])).
% 5.58/1.37 thf(zip_derived_cl993, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0)
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl906, zip_derived_cl863])).
% 5.58/1.37 thf(zip_derived_cl999, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl993])).
% 5.58/1.37 thf(zip_derived_cl833, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl25, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl835, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl79, zip_derived_cl831])).
% 5.58/1.37 thf(clause_72, axiom,
% 5.58/1.37 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B_17 ) ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ B_17 ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ) ) |
% 5.58/1.37 ( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_17 ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_17 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ B_17 ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_17 ) ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 5.58/1.37 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 5.58/1.37 ( ~( E @ 0 @ ( f @ A_4 ) ) ))).
% 5.58/1.37 thf(zip_derived_cl93, plain,
% 5.58/1.37 (![X0 : $i, X1 : $i]:
% 5.58/1.37 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X1))))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X1)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.58/1.37 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X1)))),
% 5.58/1.37 inference('cnf', [status(esa)], [clause_72])).
% 5.58/1.37 thf(zip_derived_cl397, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('eq_fact', [status(thm)], [zip_derived_cl93])).
% 5.58/1.37 thf(zip_derived_cl398, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0)))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl397])).
% 5.58/1.37 thf(zip_derived_cl865, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0)
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl835, zip_derived_cl398])).
% 5.58/1.37 thf(zip_derived_cl950, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0)
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl833, zip_derived_cl865])).
% 5.58/1.37 thf(zip_derived_cl953, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('simplify', [status(thm)], [zip_derived_cl950])).
% 5.58/1.37 thf(zip_derived_cl832, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl954, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0)
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl953, zip_derived_cl832])).
% 5.58/1.37 thf(zip_derived_cl836, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl99, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl955, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl954, zip_derived_cl836])).
% 5.58/1.37 thf(zip_derived_cl834, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl42, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl133, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl122, zip_derived_cl82])).
% 5.58/1.37 thf(zip_derived_cl843, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0)
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl834, zip_derived_cl133])).
% 5.58/1.37 thf(zip_derived_cl832, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl867, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ (f @ X0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl843, zip_derived_cl832])).
% 5.58/1.37 thf(zip_derived_cl956, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0)
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl955, zip_derived_cl867])).
% 5.58/1.37 thf(zip_derived_cl906, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl905, zip_derived_cl834])).
% 5.58/1.37 thf(zip_derived_cl957, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl956, zip_derived_cl906])).
% 5.58/1.37 thf(zip_derived_cl836, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl99, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl228, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl227, zip_derived_cl133])).
% 5.58/1.37 thf(zip_derived_cl854, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0)
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('sup-', [status(thm)], [zip_derived_cl836, zip_derived_cl228])).
% 5.58/1.37 thf(zip_derived_cl832, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl874, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl854, zip_derived_cl832])).
% 5.58/1.37 thf(zip_derived_cl834, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl42, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl875, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0) | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl874, zip_derived_cl834])).
% 5.58/1.37 thf(zip_derived_cl958, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0)
% 5.58/1.37 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl957, zip_derived_cl875])).
% 5.58/1.37 thf(zip_derived_cl834, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl42, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl959, plain,
% 5.58/1.37 (![X0 : $i]: (~ (iLEQ @ (suc @ X0) @ (suc @ X0)) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl958, zip_derived_cl834])).
% 5.58/1.37 thf(zip_derived_cl1005, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0)
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0)))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl999, zip_derived_cl959])).
% 5.58/1.37 thf(zip_derived_cl133, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl122, zip_derived_cl82])).
% 5.58/1.37 thf(zip_derived_cl1006, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ 0 @ (f @ X0))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl1005, zip_derived_cl133])).
% 5.58/1.37 thf(zip_derived_cl832, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl1007, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0)
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl1006, zip_derived_cl832])).
% 5.58/1.37 thf(zip_derived_cl833, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl25, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl1008, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl1007, zip_derived_cl833])).
% 5.58/1.37 thf(zip_derived_cl875, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0) | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl874, zip_derived_cl834])).
% 5.58/1.37 thf(zip_derived_cl1009, plain,
% 5.58/1.37 (![X0 : $i]:
% 5.58/1.37 ( (LE @ (f @ X0) @ 0)
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.58/1.37 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl1008, zip_derived_cl875])).
% 5.58/1.37 thf(zip_derived_cl836, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl99, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl1010, plain,
% 5.58/1.37 (![X0 : $i]: (~ (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl1009, zip_derived_cl836])).
% 5.58/1.37 thf(zip_derived_cl834, plain,
% 5.58/1.37 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl42, zip_derived_cl831])).
% 5.58/1.37 thf(zip_derived_cl1011, plain, (![X0 : $i]: (LE @ (f @ X0) @ 0)),
% 5.58/1.37 inference('clc', [status(thm)], [zip_derived_cl1010, zip_derived_cl834])).
% 5.58/1.37 thf(zip_derived_cl1012, plain, ($false),
% 5.58/1.37 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl1011])).
% 5.58/1.37
% 5.58/1.37 % SZS output end Refutation
% 5.58/1.37
% 5.58/1.37
% 5.58/1.37 % Terminating...
% 5.58/1.44 % Runner terminated.
% 5.58/1.45 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------