TSTP Solution File: SYO682-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO682-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.zlfAeZTQCX true
% Computer : n019.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 05:52:33 EDT 2023
% Result : Unsatisfiable 8.47s 1.86s
% Output : Refutation 9.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO682-1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.zlfAeZTQCX true
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sat Aug 26 03:38:58 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.35 % Number of cores: 8
% 0.15/0.35 % Python version: Python 3.6.8
% 0.15/0.35 % Running in FO mode
% 0.20/0.66 % Total configuration time : 435
% 0.20/0.66 % Estimated wc time : 1092
% 0.20/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.77 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.77 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.20/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.35/0.83 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 8.47/1.86 % Solved by fo/fo7.sh.
% 8.47/1.86 % done 555 iterations in 0.993s
% 8.47/1.86 % SZS status Unsatisfiable for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 8.47/1.86 % SZS output start Refutation
% 8.47/1.86 thf(f_type, type, f: $i > $i).
% 8.47/1.86 thf(0_type, type, 0: $i).
% 8.47/1.86 thf(iLEQ_type, type, iLEQ: $i > $i > $o).
% 8.47/1.86 thf(LE_type, type, LE: $i > $i > $o).
% 8.47/1.86 thf(s_type, type, s: $i > $i).
% 8.47/1.86 thf(z_type, type, z: $i).
% 8.47/1.86 thf(E_type, type, E: $i > $i > $o).
% 8.47/1.86 thf(suc_type, type, suc: $i > $i).
% 8.47/1.86 thf(clause_2217, axiom,
% 8.47/1.86 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 8.47/1.86 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 8.47/1.86 ( ~( E @ 0 @ ( f @ A_4 ) ) ) | ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 8.47/1.86 thf(zip_derived_cl9, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ 0 @ (f @ X0))
% 8.47/1.86 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2217])).
% 8.47/1.86 thf(clause_2899, axiom,
% 8.47/1.86 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_140 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ 0 ) @ ( f @ B_140 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_138 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ 0 ) @ ( f @ B_138 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_139 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 8.47/1.86 ( ~( iLEQ @ ( suc @ B_139 ) @ ( suc @ B_140 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ 0 ) @ ( f @ B_139 ) ) ) |
% 8.47/1.86 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_138 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 8.47/1.86 ( ~( iLEQ @ ( suc @ B_138 ) @ ( suc @ B_139 ) ) ) |
% 8.47/1.86 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 8.47/1.86 ( E @ ( f @ B_138 ) @ ( f @ ( suc @ B_138 ) ) ) |
% 8.47/1.86 ( E @ ( f @ B_139 ) @ ( f @ ( suc @ B_139 ) ) ) |
% 8.47/1.86 ( E @ ( f @ B_140 ) @ ( f @ ( suc @ B_140 ) ) ))).
% 8.47/1.86 thf(zip_derived_cl74, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 8.47/1.86 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ X1))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ X2))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X3) @ (suc @ X1))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ X3))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 8.47/1.86 | (E @ (f @ X3) @ (f @ (suc @ X3)))
% 8.47/1.86 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2899])).
% 8.47/1.86 thf(zip_derived_cl477, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i]:
% 8.47/1.86 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ X1))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ X1))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('eq_fact', [status(thm)], [zip_derived_cl74])).
% 8.47/1.86 thf(zip_derived_cl479, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i]:
% 8.47/1.86 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ X1))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.47/1.86 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl477])).
% 8.47/1.86 thf(zip_derived_cl493, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('eq_fact', [status(thm)], [zip_derived_cl479])).
% 8.47/1.86 thf(zip_derived_cl494, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl493])).
% 8.47/1.86 thf(clause_2240, axiom,
% 8.47/1.86 (( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 8.47/1.86 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 8.47/1.86 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 8.47/1.86 thf(zip_derived_cl51, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ 0) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2240])).
% 8.47/1.86 thf(zip_derived_cl501, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl494, zip_derived_cl51])).
% 8.47/1.86 thf(clause_491, axiom,
% 8.47/1.86 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 8.47/1.86 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 8.47/1.86 thf(zip_derived_cl39, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.47/1.86 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_491])).
% 8.47/1.86 thf(clause_2095, axiom,
% 8.47/1.86 (( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_113 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 8.47/1.86 ( ~( iLEQ @ ( suc @ B_114 ) @ ( suc @ B_115 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_115 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_114 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_114 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_113 ) ) ) |
% 8.47/1.86 ( ~( iLEQ @ ( suc @ B_113 ) @ ( suc @ B_114 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_115 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_113 ) ) ) ) |
% 8.47/1.86 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 8.47/1.86 ( E @ ( f @ B_113 ) @ ( f @ ( suc @ B_113 ) ) ) |
% 8.47/1.86 ( E @ ( f @ B_114 ) @ ( f @ ( suc @ B_114 ) ) ) |
% 8.47/1.86 ( E @ ( f @ B_115 ) @ ( f @ ( suc @ B_115 ) ) ))).
% 8.47/1.86 thf(zip_derived_cl72, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 8.47/1.86 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X3))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X3)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.47/1.86 | (E @ (f @ X3) @ (f @ (suc @ X3))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2095])).
% 8.47/1.86 thf(zip_derived_cl536, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i]:
% 8.47/1.86 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1))))),
% 8.47/1.86 inference('eq_fact', [status(thm)], [zip_derived_cl72])).
% 8.47/1.86 thf(zip_derived_cl538, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i]:
% 8.47/1.86 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl536])).
% 8.47/1.86 thf(zip_derived_cl557, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('eq_fact', [status(thm)], [zip_derived_cl538])).
% 8.47/1.86 thf(zip_derived_cl558, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl557])).
% 8.47/1.86 thf(clause_1537, axiom,
% 8.47/1.86 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 8.47/1.86 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 8.47/1.86 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 8.47/1.86 thf(zip_derived_cl26, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1537])).
% 8.47/1.86 thf(zip_derived_cl564, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl558, zip_derived_cl26])).
% 8.47/1.86 thf(clause_777, axiom,
% 8.47/1.86 (( ~( LE @ ( f @ B_68 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 8.47/1.86 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_68 ) ) |
% 8.47/1.86 ( LE @ ( f @ B_68 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 8.47/1.86 thf(zip_derived_cl47, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_777])).
% 8.47/1.86 thf(clause_2205, axiom, (LE @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 8.47/1.86 thf(zip_derived_cl22, plain,
% 8.47/1.86 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2205])).
% 8.47/1.86 thf(zip_derived_cl109, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 8.47/1.86 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl22])).
% 8.47/1.86 thf(clause_679, axiom,
% 8.47/1.86 (( ~( LE @ ( f @ ( suc @ ( suc @ B_112 ) ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 8.47/1.86 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_112 ) ) ) ) |
% 8.47/1.86 ( LE @ ( f @ B_112 ) @ ( s @ ( s @ 0 ) ) ))).
% 8.47/1.86 thf(zip_derived_cl67, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_679])).
% 8.47/1.86 thf(zip_derived_cl112, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl67])).
% 8.47/1.86 thf(clause_1799, axiom,
% 8.47/1.86 (( ~( LE @ ( f @ ( suc @ ( suc @ B_137 ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 8.47/1.86 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_137 ) ) ) ) |
% 8.47/1.86 ( LE @ ( f @ B_137 ) @ ( s @ 0 ) ))).
% 8.47/1.86 thf(zip_derived_cl27, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1799])).
% 8.47/1.86 thf(zip_derived_cl126, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl112, zip_derived_cl27])).
% 8.47/1.86 thf(clause_165, axiom,
% 8.47/1.86 (( ~( LE @ ( f @ B_149 ) @ ( s @ 0 ) ) ) | ( E @ 0 @ ( f @ B_149 ) ) |
% 8.47/1.86 ( LE @ ( f @ B_149 ) @ 0 ))).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl398, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl126, zip_derived_cl42])).
% 8.47/1.86 thf(clause_1450, axiom, (~( LE @ ( f @ z ) @ 0 ))).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl517, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl398, zip_derived_cl52])).
% 8.47/1.86 thf(clause_1131, axiom,
% 8.47/1.86 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 8.47/1.86 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 8.47/1.86 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 8.47/1.86 thf(zip_derived_cl85, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1131])).
% 8.47/1.86 thf(clause_2897, axiom,
% 8.47/1.86 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_69 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_70 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_71 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_70 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_69 ) ) ) ) |
% 8.47/1.86 ( ~( iLEQ @ ( suc @ B_70 ) @ ( suc @ B_71 ) ) ) |
% 8.47/1.86 ( ~( iLEQ @ ( suc @ B_69 ) @ ( suc @ B_70 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 8.47/1.86 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_69 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_71 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 8.47/1.86 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 8.47/1.86 ( E @ ( f @ B_69 ) @ ( f @ ( suc @ B_69 ) ) ) |
% 8.47/1.86 ( E @ ( f @ B_70 ) @ ( f @ ( suc @ B_70 ) ) ) |
% 8.47/1.86 ( E @ ( f @ B_71 ) @ ( f @ ( suc @ B_71 ) ) ))).
% 8.47/1.86 thf(zip_derived_cl66, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X3))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X3)))
% 8.47/1.86 | (E @ (f @ X3) @ (f @ (suc @ X3)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | (E @ (f @ X2) @ (f @ (suc @ X2))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2897])).
% 8.47/1.86 thf(zip_derived_cl589, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i]:
% 8.47/1.86 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 8.47/1.86 inference('eq_fact', [status(thm)], [zip_derived_cl66])).
% 8.47/1.86 thf(zip_derived_cl591, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 8.47/1.86 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl589])).
% 8.47/1.86 thf(zip_derived_cl85, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1131])).
% 8.47/1.86 thf(zip_derived_cl597, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i]:
% 8.47/1.86 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl591, zip_derived_cl85])).
% 8.47/1.86 thf(zip_derived_cl601, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl597])).
% 8.47/1.86 thf(zip_derived_cl605, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl601])).
% 8.47/1.86 thf(clause_190, axiom,
% 8.47/1.86 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_71 ) ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_69 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_70 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_71 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_70 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_69 ) ) ) ) |
% 8.47/1.86 ( ~( iLEQ @ ( suc @ B_70 ) @ ( suc @ B_71 ) ) ) |
% 8.47/1.86 ( ~( E @ ( f @ B_69 ) @ ( f @ ( suc @ B_69 ) ) ) ) |
% 8.47/1.86 ( ~( iLEQ @ ( suc @ B_69 ) @ ( suc @ B_70 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 8.47/1.86 ( ~( E @ ( f @ B_70 ) @ ( f @ ( suc @ B_70 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_69 ) ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_70 ) ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 8.47/1.86 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_69 ) ) ) |
% 8.47/1.86 ( ~( E @ ( f @ B_71 ) @ ( f @ ( suc @ B_71 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_71 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ))).
% 8.47/1.86 thf(zip_derived_cl43, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X3))
% 8.47/1.86 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X3))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X2))))
% 8.47/1.86 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X3) @ (suc @ X1))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X3))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_190])).
% 8.47/1.86 thf(zip_derived_cl184, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1))))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('eq_fact', [status(thm)], [zip_derived_cl43])).
% 8.47/1.86 thf(zip_derived_cl186, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl184])).
% 8.47/1.86 thf(zip_derived_cl202, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('eq_fact', [status(thm)], [zip_derived_cl186])).
% 8.47/1.86 thf(zip_derived_cl203, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl202])).
% 8.47/1.86 thf(clause_2710, axiom,
% 8.47/1.86 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 8.47/1.86 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 8.47/1.86 thf(zip_derived_cl7, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2710])).
% 8.47/1.86 thf(zip_derived_cl208, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl203, zip_derived_cl7])).
% 8.47/1.86 thf(zip_derived_cl606, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl605, zip_derived_cl208])).
% 8.47/1.86 thf(zip_derived_cl607, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 8.47/1.86 thf(zip_derived_cl656, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl517, zip_derived_cl607])).
% 8.47/1.86 thf(clause_1426, axiom,
% 8.47/1.86 (( ~( LE @ ( f @ ( suc @ B_68 ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 8.47/1.86 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_68 ) ) ) |
% 8.47/1.86 ( LE @ ( f @ B_68 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 8.47/1.86 thf(zip_derived_cl69, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ (s @ 0)))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1426])).
% 8.47/1.86 thf(zip_derived_cl22, plain,
% 8.47/1.86 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2205])).
% 8.47/1.86 thf(zip_derived_cl130, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 8.47/1.86 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl22])).
% 8.47/1.86 thf(zip_derived_cl67, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_679])).
% 8.47/1.86 thf(zip_derived_cl132, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl67])).
% 8.47/1.86 thf(zip_derived_cl27, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1799])).
% 8.47/1.86 thf(zip_derived_cl155, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl27])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl435, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl155, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl529, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl435, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl857, plain,
% 8.47/1.86 ((~ (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl656, zip_derived_cl529])).
% 8.47/1.86 thf(clause_1737, axiom,
% 8.47/1.86 (( ~( LE @
% 8.47/1.86 ( f @ ( suc @ ( suc @ B_68 ) ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 8.47/1.86 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_68 ) ) ) ) |
% 8.47/1.86 ( LE @ ( f @ B_68 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 8.47/1.86 thf(zip_derived_cl10, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ (s @ 0)))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1737])).
% 8.47/1.86 thf(zip_derived_cl22, plain,
% 8.47/1.86 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2205])).
% 8.47/1.86 thf(zip_derived_cl134, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 8.47/1.86 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl22])).
% 8.47/1.86 thf(zip_derived_cl67, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_679])).
% 8.47/1.86 thf(zip_derived_cl136, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl67])).
% 8.47/1.86 thf(zip_derived_cl27, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1799])).
% 8.47/1.86 thf(zip_derived_cl158, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl27])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl439, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl158, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl550, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl439, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl858, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | (E @ 0 @ (f @ z)))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl857, zip_derived_cl550])).
% 8.47/1.86 thf(zip_derived_cl109, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 8.47/1.86 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl22])).
% 8.47/1.86 thf(clause_988, axiom,
% 8.47/1.86 (( ~( LE @ ( f @ ( suc @ B_112 ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 8.47/1.86 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_112 ) ) ) |
% 8.47/1.86 ( LE @ ( f @ B_112 ) @ ( s @ ( s @ 0 ) ) ))).
% 8.47/1.86 thf(zip_derived_cl82, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_988])).
% 8.47/1.86 thf(zip_derived_cl111, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl82])).
% 8.47/1.86 thf(zip_derived_cl27, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1799])).
% 8.47/1.86 thf(zip_derived_cl118, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl27])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl250, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl445, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl250, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl607, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 8.47/1.86 thf(zip_derived_cl640, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl445, zip_derived_cl607])).
% 8.47/1.86 thf(zip_derived_cl130, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 8.47/1.86 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl22])).
% 8.47/1.86 thf(zip_derived_cl82, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_988])).
% 8.47/1.86 thf(zip_derived_cl133, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl82])).
% 8.47/1.86 thf(zip_derived_cl27, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1799])).
% 8.47/1.86 thf(zip_derived_cl149, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl27])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl352, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl149, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl468, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl352, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl820, plain,
% 8.47/1.86 ((~ (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl640, zip_derived_cl468])).
% 8.47/1.86 thf(zip_derived_cl134, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 8.47/1.86 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl22])).
% 8.47/1.86 thf(zip_derived_cl82, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_988])).
% 8.47/1.86 thf(zip_derived_cl137, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl82])).
% 8.47/1.86 thf(zip_derived_cl27, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1799])).
% 8.47/1.86 thf(zip_derived_cl152, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl27])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl401, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl152, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl518, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl401, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl821, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ 0 @ (f @ z)))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl820, zip_derived_cl518])).
% 8.47/1.86 thf(zip_derived_cl109, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 8.47/1.86 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl22])).
% 8.47/1.86 thf(clause_2414, axiom,
% 8.47/1.86 (( ~( LE @ ( f @ B_112 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 8.47/1.86 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_112 ) ) |
% 8.47/1.86 ( LE @ ( f @ B_112 ) @ ( s @ ( s @ 0 ) ) ))).
% 8.47/1.86 thf(zip_derived_cl59, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2414])).
% 8.47/1.86 thf(zip_derived_cl110, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl59])).
% 8.47/1.86 thf(zip_derived_cl27, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1799])).
% 8.47/1.86 thf(zip_derived_cl115, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl27])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl228, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl115, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl363, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl228, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl607, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 8.47/1.86 thf(zip_derived_cl627, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl363, zip_derived_cl607])).
% 8.47/1.86 thf(zip_derived_cl130, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 8.47/1.86 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl22])).
% 8.47/1.86 thf(zip_derived_cl59, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2414])).
% 8.47/1.86 thf(zip_derived_cl131, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl59])).
% 8.47/1.86 thf(zip_derived_cl27, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1799])).
% 8.47/1.86 thf(zip_derived_cl140, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl27])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl244, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl140, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl407, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl244, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl769, plain,
% 8.47/1.86 ((~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl627, zip_derived_cl407])).
% 8.47/1.86 thf(zip_derived_cl134, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 8.47/1.86 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl22])).
% 8.47/1.86 thf(zip_derived_cl59, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2414])).
% 8.47/1.86 thf(zip_derived_cl135, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl59])).
% 8.47/1.86 thf(zip_derived_cl27, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1799])).
% 8.47/1.86 thf(zip_derived_cl143, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl135, zip_derived_cl27])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl346, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl446, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl346, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl770, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ 0 @ (f @ z)))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl769, zip_derived_cl446])).
% 8.47/1.86 thf(clause_1659, axiom,
% 8.47/1.86 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 8.47/1.86 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 8.47/1.86 thf(zip_derived_cl78, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1659])).
% 8.47/1.86 thf(clause_2044, axiom,
% 8.47/1.86 (( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_113 ) ) ) |
% 8.47/1.86 ( ~( E @ ( f @ B_113 ) @ ( f @ ( suc @ B_113 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_114 ) ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 8.47/1.86 ( ~( iLEQ @ ( suc @ B_114 ) @ ( suc @ B_115 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_113 ) ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_115 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_114 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_115 ) ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_114 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_113 ) ) ) |
% 8.47/1.86 ( ~( iLEQ @ ( suc @ B_113 ) @ ( suc @ B_114 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_115 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( f @ B_114 ) @ ( f @ ( suc @ B_114 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 8.47/1.86 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_113 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 8.47/1.86 ( ~( E @ ( f @ B_115 ) @ ( f @ ( suc @ B_115 ) ) ) ))).
% 8.47/1.86 thf(zip_derived_cl70, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 8.47/1.86 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.47/1.86 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X2))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X3))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X3))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X3)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (f @ X3) @ (f @ (suc @ X3))))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2044])).
% 8.47/1.86 thf(zip_derived_cl86, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i]:
% 8.47/1.86 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 8.47/1.86 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('eq_fact', [status(thm)], [zip_derived_cl70])).
% 8.47/1.86 thf(zip_derived_cl88, plain,
% 8.47/1.86 (![X0 : $i, X1 : $i]:
% 8.47/1.86 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl86])).
% 8.47/1.86 thf(zip_derived_cl90, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('eq_fact', [status(thm)], [zip_derived_cl88])).
% 8.47/1.86 thf(zip_derived_cl91, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl90])).
% 8.47/1.86 thf(zip_derived_cl129, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl78, zip_derived_cl91])).
% 8.47/1.86 thf(zip_derived_cl771, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl770, zip_derived_cl129])).
% 8.47/1.86 thf(zip_derived_cl823, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ 0 @ (f @ z)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl821, zip_derived_cl771])).
% 8.47/1.86 thf(zip_derived_cl825, plain,
% 8.47/1.86 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ 0 @ (f @ z)))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl823])).
% 8.47/1.86 thf(zip_derived_cl861, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl858, zip_derived_cl825])).
% 8.47/1.86 thf(zip_derived_cl865, plain,
% 8.47/1.86 ((~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ 0 @ (f @ z)))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl861])).
% 8.47/1.86 thf(zip_derived_cl869, plain,
% 8.47/1.86 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl564, zip_derived_cl865])).
% 8.47/1.86 thf(zip_derived_cl770, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ 0 @ (f @ z)))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl769, zip_derived_cl446])).
% 8.47/1.86 thf(zip_derived_cl871, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl869, zip_derived_cl770])).
% 8.47/1.86 thf(zip_derived_cl821, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ 0 @ (f @ z)))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl820, zip_derived_cl518])).
% 8.47/1.86 thf(zip_derived_cl872, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl871, zip_derived_cl821])).
% 8.47/1.86 thf(zip_derived_cl132, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl67])).
% 8.47/1.86 thf(clause_2463, axiom,
% 8.47/1.86 (( ~( LE @ ( f @ ( suc @ B_137 ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 8.47/1.86 ( E @ ( s @ 0 ) @ ( f @ ( suc @ B_137 ) ) ) |
% 8.47/1.86 ( LE @ ( f @ B_137 ) @ ( s @ 0 ) ))).
% 8.47/1.86 thf(zip_derived_cl12, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2463])).
% 8.47/1.86 thf(zip_derived_cl154, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl12])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl349, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl154, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl447, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl349, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl112, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl67])).
% 8.47/1.86 thf(zip_derived_cl12, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2463])).
% 8.47/1.86 thf(zip_derived_cl125, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl112, zip_derived_cl12])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl241, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl125, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl406, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl241, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl607, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 8.47/1.86 thf(zip_derived_cl636, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl406, zip_derived_cl607])).
% 8.47/1.86 thf(zip_derived_cl564, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl558, zip_derived_cl26])).
% 8.47/1.86 thf(zip_derived_cl111, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl82])).
% 8.47/1.86 thf(zip_derived_cl12, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2463])).
% 8.47/1.86 thf(zip_derived_cl117, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl12])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl219, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl117, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl355, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl219, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl607, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 8.47/1.86 thf(zip_derived_cl625, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl355, zip_derived_cl607])).
% 8.47/1.86 thf(zip_derived_cl133, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl82])).
% 8.47/1.86 thf(zip_derived_cl12, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2463])).
% 8.47/1.86 thf(zip_derived_cl148, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl12])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl231, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl148, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl364, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl231, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl726, plain,
% 8.47/1.86 ((~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl625, zip_derived_cl364])).
% 8.47/1.86 thf(zip_derived_cl137, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl82])).
% 8.47/1.86 thf(zip_derived_cl12, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2463])).
% 8.47/1.86 thf(zip_derived_cl151, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl12])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl247, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @
% 8.47/1.86 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl408, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl247, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl727, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ 0 @ (f @ z)))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl726, zip_derived_cl408])).
% 8.47/1.86 thf(zip_derived_cl110, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl59])).
% 8.47/1.86 thf(zip_derived_cl12, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2463])).
% 8.47/1.86 thf(zip_derived_cl114, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl12])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl168, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl234, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl168, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl607, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 8.47/1.86 thf(zip_derived_cl618, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl234, zip_derived_cl607])).
% 8.47/1.86 thf(zip_derived_cl131, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl59])).
% 8.47/1.86 thf(zip_derived_cl12, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2463])).
% 8.47/1.86 thf(zip_derived_cl139, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl12])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl213, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl139, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl253, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl213, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl697, plain,
% 8.47/1.86 ((~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl618, zip_derived_cl253])).
% 8.47/1.86 thf(zip_derived_cl135, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl59])).
% 8.47/1.86 thf(zip_derived_cl12, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_2463])).
% 8.47/1.86 thf(zip_derived_cl142, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl135, zip_derived_cl12])).
% 8.47/1.86 thf(zip_derived_cl42, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.47/1.86 | (E @ 0 @ (f @ X0))
% 8.47/1.86 | (LE @ (f @ X0) @ 0))),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_165])).
% 8.47/1.86 thf(zip_derived_cl222, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | (LE @ (f @ X0) @ 0)
% 8.47/1.86 | (E @ 0 @ (f @ X0)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl42])).
% 8.47/1.86 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.47/1.86 inference('cnf', [status(esa)], [clause_1450])).
% 8.47/1.86 thf(zip_derived_cl356, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl222, zip_derived_cl52])).
% 8.47/1.86 thf(zip_derived_cl698, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ 0 @ (f @ z)))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl697, zip_derived_cl356])).
% 8.47/1.86 thf(zip_derived_cl129, plain,
% 8.47/1.86 (![X0 : $i]:
% 8.47/1.86 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.47/1.86 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl78, zip_derived_cl91])).
% 8.47/1.86 thf(zip_derived_cl699, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl698, zip_derived_cl129])).
% 8.47/1.86 thf(zip_derived_cl729, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.47/1.86 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ 0 @ (f @ z)))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl727, zip_derived_cl699])).
% 8.47/1.86 thf(zip_derived_cl731, plain,
% 8.47/1.86 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ 0 @ (f @ z)))),
% 8.47/1.86 inference('simplify', [status(thm)], [zip_derived_cl729])).
% 8.47/1.86 thf(zip_derived_cl734, plain,
% 8.47/1.86 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.47/1.86 inference('sup-', [status(thm)], [zip_derived_cl564, zip_derived_cl731])).
% 8.47/1.86 thf(zip_derived_cl698, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ 0 @ (f @ z)))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl697, zip_derived_cl356])).
% 8.47/1.86 thf(zip_derived_cl736, plain,
% 8.47/1.86 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ 0 @ (f @ z))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z)))))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl734, zip_derived_cl698])).
% 8.47/1.86 thf(zip_derived_cl727, plain,
% 8.47/1.86 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.47/1.86 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.47/1.86 | (E @ 0 @ (f @ z)))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl726, zip_derived_cl408])).
% 8.47/1.86 thf(zip_derived_cl737, plain,
% 8.47/1.86 (( (E @ 0 @ (f @ z))
% 8.47/1.86 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.47/1.86 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.47/1.86 inference('clc', [status(thm)], [zip_derived_cl736, zip_derived_cl727])).
% 8.97/1.87 thf(zip_derived_cl772, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl636, zip_derived_cl737])).
% 8.97/1.87 thf(zip_derived_cl773, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl447, zip_derived_cl772])).
% 8.97/1.87 thf(zip_derived_cl788, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl773])).
% 8.97/1.87 thf(zip_derived_cl136, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl67])).
% 8.97/1.87 thf(zip_derived_cl12, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2463])).
% 8.97/1.87 thf(zip_derived_cl157, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl12])).
% 8.97/1.87 thf(zip_derived_cl42, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_165])).
% 8.97/1.87 thf(zip_derived_cl358, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl157, zip_derived_cl42])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl469, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl358, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl792, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl788, zip_derived_cl469])).
% 8.97/1.87 thf(zip_derived_cl737, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl736, zip_derived_cl727])).
% 8.97/1.87 thf(zip_derived_cl793, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl792, zip_derived_cl737])).
% 8.97/1.87 thf(zip_derived_cl132, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl67])).
% 8.97/1.87 thf(clause_1914, axiom,
% 8.97/1.87 (( ~( LE @ ( f @ B_137 ) @ ( s @ ( s @ 0 ) ) ) ) |
% 8.97/1.87 ( E @ ( s @ 0 ) @ ( f @ B_137 ) ) | ( LE @ ( f @ B_137 ) @ ( s @ 0 ) ))).
% 8.97/1.87 thf(zip_derived_cl21, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1914])).
% 8.97/1.87 thf(zip_derived_cl153, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl21])).
% 8.97/1.87 thf(zip_derived_cl42, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_165])).
% 8.97/1.87 thf(zip_derived_cl225, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl153, zip_derived_cl42])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl357, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl225, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl112, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl67])).
% 8.97/1.87 thf(zip_derived_cl21, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1914])).
% 8.97/1.87 thf(zip_derived_cl124, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl112, zip_derived_cl21])).
% 8.97/1.87 thf(zip_derived_cl42, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_165])).
% 8.97/1.87 thf(zip_derived_cl174, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl124, zip_derived_cl42])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl237, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl174, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl607, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 8.97/1.87 thf(zip_derived_cl622, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl237, zip_derived_cl607])).
% 8.97/1.87 thf(zip_derived_cl111, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl82])).
% 8.97/1.87 thf(zip_derived_cl21, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1914])).
% 8.97/1.87 thf(zip_derived_cl116, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl21])).
% 8.97/1.87 thf(zip_derived_cl42, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_165])).
% 8.97/1.87 thf(zip_derived_cl162, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl42])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl211, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl162, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl607, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 8.97/1.87 thf(zip_derived_cl617, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl211, zip_derived_cl607])).
% 8.97/1.87 thf(zip_derived_cl133, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl82])).
% 8.97/1.87 thf(zip_derived_cl21, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1914])).
% 8.97/1.87 thf(zip_derived_cl147, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl21])).
% 8.97/1.87 thf(zip_derived_cl42, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_165])).
% 8.97/1.87 thf(zip_derived_cl171, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl147, zip_derived_cl42])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl235, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl171, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl682, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl617, zip_derived_cl235])).
% 8.97/1.87 thf(zip_derived_cl137, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl82])).
% 8.97/1.87 thf(zip_derived_cl21, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1914])).
% 8.97/1.87 thf(zip_derived_cl150, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl21])).
% 8.97/1.87 thf(zip_derived_cl42, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_165])).
% 8.97/1.87 thf(zip_derived_cl216, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl150, zip_derived_cl42])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl254, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl216, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl683, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl682, zip_derived_cl254])).
% 8.97/1.87 thf(zip_derived_cl564, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl558, zip_derived_cl26])).
% 8.97/1.87 thf(zip_derived_cl110, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl59])).
% 8.97/1.87 thf(zip_derived_cl21, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1914])).
% 8.97/1.87 thf(zip_derived_cl113, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl21])).
% 8.97/1.87 thf(zip_derived_cl42, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_165])).
% 8.97/1.87 thf(zip_derived_cl144, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl113, zip_derived_cl42])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl209, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ z))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl144, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl607, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 8.97/1.87 thf(zip_derived_cl615, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ z))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl209, zip_derived_cl607])).
% 8.97/1.87 thf(zip_derived_cl131, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl59])).
% 8.97/1.87 thf(zip_derived_cl21, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1914])).
% 8.97/1.87 thf(zip_derived_cl138, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl21])).
% 8.97/1.87 thf(zip_derived_cl42, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_165])).
% 8.97/1.87 thf(zip_derived_cl159, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl138, zip_derived_cl42])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl210, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl159, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl674, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ z))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl615, zip_derived_cl210])).
% 8.97/1.87 thf(zip_derived_cl135, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl59])).
% 8.97/1.87 thf(zip_derived_cl21, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1914])).
% 8.97/1.87 thf(zip_derived_cl141, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl135, zip_derived_cl21])).
% 8.97/1.87 thf(zip_derived_cl42, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_165])).
% 8.97/1.87 thf(zip_derived_cl165, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl141, zip_derived_cl42])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl212, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl165, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl675, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ z))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl674, zip_derived_cl212])).
% 8.97/1.87 thf(zip_derived_cl129, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl78, zip_derived_cl91])).
% 8.97/1.87 thf(zip_derived_cl676, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (f @ z) @ (f @ (suc @ z))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl675, zip_derived_cl129])).
% 8.97/1.87 thf(zip_derived_cl678, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ 0)) @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl564, zip_derived_cl676])).
% 8.97/1.87 thf(zip_derived_cl680, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ z)))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl678])).
% 8.97/1.87 thf(zip_derived_cl675, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ z))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl674, zip_derived_cl212])).
% 8.97/1.87 thf(zip_derived_cl681, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl680, zip_derived_cl675])).
% 8.97/1.87 thf(zip_derived_cl685, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl683, zip_derived_cl681])).
% 8.97/1.87 thf(zip_derived_cl686, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl685])).
% 8.97/1.87 thf(zip_derived_cl700, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl622, zip_derived_cl686])).
% 8.97/1.87 thf(zip_derived_cl701, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl357, zip_derived_cl700])).
% 8.97/1.87 thf(zip_derived_cl715, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl701])).
% 8.97/1.87 thf(zip_derived_cl136, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl67])).
% 8.97/1.87 thf(zip_derived_cl21, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0)))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1914])).
% 8.97/1.87 thf(zip_derived_cl156, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl21])).
% 8.97/1.87 thf(zip_derived_cl42, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ X0))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_165])).
% 8.97/1.87 thf(zip_derived_cl238, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl156, zip_derived_cl42])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl365, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl238, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl720, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl715, zip_derived_cl365])).
% 8.97/1.87 thf(zip_derived_cl686, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl685])).
% 8.97/1.87 thf(zip_derived_cl721, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl720, zip_derived_cl686])).
% 8.97/1.87 thf(zip_derived_cl501, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl494, zip_derived_cl51])).
% 8.97/1.87 thf(zip_derived_cl721, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl720, zip_derived_cl686])).
% 8.97/1.87 thf(clause_1275, axiom,
% 8.97/1.87 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_140 ) ) ) ) |
% 8.97/1.87 ( ~( E @ ( s @ 0 ) @ ( f @ B_140 ) ) ) |
% 8.97/1.87 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_138 ) ) ) ) |
% 8.97/1.87 ( ~( E @ ( s @ 0 ) @ ( f @ B_138 ) ) ) |
% 8.97/1.87 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_139 ) ) ) ) |
% 8.97/1.87 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 8.97/1.87 ( ~( iLEQ @ ( suc @ B_139 ) @ ( suc @ B_140 ) ) ) |
% 8.97/1.87 ( ~( E @ ( f @ B_138 ) @ ( f @ ( suc @ B_138 ) ) ) ) |
% 8.97/1.87 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_140 ) ) ) ) ) |
% 8.97/1.87 ( ~( E @ ( f @ B_140 ) @ ( f @ ( suc @ B_140 ) ) ) ) |
% 8.97/1.87 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 8.97/1.87 ( ~( E @ ( f @ B_139 ) @ ( f @ ( suc @ B_139 ) ) ) ) |
% 8.97/1.87 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_139 ) ) ) ) ) |
% 8.97/1.87 ( ~( E @ ( s @ 0 ) @ ( f @ B_139 ) ) ) |
% 8.97/1.87 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_138 ) ) ) |
% 8.97/1.87 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 8.97/1.87 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_138 ) ) ) ) ) |
% 8.97/1.87 ( ~( iLEQ @ ( suc @ B_138 ) @ ( suc @ B_139 ) ) ) |
% 8.97/1.87 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ))).
% 8.97/1.87 thf(zip_derived_cl6, plain,
% 8.97/1.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 8.97/1.87 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 8.97/1.87 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 8.97/1.87 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X2))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X3) @ (suc @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X3))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X3)))))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1275])).
% 8.97/1.87 thf(zip_derived_cl722, plain,
% 8.97/1.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.97/1.87 ( (E @ 0 @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 8.97/1.87 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X2))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl721, zip_derived_cl6])).
% 8.97/1.87 thf(zip_derived_cl1030, plain,
% 8.97/1.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.97/1.87 (~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X1))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X2))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl501, zip_derived_cl722])).
% 8.97/1.87 thf(zip_derived_cl1033, plain,
% 8.97/1.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.97/1.87 ( (E @ 0 @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X2))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 8.97/1.87 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl1030])).
% 8.97/1.87 thf(zip_derived_cl1034, plain,
% 8.97/1.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.97/1.87 ( (E @ 0 @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X1))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X2))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl721, zip_derived_cl1033])).
% 8.97/1.87 thf(zip_derived_cl1035, plain,
% 8.97/1.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.97/1.87 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X2))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 8.97/1.87 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl1034])).
% 8.97/1.87 thf(zip_derived_cl1036, plain,
% 8.97/1.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.97/1.87 ( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X1))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X2))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl793, zip_derived_cl1035])).
% 8.97/1.87 thf(zip_derived_cl1038, plain,
% 8.97/1.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.97/1.87 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X2))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 8.97/1.87 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl1036])).
% 8.97/1.87 thf(zip_derived_cl1039, plain,
% 8.97/1.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.97/1.87 ( (E @ 0 @ (f @ z))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X1))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X2))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl872, zip_derived_cl1038])).
% 8.97/1.87 thf(zip_derived_cl1042, plain,
% 8.97/1.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.97/1.87 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X2))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X1))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 8.97/1.87 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl1039])).
% 8.97/1.87 thf(zip_derived_cl1046, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ 0 @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('eq_fact', [status(thm)], [zip_derived_cl1042])).
% 8.97/1.87 thf(zip_derived_cl1048, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl1046])).
% 8.97/1.87 thf(zip_derived_cl39, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_491])).
% 8.97/1.87 thf(zip_derived_cl1053, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ 0 @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl1048, zip_derived_cl39])).
% 8.97/1.87 thf(zip_derived_cl501, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl494, zip_derived_cl51])).
% 8.97/1.87 thf(zip_derived_cl1054, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl1053, zip_derived_cl501])).
% 8.97/1.87 thf(zip_derived_cl1056, plain,
% 8.97/1.87 ((~ (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ 0 @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl1054])).
% 8.97/1.87 thf(zip_derived_cl1058, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl1056])).
% 8.97/1.87 thf(zip_derived_cl872, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl871, zip_derived_cl821])).
% 8.97/1.87 thf(zip_derived_cl1059, plain,
% 8.97/1.87 ((~ (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl1058, zip_derived_cl872])).
% 8.97/1.87 thf(zip_derived_cl721, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl720, zip_derived_cl686])).
% 8.97/1.87 thf(zip_derived_cl1060, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (f @ z) @ (f @ (suc @ z))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl1059, zip_derived_cl721])).
% 8.97/1.87 thf(zip_derived_cl793, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl792, zip_derived_cl737])).
% 8.97/1.87 thf(zip_derived_cl1061, plain,
% 8.97/1.87 ((~ (E @ (f @ z) @ (f @ (suc @ z))) | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl1060, zip_derived_cl793])).
% 8.97/1.87 thf(zip_derived_cl1062, plain,
% 8.97/1.87 ((~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ z))
% 8.97/1.87 | (E @ 0 @ (f @ z)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl501, zip_derived_cl1061])).
% 8.97/1.87 thf(zip_derived_cl793, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl792, zip_derived_cl737])).
% 8.97/1.87 thf(zip_derived_cl1065, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z)) | ~ (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl1062, zip_derived_cl793])).
% 8.97/1.87 thf(zip_derived_cl721, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ z)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl720, zip_derived_cl686])).
% 8.97/1.87 thf(zip_derived_cl1066, plain, ( (E @ 0 @ (f @ z))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl1065, zip_derived_cl721])).
% 8.97/1.87 thf(zip_derived_cl1066, plain, ( (E @ 0 @ (f @ z))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl1065, zip_derived_cl721])).
% 8.97/1.87 thf(zip_derived_cl1066, plain, ( (E @ 0 @ (f @ z))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl1065, zip_derived_cl721])).
% 8.97/1.87 thf(clause_2749, axiom,
% 8.97/1.87 (( ~( E @ 0 @ ( f @ B_152 ) ) ) | ( ~( E @ 0 @ ( f @ B_151 ) ) ) |
% 8.97/1.87 ( ~( iLEQ @ ( suc @ B_151 ) @ ( suc @ B_152 ) ) ) |
% 8.97/1.87 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 8.97/1.87 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_150 ) ) ) ) ) |
% 8.97/1.87 ( ~( E @ ( f @ B_150 ) @ ( f @ ( suc @ B_150 ) ) ) ) |
% 8.97/1.87 ( ~( E @ 0 @ ( f @ ( suc @ B_150 ) ) ) ) |
% 8.97/1.87 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_152 ) ) ) ) ) |
% 8.97/1.87 ( ~( E @ 0 @ ( f @ B_150 ) ) ) |
% 8.97/1.87 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_151 ) ) ) ) ) |
% 8.97/1.87 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 8.97/1.87 ( ~( E @ 0 @ ( f @ ( suc @ B_152 ) ) ) ) |
% 8.97/1.87 ( ~( iLEQ @ ( suc @ B_150 ) @ ( suc @ B_151 ) ) ) |
% 8.97/1.87 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 8.97/1.87 ( ~( E @ ( f @ B_151 ) @ ( f @ ( suc @ B_151 ) ) ) ) |
% 8.97/1.87 ( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_150 ) ) ) |
% 8.97/1.87 ( ~( E @ ( f @ B_152 ) @ ( f @ ( suc @ B_152 ) ) ) ) |
% 8.97/1.87 ( ~( E @ 0 @ ( f @ A_4 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ B_151 ) ) ) ))).
% 8.97/1.87 thf(zip_derived_cl48, plain,
% 8.97/1.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 8.97/1.87 (~ (E @ 0 @ (f @ X0))
% 8.97/1.87 | ~ (E @ 0 @ (f @ X1))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 8.97/1.87 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ 0 @ (f @ (suc @ (suc @ X3))))
% 8.97/1.87 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 8.97/1.87 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 8.97/1.87 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ 0 @ (f @ X3))
% 8.97/1.87 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 8.97/1.87 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 8.97/1.87 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X3) @ (suc @ X1))
% 8.97/1.87 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ 0 @ (f @ X2))
% 8.97/1.87 | ~ (E @ 0 @ (f @ (suc @ X1))))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2749])).
% 8.97/1.87 thf(zip_derived_cl1074, plain,
% 8.97/1.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.97/1.87 (~ (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ 0 @ (f @ X1))
% 8.97/1.87 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 8.97/1.87 | ~ (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 8.97/1.87 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ 0 @ (f @ X2))
% 8.97/1.87 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 8.97/1.87 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 8.97/1.87 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 8.97/1.87 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 8.97/1.87 | ~ (E @ 0 @ (f @ X0)))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl1066, zip_derived_cl48])).
% 8.97/1.87 thf(zip_derived_cl501, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl494, zip_derived_cl51])).
% 8.97/1.87 thf(zip_derived_cl39, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ 0) @ (f @ X0))
% 8.97/1.87 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_491])).
% 8.97/1.87 thf(zip_derived_cl564, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl558, zip_derived_cl26])).
% 8.97/1.87 thf(zip_derived_cl126, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl112, zip_derived_cl27])).
% 8.97/1.87 thf(clause_2704, axiom,
% 8.97/1.87 (( ~( LE @ ( f @ ( suc @ B_149 ) ) @ ( s @ 0 ) ) ) |
% 8.97/1.87 ( E @ 0 @ ( f @ ( suc @ B_149 ) ) ) | ( LE @ ( f @ B_149 ) @ 0 ))).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl400, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl126, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl690, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl400, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl607, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 8.97/1.87 thf(zip_derived_cl836, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl690, zip_derived_cl607])).
% 8.97/1.87 thf(zip_derived_cl155, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl27])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl437, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl155, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl762, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl437, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl986, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl836, zip_derived_cl762])).
% 8.97/1.87 thf(zip_derived_cl158, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl27])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl441, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl158, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl766, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl441, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl987, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl986, zip_derived_cl766])).
% 8.97/1.87 thf(zip_derived_cl118, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl27])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl252, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl547, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl252, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl607, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 8.97/1.87 thf(zip_derived_cl662, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl547, zip_derived_cl607])).
% 8.97/1.87 thf(zip_derived_cl149, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl27])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl354, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl149, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl580, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl354, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl970, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl662, zip_derived_cl580])).
% 8.97/1.87 thf(zip_derived_cl152, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl27])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl403, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl152, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl691, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl403, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl971, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl970, zip_derived_cl691])).
% 8.97/1.87 thf(zip_derived_cl115, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl27])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl230, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl115, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl514, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl230, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl607, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 8.97/1.87 thf(zip_derived_cl644, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl514, zip_derived_cl607])).
% 8.97/1.87 thf(zip_derived_cl140, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl27])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl246, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl140, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl527, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl246, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl901, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl644, zip_derived_cl527])).
% 8.97/1.87 thf(zip_derived_cl143, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl135, zip_derived_cl27])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl348, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl548, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl902, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl901, zip_derived_cl548])).
% 8.97/1.87 thf(zip_derived_cl129, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl78, zip_derived_cl91])).
% 8.97/1.87 thf(zip_derived_cl903, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | ~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl902, zip_derived_cl129])).
% 8.97/1.87 thf(zip_derived_cl973, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | ~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl971, zip_derived_cl903])).
% 8.97/1.87 thf(zip_derived_cl975, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | ~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl973])).
% 8.97/1.87 thf(zip_derived_cl990, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | ~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl987, zip_derived_cl975])).
% 8.97/1.87 thf(zip_derived_cl995, plain,
% 8.97/1.87 ((~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl990])).
% 8.97/1.87 thf(zip_derived_cl999, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl564, zip_derived_cl995])).
% 8.97/1.87 thf(zip_derived_cl902, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl901, zip_derived_cl548])).
% 8.97/1.87 thf(zip_derived_cl1002, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl999, zip_derived_cl902])).
% 8.97/1.87 thf(zip_derived_cl971, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl970, zip_derived_cl691])).
% 8.97/1.87 thf(zip_derived_cl1003, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl1002, zip_derived_cl971])).
% 8.97/1.87 thf(zip_derived_cl564, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl558, zip_derived_cl26])).
% 8.97/1.87 thf(zip_derived_cl125, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl112, zip_derived_cl12])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl243, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl125, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl526, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl243, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl607, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 8.97/1.87 thf(zip_derived_cl658, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl526, zip_derived_cl607])).
% 8.97/1.87 thf(zip_derived_cl154, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl12])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl351, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl154, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl549, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl351, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl904, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl658, zip_derived_cl549])).
% 8.97/1.87 thf(zip_derived_cl157, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl12])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl360, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl157, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl581, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl360, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl905, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl904, zip_derived_cl581])).
% 8.97/1.87 thf(zip_derived_cl117, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl12])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl221, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl117, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl465, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl221, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl607, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 8.97/1.87 thf(zip_derived_cl642, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl465, zip_derived_cl607])).
% 8.97/1.87 thf(zip_derived_cl148, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl12])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl233, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl148, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl515, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl233, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl849, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl642, zip_derived_cl515])).
% 8.97/1.87 thf(zip_derived_cl151, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl12])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl249, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl528, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl249, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl850, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl849, zip_derived_cl528])).
% 8.97/1.87 thf(zip_derived_cl114, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl12])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl170, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl404, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl170, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl607, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 8.97/1.87 thf(zip_derived_cl628, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl404, zip_derived_cl607])).
% 8.97/1.87 thf(zip_derived_cl139, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl12])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl215, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl139, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl443, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl215, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl795, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl628, zip_derived_cl443])).
% 8.97/1.87 thf(zip_derived_cl142, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 8.97/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl135, zip_derived_cl12])).
% 8.97/1.87 thf(zip_derived_cl75, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 8.97/1.87 | (LE @ (f @ X0) @ 0))),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 8.97/1.87 thf(zip_derived_cl224, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 8.97/1.87 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 8.97/1.87 | (LE @ (f @ X0) @ 0)
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl75])).
% 8.97/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 8.97/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 8.97/1.87 thf(zip_derived_cl466, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl224, zip_derived_cl52])).
% 8.97/1.87 thf(zip_derived_cl796, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl795, zip_derived_cl466])).
% 8.97/1.87 thf(zip_derived_cl129, plain,
% 8.97/1.87 (![X0 : $i]:
% 8.97/1.87 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 8.97/1.87 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl78, zip_derived_cl91])).
% 8.97/1.87 thf(zip_derived_cl797, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl796, zip_derived_cl129])).
% 8.97/1.87 thf(zip_derived_cl852, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl850, zip_derived_cl797])).
% 8.97/1.87 thf(zip_derived_cl854, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 8.97/1.87 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl852])).
% 8.97/1.87 thf(zip_derived_cl908, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl905, zip_derived_cl854])).
% 8.97/1.87 thf(zip_derived_cl913, plain,
% 8.97/1.87 ((~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('simplify', [status(thm)], [zip_derived_cl908])).
% 8.97/1.87 thf(zip_derived_cl918, plain,
% 8.97/1.87 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('sup-', [status(thm)], [zip_derived_cl564, zip_derived_cl913])).
% 8.97/1.87 thf(zip_derived_cl796, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl795, zip_derived_cl466])).
% 8.97/1.87 thf(zip_derived_cl920, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z)))
% 8.97/1.87 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl918, zip_derived_cl796])).
% 8.97/1.87 thf(zip_derived_cl850, plain,
% 8.97/1.87 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 8.97/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 8.97/1.87 | (E @ 0 @ (f @ (suc @ z))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl849, zip_derived_cl528])).
% 8.97/1.87 thf(zip_derived_cl921, plain,
% 8.97/1.87 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 8.97/1.87 inference('clc', [status(thm)], [zip_derived_cl920, zip_derived_cl850])).
% 9.03/1.87 thf(zip_derived_cl153, plain,
% 9.03/1.87 (![X0 : $i]:
% 9.03/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.87 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.87 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl21])).
% 9.03/1.87 thf(zip_derived_cl75, plain,
% 9.03/1.87 (![X0 : $i]:
% 9.03/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 9.03/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.87 | (LE @ (f @ X0) @ 0))),
% 9.03/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 9.03/1.87 thf(zip_derived_cl227, plain,
% 9.03/1.87 (![X0 : $i]:
% 9.03/1.87 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.87 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.87 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.87 | (LE @ (f @ X0) @ 0)
% 9.03/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 9.03/1.87 inference('sup-', [status(thm)], [zip_derived_cl153, zip_derived_cl75])).
% 9.03/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.87 thf(zip_derived_cl467, plain,
% 9.03/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.87 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.87 inference('sup-', [status(thm)], [zip_derived_cl227, zip_derived_cl52])).
% 9.03/1.87 thf(zip_derived_cl124, plain,
% 9.03/1.87 (![X0 : $i]:
% 9.03/1.87 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.87 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.87 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.87 inference('sup-', [status(thm)], [zip_derived_cl112, zip_derived_cl21])).
% 9.03/1.87 thf(zip_derived_cl75, plain,
% 9.03/1.87 (![X0 : $i]:
% 9.03/1.87 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 9.03/1.87 | (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.87 | (LE @ (f @ X0) @ 0))),
% 9.03/1.87 inference('cnf', [status(esa)], [clause_2704])).
% 9.03/1.87 thf(zip_derived_cl176, plain,
% 9.03/1.87 (![X0 : $i]:
% 9.03/1.87 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.87 | (LE @ (f @ X0) @ 0)
% 9.03/1.87 | (E @ 0 @ (f @ (suc @ X0))))),
% 9.03/1.87 inference('sup-', [status(thm)], [zip_derived_cl124, zip_derived_cl75])).
% 9.03/1.87 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.87 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.87 thf(zip_derived_cl442, plain,
% 9.03/1.87 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.87 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.87 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.87 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.87 inference('sup-', [status(thm)], [zip_derived_cl176, zip_derived_cl52])).
% 9.03/1.87 thf(zip_derived_cl607, plain,
% 9.03/1.87 (![X0 : $i]:
% 9.03/1.87 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 9.03/1.87 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 9.03/1.87 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 9.03/1.87 thf(zip_derived_cl638, plain,
% 9.03/1.87 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl442, zip_derived_cl607])).
% 9.03/1.88 thf(zip_derived_cl564, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl558, zip_derived_cl26])).
% 9.03/1.88 thf(zip_derived_cl116, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl75, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2704])).
% 9.03/1.88 thf(zip_derived_cl164, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl75])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl361, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl164, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl607, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 9.03/1.88 thf(zip_derived_cl626, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl361, zip_derived_cl607])).
% 9.03/1.88 thf(zip_derived_cl147, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl75, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2704])).
% 9.03/1.88 thf(zip_derived_cl173, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl147, zip_derived_cl75])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl405, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl173, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl745, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl626, zip_derived_cl405])).
% 9.03/1.88 thf(zip_derived_cl150, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl75, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2704])).
% 9.03/1.88 thf(zip_derived_cl218, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl150, zip_derived_cl75])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl444, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl218, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl746, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl745, zip_derived_cl444])).
% 9.03/1.88 thf(zip_derived_cl113, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ X0))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl75, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2704])).
% 9.03/1.88 thf(zip_derived_cl146, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl113, zip_derived_cl75])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl236, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl146, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl607, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 9.03/1.88 thf(zip_derived_cl619, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl236, zip_derived_cl607])).
% 9.03/1.88 thf(zip_derived_cl138, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ X0))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl75, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2704])).
% 9.03/1.88 thf(zip_derived_cl161, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl138, zip_derived_cl75])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl345, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl161, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl723, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl619, zip_derived_cl345])).
% 9.03/1.88 thf(zip_derived_cl141, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ X0))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl135, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl75, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2704])).
% 9.03/1.88 thf(zip_derived_cl167, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl141, zip_derived_cl75])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl362, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl167, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl724, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl723, zip_derived_cl362])).
% 9.03/1.88 thf(zip_derived_cl129, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl78, zip_derived_cl91])).
% 9.03/1.88 thf(zip_derived_cl725, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl724, zip_derived_cl129])).
% 9.03/1.88 thf(zip_derived_cl748, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl746, zip_derived_cl725])).
% 9.03/1.88 thf(zip_derived_cl749, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl748])).
% 9.03/1.88 thf(zip_derived_cl751, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl564, zip_derived_cl749])).
% 9.03/1.88 thf(zip_derived_cl724, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl723, zip_derived_cl362])).
% 9.03/1.88 thf(zip_derived_cl759, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl751, zip_derived_cl724])).
% 9.03/1.88 thf(zip_derived_cl746, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl745, zip_derived_cl444])).
% 9.03/1.88 thf(zip_derived_cl760, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl759, zip_derived_cl746])).
% 9.03/1.88 thf(zip_derived_cl798, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl638, zip_derived_cl760])).
% 9.03/1.88 thf(zip_derived_cl799, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl467, zip_derived_cl798])).
% 9.03/1.88 thf(zip_derived_cl812, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl799])).
% 9.03/1.88 thf(zip_derived_cl156, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl75, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2704])).
% 9.03/1.88 thf(zip_derived_cl240, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl156, zip_derived_cl75])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl516, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl240, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl817, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl812, zip_derived_cl516])).
% 9.03/1.88 thf(zip_derived_cl760, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl759, zip_derived_cl746])).
% 9.03/1.88 thf(zip_derived_cl818, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl817, zip_derived_cl760])).
% 9.03/1.88 thf(zip_derived_cl501, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl494, zip_derived_cl51])).
% 9.03/1.88 thf(zip_derived_cl921, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl920, zip_derived_cl850])).
% 9.03/1.88 thf(zip_derived_cl818, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl817, zip_derived_cl760])).
% 9.03/1.88 thf(zip_derived_cl6, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.03/1.88 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X3))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X3)))))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1275])).
% 9.03/1.88 thf(zip_derived_cl819, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 ( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl818, zip_derived_cl6])).
% 9.03/1.88 thf(zip_derived_cl1106, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 ( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl921, zip_derived_cl819])).
% 9.03/1.88 thf(zip_derived_cl1108, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1106])).
% 9.03/1.88 thf(zip_derived_cl1109, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl501, zip_derived_cl1108])).
% 9.03/1.88 thf(zip_derived_cl1112, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 ( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl818, zip_derived_cl1109])).
% 9.03/1.88 thf(zip_derived_cl1113, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1112])).
% 9.03/1.88 thf(zip_derived_cl1114, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 ( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl921, zip_derived_cl1113])).
% 9.03/1.88 thf(zip_derived_cl1116, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 (~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1114])).
% 9.03/1.88 thf(zip_derived_cl1117, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 ( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl1003, zip_derived_cl1116])).
% 9.03/1.88 thf(zip_derived_cl1119, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 (~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1117])).
% 9.03/1.88 thf(zip_derived_cl1124, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('eq_fact', [status(thm)], [zip_derived_cl1119])).
% 9.03/1.88 thf(zip_derived_cl1126, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1124])).
% 9.03/1.88 thf(zip_derived_cl501, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl494, zip_derived_cl51])).
% 9.03/1.88 thf(zip_derived_cl1130, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1126, zip_derived_cl501])).
% 9.03/1.88 thf(zip_derived_cl1134, plain,
% 9.03/1.88 ((~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('eq_fact', [status(thm)], [zip_derived_cl1130])).
% 9.03/1.88 thf(zip_derived_cl921, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl920, zip_derived_cl850])).
% 9.03/1.88 thf(zip_derived_cl1136, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1134, zip_derived_cl921])).
% 9.03/1.88 thf(zip_derived_cl1003, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1002, zip_derived_cl971])).
% 9.03/1.88 thf(zip_derived_cl1137, plain,
% 9.03/1.88 ((~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1136, zip_derived_cl1003])).
% 9.03/1.88 thf(zip_derived_cl818, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl817, zip_derived_cl760])).
% 9.03/1.88 thf(zip_derived_cl1138, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1137, zip_derived_cl818])).
% 9.03/1.88 thf(zip_derived_cl1140, plain,
% 9.03/1.88 ((~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl1138])).
% 9.03/1.88 thf(zip_derived_cl818, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl817, zip_derived_cl760])).
% 9.03/1.88 thf(zip_derived_cl1142, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1140, zip_derived_cl818])).
% 9.03/1.88 thf(zip_derived_cl1003, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1002, zip_derived_cl971])).
% 9.03/1.88 thf(zip_derived_cl1143, plain,
% 9.03/1.88 ((~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1142, zip_derived_cl1003])).
% 9.03/1.88 thf(zip_derived_cl921, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl920, zip_derived_cl850])).
% 9.03/1.88 thf(zip_derived_cl1144, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1143, zip_derived_cl921])).
% 9.03/1.88 thf(zip_derived_cl1145, plain,
% 9.03/1.88 ((~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ z))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl501, zip_derived_cl1144])).
% 9.03/1.88 thf(zip_derived_cl921, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl920, zip_derived_cl850])).
% 9.03/1.88 thf(zip_derived_cl1148, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z))) | ~ (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1145, zip_derived_cl921])).
% 9.03/1.88 thf(zip_derived_cl818, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl817, zip_derived_cl760])).
% 9.03/1.88 thf(zip_derived_cl1149, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1148, zip_derived_cl818])).
% 9.03/1.88 thf(zip_derived_cl1157, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 (~ (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X1))
% 9.03/1.88 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X2))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X0)))),
% 9.03/1.88 inference('demod', [status(thm)],
% 9.03/1.88 [zip_derived_cl1074, zip_derived_cl1149])).
% 9.03/1.88 thf(clause_2902, axiom,
% 9.03/1.88 (( ~( E @ 0 @ ( f @ A_4 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 9.03/1.88 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) |
% 9.03/1.88 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 9.03/1.88 thf(zip_derived_cl45, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ 0 @ (f @ X0))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2902])).
% 9.03/1.88 thf(zip_derived_cl1066, plain, ( (E @ 0 @ (f @ z))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1065, zip_derived_cl721])).
% 9.03/1.88 thf(zip_derived_cl1066, plain, ( (E @ 0 @ (f @ z))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1065, zip_derived_cl721])).
% 9.03/1.88 thf(zip_derived_cl1066, plain, ( (E @ 0 @ (f @ z))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1065, zip_derived_cl721])).
% 9.03/1.88 thf(clause_2160, axiom,
% 9.03/1.88 (( ~( E @ 0 @ ( f @ B_152 ) ) ) | ( ~( E @ 0 @ ( f @ B_151 ) ) ) |
% 9.03/1.88 ( ~( iLEQ @ ( suc @ B_151 ) @ ( suc @ B_152 ) ) ) |
% 9.03/1.88 ( ~( E @ 0 @ ( f @ ( suc @ B_150 ) ) ) ) |
% 9.03/1.88 ( ~( E @ 0 @ ( f @ B_150 ) ) ) |
% 9.03/1.88 ( ~( E @ 0 @ ( f @ ( suc @ B_152 ) ) ) ) |
% 9.03/1.88 ( ~( iLEQ @ ( suc @ B_150 ) @ ( suc @ B_151 ) ) ) |
% 9.03/1.88 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 9.03/1.88 ( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_150 ) ) ) |
% 9.03/1.88 ( ~( E @ 0 @ ( f @ A_4 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ B_151 ) ) ) ) |
% 9.03/1.88 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) |
% 9.03/1.88 ( E @ ( f @ B_150 ) @ ( f @ ( suc @ B_150 ) ) ) |
% 9.03/1.88 ( E @ ( f @ B_151 ) @ ( f @ ( suc @ B_151 ) ) ) |
% 9.03/1.88 ( E @ ( f @ B_152 ) @ ( f @ ( suc @ B_152 ) ) ))).
% 9.03/1.88 thf(zip_derived_cl79, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.03/1.88 (~ (E @ 0 @ (f @ X0))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X2))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X3))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 9.03/1.88 | (E @ (f @ X3) @ (f @ (suc @ X3)))
% 9.03/1.88 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2160])).
% 9.03/1.88 thf(zip_derived_cl1080, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 ( (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X2))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X1))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl1066, zip_derived_cl79])).
% 9.03/1.88 thf(zip_derived_cl1149, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1148, zip_derived_cl818])).
% 9.03/1.88 thf(zip_derived_cl1163, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 ( (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X2))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X1))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X0)))),
% 9.03/1.88 inference('demod', [status(thm)],
% 9.03/1.88 [zip_derived_cl1080, zip_derived_cl1149])).
% 9.03/1.88 thf(zip_derived_cl1212, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i]:
% 9.03/1.88 (~ (E @ 0 @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (f @ z) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl1066, zip_derived_cl1163])).
% 9.03/1.88 thf(zip_derived_cl1149, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1148, zip_derived_cl818])).
% 9.03/1.88 thf(zip_derived_cl1214, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i]:
% 9.03/1.88 (~ (E @ 0 @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (f @ z) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('demod', [status(thm)],
% 9.03/1.88 [zip_derived_cl1212, zip_derived_cl1149])).
% 9.03/1.88 thf(zip_derived_cl1215, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i]:
% 9.03/1.88 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X1))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X0)))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1214])).
% 9.03/1.88 thf(zip_derived_cl1216, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ 0 @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl1066, zip_derived_cl1215])).
% 9.03/1.88 thf(zip_derived_cl1149, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1148, zip_derived_cl818])).
% 9.03/1.88 thf(zip_derived_cl1218, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ 0 @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 9.03/1.88 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('demod', [status(thm)],
% 9.03/1.88 [zip_derived_cl1216, zip_derived_cl1149])).
% 9.03/1.88 thf(zip_derived_cl1219, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 9.03/1.88 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X0)))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1218])).
% 9.03/1.88 thf(zip_derived_cl1224, plain,
% 9.03/1.88 ((~ (E @ 0 @ (f @ z))
% 9.03/1.88 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 9.03/1.88 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.88 | (E @ (f @ z) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('eq_fact', [status(thm)], [zip_derived_cl1219])).
% 9.03/1.88 thf(zip_derived_cl1226, plain,
% 9.03/1.88 (( (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 9.03/1.88 | ~ (E @ 0 @ (f @ z)))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1224])).
% 9.03/1.88 thf(zip_derived_cl1149, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1148, zip_derived_cl818])).
% 9.03/1.88 thf(zip_derived_cl1066, plain, ( (E @ 0 @ (f @ z))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1065, zip_derived_cl721])).
% 9.03/1.88 thf(zip_derived_cl1227, plain,
% 9.03/1.88 (( (E @ (f @ z) @ (f @ (suc @ z))) | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 9.03/1.88 inference('demod', [status(thm)],
% 9.03/1.88 [zip_derived_cl1226, zip_derived_cl1149, zip_derived_cl1066])).
% 9.03/1.88 thf(zip_derived_cl1234, plain,
% 9.03/1.88 (( (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ z))
% 9.03/1.88 | (E @ (f @ z) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl1227])).
% 9.03/1.88 thf(zip_derived_cl1149, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1148, zip_derived_cl818])).
% 9.03/1.88 thf(zip_derived_cl1066, plain, ( (E @ 0 @ (f @ z))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1065, zip_derived_cl721])).
% 9.03/1.88 thf(zip_derived_cl1236, plain,
% 9.03/1.88 (( (E @ (f @ z) @ (f @ (suc @ z))) | (E @ (f @ z) @ (f @ (suc @ z))))),
% 9.03/1.88 inference('demod', [status(thm)],
% 9.03/1.88 [zip_derived_cl1234, zip_derived_cl1149, zip_derived_cl1066])).
% 9.03/1.88 thf(zip_derived_cl1237, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1236])).
% 9.03/1.88 thf(zip_derived_cl1240, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 (~ (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X2))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X0)))),
% 9.03/1.88 inference('demod', [status(thm)],
% 9.03/1.88 [zip_derived_cl1157, zip_derived_cl1237])).
% 9.03/1.88 thf(zip_derived_cl501, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl494, zip_derived_cl51])).
% 9.03/1.88 thf(zip_derived_cl39, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_491])).
% 9.03/1.88 thf(zip_derived_cl564, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl558, zip_derived_cl26])).
% 9.03/1.88 thf(zip_derived_cl125, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl112, zip_derived_cl12])).
% 9.03/1.88 thf(clause_2548, axiom,
% 9.03/1.88 (( ~( LE @ ( f @ ( suc @ ( suc @ B_149 ) ) ) @ ( s @ 0 ) ) ) |
% 9.03/1.88 ( E @ 0 @ ( f @ ( suc @ ( suc @ B_149 ) ) ) ) | ( LE @ ( f @ B_149 ) @ 0 ))).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl242, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl125, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl692, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl242, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl607, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 9.03/1.88 thf(zip_derived_cl842, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl692, zip_derived_cl607])).
% 9.03/1.88 thf(zip_derived_cl154, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl12])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl350, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl154, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl765, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl350, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl1010, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl842, zip_derived_cl765])).
% 9.03/1.88 thf(zip_derived_cl157, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl12])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl359, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl157, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl839, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl359, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl1011, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1010, zip_derived_cl839])).
% 9.03/1.88 thf(zip_derived_cl117, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl12])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl220, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl117, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl551, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl220, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl607, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 9.03/1.88 thf(zip_derived_cl663, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl551, zip_derived_cl607])).
% 9.03/1.88 thf(zip_derived_cl148, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl12])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl232, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl148, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl583, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl232, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl978, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl663, zip_derived_cl583])).
% 9.03/1.88 thf(zip_derived_cl151, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl12])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl248, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl694, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl248, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl979, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl978, zip_derived_cl694])).
% 9.03/1.88 thf(zip_derived_cl114, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl12])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl169, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl524, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl169, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl607, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 9.03/1.88 thf(zip_derived_cl645, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl524, zip_derived_cl607])).
% 9.03/1.88 thf(zip_derived_cl139, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl12])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl214, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl139, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl545, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl214, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl951, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl645, zip_derived_cl545])).
% 9.03/1.88 thf(zip_derived_cl142, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl135, zip_derived_cl12])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl223, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl578, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl223, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl952, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl951, zip_derived_cl578])).
% 9.03/1.88 thf(zip_derived_cl129, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl78, zip_derived_cl91])).
% 9.03/1.88 thf(zip_derived_cl953, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl952, zip_derived_cl129])).
% 9.03/1.88 thf(zip_derived_cl981, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl979, zip_derived_cl953])).
% 9.03/1.88 thf(zip_derived_cl982, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl981])).
% 9.03/1.88 thf(zip_derived_cl1014, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl1011, zip_derived_cl982])).
% 9.03/1.88 thf(zip_derived_cl1017, plain,
% 9.03/1.88 ((~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1014])).
% 9.03/1.88 thf(zip_derived_cl1020, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl564, zip_derived_cl1017])).
% 9.03/1.88 thf(zip_derived_cl952, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl951, zip_derived_cl578])).
% 9.03/1.88 thf(zip_derived_cl1022, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1020, zip_derived_cl952])).
% 9.03/1.88 thf(zip_derived_cl979, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl978, zip_derived_cl694])).
% 9.03/1.88 thf(zip_derived_cl1023, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1022, zip_derived_cl979])).
% 9.03/1.88 thf(zip_derived_cl564, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl558, zip_derived_cl26])).
% 9.03/1.88 thf(zip_derived_cl124, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl112, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl175, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl124, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl530, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl175, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl607, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 9.03/1.88 thf(zip_derived_cl660, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl530, zip_derived_cl607])).
% 9.03/1.88 thf(zip_derived_cl153, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl226, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl153, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl579, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl226, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl954, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl660, zip_derived_cl579])).
% 9.03/1.88 thf(zip_derived_cl156, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl239, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl156, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl584, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl239, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl955, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl954, zip_derived_cl584])).
% 9.03/1.88 thf(zip_derived_cl116, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl163, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl470, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl163, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl607, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 9.03/1.88 thf(zip_derived_cl643, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl470, zip_derived_cl607])).
% 9.03/1.88 thf(zip_derived_cl147, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl172, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl147, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl525, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl172, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl896, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl643, zip_derived_cl525])).
% 9.03/1.88 thf(zip_derived_cl150, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl217, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl150, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl546, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl217, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl897, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl896, zip_derived_cl546])).
% 9.03/1.88 thf(zip_derived_cl113, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ X0))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl145, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl113, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl438, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl607, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 9.03/1.88 thf(zip_derived_cl629, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl438, zip_derived_cl607])).
% 9.03/1.88 thf(zip_derived_cl138, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ X0))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl160, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl138, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl464, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl160, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl843, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl629, zip_derived_cl464])).
% 9.03/1.88 thf(zip_derived_cl141, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ X0))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ X0)))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl135, zip_derived_cl21])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl166, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl141, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl513, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl166, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl844, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl843, zip_derived_cl513])).
% 9.03/1.88 thf(zip_derived_cl129, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl78, zip_derived_cl91])).
% 9.03/1.88 thf(zip_derived_cl845, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl844, zip_derived_cl129])).
% 9.03/1.88 thf(zip_derived_cl899, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl897, zip_derived_cl845])).
% 9.03/1.88 thf(zip_derived_cl900, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl899])).
% 9.03/1.88 thf(zip_derived_cl958, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl955, zip_derived_cl900])).
% 9.03/1.88 thf(zip_derived_cl961, plain,
% 9.03/1.88 ((~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl958])).
% 9.03/1.88 thf(zip_derived_cl963, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl564, zip_derived_cl961])).
% 9.03/1.88 thf(zip_derived_cl844, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl843, zip_derived_cl513])).
% 9.03/1.88 thf(zip_derived_cl965, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl963, zip_derived_cl844])).
% 9.03/1.88 thf(zip_derived_cl897, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl896, zip_derived_cl546])).
% 9.03/1.88 thf(zip_derived_cl966, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl965, zip_derived_cl897])).
% 9.03/1.88 thf(zip_derived_cl501, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl494, zip_derived_cl51])).
% 9.03/1.88 thf(zip_derived_cl564, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl558, zip_derived_cl26])).
% 9.03/1.88 thf(zip_derived_cl126, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl112, zip_derived_cl27])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl399, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl126, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl840, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl399, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl607, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 9.03/1.88 thf(zip_derived_cl944, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @
% 9.03/1.88 (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl840, zip_derived_cl607])).
% 9.03/1.88 thf(zip_derived_cl155, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl27])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl436, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl155, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl891, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl436, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl1090, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @
% 9.03/1.88 (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl944, zip_derived_cl891])).
% 9.03/1.88 thf(zip_derived_cl158, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl27])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl440, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @
% 9.03/1.88 (suc @
% 9.03/1.88 (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl158, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl892, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @
% 9.03/1.88 (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl440, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl1091, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1090, zip_derived_cl892])).
% 9.03/1.88 thf(zip_derived_cl118, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl27])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl251, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl763, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl251, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl607, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 9.03/1.88 thf(zip_derived_cl890, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl763, zip_derived_cl607])).
% 9.03/1.88 thf(zip_derived_cl149, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl27])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl353, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl149, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl838, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl353, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl1085, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl890, zip_derived_cl838])).
% 9.03/1.88 thf(zip_derived_cl152, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl27])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl402, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl152, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl841, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl402, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl1086, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1085, zip_derived_cl841])).
% 9.03/1.88 thf(zip_derived_cl115, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl27])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl229, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl115, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl582, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl229, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl607, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl606])).
% 9.03/1.88 thf(zip_derived_cl761, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl582, zip_derived_cl607])).
% 9.03/1.88 thf(zip_derived_cl140, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl27])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl245, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl140, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl693, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl245, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl983, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl761, zip_derived_cl693])).
% 9.03/1.88 thf(zip_derived_cl143, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ (s @ 0))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl135, zip_derived_cl27])).
% 9.03/1.88 thf(zip_derived_cl3, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_2548])).
% 9.03/1.88 thf(zip_derived_cl347, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 9.03/1.88 | (LE @ (f @ X0) @ 0)
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl3])).
% 9.03/1.88 thf(zip_derived_cl52, plain, (~ (LE @ (f @ z) @ 0)),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1450])).
% 9.03/1.88 thf(zip_derived_cl764, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ (s @ 0))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl347, zip_derived_cl52])).
% 9.03/1.88 thf(zip_derived_cl984, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl983, zip_derived_cl764])).
% 9.03/1.88 thf(zip_derived_cl129, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl78, zip_derived_cl91])).
% 9.03/1.88 thf(zip_derived_cl985, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ (suc @ (suc @ z))))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl984, zip_derived_cl129])).
% 9.03/1.88 thf(zip_derived_cl1088, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ (suc @ (suc @ z))))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl1086, zip_derived_cl985])).
% 9.03/1.88 thf(zip_derived_cl1089, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ (suc @ (suc @ z))))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1088])).
% 9.03/1.88 thf(zip_derived_cl1094, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ (suc @ (suc @ z))))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl1091, zip_derived_cl1089])).
% 9.03/1.88 thf(zip_derived_cl1096, plain,
% 9.03/1.88 ((~ (E @ (f @ (suc @ (suc @ (suc @ (suc @ z))))) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1094])).
% 9.03/1.88 thf(zip_derived_cl1098, plain,
% 9.03/1.88 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl564, zip_derived_cl1096])).
% 9.03/1.88 thf(zip_derived_cl984, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl983, zip_derived_cl764])).
% 9.03/1.88 thf(zip_derived_cl1100, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ (s @ 0)) @
% 9.03/1.88 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1098, zip_derived_cl984])).
% 9.03/1.88 thf(zip_derived_cl1086, plain,
% 9.03/1.88 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1085, zip_derived_cl841])).
% 9.03/1.88 thf(zip_derived_cl1101, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1100, zip_derived_cl1086])).
% 9.03/1.88 thf(zip_derived_cl1023, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1022, zip_derived_cl979])).
% 9.03/1.88 thf(zip_derived_cl966, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl965, zip_derived_cl897])).
% 9.03/1.88 thf(zip_derived_cl6, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.03/1.88 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X3))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X3)))))),
% 9.03/1.88 inference('cnf', [status(esa)], [clause_1275])).
% 9.03/1.88 thf(zip_derived_cl967, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 ( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl966, zip_derived_cl6])).
% 9.03/1.88 thf(zip_derived_cl1252, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 ( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl1023, zip_derived_cl967])).
% 9.03/1.88 thf(zip_derived_cl1253, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1252])).
% 9.03/1.88 thf(zip_derived_cl1254, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 ( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl1101, zip_derived_cl1253])).
% 9.03/1.88 thf(zip_derived_cl1255, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1254])).
% 9.03/1.88 thf(zip_derived_cl1256, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl501, zip_derived_cl1255])).
% 9.03/1.88 thf(zip_derived_cl1259, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 ( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl966, zip_derived_cl1256])).
% 9.03/1.88 thf(zip_derived_cl1260, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1259])).
% 9.03/1.88 thf(zip_derived_cl1261, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 ( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl1023, zip_derived_cl1260])).
% 9.03/1.88 thf(zip_derived_cl1262, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 (~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1261])).
% 9.03/1.88 thf(zip_derived_cl1267, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('eq_fact', [status(thm)], [zip_derived_cl1262])).
% 9.03/1.88 thf(zip_derived_cl1269, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1267])).
% 9.03/1.88 thf(zip_derived_cl501, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl494, zip_derived_cl51])).
% 9.03/1.88 thf(zip_derived_cl1273, plain,
% 9.03/1.88 (![X0 : $i]:
% 9.03/1.88 ( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1269, zip_derived_cl501])).
% 9.03/1.88 thf(zip_derived_cl1277, plain,
% 9.03/1.88 ((~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('eq_fact', [status(thm)], [zip_derived_cl1273])).
% 9.03/1.88 thf(zip_derived_cl1023, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1022, zip_derived_cl979])).
% 9.03/1.88 thf(zip_derived_cl1279, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1277, zip_derived_cl1023])).
% 9.03/1.88 thf(zip_derived_cl1101, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1100, zip_derived_cl1086])).
% 9.03/1.88 thf(zip_derived_cl1280, plain,
% 9.03/1.88 ((~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1279, zip_derived_cl1101])).
% 9.03/1.88 thf(zip_derived_cl966, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl965, zip_derived_cl897])).
% 9.03/1.88 thf(zip_derived_cl1281, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1280, zip_derived_cl966])).
% 9.03/1.88 thf(zip_derived_cl1283, plain,
% 9.03/1.88 ((~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl1281])).
% 9.03/1.88 thf(zip_derived_cl966, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl965, zip_derived_cl897])).
% 9.03/1.88 thf(zip_derived_cl1285, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1283, zip_derived_cl966])).
% 9.03/1.88 thf(zip_derived_cl1101, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1100, zip_derived_cl1086])).
% 9.03/1.88 thf(zip_derived_cl1286, plain,
% 9.03/1.88 ((~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1285, zip_derived_cl1101])).
% 9.03/1.88 thf(zip_derived_cl1023, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1022, zip_derived_cl979])).
% 9.03/1.88 thf(zip_derived_cl1287, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1286, zip_derived_cl1023])).
% 9.03/1.88 thf(zip_derived_cl1288, plain,
% 9.03/1.88 ((~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl501, zip_derived_cl1287])).
% 9.03/1.88 thf(zip_derived_cl1023, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1022, zip_derived_cl979])).
% 9.03/1.88 thf(zip_derived_cl1291, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1288, zip_derived_cl1023])).
% 9.03/1.88 thf(zip_derived_cl966, plain,
% 9.03/1.88 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl965, zip_derived_cl897])).
% 9.03/1.88 thf(zip_derived_cl1292, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1291, zip_derived_cl966])).
% 9.03/1.88 thf(zip_derived_cl1311, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.03/1.88 (~ (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X1))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X2))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X0)))),
% 9.03/1.88 inference('demod', [status(thm)],
% 9.03/1.88 [zip_derived_cl1240, zip_derived_cl1292])).
% 9.03/1.88 thf(zip_derived_cl1349, plain,
% 9.03/1.88 (![X0 : $i, X1 : $i]:
% 9.03/1.88 (~ (E @ 0 @ (f @ X0))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 9.03/1.88 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 9.03/1.88 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 9.03/1.88 | ~ (E @ 0 @ (f @ X1))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.88 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.88 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 9.03/1.88 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 9.03/1.88 inference('sup-', [status(thm)], [zip_derived_cl1066, zip_derived_cl1311])).
% 9.03/1.88 thf(zip_derived_cl1237, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 9.03/1.88 inference('simplify', [status(thm)], [zip_derived_cl1236])).
% 9.03/1.88 thf(zip_derived_cl1292, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 9.03/1.88 inference('clc', [status(thm)], [zip_derived_cl1291, zip_derived_cl966])).
% 9.03/1.89 thf(zip_derived_cl1149, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 9.03/1.89 inference('clc', [status(thm)], [zip_derived_cl1148, zip_derived_cl818])).
% 9.03/1.89 thf(zip_derived_cl1352, plain,
% 9.03/1.89 (![X0 : $i, X1 : $i]:
% 9.03/1.89 (~ (E @ 0 @ (f @ X0))
% 9.03/1.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 9.03/1.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 9.03/1.89 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 9.03/1.89 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 9.03/1.89 | ~ (E @ 0 @ (f @ X1))
% 9.03/1.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.89 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 9.03/1.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.89 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 9.03/1.89 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 9.03/1.89 inference('demod', [status(thm)],
% 9.03/1.89 [zip_derived_cl1349, zip_derived_cl1237, zip_derived_cl1292,
% 9.03/1.89 zip_derived_cl1149])).
% 9.03/1.89 thf(zip_derived_cl1354, plain,
% 9.03/1.89 (![X0 : $i]:
% 9.03/1.89 (~ (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.89 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 9.03/1.89 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 9.03/1.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.89 | ~ (E @ 0 @ (f @ X0))
% 9.03/1.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.89 | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 9.03/1.89 inference('sup-', [status(thm)], [zip_derived_cl1066, zip_derived_cl1352])).
% 9.03/1.89 thf(zip_derived_cl1149, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 9.03/1.89 inference('clc', [status(thm)], [zip_derived_cl1148, zip_derived_cl818])).
% 9.03/1.89 thf(zip_derived_cl1237, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 9.03/1.89 inference('simplify', [status(thm)], [zip_derived_cl1236])).
% 9.03/1.89 thf(zip_derived_cl1292, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 9.03/1.89 inference('clc', [status(thm)], [zip_derived_cl1291, zip_derived_cl966])).
% 9.03/1.89 thf(zip_derived_cl1357, plain,
% 9.03/1.89 (![X0 : $i]:
% 9.03/1.89 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 9.03/1.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 9.03/1.89 | ~ (E @ 0 @ (f @ X0))
% 9.03/1.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 9.03/1.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 9.03/1.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 9.03/1.89 | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 9.03/1.89 inference('demod', [status(thm)],
% 9.03/1.89 [zip_derived_cl1354, zip_derived_cl1149, zip_derived_cl1237,
% 9.03/1.89 zip_derived_cl1292])).
% 9.03/1.89 thf(zip_derived_cl1363, plain,
% 9.03/1.89 ((~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 9.03/1.89 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.89 | ~ (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.89 | ~ (E @ 0 @ (f @ z))
% 9.03/1.89 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 9.03/1.89 | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 9.03/1.89 inference('eq_fact', [status(thm)], [zip_derived_cl1357])).
% 9.03/1.89 thf(zip_derived_cl1365, plain,
% 9.03/1.89 ((~ (iLEQ @ (suc @ z) @ (suc @ z))
% 9.03/1.89 | ~ (E @ 0 @ (f @ z))
% 9.03/1.89 | ~ (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.89 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.89 inference('simplify', [status(thm)], [zip_derived_cl1363])).
% 9.03/1.89 thf(zip_derived_cl1066, plain, ( (E @ 0 @ (f @ z))),
% 9.03/1.89 inference('clc', [status(thm)], [zip_derived_cl1065, zip_derived_cl721])).
% 9.03/1.89 thf(zip_derived_cl1149, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 9.03/1.89 inference('clc', [status(thm)], [zip_derived_cl1148, zip_derived_cl818])).
% 9.03/1.89 thf(zip_derived_cl1237, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 9.03/1.89 inference('simplify', [status(thm)], [zip_derived_cl1236])).
% 9.03/1.89 thf(zip_derived_cl1292, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 9.03/1.89 inference('clc', [status(thm)], [zip_derived_cl1291, zip_derived_cl966])).
% 9.03/1.89 thf(zip_derived_cl1366, plain, (~ (iLEQ @ (suc @ z) @ (suc @ z))),
% 9.03/1.89 inference('demod', [status(thm)],
% 9.03/1.89 [zip_derived_cl1365, zip_derived_cl1066, zip_derived_cl1149,
% 9.03/1.89 zip_derived_cl1237, zip_derived_cl1292])).
% 9.03/1.89 thf(zip_derived_cl1371, plain,
% 9.03/1.89 ((~ (E @ 0 @ (f @ z))
% 9.03/1.89 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 9.03/1.89 | ~ (E @ 0 @ (f @ (suc @ z)))
% 9.03/1.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 9.03/1.89 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl1366])).
% 9.03/1.89 thf(zip_derived_cl1066, plain, ( (E @ 0 @ (f @ z))),
% 9.03/1.89 inference('clc', [status(thm)], [zip_derived_cl1065, zip_derived_cl721])).
% 9.03/1.89 thf(zip_derived_cl1237, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 9.03/1.89 inference('simplify', [status(thm)], [zip_derived_cl1236])).
% 9.03/1.89 thf(zip_derived_cl1149, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 9.03/1.89 inference('clc', [status(thm)], [zip_derived_cl1148, zip_derived_cl818])).
% 9.03/1.89 thf(zip_derived_cl1292, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 9.03/1.89 inference('clc', [status(thm)], [zip_derived_cl1291, zip_derived_cl966])).
% 9.03/1.89 thf(zip_derived_cl1374, plain, ($false),
% 9.03/1.89 inference('demod', [status(thm)],
% 9.03/1.89 [zip_derived_cl1371, zip_derived_cl1066, zip_derived_cl1237,
% 9.03/1.89 zip_derived_cl1149, zip_derived_cl1292])).
% 9.03/1.89
% 9.03/1.89 % SZS output end Refutation
% 9.03/1.89
% 9.03/1.89
% 9.03/1.89 % Terminating...
% 9.38/1.97 % Runner terminated.
% 9.38/1.99 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------