%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO673-1 : TPTP v9.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.zxidALYKB4 true
% Computer : n029.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 : Thu Oct 2 05:08:07 PM UTC 2025
% Result : Unsatisfiable 5.46s 1.47s
% Output : Refutation 5.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYO673-1 : TPTP v9.2.0. Released v7.3.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.zxidALYKB4 true
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 18:12:08 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.58/0.68 % Total configuration time : 435
% 0.58/0.68 % Estimated wc time : 1092
% 0.58/0.68 % Estimated cpu time (7 cpus) : 156.0
% 0.58/0.74 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.58/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.58/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.58/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.58/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.58/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.59/0.88 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 5.46/1.47 % Solved by fo/fo7.sh.
% 5.46/1.47 % done 363 iterations in 0.625s
% 5.46/1.47 % SZS status Unsatisfiable for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 5.46/1.47 % SZS output start Refutation
% 5.46/1.47 thf(LE_type, type, LE: $i > $i > $o).
% 5.46/1.47 thf(f_type, type, f: $i > $i).
% 5.46/1.47 thf(0_type, type, 0: $i).
% 5.46/1.47 thf(iLEQ_type, type, iLEQ: $i > $i > $o).
% 5.46/1.47 thf(suc_type, type, suc: $i > $i).
% 5.46/1.47 thf(z_type, type, z: $i).
% 5.46/1.47 thf(s_type, type, s: $i > $i).
% 5.46/1.47 thf(E_type, type, E: $i > $i > $o).
% 5.46/1.47 thf(clause_418, axiom,
% 5.46/1.47 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 5.46/1.47 ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.46/1.47 ( ~( E @ 0 @ ( f @ A_3 ) ) ) | ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 5.46/1.47 thf(zip_derived_cl13, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_418])).
% 5.46/1.47 thf(clause_1322, axiom,
% 5.46/1.47 (( ~( E @ ( s @ 0 ) @ ( f @ B_69 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ B_68 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ B_69 ) @ ( suc @ B_70 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_69 ) ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_68 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_70 ) ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ B_68 ) @ ( suc @ B_69 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ B_70 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_68 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 5.46/1.47 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 5.46/1.47 ( E @ ( f @ B_68 ) @ ( f @ ( suc @ B_68 ) ) ) |
% 5.46/1.47 ( E @ ( f @ B_69 ) @ ( f @ ( suc @ B_69 ) ) ) |
% 5.46/1.47 ( E @ ( f @ B_70 ) @ ( f @ ( suc @ B_70 ) ) ))).
% 5.46/1.47 thf(zip_derived_cl35, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X3))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ X3) @ (f @ (suc @ X3))))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1322])).
% 5.46/1.47 thf(zip_derived_cl407, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 5.46/1.47 inference('eq_fact', [status(thm)], [zip_derived_cl35])).
% 5.46/1.47 thf(zip_derived_cl409, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl407])).
% 5.46/1.47 thf(zip_derived_cl421, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('eq_fact', [status(thm)], [zip_derived_cl409])).
% 5.46/1.47 thf(zip_derived_cl422, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl421])).
% 5.46/1.47 thf(clause_243, axiom,
% 5.46/1.47 (( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.46/1.47 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 5.46/1.47 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 5.46/1.47 thf(zip_derived_cl31, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_243])).
% 5.46/1.47 thf(zip_derived_cl428, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl422, zip_derived_cl31])).
% 5.46/1.47 thf(clause_165, axiom,
% 5.46/1.47 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 5.46/1.47 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 5.46/1.47 thf(zip_derived_cl24, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_165])).
% 5.46/1.47 thf(clause_1106, axiom,
% 5.46/1.47 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_44 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_43 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_45 ) ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ B_44 ) @ ( suc @ B_45 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_43 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_44 ) ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ B_43 ) @ ( suc @ B_44 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_45 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_43 ) ) ) |
% 5.46/1.47 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 5.46/1.47 ( E @ ( f @ B_43 ) @ ( f @ ( suc @ B_43 ) ) ) |
% 5.46/1.47 ( E @ ( f @ B_44 ) @ ( f @ ( suc @ B_44 ) ) ) |
% 5.46/1.47 ( E @ ( f @ B_45 ) @ ( f @ ( suc @ B_45 ) ) ))).
% 5.46/1.47 thf(zip_derived_cl51, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X3)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X3))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X3))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | (E @ (f @ X3) @ (f @ (suc @ X3))))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1106])).
% 5.46/1.47 thf(zip_derived_cl463, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X1)))),
% 5.46/1.47 inference('eq_fact', [status(thm)], [zip_derived_cl51])).
% 5.46/1.47 thf(zip_derived_cl465, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl463])).
% 5.46/1.47 thf(zip_derived_cl475, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 5.46/1.47 inference('eq_fact', [status(thm)], [zip_derived_cl465])).
% 5.46/1.47 thf(zip_derived_cl476, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl475])).
% 5.46/1.47 thf(clause_120, axiom,
% 5.46/1.47 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.46/1.47 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 5.46/1.47 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 5.46/1.47 thf(zip_derived_cl30, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_120])).
% 5.46/1.47 thf(zip_derived_cl481, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl476, zip_derived_cl30])).
% 5.46/1.47 thf(clause_1439, axiom,
% 5.46/1.47 (( ~( LE @ ( f @ ( suc @ B_42 ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 5.46/1.47 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_42 ) ) ) |
% 5.46/1.47 ( LE @ ( f @ B_42 ) @ ( s @ ( s @ 0 ) ) ))).
% 5.46/1.47 thf(zip_derived_cl37, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1439])).
% 5.46/1.47 thf(clause_1497, axiom, (LE @ ( f @ A ) @ ( s @ ( s @ ( s @ 0 ) ) ))).
% 5.46/1.47 thf(zip_derived_cl5, plain,
% 5.46/1.47 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1497])).
% 5.46/1.47 thf(zip_derived_cl90, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.46/1.47 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl5])).
% 5.46/1.47 thf(clause_1246, axiom,
% 5.46/1.47 (( ~( LE @ ( f @ ( suc @ B_67 ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 5.46/1.47 ( E @ ( s @ 0 ) @ ( f @ ( suc @ B_67 ) ) ) |
% 5.46/1.47 ( LE @ ( f @ B_67 ) @ ( s @ 0 ) ))).
% 5.46/1.47 thf(zip_derived_cl33, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1246])).
% 5.46/1.47 thf(zip_derived_cl93, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl90, zip_derived_cl33])).
% 5.46/1.47 thf(clause_509, axiom,
% 5.46/1.47 (( ~( LE @ ( f @ B_79 ) @ ( s @ 0 ) ) ) | ( E @ 0 @ ( f @ B_79 ) ) |
% 5.46/1.47 ( LE @ ( f @ B_79 ) @ 0 ))).
% 5.46/1.47 thf(zip_derived_cl61, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_509])).
% 5.46/1.47 thf(zip_derived_cl102, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl61])).
% 5.46/1.47 thf(clause_709, axiom, (~( LE @ ( f @ z ) @ 0 ))).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl146, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl102, zip_derived_cl25])).
% 5.46/1.47 thf(clause_1442, axiom,
% 5.46/1.47 (( ~( LE @ ( f @ B_42 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 5.46/1.47 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_42 ) ) |
% 5.46/1.47 ( LE @ ( f @ B_42 ) @ ( s @ ( s @ 0 ) ) ))).
% 5.46/1.47 thf(zip_derived_cl49, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1442])).
% 5.46/1.47 thf(zip_derived_cl5, plain,
% 5.46/1.47 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1497])).
% 5.46/1.47 thf(zip_derived_cl79, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.46/1.47 inference('demod', [status(thm)], [zip_derived_cl49, zip_derived_cl5])).
% 5.46/1.47 thf(zip_derived_cl33, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1246])).
% 5.46/1.47 thf(zip_derived_cl81, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl33])).
% 5.46/1.47 thf(zip_derived_cl61, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_509])).
% 5.46/1.47 thf(zip_derived_cl99, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl81, zip_derived_cl61])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl126, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl99, zip_derived_cl25])).
% 5.46/1.47 thf(clause_1017, axiom,
% 5.46/1.47 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_45 ) ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_44 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_43 ) ) ) |
% 5.46/1.47 ( ~( E @ ( f @ B_44 ) @ ( f @ ( suc @ B_44 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( f @ B_43 ) @ ( f @ ( suc @ B_43 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_45 ) ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ B_44 ) @ ( suc @ B_45 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_43 ) ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_43 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_44 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ B_43 ) @ ( suc @ B_44 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_45 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_44 ) ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( f @ B_45 ) @ ( f @ ( suc @ B_45 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_43 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ))).
% 5.46/1.47 thf(zip_derived_cl38, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X3))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X3)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X3))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1017])).
% 5.46/1.47 thf(zip_derived_cl65, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X1)))),
% 5.46/1.47 inference('eq_fact', [status(thm)], [zip_derived_cl38])).
% 5.46/1.47 thf(zip_derived_cl67, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1)))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl65])).
% 5.46/1.47 thf(zip_derived_cl69, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 5.46/1.47 inference('eq_fact', [status(thm)], [zip_derived_cl67])).
% 5.46/1.47 thf(zip_derived_cl70, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl69])).
% 5.46/1.47 thf(clause_345, axiom,
% 5.46/1.47 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 5.46/1.47 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 5.46/1.47 thf(zip_derived_cl6, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_345])).
% 5.46/1.47 thf(zip_derived_cl94, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl70, zip_derived_cl6])).
% 5.46/1.47 thf(zip_derived_cl128, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl126, zip_derived_cl94])).
% 5.46/1.47 thf(zip_derived_cl149, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl146, zip_derived_cl128])).
% 5.46/1.47 thf(zip_derived_cl151, plain,
% 5.46/1.47 ((~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl149])).
% 5.46/1.47 thf(zip_derived_cl483, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl481, zip_derived_cl151])).
% 5.46/1.47 thf(zip_derived_cl146, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl102, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl525, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl483, zip_derived_cl146])).
% 5.46/1.47 thf(clause_1261, axiom,
% 5.46/1.47 (( ~( LE @ ( f @ ( suc @ ( suc @ B_42 ) ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 5.46/1.47 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_42 ) ) ) ) |
% 5.46/1.47 ( LE @ ( f @ B_42 ) @ ( s @ ( s @ 0 ) ) ))).
% 5.46/1.47 thf(zip_derived_cl63, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1261])).
% 5.46/1.47 thf(zip_derived_cl5, plain,
% 5.46/1.47 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1497])).
% 5.46/1.47 thf(zip_derived_cl116, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.46/1.47 inference('demod', [status(thm)], [zip_derived_cl63, zip_derived_cl5])).
% 5.46/1.47 thf(zip_derived_cl33, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1246])).
% 5.46/1.47 thf(zip_derived_cl119, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl33])).
% 5.46/1.47 thf(zip_derived_cl61, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_509])).
% 5.46/1.47 thf(zip_derived_cl129, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl119, zip_derived_cl61])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl165, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl129, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl526, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl525, zip_derived_cl165])).
% 5.46/1.47 thf(zip_derived_cl126, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl99, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl527, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl526, zip_derived_cl126])).
% 5.46/1.47 thf(zip_derived_cl481, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl476, zip_derived_cl30])).
% 5.46/1.47 thf(zip_derived_cl79, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.46/1.47 inference('demod', [status(thm)], [zip_derived_cl49, zip_derived_cl5])).
% 5.46/1.47 thf(clause_1415, axiom,
% 5.46/1.47 (( ~( LE @ ( f @ B_67 ) @ ( s @ ( s @ 0 ) ) ) ) |
% 5.46/1.47 ( E @ ( s @ 0 ) @ ( f @ B_67 ) ) | ( LE @ ( f @ B_67 ) @ ( s @ 0 ) ))).
% 5.46/1.47 thf(zip_derived_cl17, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1415])).
% 5.46/1.47 thf(zip_derived_cl80, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl17])).
% 5.46/1.47 thf(zip_derived_cl61, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_509])).
% 5.46/1.47 thf(zip_derived_cl87, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl61])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl120, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ z))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ z)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl87, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl94, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl70, zip_derived_cl6])).
% 5.46/1.47 thf(zip_derived_cl124, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ z))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl120, zip_derived_cl94])).
% 5.46/1.47 thf(zip_derived_cl499, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ z)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl481, zip_derived_cl124])).
% 5.46/1.47 thf(zip_derived_cl500, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ z))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl499])).
% 5.46/1.47 thf(zip_derived_cl116, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.46/1.47 inference('demod', [status(thm)], [zip_derived_cl63, zip_derived_cl5])).
% 5.46/1.47 thf(zip_derived_cl17, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1415])).
% 5.46/1.47 thf(zip_derived_cl117, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl17])).
% 5.46/1.47 thf(zip_derived_cl61, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_509])).
% 5.46/1.47 thf(zip_derived_cl121, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl117, zip_derived_cl61])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl135, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ z)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl121, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl521, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ z))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl500, zip_derived_cl135])).
% 5.46/1.47 thf(zip_derived_cl90, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.46/1.47 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl5])).
% 5.46/1.47 thf(zip_derived_cl17, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1415])).
% 5.46/1.47 thf(zip_derived_cl91, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl90, zip_derived_cl17])).
% 5.46/1.47 thf(zip_derived_cl61, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_509])).
% 5.46/1.47 thf(zip_derived_cl96, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl91, zip_derived_cl61])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl125, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ z)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl96, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl522, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ z))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl521, zip_derived_cl125])).
% 5.46/1.47 thf(zip_derived_cl120, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ z))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ z)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl87, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl523, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl522, zip_derived_cl120])).
% 5.46/1.47 thf(zip_derived_cl428, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl422, zip_derived_cl31])).
% 5.46/1.47 thf(zip_derived_cl527, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl526, zip_derived_cl126])).
% 5.46/1.47 thf(zip_derived_cl523, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl522, zip_derived_cl120])).
% 5.46/1.47 thf(zip_derived_cl481, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl476, zip_derived_cl30])).
% 5.46/1.47 thf(zip_derived_cl90, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.46/1.47 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl5])).
% 5.46/1.47 thf(clause_1472, axiom,
% 5.46/1.47 (( ~( LE @ ( f @ ( suc @ ( suc @ B_67 ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 5.46/1.47 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_67 ) ) ) ) |
% 5.46/1.47 ( LE @ ( f @ B_67 ) @ ( s @ 0 ) ))).
% 5.46/1.47 thf(zip_derived_cl20, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1472])).
% 5.46/1.47 thf(zip_derived_cl92, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl90, zip_derived_cl20])).
% 5.46/1.47 thf(zip_derived_cl61, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_509])).
% 5.46/1.47 thf(zip_derived_cl132, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl61])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl178, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl79, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.46/1.47 inference('demod', [status(thm)], [zip_derived_cl49, zip_derived_cl5])).
% 5.46/1.47 thf(zip_derived_cl20, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1472])).
% 5.46/1.47 thf(zip_derived_cl86, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl20])).
% 5.46/1.47 thf(zip_derived_cl61, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_509])).
% 5.46/1.47 thf(zip_derived_cl105, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl86, zip_derived_cl61])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl159, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl94, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl70, zip_derived_cl6])).
% 5.46/1.47 thf(zip_derived_cl163, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl159, zip_derived_cl94])).
% 5.46/1.47 thf(zip_derived_cl200, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl178, zip_derived_cl163])).
% 5.46/1.47 thf(zip_derived_cl203, plain,
% 5.46/1.47 ((~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl200])).
% 5.46/1.47 thf(zip_derived_cl116, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 5.46/1.47 inference('demod', [status(thm)], [zip_derived_cl63, zip_derived_cl5])).
% 5.46/1.47 thf(zip_derived_cl20, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1472])).
% 5.46/1.47 thf(zip_derived_cl118, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl20])).
% 5.46/1.47 thf(zip_derived_cl61, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_509])).
% 5.46/1.47 thf(zip_derived_cl141, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl61])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl181, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl141, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl243, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl203, zip_derived_cl181])).
% 5.46/1.47 thf(zip_derived_cl487, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl481, zip_derived_cl243])).
% 5.46/1.47 thf(zip_derived_cl178, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl501, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl487, zip_derived_cl178])).
% 5.46/1.47 thf(zip_derived_cl159, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl502, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl501, zip_derived_cl159])).
% 5.46/1.47 thf(zip_derived_cl527, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl526, zip_derived_cl126])).
% 5.46/1.47 thf(zip_derived_cl523, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl522, zip_derived_cl120])).
% 5.46/1.47 thf(zip_derived_cl428, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl422, zip_derived_cl31])).
% 5.46/1.47 thf(zip_derived_cl527, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl526, zip_derived_cl126])).
% 5.46/1.47 thf(zip_derived_cl523, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl522, zip_derived_cl120])).
% 5.46/1.47 thf(clause_1132, axiom,
% 5.46/1.47 (( ~( E @ ( s @ 0 ) @ ( f @ B_69 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ B_68 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_69 ) ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( f @ B_69 ) @ ( f @ ( suc @ B_69 ) ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ B_69 ) @ ( suc @ B_70 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_69 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_68 ) ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_70 ) ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( f @ B_70 ) @ ( f @ ( suc @ B_70 ) ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_68 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_70 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( f @ B_68 ) @ ( f @ ( suc @ B_68 ) ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ B_68 ) @ ( suc @ B_69 ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ B_70 ) ) ) |
% 5.46/1.47 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_68 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ))).
% 5.46/1.47 thf(zip_derived_cl59, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X3))))
% 5.46/1.47 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X3))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1132])).
% 5.46/1.47 thf(zip_derived_cl524, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl523, zip_derived_cl59])).
% 5.46/1.47 thf(zip_derived_cl547, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl527, zip_derived_cl524])).
% 5.46/1.47 thf(zip_derived_cl549, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl547])).
% 5.46/1.47 thf(zip_derived_cl550, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ z))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl428, zip_derived_cl549])).
% 5.46/1.47 thf(zip_derived_cl552, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl523, zip_derived_cl550])).
% 5.46/1.47 thf(zip_derived_cl553, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl552])).
% 5.46/1.47 thf(zip_derived_cl554, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl527, zip_derived_cl553])).
% 5.46/1.47 thf(zip_derived_cl556, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl554])).
% 5.46/1.47 thf(zip_derived_cl557, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl502, zip_derived_cl556])).
% 5.46/1.47 thf(zip_derived_cl560, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl557])).
% 5.46/1.47 thf(zip_derived_cl564, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 5.46/1.47 inference('eq_fact', [status(thm)], [zip_derived_cl560])).
% 5.46/1.47 thf(zip_derived_cl566, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ z))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl564])).
% 5.46/1.47 thf(zip_derived_cl570, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl523, zip_derived_cl566])).
% 5.46/1.47 thf(zip_derived_cl571, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl570])).
% 5.46/1.47 thf(zip_derived_cl572, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl527, zip_derived_cl571])).
% 5.46/1.47 thf(zip_derived_cl574, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl572])).
% 5.46/1.47 thf(zip_derived_cl575, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ z))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl428, zip_derived_cl574])).
% 5.46/1.47 thf(zip_derived_cl577, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl523, zip_derived_cl575])).
% 5.46/1.47 thf(zip_derived_cl578, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl577])).
% 5.46/1.47 thf(zip_derived_cl579, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl527, zip_derived_cl578])).
% 5.46/1.47 thf(zip_derived_cl581, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl579])).
% 5.46/1.47 thf(zip_derived_cl502, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl501, zip_derived_cl159])).
% 5.46/1.47 thf(zip_derived_cl582, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl581, zip_derived_cl502])).
% 5.46/1.47 thf(zip_derived_cl428, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl422, zip_derived_cl31])).
% 5.46/1.47 thf(zip_derived_cl583, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl582, zip_derived_cl428])).
% 5.46/1.47 thf(zip_derived_cl587, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('eq_fact', [status(thm)], [zip_derived_cl583])).
% 5.46/1.47 thf(zip_derived_cl502, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl501, zip_derived_cl159])).
% 5.46/1.47 thf(zip_derived_cl589, plain,
% 5.46/1.47 ((~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ z))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl587, zip_derived_cl502])).
% 5.46/1.47 thf(zip_derived_cl527, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl526, zip_derived_cl126])).
% 5.46/1.47 thf(zip_derived_cl590, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl589, zip_derived_cl527])).
% 5.46/1.47 thf(zip_derived_cl523, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl522, zip_derived_cl120])).
% 5.46/1.47 thf(zip_derived_cl591, plain,
% 5.46/1.47 ((~ (iLEQ @ (suc @ z) @ (suc @ z)) | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl590, zip_derived_cl523])).
% 5.46/1.47 thf(zip_derived_cl593, plain,
% 5.46/1.47 ((~ (E @ (s @ 0) @ (f @ z))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl591])).
% 5.46/1.47 thf(zip_derived_cl523, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl522, zip_derived_cl120])).
% 5.46/1.47 thf(zip_derived_cl595, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl593, zip_derived_cl523])).
% 5.46/1.47 thf(zip_derived_cl502, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl501, zip_derived_cl159])).
% 5.46/1.47 thf(zip_derived_cl596, plain,
% 5.46/1.47 ((~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl595, zip_derived_cl502])).
% 5.46/1.47 thf(zip_derived_cl527, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl526, zip_derived_cl126])).
% 5.46/1.47 thf(zip_derived_cl597, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | ~ (E @ (f @ z) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl596, zip_derived_cl527])).
% 5.46/1.47 thf(zip_derived_cl598, plain,
% 5.46/1.47 ((~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ z))
% 5.46/1.47 | (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl428, zip_derived_cl597])).
% 5.46/1.47 thf(zip_derived_cl527, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl526, zip_derived_cl126])).
% 5.46/1.47 thf(zip_derived_cl600, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | ~ (E @ (s @ 0) @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl598, zip_derived_cl527])).
% 5.46/1.47 thf(zip_derived_cl523, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ z)) | (E @ (s @ 0) @ (f @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl522, zip_derived_cl120])).
% 5.46/1.47 thf(zip_derived_cl601, plain, ( (E @ 0 @ (f @ z))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl600, zip_derived_cl523])).
% 5.46/1.47 thf(zip_derived_cl601, plain, ( (E @ 0 @ (f @ z))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl600, zip_derived_cl523])).
% 5.46/1.47 thf(zip_derived_cl601, plain, ( (E @ 0 @ (f @ z))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl600, zip_derived_cl523])).
% 5.46/1.47 thf(clause_1397, axiom,
% 5.46/1.47 (( ~( E @ 0 @ ( f @ ( suc @ B_82 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( f @ B_82 ) @ ( f @ ( suc @ B_82 ) ) ) ) |
% 5.46/1.47 ( ~( E @ 0 @ ( f @ B_80 ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ B_80 ) @ ( suc @ B_81 ) ) ) |
% 5.46/1.47 ( ~( E @ ( f @ B_81 ) @ ( f @ ( suc @ B_81 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( f @ B_80 ) @ ( f @ ( suc @ B_80 ) ) ) ) |
% 5.46/1.47 ( ~( E @ 0 @ ( f @ ( suc @ B_81 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_81 ) ) ) |
% 5.46/1.47 ( ~( E @ 0 @ ( f @ A_3 ) ) ) | ( ~( E @ 0 @ ( f @ B_82 ) ) ) |
% 5.46/1.47 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_82 ) ) ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_80 ) ) ) |
% 5.46/1.47 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 5.46/1.47 ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.46/1.47 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.46/1.47 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_80 ) ) ) ) ) |
% 5.46/1.47 ( ~( E @ 0 @ ( f @ ( suc @ B_80 ) ) ) ) |
% 5.46/1.47 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_81 ) ) ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ B_81 ) @ ( suc @ B_82 ) ) ))).
% 5.46/1.47 thf(zip_derived_cl12, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 5.46/1.47 (~ (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X1))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X2))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X3))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X3) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X3))))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 5.46/1.47 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1397])).
% 5.46/1.47 thf(zip_derived_cl606, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X2) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X2))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X1))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl601, zip_derived_cl12])).
% 5.46/1.47 thf(zip_derived_cl428, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl422, zip_derived_cl31])).
% 5.46/1.47 thf(zip_derived_cl481, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl476, zip_derived_cl30])).
% 5.46/1.47 thf(zip_derived_cl91, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl90, zip_derived_cl17])).
% 5.46/1.47 thf(clause_1256, axiom,
% 5.46/1.47 (( ~( LE @ ( f @ ( suc @ B_79 ) ) @ ( s @ 0 ) ) ) |
% 5.46/1.47 ( E @ 0 @ ( f @ ( suc @ B_79 ) ) ) | ( LE @ ( f @ B_79 ) @ 0 ))).
% 5.46/1.47 thf(zip_derived_cl42, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1256])).
% 5.46/1.47 thf(zip_derived_cl98, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl91, zip_derived_cl42])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl158, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl98, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl80, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl17])).
% 5.46/1.47 thf(zip_derived_cl42, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1256])).
% 5.46/1.47 thf(zip_derived_cl89, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl42])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl144, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl89, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl94, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl70, zip_derived_cl6])).
% 5.46/1.47 thf(zip_derived_cl145, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl144, zip_derived_cl94])).
% 5.46/1.47 thf(zip_derived_cl161, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl158, zip_derived_cl145])).
% 5.46/1.47 thf(zip_derived_cl162, plain,
% 5.46/1.47 ((~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl161])).
% 5.46/1.47 thf(zip_derived_cl484, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl481, zip_derived_cl162])).
% 5.46/1.47 thf(zip_derived_cl158, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl98, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl529, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl484, zip_derived_cl158])).
% 5.46/1.47 thf(zip_derived_cl117, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl17])).
% 5.46/1.47 thf(zip_derived_cl42, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1256])).
% 5.46/1.47 thf(zip_derived_cl123, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl117, zip_derived_cl42])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl177, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl123, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl530, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl529, zip_derived_cl177])).
% 5.46/1.47 thf(zip_derived_cl144, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl89, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl531, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl530, zip_derived_cl144])).
% 5.46/1.47 thf(zip_derived_cl24, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_165])).
% 5.46/1.47 thf(zip_derived_cl481, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl476, zip_derived_cl30])).
% 5.46/1.47 thf(zip_derived_cl86, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl20])).
% 5.46/1.47 thf(zip_derived_cl42, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1256])).
% 5.46/1.47 thf(zip_derived_cl107, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl86, zip_derived_cl42])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl187, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl107, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl94, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl70, zip_derived_cl6])).
% 5.46/1.47 thf(zip_derived_cl224, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl187, zip_derived_cl94])).
% 5.46/1.47 thf(zip_derived_cl92, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl90, zip_derived_cl20])).
% 5.46/1.47 thf(zip_derived_cl42, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1256])).
% 5.46/1.47 thf(zip_derived_cl134, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl42])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl239, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl302, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl224, zip_derived_cl239])).
% 5.46/1.47 thf(zip_derived_cl118, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl20])).
% 5.46/1.47 thf(zip_derived_cl42, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1256])).
% 5.46/1.47 thf(zip_derived_cl143, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl42])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl241, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl303, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl302, zip_derived_cl241])).
% 5.46/1.47 thf(zip_derived_cl494, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl481, zip_derived_cl303])).
% 5.46/1.47 thf(zip_derived_cl239, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl533, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl494, zip_derived_cl239])).
% 5.46/1.47 thf(zip_derived_cl187, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl107, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl534, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl533, zip_derived_cl187])).
% 5.46/1.47 thf(zip_derived_cl481, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl476, zip_derived_cl30])).
% 5.46/1.47 thf(zip_derived_cl93, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl90, zip_derived_cl33])).
% 5.46/1.47 thf(zip_derived_cl42, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1256])).
% 5.46/1.47 thf(zip_derived_cl104, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl42])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl180, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl104, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl81, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl33])).
% 5.46/1.47 thf(zip_derived_cl42, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1256])).
% 5.46/1.47 thf(zip_derived_cl101, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl81, zip_derived_cl42])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl175, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl101, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl94, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl70, zip_derived_cl6])).
% 5.46/1.47 thf(zip_derived_cl176, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl175, zip_derived_cl94])).
% 5.46/1.47 thf(zip_derived_cl210, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl180, zip_derived_cl176])).
% 5.46/1.47 thf(zip_derived_cl213, plain,
% 5.46/1.47 ((~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl210])).
% 5.46/1.47 thf(zip_derived_cl119, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl33])).
% 5.46/1.47 thf(zip_derived_cl42, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1256])).
% 5.46/1.47 thf(zip_derived_cl131, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl119, zip_derived_cl42])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl188, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl244, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl213, zip_derived_cl188])).
% 5.46/1.47 thf(zip_derived_cl488, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl481, zip_derived_cl244])).
% 5.46/1.47 thf(zip_derived_cl180, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl104, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl507, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl488, zip_derived_cl180])).
% 5.46/1.47 thf(zip_derived_cl175, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl101, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl508, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl507, zip_derived_cl175])).
% 5.46/1.47 thf(zip_derived_cl531, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl530, zip_derived_cl144])).
% 5.46/1.47 thf(zip_derived_cl428, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl422, zip_derived_cl31])).
% 5.46/1.47 thf(zip_derived_cl508, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl507, zip_derived_cl175])).
% 5.46/1.47 thf(zip_derived_cl531, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl530, zip_derived_cl144])).
% 5.46/1.47 thf(zip_derived_cl59, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X3))))
% 5.46/1.47 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X3))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1132])).
% 5.46/1.47 thf(zip_derived_cl532, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl531, zip_derived_cl59])).
% 5.46/1.47 thf(zip_derived_cl623, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl508, zip_derived_cl532])).
% 5.46/1.47 thf(zip_derived_cl625, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl623])).
% 5.46/1.47 thf(zip_derived_cl626, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl428, zip_derived_cl625])).
% 5.46/1.47 thf(zip_derived_cl628, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl531, zip_derived_cl626])).
% 5.46/1.47 thf(zip_derived_cl629, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl628])).
% 5.46/1.47 thf(zip_derived_cl630, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl508, zip_derived_cl629])).
% 5.46/1.47 thf(zip_derived_cl632, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl630])).
% 5.46/1.47 thf(zip_derived_cl633, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl534, zip_derived_cl632])).
% 5.46/1.47 thf(zip_derived_cl635, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl633])).
% 5.46/1.47 thf(zip_derived_cl637, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl635])).
% 5.46/1.47 thf(zip_derived_cl644, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl637])).
% 5.46/1.47 thf(zip_derived_cl646, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl531, zip_derived_cl644])).
% 5.46/1.47 thf(zip_derived_cl652, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl646])).
% 5.46/1.47 thf(zip_derived_cl658, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('eq_fact', [status(thm)], [zip_derived_cl652])).
% 5.46/1.47 thf(zip_derived_cl659, plain,
% 5.46/1.47 ((~ (iLEQ @ (suc @ (suc @ z)) @ (suc @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl658])).
% 5.46/1.47 thf(zip_derived_cl24, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_165])).
% 5.46/1.47 thf(zip_derived_cl662, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl659, zip_derived_cl24])).
% 5.46/1.47 thf(zip_derived_cl531, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl530, zip_derived_cl144])).
% 5.46/1.47 thf(zip_derived_cl663, plain,
% 5.46/1.47 ((~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl662, zip_derived_cl531])).
% 5.46/1.47 thf(zip_derived_cl534, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl533, zip_derived_cl187])).
% 5.46/1.47 thf(zip_derived_cl664, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl663, zip_derived_cl534])).
% 5.46/1.47 thf(zip_derived_cl508, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl507, zip_derived_cl175])).
% 5.46/1.47 thf(zip_derived_cl665, plain,
% 5.46/1.47 ((~ (E @ (f @ (suc @ z)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl664, zip_derived_cl508])).
% 5.46/1.47 thf(zip_derived_cl666, plain,
% 5.46/1.47 ((~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl428, zip_derived_cl665])).
% 5.46/1.47 thf(zip_derived_cl508, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl507, zip_derived_cl175])).
% 5.46/1.47 thf(zip_derived_cl668, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z))) | ~ (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl666, zip_derived_cl508])).
% 5.46/1.47 thf(zip_derived_cl531, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ z))) | (E @ (s @ 0) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl530, zip_derived_cl144])).
% 5.46/1.47 thf(zip_derived_cl669, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl668, zip_derived_cl531])).
% 5.46/1.47 thf(zip_derived_cl674, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X2) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X2))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X1))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('demod', [status(thm)], [zip_derived_cl606, zip_derived_cl669])).
% 5.46/1.47 thf(clause_332, axiom,
% 5.46/1.47 (( ~( E @ 0 @ ( f @ A_3 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.46/1.47 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 5.46/1.47 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 5.46/1.47 thf(zip_derived_cl36, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_332])).
% 5.46/1.47 thf(zip_derived_cl601, plain, ( (E @ 0 @ (f @ z))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl600, zip_derived_cl523])).
% 5.46/1.47 thf(zip_derived_cl601, plain, ( (E @ 0 @ (f @ z))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl600, zip_derived_cl523])).
% 5.46/1.47 thf(zip_derived_cl601, plain, ( (E @ 0 @ (f @ z))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl600, zip_derived_cl523])).
% 5.46/1.47 thf(clause_1370, axiom,
% 5.46/1.47 (( ~( E @ 0 @ ( f @ ( suc @ B_82 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_80 ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ B_80 ) @ ( suc @ B_81 ) ) ) |
% 5.46/1.47 ( ~( E @ 0 @ ( f @ ( suc @ B_81 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_81 ) ) ) |
% 5.46/1.47 ( ~( E @ 0 @ ( f @ A_3 ) ) ) | ( ~( E @ 0 @ ( f @ B_82 ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_80 ) ) ) |
% 5.46/1.47 ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 5.46/1.47 ( ~( E @ 0 @ ( f @ ( suc @ B_80 ) ) ) ) |
% 5.46/1.47 ( ~( iLEQ @ ( suc @ B_81 ) @ ( suc @ B_82 ) ) ) |
% 5.46/1.47 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 5.46/1.47 ( E @ ( f @ B_80 ) @ ( f @ ( suc @ B_80 ) ) ) |
% 5.46/1.47 ( E @ ( f @ B_81 ) @ ( f @ ( suc @ B_81 ) ) ) |
% 5.46/1.47 ( E @ ( f @ B_82 ) @ ( f @ ( suc @ B_82 ) ) ))).
% 5.46/1.47 thf(zip_derived_cl1, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 5.46/1.47 (~ (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X1))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X2))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X3))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X3) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 5.46/1.47 | (E @ (f @ X3) @ (f @ (suc @ X3)))
% 5.46/1.47 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1370])).
% 5.46/1.47 thf(zip_derived_cl602, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X2) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X2))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X1))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl601, zip_derived_cl1])).
% 5.46/1.47 thf(zip_derived_cl669, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl668, zip_derived_cl531])).
% 5.46/1.47 thf(zip_derived_cl670, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X2) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X2))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X1))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('demod', [status(thm)], [zip_derived_cl602, zip_derived_cl669])).
% 5.46/1.47 thf(zip_derived_cl711, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i]:
% 5.46/1.47 (~ (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X1))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ z) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl601, zip_derived_cl670])).
% 5.46/1.47 thf(zip_derived_cl669, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl668, zip_derived_cl531])).
% 5.46/1.47 thf(zip_derived_cl713, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X1))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ z) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('demod', [status(thm)], [zip_derived_cl711, zip_derived_cl669])).
% 5.46/1.47 thf(zip_derived_cl714, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X1))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl713])).
% 5.46/1.47 thf(zip_derived_cl715, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl601, zip_derived_cl714])).
% 5.46/1.47 thf(zip_derived_cl669, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl668, zip_derived_cl531])).
% 5.46/1.47 thf(zip_derived_cl717, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('demod', [status(thm)], [zip_derived_cl715, zip_derived_cl669])).
% 5.46/1.47 thf(zip_derived_cl718, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl717])).
% 5.46/1.47 thf(zip_derived_cl723, plain,
% 5.46/1.47 ((~ (iLEQ @ (suc @ z) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 5.46/1.47 | (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | (E @ (f @ z) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('eq_fact', [status(thm)], [zip_derived_cl718])).
% 5.46/1.47 thf(zip_derived_cl725, plain,
% 5.46/1.47 (( (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl723])).
% 5.46/1.47 thf(zip_derived_cl601, plain, ( (E @ 0 @ (f @ z))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl600, zip_derived_cl523])).
% 5.46/1.47 thf(zip_derived_cl669, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl668, zip_derived_cl531])).
% 5.46/1.47 thf(zip_derived_cl726, plain,
% 5.46/1.47 (( (E @ (f @ z) @ (f @ (suc @ z))) | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 5.46/1.47 inference('demod', [status(thm)],
% 5.46/1.47 [zip_derived_cl725, zip_derived_cl601, zip_derived_cl669])).
% 5.46/1.47 thf(zip_derived_cl733, plain,
% 5.46/1.47 (( (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ z))
% 5.46/1.47 | (E @ (f @ z) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl726])).
% 5.46/1.47 thf(zip_derived_cl669, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl668, zip_derived_cl531])).
% 5.46/1.47 thf(zip_derived_cl601, plain, ( (E @ 0 @ (f @ z))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl600, zip_derived_cl523])).
% 5.46/1.47 thf(zip_derived_cl735, plain,
% 5.46/1.47 (( (E @ (f @ z) @ (f @ (suc @ z))) | (E @ (f @ z) @ (f @ (suc @ z))))),
% 5.46/1.47 inference('demod', [status(thm)],
% 5.46/1.47 [zip_derived_cl733, zip_derived_cl669, zip_derived_cl601])).
% 5.46/1.47 thf(zip_derived_cl736, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl735])).
% 5.46/1.47 thf(zip_derived_cl737, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X2) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X2))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X1))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('demod', [status(thm)], [zip_derived_cl674, zip_derived_cl736])).
% 5.46/1.47 thf(zip_derived_cl428, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl422, zip_derived_cl31])).
% 5.46/1.47 thf(zip_derived_cl481, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl476, zip_derived_cl30])).
% 5.46/1.47 thf(zip_derived_cl81, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl33])).
% 5.46/1.47 thf(clause_225, axiom,
% 5.46/1.47 (( ~( LE @ ( f @ ( suc @ ( suc @ B_79 ) ) ) @ ( s @ 0 ) ) ) |
% 5.46/1.47 ( E @ 0 @ ( f @ ( suc @ ( suc @ B_79 ) ) ) ) | ( LE @ ( f @ B_79 ) @ 0 ))).
% 5.46/1.47 thf(zip_derived_cl21, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_225])).
% 5.46/1.47 thf(zip_derived_cl100, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl81, zip_derived_cl21])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl189, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl100, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl94, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl70, zip_derived_cl6])).
% 5.46/1.47 thf(zip_derived_cl233, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl189, zip_derived_cl94])).
% 5.46/1.47 thf(zip_derived_cl93, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl90, zip_derived_cl33])).
% 5.46/1.47 thf(zip_derived_cl21, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_225])).
% 5.46/1.47 thf(zip_derived_cl103, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl21])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl240, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl103, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl310, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl233, zip_derived_cl240])).
% 5.46/1.47 thf(zip_derived_cl119, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl33])).
% 5.46/1.47 thf(zip_derived_cl21, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_225])).
% 5.46/1.47 thf(zip_derived_cl130, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl119, zip_derived_cl21])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl277, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl311, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ (suc @ z)))) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl310, zip_derived_cl277])).
% 5.46/1.47 thf(zip_derived_cl495, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl481, zip_derived_cl311])).
% 5.46/1.47 thf(zip_derived_cl240, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl103, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl541, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl495, zip_derived_cl240])).
% 5.46/1.47 thf(zip_derived_cl189, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl100, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl542, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl541, zip_derived_cl189])).
% 5.46/1.47 thf(zip_derived_cl481, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl476, zip_derived_cl30])).
% 5.46/1.47 thf(zip_derived_cl117, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl17])).
% 5.46/1.47 thf(zip_derived_cl21, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_225])).
% 5.46/1.47 thf(zip_derived_cl122, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl117, zip_derived_cl21])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl238, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl80, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl17])).
% 5.46/1.47 thf(zip_derived_cl21, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_225])).
% 5.46/1.47 thf(zip_derived_cl88, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl21])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl179, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl94, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl70, zip_derived_cl6])).
% 5.46/1.47 thf(zip_derived_cl205, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl179, zip_derived_cl94])).
% 5.46/1.47 thf(zip_derived_cl91, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl90, zip_derived_cl17])).
% 5.46/1.47 thf(zip_derived_cl21, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_225])).
% 5.46/1.47 thf(zip_derived_cl97, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl91, zip_derived_cl21])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl186, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl97, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl249, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl205, zip_derived_cl186])).
% 5.46/1.47 thf(zip_derived_cl260, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl238, zip_derived_cl249])).
% 5.46/1.47 thf(zip_derived_cl261, plain,
% 5.46/1.47 ((~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl260])).
% 5.46/1.47 thf(zip_derived_cl489, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl481, zip_derived_cl261])).
% 5.46/1.47 thf(zip_derived_cl186, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl97, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl513, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl489, zip_derived_cl186])).
% 5.46/1.47 thf(zip_derived_cl179, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl514, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl513, zip_derived_cl179])).
% 5.46/1.47 thf(zip_derived_cl24, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_165])).
% 5.46/1.47 thf(zip_derived_cl542, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl541, zip_derived_cl189])).
% 5.46/1.47 thf(zip_derived_cl514, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl513, zip_derived_cl179])).
% 5.46/1.47 thf(zip_derived_cl428, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl422, zip_derived_cl31])).
% 5.46/1.47 thf(zip_derived_cl481, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl476, zip_derived_cl30])).
% 5.46/1.47 thf(zip_derived_cl86, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl20])).
% 5.46/1.47 thf(zip_derived_cl21, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_225])).
% 5.46/1.47 thf(zip_derived_cl106, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl86, zip_derived_cl21])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl242, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl94, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl70, zip_derived_cl6])).
% 5.46/1.47 thf(zip_derived_cl274, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ (suc @ (suc @ z))))) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl242, zip_derived_cl94])).
% 5.46/1.47 thf(zip_derived_cl92, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl90, zip_derived_cl20])).
% 5.46/1.47 thf(zip_derived_cl21, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_225])).
% 5.46/1.47 thf(zip_derived_cl133, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ X0)))))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl21])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl282, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl347, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ (suc @ (suc @ z))))) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl274, zip_derived_cl282])).
% 5.46/1.47 thf(zip_derived_cl118, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.46/1.47 | (LE @ (f @ X0) @ (s @ 0))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl20])).
% 5.46/1.47 thf(zip_derived_cl21, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_225])).
% 5.46/1.47 thf(zip_derived_cl142, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ X0))))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ X0))))))))
% 5.46/1.47 | (LE @ (f @ X0) @ 0)
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl21])).
% 5.46/1.47 thf(zip_derived_cl25, plain, (~ (LE @ (f @ z) @ 0)),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_709])).
% 5.46/1.47 thf(zip_derived_cl283, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl348, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ (suc @ (suc @ z))))) @
% 5.46/1.47 (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z))))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl347, zip_derived_cl283])).
% 5.46/1.47 thf(zip_derived_cl498, plain,
% 5.46/1.47 ((~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl481, zip_derived_cl348])).
% 5.46/1.47 thf(zip_derived_cl282, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ (suc @ z)))))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl544, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl498, zip_derived_cl282])).
% 5.46/1.47 thf(zip_derived_cl242, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl25])).
% 5.46/1.47 thf(zip_derived_cl545, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl544, zip_derived_cl242])).
% 5.46/1.47 thf(zip_derived_cl542, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl541, zip_derived_cl189])).
% 5.46/1.47 thf(zip_derived_cl514, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl513, zip_derived_cl179])).
% 5.46/1.47 thf(zip_derived_cl59, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X3))))
% 5.46/1.47 | ~ (E @ (f @ X3) @ (f @ (suc @ X3)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X3))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_1132])).
% 5.46/1.47 thf(zip_derived_cl515, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl514, zip_derived_cl59])).
% 5.46/1.47 thf(zip_derived_cl753, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl542, zip_derived_cl515])).
% 5.46/1.47 thf(zip_derived_cl754, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl753])).
% 5.46/1.47 thf(zip_derived_cl755, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl545, zip_derived_cl754])).
% 5.46/1.47 thf(zip_derived_cl756, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl755])).
% 5.46/1.47 thf(zip_derived_cl757, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl428, zip_derived_cl756])).
% 5.46/1.47 thf(zip_derived_cl759, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl514, zip_derived_cl757])).
% 5.46/1.47 thf(zip_derived_cl760, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl759])).
% 5.46/1.47 thf(zip_derived_cl761, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl542, zip_derived_cl760])).
% 5.46/1.47 thf(zip_derived_cl762, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ X2))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X2))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl761])).
% 5.46/1.47 thf(zip_derived_cl764, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl762])).
% 5.46/1.47 thf(zip_derived_cl771, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X1))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl764])).
% 5.46/1.47 thf(zip_derived_cl773, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl514, zip_derived_cl771])).
% 5.46/1.47 thf(zip_derived_cl776, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl773])).
% 5.46/1.47 thf(zip_derived_cl779, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 ( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl542, zip_derived_cl776])).
% 5.46/1.47 thf(zip_derived_cl780, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl779])).
% 5.46/1.47 thf(zip_derived_cl784, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('eq_fact', [status(thm)], [zip_derived_cl780])).
% 5.46/1.47 thf(zip_derived_cl785, plain,
% 5.46/1.47 ((~ (iLEQ @ (suc @ (suc @ (suc @ z))) @ (suc @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl784])).
% 5.46/1.47 thf(zip_derived_cl24, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ X0))
% 5.46/1.47 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 5.46/1.47 inference('cnf', [status(esa)], [clause_165])).
% 5.46/1.47 thf(zip_derived_cl788, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl785, zip_derived_cl24])).
% 5.46/1.47 thf(zip_derived_cl514, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl513, zip_derived_cl179])).
% 5.46/1.47 thf(zip_derived_cl789, plain,
% 5.46/1.47 ((~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z))))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl788, zip_derived_cl514])).
% 5.46/1.47 thf(zip_derived_cl545, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ (suc @ z)))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl544, zip_derived_cl242])).
% 5.46/1.47 thf(zip_derived_cl790, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl789, zip_derived_cl545])).
% 5.46/1.47 thf(zip_derived_cl542, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl541, zip_derived_cl189])).
% 5.46/1.47 thf(zip_derived_cl791, plain,
% 5.46/1.47 ((~ (E @ (f @ (suc @ (suc @ z))) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl790, zip_derived_cl542])).
% 5.46/1.47 thf(zip_derived_cl792, plain,
% 5.46/1.47 ((~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z)))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl428, zip_derived_cl791])).
% 5.46/1.47 thf(zip_derived_cl542, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ z))))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl541, zip_derived_cl189])).
% 5.46/1.47 thf(zip_derived_cl794, plain,
% 5.46/1.47 (( (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl792, zip_derived_cl542])).
% 5.46/1.47 thf(zip_derived_cl514, plain,
% 5.46/1.47 (( (E @ (s @ 0) @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl513, zip_derived_cl179])).
% 5.46/1.47 thf(zip_derived_cl795, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl794, zip_derived_cl514])).
% 5.46/1.47 thf(zip_derived_cl812, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X2) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X2))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X1))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X1))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 5.46/1.47 inference('demod', [status(thm)], [zip_derived_cl737, zip_derived_cl795])).
% 5.46/1.47 thf(zip_derived_cl836, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i]:
% 5.46/1.47 (~ (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X1))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl601, zip_derived_cl812])).
% 5.46/1.47 thf(zip_derived_cl669, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl668, zip_derived_cl531])).
% 5.46/1.47 thf(zip_derived_cl736, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl735])).
% 5.46/1.47 thf(zip_derived_cl795, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl794, zip_derived_cl514])).
% 5.46/1.47 thf(zip_derived_cl839, plain,
% 5.46/1.47 (![X0 : $i, X1 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ z) @ (suc @ X0))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X1))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X1) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z)))),
% 5.46/1.47 inference('demod', [status(thm)],
% 5.46/1.47 [zip_derived_cl836, zip_derived_cl669, zip_derived_cl736,
% 5.46/1.47 zip_derived_cl795])).
% 5.46/1.47 thf(zip_derived_cl841, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ z) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl601, zip_derived_cl839])).
% 5.46/1.47 thf(zip_derived_cl795, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl794, zip_derived_cl514])).
% 5.46/1.47 thf(zip_derived_cl669, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl668, zip_derived_cl531])).
% 5.46/1.47 thf(zip_derived_cl736, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl735])).
% 5.46/1.47 thf(zip_derived_cl844, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (iLEQ @ (suc @ z) @ (suc @ z))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 5.46/1.47 inference('demod', [status(thm)],
% 5.46/1.47 [zip_derived_cl841, zip_derived_cl795, zip_derived_cl669,
% 5.46/1.47 zip_derived_cl736])).
% 5.46/1.47 thf(zip_derived_cl845, plain,
% 5.46/1.47 (![X0 : $i]:
% 5.46/1.47 (~ (E @ 0 @ (f @ X0))
% 5.46/1.47 | ~ (iLEQ @ (suc @ X0) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl844])).
% 5.46/1.47 thf(zip_derived_cl850, plain,
% 5.46/1.47 ((~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ z))))
% 5.46/1.47 | ~ (iLEQ @ (suc @ z) @ (suc @ z))
% 5.46/1.47 | ~ (E @ 0 @ (f @ z)))),
% 5.46/1.47 inference('eq_fact', [status(thm)], [zip_derived_cl845])).
% 5.46/1.47 thf(zip_derived_cl736, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl735])).
% 5.46/1.47 thf(zip_derived_cl669, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl668, zip_derived_cl531])).
% 5.46/1.47 thf(zip_derived_cl795, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl794, zip_derived_cl514])).
% 5.46/1.47 thf(zip_derived_cl601, plain, ( (E @ 0 @ (f @ z))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl600, zip_derived_cl523])).
% 5.46/1.47 thf(zip_derived_cl851, plain, (~ (iLEQ @ (suc @ z) @ (suc @ z))),
% 5.46/1.47 inference('demod', [status(thm)],
% 5.46/1.47 [zip_derived_cl850, zip_derived_cl736, zip_derived_cl669,
% 5.46/1.47 zip_derived_cl795, zip_derived_cl601])).
% 5.46/1.47 thf(zip_derived_cl855, plain,
% 5.46/1.47 ((~ (E @ 0 @ (f @ z))
% 5.46/1.47 | ~ (E @ (f @ z) @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ z)))
% 5.46/1.47 | ~ (E @ 0 @ (f @ (suc @ (suc @ z)))))),
% 5.46/1.47 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl851])).
% 5.46/1.47 thf(zip_derived_cl601, plain, ( (E @ 0 @ (f @ z))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl600, zip_derived_cl523])).
% 5.46/1.47 thf(zip_derived_cl736, plain, ( (E @ (f @ z) @ (f @ (suc @ z)))),
% 5.46/1.47 inference('simplify', [status(thm)], [zip_derived_cl735])).
% 5.46/1.47 thf(zip_derived_cl669, plain, ( (E @ 0 @ (f @ (suc @ z)))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl668, zip_derived_cl531])).
% 5.46/1.47 thf(zip_derived_cl795, plain, ( (E @ 0 @ (f @ (suc @ (suc @ z))))),
% 5.46/1.47 inference('clc', [status(thm)], [zip_derived_cl794, zip_derived_cl514])).
% 5.46/1.47 thf(zip_derived_cl858, plain, ($false),
% 5.46/1.47 inference('demod', [status(thm)],
% 5.46/1.47 [zip_derived_cl855, zip_derived_cl601, zip_derived_cl736,
% 5.46/1.47 zip_derived_cl669, zip_derived_cl795])).
% 5.46/1.47
% 5.46/1.47 % SZS output end Refutation
% 5.46/1.47
% 5.46/1.47
% 5.46/1.48 % Terminating...
% 5.92/1.58 % Runner terminated.
% 5.92/1.59 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------