TSTP Solution File: SYO688-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO688-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.y6XNjIBvAG true
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 05:52:35 EDT 2023
% Result : Unsatisfiable 30.20s 5.00s
% Output : Refutation 30.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO688-1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.y6XNjIBvAG true
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 06:36:26 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.13/0.33 % Running portfolio for 300 s
% 0.13/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.33 % Number of cores: 8
% 0.13/0.33 % Python version: Python 3.6.8
% 0.13/0.33 % Running in FO mode
% 0.19/0.62 % Total configuration time : 435
% 0.19/0.62 % Estimated wc time : 1092
% 0.19/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.19/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.19/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.19/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.19/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.19/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.19/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.19/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 2.43/1.01 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 2.43/1.01 % /export/starexec/sandbox2/solver/bin/fo/fo17_bce.sh running for 50s
% 2.43/1.01 % /export/starexec/sandbox2/solver/bin/fo/fo8.sh running for 50s
% 30.20/5.00 % Solved by fo/fo1_lcnf.sh.
% 30.20/5.00 % done 2404 iterations in 3.944s
% 30.20/5.00 % SZS status Unsatisfiable for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 30.20/5.00 % SZS output start Refutation
% 30.20/5.00 thf(suc_type, type, suc: $i > $i).
% 30.20/5.00 thf(iLEQ_type, type, iLEQ: $i > $i > $o).
% 30.20/5.00 thf(0_type, type, 0: $i).
% 30.20/5.00 thf(z_type, type, z: $i).
% 30.20/5.00 thf(LE_type, type, LE: $i > $i > $o).
% 30.20/5.00 thf(s_type, type, s: $i > $i).
% 30.20/5.00 thf(f_type, type, f: $i > $i).
% 30.20/5.00 thf(E_type, type, E: $i > $i > $o).
% 30.20/5.00 thf(clause_546, axiom, (~( LE @ ( f @ z ) @ 0 ))).
% 30.20/5.00 thf(zip_derived_cl365, plain, (~ (LE @ (f @ z) @ 0)),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_546])).
% 30.20/5.00 thf(clause_840, axiom,
% 30.20/5.00 (( ~( LE @ ( f @ ( suc @ ( suc @ B_93 ) ) ) @ ( s @ 0 ) ) ) |
% 30.20/5.00 ( E @ 0 @ ( f @ ( suc @ ( suc @ B_93 ) ) ) ) | ( LE @ ( f @ B_93 ) @ 0 ))).
% 30.20/5.00 thf(zip_derived_cl659, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0)))) |
% 30.20/5.00 (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0)))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_840])).
% 30.20/5.00 thf(zip_derived_cl1171, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 30.20/5.00 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl659])).
% 30.20/5.00 thf(clause_149, axiom,
% 30.20/5.00 (( ~( LE @ ( f @ ( suc @ B_86 ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 30.20/5.00 ( E @ ( s @ 0 ) @ ( f @ ( suc @ B_86 ) ) ) |
% 30.20/5.00 ( LE @ ( f @ B_86 ) @ ( s @ 0 ) ))).
% 30.20/5.00 thf(zip_derived_cl691, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0))))) |
% 30.20/5.00 (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_149])).
% 30.20/5.00 thf(zip_derived_cl1172, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 30.20/5.00 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl691])).
% 30.20/5.00 thf(clause_569, axiom,
% 30.20/5.00 (( ~( LE @ ( f @ ( suc @ ( suc @ B_74 ) ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 30.20/5.00 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_74 ) ) ) ) |
% 30.20/5.00 ( LE @ ( f @ B_74 ) @ ( s @ ( s @ 0 ) ) ))).
% 30.20/5.00 thf(zip_derived_cl913, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0)))))) |
% 30.20/5.00 (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))) |
% 30.20/5.00 (LE @ (f @ X0) @ (s @ (s @ 0)))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_569])).
% 30.20/5.00 thf(zip_derived_cl1186, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0))))
% 30.20/5.00 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl913])).
% 30.20/5.00 thf(clause_1123, axiom,
% 30.20/5.00 (( ~( LE @
% 30.20/5.00 ( f @ ( suc @ ( suc @ B_56 ) ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 30.20/5.00 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_56 ) ) ) ) |
% 30.20/5.00 ( LE @ ( f @ B_56 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 30.20/5.00 thf(zip_derived_cl138, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ (s @ 0))))))) |
% 30.20/5.00 (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))) |
% 30.20/5.00 (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_1123])).
% 30.20/5.00 thf(zip_derived_cl1194, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ (s @ 0)))))
% 30.20/5.00 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl138])).
% 30.20/5.00 thf(clause_231, axiom,
% 30.20/5.00 (( ~( LE @
% 30.20/5.00 ( f @ ( suc @ ( suc @ B_31 ) ) ) @
% 30.20/5.00 ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) ) |
% 30.20/5.00 ( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ B_31 ) ) ) ) |
% 30.20/5.00 ( LE @ ( f @ B_31 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 30.20/5.00 thf(zip_derived_cl579, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (LE @ (f @ (suc @ (suc @ X0))) @
% 30.20/5.00 (s @ (s @ (s @ (s @ (s @ 0)))))))) |
% 30.20/5.00 (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))) |
% 30.20/5.00 (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_231])).
% 30.20/5.00 thf(clause_299, axiom,
% 30.20/5.00 (LE @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 30.20/5.00 thf(zip_derived_cl91, plain,
% 30.20/5.00 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_299])).
% 30.20/5.00 thf(zip_derived_cl1214, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ ($true))) |
% 30.20/5.00 (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))) |
% 30.20/5.00 (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))))),
% 30.20/5.00 inference('demod', [status(thm)], [zip_derived_cl579, zip_derived_cl91])).
% 30.20/5.00 thf(zip_derived_cl1215, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))) | (LE @
% 30.20/5.00 (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))))),
% 30.20/5.00 inference('simplify boolean subterms', [status(thm)],
% 30.20/5.00 [zip_derived_cl1214])).
% 30.20/5.00 thf(zip_derived_cl1216, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1215])).
% 30.20/5.00 thf(clause_436, axiom,
% 30.20/5.00 (( ~( E @
% 30.20/5.00 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ B_33 ) ) ) ) ) |
% 30.20/5.00 ( ~( E @
% 30.20/5.00 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ B_32 ) @ ( f @ ( suc @ B_32 ) ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ B_32 ) @ ( suc @ B_33 ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ B_33 ) @ ( f @ ( suc @ B_33 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_33 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_32 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 30.20/5.00 ( ~( E @
% 30.20/5.00 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ B_32 ) ) ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_32 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_32 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_33 ) ) ) ))).
% 30.20/5.00 thf(zip_derived_cl401, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (((((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X1)))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X2) @ (f @ (suc @ X2))))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X2) @ (suc @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X2))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X1) @ (f @ (suc @ X1))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X2)))))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X1) @ (suc @ X2)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X2)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_436])).
% 30.20/5.00 thf(zip_derived_cl4812, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X1))))
% 30.20/5.00 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X2))))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X2))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl401])).
% 30.20/5.00 thf(zip_derived_cl4816, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X1))))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl4812])).
% 30.20/5.00 thf(zip_derived_cl4818, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X1))))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl4816])).
% 30.20/5.00 thf(zip_derived_cl4828, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl4818])).
% 30.20/5.00 thf(zip_derived_cl4829, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl4828])).
% 30.20/5.00 thf(clause_105, axiom,
% 30.20/5.00 (( ~( iLEQ @ ( suc @ B_32 ) @ ( suc @ B_33 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_33 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_32 ) ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_32 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_32 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_33 ) ) ) ) |
% 30.20/5.00 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 30.20/5.00 ( E @ ( f @ B_32 ) @ ( f @ ( suc @ B_32 ) ) ) |
% 30.20/5.00 ( E @ ( f @ B_33 ) @ ( f @ ( suc @ B_33 ) ) ))).
% 30.20/5.00 thf(zip_derived_cl808, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (((((~) @ (iLEQ @ (suc @ X0) @ (suc @ X1)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X2))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X2) @ (suc @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X2)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1))))) |
% 30.20/5.00 (E @ (f @ X2) @ (f @ (suc @ X2))) |
% 30.20/5.00 (E @ (f @ X0) @ (f @ (suc @ X0))) |
% 30.20/5.00 (E @ (f @ X1) @ (f @ (suc @ X1)))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_105])).
% 30.20/5.00 thf(zip_derived_cl4112, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X2))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl808])).
% 30.20/5.00 thf(zip_derived_cl4116, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1)))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl4112])).
% 30.20/5.00 thf(zip_derived_cl4118, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl4116])).
% 30.20/5.00 thf(clause_698, axiom,
% 30.20/5.00 (( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 30.20/5.00 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 30.20/5.00 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 30.20/5.00 thf(zip_derived_cl1084, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (E @ (f @ X0) @ (f @ (suc @ X0))) |
% 30.20/5.00 (iLEQ @ (suc @ X0) @ (suc @ X0))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_698])).
% 30.20/5.00 thf(zip_derived_cl1209, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1084])).
% 30.20/5.00 thf(zip_derived_cl4124, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl4118, zip_derived_cl1209])).
% 30.20/5.00 thf(zip_derived_cl4128, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl4124])).
% 30.20/5.00 thf(zip_derived_cl4129, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl4128])).
% 30.20/5.00 thf(zip_derived_cl1209, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1084])).
% 30.20/5.00 thf(zip_derived_cl4130, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl4129, zip_derived_cl1209])).
% 30.20/5.00 thf(zip_derived_cl4830, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl4829, zip_derived_cl4130])).
% 30.20/5.00 thf(clause_473, axiom,
% 30.20/5.00 (( ~( E @
% 30.20/5.00 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 30.20/5.00 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 30.20/5.00 thf(zip_derived_cl469, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))) |
% 30.20/5.00 (iLEQ @ (suc @ X0) @ (suc @ X0))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_473])).
% 30.20/5.00 thf(zip_derived_cl1306, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl469])).
% 30.20/5.00 thf(zip_derived_cl1209, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1084])).
% 30.20/5.00 thf(zip_derived_cl1307, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl1306, zip_derived_cl1209])).
% 30.20/5.00 thf(zip_derived_cl4831, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl4830, zip_derived_cl1307])).
% 30.20/5.00 thf(zip_derived_cl4833, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl1216, zip_derived_cl4831])).
% 30.20/5.00 thf(clause_298, axiom,
% 30.20/5.00 (( ~( LE @ ( f @ B_31 ) @ ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) ) |
% 30.20/5.00 ( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_31 ) ) |
% 30.20/5.00 ( LE @ ( f @ B_31 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 30.20/5.00 thf(zip_derived_cl893, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0)))))))) |
% 30.20/5.00 (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)) |
% 30.20/5.00 (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_298])).
% 30.20/5.00 thf(zip_derived_cl91, plain,
% 30.20/5.00 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_299])).
% 30.20/5.00 thf(zip_derived_cl1191, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ ($true))) | (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)) |
% 30.20/5.00 (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))))),
% 30.20/5.00 inference('demod', [status(thm)], [zip_derived_cl893, zip_derived_cl91])).
% 30.20/5.00 thf(zip_derived_cl1192, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)) | (LE @ (f @ X0) @
% 30.20/5.00 (s @ (s @ (s @ (s @ 0)))))))),
% 30.20/5.00 inference('simplify boolean subterms', [status(thm)],
% 30.20/5.00 [zip_derived_cl1191])).
% 30.20/5.00 thf(zip_derived_cl1193, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1192])).
% 30.20/5.00 thf(zip_derived_cl4835, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl4833, zip_derived_cl1193])).
% 30.20/5.00 thf(clause_297, axiom,
% 30.20/5.00 (( ~( LE @
% 30.20/5.00 ( f @ ( suc @ B_31 ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) ) |
% 30.20/5.00 ( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_31 ) ) ) |
% 30.20/5.00 ( LE @ ( f @ B_31 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 30.20/5.00 thf(zip_derived_cl1150, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ (s @ (s @ 0)))))))) |
% 30.20/5.00 (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))) |
% 30.20/5.00 (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_297])).
% 30.20/5.00 thf(zip_derived_cl91, plain,
% 30.20/5.00 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_299])).
% 30.20/5.00 thf(zip_derived_cl1198, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ ($true))) |
% 30.20/5.00 (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))) |
% 30.20/5.00 (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))))),
% 30.20/5.00 inference('demod', [status(thm)], [zip_derived_cl1150, zip_derived_cl91])).
% 30.20/5.00 thf(zip_derived_cl1199, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))) | (LE @
% 30.20/5.00 (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))))),
% 30.20/5.00 inference('simplify boolean subterms', [status(thm)],
% 30.20/5.00 [zip_derived_cl1198])).
% 30.20/5.00 thf(zip_derived_cl1200, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1199])).
% 30.20/5.00 thf(zip_derived_cl4836, plain,
% 30.20/5.00 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl4835, zip_derived_cl1200])).
% 30.20/5.00 thf(zip_derived_cl4839, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1194, zip_derived_cl4836])).
% 30.20/5.00 thf(clause_1016, axiom,
% 30.20/5.00 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_58 ) ) ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_57 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_57 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ B_57 ) @ ( suc @ B_58 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_57 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ B_58 ) @ ( f @ ( suc @ B_58 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ B_57 ) @ ( f @ ( suc @ B_57 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_58 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_58 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_57 ) ) ) ) ))).
% 30.20/5.00 thf(zip_derived_cl931, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (((((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X1) @ (suc @ X2)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ X2)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1))))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X2) @ (suc @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ X1)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X2) @ (f @ (suc @ X2))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1)))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X1) @ (f @ (suc @ X1))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X2))))))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_1016])).
% 30.20/5.00 thf(zip_derived_cl5294, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1))))
% 30.20/5.00 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X2)))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl931])).
% 30.20/5.00 thf(zip_derived_cl5298, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1))))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1)))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl5294])).
% 30.20/5.00 thf(zip_derived_cl5300, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1)))))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl5298])).
% 30.20/5.00 thf(zip_derived_cl5319, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl5300])).
% 30.20/5.00 thf(zip_derived_cl5320, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl5319])).
% 30.20/5.00 thf(clause_1023, axiom,
% 30.20/5.00 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 30.20/5.00 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 30.20/5.00 thf(zip_derived_cl189, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))) |
% 30.20/5.00 (iLEQ @ (suc @ X0) @ (suc @ X0))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_1023])).
% 30.20/5.00 thf(zip_derived_cl1264, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl189])).
% 30.20/5.00 thf(clause_171, axiom,
% 30.20/5.00 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 30.20/5.00 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 30.20/5.00 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 30.20/5.00 thf(zip_derived_cl147, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (E @ (f @ X0) @ (f @ (suc @ X0))) |
% 30.20/5.00 (iLEQ @ (suc @ X0) @ (suc @ X0))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_171])).
% 30.20/5.00 thf(zip_derived_cl1195, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl147])).
% 30.20/5.00 thf(zip_derived_cl1265, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl1264, zip_derived_cl1195])).
% 30.20/5.00 thf(zip_derived_cl5321, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5320, zip_derived_cl1265])).
% 30.20/5.00 thf(clause_249, axiom,
% 30.20/5.00 (( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_57 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_57 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ B_57 ) @ ( suc @ B_58 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_57 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_58 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_58 ) ) ) ) |
% 30.20/5.00 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 30.20/5.00 ( E @ ( f @ B_57 ) @ ( f @ ( suc @ B_57 ) ) ) |
% 30.20/5.00 ( E @ ( f @ B_58 ) @ ( f @ ( suc @ B_58 ) ) ))).
% 30.20/5.00 thf(zip_derived_cl1159, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (((((~) @ (iLEQ @ (suc @ X0) @ (suc @ X1)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ X1)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X1) @ (suc @ X2)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ X2)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2))))) |
% 30.20/5.00 (E @ (f @ X0) @ (f @ (suc @ X0))) |
% 30.20/5.00 (E @ (f @ X1) @ (f @ (suc @ X1))) |
% 30.20/5.00 (E @ (f @ X2) @ (f @ (suc @ X2)))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_249])).
% 30.20/5.00 thf(zip_derived_cl3457, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X2) @ (f @ (suc @ X2))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1159])).
% 30.20/5.00 thf(zip_derived_cl3461, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl3457])).
% 30.20/5.00 thf(zip_derived_cl3463, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl3461])).
% 30.20/5.00 thf(zip_derived_cl1195, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl147])).
% 30.20/5.00 thf(zip_derived_cl3468, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl3463, zip_derived_cl1195])).
% 30.20/5.00 thf(zip_derived_cl3472, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl3468])).
% 30.20/5.00 thf(zip_derived_cl3473, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl3472])).
% 30.20/5.00 thf(zip_derived_cl1195, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl147])).
% 30.20/5.00 thf(zip_derived_cl3474, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl3473, zip_derived_cl1195])).
% 30.20/5.00 thf(zip_derived_cl5322, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5321, zip_derived_cl3474])).
% 30.20/5.00 thf(zip_derived_cl5325, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl4839, zip_derived_cl5322])).
% 30.20/5.00 thf(clause_24, axiom,
% 30.20/5.00 (( ~( LE @ ( f @ B_56 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 30.20/5.00 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_56 ) ) |
% 30.20/5.00 ( LE @ ( f @ B_56 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 30.20/5.00 thf(zip_derived_cl1030, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))) |
% 30.20/5.00 (E @ (s @ (s @ (s @ 0))) @ (f @ X0)) |
% 30.20/5.00 (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_24])).
% 30.20/5.00 thf(zip_derived_cl1179, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 30.20/5.00 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1030])).
% 30.20/5.00 thf(zip_derived_cl4836, plain,
% 30.20/5.00 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl4835, zip_derived_cl1200])).
% 30.20/5.00 thf(zip_derived_cl4837, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1179, zip_derived_cl4836])).
% 30.20/5.00 thf(zip_derived_cl5327, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5325, zip_derived_cl4837])).
% 30.20/5.00 thf(clause_269, axiom,
% 30.20/5.00 (( ~( LE @ ( f @ ( suc @ B_56 ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 30.20/5.00 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_56 ) ) ) |
% 30.20/5.00 ( LE @ ( f @ B_56 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 30.20/5.00 thf(zip_derived_cl168, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ (s @ 0))))))) |
% 30.20/5.00 (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))) |
% 30.20/5.00 (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_269])).
% 30.20/5.00 thf(zip_derived_cl1190, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ (s @ 0)))))
% 30.20/5.00 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl168])).
% 30.20/5.00 thf(zip_derived_cl4836, plain,
% 30.20/5.00 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl4835, zip_derived_cl1200])).
% 30.20/5.00 thf(zip_derived_cl4838, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1190, zip_derived_cl4836])).
% 30.20/5.00 thf(zip_derived_cl5328, plain,
% 30.20/5.00 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5327, zip_derived_cl4838])).
% 30.20/5.00 thf(zip_derived_cl5331, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1186, zip_derived_cl5328])).
% 30.20/5.00 thf(clause_115, axiom,
% 30.20/5.00 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_75 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_76 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ B_76 ) @ ( f @ ( suc @ B_76 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_76 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ B_75 ) @ ( suc @ B_76 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_76 ) ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_75 ) ) ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_75 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_75 ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ B_75 ) @ ( f @ ( suc @ B_75 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ))).
% 30.20/5.00 thf(zip_derived_cl981, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (((((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X2) @ (f @ (suc @ X2))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ X2)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1)))))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X0) @ (suc @ X2)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X2)))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X1) @ (f @ (suc @ X1))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X1) @ (suc @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ X1))))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_115])).
% 30.20/5.00 thf(zip_derived_cl5005, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X2))))
% 30.20/5.00 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X1)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl981])).
% 30.20/5.00 thf(zip_derived_cl5009, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1))))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl5005])).
% 30.20/5.00 thf(zip_derived_cl5011, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 30.20/5.00 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl5009])).
% 30.20/5.00 thf(zip_derived_cl5194, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl5011])).
% 30.20/5.00 thf(zip_derived_cl5195, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl5194])).
% 30.20/5.00 thf(clause_237, axiom,
% 30.20/5.00 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 30.20/5.00 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 30.20/5.00 thf(zip_derived_cl278, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ X0)))) |
% 30.20/5.00 (iLEQ @ (suc @ X0) @ (suc @ X0))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_237])).
% 30.20/5.00 thf(zip_derived_cl1243, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl278])).
% 30.20/5.00 thf(clause_794, axiom,
% 30.20/5.00 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 30.20/5.00 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 30.20/5.00 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 30.20/5.00 thf(zip_derived_cl942, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (E @ (s @ (s @ 0)) @ (f @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (E @ (f @ X0) @ (f @ (suc @ X0))) |
% 30.20/5.00 (iLEQ @ (suc @ X0) @ (suc @ X0))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_794])).
% 30.20/5.00 thf(zip_derived_cl1189, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl942])).
% 30.20/5.00 thf(zip_derived_cl1244, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl1243, zip_derived_cl1189])).
% 30.20/5.00 thf(zip_derived_cl5196, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5195, zip_derived_cl1244])).
% 30.20/5.00 thf(clause_778, axiom,
% 30.20/5.00 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_75 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_76 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_76 ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ B_75 ) @ ( suc @ B_76 ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_75 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_75 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 30.20/5.00 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 30.20/5.00 ( E @ ( f @ B_75 ) @ ( f @ ( suc @ B_75 ) ) ) |
% 30.20/5.00 ( E @ ( f @ B_76 ) @ ( f @ ( suc @ B_76 ) ) ))).
% 30.20/5.00 thf(zip_derived_cl586, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (((((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2))))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ X2)))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X0) @ (suc @ X2)))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X1) @ (suc @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ (s @ 0)) @ (f @ X1)))) |
% 30.20/5.00 (E @ (f @ X1) @ (f @ (suc @ X1))) |
% 30.20/5.00 (E @ (f @ X0) @ (f @ (suc @ X0))) |
% 30.20/5.00 (E @ (f @ X2) @ (f @ (suc @ X2)))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_778])).
% 30.20/5.00 thf(zip_derived_cl2746, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X2) @ (f @ (suc @ X2))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl586])).
% 30.20/5.00 thf(zip_derived_cl2747, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl2746])).
% 30.20/5.00 thf(zip_derived_cl2749, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl2747])).
% 30.20/5.00 thf(zip_derived_cl1189, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl942])).
% 30.20/5.00 thf(zip_derived_cl2752, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl2749, zip_derived_cl1189])).
% 30.20/5.00 thf(zip_derived_cl2753, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl2752])).
% 30.20/5.00 thf(zip_derived_cl2754, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl2753])).
% 30.20/5.00 thf(zip_derived_cl1189, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl942])).
% 30.20/5.00 thf(zip_derived_cl2755, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl2754, zip_derived_cl1189])).
% 30.20/5.00 thf(zip_derived_cl5197, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5196, zip_derived_cl2755])).
% 30.20/5.00 thf(zip_derived_cl5343, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl5331, zip_derived_cl5197])).
% 30.20/5.00 thf(clause_773, axiom,
% 30.20/5.00 (( ~( LE @ ( f @ ( suc @ B_74 ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 30.20/5.00 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_74 ) ) ) |
% 30.20/5.00 ( LE @ ( f @ B_74 ) @ ( s @ ( s @ 0 ) ) ))).
% 30.20/5.00 thf(zip_derived_cl134, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0)))))) |
% 30.20/5.00 (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))) |
% 30.20/5.00 (LE @ (f @ X0) @ (s @ (s @ 0)))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_773])).
% 30.20/5.00 thf(zip_derived_cl1178, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0))))
% 30.20/5.00 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl134])).
% 30.20/5.00 thf(zip_derived_cl5328, plain,
% 30.20/5.00 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5327, zip_derived_cl4838])).
% 30.20/5.00 thf(zip_derived_cl5330, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1178, zip_derived_cl5328])).
% 30.20/5.00 thf(zip_derived_cl5344, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5343, zip_derived_cl5330])).
% 30.20/5.00 thf(clause_1143, axiom,
% 30.20/5.00 (( ~( LE @ ( f @ B_74 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 30.20/5.00 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_74 ) ) |
% 30.20/5.00 ( LE @ ( f @ B_74 ) @ ( s @ ( s @ 0 ) ) ))).
% 30.20/5.00 thf(zip_derived_cl501, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))) |
% 30.20/5.00 (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0)))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_1143])).
% 30.20/5.00 thf(zip_derived_cl1173, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 30.20/5.00 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl501])).
% 30.20/5.00 thf(zip_derived_cl5328, plain,
% 30.20/5.00 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5327, zip_derived_cl4838])).
% 30.20/5.00 thf(zip_derived_cl5329, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1173, zip_derived_cl5328])).
% 30.20/5.00 thf(zip_derived_cl5345, plain,
% 30.20/5.00 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5344, zip_derived_cl5329])).
% 30.20/5.00 thf(zip_derived_cl5347, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1172, zip_derived_cl5345])).
% 30.20/5.00 thf(clause_1089, axiom,
% 30.20/5.00 (( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 30.20/5.00 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) |
% 30.20/5.00 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 30.20/5.00 thf(zip_derived_cl851, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (E @ (s @ 0) @ (f @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (E @ (f @ X0) @ (f @ (suc @ X0))) |
% 30.20/5.00 (iLEQ @ (suc @ X0) @ (suc @ X0))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_1089])).
% 30.20/5.00 thf(zip_derived_cl1182, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl851])).
% 30.20/5.00 thf(zip_derived_cl5364, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ 0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl5347, zip_derived_cl1182])).
% 30.20/5.00 thf(clause_1158, axiom,
% 30.20/5.00 (( ~( LE @ ( f @ B_86 ) @ ( s @ ( s @ 0 ) ) ) ) |
% 30.20/5.00 ( E @ ( s @ 0 ) @ ( f @ B_86 ) ) | ( LE @ ( f @ B_86 ) @ ( s @ 0 ) ))).
% 30.20/5.00 thf(zip_derived_cl152, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (LE @ (f @ X0) @ (s @ (s @ 0))))) |
% 30.20/5.00 (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_1158])).
% 30.20/5.00 thf(zip_derived_cl1169, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 30.20/5.00 | (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl152])).
% 30.20/5.00 thf(zip_derived_cl5345, plain,
% 30.20/5.00 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5344, zip_derived_cl5329])).
% 30.20/5.00 thf(zip_derived_cl5346, plain,
% 30.20/5.00 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1169, zip_derived_cl5345])).
% 30.20/5.00 thf(zip_derived_cl5378, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5364, zip_derived_cl5346])).
% 30.20/5.00 thf(clause_160, axiom,
% 30.20/5.00 (( ~( LE @ ( f @ ( suc @ ( suc @ B_86 ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 30.20/5.00 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_86 ) ) ) ) |
% 30.20/5.00 ( LE @ ( f @ B_86 ) @ ( s @ 0 ) ))).
% 30.20/5.00 thf(zip_derived_cl534, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0))))) |
% 30.20/5.00 (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))) |
% 30.20/5.00 (LE @ (f @ X0) @ (s @ 0))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_160])).
% 30.20/5.00 thf(zip_derived_cl1177, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 30.20/5.00 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl534])).
% 30.20/5.00 thf(zip_derived_cl5345, plain,
% 30.20/5.00 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5344, zip_derived_cl5329])).
% 30.20/5.00 thf(zip_derived_cl5348, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1177, zip_derived_cl5345])).
% 30.20/5.00 thf(clause_813, axiom,
% 30.20/5.00 (( ~( E @ ( s @ 0 ) @ ( f @ B_88 ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_88 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_87 ) ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ B_87 ) @ ( f @ ( suc @ B_87 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ B_88 ) @ ( f @ ( suc @ B_88 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_87 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ B_87 ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ B_87 ) @ ( suc @ B_88 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_88 ) ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_87 ) ) ))).
% 30.20/5.00 thf(zip_derived_cl383, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (((((~) @ (E @ (s @ 0) @ (f @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (f @ X1) @ (f @ (suc @ X1))))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1)))))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2)))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X2) @ (f @ (suc @ X2))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ (suc @ X2))))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ X2)))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X2) @ (suc @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ (suc @ X1))))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ X1)))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X1) @ (suc @ X2))))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_813])).
% 30.20/5.00 thf(zip_derived_cl4485, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 30.20/5.00 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X2))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X1))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl383])).
% 30.20/5.00 thf(zip_derived_cl4486, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl4485])).
% 30.20/5.00 thf(zip_derived_cl4488, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 (~ (E @ (s @ 0) @ (f @ X1))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl4486])).
% 30.20/5.00 thf(zip_derived_cl4492, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl4488])).
% 30.20/5.00 thf(zip_derived_cl4493, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl4492])).
% 30.20/5.00 thf(clause_340, axiom,
% 30.20/5.00 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 30.20/5.00 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 30.20/5.00 thf(zip_derived_cl359, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ X0)))) |
% 30.20/5.00 (iLEQ @ (suc @ X0) @ (suc @ X0))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_340])).
% 30.20/5.00 thf(zip_derived_cl1226, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl359])).
% 30.20/5.00 thf(zip_derived_cl1182, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl851])).
% 30.20/5.00 thf(zip_derived_cl1227, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl1226, zip_derived_cl1182])).
% 30.20/5.00 thf(zip_derived_cl4494, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl4493, zip_derived_cl1227])).
% 30.20/5.00 thf(zip_derived_cl5373, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ 0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl5348, zip_derived_cl4494])).
% 30.20/5.00 thf(zip_derived_cl5346, plain,
% 30.20/5.00 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1169, zip_derived_cl5345])).
% 30.20/5.00 thf(zip_derived_cl5374, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5373, zip_derived_cl5346])).
% 30.20/5.00 thf(zip_derived_cl5347, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1172, zip_derived_cl5345])).
% 30.20/5.00 thf(zip_derived_cl5375, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ 0)) | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5374, zip_derived_cl5347])).
% 30.20/5.00 thf(zip_derived_cl5379, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ 0)) | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5378, zip_derived_cl5375])).
% 30.20/5.00 thf(zip_derived_cl5379, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ 0)) | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5378, zip_derived_cl5375])).
% 30.20/5.00 thf(zip_derived_cl5346, plain,
% 30.20/5.00 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1169, zip_derived_cl5345])).
% 30.20/5.00 thf(zip_derived_cl5347, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1172, zip_derived_cl5345])).
% 30.20/5.00 thf(zip_derived_cl5347, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1172, zip_derived_cl5345])).
% 30.20/5.00 thf(zip_derived_cl5347, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1172, zip_derived_cl5345])).
% 30.20/5.00 thf(clause_694, axiom,
% 30.20/5.00 (( ~( E @ ( s @ 0 ) @ ( f @ B_88 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_88 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_87 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ B_87 ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ B_87 ) @ ( suc @ B_88 ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_87 ) ) ) |
% 30.20/5.00 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) |
% 30.20/5.00 ( E @ ( f @ B_87 ) @ ( f @ ( suc @ B_87 ) ) ) |
% 30.20/5.00 ( E @ ( f @ B_88 ) @ ( f @ ( suc @ B_88 ) ) ))).
% 30.20/5.00 thf(zip_derived_cl755, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (((((~) @ (E @ (s @ 0) @ (f @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ (suc @ X1))))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ X1)))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X1) @ (suc @ X0)))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ (suc @ X2))))) |
% 30.20/5.00 (((~) @ (E @ (s @ 0) @ (f @ X2)))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X2) @ (suc @ X1)))) |
% 30.20/5.00 (E @ (f @ X2) @ (f @ (suc @ X2))) |
% 30.20/5.00 (E @ (f @ X1) @ (f @ (suc @ X1))) |
% 30.20/5.00 (E @ (f @ X0) @ (f @ (suc @ X0)))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_694])).
% 30.20/5.00 thf(zip_derived_cl2316, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X1))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X2))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 30.20/5.00 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl755])).
% 30.20/5.00 thf(zip_derived_cl5365, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ 0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X1))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X2))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 30.20/5.00 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl5347, zip_derived_cl2316])).
% 30.20/5.00 thf(zip_derived_cl5466, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ 0))
% 30.20/5.00 | (LE @ (f @ X1) @ (s @ 0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X1))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X2))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 30.20/5.00 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl5347, zip_derived_cl5365])).
% 30.20/5.00 thf(zip_derived_cl5507, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ 0))
% 30.20/5.00 | (LE @ (f @ X1) @ (s @ 0))
% 30.20/5.00 | (LE @ (f @ X2) @ (s @ 0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X2))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X1))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X2) @ (f @ (suc @ X2))))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl5347, zip_derived_cl5466])).
% 30.20/5.00 thf(zip_derived_cl6689, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ 0))
% 30.20/5.00 | (LE @ (f @ X1) @ (s @ 0))
% 30.20/5.00 | (LE @ (f @ X2) @ (s @ 0))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ 0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X2))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X1))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl5346, zip_derived_cl5507])).
% 30.20/5.00 thf(zip_derived_cl6690, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X1))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X2))
% 30.20/5.00 | (LE @ (f @ X2) @ (s @ 0))
% 30.20/5.00 | (LE @ (f @ X1) @ (s @ 0))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl6689])).
% 30.20/5.00 thf(zip_derived_cl6691, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ 0))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ 0))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ 0))
% 30.20/5.00 | (LE @ (f @ X1) @ (s @ 0)))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl5379, zip_derived_cl6690])).
% 30.20/5.00 thf(zip_derived_cl6695, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (LE @ (f @ X1) @ (s @ 0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ (s @ 0) @ (f @ X0))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl6691])).
% 30.20/5.00 thf(zip_derived_cl5346, plain,
% 30.20/5.00 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1169, zip_derived_cl5345])).
% 30.20/5.00 thf(zip_derived_cl6699, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ 0))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | (LE @ (f @ X1) @ (s @ 0)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl6695, zip_derived_cl5346])).
% 30.20/5.00 thf(zip_derived_cl5375, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ 0)) | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5374, zip_derived_cl5347])).
% 30.20/5.00 thf(zip_derived_cl6700, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (LE @ (f @ X1) @ (s @ 0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl6699, zip_derived_cl5375])).
% 30.20/5.00 thf(zip_derived_cl5375, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ 0)) | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl5374, zip_derived_cl5347])).
% 30.20/5.00 thf(zip_derived_cl6701, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ 0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | (LE @ (f @ X1) @ (s @ 0)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl6700, zip_derived_cl5375])).
% 30.20/5.00 thf(zip_derived_cl6702, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ (s @ 0))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ 0))
% 30.20/5.00 | (LE @ (f @ X0) @ (s @ 0)))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl5379, zip_derived_cl6701])).
% 30.20/5.00 thf(zip_derived_cl6706, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl6702])).
% 30.20/5.00 thf(zip_derived_cl6712, plain,
% 30.20/5.00 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1171, zip_derived_cl6706])).
% 30.20/5.00 thf(clause_256, axiom,
% 30.20/5.00 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 30.20/5.00 ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) ) |
% 30.20/5.00 ( ~( E @ 0 @ ( f @ A_5 ) ) ) | ( iLEQ @ ( suc @ A_5 ) @ ( suc @ A_5 ) ))).
% 30.20/5.00 thf(zip_derived_cl719, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (E @ 0 @ (f @ (suc @ (suc @ X0)))))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ X0)))) | (iLEQ @ (suc @ X0) @ (suc @ X0))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_256])).
% 30.20/5.00 thf(zip_derived_cl1205, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl719])).
% 30.20/5.00 thf(clause_106, axiom,
% 30.20/5.00 (( ~( E @ 0 @ ( f @ A_5 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 30.20/5.00 ( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) |
% 30.20/5.00 ( iLEQ @ ( suc @ A_5 ) @ ( suc @ A_5 ) ))).
% 30.20/5.00 thf(zip_derived_cl580, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (E @ 0 @ (f @ X0)))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ (suc @ X0))))) |
% 30.20/5.00 (E @ (f @ X0) @ (f @ (suc @ X0))) |
% 30.20/5.00 (iLEQ @ (suc @ X0) @ (suc @ X0))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_106])).
% 30.20/5.00 thf(zip_derived_cl1176, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl580])).
% 30.20/5.00 thf(zip_derived_cl1206, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl1205, zip_derived_cl1176])).
% 30.20/5.00 thf(zip_derived_cl6719, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ 0)
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl6712, zip_derived_cl1206])).
% 30.20/5.00 thf(clause_199, axiom,
% 30.20/5.00 (( ~( LE @ ( f @ B_93 ) @ ( s @ 0 ) ) ) | ( E @ 0 @ ( f @ B_93 ) ) |
% 30.20/5.00 ( LE @ ( f @ B_93 ) @ 0 ))).
% 30.20/5.00 thf(zip_derived_cl225, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (LE @ (f @ X0) @ (s @ 0)))) | (E @ 0 @ (f @ X0)) |
% 30.20/5.00 (LE @ (f @ X0) @ 0)))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_199])).
% 30.20/5.00 thf(zip_derived_cl1167, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (LE @ (f @ X0) @ (s @ 0))
% 30.20/5.00 | (E @ 0 @ (f @ X0))
% 30.20/5.00 | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl225])).
% 30.20/5.00 thf(zip_derived_cl6706, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl6702])).
% 30.20/5.00 thf(zip_derived_cl6710, plain,
% 30.20/5.00 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1167, zip_derived_cl6706])).
% 30.20/5.00 thf(zip_derived_cl6721, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl6719, zip_derived_cl6710])).
% 30.20/5.00 thf(clause_713, axiom,
% 30.20/5.00 (( ~( LE @ ( f @ ( suc @ B_93 ) ) @ ( s @ 0 ) ) ) |
% 30.20/5.00 ( E @ 0 @ ( f @ ( suc @ B_93 ) ) ) | ( LE @ ( f @ B_93 ) @ 0 ))).
% 30.20/5.00 thf(zip_derived_cl1074, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (((((~) @ (LE @ (f @ (suc @ X0)) @ (s @ 0)))) |
% 30.20/5.00 (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0)))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_713])).
% 30.20/5.00 thf(zip_derived_cl1168, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 30.20/5.00 | (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1074])).
% 30.20/5.00 thf(zip_derived_cl6706, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl6702])).
% 30.20/5.00 thf(zip_derived_cl6711, plain,
% 30.20/5.00 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1168, zip_derived_cl6706])).
% 30.20/5.00 thf(zip_derived_cl6722, plain,
% 30.20/5.00 (![X0 : $i]: ( (LE @ (f @ X0) @ 0) | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl6721, zip_derived_cl6711])).
% 30.20/5.00 thf(zip_derived_cl6711, plain,
% 30.20/5.00 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1168, zip_derived_cl6706])).
% 30.20/5.00 thf(zip_derived_cl6722, plain,
% 30.20/5.00 (![X0 : $i]: ( (LE @ (f @ X0) @ 0) | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl6721, zip_derived_cl6711])).
% 30.20/5.00 thf(clause_303, axiom,
% 30.20/5.00 (( ~( iLEQ @ ( suc @ A_5 ) @ ( suc @ B_94 ) ) ) |
% 30.20/5.00 ( ~( E @ 0 @ ( f @ A_5 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ B_94 ) ) ) ) |
% 30.20/5.00 ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ B_94 ) @ ( suc @ B_95 ) ) ) |
% 30.20/5.00 ( ~( E @ 0 @ ( f @ B_94 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ B_95 ) ) ) ) |
% 30.20/5.00 ( ~( E @ 0 @ ( f @ B_95 ) ) ) |
% 30.20/5.00 ( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) |
% 30.20/5.00 ( E @ ( f @ B_94 ) @ ( f @ ( suc @ B_94 ) ) ) |
% 30.20/5.00 ( E @ ( f @ B_95 ) @ ( f @ ( suc @ B_95 ) ) ))).
% 30.20/5.00 thf(zip_derived_cl1029, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (((((~) @ (iLEQ @ (suc @ X0) @ (suc @ X1)))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ X0)))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ (suc @ X1))))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X1) @ (suc @ X2)))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ X1)))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ (suc @ X2))))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ X2)))) | (E @ (f @ X0) @ (f @ (suc @ X0))) |
% 30.20/5.00 (E @ (f @ X1) @ (f @ (suc @ X1))) |
% 30.20/5.00 (E @ (f @ X2) @ (f @ (suc @ X2)))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_303])).
% 30.20/5.00 thf(zip_derived_cl1934, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X1))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X2))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X2) @ (f @ (suc @ X2))))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1029])).
% 30.20/5.00 thf(zip_derived_cl6723, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ 0)
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X1))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl6722, zip_derived_cl1934])).
% 30.20/5.00 thf(zip_derived_cl6724, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X1))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl6723])).
% 30.20/5.00 thf(zip_derived_cl6711, plain,
% 30.20/5.00 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1168, zip_derived_cl6706])).
% 30.20/5.00 thf(zip_derived_cl6757, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ 0)
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X1))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl6724, zip_derived_cl6711])).
% 30.20/5.00 thf(zip_derived_cl6710, plain,
% 30.20/5.00 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1167, zip_derived_cl6706])).
% 30.20/5.00 thf(zip_derived_cl6758, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X1))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl6757, zip_derived_cl6710])).
% 30.20/5.00 thf(zip_derived_cl6760, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ 0)
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 30.20/5.00 | (LE @ (f @ X1) @ 0))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl6711, zip_derived_cl6758])).
% 30.20/5.00 thf(zip_derived_cl6710, plain,
% 30.20/5.00 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1167, zip_derived_cl6706])).
% 30.20/5.00 thf(zip_derived_cl6762, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 ( (LE @ (f @ X1) @ 0)
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 30.20/5.00 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl6760, zip_derived_cl6710])).
% 30.20/5.00 thf(zip_derived_cl6763, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ 0)
% 30.20/5.00 | (LE @ (f @ X0) @ 0)
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl6722, zip_derived_cl6762])).
% 30.20/5.00 thf(zip_derived_cl6767, plain,
% 30.20/5.00 (![X0 : $i]: ( (E @ (f @ X0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl6763])).
% 30.20/5.00 thf(clause_743, axiom,
% 30.20/5.00 (( ~( iLEQ @ ( suc @ A_5 ) @ ( suc @ B_94 ) ) ) |
% 30.20/5.00 ( ~( E @ 0 @ ( f @ A_5 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ B_94 ) ) ) ) |
% 30.20/5.00 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_94 ) ) ) ) ) |
% 30.20/5.00 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_95 ) ) ) ) ) |
% 30.20/5.00 ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 30.20/5.00 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ B_95 ) @ ( f @ ( suc @ B_95 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ B_94 ) @ ( f @ ( suc @ B_94 ) ) ) ) |
% 30.20/5.00 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) ) |
% 30.20/5.00 ( ~( iLEQ @ ( suc @ B_94 ) @ ( suc @ B_95 ) ) ) |
% 30.20/5.00 ( ~( E @ 0 @ ( f @ B_94 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ B_95 ) ) ) ) |
% 30.20/5.00 ( ~( E @ 0 @ ( f @ B_95 ) ) ))).
% 30.20/5.00 thf(zip_derived_cl124, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (((((~) @ (iLEQ @ (suc @ X0) @ (suc @ X1)))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ X0)))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ (suc @ X1))))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ (suc @ (suc @ X1)))))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ (suc @ (suc @ X2)))))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ (suc @ (suc @ X0)))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X2) @ (f @ (suc @ X2))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X1) @ (f @ (suc @ X1))))) |
% 30.20/5.00 (((~) @ (E @ (f @ X0) @ (f @ (suc @ X0))))) |
% 30.20/5.00 (((~) @ (iLEQ @ (suc @ X1) @ (suc @ X2)))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ X1)))) |
% 30.20/5.00 (((~) @ (E @ 0 @ (f @ (suc @ X2))))) | (((~) @ (E @ 0 @ (f @ X2))))))),
% 30.20/5.00 inference('cnf', [status(esa)], [clause_743])).
% 30.20/5.00 thf(zip_derived_cl3397, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.20/5.00 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X1))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X2)))),
% 30.20/5.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl124])).
% 30.20/5.00 thf(zip_derived_cl3398, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 (~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X1))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0)))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl3397])).
% 30.20/5.00 thf(zip_derived_cl3400, plain,
% 30.20/5.00 (![X0 : $i, X1 : $i]:
% 30.20/5.00 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X1))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0)))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl3398])).
% 30.20/5.00 thf(zip_derived_cl3409, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 30.20/5.00 inference('eq_fact', [status(thm)], [zip_derived_cl3400])).
% 30.20/5.00 thf(zip_derived_cl3410, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0)))),
% 30.20/5.00 inference('simplify', [status(thm)], [zip_derived_cl3409])).
% 30.20/5.00 thf(zip_derived_cl1206, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl1205, zip_derived_cl1176])).
% 30.20/5.00 thf(zip_derived_cl3411, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl3410, zip_derived_cl1206])).
% 30.20/5.00 thf(zip_derived_cl6771, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 ( (LE @ (f @ X0) @ 0)
% 30.20/5.00 | ~ (E @ 0 @ (f @ X0))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 30.20/5.00 inference('s_sup-', [status(thm)],
% 30.20/5.00 [zip_derived_cl6767, zip_derived_cl3411])).
% 30.20/5.00 thf(zip_derived_cl6710, plain,
% 30.20/5.00 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1167, zip_derived_cl6706])).
% 30.20/5.00 thf(zip_derived_cl6774, plain,
% 30.20/5.00 (![X0 : $i]:
% 30.20/5.00 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 30.20/5.00 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 30.20/5.00 | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl6771, zip_derived_cl6710])).
% 30.20/5.00 thf(zip_derived_cl6712, plain,
% 30.20/5.00 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1171, zip_derived_cl6706])).
% 30.20/5.00 thf(zip_derived_cl6775, plain,
% 30.20/5.00 (![X0 : $i]: ( (LE @ (f @ X0) @ 0) | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl6774, zip_derived_cl6712])).
% 30.20/5.00 thf(zip_derived_cl6711, plain,
% 30.20/5.00 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 30.20/5.00 inference('demod', [status(thm)],
% 30.20/5.00 [zip_derived_cl1168, zip_derived_cl6706])).
% 30.20/5.00 thf(zip_derived_cl6776, plain, (![X0 : $i]: (LE @ (f @ X0) @ 0)),
% 30.20/5.00 inference('clc', [status(thm)], [zip_derived_cl6775, zip_derived_cl6711])).
% 30.20/5.00 thf(zip_derived_cl6777, plain, ($false),
% 30.20/5.00 inference('demod', [status(thm)], [zip_derived_cl365, zip_derived_cl6776])).
% 30.20/5.00
% 30.20/5.00 % SZS output end Refutation
% 30.20/5.00
% 30.20/5.00
% 30.20/5.00 % Terminating...
% 30.90/5.04 % Runner terminated.
% 30.90/5.05 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------