TSTP Solution File: SYO689-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO689-1 : 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.cdGdQMIskU true
% Computer : n032.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 1.95s 0.88s
% Output : Refutation 1.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO689-1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.10 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.cdGdQMIskU true
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Sat Aug 26 02:34:43 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.10/0.29 % Running portfolio for 300 s
% 0.10/0.29 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.29 % Number of cores: 8
% 0.10/0.29 % Python version: Python 3.6.8
% 0.10/0.29 % Running in FO mode
% 0.14/0.47 % Total configuration time : 435
% 0.14/0.47 % Estimated wc time : 1092
% 0.14/0.47 % Estimated cpu time (7 cpus) : 156.0
% 0.14/0.53 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.14/0.53 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.14/0.53 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.14/0.56 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.14/0.56 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.14/0.56 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.14/0.56 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.95/0.88 % Solved by fo/fo4.sh.
% 1.95/0.88 % done 174 iterations in 0.270s
% 1.95/0.88 % SZS status Unsatisfiable for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.95/0.88 % SZS output start Refutation
% 1.95/0.88 thf(f_type, type, f: $i > $i).
% 1.95/0.88 thf(0_type, type, 0: $i).
% 1.95/0.88 thf(suc_type, type, suc: $i > $i).
% 1.95/0.88 thf(s_type, type, s: $i > $i).
% 1.95/0.88 thf(z_type, type, z: $i).
% 1.95/0.88 thf(E_type, type, E: $i > $i > $o).
% 1.95/0.88 thf(LE_type, type, LE: $i > $i > $o).
% 1.95/0.88 thf(iLEQ_type, type, iLEQ: $i > $i > $o).
% 1.95/0.88 thf(clause_1092, axiom, (~( LE @ ( f @ z ) @ 0 ))).
% 1.95/0.88 thf(zip_derived_cl10, plain, (~ (LE @ (f @ z) @ 0)),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_1092])).
% 1.95/0.88 thf(clause_113, axiom,
% 1.95/0.88 (( ~( LE @ ( f @ ( suc @ B_1161 ) ) @ ( s @ 0 ) ) ) |
% 1.95/0.88 ( E @ 0 @ ( f @ ( suc @ B_1161 ) ) ) | ( LE @ ( f @ B_1161 ) @ 0 ))).
% 1.95/0.88 thf(zip_derived_cl21, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 1.95/0.88 | (E @ 0 @ (f @ (suc @ X0)))
% 1.95/0.88 | (LE @ (f @ X0) @ 0))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_113])).
% 1.95/0.88 thf(clause_1440, axiom,
% 1.95/0.88 (( ~( LE @ ( f @ ( suc @ B_1136 ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 1.95/0.88 ( E @ ( s @ 0 ) @ ( f @ ( suc @ B_1136 ) ) ) |
% 1.95/0.88 ( LE @ ( f @ B_1136 ) @ ( s @ 0 ) ))).
% 1.95/0.88 thf(zip_derived_cl18, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 1.95/0.88 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.95/0.88 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_1440])).
% 1.95/0.88 thf(clause_388, axiom,
% 1.95/0.88 (( ~( LE @ ( f @ ( suc @ B_1066 ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 1.95/0.88 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_1066 ) ) ) |
% 1.95/0.88 ( LE @ ( f @ B_1066 ) @ ( s @ ( s @ 0 ) ) ))).
% 1.95/0.88 thf(zip_derived_cl5, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0))))
% 1.95/0.88 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_388])).
% 1.95/0.88 thf(clause_1935, axiom,
% 1.95/0.88 (( ~( LE @ ( f @ ( suc @ B_906 ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 1.95/0.88 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_906 ) ) ) |
% 1.95/0.88 ( LE @ ( f @ B_906 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 1.95/0.88 thf(zip_derived_cl15, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ (s @ 0)))))
% 1.95/0.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.95/0.88 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_1935])).
% 1.95/0.88 thf(clause_2050, axiom,
% 1.95/0.88 (( ~( LE @
% 1.95/0.88 ( f @ ( suc @ B_585 ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) ) |
% 1.95/0.88 ( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_585 ) ) ) |
% 1.95/0.88 ( LE @ ( f @ B_585 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 1.95/0.88 thf(zip_derived_cl19, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ (s @ (s @ 0))))))
% 1.95/0.88 | (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_2050])).
% 1.95/0.88 thf(clause_583, axiom,
% 1.95/0.88 (LE @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 1.95/0.88 thf(zip_derived_cl3, plain,
% 1.95/0.88 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_583])).
% 1.95/0.88 thf(zip_derived_cl37, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 1.95/0.88 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl3])).
% 1.95/0.88 thf(clause_1514, axiom,
% 1.95/0.88 (( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_588 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_588 ) ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_586 ) @ ( suc @ B_587 ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_588 ) @ ( suc @ B_589 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_587 ) ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_589 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_590 ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_587 ) @ ( suc @ B_588 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_586 ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_589 ) @ ( suc @ B_590 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_590 ) ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_586 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_586 ) ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_589 ) ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_587 ) ) ))).
% 1.95/0.88 thf(zip_derived_cl13, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X4))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X4))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X4)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X5)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X5) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X5))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X2)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_1514])).
% 1.95/0.88 thf(zip_derived_cl96, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X4)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X4))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X3))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X4))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 1.95/0.88 thf(zip_derived_cl101, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.95/0.88 (~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X4))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X3))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X4))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X4)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl96])).
% 1.95/0.88 thf(zip_derived_cl382, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl101])).
% 1.95/0.88 thf(zip_derived_cl386, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.95/0.88 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X3))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl382])).
% 1.95/0.88 thf(zip_derived_cl391, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X2))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl386])).
% 1.95/0.88 thf(zip_derived_cl394, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.95/0.88 (~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X2))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl391])).
% 1.95/0.88 thf(zip_derived_cl400, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl394])).
% 1.95/0.88 thf(zip_derived_cl402, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i]:
% 1.95/0.88 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl400])).
% 1.95/0.88 thf(clause_1581, axiom,
% 1.95/0.88 (( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.95/0.88 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 1.95/0.88 thf(zip_derived_cl0, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_1581])).
% 1.95/0.88 thf(zip_derived_cl404, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1)))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl402, zip_derived_cl0])).
% 1.95/0.88 thf(zip_derived_cl408, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl404])).
% 1.95/0.88 thf(zip_derived_cl409, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl408])).
% 1.95/0.88 thf(zip_derived_cl0, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 1.95/0.88 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_1581])).
% 1.95/0.88 thf(zip_derived_cl410, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl409, zip_derived_cl0])).
% 1.95/0.88 thf(zip_derived_cl413, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 1.95/0.88 inference('sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl410])).
% 1.95/0.88 thf(clause_2115, axiom,
% 1.95/0.88 (( ~( LE @ ( f @ B_585 ) @ ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) ) |
% 1.95/0.88 ( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_585 ) ) |
% 1.95/0.88 ( LE @ ( f @ B_585 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 1.95/0.88 thf(zip_derived_cl16, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))
% 1.95/0.88 | (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_2115])).
% 1.95/0.88 thf(zip_derived_cl3, plain,
% 1.95/0.88 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_583])).
% 1.95/0.88 thf(zip_derived_cl32, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 1.95/0.88 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 1.95/0.88 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl3])).
% 1.95/0.88 thf(zip_derived_cl414, plain,
% 1.95/0.88 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl413, zip_derived_cl32])).
% 1.95/0.88 thf(zip_derived_cl416, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.95/0.88 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 1.95/0.88 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl414])).
% 1.95/0.88 thf(clause_657, axiom,
% 1.95/0.88 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_907 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_911 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_910 ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_909 ) @ ( suc @ B_910 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_910 ) ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_908 ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_907 ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_908 ) @ ( suc @ B_909 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_908 ) ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_909 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_911 ) ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_907 ) ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_910 ) @ ( suc @ B_911 ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_907 ) @ ( suc @ B_908 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_909 ) ) ) ))).
% 1.95/0.88 thf(zip_derived_cl6, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X3))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X4) @ (suc @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X5))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X5) @ (suc @ X4))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X5)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X4))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X5))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X4))))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_657])).
% 1.95/0.88 thf(zip_derived_cl83, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X4))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X4)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X4))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X3)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl6])).
% 1.95/0.88 thf(zip_derived_cl88, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X4))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X4)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X4))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1))))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl83])).
% 1.95/0.88 thf(zip_derived_cl305, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl88])).
% 1.95/0.88 thf(zip_derived_cl309, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X3))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1))))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl305])).
% 1.95/0.88 thf(zip_derived_cl319, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl309])).
% 1.95/0.88 thf(zip_derived_cl322, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1))))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl319])).
% 1.95/0.88 thf(zip_derived_cl329, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl322])).
% 1.95/0.88 thf(zip_derived_cl331, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i]:
% 1.95/0.88 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1))))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl329])).
% 1.95/0.88 thf(clause_2227, axiom,
% 1.95/0.88 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.95/0.88 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 1.95/0.88 thf(zip_derived_cl17, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.95/0.88 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_2227])).
% 1.95/0.88 thf(zip_derived_cl333, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0)))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl331, zip_derived_cl17])).
% 1.95/0.88 thf(zip_derived_cl339, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl333])).
% 1.95/0.88 thf(zip_derived_cl340, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl339])).
% 1.95/0.88 thf(zip_derived_cl17, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.95/0.88 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_2227])).
% 1.95/0.88 thf(zip_derived_cl341, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl340, zip_derived_cl17])).
% 1.95/0.88 thf(zip_derived_cl422, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 1.95/0.88 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 1.95/0.88 inference('sup-', [status(thm)], [zip_derived_cl416, zip_derived_cl341])).
% 1.95/0.88 thf(clause_1230, axiom,
% 1.95/0.88 (( ~( LE @ ( f @ B_906 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 1.95/0.88 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_906 ) ) |
% 1.95/0.88 ( LE @ ( f @ B_906 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 1.95/0.88 thf(zip_derived_cl11, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 1.95/0.88 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_1230])).
% 1.95/0.88 thf(zip_derived_cl414, plain,
% 1.95/0.88 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl413, zip_derived_cl32])).
% 1.95/0.88 thf(zip_derived_cl415, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.95/0.88 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 1.95/0.88 inference('demod', [status(thm)], [zip_derived_cl11, zip_derived_cl414])).
% 1.95/0.88 thf(zip_derived_cl423, plain,
% 1.95/0.88 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl422, zip_derived_cl415])).
% 1.95/0.88 thf(zip_derived_cl424, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.95/0.88 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl423])).
% 1.95/0.88 thf(clause_1712, axiom,
% 1.95/0.88 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_1069 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_1067 ) ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_1070 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_1068 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_1068 ) ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_1067 ) @ ( suc @ B_1068 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_1067 ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_1068 ) @ ( suc @ B_1069 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_1071 ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_1067 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_1069 ) ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_1069 ) @ ( suc @ B_1070 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_1071 ) ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_1070 ) ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_1070 ) @ ( suc @ B_1071 ) ) ))).
% 1.95/0.88 thf(zip_derived_cl20, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X4)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X5))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X4) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X5)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X4))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X5)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_1712])).
% 1.95/0.88 thf(zip_derived_cl73, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.95/0.88 (~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X4) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X4)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X4))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X4)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl20])).
% 1.95/0.88 thf(zip_derived_cl78, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ 0)) @ (f @ X4))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X4))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X4)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X4) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X3))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl73])).
% 1.95/0.88 thf(zip_derived_cl240, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.95/0.88 (~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X3)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl78])).
% 1.95/0.88 thf(zip_derived_cl244, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ 0)) @ (f @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl240])).
% 1.95/0.88 thf(zip_derived_cl248, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.95/0.88 (~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl244])).
% 1.95/0.88 thf(zip_derived_cl251, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl248])).
% 1.95/0.88 thf(zip_derived_cl255, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i]:
% 1.95/0.88 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl251])).
% 1.95/0.88 thf(zip_derived_cl257, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl255])).
% 1.95/0.88 thf(clause_1218, axiom,
% 1.95/0.88 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.95/0.88 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 1.95/0.88 thf(zip_derived_cl1, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_1218])).
% 1.95/0.88 thf(zip_derived_cl258, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i]:
% 1.95/0.88 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X1)))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl257, zip_derived_cl1])).
% 1.95/0.88 thf(zip_derived_cl259, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl258])).
% 1.95/0.88 thf(zip_derived_cl260, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl259])).
% 1.95/0.88 thf(zip_derived_cl1, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.95/0.88 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_1218])).
% 1.95/0.88 thf(zip_derived_cl261, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl260, zip_derived_cl1])).
% 1.95/0.88 thf(zip_derived_cl428, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 ( (LE @ (f @ X0) @ (s @ (s @ 0))) | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 1.95/0.88 inference('sup-', [status(thm)], [zip_derived_cl424, zip_derived_cl261])).
% 1.95/0.88 thf(clause_1314, axiom,
% 1.95/0.88 (( ~( LE @ ( f @ B_1066 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 1.95/0.88 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_1066 ) ) |
% 1.95/0.88 ( LE @ ( f @ B_1066 ) @ ( s @ ( s @ 0 ) ) ))).
% 1.95/0.88 thf(zip_derived_cl8, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 1.95/0.88 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.95/0.88 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_1314])).
% 1.95/0.88 thf(zip_derived_cl423, plain,
% 1.95/0.88 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl422, zip_derived_cl415])).
% 1.95/0.88 thf(zip_derived_cl425, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.95/0.88 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl423])).
% 1.95/0.88 thf(zip_derived_cl429, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl428, zip_derived_cl425])).
% 1.95/0.88 thf(zip_derived_cl431, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 1.95/0.88 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl429])).
% 1.95/0.88 thf(clause_327, axiom,
% 1.95/0.88 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_1137 ) ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ 0 ) @ ( f @ B_1140 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_1139 ) ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_1138 ) @ ( suc @ B_1139 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ 0 ) @ ( f @ B_1141 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ 0 ) @ ( f @ B_1137 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_1138 ) ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_1137 ) @ ( suc @ B_1138 ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_1137 ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_1139 ) @ ( suc @ B_1140 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_1140 ) ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_1140 ) @ ( suc @ B_1141 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_1141 ) ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ 0 ) @ ( f @ B_1139 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ 0 ) @ ( f @ B_1138 ) ) ))).
% 1.95/0.88 thf(zip_derived_cl2, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.95/0.88 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X4))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X5) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X4))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X5)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X4)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X5))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X3)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_327])).
% 1.95/0.88 thf(zip_derived_cl22, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.95/0.88 (~ (E @ (s @ 0) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X4) @ (suc @ X3))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X4)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X4))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X3))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X4)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl2])).
% 1.95/0.88 thf(zip_derived_cl27, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.95/0.88 (~ (E @ (s @ 0) @ (f @ X4))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X3))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X4))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X4)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X4) @ (suc @ X3))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl22])).
% 1.95/0.88 thf(zip_derived_cl134, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.95/0.88 (~ (E @ (s @ 0) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X3)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl27])).
% 1.95/0.88 thf(zip_derived_cl138, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.95/0.88 (~ (E @ (s @ 0) @ (f @ X3))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X3))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl134])).
% 1.95/0.88 thf(zip_derived_cl160, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.95/0.88 (~ (E @ (s @ 0) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X2))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl138])).
% 1.95/0.88 thf(zip_derived_cl163, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.95/0.88 (~ (E @ (s @ 0) @ (f @ X2))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X1))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl160])).
% 1.95/0.88 thf(zip_derived_cl166, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i]:
% 1.95/0.88 (~ (E @ (s @ 0) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl163])).
% 1.95/0.88 thf(zip_derived_cl168, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i]:
% 1.95/0.88 (~ (E @ (s @ 0) @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl166])).
% 1.95/0.88 thf(clause_1329, axiom,
% 1.95/0.88 (( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 1.95/0.88 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 1.95/0.88 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 1.95/0.88 thf(zip_derived_cl14, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ 0) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.95/0.88 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_1329])).
% 1.95/0.88 thf(zip_derived_cl170, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i]:
% 1.95/0.88 (~ (E @ (s @ 0) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X1)))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl168, zip_derived_cl14])).
% 1.95/0.88 thf(zip_derived_cl171, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ 0) @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl170])).
% 1.95/0.88 thf(zip_derived_cl172, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl171])).
% 1.95/0.88 thf(zip_derived_cl14, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ 0) @ (f @ X0))
% 1.95/0.88 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.95/0.88 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_1329])).
% 1.95/0.88 thf(zip_derived_cl173, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ (s @ 0) @ (f @ X0)) | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl172, zip_derived_cl14])).
% 1.95/0.88 thf(zip_derived_cl434, plain,
% 1.95/0.88 (![X0 : $i]: ( (LE @ (f @ X0) @ (s @ 0)) | ~ (E @ (s @ 0) @ (f @ X0)))),
% 1.95/0.88 inference('sup-', [status(thm)], [zip_derived_cl431, zip_derived_cl173])).
% 1.95/0.88 thf(clause_740, axiom,
% 1.95/0.88 (( ~( LE @ ( f @ B_1136 ) @ ( s @ ( s @ 0 ) ) ) ) |
% 1.95/0.88 ( E @ ( s @ 0 ) @ ( f @ B_1136 ) ) | ( LE @ ( f @ B_1136 ) @ ( s @ 0 ) ))).
% 1.95/0.88 thf(zip_derived_cl4, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.95/0.88 | (E @ (s @ 0) @ (f @ X0))
% 1.95/0.88 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_740])).
% 1.95/0.88 thf(zip_derived_cl429, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl428, zip_derived_cl425])).
% 1.95/0.88 thf(zip_derived_cl430, plain,
% 1.95/0.88 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 1.95/0.88 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl429])).
% 1.95/0.88 thf(zip_derived_cl435, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl434, zip_derived_cl430])).
% 1.95/0.88 thf(zip_derived_cl437, plain,
% 1.95/0.88 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 1.95/0.88 inference('demod', [status(thm)], [zip_derived_cl21, zip_derived_cl435])).
% 1.95/0.88 thf(clause_421, axiom,
% 1.95/0.88 (( ~( E @ 0 @ ( f @ B_1165 ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_1162 ) @ ( suc @ B_1163 ) ) ) |
% 1.95/0.88 ( ~( E @ 0 @ ( f @ ( suc @ B_1163 ) ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ A_5 ) @ ( suc @ B_1162 ) ) ) |
% 1.95/0.88 ( ~( E @ 0 @ ( f @ A_5 ) ) ) | ( ~( E @ 0 @ ( f @ B_1162 ) ) ) |
% 1.95/0.88 ( ~( E @ 0 @ ( f @ B_1164 ) ) ) |
% 1.95/0.88 ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 1.95/0.88 ( ~( E @ 0 @ ( f @ ( suc @ B_1166 ) ) ) ) |
% 1.95/0.88 ( ~( E @ 0 @ ( f @ B_1166 ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_1165 ) @ ( suc @ B_1166 ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_1163 ) @ ( suc @ B_1164 ) ) ) |
% 1.95/0.88 ( ~( E @ 0 @ ( f @ ( suc @ B_1165 ) ) ) ) |
% 1.95/0.88 ( ~( E @ 0 @ ( f @ ( suc @ B_1164 ) ) ) ) |
% 1.95/0.88 ( ~( E @ 0 @ ( f @ ( suc @ B_1162 ) ) ) ) |
% 1.95/0.88 ( ~( iLEQ @ ( suc @ B_1164 ) @ ( suc @ B_1165 ) ) ) |
% 1.95/0.88 ( ~( E @ 0 @ ( f @ B_1163 ) ) ))).
% 1.95/0.88 thf(zip_derived_cl12, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.95/0.88 (~ (E @ 0 @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X3) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X3))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X1))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X4))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X5)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X5))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X5))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X4))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X4)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X4) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X2)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_421])).
% 1.95/0.88 thf(zip_derived_cl58, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.95/0.88 (~ (E @ 0 @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X3))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X3))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X2))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X0))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X1)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl12])).
% 1.95/0.88 thf(zip_derived_cl62, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.95/0.88 (~ (E @ 0 @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X2))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X3)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X3))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X1) @ (suc @ X3))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X2))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X2) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X0)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl58])).
% 1.95/0.88 thf(zip_derived_cl115, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i]:
% 1.95/0.88 (~ (E @ 0 @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X1))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X0))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X0)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl62])).
% 1.95/0.88 thf(zip_derived_cl118, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i]:
% 1.95/0.88 (~ (E @ 0 @ (f @ (suc @ X1)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X1))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X0)))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl115])).
% 1.95/0.88 thf(clause_2293, axiom,
% 1.95/0.88 (( ~( E @ 0 @ ( f @ A_5 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 1.95/0.88 ( iLEQ @ ( suc @ A_5 ) @ ( suc @ A_5 ) ))).
% 1.95/0.88 thf(zip_derived_cl9, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ 0 @ (f @ X0))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.95/0.88 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_2293])).
% 1.95/0.88 thf(zip_derived_cl120, plain,
% 1.95/0.88 (![X0 : $i, X1 : $i]:
% 1.95/0.88 (~ (E @ 0 @ (f @ X0))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X1))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X1))))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl118, zip_derived_cl9])).
% 1.95/0.88 thf(zip_derived_cl121, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ 0 @ (f @ (suc @ X0)))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X0))
% 1.95/0.88 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X0)))),
% 1.95/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl120])).
% 1.95/0.88 thf(zip_derived_cl122, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.95/0.88 | ~ (E @ 0 @ (f @ X0))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 1.95/0.88 inference('simplify', [status(thm)], [zip_derived_cl121])).
% 1.95/0.88 thf(zip_derived_cl9, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (E @ 0 @ (f @ X0))
% 1.95/0.88 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.95/0.88 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_2293])).
% 1.95/0.88 thf(zip_derived_cl123, plain,
% 1.95/0.88 (![X0 : $i]: (~ (E @ 0 @ (f @ (suc @ X0))) | ~ (E @ 0 @ (f @ X0)))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl122, zip_derived_cl9])).
% 1.95/0.88 thf(zip_derived_cl439, plain,
% 1.95/0.88 (![X0 : $i]: ( (LE @ (f @ X0) @ 0) | ~ (E @ 0 @ (f @ X0)))),
% 1.95/0.88 inference('sup-', [status(thm)], [zip_derived_cl437, zip_derived_cl123])).
% 1.95/0.88 thf(clause_328, axiom,
% 1.95/0.88 (( ~( LE @ ( f @ B_1161 ) @ ( s @ 0 ) ) ) | ( E @ 0 @ ( f @ B_1161 ) ) |
% 1.95/0.88 ( LE @ ( f @ B_1161 ) @ 0 ))).
% 1.95/0.88 thf(zip_derived_cl7, plain,
% 1.95/0.88 (![X0 : $i]:
% 1.95/0.88 (~ (LE @ (f @ X0) @ (s @ 0))
% 1.95/0.88 | (E @ 0 @ (f @ X0))
% 1.95/0.88 | (LE @ (f @ X0) @ 0))),
% 1.95/0.88 inference('cnf', [status(esa)], [clause_328])).
% 1.95/0.88 thf(zip_derived_cl435, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl434, zip_derived_cl430])).
% 1.95/0.88 thf(zip_derived_cl436, plain,
% 1.95/0.88 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 1.95/0.88 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl435])).
% 1.95/0.88 thf(zip_derived_cl440, plain, (![X0 : $i]: (LE @ (f @ X0) @ 0)),
% 1.95/0.88 inference('clc', [status(thm)], [zip_derived_cl439, zip_derived_cl436])).
% 1.95/0.88 thf(zip_derived_cl441, plain, ($false),
% 1.95/0.88 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl440])).
% 1.95/0.88
% 1.95/0.88 % SZS output end Refutation
% 1.95/0.88
% 1.95/0.88
% 1.95/0.88 % Terminating...
% 3.27/0.98 % Runner terminated.
% 3.27/0.98 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------