TSTP Solution File: SYO681-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO681-1 : 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.519F5vM3Wy true
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 05:52:33 EDT 2023
% Result : Unsatisfiable 1.34s 0.96s
% Output : Refutation 1.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO681-1 : TPTP v8.1.2. Released v7.3.0.
% 0.15/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.519F5vM3Wy true
% 0.15/0.35 % Computer : n005.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 04:28:08 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % Running in FO mode
% 0.22/0.68 % Total configuration time : 435
% 0.22/0.68 % Estimated wc time : 1092
% 0.22/0.68 % Estimated cpu time (7 cpus) : 156.0
% 1.03/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 1.03/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 1.03/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 1.03/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 1.03/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.03/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.03/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 1.32/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 1.34/0.96 % Solved by fo/fo3_bce.sh.
% 1.34/0.96 % BCE start: 54
% 1.34/0.96 % BCE eliminated: 0
% 1.34/0.96 % PE start: 54
% 1.34/0.96 logic: neq
% 1.34/0.96 % PE eliminated: 0
% 1.34/0.96 % done 113 iterations in 0.174s
% 1.34/0.96 % SZS status Unsatisfiable for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.34/0.96 % SZS output start Refutation
% 1.34/0.96 thf(0_type, type, 0: $i).
% 1.34/0.96 thf(z_type, type, z: $i).
% 1.34/0.96 thf(s_type, type, s: $i > $i).
% 1.34/0.96 thf(suc_type, type, suc: $i > $i).
% 1.34/0.96 thf(f_type, type, f: $i > $i).
% 1.34/0.96 thf(iLEQ_type, type, iLEQ: $i > $i > $o).
% 1.34/0.96 thf(LE_type, type, LE: $i > $i > $o).
% 1.34/0.96 thf(E_type, type, E: $i > $i > $o).
% 1.34/0.96 thf(clause_359, axiom, (~( LE @ ( f @ z ) @ 0 ))).
% 1.34/0.96 thf(zip_derived_cl16, plain, (~ (LE @ (f @ z) @ 0)),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_359])).
% 1.34/0.96 thf(clause_497, axiom,
% 1.34/0.96 (( ~( LE @ ( f @ B_60 ) @ ( s @ 0 ) ) ) | ( E @ 0 @ ( f @ B_60 ) ) |
% 1.34/0.96 ( LE @ ( f @ B_60 ) @ 0 ))).
% 1.34/0.96 thf(zip_derived_cl17, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (LE @ (f @ X0) @ (s @ 0))
% 1.34/0.96 | (E @ 0 @ (f @ X0))
% 1.34/0.96 | (LE @ (f @ X0) @ 0))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_497])).
% 1.34/0.96 thf(clause_595, axiom,
% 1.34/0.96 (( ~( LE @ ( f @ ( suc @ B_60 ) ) @ ( s @ 0 ) ) ) |
% 1.34/0.96 ( E @ 0 @ ( f @ ( suc @ B_60 ) ) ) | ( LE @ ( f @ B_60 ) @ 0 ))).
% 1.34/0.96 thf(zip_derived_cl50, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 1.34/0.96 | (E @ 0 @ (f @ (suc @ X0)))
% 1.34/0.96 | (LE @ (f @ X0) @ 0))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_595])).
% 1.34/0.96 thf(clause_363, axiom,
% 1.34/0.96 (( ~( E @ 0 @ ( f @ ( suc @ B_61 ) ) ) ) |
% 1.34/0.96 ( ~( iLEQ @ ( suc @ B_61 ) @ ( suc @ B_62 ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 1.34/0.96 ( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_61 ) ) ) |
% 1.34/0.96 ( ~( E @ 0 @ ( f @ ( suc @ B_62 ) ) ) ) |
% 1.34/0.96 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ B_62 ) @ ( f @ ( suc @ B_62 ) ) ) ) |
% 1.34/0.96 ( ~( E @ 0 @ ( f @ B_61 ) ) ) |
% 1.34/0.96 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_62 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_62 ) ) ) |
% 1.34/0.96 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_61 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ B_61 ) @ ( f @ ( suc @ B_61 ) ) ) ) |
% 1.34/0.96 ( ~( E @ 0 @ ( f @ A_4 ) ) ))).
% 1.34/0.96 thf(zip_derived_cl48, plain,
% 1.34/0.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/0.96 (~ (E @ 0 @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.34/0.96 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ (suc @ X2))))
% 1.34/0.96 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X1))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X2)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_363])).
% 1.34/0.96 thf(zip_derived_cl156, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl48])).
% 1.34/0.96 thf(zip_derived_cl157, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X0)))),
% 1.34/0.96 inference('simplify', [status(thm)], [zip_derived_cl156])).
% 1.34/0.96 thf(clause_560, axiom,
% 1.34/0.96 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 1.34/0.96 ( ~( E @ 0 @ ( f @ A_4 ) ) ) | ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 1.34/0.96 thf(zip_derived_cl26, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_560])).
% 1.34/0.96 thf(clause_713, axiom,
% 1.34/0.96 (( ~( E @ 0 @ ( f @ A_4 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 1.34/0.96 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) |
% 1.34/0.96 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 1.34/0.96 thf(zip_derived_cl25, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_713])).
% 1.34/0.96 thf(zip_derived_cl55, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl26, zip_derived_cl25])).
% 1.34/0.96 thf(zip_derived_cl178, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl157, zip_derived_cl55])).
% 1.34/0.96 thf(clause_614, axiom,
% 1.34/0.96 (( ~( E @ 0 @ ( f @ ( suc @ B_61 ) ) ) ) |
% 1.34/0.96 ( ~( iLEQ @ ( suc @ B_61 ) @ ( suc @ B_62 ) ) ) |
% 1.34/0.96 ( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_61 ) ) ) |
% 1.34/0.96 ( ~( E @ 0 @ ( f @ ( suc @ B_62 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_61 ) ) ) |
% 1.34/0.96 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_62 ) ) ) |
% 1.34/0.96 ( ~( E @ 0 @ ( f @ A_4 ) ) ) |
% 1.34/0.96 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) |
% 1.34/0.96 ( E @ ( f @ B_61 ) @ ( f @ ( suc @ B_61 ) ) ) |
% 1.34/0.96 ( E @ ( f @ B_62 ) @ ( f @ ( suc @ B_62 ) ) ))).
% 1.34/0.96 thf(zip_derived_cl8, plain,
% 1.34/0.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/0.96 (~ (E @ 0 @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X2)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X1))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X2))
% 1.34/0.96 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_614])).
% 1.34/0.96 thf(zip_derived_cl87, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl8])).
% 1.34/0.96 thf(zip_derived_cl88, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('simplify', [status(thm)], [zip_derived_cl87])).
% 1.34/0.96 thf(zip_derived_cl25, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_713])).
% 1.34/0.96 thf(zip_derived_cl97, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl88, zip_derived_cl25])).
% 1.34/0.96 thf(zip_derived_cl179, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ 0 @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ 0 @ (f @ X0)))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl178, zip_derived_cl97])).
% 1.34/0.96 thf(clause_61, axiom,
% 1.34/0.96 (( ~( LE @ ( f @ ( suc @ ( suc @ B_60 ) ) ) @ ( s @ 0 ) ) ) |
% 1.34/0.96 ( E @ 0 @ ( f @ ( suc @ ( suc @ B_60 ) ) ) ) | ( LE @ ( f @ B_60 ) @ 0 ))).
% 1.34/0.96 thf(zip_derived_cl24, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 1.34/0.96 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | (LE @ (f @ X0) @ 0))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_61])).
% 1.34/0.96 thf(zip_derived_cl182, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 1.34/0.96 | (LE @ (f @ X0) @ 0)
% 1.34/0.96 | ~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0)))),
% 1.34/0.96 inference('sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl24])).
% 1.34/0.96 thf(zip_derived_cl189, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (LE @ (f @ X0) @ 0)
% 1.34/0.96 | ~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 1.34/0.96 | ~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 1.34/0.96 | (LE @ (f @ X0) @ 0)
% 1.34/0.96 | ~ (E @ 0 @ (f @ X0)))),
% 1.34/0.96 inference('sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl182])).
% 1.34/0.96 thf(zip_derived_cl192, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ 0 @ (f @ X0))
% 1.34/0.96 | ~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 1.34/0.96 | ~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 1.34/0.96 | (LE @ (f @ X0) @ 0))),
% 1.34/0.96 inference('simplify', [status(thm)], [zip_derived_cl189])).
% 1.34/0.96 thf(zip_derived_cl198, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (LE @ (f @ X0) @ 0)
% 1.34/0.96 | ~ (LE @ (f @ X0) @ (s @ 0))
% 1.34/0.96 | (LE @ (f @ X0) @ 0)
% 1.34/0.96 | ~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 1.34/0.96 | ~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0)))),
% 1.34/0.96 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl192])).
% 1.34/0.96 thf(zip_derived_cl200, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 1.34/0.96 | ~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 1.34/0.96 | ~ (LE @ (f @ X0) @ (s @ 0))
% 1.34/0.96 | (LE @ (f @ X0) @ 0))),
% 1.34/0.96 inference('simplify', [status(thm)], [zip_derived_cl198])).
% 1.34/0.96 thf(clause_44, axiom,
% 1.34/0.96 (( ~( LE @ ( f @ B_53 ) @ ( s @ ( s @ 0 ) ) ) ) |
% 1.34/0.96 ( E @ ( s @ 0 ) @ ( f @ B_53 ) ) | ( LE @ ( f @ B_53 ) @ ( s @ 0 ) ))).
% 1.34/0.96 thf(zip_derived_cl41, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.34/0.96 | (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_44])).
% 1.34/0.96 thf(clause_95, axiom,
% 1.34/0.96 (( ~( LE @ ( f @ ( suc @ B_53 ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 1.34/0.96 ( E @ ( s @ 0 ) @ ( f @ ( suc @ B_53 ) ) ) |
% 1.34/0.96 ( LE @ ( f @ B_53 ) @ ( s @ 0 ) ))).
% 1.34/0.96 thf(zip_derived_cl21, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 1.34/0.96 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_95])).
% 1.34/0.96 thf(clause_41, axiom,
% 1.34/0.96 (( ~( iLEQ @ ( suc @ B_54 ) @ ( suc @ B_55 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ B_55 ) @ ( f @ ( suc @ B_55 ) ) ) ) |
% 1.34/0.96 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_54 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_55 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_54 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ B_54 ) @ ( f @ ( suc @ B_54 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ B_55 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_55 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_54 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ B_54 ) ) ))).
% 1.34/0.96 thf(zip_derived_cl39, plain,
% 1.34/0.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/0.96 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 1.34/0.96 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X2))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X1))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X2))))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_41])).
% 1.34/0.96 thf(zip_derived_cl219, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl39])).
% 1.34/0.96 thf(zip_derived_cl220, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 1.34/0.96 inference('simplify', [status(thm)], [zip_derived_cl219])).
% 1.34/0.96 thf(clause_125, axiom,
% 1.34/0.96 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 1.34/0.96 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 1.34/0.96 thf(zip_derived_cl23, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_125])).
% 1.34/0.96 thf(clause_563, axiom,
% 1.34/0.96 (( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.34/0.96 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 1.34/0.96 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 1.34/0.96 thf(zip_derived_cl28, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_563])).
% 1.34/0.96 thf(zip_derived_cl68, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl23, zip_derived_cl28])).
% 1.34/0.96 thf(zip_derived_cl360, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl220, zip_derived_cl68])).
% 1.34/0.96 thf(clause_687, axiom,
% 1.34/0.96 (( ~( iLEQ @ ( suc @ B_54 ) @ ( suc @ B_55 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 1.34/0.96 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_54 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_55 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ B_55 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_54 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ 0 ) @ ( f @ B_54 ) ) ) |
% 1.34/0.96 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 1.34/0.96 ( E @ ( f @ B_54 ) @ ( f @ ( suc @ B_54 ) ) ) |
% 1.34/0.96 ( E @ ( f @ B_55 ) @ ( f @ ( suc @ B_55 ) ) ))).
% 1.34/0.96 thf(zip_derived_cl14, plain,
% 1.34/0.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/0.96 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X2)))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X2))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X1))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_687])).
% 1.34/0.96 thf(zip_derived_cl130, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl14])).
% 1.34/0.96 thf(zip_derived_cl131, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('simplify', [status(thm)], [zip_derived_cl130])).
% 1.34/0.96 thf(zip_derived_cl28, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_563])).
% 1.34/0.96 thf(zip_derived_cl139, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl131, zip_derived_cl28])).
% 1.34/0.96 thf(zip_derived_cl361, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl360, zip_derived_cl139])).
% 1.34/0.96 thf(clause_508, axiom,
% 1.34/0.96 (( ~( LE @ ( f @ ( suc @ ( suc @ B_53 ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 1.34/0.96 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_53 ) ) ) ) |
% 1.34/0.96 ( LE @ ( f @ B_53 ) @ ( s @ 0 ) ))).
% 1.34/0.96 thf(zip_derived_cl51, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 1.34/0.96 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_508])).
% 1.34/0.96 thf(zip_derived_cl362, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ 0))
% 1.34/0.96 | ~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0))))),
% 1.34/0.96 inference('sup+', [status(thm)], [zip_derived_cl361, zip_derived_cl51])).
% 1.34/0.96 thf(zip_derived_cl372, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (LE @ (f @ X0) @ (s @ 0))
% 1.34/0.96 | ~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 1.34/0.96 | ~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ 0))
% 1.34/0.96 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 1.34/0.96 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl362])).
% 1.34/0.96 thf(zip_derived_cl374, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ 0) @ (f @ X0))
% 1.34/0.96 | ~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 1.34/0.96 | ~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.34/0.96 inference('simplify', [status(thm)], [zip_derived_cl372])).
% 1.34/0.96 thf(zip_derived_cl382, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (LE @ (f @ X0) @ (s @ 0))
% 1.34/0.96 | ~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ 0))
% 1.34/0.96 | ~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 1.34/0.96 | ~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0))))),
% 1.34/0.96 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl374])).
% 1.34/0.96 thf(zip_derived_cl383, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 1.34/0.96 | ~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 1.34/0.96 | ~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ 0)))),
% 1.34/0.96 inference('simplify', [status(thm)], [zip_derived_cl382])).
% 1.34/0.96 thf(clause_528, axiom,
% 1.34/0.96 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_42 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ B_43 ) @ ( f @ ( suc @ B_43 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_42 ) ) ) |
% 1.34/0.96 ( ~( iLEQ @ ( suc @ B_42 ) @ ( suc @ B_43 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_42 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_43 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_43 ) ) ) ) |
% 1.34/0.96 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_42 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_43 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ B_42 ) @ ( f @ ( suc @ B_42 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ))).
% 1.34/0.96 thf(zip_derived_cl15, plain,
% 1.34/0.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X2))))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 1.34/0.96 | ~ (E @ (f @ X2) @ (f @ (suc @ X2))))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_528])).
% 1.34/0.96 thf(zip_derived_cl338, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl15])).
% 1.34/0.96 thf(zip_derived_cl339, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('simplify', [status(thm)], [zip_derived_cl338])).
% 1.34/0.96 thf(clause_415, axiom,
% 1.34/0.96 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 1.34/0.96 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 1.34/0.96 thf(zip_derived_cl7, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_415])).
% 1.34/0.96 thf(clause_383, axiom,
% 1.34/0.96 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.34/0.96 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 1.34/0.96 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 1.34/0.96 thf(zip_derived_cl45, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_383])).
% 1.34/0.96 thf(zip_derived_cl71, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl7, zip_derived_cl45])).
% 1.34/0.96 thf(zip_derived_cl385, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl339, zip_derived_cl71])).
% 1.34/0.96 thf(clause_463, axiom,
% 1.34/0.96 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_42 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_42 ) ) ) |
% 1.34/0.96 ( ~( iLEQ @ ( suc @ B_42 ) @ ( suc @ B_43 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_43 ) ) ) ) |
% 1.34/0.96 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_42 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_43 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 1.34/0.96 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 1.34/0.96 ( E @ ( f @ B_42 ) @ ( f @ ( suc @ B_42 ) ) ) |
% 1.34/0.96 ( E @ ( f @ B_43 ) @ ( f @ ( suc @ B_43 ) ) ))).
% 1.34/0.96 thf(zip_derived_cl18, plain,
% 1.34/0.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X2)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X2))
% 1.34/0.96 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_463])).
% 1.34/0.96 thf(zip_derived_cl170, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl18])).
% 1.34/0.96 thf(zip_derived_cl171, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('simplify', [status(thm)], [zip_derived_cl170])).
% 1.34/0.96 thf(zip_derived_cl45, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_383])).
% 1.34/0.96 thf(zip_derived_cl330, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl171, zip_derived_cl45])).
% 1.34/0.96 thf(zip_derived_cl386, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl385, zip_derived_cl330])).
% 1.34/0.96 thf(clause_607, axiom,
% 1.34/0.96 (( ~( LE @ ( f @ ( suc @ ( suc @ B_41 ) ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 1.34/0.96 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_41 ) ) ) ) |
% 1.34/0.96 ( LE @ ( f @ B_41 ) @ ( s @ ( s @ 0 ) ) ))).
% 1.34/0.96 thf(zip_derived_cl9, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0))))
% 1.34/0.96 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_607])).
% 1.34/0.96 thf(zip_derived_cl388, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.34/0.96 | ~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0)))))),
% 1.34/0.96 inference('sup+', [status(thm)], [zip_derived_cl386, zip_derived_cl9])).
% 1.34/0.96 thf(clause_131, axiom,
% 1.34/0.96 (( ~( iLEQ @ ( suc @ B_24 ) @ ( suc @ B_25 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_24 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_25 ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ B_24 ) @ ( f @ ( suc @ B_24 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_24 ) ) ) |
% 1.34/0.96 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_24 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ B_25 ) @ ( f @ ( suc @ B_25 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_24 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_25 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_25 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ))).
% 1.34/0.96 thf(zip_derived_cl37, plain,
% 1.34/0.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/0.96 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X2))))
% 1.34/0.96 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 1.34/0.96 | ~ (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1))))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2))))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_131])).
% 1.34/0.96 thf(zip_derived_cl351, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 1.34/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl37])).
% 1.34/0.96 thf(zip_derived_cl352, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('simplify', [status(thm)], [zip_derived_cl351])).
% 1.34/0.96 thf(clause_663, axiom,
% 1.34/0.96 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 1.34/0.96 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 1.34/0.96 thf(zip_derived_cl35, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_663])).
% 1.34/0.96 thf(clause_283, axiom,
% 1.34/0.96 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.34/0.96 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 1.34/0.96 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 1.34/0.96 thf(zip_derived_cl31, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_283])).
% 1.34/0.96 thf(zip_derived_cl74, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl35, zip_derived_cl31])).
% 1.34/0.96 thf(zip_derived_cl431, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl352, zip_derived_cl74])).
% 1.34/0.96 thf(clause_486, axiom,
% 1.34/0.96 (( ~( iLEQ @ ( suc @ B_24 ) @ ( suc @ B_25 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_25 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_24 ) ) ) |
% 1.34/0.96 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_24 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_24 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_25 ) ) ) ) |
% 1.34/0.96 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 1.34/0.96 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 1.34/0.96 ( E @ ( f @ B_24 ) @ ( f @ ( suc @ B_24 ) ) ) |
% 1.34/0.96 ( E @ ( f @ B_25 ) @ ( f @ ( suc @ B_25 ) ) ))).
% 1.34/0.96 thf(zip_derived_cl13, plain,
% 1.34/0.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.34/0.96 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X2) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X2))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X2)))
% 1.34/0.96 | (E @ (f @ X2) @ (f @ (suc @ X2)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_486])).
% 1.34/0.96 thf(zip_derived_cl231, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 1.34/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 1.34/0.96 thf(zip_derived_cl232, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('simplify', [status(thm)], [zip_derived_cl231])).
% 1.34/0.96 thf(zip_derived_cl31, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_283])).
% 1.34/0.96 thf(zip_derived_cl344, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl232, zip_derived_cl31])).
% 1.34/0.96 thf(zip_derived_cl432, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl431, zip_derived_cl344])).
% 1.34/0.96 thf(clause_103, axiom,
% 1.34/0.96 (( ~( LE @
% 1.34/0.96 ( f @ ( suc @ ( suc @ B_23 ) ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 1.34/0.96 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_23 ) ) ) ) |
% 1.34/0.96 ( LE @ ( f @ B_23 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 1.34/0.96 thf(zip_derived_cl27, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ (s @ 0)))))
% 1.34/0.96 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_103])).
% 1.34/0.96 thf(clause_556, axiom, (LE @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 1.34/0.96 thf(zip_derived_cl2, plain,
% 1.34/0.96 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_556])).
% 1.34/0.96 thf(zip_derived_cl78, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 1.34/0.96 inference('demod', [status(thm)], [zip_derived_cl27, zip_derived_cl2])).
% 1.34/0.96 thf(zip_derived_cl434, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 1.34/0.96 inference('sup+', [status(thm)], [zip_derived_cl432, zip_derived_cl78])).
% 1.34/0.96 thf(clause_550, axiom,
% 1.34/0.96 (( ~( LE @ ( f @ ( suc @ B_23 ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 1.34/0.96 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_23 ) ) ) |
% 1.34/0.96 ( LE @ ( f @ B_23 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 1.34/0.96 thf(zip_derived_cl42, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ (s @ 0)))))
% 1.34/0.96 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_550])).
% 1.34/0.96 thf(zip_derived_cl2, plain,
% 1.34/0.96 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_556])).
% 1.34/0.96 thf(zip_derived_cl77, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 1.34/0.96 inference('demod', [status(thm)], [zip_derived_cl42, zip_derived_cl2])).
% 1.34/0.96 thf(zip_derived_cl439, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 1.34/0.96 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl434, zip_derived_cl77])).
% 1.34/0.96 thf(clause_658, axiom,
% 1.34/0.96 (( ~( LE @ ( f @ B_23 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 1.34/0.96 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_23 ) ) |
% 1.34/0.96 ( LE @ ( f @ B_23 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 1.34/0.96 thf(zip_derived_cl0, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 1.34/0.96 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_658])).
% 1.34/0.96 thf(zip_derived_cl2, plain,
% 1.34/0.96 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_556])).
% 1.34/0.96 thf(zip_derived_cl54, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 1.34/0.96 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 1.34/0.96 thf(zip_derived_cl440, plain,
% 1.34/0.96 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl439, zip_derived_cl54])).
% 1.34/0.96 thf(zip_derived_cl445, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.34/0.96 inference('demod', [status(thm)], [zip_derived_cl388, zip_derived_cl440])).
% 1.34/0.96 thf(clause_457, axiom,
% 1.34/0.96 (( ~( LE @ ( f @ ( suc @ B_41 ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 1.34/0.96 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_41 ) ) ) |
% 1.34/0.96 ( LE @ ( f @ B_41 ) @ ( s @ ( s @ 0 ) ) ))).
% 1.34/0.96 thf(zip_derived_cl33, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0))))
% 1.34/0.96 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_457])).
% 1.34/0.96 thf(zip_derived_cl440, plain,
% 1.34/0.96 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl439, zip_derived_cl54])).
% 1.34/0.96 thf(zip_derived_cl443, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.34/0.96 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl440])).
% 1.34/0.96 thf(zip_derived_cl455, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 1.34/0.96 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.34/0.96 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl443])).
% 1.34/0.96 thf(zip_derived_cl456, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.34/0.96 inference('simplify', [status(thm)], [zip_derived_cl455])).
% 1.34/0.96 thf(clause_300, axiom,
% 1.34/0.96 (( ~( LE @ ( f @ B_41 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 1.34/0.96 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_41 ) ) |
% 1.34/0.96 ( LE @ ( f @ B_41 ) @ ( s @ ( s @ 0 ) ) ))).
% 1.34/0.96 thf(zip_derived_cl6, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 1.34/0.96 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 1.34/0.96 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.34/0.96 inference('cnf', [status(esa)], [clause_300])).
% 1.34/0.96 thf(zip_derived_cl440, plain,
% 1.34/0.96 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl439, zip_derived_cl54])).
% 1.34/0.96 thf(zip_derived_cl441, plain,
% 1.34/0.96 (![X0 : $i]:
% 1.34/0.96 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 1.34/0.96 inference('demod', [status(thm)], [zip_derived_cl6, zip_derived_cl440])).
% 1.34/0.96 thf(zip_derived_cl458, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl456, zip_derived_cl441])).
% 1.34/0.96 thf(zip_derived_cl458, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl456, zip_derived_cl441])).
% 1.34/0.96 thf(zip_derived_cl458, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 1.34/0.96 inference('clc', [status(thm)], [zip_derived_cl456, zip_derived_cl441])).
% 1.34/0.96 thf(zip_derived_cl470, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 1.34/0.96 inference('demod', [status(thm)],
% 1.34/0.96 [zip_derived_cl383, zip_derived_cl458, zip_derived_cl458,
% 1.34/0.96 zip_derived_cl458])).
% 1.34/0.96 thf(zip_derived_cl470, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 1.34/0.96 inference('demod', [status(thm)],
% 1.34/0.96 [zip_derived_cl383, zip_derived_cl458, zip_derived_cl458,
% 1.34/0.96 zip_derived_cl458])).
% 1.34/0.96 thf(zip_derived_cl470, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 1.34/0.96 inference('demod', [status(thm)],
% 1.34/0.96 [zip_derived_cl383, zip_derived_cl458, zip_derived_cl458,
% 1.34/0.96 zip_derived_cl458])).
% 1.34/0.96 thf(zip_derived_cl479, plain, (![X0 : $i]: (LE @ (f @ X0) @ 0)),
% 1.34/0.96 inference('demod', [status(thm)],
% 1.34/0.96 [zip_derived_cl200, zip_derived_cl470, zip_derived_cl470,
% 1.34/0.96 zip_derived_cl470])).
% 1.34/0.96 thf(zip_derived_cl481, plain, ($false),
% 1.34/0.96 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl479])).
% 1.34/0.96
% 1.34/0.96 % SZS output end Refutation
% 1.34/0.96
% 1.34/0.96
% 1.34/0.96 % Terminating...
% 1.58/1.07 % Runner terminated.
% 1.58/1.09 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------