TSTP Solution File: SYO686-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO686-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.NmJaAUNF2c true
% Computer : n023.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 05:52:34 EDT 2023
% Result : Unsatisfiable 3.55s 1.12s
% Output : Refutation 3.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO686-1 : TPTP v8.1.2. Released v7.3.0.
% 0.03/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.NmJaAUNF2c true
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 07:16:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.54/0.64 % Total configuration time : 435
% 0.54/0.64 % Estimated wc time : 1092
% 0.54/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.55/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.55/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.55/0.79 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 3.55/1.12 % Solved by fo/fo5.sh.
% 3.55/1.12 % done 238 iterations in 0.318s
% 3.55/1.12 % SZS status Unsatisfiable for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 3.55/1.12 % SZS output start Refutation
% 3.55/1.12 thf(f_type, type, f: $i > $i).
% 3.55/1.12 thf(0_type, type, 0: $i).
% 3.55/1.12 thf(s_type, type, s: $i > $i).
% 3.55/1.12 thf(E_type, type, E: $i > $i > $o).
% 3.55/1.12 thf(iLEQ_type, type, iLEQ: $i > $i > $o).
% 3.55/1.12 thf(LE_type, type, LE: $i > $i > $o).
% 3.55/1.12 thf(z_type, type, z: $i).
% 3.55/1.12 thf(suc_type, type, suc: $i > $i).
% 3.55/1.12 thf(clause_295, axiom, (~( LE @ ( f @ z ) @ 0 ))).
% 3.55/1.12 thf(zip_derived_cl76, plain, (~ (LE @ (f @ z) @ 0)),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_295])).
% 3.55/1.12 thf(clause_478, axiom,
% 3.55/1.12 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ B_23 ) ) ) ) @ ( s @ 0 ) ) ) |
% 3.55/1.12 ( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_23 ) ) ) ) ) |
% 3.55/1.12 ( LE @ ( f @ B_23 ) @ 0 ))).
% 3.55/1.12 thf(zip_derived_cl27, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0))
% 3.55/1.12 | (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | (LE @ (f @ X0) @ 0))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_478])).
% 3.55/1.12 thf(clause_313, axiom,
% 3.55/1.12 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ B_20 ) ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 3.55/1.12 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_20 ) ) ) ) ) |
% 3.55/1.12 ( LE @ ( f @ B_20 ) @ ( s @ 0 ) ))).
% 3.55/1.12 thf(zip_derived_cl8, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ 0)))
% 3.55/1.12 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ 0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_313])).
% 3.55/1.12 thf(clause_232, axiom,
% 3.55/1.12 (( ~( LE @
% 3.55/1.12 ( f @ ( suc @ ( suc @ ( suc @ B_16 ) ) ) ) @
% 3.55/1.12 ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 3.55/1.12 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_16 ) ) ) ) ) |
% 3.55/1.12 ( LE @ ( f @ B_16 ) @ ( s @ ( s @ 0 ) ) ))).
% 3.55/1.12 thf(zip_derived_cl35, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ (s @ 0))))
% 3.55/1.12 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_232])).
% 3.55/1.12 thf(clause_327, axiom,
% 3.55/1.12 (( ~( LE @
% 3.55/1.12 ( f @ ( suc @ ( suc @ ( suc @ B_11 ) ) ) ) @
% 3.55/1.12 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 3.55/1.12 ( E @
% 3.55/1.12 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_11 ) ) ) ) ) |
% 3.55/1.12 ( LE @ ( f @ B_11 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl9, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ (s @ (s @ 0)))))
% 3.55/1.12 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_327])).
% 3.55/1.12 thf(clause_603, axiom,
% 3.55/1.12 (( ~( LE @
% 3.55/1.12 ( f @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) @
% 3.55/1.12 ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) ) |
% 3.55/1.12 ( E @
% 3.55/1.12 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @
% 3.55/1.12 ( f @ ( suc @ ( suc @ ( suc @ B_5 ) ) ) ) ) |
% 3.55/1.12 ( LE @ ( f @ B_5 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl70, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @
% 3.55/1.12 (s @ (s @ (s @ (s @ (s @ 0))))))
% 3.55/1.12 | (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_603])).
% 3.55/1.12 thf(clause_159, axiom,
% 3.55/1.12 (LE @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl15, plain,
% 3.55/1.12 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_159])).
% 3.55/1.12 thf(zip_derived_cl152, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl15])).
% 3.55/1.12 thf(clause_93, axiom,
% 3.55/1.12 (( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_6 ) ) ) |
% 3.55/1.12 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_6 ) ) ) |
% 3.55/1.12 ( ~( E @
% 3.55/1.12 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_6 ) ) ) ) |
% 3.55/1.12 ( ~( E @
% 3.55/1.12 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @
% 3.55/1.12 ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 3.55/1.12 ( ~( E @
% 3.55/1.12 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 3.55/1.12 ( ~( E @
% 3.55/1.12 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @
% 3.55/1.12 ( f @ ( suc @ ( suc @ ( suc @ B_6 ) ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ B_6 ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl42, plain,
% 3.55/1.12 (![X0 : $i, X1 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X1))))
% 3.55/1.12 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_93])).
% 3.55/1.12 thf(zip_derived_cl475, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 3.55/1.12 inference('eq_fact', [status(thm)], [zip_derived_cl42])).
% 3.55/1.12 thf(zip_derived_cl476, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('simplify', [status(thm)], [zip_derived_cl475])).
% 3.55/1.12 thf(clause_614, axiom,
% 3.55/1.12 (( ~( E @
% 3.55/1.12 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @
% 3.55/1.12 ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 3.55/1.12 ( ~( E @
% 3.55/1.12 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 3.55/1.12 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 3.55/1.12 thf(zip_derived_cl17, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_614])).
% 3.55/1.12 thf(clause_267, axiom,
% 3.55/1.12 (( ~( E @
% 3.55/1.12 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) |
% 3.55/1.12 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 3.55/1.12 thf(zip_derived_cl43, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_267])).
% 3.55/1.12 thf(clause_380, axiom,
% 3.55/1.12 (( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 3.55/1.12 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 3.55/1.12 thf(zip_derived_cl3, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_380])).
% 3.55/1.12 thf(zip_derived_cl195, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl43, zip_derived_cl3])).
% 3.55/1.12 thf(zip_derived_cl257, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl17, zip_derived_cl195])).
% 3.55/1.12 thf(zip_derived_cl3, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_380])).
% 3.55/1.12 thf(zip_derived_cl258, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl257, zip_derived_cl3])).
% 3.55/1.12 thf(zip_derived_cl544, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl476, zip_derived_cl258])).
% 3.55/1.12 thf(clause_105, axiom,
% 3.55/1.12 (( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_6 ) ) ) |
% 3.55/1.12 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_6 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_6 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 3.55/1.12 ( E @ ( f @ B_6 ) @ ( f @ ( suc @ B_6 ) ) ))).
% 3.55/1.12 thf(zip_derived_cl71, plain,
% 3.55/1.12 (![X0 : $i, X1 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 3.55/1.12 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_105])).
% 3.55/1.12 thf(zip_derived_cl255, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 3.55/1.12 inference('eq_fact', [status(thm)], [zip_derived_cl71])).
% 3.55/1.12 thf(zip_derived_cl256, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('simplify', [status(thm)], [zip_derived_cl255])).
% 3.55/1.12 thf(zip_derived_cl3, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_380])).
% 3.55/1.12 thf(zip_derived_cl276, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl256, zip_derived_cl3])).
% 3.55/1.12 thf(zip_derived_cl545, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl544, zip_derived_cl276])).
% 3.55/1.12 thf(clause_425, axiom,
% 3.55/1.12 (( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_6 ) ) ) |
% 3.55/1.12 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_6 ) ) ) |
% 3.55/1.12 ( ~( E @
% 3.55/1.12 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_6 ) ) ) ) |
% 3.55/1.12 ( ~( E @
% 3.55/1.12 ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ A_1 ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ B_6 ) @ ( f @ ( suc @ B_6 ) ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) |
% 3.55/1.12 ( E @ ( f @ B_6 ) @ ( f @ ( suc @ ( suc @ B_6 ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl50, plain,
% 3.55/1.12 (![X0 : $i, X1 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X1))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X1))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_425])).
% 3.55/1.12 thf(zip_derived_cl450, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 3.55/1.12 inference('eq_fact', [status(thm)], [zip_derived_cl50])).
% 3.55/1.12 thf(zip_derived_cl451, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('simplify', [status(thm)], [zip_derived_cl450])).
% 3.55/1.12 thf(zip_derived_cl195, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl43, zip_derived_cl3])).
% 3.55/1.12 thf(zip_derived_cl482, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl451, zip_derived_cl195])).
% 3.55/1.12 thf(zip_derived_cl276, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl256, zip_derived_cl3])).
% 3.55/1.12 thf(zip_derived_cl483, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl482, zip_derived_cl276])).
% 3.55/1.12 thf(zip_derived_cl546, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl545, zip_derived_cl483])).
% 3.55/1.12 thf(zip_derived_cl550, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0)))),
% 3.55/1.12 inference('sup-', [status(thm)], [zip_derived_cl152, zip_derived_cl546])).
% 3.55/1.12 thf(clause_282, axiom,
% 3.55/1.12 (( ~( LE @
% 3.55/1.12 ( f @ ( suc @ ( suc @ B_5 ) ) ) @
% 3.55/1.12 ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) ) |
% 3.55/1.12 ( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ ( suc @ B_5 ) ) ) ) |
% 3.55/1.12 ( LE @ ( f @ B_5 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl51, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ (s @ (s @ 0))))))
% 3.55/1.12 | (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_282])).
% 3.55/1.12 thf(zip_derived_cl15, plain,
% 3.55/1.12 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_159])).
% 3.55/1.12 thf(zip_derived_cl118, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl15])).
% 3.55/1.12 thf(zip_derived_cl551, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl550, zip_derived_cl118])).
% 3.55/1.12 thf(clause_345, axiom,
% 3.55/1.12 (( ~( LE @ ( f @ B_5 ) @ ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) ) |
% 3.55/1.12 ( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ B_5 ) ) |
% 3.55/1.12 ( LE @ ( f @ B_5 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl78, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))
% 3.55/1.12 | (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_345])).
% 3.55/1.12 thf(zip_derived_cl15, plain,
% 3.55/1.12 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_159])).
% 3.55/1.12 thf(zip_derived_cl84, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ X0))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl78, zip_derived_cl15])).
% 3.55/1.12 thf(zip_derived_cl552, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl551, zip_derived_cl84])).
% 3.55/1.12 thf(clause_569, axiom,
% 3.55/1.12 (( ~( LE @
% 3.55/1.12 ( f @ ( suc @ B_5 ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) ) |
% 3.55/1.12 ( E @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) @ ( f @ ( suc @ B_5 ) ) ) |
% 3.55/1.12 ( LE @ ( f @ B_5 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl22, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ (s @ (s @ 0))))))
% 3.55/1.12 | (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_569])).
% 3.55/1.12 thf(zip_derived_cl15, plain,
% 3.55/1.12 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ (s @ 0))))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_159])).
% 3.55/1.12 thf(zip_derived_cl113, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ (s @ (s @ (s @ 0)))) @ (f @ (suc @ X0)))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0))))))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl22, zip_derived_cl15])).
% 3.55/1.12 thf(zip_derived_cl553, plain,
% 3.55/1.12 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl552, zip_derived_cl113])).
% 3.55/1.12 thf(zip_derived_cl554, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl553])).
% 3.55/1.12 thf(clause_149, axiom,
% 3.55/1.12 (( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_12 ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 3.55/1.12 ( ~( E @
% 3.55/1.12 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_12 ) ) ) |
% 3.55/1.12 ( ~( E @
% 3.55/1.12 ( s @ ( s @ ( s @ 0 ) ) ) @
% 3.55/1.12 ( f @ ( suc @ ( suc @ ( suc @ B_12 ) ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ B_12 ) @ ( f @ ( suc @ ( suc @ B_12 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ B_12 ) @ ( f @ ( suc @ B_12 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_12 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_12 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl56, plain,
% 3.55/1.12 (![X0 : $i, X1 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 3.55/1.12 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_149])).
% 3.55/1.12 thf(zip_derived_cl452, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('eq_fact', [status(thm)], [zip_derived_cl56])).
% 3.55/1.12 thf(zip_derived_cl453, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('simplify', [status(thm)], [zip_derived_cl452])).
% 3.55/1.12 thf(clause_323, axiom,
% 3.55/1.12 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 3.55/1.12 ( ~( E @
% 3.55/1.12 ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 3.55/1.12 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 3.55/1.12 thf(zip_derived_cl63, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_323])).
% 3.55/1.12 thf(clause_57, axiom,
% 3.55/1.12 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) |
% 3.55/1.12 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 3.55/1.12 thf(zip_derived_cl47, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_57])).
% 3.55/1.12 thf(clause_86, axiom,
% 3.55/1.12 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 3.55/1.12 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 3.55/1.12 thf(zip_derived_cl26, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_86])).
% 3.55/1.12 thf(zip_derived_cl158, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl47, zip_derived_cl26])).
% 3.55/1.12 thf(zip_derived_cl205, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl63, zip_derived_cl158])).
% 3.55/1.12 thf(zip_derived_cl26, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_86])).
% 3.55/1.12 thf(zip_derived_cl206, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl205, zip_derived_cl26])).
% 3.55/1.12 thf(zip_derived_cl540, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl453, zip_derived_cl206])).
% 3.55/1.12 thf(clause_139, axiom,
% 3.55/1.12 (( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_12 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_12 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_12 ) ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 3.55/1.12 ( E @ ( f @ B_12 ) @ ( f @ ( suc @ B_12 ) ) ))).
% 3.55/1.12 thf(zip_derived_cl38, plain,
% 3.55/1.12 (![X0 : $i, X1 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_139])).
% 3.55/1.12 thf(zip_derived_cl203, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('eq_fact', [status(thm)], [zip_derived_cl38])).
% 3.55/1.12 thf(zip_derived_cl204, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('simplify', [status(thm)], [zip_derived_cl203])).
% 3.55/1.12 thf(zip_derived_cl26, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_86])).
% 3.55/1.12 thf(zip_derived_cl217, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl204, zip_derived_cl26])).
% 3.55/1.12 thf(zip_derived_cl541, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl540, zip_derived_cl217])).
% 3.55/1.12 thf(clause_308, axiom,
% 3.55/1.12 (( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_12 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_12 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_2 ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ B_12 ) @ ( f @ ( suc @ B_12 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_12 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_12 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) |
% 3.55/1.12 ( E @ ( f @ B_12 ) @ ( f @ ( suc @ ( suc @ B_12 ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl20, plain,
% 3.55/1.12 (![X0 : $i, X1 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1)))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_308])).
% 3.55/1.12 thf(zip_derived_cl418, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('eq_fact', [status(thm)], [zip_derived_cl20])).
% 3.55/1.12 thf(zip_derived_cl419, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('simplify', [status(thm)], [zip_derived_cl418])).
% 3.55/1.12 thf(zip_derived_cl158, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl47, zip_derived_cl26])).
% 3.55/1.12 thf(zip_derived_cl424, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl419, zip_derived_cl158])).
% 3.55/1.12 thf(zip_derived_cl217, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl204, zip_derived_cl26])).
% 3.55/1.12 thf(zip_derived_cl425, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl424, zip_derived_cl217])).
% 3.55/1.12 thf(zip_derived_cl542, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl541, zip_derived_cl425])).
% 3.55/1.12 thf(zip_derived_cl592, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('sup-', [status(thm)], [zip_derived_cl554, zip_derived_cl542])).
% 3.55/1.12 thf(clause_294, axiom,
% 3.55/1.12 (( ~( LE @ ( f @ B_11 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 3.55/1.12 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_11 ) ) |
% 3.55/1.12 ( LE @ ( f @ B_11 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl44, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 3.55/1.12 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_294])).
% 3.55/1.12 thf(zip_derived_cl553, plain,
% 3.55/1.12 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl552, zip_derived_cl113])).
% 3.55/1.12 thf(zip_derived_cl555, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl44, zip_derived_cl553])).
% 3.55/1.12 thf(zip_derived_cl600, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl592, zip_derived_cl555])).
% 3.55/1.12 thf(clause_158, axiom,
% 3.55/1.12 (( ~( LE @
% 3.55/1.12 ( f @ ( suc @ ( suc @ B_11 ) ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 3.55/1.12 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_11 ) ) ) ) |
% 3.55/1.12 ( LE @ ( f @ B_11 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl75, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ (s @ 0)))))
% 3.55/1.12 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_158])).
% 3.55/1.12 thf(zip_derived_cl553, plain,
% 3.55/1.12 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl552, zip_derived_cl113])).
% 3.55/1.12 thf(zip_derived_cl557, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl75, zip_derived_cl553])).
% 3.55/1.12 thf(zip_derived_cl601, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl600, zip_derived_cl557])).
% 3.55/1.12 thf(clause_335, axiom,
% 3.55/1.12 (( ~( LE @ ( f @ ( suc @ B_11 ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 3.55/1.12 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_11 ) ) ) |
% 3.55/1.12 ( LE @ ( f @ B_11 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl59, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ (s @ 0)))))
% 3.55/1.12 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_335])).
% 3.55/1.12 thf(zip_derived_cl553, plain,
% 3.55/1.12 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl552, zip_derived_cl113])).
% 3.55/1.12 thf(zip_derived_cl556, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl553])).
% 3.55/1.12 thf(zip_derived_cl602, plain,
% 3.55/1.12 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl601, zip_derived_cl556])).
% 3.55/1.12 thf(zip_derived_cl604, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl35, zip_derived_cl602])).
% 3.55/1.12 thf(clause_226, axiom,
% 3.55/1.12 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_17 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 3.55/1.12 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_17 ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_17 ) ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl13, plain,
% 3.55/1.12 (![X0 : $i, X1 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_226])).
% 3.55/1.12 thf(zip_derived_cl373, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 3.55/1.12 thf(zip_derived_cl374, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('simplify', [status(thm)], [zip_derived_cl373])).
% 3.55/1.12 thf(clause_575, axiom,
% 3.55/1.12 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 3.55/1.12 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 3.55/1.12 thf(zip_derived_cl14, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_575])).
% 3.55/1.12 thf(clause_638, axiom,
% 3.55/1.12 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) |
% 3.55/1.12 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 3.55/1.12 thf(zip_derived_cl19, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_638])).
% 3.55/1.12 thf(clause_432, axiom,
% 3.55/1.12 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 3.55/1.12 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 3.55/1.12 thf(zip_derived_cl16, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_432])).
% 3.55/1.12 thf(zip_derived_cl157, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl19, zip_derived_cl16])).
% 3.55/1.12 thf(zip_derived_cl193, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl14, zip_derived_cl157])).
% 3.55/1.12 thf(clause_355, axiom,
% 3.55/1.12 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_17 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 3.55/1.12 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_17 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 3.55/1.12 ( E @ ( f @ B_17 ) @ ( f @ ( suc @ B_17 ) ) ))).
% 3.55/1.12 thf(zip_derived_cl32, plain,
% 3.55/1.12 (![X0 : $i, X1 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 3.55/1.12 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_355])).
% 3.55/1.12 thf(zip_derived_cl162, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 3.55/1.12 inference('eq_fact', [status(thm)], [zip_derived_cl32])).
% 3.55/1.12 thf(zip_derived_cl163, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('simplify', [status(thm)], [zip_derived_cl162])).
% 3.55/1.12 thf(zip_derived_cl16, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_432])).
% 3.55/1.12 thf(zip_derived_cl174, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl163, zip_derived_cl16])).
% 3.55/1.12 thf(zip_derived_cl194, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl193, zip_derived_cl174])).
% 3.55/1.12 thf(zip_derived_cl380, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl374, zip_derived_cl194])).
% 3.55/1.12 thf(zip_derived_cl174, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl163, zip_derived_cl16])).
% 3.55/1.12 thf(zip_derived_cl381, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl380, zip_derived_cl174])).
% 3.55/1.12 thf(zip_derived_cl622, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('sup-', [status(thm)], [zip_derived_cl604, zip_derived_cl381])).
% 3.55/1.12 thf(clause_300, axiom,
% 3.55/1.12 (( ~( LE @ ( f @ ( suc @ ( suc @ B_16 ) ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 3.55/1.12 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_16 ) ) ) ) |
% 3.55/1.12 ( LE @ ( f @ B_16 ) @ ( s @ ( s @ 0 ) ) ))).
% 3.55/1.12 thf(zip_derived_cl29, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0))))
% 3.55/1.12 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_300])).
% 3.55/1.12 thf(zip_derived_cl602, plain,
% 3.55/1.12 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl601, zip_derived_cl556])).
% 3.55/1.12 thf(zip_derived_cl603, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl29, zip_derived_cl602])).
% 3.55/1.12 thf(zip_derived_cl647, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl622, zip_derived_cl603])).
% 3.55/1.12 thf(clause_263, axiom,
% 3.55/1.12 (( ~( LE @ ( f @ ( suc @ B_16 ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 3.55/1.12 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_16 ) ) ) |
% 3.55/1.12 ( LE @ ( f @ B_16 ) @ ( s @ ( s @ 0 ) ) ))).
% 3.55/1.12 thf(zip_derived_cl40, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0))))
% 3.55/1.12 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_263])).
% 3.55/1.12 thf(zip_derived_cl602, plain,
% 3.55/1.12 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl601, zip_derived_cl556])).
% 3.55/1.12 thf(zip_derived_cl605, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl602])).
% 3.55/1.12 thf(zip_derived_cl648, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl647, zip_derived_cl605])).
% 3.55/1.12 thf(clause_368, axiom,
% 3.55/1.12 (( ~( LE @ ( f @ B_16 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 3.55/1.12 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_16 ) ) |
% 3.55/1.12 ( LE @ ( f @ B_16 ) @ ( s @ ( s @ 0 ) ) ))).
% 3.55/1.12 thf(zip_derived_cl64, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 3.55/1.12 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_368])).
% 3.55/1.12 thf(zip_derived_cl602, plain,
% 3.55/1.12 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl601, zip_derived_cl556])).
% 3.55/1.12 thf(zip_derived_cl606, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl602])).
% 3.55/1.12 thf(zip_derived_cl649, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl648, zip_derived_cl606])).
% 3.55/1.12 thf(zip_derived_cl603, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl29, zip_derived_cl602])).
% 3.55/1.12 thf(clause_550, axiom,
% 3.55/1.12 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_17 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 3.55/1.12 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_17 ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_3 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) |
% 3.55/1.12 ( E @ ( f @ B_17 ) @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl67, plain,
% 3.55/1.12 (![X0 : $i, X1 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_550])).
% 3.55/1.12 thf(zip_derived_cl395, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('eq_fact', [status(thm)], [zip_derived_cl67])).
% 3.55/1.12 thf(zip_derived_cl396, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('simplify', [status(thm)], [zip_derived_cl395])).
% 3.55/1.12 thf(zip_derived_cl157, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl19, zip_derived_cl16])).
% 3.55/1.12 thf(zip_derived_cl422, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl396, zip_derived_cl157])).
% 3.55/1.12 thf(zip_derived_cl174, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl163, zip_derived_cl16])).
% 3.55/1.12 thf(zip_derived_cl423, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl422, zip_derived_cl174])).
% 3.55/1.12 thf(zip_derived_cl616, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('sup-', [status(thm)], [zip_derived_cl603, zip_derived_cl423])).
% 3.55/1.12 thf(zip_derived_cl606, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl602])).
% 3.55/1.12 thf(zip_derived_cl631, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl616, zip_derived_cl606])).
% 3.55/1.12 thf(zip_derived_cl605, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl602])).
% 3.55/1.12 thf(zip_derived_cl632, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl631, zip_derived_cl605])).
% 3.55/1.12 thf(zip_derived_cl650, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl649, zip_derived_cl632])).
% 3.55/1.12 thf(zip_derived_cl652, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ 0)))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl650])).
% 3.55/1.12 thf(clause_340, axiom,
% 3.55/1.12 (( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_21 ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_21 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_21 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ B_21 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_21 ) ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ B_21 ) @ ( f @ ( suc @ B_21 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ B_21 ) @ ( f @ ( suc @ ( suc @ B_21 ) ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl5, plain,
% 3.55/1.12 (![X0 : $i, X1 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X1))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1)))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_340])).
% 3.55/1.12 thf(zip_derived_cl171, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('eq_fact', [status(thm)], [zip_derived_cl5])).
% 3.55/1.12 thf(zip_derived_cl172, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('simplify', [status(thm)], [zip_derived_cl171])).
% 3.55/1.12 thf(clause_322, axiom,
% 3.55/1.12 (( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_4 ) ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 3.55/1.12 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 3.55/1.12 thf(zip_derived_cl2, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_322])).
% 3.55/1.12 thf(clause_601, axiom,
% 3.55/1.12 (( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) |
% 3.55/1.12 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 3.55/1.12 thf(zip_derived_cl74, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_601])).
% 3.55/1.12 thf(zip_derived_cl134, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl2, zip_derived_cl74])).
% 3.55/1.12 thf(clause_354, axiom,
% 3.55/1.12 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) |
% 3.55/1.12 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 3.55/1.12 thf(zip_derived_cl24, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_354])).
% 3.55/1.12 thf(zip_derived_cl74, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_601])).
% 3.55/1.12 thf(zip_derived_cl123, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl24, zip_derived_cl74])).
% 3.55/1.12 thf(zip_derived_cl135, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl134, zip_derived_cl123])).
% 3.55/1.12 thf(zip_derived_cl175, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl172, zip_derived_cl135])).
% 3.55/1.12 thf(clause_264, axiom,
% 3.55/1.12 (( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_21 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_21 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ B_21 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) |
% 3.55/1.12 ( E @ ( f @ B_21 ) @ ( f @ ( suc @ B_21 ) ) ))).
% 3.55/1.12 thf(zip_derived_cl66, plain,
% 3.55/1.12 (![X0 : $i, X1 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X1))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_264])).
% 3.55/1.12 thf(zip_derived_cl155, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('eq_fact', [status(thm)], [zip_derived_cl66])).
% 3.55/1.12 thf(zip_derived_cl156, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('simplify', [status(thm)], [zip_derived_cl155])).
% 3.55/1.12 thf(zip_derived_cl74, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_601])).
% 3.55/1.12 thf(zip_derived_cl173, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl156, zip_derived_cl74])).
% 3.55/1.12 thf(zip_derived_cl176, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl175, zip_derived_cl173])).
% 3.55/1.12 thf(zip_derived_cl669, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (LE @ (f @ X0) @ (s @ 0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('sup-', [status(thm)], [zip_derived_cl652, zip_derived_cl176])).
% 3.55/1.12 thf(clause_558, axiom,
% 3.55/1.12 (( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_21 ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_21 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_21 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ B_21 ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ B_21 ) @ ( f @ ( suc @ B_21 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( s @ 0 ) @ ( f @ A_4 ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) |
% 3.55/1.12 ( E @ ( f @ B_21 ) @ ( f @ ( suc @ ( suc @ B_21 ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl34, plain,
% 3.55/1.12 (![X0 : $i, X1 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X1))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1)))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_558])).
% 3.55/1.12 thf(zip_derived_cl361, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('eq_fact', [status(thm)], [zip_derived_cl34])).
% 3.55/1.12 thf(zip_derived_cl362, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('simplify', [status(thm)], [zip_derived_cl361])).
% 3.55/1.12 thf(zip_derived_cl123, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl24, zip_derived_cl74])).
% 3.55/1.12 thf(zip_derived_cl375, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl362, zip_derived_cl123])).
% 3.55/1.12 thf(zip_derived_cl173, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl156, zip_derived_cl74])).
% 3.55/1.12 thf(zip_derived_cl376, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl375, zip_derived_cl173])).
% 3.55/1.12 thf(zip_derived_cl682, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ 0)))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl669, zip_derived_cl376])).
% 3.55/1.12 thf(clause_356, axiom,
% 3.55/1.12 (( ~( LE @ ( f @ ( suc @ ( suc @ B_20 ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 3.55/1.12 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_20 ) ) ) ) |
% 3.55/1.12 ( LE @ ( f @ B_20 ) @ ( s @ 0 ) ))).
% 3.55/1.12 thf(zip_derived_cl69, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 3.55/1.12 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ 0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_356])).
% 3.55/1.12 thf(zip_derived_cl650, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl649, zip_derived_cl632])).
% 3.55/1.12 thf(zip_derived_cl653, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ 0)))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl650])).
% 3.55/1.12 thf(zip_derived_cl683, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (LE @ (f @ X0) @ (s @ 0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl682, zip_derived_cl653])).
% 3.55/1.12 thf(clause_534, axiom,
% 3.55/1.12 (( ~( LE @ ( f @ B_20 ) @ ( s @ ( s @ 0 ) ) ) ) |
% 3.55/1.12 ( E @ ( s @ 0 ) @ ( f @ B_20 ) ) | ( LE @ ( f @ B_20 ) @ ( s @ 0 ) ))).
% 3.55/1.12 thf(zip_derived_cl80, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 3.55/1.12 | (E @ (s @ 0) @ (f @ X0))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ 0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_534])).
% 3.55/1.12 thf(zip_derived_cl650, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl649, zip_derived_cl632])).
% 3.55/1.12 thf(zip_derived_cl654, plain,
% 3.55/1.12 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl80, zip_derived_cl650])).
% 3.55/1.12 thf(zip_derived_cl684, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl683, zip_derived_cl654])).
% 3.55/1.12 thf(clause_92, axiom,
% 3.55/1.12 (( ~( LE @ ( f @ ( suc @ B_20 ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 3.55/1.12 ( E @ ( s @ 0 ) @ ( f @ ( suc @ B_20 ) ) ) |
% 3.55/1.12 ( LE @ ( f @ B_20 ) @ ( s @ 0 ) ))).
% 3.55/1.12 thf(zip_derived_cl6, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 3.55/1.12 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (LE @ (f @ X0) @ (s @ 0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_92])).
% 3.55/1.12 thf(zip_derived_cl650, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl649, zip_derived_cl632])).
% 3.55/1.12 thf(zip_derived_cl651, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl6, zip_derived_cl650])).
% 3.55/1.12 thf(zip_derived_cl685, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl684, zip_derived_cl651])).
% 3.55/1.12 thf(zip_derived_cl686, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))) | (LE @ (f @ X0) @ 0))),
% 3.55/1.12 inference('demod', [status(thm)], [zip_derived_cl27, zip_derived_cl685])).
% 3.55/1.12 thf(clause_250, axiom,
% 3.55/1.12 (( ~( E @ ( f @ B_24 ) @ ( f @ ( suc @ B_24 ) ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_24 ) ) ) ) ) |
% 3.55/1.12 ( ~( iLEQ @ ( suc @ A_5 ) @ ( suc @ B_24 ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ A_5 ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_5 ) ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_24 ) ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ B_24 ) @ ( f @ ( suc @ ( suc @ B_24 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ ( suc @ B_24 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_24 ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ))).
% 3.55/1.12 thf(zip_derived_cl49, plain,
% 3.55/1.12 (![X0 : $i, X1 : $i]:
% 3.55/1.12 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ 0 @ (f @ X1))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X1)))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1)))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_250])).
% 3.55/1.12 thf(zip_derived_cl363, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('eq_fact', [status(thm)], [zip_derived_cl49])).
% 3.55/1.12 thf(zip_derived_cl364, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('simplify', [status(thm)], [zip_derived_cl363])).
% 3.55/1.12 thf(clause_643, axiom,
% 3.55/1.12 (( ~( E @ 0 @ ( f @ A_5 ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_5 ) ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 3.55/1.12 ( iLEQ @ ( suc @ A_5 ) @ ( suc @ A_5 ) ))).
% 3.55/1.12 thf(zip_derived_cl28, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_643])).
% 3.55/1.12 thf(clause_494, axiom,
% 3.55/1.12 (( ~( iLEQ @ ( suc @ A_5 ) @ ( suc @ B_24 ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ A_5 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ ( suc @ B_24 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_24 ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) |
% 3.55/1.12 ( E @ ( f @ B_24 ) @ ( f @ ( suc @ B_24 ) ) ))).
% 3.55/1.12 thf(zip_derived_cl23, plain,
% 3.55/1.12 (![X0 : $i, X1 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 3.55/1.12 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ X1))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_494])).
% 3.55/1.12 thf(zip_derived_cl121, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('eq_fact', [status(thm)], [zip_derived_cl23])).
% 3.55/1.12 thf(zip_derived_cl122, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('simplify', [status(thm)], [zip_derived_cl121])).
% 3.55/1.12 thf(clause_59, axiom,
% 3.55/1.12 (( ~( E @ 0 @ ( f @ A_5 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) |
% 3.55/1.12 ( iLEQ @ ( suc @ A_5 ) @ ( suc @ A_5 ) ))).
% 3.55/1.12 thf(zip_derived_cl4, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_59])).
% 3.55/1.12 thf(zip_derived_cl136, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl122, zip_derived_cl4])).
% 3.55/1.12 thf(zip_derived_cl150, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ X0)))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl28, zip_derived_cl136])).
% 3.55/1.12 thf(clause_573, axiom,
% 3.55/1.12 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 3.55/1.12 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ A_5 ) ) ) |
% 3.55/1.12 ( E @ ( f @ A_5 ) @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) |
% 3.55/1.12 ( iLEQ @ ( suc @ A_5 ) @ ( suc @ A_5 ) ))).
% 3.55/1.12 thf(zip_derived_cl68, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_573])).
% 3.55/1.12 thf(zip_derived_cl4, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('cnf', [status(esa)], [clause_59])).
% 3.55/1.12 thf(zip_derived_cl117, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.12 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl68, zip_derived_cl4])).
% 3.55/1.12 thf(zip_derived_cl151, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl150, zip_derived_cl117])).
% 3.55/1.12 thf(zip_derived_cl377, plain,
% 3.55/1.12 (![X0 : $i]:
% 3.55/1.12 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.12 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.12 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.12 inference('clc', [status(thm)], [zip_derived_cl364, zip_derived_cl151])).
% 3.55/1.12 thf(clause_431, axiom,
% 3.55/1.12 (( ~( E @ ( f @ B_24 ) @ ( f @ ( suc @ B_24 ) ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_24 ) ) ) ) ) |
% 3.55/1.12 ( ~( iLEQ @ ( suc @ A_5 ) @ ( suc @ B_24 ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ A_5 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_5 ) ) ) ) |
% 3.55/1.12 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) ) |
% 3.55/1.13 ( ~( E @ 0 @ ( f @ ( suc @ B_24 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_24 ) ) ) |
% 3.55/1.13 ( ~( E @ ( f @ A_5 ) @ ( f @ ( suc @ A_5 ) ) ) ) |
% 3.55/1.13 ( E @ ( f @ A_5 ) @ ( f @ ( suc @ ( suc @ A_5 ) ) ) ) |
% 3.55/1.13 ( E @ ( f @ B_24 ) @ ( f @ ( suc @ ( suc @ B_24 ) ) ) ))).
% 3.55/1.13 thf(zip_derived_cl39, plain,
% 3.55/1.13 (![X0 : $i, X1 : $i]:
% 3.55/1.13 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 3.55/1.13 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 3.55/1.13 | ~ (E @ 0 @ (f @ X1))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.13 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 3.55/1.13 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 3.55/1.13 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.13 inference('cnf', [status(esa)], [clause_431])).
% 3.55/1.13 thf(zip_derived_cl309, plain,
% 3.55/1.13 (![X0 : $i]:
% 3.55/1.13 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.13 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.13 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.13 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.13 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 3.55/1.13 inference('eq_fact', [status(thm)], [zip_derived_cl39])).
% 3.55/1.13 thf(zip_derived_cl310, plain,
% 3.55/1.13 (![X0 : $i]:
% 3.55/1.13 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.13 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.13 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.13 inference('simplify', [status(thm)], [zip_derived_cl309])).
% 3.55/1.13 thf(zip_derived_cl117, plain,
% 3.55/1.13 (![X0 : $i]:
% 3.55/1.13 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 3.55/1.13 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.13 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.13 inference('clc', [status(thm)], [zip_derived_cl68, zip_derived_cl4])).
% 3.55/1.13 thf(zip_derived_cl324, plain,
% 3.55/1.13 (![X0 : $i]:
% 3.55/1.13 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 3.55/1.13 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.13 inference('clc', [status(thm)], [zip_derived_cl310, zip_derived_cl117])).
% 3.55/1.13 thf(zip_derived_cl136, plain,
% 3.55/1.13 (![X0 : $i]:
% 3.55/1.13 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 3.55/1.13 inference('clc', [status(thm)], [zip_derived_cl122, zip_derived_cl4])).
% 3.55/1.13 thf(zip_derived_cl325, plain,
% 3.55/1.13 (![X0 : $i]:
% 3.55/1.13 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.13 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.13 inference('clc', [status(thm)], [zip_derived_cl324, zip_derived_cl136])).
% 3.55/1.13 thf(zip_derived_cl378, plain,
% 3.55/1.13 (![X0 : $i]:
% 3.55/1.13 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.13 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 3.55/1.13 inference('clc', [status(thm)], [zip_derived_cl377, zip_derived_cl325])).
% 3.55/1.13 thf(zip_derived_cl136, plain,
% 3.55/1.13 (![X0 : $i]:
% 3.55/1.13 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ X0))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 3.55/1.13 inference('clc', [status(thm)], [zip_derived_cl122, zip_derived_cl4])).
% 3.55/1.13 thf(zip_derived_cl379, plain,
% 3.55/1.13 (![X0 : $i]:
% 3.55/1.13 (~ (E @ 0 @ (f @ X0))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 3.55/1.13 inference('clc', [status(thm)], [zip_derived_cl378, zip_derived_cl136])).
% 3.55/1.13 thf(zip_derived_cl702, plain,
% 3.55/1.13 (![X0 : $i]:
% 3.55/1.13 ( (LE @ (f @ X0) @ 0)
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.13 | ~ (E @ 0 @ (f @ X0)))),
% 3.55/1.13 inference('sup-', [status(thm)], [zip_derived_cl686, zip_derived_cl379])).
% 3.55/1.13 thf(clause_41, axiom,
% 3.55/1.13 (( ~( LE @ ( f @ ( suc @ ( suc @ B_23 ) ) ) @ ( s @ 0 ) ) ) |
% 3.55/1.13 ( E @ 0 @ ( f @ ( suc @ ( suc @ B_23 ) ) ) ) | ( LE @ ( f @ B_23 ) @ 0 ))).
% 3.55/1.13 thf(zip_derived_cl54, plain,
% 3.55/1.13 (![X0 : $i]:
% 3.55/1.13 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 3.55/1.13 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 3.55/1.13 | (LE @ (f @ X0) @ 0))),
% 3.55/1.13 inference('cnf', [status(esa)], [clause_41])).
% 3.55/1.13 thf(zip_derived_cl685, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 3.55/1.13 inference('clc', [status(thm)], [zip_derived_cl684, zip_derived_cl651])).
% 3.55/1.13 thf(zip_derived_cl687, plain,
% 3.55/1.13 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 3.55/1.13 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl685])).
% 3.55/1.13 thf(zip_derived_cl707, plain,
% 3.55/1.13 (![X0 : $i]:
% 3.55/1.13 (~ (E @ 0 @ (f @ X0))
% 3.55/1.13 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.13 | (LE @ (f @ X0) @ 0))),
% 3.55/1.13 inference('clc', [status(thm)], [zip_derived_cl702, zip_derived_cl687])).
% 3.55/1.13 thf(clause_503, axiom,
% 3.55/1.13 (( ~( LE @ ( f @ B_23 ) @ ( s @ 0 ) ) ) | ( E @ 0 @ ( f @ B_23 ) ) |
% 3.55/1.13 ( LE @ ( f @ B_23 ) @ 0 ))).
% 3.55/1.13 thf(zip_derived_cl55, plain,
% 3.55/1.13 (![X0 : $i]:
% 3.55/1.13 (~ (LE @ (f @ X0) @ (s @ 0))
% 3.55/1.13 | (E @ 0 @ (f @ X0))
% 3.55/1.13 | (LE @ (f @ X0) @ 0))),
% 3.55/1.13 inference('cnf', [status(esa)], [clause_503])).
% 3.55/1.13 thf(zip_derived_cl685, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 3.55/1.13 inference('clc', [status(thm)], [zip_derived_cl684, zip_derived_cl651])).
% 3.55/1.13 thf(zip_derived_cl688, plain,
% 3.55/1.13 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 3.55/1.13 inference('demod', [status(thm)], [zip_derived_cl55, zip_derived_cl685])).
% 3.55/1.13 thf(zip_derived_cl708, plain,
% 3.55/1.13 (![X0 : $i]: ( (LE @ (f @ X0) @ 0) | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 3.55/1.13 inference('clc', [status(thm)], [zip_derived_cl707, zip_derived_cl688])).
% 3.55/1.13 thf(clause_486, axiom,
% 3.55/1.13 (( ~( LE @ ( f @ ( suc @ B_23 ) ) @ ( s @ 0 ) ) ) |
% 3.55/1.13 ( E @ 0 @ ( f @ ( suc @ B_23 ) ) ) | ( LE @ ( f @ B_23 ) @ 0 ))).
% 3.55/1.13 thf(zip_derived_cl81, plain,
% 3.55/1.13 (![X0 : $i]:
% 3.55/1.13 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 3.55/1.13 | (E @ 0 @ (f @ (suc @ X0)))
% 3.55/1.13 | (LE @ (f @ X0) @ 0))),
% 3.55/1.13 inference('cnf', [status(esa)], [clause_486])).
% 3.55/1.13 thf(zip_derived_cl685, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 3.55/1.13 inference('clc', [status(thm)], [zip_derived_cl684, zip_derived_cl651])).
% 3.55/1.13 thf(zip_derived_cl689, plain,
% 3.55/1.13 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 3.55/1.13 inference('demod', [status(thm)], [zip_derived_cl81, zip_derived_cl685])).
% 3.55/1.13 thf(zip_derived_cl709, plain, (![X0 : $i]: (LE @ (f @ X0) @ 0)),
% 3.55/1.13 inference('clc', [status(thm)], [zip_derived_cl708, zip_derived_cl689])).
% 3.55/1.13 thf(zip_derived_cl710, plain, ($false),
% 3.55/1.13 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl709])).
% 3.55/1.13
% 3.55/1.13 % SZS output end Refutation
% 3.55/1.13
% 3.55/1.13
% 3.55/1.13 % Terminating...
% 4.06/1.17 % Runner terminated.
% 4.06/1.18 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------