%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO669-1 : TPTP v9.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.AYQrceJHDr true
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 05:08:06 PM UTC 2025
% Result : Unsatisfiable 4.40s 1.18s
% Output : Refutation 4.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SYO669-1 : TPTP v9.2.0. Released v7.3.0.
% 0.02/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.AYQrceJHDr true
% 0.10/0.31 % Computer : n001.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Oct 1 18:12:38 EDT 2025
% 0.16/0.31 % CPUTime :
% 0.16/0.31 % Running portfolio for 300 s
% 0.16/0.31 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.31 % Number of cores: 8
% 0.16/0.32 % Python version: Python 3.6.8
% 0.16/0.32 % Running in FO mode
% 0.48/0.58 % Total configuration time : 435
% 0.48/0.58 % Estimated wc time : 1092
% 0.48/0.58 % Estimated cpu time (7 cpus) : 156.0
% 0.48/0.69 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.48/0.69 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.48/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.48/0.69 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.48/0.69 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.48/0.70 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.48/0.70 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.49/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 4.40/1.18 % Solved by fo/fo5.sh.
% 4.40/1.18 % done 274 iterations in 0.441s
% 4.40/1.18 % SZS status Unsatisfiable for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 4.40/1.18 % SZS output start Refutation
% 4.40/1.18 thf(suc_type, type, suc: $i > $i).
% 4.40/1.18 thf(f_type, type, f: $i > $i).
% 4.40/1.18 thf(z_type, type, z: $i).
% 4.40/1.18 thf(0_type, type, 0: $i).
% 4.40/1.18 thf(E_type, type, E: $i > $i > $o).
% 4.40/1.18 thf(s_type, type, s: $i > $i).
% 4.40/1.18 thf(LE_type, type, LE: $i > $i > $o).
% 4.40/1.18 thf(iLEQ_type, type, iLEQ: $i > $i > $o).
% 4.40/1.18 thf(clause_151, axiom, (~( LE @ ( f @ z ) @ 0 ))).
% 4.40/1.18 thf(zip_derived_cl44, plain, (~ (LE @ (f @ z) @ 0)),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_151])).
% 4.40/1.18 thf(clause_207, axiom,
% 4.40/1.18 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ B_10 ) ) ) ) @ ( s @ 0 ) ) ) |
% 4.40/1.18 ( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_10 ) ) ) ) ) |
% 4.40/1.18 ( LE @ ( f @ B_10 ) @ 0 ))).
% 4.40/1.18 thf(zip_derived_cl6, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ 0))
% 4.40/1.18 | (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | (LE @ (f @ X0) @ 0))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_207])).
% 4.40/1.18 thf(clause_263, axiom,
% 4.40/1.18 (( ~( LE @ ( f @ ( suc @ ( suc @ ( suc @ B_7 ) ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 4.40/1.18 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_7 ) ) ) ) ) |
% 4.40/1.18 ( LE @ ( f @ B_7 ) @ ( s @ 0 ) ))).
% 4.40/1.18 thf(zip_derived_cl47, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ 0)))
% 4.40/1.18 | (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_263])).
% 4.40/1.18 thf(clause_88, axiom,
% 4.40/1.18 (( ~( LE @
% 4.40/1.18 ( f @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 4.40/1.18 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_3 ) ) ) ) ) |
% 4.40/1.18 ( LE @ ( f @ B_3 ) @ ( s @ ( s @ 0 ) ) ))).
% 4.40/1.18 thf(zip_derived_cl2, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (LE @ (f @ (suc @ (suc @ (suc @ X0)))) @ (s @ (s @ (s @ 0))))
% 4.40/1.18 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_88])).
% 4.40/1.18 thf(clause_299, axiom, (LE @ ( f @ A ) @ ( s @ ( s @ ( s @ 0 ) ) ))).
% 4.40/1.18 thf(zip_derived_cl13, plain,
% 4.40/1.18 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_299])).
% 4.40/1.18 thf(zip_derived_cl65, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 4.40/1.18 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 4.40/1.18 thf(clause_122, axiom,
% 4.40/1.18 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 4.40/1.18 ( ~( E @ ( f @ B_4 ) @ ( f @ ( suc @ B_4 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( f @ B_4 ) @ ( f @ ( suc @ ( suc @ B_4 ) ) ) ) ) |
% 4.40/1.18 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_4 ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_4 ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_4 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B_4 ) ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_4 ) ) ))).
% 4.40/1.18 thf(zip_derived_cl31, plain,
% 4.40/1.18 (![X0 : $i, X1 : $i]:
% 4.40/1.18 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 4.40/1.18 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X1)))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_122])).
% 4.40/1.18 thf(zip_derived_cl216, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 4.40/1.18 inference('eq_fact', [status(thm)], [zip_derived_cl31])).
% 4.40/1.18 thf(zip_derived_cl217, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 4.40/1.18 inference('simplify', [status(thm)], [zip_derived_cl216])).
% 4.40/1.18 thf(clause_267, axiom,
% 4.40/1.18 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A_1 ) ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 4.40/1.18 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 4.40/1.18 thf(zip_derived_cl11, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_267])).
% 4.40/1.18 thf(clause_246, axiom,
% 4.40/1.18 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 4.40/1.18 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) |
% 4.40/1.18 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 4.40/1.18 thf(zip_derived_cl3, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_246])).
% 4.40/1.18 thf(clause_25, axiom,
% 4.40/1.18 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 4.40/1.18 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 4.40/1.18 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 4.40/1.18 thf(zip_derived_cl14, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_25])).
% 4.40/1.18 thf(zip_derived_cl77, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.18 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.18 inference('clc', [status(thm)], [zip_derived_cl3, zip_derived_cl14])).
% 4.40/1.18 thf(zip_derived_cl108, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 4.40/1.18 inference('clc', [status(thm)], [zip_derived_cl11, zip_derived_cl77])).
% 4.40/1.18 thf(zip_derived_cl14, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_25])).
% 4.40/1.18 thf(zip_derived_cl109, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.18 inference('clc', [status(thm)], [zip_derived_cl108, zip_derived_cl14])).
% 4.40/1.18 thf(zip_derived_cl271, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.18 inference('clc', [status(thm)], [zip_derived_cl217, zip_derived_cl109])).
% 4.40/1.18 thf(clause_76, axiom,
% 4.40/1.18 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 4.40/1.18 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_4 ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_4 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_4 ) ) ) |
% 4.40/1.18 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 4.40/1.18 ( E @ ( f @ B_4 ) @ ( f @ ( suc @ B_4 ) ) ))).
% 4.40/1.18 thf(zip_derived_cl33, plain,
% 4.40/1.18 (![X0 : $i, X1 : $i]:
% 4.40/1.18 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 4.40/1.18 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_76])).
% 4.40/1.18 thf(zip_derived_cl106, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 4.40/1.18 inference('eq_fact', [status(thm)], [zip_derived_cl33])).
% 4.40/1.18 thf(zip_derived_cl107, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 4.40/1.18 inference('simplify', [status(thm)], [zip_derived_cl106])).
% 4.40/1.18 thf(zip_derived_cl14, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_25])).
% 4.40/1.18 thf(zip_derived_cl117, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 4.40/1.18 inference('clc', [status(thm)], [zip_derived_cl107, zip_derived_cl14])).
% 4.40/1.18 thf(zip_derived_cl272, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 4.40/1.18 inference('clc', [status(thm)], [zip_derived_cl271, zip_derived_cl117])).
% 4.40/1.18 thf(clause_74, axiom,
% 4.40/1.18 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_1 ) ) ) |
% 4.40/1.18 ( ~( E @ ( f @ B_4 ) @ ( f @ ( suc @ B_4 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 4.40/1.18 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_4 ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_4 ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_4 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_4 ) ) ) |
% 4.40/1.18 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) |
% 4.40/1.18 ( E @ ( f @ B_4 ) @ ( f @ ( suc @ ( suc @ B_4 ) ) ) ))).
% 4.40/1.18 thf(zip_derived_cl43, plain,
% 4.40/1.18 (![X0 : $i, X1 : $i]:
% 4.40/1.18 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 4.40/1.18 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1)))))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_74])).
% 4.40/1.18 thf(zip_derived_cl190, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 4.40/1.18 inference('eq_fact', [status(thm)], [zip_derived_cl43])).
% 4.40/1.18 thf(zip_derived_cl191, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.18 inference('simplify', [status(thm)], [zip_derived_cl190])).
% 4.40/1.18 thf(zip_derived_cl77, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.18 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.18 inference('clc', [status(thm)], [zip_derived_cl3, zip_derived_cl14])).
% 4.40/1.18 thf(zip_derived_cl225, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 4.40/1.18 inference('clc', [status(thm)], [zip_derived_cl191, zip_derived_cl77])).
% 4.40/1.18 thf(zip_derived_cl117, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 4.40/1.18 inference('clc', [status(thm)], [zip_derived_cl107, zip_derived_cl14])).
% 4.40/1.18 thf(zip_derived_cl226, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.18 inference('clc', [status(thm)], [zip_derived_cl225, zip_derived_cl117])).
% 4.40/1.18 thf(zip_derived_cl273, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 4.40/1.18 inference('clc', [status(thm)], [zip_derived_cl272, zip_derived_cl226])).
% 4.40/1.18 thf(zip_derived_cl274, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 4.40/1.18 inference('sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl273])).
% 4.40/1.18 thf(clause_153, axiom,
% 4.40/1.18 (( ~( LE @ ( f @ ( suc @ B_3 ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 4.40/1.18 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_3 ) ) ) |
% 4.40/1.18 ( LE @ ( f @ B_3 ) @ ( s @ ( s @ 0 ) ) ))).
% 4.40/1.18 thf(zip_derived_cl30, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0))))
% 4.40/1.18 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_153])).
% 4.40/1.18 thf(zip_derived_cl13, plain,
% 4.40/1.18 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_299])).
% 4.40/1.18 thf(zip_derived_cl59, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 4.40/1.18 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 4.40/1.18 inference('demod', [status(thm)], [zip_derived_cl30, zip_derived_cl13])).
% 4.40/1.18 thf(zip_derived_cl278, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 4.40/1.18 inference('clc', [status(thm)], [zip_derived_cl274, zip_derived_cl59])).
% 4.40/1.18 thf(clause_222, axiom,
% 4.40/1.18 (( ~( LE @ ( f @ B_3 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 4.40/1.18 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_3 ) ) |
% 4.40/1.18 ( LE @ ( f @ B_3 ) @ ( s @ ( s @ 0 ) ) ))).
% 4.40/1.18 thf(zip_derived_cl39, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 4.40/1.18 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 4.40/1.18 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_222])).
% 4.40/1.18 thf(zip_derived_cl13, plain,
% 4.40/1.18 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_299])).
% 4.40/1.18 thf(zip_derived_cl50, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 4.40/1.18 inference('demod', [status(thm)], [zip_derived_cl39, zip_derived_cl13])).
% 4.40/1.18 thf(zip_derived_cl279, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 4.40/1.18 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.18 inference('clc', [status(thm)], [zip_derived_cl278, zip_derived_cl50])).
% 4.40/1.18 thf(clause_301, axiom,
% 4.40/1.18 (( ~( LE @ ( f @ ( suc @ ( suc @ B_3 ) ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 4.40/1.18 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_3 ) ) ) ) |
% 4.40/1.18 ( LE @ ( f @ B_3 ) @ ( s @ ( s @ 0 ) ) ))).
% 4.40/1.18 thf(zip_derived_cl5, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0))))
% 4.40/1.18 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_301])).
% 4.40/1.18 thf(zip_derived_cl13, plain,
% 4.40/1.18 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_299])).
% 4.40/1.18 thf(zip_derived_cl62, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 4.40/1.18 inference('demod', [status(thm)], [zip_derived_cl5, zip_derived_cl13])).
% 4.40/1.18 thf(zip_derived_cl280, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 4.40/1.18 inference('clc', [status(thm)], [zip_derived_cl279, zip_derived_cl62])).
% 4.40/1.18 thf(zip_derived_cl284, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.18 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl280])).
% 4.40/1.18 thf(clause_257, axiom,
% 4.40/1.18 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 4.40/1.18 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 4.40/1.18 thf(zip_derived_cl1, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.18 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_257])).
% 4.40/1.18 thf(zip_derived_cl306, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (LE @ (f @ X0) @ (s @ 0))
% 4.40/1.18 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.18 inference('sup-', [status(thm)], [zip_derived_cl284, zip_derived_cl1])).
% 4.40/1.18 thf(zip_derived_cl284, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.18 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl280])).
% 4.40/1.18 thf(clause_292, axiom,
% 4.40/1.18 (( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ 0 ) @ ( f @ B_8 ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_8 ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( f @ B_8 ) @ ( f @ ( suc @ ( suc @ B_8 ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_8 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( f @ B_8 ) @ ( f @ ( suc @ B_8 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ B_8 ) ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ ( suc @ A_2 ) ) ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 4.40/1.18 ( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 4.40/1.18 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_8 ) ) ))).
% 4.40/1.18 thf(zip_derived_cl20, plain,
% 4.40/1.18 (![X0 : $i, X1 : $i]:
% 4.40/1.18 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ X1))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 4.40/1.18 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X1)))))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.18 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1)))),
% 4.40/1.18 inference('cnf', [status(esa)], [clause_292])).
% 4.40/1.18 thf(zip_derived_cl192, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.18 inference('eq_fact', [status(thm)], [zip_derived_cl20])).
% 4.40/1.18 thf(zip_derived_cl193, plain,
% 4.40/1.18 (![X0 : $i]:
% 4.40/1.18 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.18 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.18 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.19 inference('simplify', [status(thm)], [zip_derived_cl192])).
% 4.40/1.19 thf(clause_144, axiom,
% 4.40/1.19 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( s @ 0 ) @ ( f @ B_8 ) ) ) |
% 4.40/1.19 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_8 ) ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_8 ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( f @ B_8 ) @ ( f @ ( suc @ B_8 ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 4.40/1.19 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_8 ) ) ) |
% 4.40/1.19 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) |
% 4.40/1.19 ( E @ ( f @ B_8 ) @ ( f @ ( suc @ ( suc @ B_8 ) ) ) ))).
% 4.40/1.19 thf(zip_derived_cl19, plain,
% 4.40/1.19 (![X0 : $i, X1 : $i]:
% 4.40/1.19 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X1))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1)))))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_144])).
% 4.40/1.19 thf(zip_derived_cl161, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 4.40/1.19 thf(zip_derived_cl162, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.19 inference('simplify', [status(thm)], [zip_derived_cl161])).
% 4.40/1.19 thf(clause_7, axiom,
% 4.40/1.19 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( s @ 0 ) @ ( f @ B_8 ) ) ) |
% 4.40/1.19 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_8 ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 4.40/1.19 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_8 ) ) ) |
% 4.40/1.19 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 4.40/1.19 ( E @ ( f @ B_8 ) @ ( f @ ( suc @ B_8 ) ) ))).
% 4.40/1.19 thf(zip_derived_cl22, plain,
% 4.40/1.19 (![X0 : $i, X1 : $i]:
% 4.40/1.19 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X1))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | (E @ (f @ X1) @ (f @ (suc @ X1))))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_7])).
% 4.40/1.19 thf(zip_derived_cl100, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0)))),
% 4.40/1.19 inference('eq_fact', [status(thm)], [zip_derived_cl22])).
% 4.40/1.19 thf(zip_derived_cl101, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('simplify', [status(thm)], [zip_derived_cl100])).
% 4.40/1.19 thf(clause_44, axiom,
% 4.40/1.19 (( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 4.40/1.19 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 4.40/1.19 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 4.40/1.19 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 4.40/1.19 thf(zip_derived_cl27, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_44])).
% 4.40/1.19 thf(zip_derived_cl116, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl101, zip_derived_cl27])).
% 4.40/1.19 thf(zip_derived_cl164, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl162, zip_derived_cl116])).
% 4.40/1.19 thf(clause_72, axiom,
% 4.40/1.19 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( s @ 0 ) @ ( f @ A_2 ) ) ) |
% 4.40/1.19 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) |
% 4.40/1.19 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 4.40/1.19 thf(zip_derived_cl38, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_72])).
% 4.40/1.19 thf(zip_derived_cl27, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_44])).
% 4.40/1.19 thf(zip_derived_cl97, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl38, zip_derived_cl27])).
% 4.40/1.19 thf(zip_derived_cl165, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl164, zip_derived_cl97])).
% 4.40/1.19 thf(zip_derived_cl221, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl193, zip_derived_cl165])).
% 4.40/1.19 thf(zip_derived_cl116, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl101, zip_derived_cl27])).
% 4.40/1.19 thf(zip_derived_cl222, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl221, zip_derived_cl116])).
% 4.40/1.19 thf(zip_derived_cl307, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (LE @ (f @ X0) @ (s @ 0))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('sup-', [status(thm)], [zip_derived_cl284, zip_derived_cl222])).
% 4.40/1.19 thf(clause_272, axiom,
% 4.40/1.19 (( ~( LE @ ( f @ B_7 ) @ ( s @ ( s @ 0 ) ) ) ) |
% 4.40/1.19 ( E @ ( s @ 0 ) @ ( f @ B_7 ) ) | ( LE @ ( f @ B_7 ) @ ( s @ 0 ) ))).
% 4.40/1.19 thf(zip_derived_cl32, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 4.40/1.19 | (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_272])).
% 4.40/1.19 thf(zip_derived_cl280, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl279, zip_derived_cl62])).
% 4.40/1.19 thf(zip_derived_cl282, plain,
% 4.40/1.19 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl280])).
% 4.40/1.19 thf(zip_derived_cl322, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl307, zip_derived_cl282])).
% 4.40/1.19 thf(clause_12, axiom,
% 4.40/1.19 (( ~( LE @ ( f @ ( suc @ B_7 ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 4.40/1.19 ( E @ ( s @ 0 ) @ ( f @ ( suc @ B_7 ) ) ) |
% 4.40/1.19 ( LE @ ( f @ B_7 ) @ ( s @ 0 ) ))).
% 4.40/1.19 thf(zip_derived_cl9, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 4.40/1.19 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_12])).
% 4.40/1.19 thf(zip_derived_cl280, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl279, zip_derived_cl62])).
% 4.40/1.19 thf(zip_derived_cl281, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl280])).
% 4.40/1.19 thf(zip_derived_cl323, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (LE @ (f @ X0) @ (s @ 0))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl322, zip_derived_cl281])).
% 4.40/1.19 thf(clause_196, axiom,
% 4.40/1.19 (( ~( LE @ ( f @ ( suc @ ( suc @ B_7 ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 4.40/1.19 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_7 ) ) ) ) |
% 4.40/1.19 ( LE @ ( f @ B_7 ) @ ( s @ 0 ) ))).
% 4.40/1.19 thf(zip_derived_cl35, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 4.40/1.19 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_196])).
% 4.40/1.19 thf(zip_derived_cl280, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl279, zip_derived_cl62])).
% 4.40/1.19 thf(zip_derived_cl283, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('demod', [status(thm)], [zip_derived_cl35, zip_derived_cl280])).
% 4.40/1.19 thf(zip_derived_cl324, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (iLEQ @ (suc @ X0) @ (suc @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl323, zip_derived_cl283])).
% 4.40/1.19 thf(zip_derived_cl814, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl306, zip_derived_cl324])).
% 4.40/1.19 thf(zip_derived_cl165, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl164, zip_derived_cl97])).
% 4.40/1.19 thf(zip_derived_cl815, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (LE @ (f @ X0) @ (s @ 0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl814, zip_derived_cl165])).
% 4.40/1.19 thf(zip_derived_cl282, plain,
% 4.40/1.19 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl280])).
% 4.40/1.19 thf(zip_derived_cl816, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl815, zip_derived_cl282])).
% 4.40/1.19 thf(zip_derived_cl281, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl280])).
% 4.40/1.19 thf(zip_derived_cl817, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (LE @ (f @ X0) @ (s @ 0))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl816, zip_derived_cl281])).
% 4.40/1.19 thf(zip_derived_cl281, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl280])).
% 4.40/1.19 thf(zip_derived_cl116, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl101, zip_derived_cl27])).
% 4.40/1.19 thf(zip_derived_cl290, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (LE @ (f @ X0) @ (s @ 0))
% 4.40/1.19 | ~ (E @ (s @ 0) @ (f @ X0))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('sup-', [status(thm)], [zip_derived_cl281, zip_derived_cl116])).
% 4.40/1.19 thf(zip_derived_cl282, plain,
% 4.40/1.19 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl280])).
% 4.40/1.19 thf(zip_derived_cl295, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (f @ X0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl290, zip_derived_cl282])).
% 4.40/1.19 thf(zip_derived_cl818, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl817, zip_derived_cl295])).
% 4.40/1.19 thf(zip_derived_cl283, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | (LE @ (f @ X0) @ (s @ 0)))),
% 4.40/1.19 inference('demod', [status(thm)], [zip_derived_cl35, zip_derived_cl280])).
% 4.40/1.19 thf(zip_derived_cl819, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl818, zip_derived_cl283])).
% 4.40/1.19 thf(zip_derived_cl820, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))) | (LE @ (f @ X0) @ 0))),
% 4.40/1.19 inference('demod', [status(thm)], [zip_derived_cl6, zip_derived_cl819])).
% 4.40/1.19 thf(clause_100, axiom,
% 4.40/1.19 (( ~( E @ 0 @ ( f @ ( suc @ B_11 ) ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ B_11 ) ) ) ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_11 ) ) ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ B_11 ) ) ) |
% 4.40/1.19 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( f @ B_11 ) @ ( f @ ( suc @ ( suc @ B_11 ) ) ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ A_3 ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 4.40/1.19 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_11 ) ) ) |
% 4.40/1.19 ( ~( E @ ( f @ B_11 ) @ ( f @ ( suc @ B_11 ) ) ) ))).
% 4.40/1.19 thf(zip_derived_cl24, plain,
% 4.40/1.19 (![X0 : $i, X1 : $i]:
% 4.40/1.19 (~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X1)))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X1))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 4.40/1.19 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_100])).
% 4.40/1.19 thf(zip_derived_cl184, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('eq_fact', [status(thm)], [zip_derived_cl24])).
% 4.40/1.19 thf(zip_derived_cl185, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('simplify', [status(thm)], [zip_derived_cl184])).
% 4.40/1.19 thf(clause_106, axiom,
% 4.40/1.19 (( ~( E @ 0 @ ( f @ ( suc @ B_11 ) ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_11 ) ) ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ B_11 ) ) ) | ( ~( E @ 0 @ ( f @ A_3 ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 4.40/1.19 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_11 ) ) ) |
% 4.40/1.19 ( ~( E @ ( f @ B_11 ) @ ( f @ ( suc @ B_11 ) ) ) ) |
% 4.40/1.19 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) |
% 4.40/1.19 ( E @ ( f @ B_11 ) @ ( f @ ( suc @ ( suc @ B_11 ) ) ) ))).
% 4.40/1.19 thf(zip_derived_cl10, plain,
% 4.40/1.19 (![X0 : $i, X1 : $i]:
% 4.40/1.19 (~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X1))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 4.40/1.19 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | (E @ (f @ X1) @ (f @ (suc @ (suc @ X1))))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_106])).
% 4.40/1.19 thf(zip_derived_cl133, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('eq_fact', [status(thm)], [zip_derived_cl10])).
% 4.40/1.19 thf(zip_derived_cl134, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.19 inference('simplify', [status(thm)], [zip_derived_cl133])).
% 4.40/1.19 thf(clause_143, axiom,
% 4.40/1.19 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ A_3 ) ) ) |
% 4.40/1.19 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) |
% 4.40/1.19 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 4.40/1.19 thf(zip_derived_cl36, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_143])).
% 4.40/1.19 thf(clause_59, axiom,
% 4.40/1.19 (( ~( E @ 0 @ ( f @ A_3 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 4.40/1.19 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 4.40/1.19 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 4.40/1.19 thf(zip_derived_cl0, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_59])).
% 4.40/1.19 thf(zip_derived_cl68, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl36, zip_derived_cl0])).
% 4.40/1.19 thf(zip_derived_cl135, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl134, zip_derived_cl68])).
% 4.40/1.19 thf(clause_248, axiom,
% 4.40/1.19 (( ~( E @ 0 @ ( f @ ( suc @ B_11 ) ) ) ) | ( ~( E @ 0 @ ( f @ B_11 ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ A_3 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 4.40/1.19 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_11 ) ) ) |
% 4.40/1.19 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 4.40/1.19 ( E @ ( f @ B_11 ) @ ( f @ ( suc @ B_11 ) ) ))).
% 4.40/1.19 thf(zip_derived_cl29, plain,
% 4.40/1.19 (![X0 : $i, X1 : $i]:
% 4.40/1.19 (~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X1))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 4.40/1.19 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_248])).
% 4.40/1.19 thf(zip_derived_cl69, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0)))),
% 4.40/1.19 inference('eq_fact', [status(thm)], [zip_derived_cl29])).
% 4.40/1.19 thf(zip_derived_cl70, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('simplify', [status(thm)], [zip_derived_cl69])).
% 4.40/1.19 thf(zip_derived_cl0, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_59])).
% 4.40/1.19 thf(zip_derived_cl82, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 4.40/1.19 thf(zip_derived_cl136, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl135, zip_derived_cl82])).
% 4.40/1.19 thf(zip_derived_cl218, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl185, zip_derived_cl136])).
% 4.40/1.19 thf(zip_derived_cl82, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 4.40/1.19 thf(zip_derived_cl219, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl218, zip_derived_cl82])).
% 4.40/1.19 thf(clause_295, axiom,
% 4.40/1.19 (( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ ( suc @ A_3 ) ) ) ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ A_3 ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 4.40/1.19 ( ~( E @ 0 @ ( f @ ( suc @ A_3 ) ) ) ) |
% 4.40/1.19 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 4.40/1.19 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 4.40/1.19 thf(zip_derived_cl17, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_295])).
% 4.40/1.19 thf(zip_derived_cl68, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | (E @ (f @ X0) @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl36, zip_derived_cl0])).
% 4.40/1.19 thf(zip_derived_cl98, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 4.40/1.19 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl17, zip_derived_cl68])).
% 4.40/1.19 thf(zip_derived_cl82, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl70, zip_derived_cl0])).
% 4.40/1.19 thf(zip_derived_cl99, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0)))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl98, zip_derived_cl82])).
% 4.40/1.19 thf(zip_derived_cl220, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ (suc @ X0))))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl219, zip_derived_cl99])).
% 4.40/1.19 thf(zip_derived_cl844, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (LE @ (f @ X0) @ 0)
% 4.40/1.19 | ~ (E @ 0 @ (f @ X0))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 4.40/1.19 inference('sup-', [status(thm)], [zip_derived_cl820, zip_derived_cl220])).
% 4.40/1.19 thf(clause_18, axiom,
% 4.40/1.19 (( ~( LE @ ( f @ B_10 ) @ ( s @ 0 ) ) ) | ( E @ 0 @ ( f @ B_10 ) ) |
% 4.40/1.19 ( LE @ ( f @ B_10 ) @ 0 ))).
% 4.40/1.19 thf(zip_derived_cl8, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (LE @ (f @ X0) @ (s @ 0))
% 4.40/1.19 | (E @ 0 @ (f @ X0))
% 4.40/1.19 | (LE @ (f @ X0) @ 0))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_18])).
% 4.40/1.19 thf(zip_derived_cl819, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl818, zip_derived_cl283])).
% 4.40/1.19 thf(zip_derived_cl821, plain,
% 4.40/1.19 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 4.40/1.19 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl819])).
% 4.40/1.19 thf(zip_derived_cl846, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | (LE @ (f @ X0) @ 0))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl844, zip_derived_cl821])).
% 4.40/1.19 thf(clause_260, axiom,
% 4.40/1.19 (( ~( LE @ ( f @ ( suc @ B_10 ) ) @ ( s @ 0 ) ) ) |
% 4.40/1.19 ( E @ 0 @ ( f @ ( suc @ B_10 ) ) ) | ( LE @ ( f @ B_10 ) @ 0 ))).
% 4.40/1.19 thf(zip_derived_cl16, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 4.40/1.19 | (E @ 0 @ (f @ (suc @ X0)))
% 4.40/1.19 | (LE @ (f @ X0) @ 0))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_260])).
% 4.40/1.19 thf(zip_derived_cl819, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl818, zip_derived_cl283])).
% 4.40/1.19 thf(zip_derived_cl822, plain,
% 4.40/1.19 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 4.40/1.19 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl819])).
% 4.40/1.19 thf(zip_derived_cl847, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 ( (LE @ (f @ X0) @ 0) | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl846, zip_derived_cl822])).
% 4.40/1.19 thf(clause_4, axiom,
% 4.40/1.19 (( ~( LE @ ( f @ ( suc @ ( suc @ B_10 ) ) ) @ ( s @ 0 ) ) ) |
% 4.40/1.19 ( E @ 0 @ ( f @ ( suc @ ( suc @ B_10 ) ) ) ) | ( LE @ ( f @ B_10 ) @ 0 ))).
% 4.40/1.19 thf(zip_derived_cl23, plain,
% 4.40/1.19 (![X0 : $i]:
% 4.40/1.19 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 4.40/1.19 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 4.40/1.19 | (LE @ (f @ X0) @ 0))),
% 4.40/1.19 inference('cnf', [status(esa)], [clause_4])).
% 4.40/1.19 thf(zip_derived_cl819, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl818, zip_derived_cl283])).
% 4.40/1.19 thf(zip_derived_cl823, plain,
% 4.40/1.19 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 4.40/1.19 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl819])).
% 4.40/1.19 thf(zip_derived_cl848, plain, (![X0 : $i]: (LE @ (f @ X0) @ 0)),
% 4.40/1.19 inference('clc', [status(thm)], [zip_derived_cl847, zip_derived_cl823])).
% 4.40/1.19 thf(zip_derived_cl849, plain, ($false),
% 4.40/1.19 inference('demod', [status(thm)], [zip_derived_cl44, zip_derived_cl848])).
% 4.40/1.19
% 4.40/1.19 % SZS output end Refutation
% 4.40/1.19
% 4.40/1.19
% 4.40/1.19 % Terminating...
% 4.89/1.30 % Runner terminated.
% 4.89/1.32 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------