%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO677-1 : TPTP v9.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Pa3tolx9c6 true
% Computer : n007.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 05:08:07 PM UTC 2025
% Result : Unsatisfiable 0.50s 0.89s
% Output : Refutation 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO677-1 : TPTP v9.2.0. Released v7.3.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Pa3tolx9c6 true
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 1 18:07:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in FO mode
% 0.41/0.58 % Total configuration time : 435
% 0.41/0.58 % Estimated wc time : 1092
% 0.41/0.58 % Estimated cpu time (7 cpus) : 156.0
% 0.47/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.47/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.47/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.47/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.47/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.47/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.47/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.50/0.89 % Solved by fo/fo1_av.sh.
% 0.50/0.89 % done 106 iterations in 0.169s
% 0.50/0.89 % SZS status Unsatisfiable for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.50/0.89 % SZS output start Refutation
% 0.50/0.89 thf(z_type, type, z: $i).
% 0.50/0.89 thf(f_type, type, f: $i > $i).
% 0.50/0.89 thf(0_type, type, 0: $i).
% 0.50/0.89 thf(suc_type, type, suc: $i > $i).
% 0.50/0.89 thf(s_type, type, s: $i > $i).
% 0.50/0.89 thf(LE_type, type, LE: $i > $i > $o).
% 0.50/0.89 thf(E_type, type, E: $i > $i > $o).
% 0.50/0.89 thf(iLEQ_type, type, iLEQ: $i > $i > $o).
% 0.50/0.89 thf(clause_77, axiom, (~( LE @ ( f @ z ) @ 0 ))).
% 0.50/0.89 thf(zip_derived_cl27, plain, (~ (LE @ (f @ z) @ 0)),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_77])).
% 0.50/0.89 thf(clause_27, axiom,
% 0.50/0.89 (( ~( LE @ ( f @ ( suc @ ( suc @ B_16 ) ) ) @ ( s @ 0 ) ) ) |
% 0.50/0.89 ( E @ 0 @ ( f @ ( suc @ ( suc @ B_16 ) ) ) ) | ( LE @ ( f @ B_16 ) @ 0 ))).
% 0.50/0.89 thf(zip_derived_cl35, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ 0))
% 0.50/0.89 | (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | (LE @ (f @ X0) @ 0))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_27])).
% 0.50/0.89 thf(clause_49, axiom,
% 0.50/0.89 (( ~( LE @ ( f @ ( suc @ ( suc @ B_13 ) ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 0.50/0.89 ( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_13 ) ) ) ) |
% 0.50/0.89 ( LE @ ( f @ B_13 ) @ ( s @ 0 ) ))).
% 0.50/0.89 thf(zip_derived_cl26, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ 0)))
% 0.50/0.89 | (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_49])).
% 0.50/0.89 thf(clause_18, axiom,
% 0.50/0.89 (( ~( LE @ ( f @ ( suc @ ( suc @ B_9 ) ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 0.50/0.89 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_9 ) ) ) ) |
% 0.50/0.89 ( LE @ ( f @ B_9 ) @ ( s @ ( s @ 0 ) ) ))).
% 0.50/0.89 thf(zip_derived_cl14, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ 0))))
% 0.50/0.89 | (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_18])).
% 0.50/0.89 thf(clause_121, axiom,
% 0.50/0.89 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_5 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( f @ B_5 ) @ ( f @ ( suc @ B_5 ) ) ) ) |
% 0.50/0.89 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_5 ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_5 ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_5 ) ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ))).
% 0.50/0.89 thf(zip_derived_cl29, plain,
% 0.50/0.89 (![X0 : $i, X1 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X1))))
% 0.50/0.89 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1))))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_121])).
% 0.50/0.89 thf(zip_derived_cl211, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('eq_fact', [status(thm)], [zip_derived_cl29])).
% 0.50/0.89 thf(zip_derived_cl212, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('simplify', [status(thm)], [zip_derived_cl211])).
% 0.50/0.89 thf(clause_140, axiom,
% 0.50/0.89 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ A_1 ) ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 0.50/0.89 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 0.50/0.89 thf(zip_derived_cl21, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_140])).
% 0.50/0.89 thf(clause_65, axiom,
% 0.50/0.89 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.50/0.89 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 0.50/0.89 ( iLEQ @ ( suc @ A_1 ) @ ( suc @ A_1 ) ))).
% 0.50/0.89 thf(zip_derived_cl31, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_65])).
% 0.50/0.89 thf(zip_derived_cl55, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0)))))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl21, zip_derived_cl31])).
% 0.50/0.89 thf(zip_derived_cl213, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl212, zip_derived_cl55])).
% 0.50/0.89 thf(zip_derived_cl31, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_65])).
% 0.50/0.89 thf(clause_51, axiom,
% 0.50/0.89 (( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_5 ) ) ) ) |
% 0.50/0.89 ( ~( iLEQ @ ( suc @ A_1 ) @ ( suc @ B_5 ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_5 ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ A_1 ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ A_1 ) ) ) ) |
% 0.50/0.89 ( E @ ( f @ A_1 ) @ ( f @ ( suc @ A_1 ) ) ) |
% 0.50/0.89 ( E @ ( f @ B_5 ) @ ( f @ ( suc @ B_5 ) ) ))).
% 0.50/0.89 thf(zip_derived_cl9, plain,
% 0.50/0.89 (![X0 : $i, X1 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X1))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X1)))
% 0.50/0.89 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_51])).
% 0.50/0.89 thf(zip_derived_cl159, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('s_sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl9])).
% 0.50/0.89 thf(zip_derived_cl162, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('simplify', [status(thm)], [zip_derived_cl159])).
% 0.50/0.89 thf(zip_derived_cl214, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl213, zip_derived_cl162])).
% 0.50/0.89 thf(clause_143, axiom,
% 0.50/0.89 (( ~( LE @
% 0.50/0.89 ( f @ ( suc @ ( suc @ B_4 ) ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 0.50/0.89 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ ( suc @ B_4 ) ) ) ) |
% 0.50/0.89 ( LE @ ( f @ B_4 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 0.50/0.89 thf(zip_derived_cl2, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (LE @ (f @ (suc @ (suc @ X0))) @ (s @ (s @ (s @ (s @ 0)))))
% 0.50/0.89 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_143])).
% 0.50/0.89 thf(clause_113, axiom, (LE @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 0.50/0.89 thf(zip_derived_cl17, plain,
% 0.50/0.89 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_113])).
% 0.50/0.89 thf(zip_derived_cl51, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl17])).
% 0.50/0.89 thf(zip_derived_cl215, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.50/0.89 inference('s_sup+', [status(thm)], [zip_derived_cl214, zip_derived_cl51])).
% 0.50/0.89 thf(clause_13, axiom,
% 0.50/0.89 (( ~( LE @ ( f @ ( suc @ B_4 ) ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 0.50/0.89 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ ( suc @ B_4 ) ) ) |
% 0.50/0.89 ( LE @ ( f @ B_4 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 0.50/0.89 thf(zip_derived_cl8, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ (s @ 0)))))
% 0.50/0.89 | (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_13])).
% 0.50/0.89 thf(zip_derived_cl17, plain,
% 0.50/0.89 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_113])).
% 0.50/0.89 thf(zip_derived_cl50, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (s @ (s @ (s @ 0))) @ (f @ (suc @ X0)))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl17])).
% 0.50/0.89 thf(zip_derived_cl221, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.50/0.89 | ~ (E @ (s @ (s @ (s @ 0))) @ (f @ X0)))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl215, zip_derived_cl50])).
% 0.50/0.89 thf(clause_61, axiom,
% 0.50/0.89 (( ~( LE @ ( f @ B_4 ) @ ( s @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) ) |
% 0.50/0.89 ( E @ ( s @ ( s @ ( s @ 0 ) ) ) @ ( f @ B_4 ) ) |
% 0.50/0.89 ( LE @ ( f @ B_4 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ))).
% 0.50/0.89 thf(zip_derived_cl15, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))
% 0.50/0.89 | (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_61])).
% 0.50/0.89 thf(zip_derived_cl17, plain,
% 0.50/0.89 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ (s @ 0)))))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_113])).
% 0.50/0.89 thf(zip_derived_cl40, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (s @ (s @ (s @ 0))) @ (f @ X0))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ (s @ 0)))))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl17])).
% 0.50/0.89 thf(zip_derived_cl222, plain,
% 0.50/0.89 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl221, zip_derived_cl40])).
% 0.50/0.89 thf(zip_derived_cl223, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl222])).
% 0.50/0.89 thf(clause_97, axiom,
% 0.50/0.89 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 0.50/0.89 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 0.50/0.89 thf(zip_derived_cl11, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_97])).
% 0.50/0.89 thf(clause_84, axiom,
% 0.50/0.89 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.50/0.89 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 0.50/0.89 ( iLEQ @ ( suc @ A_2 ) @ ( suc @ A_2 ) ))).
% 0.50/0.89 thf(zip_derived_cl33, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_84])).
% 0.50/0.89 thf(zip_derived_cl45, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl11, zip_derived_cl33])).
% 0.50/0.89 thf(zip_derived_cl239, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.50/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('s_sup-', [status(thm)], [zip_derived_cl223, zip_derived_cl45])).
% 0.50/0.89 thf(clause_73, axiom,
% 0.50/0.89 (( ~( LE @ ( f @ B_9 ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 0.50/0.89 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_9 ) ) |
% 0.50/0.89 ( LE @ ( f @ B_9 ) @ ( s @ ( s @ 0 ) ) ))).
% 0.50/0.89 thf(zip_derived_cl18, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))
% 0.50/0.89 | (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_73])).
% 0.50/0.89 thf(zip_derived_cl222, plain,
% 0.50/0.89 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl221, zip_derived_cl40])).
% 0.50/0.89 thf(zip_derived_cl224, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl222])).
% 0.50/0.89 thf(zip_derived_cl255, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl239, zip_derived_cl224])).
% 0.50/0.89 thf(clause_87, axiom,
% 0.50/0.89 (( ~( LE @ ( f @ ( suc @ B_9 ) ) @ ( s @ ( s @ ( s @ 0 ) ) ) ) ) |
% 0.50/0.89 ( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_9 ) ) ) |
% 0.50/0.89 ( LE @ ( f @ B_9 ) @ ( s @ ( s @ 0 ) ) ))).
% 0.50/0.89 thf(zip_derived_cl30, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ (s @ 0))))
% 0.50/0.89 | (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_87])).
% 0.50/0.89 thf(zip_derived_cl222, plain,
% 0.50/0.89 (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ (s @ 0))))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl221, zip_derived_cl40])).
% 0.50/0.89 thf(zip_derived_cl225, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl30, zip_derived_cl222])).
% 0.50/0.89 thf(zip_derived_cl256, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (LE @ (f @ X0) @ (s @ (s @ 0))) | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl255, zip_derived_cl225])).
% 0.50/0.89 thf(zip_derived_cl223, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl222])).
% 0.50/0.89 thf(clause_24, axiom,
% 0.50/0.89 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_10 ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( f @ B_10 ) @ ( f @ ( suc @ B_10 ) ) ) ) |
% 0.50/0.89 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_10 ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_10 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ A_2 ) ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 0.50/0.89 ( ~( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ ( suc @ B_10 ) ) ) ) ))).
% 0.50/0.89 thf(zip_derived_cl0, plain,
% 0.50/0.89 (![X0 : $i, X1 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X1))))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 0.50/0.89 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_24])).
% 0.50/0.89 thf(zip_derived_cl38, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ X0)))),
% 0.50/0.89 inference('eq_fact', [status(thm)], [zip_derived_cl0])).
% 0.50/0.89 thf(zip_derived_cl39, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ (suc @ X0)))))),
% 0.50/0.89 inference('simplify', [status(thm)], [zip_derived_cl38])).
% 0.50/0.89 thf(zip_derived_cl238, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('s_sup-', [status(thm)], [zip_derived_cl223, zip_derived_cl39])).
% 0.50/0.89 thf(zip_derived_cl225, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl30, zip_derived_cl222])).
% 0.50/0.89 thf(zip_derived_cl253, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl238, zip_derived_cl225])).
% 0.50/0.89 thf(zip_derived_cl224, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl222])).
% 0.50/0.89 thf(zip_derived_cl254, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl253, zip_derived_cl224])).
% 0.50/0.89 thf(zip_derived_cl257, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('s_sup-', [status(thm)], [zip_derived_cl256, zip_derived_cl254])).
% 0.50/0.89 thf(zip_derived_cl258, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.50/0.89 inference('simplify', [status(thm)], [zip_derived_cl257])).
% 0.50/0.89 thf(zip_derived_cl33, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_84])).
% 0.50/0.89 thf(clause_38, axiom,
% 0.50/0.89 (( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ B_10 ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ A_2 ) ) ) ) |
% 0.50/0.89 ( ~( iLEQ @ ( suc @ A_2 ) @ ( suc @ B_10 ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ ( suc @ B_10 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ ( s @ 0 ) ) @ ( f @ A_2 ) ) ) |
% 0.50/0.89 ( E @ ( f @ A_2 ) @ ( f @ ( suc @ A_2 ) ) ) |
% 0.50/0.89 ( E @ ( f @ B_10 ) @ ( f @ ( suc @ B_10 ) ) ))).
% 0.50/0.89 thf(zip_derived_cl5, plain,
% 0.50/0.89 (![X0 : $i, X1 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ X1))
% 0.50/0.89 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_38])).
% 0.50/0.89 thf(zip_derived_cl130, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('s_sup-', [status(thm)], [zip_derived_cl33, zip_derived_cl5])).
% 0.50/0.89 thf(zip_derived_cl134, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('simplify', [status(thm)], [zip_derived_cl130])).
% 0.50/0.89 thf(zip_derived_cl261, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('s_sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl134])).
% 0.50/0.89 thf(zip_derived_cl224, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (s @ (s @ 0)) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl222])).
% 0.50/0.89 thf(zip_derived_cl276, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl261, zip_derived_cl224])).
% 0.50/0.89 thf(zip_derived_cl225, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (s @ (s @ 0)) @ (f @ (suc @ X0)))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ (s @ 0))))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl30, zip_derived_cl222])).
% 0.50/0.89 thf(zip_derived_cl277, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl276, zip_derived_cl225])).
% 0.50/0.89 thf(zip_derived_cl280, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl277])).
% 0.50/0.89 thf(clause_31, axiom,
% 0.50/0.89 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 0.50/0.89 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 0.50/0.89 thf(zip_derived_cl23, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_31])).
% 0.50/0.89 thf(clause_115, axiom,
% 0.50/0.89 (( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.50/0.89 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 0.50/0.89 ( iLEQ @ ( suc @ A_3 ) @ ( suc @ A_3 ) ))).
% 0.50/0.89 thf(zip_derived_cl36, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_115])).
% 0.50/0.89 thf(zip_derived_cl44, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl23, zip_derived_cl36])).
% 0.50/0.89 thf(zip_derived_cl36, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_115])).
% 0.50/0.89 thf(clause_112, axiom,
% 0.50/0.89 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_14 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ 0 ) @ ( f @ B_14 ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 0.50/0.89 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_14 ) ) ) |
% 0.50/0.89 ( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) |
% 0.50/0.89 ( E @ ( f @ B_14 ) @ ( f @ ( suc @ B_14 ) ) ))).
% 0.50/0.89 thf(zip_derived_cl34, plain,
% 0.50/0.89 (![X0 : $i, X1 : $i]:
% 0.50/0.89 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X1))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.50/0.89 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_112])).
% 0.50/0.89 thf(zip_derived_cl82, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('s_sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl34])).
% 0.50/0.89 thf(zip_derived_cl89, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('simplify', [status(thm)], [zip_derived_cl82])).
% 0.50/0.89 thf(clause_57, axiom,
% 0.50/0.89 (( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ B_14 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ B_14 ) ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ 0 ) @ ( f @ B_14 ) ) ) |
% 0.50/0.89 ( ~( E @ ( f @ B_14 ) @ ( f @ ( suc @ B_14 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( f @ A_3 ) @ ( f @ ( suc @ A_3 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ 0 ) @ ( f @ A_3 ) ) ) |
% 0.50/0.89 ( ~( E @ ( s @ 0 ) @ ( f @ ( suc @ ( suc @ A_3 ) ) ) ) ) |
% 0.50/0.89 ( ~( iLEQ @ ( suc @ A_3 ) @ ( suc @ B_14 ) ) ))).
% 0.50/0.89 thf(zip_derived_cl28, plain,
% 0.50/0.89 (![X0 : $i, X1 : $i]:
% 0.50/0.89 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X1))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_57])).
% 0.50/0.89 thf(zip_derived_cl97, plain,
% 0.50/0.89 (![X0 : $i, X1 : $i]:
% 0.50/0.89 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X1))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0)))),
% 0.50/0.89 inference('s_sup-', [status(thm)], [zip_derived_cl89, zip_derived_cl28])).
% 0.50/0.89 thf(zip_derived_cl98, plain,
% 0.50/0.89 (![X0 : $i, X1 : $i]:
% 0.50/0.89 (~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X1))
% 0.50/0.89 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('simplify', [status(thm)], [zip_derived_cl97])).
% 0.50/0.89 thf(zip_derived_cl89, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('simplify', [status(thm)], [zip_derived_cl82])).
% 0.50/0.89 thf(zip_derived_cl179, plain,
% 0.50/0.89 (![X0 : $i, X1 : $i]:
% 0.50/0.89 (~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X1))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X1))))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0)))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl98, zip_derived_cl89])).
% 0.50/0.89 thf(zip_derived_cl182, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 0.50/0.89 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl179])).
% 0.50/0.89 thf(zip_derived_cl184, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ (suc @ X0)))))),
% 0.50/0.89 inference('simplify', [status(thm)], [zip_derived_cl182])).
% 0.50/0.89 thf(zip_derived_cl289, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (LE @ (f @ X0) @ (s @ 0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | ~ (E @ (s @ 0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('s_sup-', [status(thm)], [zip_derived_cl280, zip_derived_cl184])).
% 0.50/0.89 thf(clause_15, axiom,
% 0.50/0.89 (( ~( LE @ ( f @ B_13 ) @ ( s @ ( s @ 0 ) ) ) ) |
% 0.50/0.89 ( E @ ( s @ 0 ) @ ( f @ B_13 ) ) | ( LE @ ( f @ B_13 ) @ ( s @ 0 ) ))).
% 0.50/0.89 thf(zip_derived_cl6, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (LE @ (f @ X0) @ (s @ (s @ 0)))
% 0.50/0.89 | (E @ (s @ 0) @ (f @ X0))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_15])).
% 0.50/0.89 thf(zip_derived_cl277, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl276, zip_derived_cl225])).
% 0.50/0.89 thf(zip_derived_cl278, plain,
% 0.50/0.89 (![X0 : $i]: ( (E @ (s @ 0) @ (f @ X0)) | (LE @ (f @ X0) @ (s @ 0)))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl6, zip_derived_cl277])).
% 0.50/0.89 thf(zip_derived_cl290, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl289, zip_derived_cl278])).
% 0.50/0.89 thf(clause_39, axiom,
% 0.50/0.89 (( ~( LE @ ( f @ ( suc @ B_13 ) ) @ ( s @ ( s @ 0 ) ) ) ) |
% 0.50/0.89 ( E @ ( s @ 0 ) @ ( f @ ( suc @ B_13 ) ) ) |
% 0.50/0.89 ( LE @ ( f @ B_13 ) @ ( s @ 0 ) ))).
% 0.50/0.89 thf(zip_derived_cl24, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (LE @ (f @ (suc @ X0)) @ (s @ (s @ 0)))
% 0.50/0.89 | (E @ (s @ 0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (LE @ (f @ X0) @ (s @ 0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_39])).
% 0.50/0.89 thf(zip_derived_cl277, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ (s @ 0)))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl276, zip_derived_cl225])).
% 0.50/0.89 thf(zip_derived_cl279, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (s @ 0) @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ (s @ 0)))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl24, zip_derived_cl277])).
% 0.50/0.89 thf(zip_derived_cl291, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl290, zip_derived_cl279])).
% 0.50/0.89 thf(zip_derived_cl294, plain,
% 0.50/0.89 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ (suc @ X0)))) | (LE @ (f @ X0) @ 0))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl35, zip_derived_cl291])).
% 0.50/0.89 thf(clause_114, axiom,
% 0.50/0.89 (( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 0.50/0.89 ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.50/0.89 ( ~( E @ 0 @ ( f @ A_4 ) ) ) | ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 0.50/0.89 thf(zip_derived_cl37, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_114])).
% 0.50/0.89 thf(clause_150, axiom,
% 0.50/0.89 (( ~( E @ 0 @ ( f @ A_4 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.50/0.89 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) |
% 0.50/0.89 ( iLEQ @ ( suc @ A_4 ) @ ( suc @ A_4 ) ))).
% 0.50/0.89 thf(zip_derived_cl22, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_150])).
% 0.50/0.89 thf(zip_derived_cl43, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (iLEQ @ (suc @ X0) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl37, zip_derived_cl22])).
% 0.50/0.89 thf(zip_derived_cl22, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (iLEQ @ (suc @ X0) @ (suc @ X0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_150])).
% 0.50/0.89 thf(clause_0, axiom,
% 0.50/0.89 (( ~( E @ 0 @ ( f @ ( suc @ B_17 ) ) ) ) |
% 0.50/0.89 ( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_17 ) ) ) |
% 0.50/0.89 ( ~( E @ 0 @ ( f @ B_17 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.50/0.89 ( ~( E @ 0 @ ( f @ A_4 ) ) ) |
% 0.50/0.89 ( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) |
% 0.50/0.89 ( E @ ( f @ B_17 ) @ ( f @ ( suc @ B_17 ) ) ))).
% 0.50/0.89 thf(zip_derived_cl16, plain,
% 0.50/0.89 (![X0 : $i, X1 : $i]:
% 0.50/0.89 (~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X1) @ (suc @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X1))
% 0.50/0.89 | (E @ (f @ X1) @ (f @ (suc @ X1)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_0])).
% 0.50/0.89 thf(zip_derived_cl65, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl16])).
% 0.50/0.89 thf(zip_derived_cl72, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('simplify', [status(thm)], [zip_derived_cl65])).
% 0.50/0.89 thf(clause_48, axiom,
% 0.50/0.89 (( ~( E @ ( f @ A_4 ) @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.50/0.89 ( ~( E @ 0 @ ( f @ ( suc @ B_17 ) ) ) ) |
% 0.50/0.89 ( ~( iLEQ @ ( suc @ A_4 ) @ ( suc @ B_17 ) ) ) |
% 0.50/0.89 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ B_17 ) ) ) ) ) |
% 0.50/0.89 ( ~( E @ 0 @ ( f @ ( suc @ ( suc @ A_4 ) ) ) ) ) |
% 0.50/0.89 ( ~( E @ 0 @ ( f @ B_17 ) ) ) | ( ~( E @ 0 @ ( f @ ( suc @ A_4 ) ) ) ) |
% 0.50/0.89 ( ~( E @ ( f @ B_17 ) @ ( f @ ( suc @ B_17 ) ) ) ) |
% 0.50/0.89 ( ~( E @ 0 @ ( f @ A_4 ) ) ))).
% 0.50/0.89 thf(zip_derived_cl19, plain,
% 0.50/0.89 (![X0 : $i, X1 : $i]:
% 0.50/0.89 (~ (E @ (f @ X0) @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X1))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X0)))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_48])).
% 0.50/0.89 thf(zip_derived_cl93, plain,
% 0.50/0.89 (![X0 : $i, X1 : $i]:
% 0.50/0.89 (~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X1))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X0)))),
% 0.50/0.89 inference('s_sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl19])).
% 0.50/0.89 thf(zip_derived_cl95, plain,
% 0.50/0.89 (![X0 : $i, X1 : $i]:
% 0.50/0.89 (~ (E @ (f @ X1) @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X1))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('simplify', [status(thm)], [zip_derived_cl93])).
% 0.50/0.89 thf(zip_derived_cl72, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | (E @ (f @ X0) @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('simplify', [status(thm)], [zip_derived_cl65])).
% 0.50/0.89 thf(zip_derived_cl106, plain,
% 0.50/0.89 (![X0 : $i, X1 : $i]:
% 0.50/0.89 (~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X1)))
% 0.50/0.89 | ~ (iLEQ @ (suc @ X0) @ (suc @ X1))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X1))))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X1)))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl95, zip_derived_cl72])).
% 0.50/0.89 thf(zip_derived_cl114, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0))))
% 0.50/0.89 | ~ (E @ 0 @ (f @ X0)))),
% 0.50/0.89 inference('s_sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl106])).
% 0.50/0.89 thf(zip_derived_cl119, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ (suc @ X0)))))),
% 0.50/0.89 inference('simplify', [status(thm)], [zip_derived_cl114])).
% 0.50/0.89 thf(zip_derived_cl300, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 ( (LE @ (f @ X0) @ 0)
% 0.50/0.89 | ~ (E @ 0 @ (f @ X0))
% 0.50/0.89 | ~ (E @ 0 @ (f @ (suc @ X0))))),
% 0.50/0.89 inference('s_sup-', [status(thm)], [zip_derived_cl294, zip_derived_cl119])).
% 0.50/0.89 thf(clause_145, axiom,
% 0.50/0.89 (( ~( LE @ ( f @ B_16 ) @ ( s @ 0 ) ) ) | ( E @ 0 @ ( f @ B_16 ) ) |
% 0.50/0.89 ( LE @ ( f @ B_16 ) @ 0 ))).
% 0.50/0.89 thf(zip_derived_cl13, plain,
% 0.50/0.89 (![X0 : $i]:
% 0.50/0.89 (~ (LE @ (f @ X0) @ (s @ 0))
% 0.50/0.89 | (E @ 0 @ (f @ X0))
% 0.50/0.89 | (LE @ (f @ X0) @ 0))),
% 0.50/0.89 inference('cnf', [status(esa)], [clause_145])).
% 0.50/0.89 thf(zip_derived_cl291, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 0.50/0.89 inference('clc', [status(thm)], [zip_derived_cl290, zip_derived_cl279])).
% 0.50/0.89 thf(zip_derived_cl293, plain,
% 0.50/0.89 (![X0 : $i]: ( (E @ 0 @ (f @ X0)) | (LE @ (f @ X0) @ 0))),
% 0.50/0.89 inference('demod', [status(thm)], [zip_derived_cl13, zip_derived_cl291])).
% 0.50/0.89 thf(zip_derived_cl301, plain,
% 0.50/0.90 (![X0 : $i]: (~ (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 0.50/0.90 inference('clc', [status(thm)], [zip_derived_cl300, zip_derived_cl293])).
% 0.50/0.90 thf(clause_2, axiom,
% 0.50/0.90 (( ~( LE @ ( f @ ( suc @ B_16 ) ) @ ( s @ 0 ) ) ) |
% 0.50/0.90 ( E @ 0 @ ( f @ ( suc @ B_16 ) ) ) | ( LE @ ( f @ B_16 ) @ 0 ))).
% 0.50/0.90 thf(zip_derived_cl12, plain,
% 0.50/0.90 (![X0 : $i]:
% 0.50/0.90 (~ (LE @ (f @ (suc @ X0)) @ (s @ 0))
% 0.50/0.90 | (E @ 0 @ (f @ (suc @ X0)))
% 0.50/0.90 | (LE @ (f @ X0) @ 0))),
% 0.50/0.90 inference('cnf', [status(esa)], [clause_2])).
% 0.50/0.90 thf(zip_derived_cl291, plain, (![X0 : $i]: (LE @ (f @ X0) @ (s @ 0))),
% 0.50/0.90 inference('clc', [status(thm)], [zip_derived_cl290, zip_derived_cl279])).
% 0.50/0.90 thf(zip_derived_cl292, plain,
% 0.50/0.90 (![X0 : $i]: ( (E @ 0 @ (f @ (suc @ X0))) | (LE @ (f @ X0) @ 0))),
% 0.50/0.90 inference('demod', [status(thm)], [zip_derived_cl12, zip_derived_cl291])).
% 0.50/0.90 thf(zip_derived_cl302, plain, (![X0 : $i]: (LE @ (f @ X0) @ 0)),
% 0.50/0.90 inference('clc', [status(thm)], [zip_derived_cl301, zip_derived_cl292])).
% 0.50/0.90 thf(zip_derived_cl303, plain, ($false),
% 0.50/0.90 inference('demod', [status(thm)], [zip_derived_cl27, zip_derived_cl302])).
% 0.50/0.90
% 0.50/0.90 % SZS output end Refutation
% 0.50/0.90
% 0.50/0.90
% 0.50/0.90 % Terminating...
% 0.52/1.00 % Runner terminated.
% 0.52/1.01 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------