%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUN135-1.006 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.4Gn2nD6q8w 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 : Tue May 5 06:48:44 PM UTC 2026
% Result : Unsatisfiable 0.56s 0.83s
% Output : Refutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN135-1.006 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.4Gn2nD6q8w true
% 0.18/0.34 % Computer : n007.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue May 5 04:49:08 EDT 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 % Running portfolio for 300 s
% 0.18/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.35 % Number of cores: 8
% 0.18/0.35 % Python version: Python 3.6.8
% 0.18/0.35 % Running in FO mode
% 0.50/0.64 % Total configuration time : 435
% 0.50/0.64 % Estimated wc time : 1092
% 0.50/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.55/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.55/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.55/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.55/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.55/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.55/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.56/0.83 % Solved by fo/fo3_bce.sh.
% 0.56/0.83 % BCE start: 14
% 0.56/0.83 % BCE eliminated: 0
% 0.56/0.83 % PE start: 14
% 0.56/0.83 logic: eq
% 0.56/0.83 % PE eliminated: 0
% 0.56/0.83 % done 114 iterations in 0.076s
% 0.56/0.83 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.56/0.83 % SZS output start Refutation
% 0.56/0.83 thf(f_type, type, f: $i > $i > $i > $i > $i).
% 0.56/0.83 thf(<=_type, type, <=: $i > $i > $i).
% 0.56/0.83 thf(perfectp_type, type, perfectp: $i > $i).
% 0.56/0.83 thf(zero_type, type, zero: $i).
% 0.56/0.83 thf(minus_type, type, minus: $i > $i > $i).
% 0.56/0.83 thf(true_type, type, true: $i).
% 0.56/0.83 thf(s_type, type, s: $i > $i).
% 0.56/0.83 thf(false_type, type, false: $i).
% 0.56/0.83 thf(if_type, type, if: $i > $i > $i > $i).
% 0.56/0.83 thf(rule1, axiom, (( minus @ X @ zero ) = ( X ))).
% 0.56/0.83 thf(zip_derived_cl0, plain, (![X0 : $i]: ((minus @ X0 @ zero) = (X0))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule1])).
% 0.56/0.83 thf(rule2, axiom, (( minus @ ( s @ X ) @ ( s @ Y ) ) = ( minus @ X @ Y ))).
% 0.56/0.83 thf(zip_derived_cl1, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((minus @ (s @ X0) @ (s @ X1)) = (minus @ X0 @ X1))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule2])).
% 0.56/0.83 thf(zip_derived_cl1, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((minus @ (s @ X0) @ (s @ X1)) = (minus @ X0 @ X1))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule2])).
% 0.56/0.83 thf(zip_derived_cl1, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((minus @ (s @ X0) @ (s @ X1)) = (minus @ X0 @ X1))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule2])).
% 0.56/0.83 thf(rule13, axiom,
% 0.56/0.83 (( f @ ( s @ X ) @ ( s @ Y ) @ Z @ U ) =
% 0.56/0.83 ( if @
% 0.56/0.83 ( <= @ X @ Y ) @ ( f @ ( s @ X ) @ ( minus @ Y @ X ) @ Z @ U ) @
% 0.56/0.83 ( f @ X @ U @ Z @ U ) ))).
% 0.56/0.83 thf(zip_derived_cl12, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/0.83 ((f @ (s @ X0) @ (s @ X1) @ X2 @ X3)
% 0.56/0.83 = (if @ (<= @ X0 @ X1) @
% 0.56/0.83 (f @ (s @ X0) @ (minus @ X1 @ X0) @ X2 @ X3) @
% 0.56/0.83 (f @ X0 @ X3 @ X2 @ X3)))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule13])).
% 0.56/0.83 thf(zip_derived_cl22, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ X0)) @ (s @ (s @ X1)) @ X3 @ X2)
% 0.56/0.83 = (if @ (<= @ (s @ X0) @ (s @ X1)) @
% 0.56/0.83 (f @ (s @ (s @ X0)) @ (minus @ X1 @ X0) @ X3 @ X2) @
% 0.56/0.83 (f @ (s @ X0) @ X2 @ X3 @ X2)))),
% 0.56/0.83 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl12])).
% 0.56/0.83 thf(rule5, axiom, (( <= @ ( s @ X ) @ ( s @ Y ) ) = ( <= @ X @ Y ))).
% 0.56/0.83 thf(zip_derived_cl4, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((<= @ (s @ X0) @ (s @ X1)) = (<= @ X0 @ X1))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule5])).
% 0.56/0.83 thf(zip_derived_cl30, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ X0)) @ (s @ (s @ X1)) @ X3 @ X2)
% 0.56/0.83 = (if @ (<= @ X0 @ X1) @
% 0.56/0.83 (f @ (s @ (s @ X0)) @ (minus @ X1 @ X0) @ X3 @ X2) @
% 0.56/0.83 (f @ (s @ X0) @ X2 @ X3 @ X2)))),
% 0.56/0.83 inference('demod', [status(thm)], [zip_derived_cl22, zip_derived_cl4])).
% 0.56/0.83 thf(zip_derived_cl72, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ (s @ X0))) @ (s @ (s @ (s @ X1))) @ X3 @ X2)
% 0.56/0.83 = (if @ (<= @ (s @ X0) @ (s @ X1)) @
% 0.56/0.83 (f @ (s @ (s @ (s @ X0))) @ (minus @ X1 @ X0) @ X3 @ X2) @
% 0.56/0.83 (f @ (s @ (s @ X0)) @ X2 @ X3 @ X2)))),
% 0.56/0.83 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl30])).
% 0.56/0.83 thf(zip_derived_cl4, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((<= @ (s @ X0) @ (s @ X1)) = (<= @ X0 @ X1))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule5])).
% 0.56/0.83 thf(zip_derived_cl78, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ (s @ X0))) @ (s @ (s @ (s @ X1))) @ X3 @ X2)
% 0.56/0.83 = (if @ (<= @ X0 @ X1) @
% 0.56/0.83 (f @ (s @ (s @ (s @ X0))) @ (minus @ X1 @ X0) @ X3 @ X2) @
% 0.56/0.83 (f @ (s @ (s @ X0)) @ X2 @ X3 @ X2)))),
% 0.56/0.83 inference('demod', [status(thm)], [zip_derived_cl72, zip_derived_cl4])).
% 0.56/0.83 thf(zip_derived_cl129, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ (s @ (s @ X0)))) @ (s @ (s @ (s @ (s @ X1)))) @ X3 @
% 0.56/0.83 X2)
% 0.56/0.83 = (if @ (<= @ (s @ X0) @ (s @ X1)) @
% 0.56/0.83 (f @ (s @ (s @ (s @ (s @ X0)))) @ (minus @ X1 @ X0) @ X3 @ X2) @
% 0.56/0.83 (f @ (s @ (s @ (s @ X0))) @ X2 @ X3 @ X2)))),
% 0.56/0.83 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl78])).
% 0.56/0.83 thf(zip_derived_cl4, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((<= @ (s @ X0) @ (s @ X1)) = (<= @ X0 @ X1))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule5])).
% 0.56/0.83 thf(zip_derived_cl136, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ (s @ (s @ X0)))) @ (s @ (s @ (s @ (s @ X1)))) @ X3 @
% 0.56/0.83 X2)
% 0.56/0.83 = (if @ (<= @ X0 @ X1) @
% 0.56/0.83 (f @ (s @ (s @ (s @ (s @ X0)))) @ (minus @ X1 @ X0) @ X3 @ X2) @
% 0.56/0.83 (f @ (s @ (s @ (s @ X0))) @ X2 @ X3 @ X2)))),
% 0.56/0.83 inference('demod', [status(thm)], [zip_derived_cl129, zip_derived_cl4])).
% 0.56/0.83 thf(zip_derived_cl303, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ (s @ (s @ zero)))) @ (s @ (s @ (s @ (s @ X0)))) @
% 0.56/0.83 X2 @ X1)
% 0.56/0.83 = (if @ (<= @ zero @ X0) @
% 0.56/0.83 (f @ (s @ (s @ (s @ (s @ zero)))) @ X0 @ X2 @ X1) @
% 0.56/0.83 (f @ (s @ (s @ (s @ zero))) @ X1 @ X2 @ X1)))),
% 0.56/0.83 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl136])).
% 0.56/0.83 thf(rule3, axiom, (( <= @ zero @ Y ) = ( true ))).
% 0.56/0.83 thf(zip_derived_cl2, plain, (![X0 : $i]: ((<= @ zero @ X0) = (true))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule3])).
% 0.56/0.83 thf(rule6, axiom, (( if @ true @ X @ Y ) = ( X ))).
% 0.56/0.83 thf(zip_derived_cl5, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((if @ true @ X0 @ X1) = (X0))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule6])).
% 0.56/0.83 thf(zip_derived_cl311, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ (s @ (s @ zero)))) @ (s @ (s @ (s @ (s @ X0)))) @
% 0.56/0.83 X2 @ X1) = (f @ (s @ (s @ (s @ (s @ zero)))) @ X0 @ X2 @ X1))),
% 0.56/0.83 inference('demod', [status(thm)],
% 0.56/0.83 [zip_derived_cl303, zip_derived_cl2, zip_derived_cl5])).
% 0.56/0.83 thf(rule4, axiom, (( <= @ ( s @ X ) @ zero ) = ( false ))).
% 0.56/0.83 thf(zip_derived_cl3, plain, (![X0 : $i]: ((<= @ (s @ X0) @ zero) = (false))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule4])).
% 0.56/0.83 thf(zip_derived_cl12, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/0.83 ((f @ (s @ X0) @ (s @ X1) @ X2 @ X3)
% 0.56/0.83 = (if @ (<= @ X0 @ X1) @
% 0.56/0.83 (f @ (s @ X0) @ (minus @ X1 @ X0) @ X2 @ X3) @
% 0.56/0.83 (f @ X0 @ X3 @ X2 @ X3)))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule13])).
% 0.56/0.83 thf(zip_derived_cl24, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ X2)) @ (s @ zero) @ X1 @ X0)
% 0.56/0.83 = (if @ false @
% 0.56/0.83 (f @ (s @ (s @ X2)) @ (minus @ zero @ (s @ X2)) @ X1 @ X0) @
% 0.56/0.83 (f @ (s @ X2) @ X0 @ X1 @ X0)))),
% 0.56/0.83 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl12])).
% 0.56/0.83 thf(rule7, axiom, (( if @ false @ X @ Y ) = ( Y ))).
% 0.56/0.83 thf(zip_derived_cl6, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((if @ false @ X1 @ X0) = (X0))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule7])).
% 0.56/0.83 thf(zip_derived_cl32, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ X2)) @ (s @ zero) @ X1 @ X0)
% 0.56/0.83 = (f @ (s @ X2) @ X0 @ X1 @ X0))),
% 0.56/0.83 inference('demod', [status(thm)], [zip_derived_cl24, zip_derived_cl6])).
% 0.56/0.83 thf(rule9, axiom,
% 0.56/0.83 (( perfectp @ ( s @ X ) ) =
% 0.56/0.83 ( f @ X @ ( s @ zero ) @ ( s @ X ) @ ( s @ X ) ))).
% 0.56/0.83 thf(zip_derived_cl8, plain,
% 0.56/0.83 (![X0 : $i]:
% 0.56/0.83 ((perfectp @ (s @ X0)) = (f @ X0 @ (s @ zero) @ (s @ X0) @ (s @ X0)))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule9])).
% 0.56/0.83 thf(zip_derived_cl38, plain,
% 0.56/0.83 (![X0 : $i]:
% 0.56/0.83 ((perfectp @ (s @ (s @ (s @ X0))))
% 0.56/0.83 = (f @ (s @ X0) @ (s @ (s @ (s @ X0))) @ (s @ (s @ (s @ X0))) @
% 0.56/0.83 (s @ (s @ (s @ X0)))))),
% 0.56/0.83 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl8])).
% 0.56/0.83 thf(zip_derived_cl320, plain,
% 0.56/0.83 (((perfectp @ (s @ (s @ (s @ (s @ (s @ (s @ zero)))))))
% 0.56/0.83 = (f @ (s @ (s @ (s @ (s @ zero)))) @ (s @ (s @ zero)) @
% 0.56/0.83 (s @ (s @ (s @ (s @ (s @ (s @ zero)))))) @
% 0.56/0.83 (s @ (s @ (s @ (s @ (s @ (s @ zero))))))))),
% 0.56/0.83 inference('sup+', [status(thm)], [zip_derived_cl311, zip_derived_cl38])).
% 0.56/0.83 thf(zip_derived_cl3, plain, (![X0 : $i]: ((<= @ (s @ X0) @ zero) = (false))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule4])).
% 0.56/0.83 thf(zip_derived_cl30, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ X0)) @ (s @ (s @ X1)) @ X3 @ X2)
% 0.56/0.83 = (if @ (<= @ X0 @ X1) @
% 0.56/0.83 (f @ (s @ (s @ X0)) @ (minus @ X1 @ X0) @ X3 @ X2) @
% 0.56/0.83 (f @ (s @ X0) @ X2 @ X3 @ X2)))),
% 0.56/0.83 inference('demod', [status(thm)], [zip_derived_cl22, zip_derived_cl4])).
% 0.56/0.83 thf(zip_derived_cl74, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ (s @ X2))) @ (s @ (s @ zero)) @ X1 @ X0)
% 0.56/0.83 = (if @ false @
% 0.56/0.83 (f @ (s @ (s @ (s @ X2))) @ (minus @ zero @ (s @ X2)) @ X1 @ X0) @
% 0.56/0.83 (f @ (s @ (s @ X2)) @ X0 @ X1 @ X0)))),
% 0.56/0.83 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl30])).
% 0.56/0.83 thf(zip_derived_cl6, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((if @ false @ X1 @ X0) = (X0))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule7])).
% 0.56/0.83 thf(zip_derived_cl80, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ (s @ X2))) @ (s @ (s @ zero)) @ X1 @ X0)
% 0.56/0.83 = (f @ (s @ (s @ X2)) @ X0 @ X1 @ X0))),
% 0.56/0.83 inference('demod', [status(thm)], [zip_derived_cl74, zip_derived_cl6])).
% 0.56/0.83 thf(zip_derived_cl325, plain,
% 0.56/0.83 (((perfectp @ (s @ (s @ (s @ (s @ (s @ (s @ zero)))))))
% 0.56/0.83 = (f @ (s @ (s @ (s @ zero))) @
% 0.56/0.83 (s @ (s @ (s @ (s @ (s @ (s @ zero)))))) @
% 0.56/0.83 (s @ (s @ (s @ (s @ (s @ (s @ zero)))))) @
% 0.56/0.83 (s @ (s @ (s @ (s @ (s @ (s @ zero))))))))),
% 0.56/0.83 inference('sup+', [status(thm)], [zip_derived_cl320, zip_derived_cl80])).
% 0.56/0.83 thf(zip_derived_cl0, plain, (![X0 : $i]: ((minus @ X0 @ zero) = (X0))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule1])).
% 0.56/0.83 thf(zip_derived_cl78, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ (s @ X0))) @ (s @ (s @ (s @ X1))) @ X3 @ X2)
% 0.56/0.83 = (if @ (<= @ X0 @ X1) @
% 0.56/0.83 (f @ (s @ (s @ (s @ X0))) @ (minus @ X1 @ X0) @ X3 @ X2) @
% 0.56/0.83 (f @ (s @ (s @ X0)) @ X2 @ X3 @ X2)))),
% 0.56/0.83 inference('demod', [status(thm)], [zip_derived_cl72, zip_derived_cl4])).
% 0.56/0.83 thf(zip_derived_cl128, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ (s @ zero))) @ (s @ (s @ (s @ X0))) @ X2 @ X1)
% 0.56/0.83 = (if @ (<= @ zero @ X0) @
% 0.56/0.83 (f @ (s @ (s @ (s @ zero))) @ X0 @ X2 @ X1) @
% 0.56/0.83 (f @ (s @ (s @ zero)) @ X1 @ X2 @ X1)))),
% 0.56/0.83 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl78])).
% 0.56/0.83 thf(zip_derived_cl2, plain, (![X0 : $i]: ((<= @ zero @ X0) = (true))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule3])).
% 0.56/0.83 thf(zip_derived_cl5, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((if @ true @ X0 @ X1) = (X0))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule6])).
% 0.56/0.83 thf(zip_derived_cl135, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ (s @ zero))) @ (s @ (s @ (s @ X0))) @ X2 @ X1)
% 0.56/0.83 = (f @ (s @ (s @ (s @ zero))) @ X0 @ X2 @ X1))),
% 0.56/0.83 inference('demod', [status(thm)],
% 0.56/0.83 [zip_derived_cl128, zip_derived_cl2, zip_derived_cl5])).
% 0.56/0.83 thf(zip_derived_cl330, plain,
% 0.56/0.83 (((perfectp @ (s @ (s @ (s @ (s @ (s @ (s @ zero)))))))
% 0.56/0.83 = (f @ (s @ (s @ (s @ zero))) @ (s @ (s @ (s @ zero))) @
% 0.56/0.83 (s @ (s @ (s @ (s @ (s @ (s @ zero)))))) @
% 0.56/0.83 (s @ (s @ (s @ (s @ (s @ (s @ zero))))))))),
% 0.56/0.83 inference('sup+', [status(thm)], [zip_derived_cl325, zip_derived_cl135])).
% 0.56/0.83 thf(zip_derived_cl135, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ (s @ zero))) @ (s @ (s @ (s @ X0))) @ X2 @ X1)
% 0.56/0.83 = (f @ (s @ (s @ (s @ zero))) @ X0 @ X2 @ X1))),
% 0.56/0.83 inference('demod', [status(thm)],
% 0.56/0.83 [zip_derived_cl128, zip_derived_cl2, zip_derived_cl5])).
% 0.56/0.83 thf(zip_derived_cl332, plain,
% 0.56/0.83 (((perfectp @ (s @ (s @ (s @ (s @ (s @ (s @ zero)))))))
% 0.56/0.83 = (f @ (s @ (s @ (s @ zero))) @ zero @
% 0.56/0.83 (s @ (s @ (s @ (s @ (s @ (s @ zero)))))) @
% 0.56/0.83 (s @ (s @ (s @ (s @ (s @ (s @ zero))))))))),
% 0.56/0.83 inference('sup+', [status(thm)], [zip_derived_cl330, zip_derived_cl135])).
% 0.56/0.83 thf(rule12, axiom,
% 0.56/0.83 (( f @ ( s @ X ) @ zero @ Z @ U ) =
% 0.56/0.83 ( f @ X @ U @ ( minus @ Z @ ( s @ X ) ) @ U ))).
% 0.56/0.83 thf(zip_derived_cl11, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ X0) @ zero @ X2 @ X1)
% 0.56/0.83 = (f @ X0 @ X1 @ (minus @ X2 @ (s @ X0)) @ X1))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule12])).
% 0.56/0.83 thf(zip_derived_cl333, plain,
% 0.56/0.83 (((perfectp @ (s @ (s @ (s @ (s @ (s @ (s @ zero)))))))
% 0.56/0.83 = (f @ (s @ (s @ zero)) @ (s @ (s @ (s @ (s @ (s @ (s @ zero)))))) @
% 0.56/0.83 (minus @ (s @ (s @ (s @ (s @ (s @ (s @ zero)))))) @
% 0.56/0.83 (s @ (s @ (s @ zero)))) @
% 0.56/0.83 (s @ (s @ (s @ (s @ (s @ (s @ zero))))))))),
% 0.56/0.83 inference('sup+', [status(thm)], [zip_derived_cl332, zip_derived_cl11])).
% 0.56/0.83 thf(zip_derived_cl1, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((minus @ (s @ X0) @ (s @ X1)) = (minus @ X0 @ X1))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule2])).
% 0.56/0.83 thf(zip_derived_cl1, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((minus @ (s @ X0) @ (s @ X1)) = (minus @ X0 @ X1))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule2])).
% 0.56/0.83 thf(zip_derived_cl1, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((minus @ (s @ X0) @ (s @ X1)) = (minus @ X0 @ X1))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule2])).
% 0.56/0.83 thf(zip_derived_cl0, plain, (![X0 : $i]: ((minus @ X0 @ zero) = (X0))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule1])).
% 0.56/0.83 thf(zip_derived_cl0, plain, (![X0 : $i]: ((minus @ X0 @ zero) = (X0))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule1])).
% 0.56/0.83 thf(zip_derived_cl30, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ X0)) @ (s @ (s @ X1)) @ X3 @ X2)
% 0.56/0.83 = (if @ (<= @ X0 @ X1) @
% 0.56/0.83 (f @ (s @ (s @ X0)) @ (minus @ X1 @ X0) @ X3 @ X2) @
% 0.56/0.83 (f @ (s @ X0) @ X2 @ X3 @ X2)))),
% 0.56/0.83 inference('demod', [status(thm)], [zip_derived_cl22, zip_derived_cl4])).
% 0.56/0.83 thf(zip_derived_cl71, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ zero)) @ (s @ (s @ X0)) @ X2 @ X1)
% 0.56/0.83 = (if @ (<= @ zero @ X0) @ (f @ (s @ (s @ zero)) @ X0 @ X2 @ X1) @
% 0.56/0.83 (f @ (s @ zero) @ X1 @ X2 @ X1)))),
% 0.56/0.83 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl30])).
% 0.56/0.83 thf(zip_derived_cl2, plain, (![X0 : $i]: ((<= @ zero @ X0) = (true))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule3])).
% 0.56/0.83 thf(zip_derived_cl5, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((if @ true @ X0 @ X1) = (X0))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule6])).
% 0.56/0.83 thf(zip_derived_cl77, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ zero)) @ (s @ (s @ X0)) @ X2 @ X1)
% 0.56/0.83 = (f @ (s @ (s @ zero)) @ X0 @ X2 @ X1))),
% 0.56/0.83 inference('demod', [status(thm)],
% 0.56/0.83 [zip_derived_cl71, zip_derived_cl2, zip_derived_cl5])).
% 0.56/0.83 thf(zip_derived_cl77, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ zero)) @ (s @ (s @ X0)) @ X2 @ X1)
% 0.56/0.83 = (f @ (s @ (s @ zero)) @ X0 @ X2 @ X1))),
% 0.56/0.83 inference('demod', [status(thm)],
% 0.56/0.83 [zip_derived_cl71, zip_derived_cl2, zip_derived_cl5])).
% 0.56/0.83 thf(zip_derived_cl77, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ (s @ zero)) @ (s @ (s @ X0)) @ X2 @ X1)
% 0.56/0.83 = (f @ (s @ (s @ zero)) @ X0 @ X2 @ X1))),
% 0.56/0.83 inference('demod', [status(thm)],
% 0.56/0.83 [zip_derived_cl71, zip_derived_cl2, zip_derived_cl5])).
% 0.56/0.83 thf(zip_derived_cl11, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ X0) @ zero @ X2 @ X1)
% 0.56/0.83 = (f @ X0 @ X1 @ (minus @ X2 @ (s @ X0)) @ X1))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule12])).
% 0.56/0.83 thf(zip_derived_cl1, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((minus @ (s @ X0) @ (s @ X1)) = (minus @ X0 @ X1))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule2])).
% 0.56/0.83 thf(zip_derived_cl1, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((minus @ (s @ X0) @ (s @ X1)) = (minus @ X0 @ X1))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule2])).
% 0.56/0.83 thf(zip_derived_cl0, plain, (![X0 : $i]: ((minus @ X0 @ zero) = (X0))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule1])).
% 0.56/0.83 thf(zip_derived_cl0, plain, (![X0 : $i]: ((minus @ X0 @ zero) = (X0))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule1])).
% 0.56/0.83 thf(zip_derived_cl12, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/0.83 ((f @ (s @ X0) @ (s @ X1) @ X2 @ X3)
% 0.56/0.83 = (if @ (<= @ X0 @ X1) @
% 0.56/0.83 (f @ (s @ X0) @ (minus @ X1 @ X0) @ X2 @ X3) @
% 0.56/0.83 (f @ X0 @ X3 @ X2 @ X3)))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule13])).
% 0.56/0.83 thf(zip_derived_cl21, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ zero) @ (s @ X0) @ X2 @ X1)
% 0.56/0.83 = (if @ (<= @ zero @ X0) @ (f @ (s @ zero) @ X0 @ X2 @ X1) @
% 0.56/0.83 (f @ zero @ X1 @ X2 @ X1)))),
% 0.56/0.83 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl12])).
% 0.56/0.83 thf(zip_derived_cl2, plain, (![X0 : $i]: ((<= @ zero @ X0) = (true))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule3])).
% 0.56/0.83 thf(zip_derived_cl5, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((if @ true @ X0 @ X1) = (X0))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule6])).
% 0.56/0.83 thf(zip_derived_cl29, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ zero) @ (s @ X0) @ X2 @ X1)
% 0.56/0.83 = (f @ (s @ zero) @ X0 @ X2 @ X1))),
% 0.56/0.83 inference('demod', [status(thm)],
% 0.56/0.83 [zip_derived_cl21, zip_derived_cl2, zip_derived_cl5])).
% 0.56/0.83 thf(zip_derived_cl29, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ zero) @ (s @ X0) @ X2 @ X1)
% 0.56/0.83 = (f @ (s @ zero) @ X0 @ X2 @ X1))),
% 0.56/0.83 inference('demod', [status(thm)],
% 0.56/0.83 [zip_derived_cl21, zip_derived_cl2, zip_derived_cl5])).
% 0.56/0.83 thf(zip_derived_cl29, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ zero) @ (s @ X0) @ X2 @ X1)
% 0.56/0.83 = (f @ (s @ zero) @ X0 @ X2 @ X1))),
% 0.56/0.83 inference('demod', [status(thm)],
% 0.56/0.83 [zip_derived_cl21, zip_derived_cl2, zip_derived_cl5])).
% 0.56/0.83 thf(zip_derived_cl29, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ zero) @ (s @ X0) @ X2 @ X1)
% 0.56/0.83 = (f @ (s @ zero) @ X0 @ X2 @ X1))),
% 0.56/0.83 inference('demod', [status(thm)],
% 0.56/0.83 [zip_derived_cl21, zip_derived_cl2, zip_derived_cl5])).
% 0.56/0.83 thf(zip_derived_cl29, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ zero) @ (s @ X0) @ X2 @ X1)
% 0.56/0.83 = (f @ (s @ zero) @ X0 @ X2 @ X1))),
% 0.56/0.83 inference('demod', [status(thm)],
% 0.56/0.83 [zip_derived_cl21, zip_derived_cl2, zip_derived_cl5])).
% 0.56/0.83 thf(zip_derived_cl29, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ zero) @ (s @ X0) @ X2 @ X1)
% 0.56/0.83 = (f @ (s @ zero) @ X0 @ X2 @ X1))),
% 0.56/0.83 inference('demod', [status(thm)],
% 0.56/0.83 [zip_derived_cl21, zip_derived_cl2, zip_derived_cl5])).
% 0.56/0.83 thf(zip_derived_cl11, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/0.83 ((f @ (s @ X0) @ zero @ X2 @ X1)
% 0.56/0.83 = (f @ X0 @ X1 @ (minus @ X2 @ (s @ X0)) @ X1))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule12])).
% 0.56/0.83 thf(zip_derived_cl1, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((minus @ (s @ X0) @ (s @ X1)) = (minus @ X0 @ X1))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule2])).
% 0.56/0.83 thf(zip_derived_cl0, plain, (![X0 : $i]: ((minus @ X0 @ zero) = (X0))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule1])).
% 0.56/0.83 thf(rule10, axiom, (( f @ zero @ Y @ zero @ U ) = ( true ))).
% 0.56/0.83 thf(zip_derived_cl9, plain,
% 0.56/0.83 (![X0 : $i, X1 : $i]: ((f @ zero @ X0 @ zero @ X1) = (true))),
% 0.56/0.83 inference('cnf', [status(esa)], [rule10])).
% 0.56/0.83 thf(zip_derived_cl334, plain,
% 0.56/0.83 (((perfectp @ (s @ (s @ (s @ (s @ (s @ (s @ zero))))))) = (true))),
% 0.56/0.83 inference('demod', [status(thm)],
% 0.56/0.83 [zip_derived_cl333, zip_derived_cl1, zip_derived_cl1,
% 0.56/0.83 zip_derived_cl1, zip_derived_cl0, zip_derived_cl77,
% 0.56/0.83 zip_derived_cl77, zip_derived_cl77, zip_derived_cl11,
% 0.56/0.83 zip_derived_cl1, zip_derived_cl1, zip_derived_cl0,
% 0.56/0.83 zip_derived_cl29, zip_derived_cl29, zip_derived_cl29,
% 0.56/0.83 zip_derived_cl29, zip_derived_cl29, zip_derived_cl29,
% 0.56/0.83 zip_derived_cl11, zip_derived_cl1, zip_derived_cl0,
% 0.56/0.83 zip_derived_cl9])).
% 0.56/0.83 thf(goal, conjecture, (( perfectp @ X ) = ( true ))).
% 0.56/0.83 thf(zf_stmt_0, negated_conjecture, (( perfectp @ X ) != ( true )),
% 0.56/0.83 inference('cnf.neg', [status(esa)], [goal])).
% 0.56/0.83 thf(zip_derived_cl13, plain, (![X0 : $i]: ((perfectp @ X0) != (true))),
% 0.56/0.83 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.56/0.83 thf(zip_derived_cl335, plain, ($false),
% 0.56/0.83 inference('simplify_reflect-', [status(thm)],
% 0.56/0.83 [zip_derived_cl334, zip_derived_cl13])).
% 0.56/0.83
% 0.56/0.83 % SZS output end Refutation
% 0.56/0.83
% 0.56/0.83
% 0.56/0.83 % Terminating...
% 0.62/0.95 % Runner terminated.
% 0.62/0.96 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------