%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL128-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.PsG02dGbuC true
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:35:15 PM UTC 2026
% Result : Unsatisfiable 27.23s 4.54s
% Output : Refutation 27.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL128-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.PsG02dGbuC true
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 12:17:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Running portfolio for 300 s
% 0.09/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.12.3
% 0.14/0.37 % Running in FO mode
% 0.44/0.65 % Total configuration time : 435
% 0.44/0.65 % Estimated wc time : 1092
% 0.44/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.47/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.47/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.47/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.47/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.47/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.47/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.47/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 27.23/4.54 % Solved by fo/fo13.sh.
% 27.23/4.54 % done 990 iterations in 3.712s
% 27.23/4.54 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 27.23/4.54 % SZS output start Refutation
% 27.23/4.54 thf(c_type, type, c: $i).
% 27.23/4.54 thf(is_a_theorem_type, type, is_a_theorem: $i > $o).
% 27.23/4.54 thf(equivalent_type, type, equivalent: $i > $i > $i).
% 27.23/4.54 thf(b_type, type, b: $i).
% 27.23/4.54 thf(e_type, type, e: $i).
% 27.23/4.54 thf(a_type, type, a: $i).
% 27.23/4.54 thf(s_3, axiom,
% 27.23/4.54 (is_a_theorem @
% 27.23/4.54 ( equivalent @
% 27.23/4.54 X @
% 27.23/4.54 ( equivalent @
% 27.23/4.54 X @
% 27.23/4.54 ( equivalent @
% 27.23/4.54 ( equivalent @ ( equivalent @ Y @ Z ) @ ( equivalent @ U @ Z ) ) @
% 27.23/4.54 ( equivalent @ Y @ U ) ) ) ))).
% 27.23/4.54 thf(zip_derived_cl1, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (is_a_theorem @
% 27.23/4.54 (equivalent @ X0 @
% 27.23/4.54 (equivalent @ X0 @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X3 @ X2)) @
% 27.23/4.54 (equivalent @ X1 @ X3)))))),
% 27.23/4.54 inference('cnf', [status(esa)], [s_3])).
% 27.23/4.54 thf(condensed_detachment, axiom,
% 27.23/4.54 (( ~( is_a_theorem @ ( equivalent @ X @ Y ) ) ) |
% 27.23/4.54 ( ~( is_a_theorem @ X ) ) | ( is_a_theorem @ Y ))).
% 27.23/4.54 thf(zip_derived_cl0, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 27.23/4.54 | ~ (is_a_theorem @ X0)
% 27.23/4.54 | (is_a_theorem @ X1))),
% 27.23/4.54 inference('cnf', [status(esa)], [condensed_detachment])).
% 27.23/4.54 thf(zip_derived_cl4, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ X3)
% 27.23/4.54 | (is_a_theorem @
% 27.23/4.54 (equivalent @ X3 @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)) @
% 27.23/4.54 (equivalent @ X1 @ X0)))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 27.23/4.54 thf(zip_derived_cl0, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 27.23/4.54 | ~ (is_a_theorem @ X0)
% 27.23/4.54 | (is_a_theorem @ X1))),
% 27.23/4.54 inference('cnf', [status(esa)], [condensed_detachment])).
% 27.23/4.54 thf(zip_derived_cl5, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ X3)
% 27.23/4.54 | ~ (is_a_theorem @ X3)
% 27.23/4.54 | (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)) @
% 27.23/4.54 (equivalent @ X1 @ X0))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 27.23/4.54 thf(zip_derived_cl6, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)) @
% 27.23/4.54 (equivalent @ X1 @ X0)))
% 27.23/4.54 | ~ (is_a_theorem @ X3))),
% 27.23/4.54 inference('simplify', [status(thm)], [zip_derived_cl5])).
% 27.23/4.54 thf(zip_derived_cl1, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (is_a_theorem @
% 27.23/4.54 (equivalent @ X0 @
% 27.23/4.54 (equivalent @ X0 @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X3 @ X2)) @
% 27.23/4.54 (equivalent @ X1 @ X3)))))),
% 27.23/4.54 inference('cnf', [status(esa)], [s_3])).
% 27.23/4.54 thf(zip_derived_cl11, plain,
% 27.23/4.54 (![X4 : $i, X5 : $i, X6 : $i]:
% 27.23/4.54 (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X5 @ X6) @ (equivalent @ X4 @ X6)) @
% 27.23/4.54 (equivalent @ X5 @ X4)))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 27.23/4.54 thf(zip_derived_cl11, plain,
% 27.23/4.54 (![X4 : $i, X5 : $i, X6 : $i]:
% 27.23/4.54 (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X5 @ X6) @ (equivalent @ X4 @ X6)) @
% 27.23/4.54 (equivalent @ X5 @ X4)))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 27.23/4.54 thf(zip_derived_cl0, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 27.23/4.54 | ~ (is_a_theorem @ X0)
% 27.23/4.54 | (is_a_theorem @ X1))),
% 27.23/4.54 inference('cnf', [status(esa)], [condensed_detachment])).
% 27.23/4.54 thf(zip_derived_cl30, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)))
% 27.23/4.54 | (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl0])).
% 27.23/4.54 thf(zip_derived_cl4, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ X3)
% 27.23/4.54 | (is_a_theorem @
% 27.23/4.54 (equivalent @ X3 @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)) @
% 27.23/4.54 (equivalent @ X1 @ X0)))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 27.23/4.54 thf(zip_derived_cl38, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @
% 27.23/4.54 (equivalent @ X3 @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2))))
% 27.23/4.54 | ~ (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X1 @ X0))))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl4])).
% 27.23/4.54 thf(zip_derived_cl30, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)))
% 27.23/4.54 | (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl0])).
% 27.23/4.54 thf(zip_derived_cl50, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X3 @ (equivalent @ X1 @ X0)) @
% 27.23/4.54 (equivalent @ X2 @ X1)))
% 27.23/4.54 | (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X2 @ X0))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl30])).
% 27.23/4.54 thf(zip_derived_cl11, plain,
% 27.23/4.54 (![X4 : $i, X5 : $i, X6 : $i]:
% 27.23/4.54 (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X5 @ X6) @ (equivalent @ X4 @ X6)) @
% 27.23/4.54 (equivalent @ X5 @ X4)))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 27.23/4.54 thf(zip_derived_cl109, plain,
% 27.23/4.54 (![X1 : $i, X2 : $i]:
% 27.23/4.54 (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X1 @ X2)))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl11])).
% 27.23/4.54 thf(zip_derived_cl30, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)))
% 27.23/4.54 | (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl0])).
% 27.23/4.54 thf(zip_derived_cl130, plain,
% 27.23/4.54 (![X1 : $i]: (is_a_theorem @ (equivalent @ X1 @ X1))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl30])).
% 27.23/4.54 thf(zip_derived_cl38, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @
% 27.23/4.54 (equivalent @ X3 @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2))))
% 27.23/4.54 | ~ (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X1 @ X0))))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl4])).
% 27.23/4.54 thf(zip_derived_cl0, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 27.23/4.54 | ~ (is_a_theorem @ X0)
% 27.23/4.54 | (is_a_theorem @ X1))),
% 27.23/4.54 inference('cnf', [status(esa)], [condensed_detachment])).
% 27.23/4.54 thf(zip_derived_cl46, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X2 @ X1)))
% 27.23/4.54 | ~ (is_a_theorem @ X3)
% 27.23/4.54 | (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl0])).
% 27.23/4.54 thf(zip_derived_cl146, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X1 @ X0))
% 27.23/4.54 | (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl46])).
% 27.23/4.54 thf(zip_derived_cl169, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)) @
% 27.23/4.54 X3) @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X0) @ X3)))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl146])).
% 27.23/4.54 thf(zip_derived_cl130, plain,
% 27.23/4.54 (![X1 : $i]: (is_a_theorem @ (equivalent @ X1 @ X1))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl30])).
% 27.23/4.54 thf(zip_derived_cl169, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)) @
% 27.23/4.54 X3) @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X0) @ X3)))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl146])).
% 27.23/4.54 thf(zip_derived_cl0, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 27.23/4.54 | ~ (is_a_theorem @ X0)
% 27.23/4.54 | (is_a_theorem @ X1))),
% 27.23/4.54 inference('cnf', [status(esa)], [condensed_detachment])).
% 27.23/4.54 thf(zip_derived_cl218, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X2 @ X3) @ (equivalent @ X1 @ X3)) @
% 27.23/4.54 X0))
% 27.23/4.54 | (is_a_theorem @ (equivalent @ (equivalent @ X2 @ X1) @ X0)))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl169, zip_derived_cl0])).
% 27.23/4.54 thf(zip_derived_cl146, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X1 @ X0))
% 27.23/4.54 | (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl46])).
% 27.23/4.54 thf(zip_derived_cl248, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X3 @ X1) @
% 27.23/4.54 (equivalent @ X2 @ (equivalent @ X1 @ X0))))
% 27.23/4.54 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X0) @ X2)))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl218, zip_derived_cl146])).
% 27.23/4.54 thf(zip_derived_cl30, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)))
% 27.23/4.54 | (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl0])).
% 27.23/4.54 thf(zip_derived_cl0, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 27.23/4.54 | ~ (is_a_theorem @ X0)
% 27.23/4.54 | (is_a_theorem @ X1))),
% 27.23/4.54 inference('cnf', [status(esa)], [condensed_detachment])).
% 27.23/4.54 thf(zip_derived_cl36, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @ (equivalent @ X2 @ X1))
% 27.23/4.54 | ~ (is_a_theorem @
% 27.23/4.54 (equivalent @ X3 @
% 27.23/4.54 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))
% 27.23/4.54 | ~ (is_a_theorem @ X3))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl0])).
% 27.23/4.54 thf(zip_derived_cl305, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X3 @ X0) @ (equivalent @ X2 @ X0)))
% 27.23/4.54 | (is_a_theorem @ (equivalent @ X2 @ X1))
% 27.23/4.54 | ~ (is_a_theorem @ (equivalent @ X3 @ X1)))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl248, zip_derived_cl36])).
% 27.23/4.54 thf(zip_derived_cl344, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X0 @ X1) @ (equivalent @ X2 @ X1)))
% 27.23/4.54 | (is_a_theorem @ (equivalent @ X2 @ X0)))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl305])).
% 27.23/4.54 thf(zip_derived_cl46, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X2 @ X1)))
% 27.23/4.54 | ~ (is_a_theorem @ X3)
% 27.23/4.54 | (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl0])).
% 27.23/4.54 thf(zip_derived_cl379, plain,
% 27.23/4.54 (![X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @ (equivalent @ X1 @ X2))
% 27.23/4.54 | ~ (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X2 @ X1)))
% 27.23/4.54 | ~ (is_a_theorem @ X3))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl344, zip_derived_cl46])).
% 27.23/4.54 thf(zip_derived_cl695, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @ (equivalent @ X0 @ (equivalent @ X2 @ X1)))
% 27.23/4.54 | ~ (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X2 @ X3) @ (equivalent @ X1 @ X3)) @
% 27.23/4.54 X0)))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl169, zip_derived_cl379])).
% 27.23/4.54 thf(zip_derived_cl344, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X0 @ X1) @ (equivalent @ X2 @ X1)))
% 27.23/4.54 | (is_a_theorem @ (equivalent @ X2 @ X0)))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl305])).
% 27.23/4.54 thf(zip_derived_cl146, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X1 @ X0))
% 27.23/4.54 | (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl46])).
% 27.23/4.54 thf(zip_derived_cl378, plain,
% 27.23/4.54 (![X1 : $i, X2 : $i]:
% 27.23/4.54 ( (is_a_theorem @ (equivalent @ X1 @ X2))
% 27.23/4.54 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl344, zip_derived_cl146])).
% 27.23/4.54 thf(zip_derived_cl1991, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @ (equivalent @ X0 @ (equivalent @ X3 @ X2)))
% 27.23/4.54 | ~ (is_a_theorem @
% 27.23/4.54 (equivalent @ X0 @
% 27.23/4.54 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl695, zip_derived_cl378])).
% 27.23/4.54 thf(zip_derived_cl146, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X1 @ X0))
% 27.23/4.54 | (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl46])).
% 27.23/4.54 thf(zip_derived_cl2982, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X3 @ (equivalent @ X1 @ X0)) @
% 27.23/4.54 (equivalent @ X2 @ X1)))
% 27.23/4.54 | ~ (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X2 @ X0))))),
% 27.23/4.54 inference('s_sup+', [status(thm)],
% 27.23/4.54 [zip_derived_cl1991, zip_derived_cl146])).
% 27.23/4.54 thf(zip_derived_cl50, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X3 @ (equivalent @ X1 @ X0)) @
% 27.23/4.54 (equivalent @ X2 @ X1)))
% 27.23/4.54 | (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X2 @ X0))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl30])).
% 27.23/4.54 thf(zip_derived_cl1, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (is_a_theorem @
% 27.23/4.54 (equivalent @ X0 @
% 27.23/4.54 (equivalent @ X0 @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X3 @ X2)) @
% 27.23/4.54 (equivalent @ X1 @ X3)))))),
% 27.23/4.54 inference('cnf', [status(esa)], [s_3])).
% 27.23/4.54 thf(zip_derived_cl106, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 27.23/4.54 (is_a_theorem @
% 27.23/4.54 (equivalent @ X4 @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ X4 @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)) @
% 27.23/4.54 (equivalent @ X1 @ X0)) @
% 27.23/4.54 X3)) @
% 27.23/4.54 X3)))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl1])).
% 27.23/4.54 thf(zip_derived_cl38, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @
% 27.23/4.54 (equivalent @ X3 @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2))))
% 27.23/4.54 | ~ (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X1 @ X0))))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl4])).
% 27.23/4.54 thf(zip_derived_cl11, plain,
% 27.23/4.54 (![X4 : $i, X5 : $i, X6 : $i]:
% 27.23/4.54 (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X5 @ X6) @ (equivalent @ X4 @ X6)) @
% 27.23/4.54 (equivalent @ X5 @ X4)))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 27.23/4.54 thf(zip_derived_cl6, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)) @
% 27.23/4.54 (equivalent @ X1 @ X0)))
% 27.23/4.54 | ~ (is_a_theorem @ X3))),
% 27.23/4.54 inference('simplify', [status(thm)], [zip_derived_cl5])).
% 27.23/4.54 thf(zip_derived_cl6, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)) @
% 27.23/4.54 (equivalent @ X1 @ X0)))
% 27.23/4.54 | ~ (is_a_theorem @ X3))),
% 27.23/4.54 inference('simplify', [status(thm)], [zip_derived_cl5])).
% 27.23/4.54 thf(prove_lg_2, conjecture,
% 27.23/4.54 (is_a_theorem @
% 27.23/4.54 ( equivalent @
% 27.23/4.54 a @
% 27.23/4.54 ( equivalent @
% 27.23/4.54 a @
% 27.23/4.54 ( equivalent @
% 27.23/4.54 ( equivalent @ b @ c ) @
% 27.23/4.54 ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ))).
% 27.23/4.54 thf(zf_stmt_0, negated_conjecture,
% 27.23/4.54 (~( is_a_theorem @
% 27.23/4.54 ( equivalent @
% 27.23/4.54 a @
% 27.23/4.54 ( equivalent @
% 27.23/4.54 a @
% 27.23/4.54 ( equivalent @
% 27.23/4.54 ( equivalent @ b @ c ) @
% 27.23/4.54 ( equivalent @ ( equivalent @ b @ e ) @ ( equivalent @ c @ e ) ) ) ) ) )),
% 27.23/4.54 inference('cnf.neg', [status(esa)], [prove_lg_2])).
% 27.23/4.54 thf(zip_derived_cl2, plain,
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ (equivalent @ b @ c) @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e))))))),
% 27.23/4.54 inference('cnf', [status(esa)], [zf_stmt_0])).
% 27.23/4.54 thf(zip_derived_cl0, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 27.23/4.54 | ~ (is_a_theorem @ X0)
% 27.23/4.54 | (is_a_theorem @ X1))),
% 27.23/4.54 inference('cnf', [status(esa)], [condensed_detachment])).
% 27.23/4.54 thf(zip_derived_cl3, plain,
% 27.23/4.54 (![X0 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ X0 @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ (equivalent @ b @ c) @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))))))
% 27.23/4.54 | ~ (is_a_theorem @ X0))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 27.23/4.54 thf(zip_derived_cl9, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ X1)
% 27.23/4.54 | ~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ a @ X0) @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ (equivalent @ b @ c) @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))) @
% 27.23/4.54 X0))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 27.23/4.54 thf(zip_derived_cl19, plain,
% 27.23/4.54 (![X0 : $i]:
% 27.23/4.54 ~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ a @ X0) @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ (equivalent @ b @ c) @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))) @
% 27.23/4.54 X0)))),
% 27.23/4.54 inference('condensation', [status(thm)], [zip_derived_cl9])).
% 27.23/4.54 thf(zip_derived_cl0, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 27.23/4.54 | ~ (is_a_theorem @ X0)
% 27.23/4.54 | (is_a_theorem @ X1))),
% 27.23/4.54 inference('cnf', [status(esa)], [condensed_detachment])).
% 27.23/4.54 thf(zip_derived_cl20, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ X1 @
% 27.23/4.54 (equivalent @ (equivalent @ a @ X0) @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ (equivalent @ b @ c) @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))) @
% 27.23/4.54 X0))))
% 27.23/4.54 | ~ (is_a_theorem @ X1))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl0])).
% 27.23/4.54 thf(zip_derived_cl21, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ X2)
% 27.23/4.54 | ~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ (equivalent @ a @ X0) @ X1) @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ (equivalent @ b @ c) @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))) @
% 27.23/4.54 X0) @
% 27.23/4.54 X1))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl20])).
% 27.23/4.54 thf(zip_derived_cl22, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i]:
% 27.23/4.54 ~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ (equivalent @ a @ X1) @ X0) @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ (equivalent @ b @ c) @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))) @
% 27.23/4.54 X1) @
% 27.23/4.54 X0)))),
% 27.23/4.54 inference('condensation', [status(thm)], [zip_derived_cl21])).
% 27.23/4.54 thf(zip_derived_cl0, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 27.23/4.54 | ~ (is_a_theorem @ X0)
% 27.23/4.54 | (is_a_theorem @ X1))),
% 27.23/4.54 inference('cnf', [status(esa)], [condensed_detachment])).
% 27.23/4.54 thf(zip_derived_cl23, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ X2 @
% 27.23/4.54 (equivalent @ (equivalent @ (equivalent @ a @ X1) @ X0) @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ (equivalent @ b @ c) @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))) @
% 27.23/4.54 X1) @
% 27.23/4.54 X0))))
% 27.23/4.54 | ~ (is_a_theorem @ X2))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl0])).
% 27.23/4.54 thf(zip_derived_cl35, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 ~ (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ (equivalent @ a @ X1) @ X0) @ X2) @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ (equivalent @ b @ c) @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))) @
% 27.23/4.54 X1) @
% 27.23/4.54 X0) @
% 27.23/4.54 X2)))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl23])).
% 27.23/4.54 thf(zip_derived_cl54, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 ~ (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ (equivalent @ a @ X2) @ X0) @
% 27.23/4.54 (equivalent @ X1 @ X0)) @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ (equivalent @ b @ c) @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))) @
% 27.23/4.54 X2) @
% 27.23/4.54 X1)))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl35])).
% 27.23/4.54 thf(zip_derived_cl38, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @
% 27.23/4.54 (equivalent @ X3 @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2))))
% 27.23/4.54 | ~ (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X1 @ X0))))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl4])).
% 27.23/4.54 thf(zip_derived_cl77, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 ~ (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ (equivalent @ a @ X0) @ X2) @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X0) @ X2)) @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ (equivalent @ b @ c) @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))) @
% 27.23/4.54 X1)))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl38])).
% 27.23/4.54 thf(zip_derived_cl38, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @
% 27.23/4.54 (equivalent @ X3 @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2))))
% 27.23/4.54 | ~ (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X1 @ X0))))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl4])).
% 27.23/4.54 thf(zip_derived_cl100, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 ~ (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ (equivalent @ a @ X2) @ X1) @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ X0 @
% 27.23/4.54 (equivalent @ (equivalent @ b @ c) @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))) @
% 27.23/4.54 X2) @
% 27.23/4.54 X1)) @
% 27.23/4.54 (equivalent @ a @ X0)))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl77, zip_derived_cl38])).
% 27.23/4.54 thf(zip_derived_cl0, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 27.23/4.54 | ~ (is_a_theorem @ X0)
% 27.23/4.54 | (is_a_theorem @ X1))),
% 27.23/4.54 inference('cnf', [status(esa)], [condensed_detachment])).
% 27.23/4.54 thf(zip_derived_cl157, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ X3 @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ (equivalent @ a @ X2) @ X1) @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ X0 @
% 27.23/4.54 (equivalent @ (equivalent @ b @ c) @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))) @
% 27.23/4.54 X2) @
% 27.23/4.54 X1)) @
% 27.23/4.54 (equivalent @ a @ X0))))
% 27.23/4.54 | ~ (is_a_theorem @ X3))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl0])).
% 27.23/4.54 thf(zip_derived_cl1209, plain,
% 27.23/4.54 (![X0 : $i]:
% 27.23/4.54 ~ (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ a @ (equivalent @ X0 @ (equivalent @ b @ c))) @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ X0 @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e))))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl157])).
% 27.23/4.54 thf(zip_derived_cl305, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X3 @ X0) @ (equivalent @ X2 @ X0)))
% 27.23/4.54 | (is_a_theorem @ (equivalent @ X2 @ X1))
% 27.23/4.54 | ~ (is_a_theorem @ (equivalent @ X3 @ X1)))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl248, zip_derived_cl36])).
% 27.23/4.54 thf(zip_derived_cl1218, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X2 @ X1) @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ a @ (equivalent @ X0 @ (equivalent @ b @ c))) @ X1)))
% 27.23/4.54 | ~ (is_a_theorem @
% 27.23/4.54 (equivalent @ X2 @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ X0 @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))))))),
% 27.23/4.54 inference('s_sup+', [status(thm)],
% 27.23/4.54 [zip_derived_cl1209, zip_derived_cl305])).
% 27.23/4.54 thf(zip_derived_cl146, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i]:
% 27.23/4.54 (~ (is_a_theorem @ (equivalent @ X1 @ X0))
% 27.23/4.54 | (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl46])).
% 27.23/4.54 thf(zip_derived_cl1270, plain,
% 27.23/4.54 (![X1 : $i, X2 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ X2 @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ X1 @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e))))))
% 27.23/4.54 | ~ (is_a_theorem @
% 27.23/4.54 (equivalent @ X2 @
% 27.23/4.54 (equivalent @ a @ (equivalent @ X1 @ (equivalent @ b @ c))))))),
% 27.23/4.54 inference('s_sup+', [status(thm)],
% 27.23/4.54 [zip_derived_cl1218, zip_derived_cl146])).
% 27.23/4.54 thf(zip_derived_cl378, plain,
% 27.23/4.54 (![X1 : $i, X2 : $i]:
% 27.23/4.54 ( (is_a_theorem @ (equivalent @ X1 @ X2))
% 27.23/4.54 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl344, zip_derived_cl146])).
% 27.23/4.54 thf(zip_derived_cl1317, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ X1 @
% 27.23/4.54 (equivalent @ a @ (equivalent @ X0 @ (equivalent @ b @ c)))))
% 27.23/4.54 | ~ (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ X0 @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))) @
% 27.23/4.54 X1)))),
% 27.23/4.54 inference('s_sup+', [status(thm)],
% 27.23/4.54 [zip_derived_cl1270, zip_derived_cl378])).
% 27.23/4.54 thf(zip_derived_cl4674, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ X1 @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))))
% 27.23/4.54 | ~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X0) @
% 27.23/4.54 (equivalent @ a @ (equivalent @ X0 @ (equivalent @ b @ c))))))),
% 27.23/4.54 inference('s_sup-', [status(thm)],
% 27.23/4.54 [zip_derived_cl2982, zip_derived_cl1317])).
% 27.23/4.54 thf(zip_derived_cl248, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X3 @ X1) @
% 27.23/4.54 (equivalent @ X2 @ (equivalent @ X1 @ X0))))
% 27.23/4.54 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X0) @ X2)))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl218, zip_derived_cl146])).
% 27.23/4.54 thf(zip_derived_cl4733, plain,
% 27.23/4.54 (![X1 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ X1 @
% 27.23/4.54 (equivalent @ (equivalent @ b @ e) @ (equivalent @ c @ e)))))
% 27.23/4.54 | ~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ (equivalent @ b @ c)) @ a)))),
% 27.23/4.54 inference('s_sup+', [status(thm)],
% 27.23/4.54 [zip_derived_cl4674, zip_derived_cl248])).
% 27.23/4.54 thf(zip_derived_cl38, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 ( (is_a_theorem @
% 27.23/4.54 (equivalent @ X3 @
% 27.23/4.54 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2))))
% 27.23/4.54 | ~ (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X1 @ X0))))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl4])).
% 27.23/4.54 thf(zip_derived_cl4746, plain,
% 27.23/4.54 (![X0 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @
% 27.23/4.54 (equivalent @ (equivalent @ X0 @ (equivalent @ c @ e)) @
% 27.23/4.54 (equivalent @ b @ c)) @
% 27.23/4.54 a))
% 27.23/4.54 | ~ (is_a_theorem @
% 27.23/4.54 (equivalent @ a @ (equivalent @ X0 @ (equivalent @ b @ e)))))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl4733, zip_derived_cl38])).
% 27.23/4.54 thf(zip_derived_cl378, plain,
% 27.23/4.54 (![X1 : $i, X2 : $i]:
% 27.23/4.54 ( (is_a_theorem @ (equivalent @ X1 @ X2))
% 27.23/4.54 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 27.23/4.54 inference('s_sup+', [status(thm)], [zip_derived_cl344, zip_derived_cl146])).
% 27.23/4.54 thf(zip_derived_cl4777, plain,
% 27.23/4.54 (![X0 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ a @ (equivalent @ X0 @ (equivalent @ b @ e))))
% 27.23/4.54 | ~ (is_a_theorem @
% 27.23/4.54 (equivalent @ a @
% 27.23/4.54 (equivalent @ (equivalent @ X0 @ (equivalent @ c @ e)) @
% 27.23/4.54 (equivalent @ b @ c)))))),
% 27.23/4.54 inference('s_sup+', [status(thm)],
% 27.23/4.54 [zip_derived_cl4746, zip_derived_cl378])).
% 27.23/4.54 thf(zip_derived_cl50, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.54 (~ (is_a_theorem @
% 27.23/4.54 (equivalent @ (equivalent @ X3 @ (equivalent @ X1 @ X0)) @
% 27.23/4.54 (equivalent @ X2 @ X1)))
% 27.23/4.54 | (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X2 @ X0))))),
% 27.23/4.54 inference('s_sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl30])).
% 27.23/4.54 thf(zip_derived_cl4, plain,
% 27.23/4.54 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.55 (~ (is_a_theorem @ X3)
% 27.23/4.55 | (is_a_theorem @
% 27.23/4.55 (equivalent @ X3 @
% 27.23/4.55 (equivalent @
% 27.23/4.55 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)) @
% 27.23/4.55 (equivalent @ X1 @ X0)))))),
% 27.23/4.55 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 27.23/4.55 thf(zip_derived_cl107, plain,
% 27.23/4.55 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 27.23/4.55 ( (is_a_theorem @
% 27.23/4.55 (equivalent @ X4 @
% 27.23/4.55 (equivalent @
% 27.23/4.55 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)) @
% 27.23/4.55 X3)))
% 27.23/4.55 | ~ (is_a_theorem @
% 27.23/4.55 (equivalent @ X4 @ (equivalent @ (equivalent @ X1 @ X0) @ X3))))),
% 27.23/4.55 inference('s_sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl4])).
% 27.23/4.55 thf(zip_derived_cl4941, plain,
% 27.23/4.55 (![X0 : $i]:
% 27.23/4.55 (~ (is_a_theorem @
% 27.23/4.55 (equivalent @ a @
% 27.23/4.55 (equivalent @ (equivalent @ X0 @ e) @ (equivalent @ b @ e))))
% 27.23/4.55 | ~ (is_a_theorem @
% 27.23/4.55 (equivalent @ a @
% 27.23/4.55 (equivalent @ (equivalent @ X0 @ c) @ (equivalent @ b @ c)))))),
% 27.23/4.55 inference('s_sup+', [status(thm)],
% 27.23/4.55 [zip_derived_cl4777, zip_derived_cl107])).
% 27.23/4.55 thf(zip_derived_cl38, plain,
% 27.23/4.55 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.55 ( (is_a_theorem @
% 27.23/4.55 (equivalent @ X3 @
% 27.23/4.55 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2))))
% 27.23/4.55 | ~ (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X1 @ X0))))),
% 27.23/4.55 inference('s_sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl4])).
% 27.23/4.55 thf(zip_derived_cl4953, plain,
% 27.23/4.55 (![X0 : $i]:
% 27.23/4.55 (~ (is_a_theorem @
% 27.23/4.55 (equivalent @ a @
% 27.23/4.55 (equivalent @ (equivalent @ X0 @ c) @ (equivalent @ b @ c))))
% 27.23/4.55 | ~ (is_a_theorem @ (equivalent @ a @ (equivalent @ X0 @ b))))),
% 27.23/4.55 inference('s_sup+', [status(thm)], [zip_derived_cl4941, zip_derived_cl38])).
% 27.23/4.55 thf(zip_derived_cl38, plain,
% 27.23/4.55 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 27.23/4.55 ( (is_a_theorem @
% 27.23/4.55 (equivalent @ X3 @
% 27.23/4.55 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2))))
% 27.23/4.55 | ~ (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X1 @ X0))))),
% 27.23/4.55 inference('s_sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl4])).
% 27.23/4.55 thf(zip_derived_cl4957, plain,
% 27.23/4.55 (![X0 : $i]: ~ (is_a_theorem @ (equivalent @ a @ (equivalent @ X0 @ b)))),
% 27.23/4.55 inference('clc', [status(thm)], [zip_derived_cl4953, zip_derived_cl38])).
% 27.23/4.55 thf(zip_derived_cl106, plain,
% 27.23/4.55 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 27.23/4.55 (is_a_theorem @
% 27.23/4.55 (equivalent @ X4 @
% 27.23/4.55 (equivalent @
% 27.23/4.55 (equivalent @ X4 @
% 27.23/4.55 (equivalent @
% 27.23/4.55 (equivalent @
% 27.23/4.55 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)) @
% 27.23/4.55 (equivalent @ X1 @ X0)) @
% 27.23/4.55 X3)) @
% 27.23/4.55 X3)))),
% 27.23/4.55 inference('s_sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl1])).
% 27.23/4.55 thf(zip_derived_cl4969, plain, ($false),
% 27.23/4.55 inference('s_sup+', [status(thm)],
% 27.23/4.55 [zip_derived_cl4957, zip_derived_cl106])).
% 27.23/4.55
% 27.23/4.55 % SZS output end Refutation
% 27.23/4.55
% 27.23/4.55
% 27.23/4.55 % Terminating...
% 27.23/4.59 % Runner terminated.
% 5.21/4.62 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------