%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL121-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.P2u0nOBmFo true
% Computer : n028.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 01:35:14 PM UTC 2026
% Result : Unsatisfiable 16.89s 3.41s
% Output : Refutation 16.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL121-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.P2u0nOBmFo true
% 0.11/0.37 % Computer : n028.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 6 01:36:45 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Running portfolio for 300 s
% 0.11/0.38 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.38 % Number of cores: 8
% 0.15/0.38 % Python version: Python 3.12.3
% 0.15/0.39 % Running in FO mode
% 0.45/0.66 % Total configuration time : 435
% 0.45/0.66 % Estimated wc time : 1092
% 0.45/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.49/0.74 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.49/0.81 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.49/0.81 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.49/0.81 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.49/0.81 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.49/0.81 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.49/0.81 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 16.89/3.41 % Solved by fo/fo13.sh.
% 16.89/3.41 % done 793 iterations in 2.566s
% 16.89/3.41 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 16.89/3.41 % SZS output start Refutation
% 16.89/3.41 thf(c_type, type, c: $i).
% 16.89/3.41 thf(is_a_theorem_type, type, is_a_theorem: $i > $o).
% 16.89/3.41 thf(equivalent_type, type, equivalent: $i > $i > $i).
% 16.89/3.41 thf(b_type, type, b: $i).
% 16.89/3.41 thf(a_type, type, a: $i).
% 16.89/3.41 thf(lg_2, axiom,
% 16.89/3.41 (is_a_theorem @
% 16.89/3.41 ( equivalent @
% 16.89/3.41 X @
% 16.89/3.41 ( equivalent @
% 16.89/3.41 X @
% 16.89/3.41 ( equivalent @
% 16.89/3.41 ( equivalent @ Y @ Z ) @
% 16.89/3.41 ( equivalent @ ( equivalent @ Y @ U ) @ ( equivalent @ Z @ U ) ) ) ) ))).
% 16.89/3.41 thf(zip_derived_cl1, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (is_a_theorem @
% 16.89/3.41 (equivalent @ X0 @
% 16.89/3.41 (equivalent @ X0 @
% 16.89/3.41 (equivalent @ (equivalent @ X1 @ X2) @
% 16.89/3.41 (equivalent @ (equivalent @ X1 @ X3) @ (equivalent @ X2 @ X3))))))),
% 16.89/3.41 inference('cnf', [status(esa)], [lg_2])).
% 16.89/3.41 thf(condensed_detachment, axiom,
% 16.89/3.41 (( ~( is_a_theorem @ ( equivalent @ X @ Y ) ) ) |
% 16.89/3.41 ( ~( is_a_theorem @ X ) ) | ( is_a_theorem @ Y ))).
% 16.89/3.41 thf(zip_derived_cl0, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 16.89/3.41 | ~ (is_a_theorem @ X0)
% 16.89/3.41 | (is_a_theorem @ X1))),
% 16.89/3.41 inference('cnf', [status(esa)], [condensed_detachment])).
% 16.89/3.41 thf(zip_derived_cl4, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ X3)
% 16.89/3.41 | (is_a_theorem @
% 16.89/3.41 (equivalent @ X3 @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X1) @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl0, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 16.89/3.41 | ~ (is_a_theorem @ X0)
% 16.89/3.41 | (is_a_theorem @ X1))),
% 16.89/3.41 inference('cnf', [status(esa)], [condensed_detachment])).
% 16.89/3.41 thf(zip_derived_cl5, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ X3)
% 16.89/3.41 | ~ (is_a_theorem @ X3)
% 16.89/3.41 | (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X1) @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl6, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 ( (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X1) @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))
% 16.89/3.41 | ~ (is_a_theorem @ X3))),
% 16.89/3.41 inference('simplify', [status(thm)], [zip_derived_cl5])).
% 16.89/3.41 thf(zip_derived_cl1, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (is_a_theorem @
% 16.89/3.41 (equivalent @ X0 @
% 16.89/3.41 (equivalent @ X0 @
% 16.89/3.41 (equivalent @ (equivalent @ X1 @ X2) @
% 16.89/3.41 (equivalent @ (equivalent @ X1 @ X3) @ (equivalent @ X2 @ X3))))))),
% 16.89/3.41 inference('cnf', [status(esa)], [lg_2])).
% 16.89/3.41 thf(zip_derived_cl10, plain,
% 16.89/3.41 (![X4 : $i, X5 : $i, X6 : $i]:
% 16.89/3.41 (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X6 @ X5) @
% 16.89/3.41 (equivalent @ (equivalent @ X6 @ X4) @ (equivalent @ X5 @ X4))))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 16.89/3.41 thf(zip_derived_cl6, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 ( (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X1) @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))
% 16.89/3.41 | ~ (is_a_theorem @ X3))),
% 16.89/3.41 inference('simplify', [status(thm)], [zip_derived_cl5])).
% 16.89/3.41 thf(zip_derived_cl0, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 16.89/3.41 | ~ (is_a_theorem @ X0)
% 16.89/3.41 | (is_a_theorem @ X1))),
% 16.89/3.41 inference('cnf', [status(esa)], [condensed_detachment])).
% 16.89/3.41 thf(zip_derived_cl8, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ X3)
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X2 @ X1))
% 16.89/3.41 | (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl18, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.89/3.41 ( (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 16.89/3.41 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 16.89/3.41 thf(zip_derived_cl23, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ (equivalent @ X2 @ X1) @ X3) @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)) @
% 16.89/3.41 X3)))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl18])).
% 16.89/3.41 thf(zip_derived_cl0, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 16.89/3.41 | ~ (is_a_theorem @ X0)
% 16.89/3.41 | (is_a_theorem @ X1))),
% 16.89/3.41 inference('cnf', [status(esa)], [condensed_detachment])).
% 16.89/3.41 thf(zip_derived_cl24, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 16.89/3.41 | (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 16.89/3.41 X0)))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl18, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.89/3.41 ( (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 16.89/3.41 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 16.89/3.41 thf(zip_derived_cl27, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 16.89/3.41 | (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 16.89/3.41 X4) @
% 16.89/3.41 (equivalent @ X0 @ X4))))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl18])).
% 16.89/3.41 thf(zip_derived_cl24, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 16.89/3.41 | (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 16.89/3.41 X0)))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl0, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 16.89/3.41 | ~ (is_a_theorem @ X0)
% 16.89/3.41 | (is_a_theorem @ X1))),
% 16.89/3.41 inference('cnf', [status(esa)], [condensed_detachment])).
% 16.89/3.41 thf(zip_derived_cl26, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 16.89/3.41 | ~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 16.89/3.41 | (is_a_theorem @ X0))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl74, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 16.89/3.41 | ~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ X0 @ X0))))),
% 16.89/3.41 inference('eq_fact', [status(thm)], [zip_derived_cl26])).
% 16.89/3.41 thf(zip_derived_cl18, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.89/3.41 ( (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 16.89/3.41 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 16.89/3.41 thf(zip_derived_cl89, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl18])).
% 16.89/3.41 thf(zip_derived_cl195, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X4 @ X3) @ X1))
% 16.89/3.41 | (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ X1 @ X0))))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl89])).
% 16.89/3.41 thf(zip_derived_cl26, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 16.89/3.41 | ~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 16.89/3.41 | (is_a_theorem @ X0))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl305, plain,
% 16.89/3.41 (![X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X1))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X1 @ X1) @ X4))
% 16.89/3.41 | (is_a_theorem @ X4))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl195, zip_derived_cl26])).
% 16.89/3.41 thf(zip_derived_cl410, plain,
% 16.89/3.41 (![X0 : $i]:
% 16.89/3.41 ( (is_a_theorem @ X0)
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X0 @ X0) @ X0)))),
% 16.89/3.41 inference('eq_fact', [status(thm)], [zip_derived_cl305])).
% 16.89/3.41 thf(zip_derived_cl24, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 16.89/3.41 | (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 16.89/3.41 X0)))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl415, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 16.89/3.41 | ~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X1 @ X1) @ (equivalent @ X1 @ X0))))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl410, zip_derived_cl24])).
% 16.89/3.41 thf(zip_derived_cl89, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl18])).
% 16.89/3.41 thf(zip_derived_cl422, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X1 @ (equivalent @ X0 @ X0))))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl415, zip_derived_cl89])).
% 16.89/3.41 thf(zip_derived_cl10, plain,
% 16.89/3.41 (![X4 : $i, X5 : $i, X6 : $i]:
% 16.89/3.41 (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X6 @ X5) @
% 16.89/3.41 (equivalent @ (equivalent @ X6 @ X4) @ (equivalent @ X5 @ X4))))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 16.89/3.41 thf(zip_derived_cl443, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ X1 @ X0)))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl422, zip_derived_cl10])).
% 16.89/3.41 thf(zip_derived_cl422, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X1 @ (equivalent @ X0 @ X0))))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl415, zip_derived_cl89])).
% 16.89/3.41 thf(zip_derived_cl486, plain,
% 16.89/3.41 (![X0 : $i]: (is_a_theorem @ (equivalent @ X0 @ X0))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl443, zip_derived_cl422])).
% 16.89/3.41 thf(zip_derived_cl26, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 16.89/3.41 | ~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 16.89/3.41 | (is_a_theorem @ X0))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl527, plain,
% 16.89/3.41 (![X1 : $i, X2 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X1 @ X1) @ X2))
% 16.89/3.41 | (is_a_theorem @ X2))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl486, zip_derived_cl26])).
% 16.89/3.41 thf(zip_derived_cl23, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ (equivalent @ X2 @ X1) @ X3) @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)) @
% 16.89/3.41 X3)))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl18])).
% 16.89/3.41 thf(zip_derived_cl561, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.89/3.41 (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)) @
% 16.89/3.41 (equivalent @ X1 @ X0)))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl527, zip_derived_cl23])).
% 16.89/3.41 thf(zip_derived_cl24, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 16.89/3.41 | (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 16.89/3.41 X0)))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl10, plain,
% 16.89/3.41 (![X4 : $i, X5 : $i, X6 : $i]:
% 16.89/3.41 (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X6 @ X5) @
% 16.89/3.41 (equivalent @ (equivalent @ X6 @ X4) @ (equivalent @ X5 @ X4))))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 16.89/3.41 thf(zip_derived_cl10, plain,
% 16.89/3.41 (![X4 : $i, X5 : $i, X6 : $i]:
% 16.89/3.41 (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X6 @ X5) @
% 16.89/3.41 (equivalent @ (equivalent @ X6 @ X4) @ (equivalent @ X5 @ X4))))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 16.89/3.41 thf(zip_derived_cl4, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ X3)
% 16.89/3.41 | (is_a_theorem @
% 16.89/3.41 (equivalent @ X3 @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X1) @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl24, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 16.89/3.41 | (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 16.89/3.41 X0)))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 16.89/3.41 thf(prove_lg_1, conjecture,
% 16.89/3.41 (is_a_theorem @
% 16.89/3.41 ( equivalent @
% 16.89/3.41 a @
% 16.89/3.41 ( equivalent @
% 16.89/3.41 a @ ( equivalent @ ( equivalent @ b @ ( equivalent @ c @ c ) ) @ b ) ) ))).
% 16.89/3.41 thf(zf_stmt_0, negated_conjecture,
% 16.89/3.41 (~( is_a_theorem @
% 16.89/3.41 ( equivalent @
% 16.89/3.41 a @
% 16.89/3.41 ( equivalent @
% 16.89/3.41 a @
% 16.89/3.41 ( equivalent @ ( equivalent @ b @ ( equivalent @ c @ c ) ) @ b ) ) ) )),
% 16.89/3.41 inference('cnf.neg', [status(esa)], [prove_lg_1])).
% 16.89/3.41 thf(zip_derived_cl2, plain,
% 16.89/3.41 (~ (is_a_theorem @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ (equivalent @ b @ (equivalent @ c @ c)) @ b))))),
% 16.89/3.41 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.89/3.41 thf(zip_derived_cl0, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 16.89/3.41 | ~ (is_a_theorem @ X0)
% 16.89/3.41 | (is_a_theorem @ X1))),
% 16.89/3.41 inference('cnf', [status(esa)], [condensed_detachment])).
% 16.89/3.41 thf(zip_derived_cl3, plain,
% 16.89/3.41 (![X0 : $i]:
% 16.89/3.41 (~ (is_a_theorem @
% 16.89/3.41 (equivalent @ X0 @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ (equivalent @ b @ (equivalent @ c @ c)) @ b)))))
% 16.89/3.41 | ~ (is_a_theorem @ X0))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl28, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.89/3.41 (~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X1) @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ (equivalent @ b @ (equivalent @ c @ c)) @ b)))))
% 16.89/3.41 | ~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl3])).
% 16.89/3.41 thf(zip_derived_cl0, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 16.89/3.41 | ~ (is_a_theorem @ X0)
% 16.89/3.41 | (is_a_theorem @ X1))),
% 16.89/3.41 inference('cnf', [status(esa)], [condensed_detachment])).
% 16.89/3.41 thf(zip_derived_cl29, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)))
% 16.89/3.41 | ~ (is_a_theorem @
% 16.89/3.41 (equivalent @ X3 @
% 16.89/3.41 (equivalent @ (equivalent @ X1 @ X0) @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ (equivalent @ b @ (equivalent @ c @ c)) @ b))))))
% 16.89/3.41 | ~ (is_a_theorem @ X3))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl77, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 16.89/3.41 (~ (is_a_theorem @
% 16.89/3.41 (equivalent @ X3 @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))
% 16.89/3.41 | ~ (is_a_theorem @
% 16.89/3.41 (equivalent @ X4 @
% 16.89/3.41 (equivalent @ (equivalent @ X3 @ (equivalent @ X2 @ X1)) @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ (equivalent @ b @ (equivalent @ c @ c)) @ b))))))
% 16.89/3.41 | ~ (is_a_theorem @ X4))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl29])).
% 16.89/3.41 thf(zip_derived_cl116, plain,
% 16.89/3.41 (![X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @
% 16.89/3.41 (equivalent @ X3 @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X1) @ (equivalent @ X2 @ X1)) @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ (equivalent @ b @ (equivalent @ c @ c)) @ b))))))
% 16.89/3.41 | ~ (is_a_theorem @ X3))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl77])).
% 16.89/3.41 thf(zip_derived_cl121, plain,
% 16.89/3.41 (~ (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ (equivalent @ b @ (equivalent @ c @ c)) @ b)) @
% 16.89/3.41 a))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl116])).
% 16.89/3.41 thf(zip_derived_cl26, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 16.89/3.41 | ~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 16.89/3.41 | (is_a_theorem @ X0))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl18, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.89/3.41 ( (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 16.89/3.41 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 16.89/3.41 thf(zip_derived_cl53, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 16.89/3.41 | ~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X3) @ (equivalent @ X0 @ X3)))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl18])).
% 16.89/3.41 thf(zip_derived_cl147, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 (~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ a @ X0)))
% 16.89/3.41 | ~ (is_a_theorem @
% 16.89/3.41 (equivalent @ X1 @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ (equivalent @ b @ (equivalent @ c @ c)) @ b)))))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl53])).
% 16.89/3.41 thf(zip_derived_cl18, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.89/3.41 ( (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 16.89/3.41 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 16.89/3.41 thf(zip_derived_cl165, plain,
% 16.89/3.41 (![X1 : $i]:
% 16.89/3.41 (~ (is_a_theorem @
% 16.89/3.41 (equivalent @ X1 @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ (equivalent @ b @ (equivalent @ c @ c)) @ b))))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X1 @ a)))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl147, zip_derived_cl18])).
% 16.89/3.41 thf(zip_derived_cl173, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X2 @ X1) @ a))
% 16.89/3.41 | ~ (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)) @
% 16.89/3.41 (equivalent @ a @
% 16.89/3.41 (equivalent @ (equivalent @ b @ (equivalent @ c @ c)) @ b)))))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl165])).
% 16.89/3.41 thf(zip_derived_cl18, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.89/3.41 ( (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 16.89/3.41 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 16.89/3.41 thf(zip_derived_cl352, plain,
% 16.89/3.41 (![X0 : $i]:
% 16.89/3.41 (~ (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ X0 @ (equivalent @ b @ (equivalent @ c @ c))) @ a))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X0 @ b) @ a)))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl173, zip_derived_cl18])).
% 16.89/3.41 thf(zip_derived_cl24, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 16.89/3.41 | (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 16.89/3.41 X0)))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl356, plain,
% 16.89/3.41 (![X0 : $i]:
% 16.89/3.41 (~ (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X0 @ (equivalent @ c @ c)) @ b) @ a))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X0 @ b) @ a)))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl352, zip_derived_cl24])).
% 16.89/3.41 thf(zip_derived_cl23, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ (equivalent @ X2 @ X1) @ X3) @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)) @
% 16.89/3.41 X3)))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl18])).
% 16.89/3.41 thf(zip_derived_cl18, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.89/3.41 ( (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 16.89/3.41 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 16.89/3.41 thf(zip_derived_cl25, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 16.89/3.41 (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ (equivalent @ X3 @ X2) @ X0) @ X4) @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 16.89/3.41 X0) @
% 16.89/3.41 X4)))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl18])).
% 16.89/3.41 thf(zip_derived_cl0, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 16.89/3.41 | ~ (is_a_theorem @ X0)
% 16.89/3.41 | (is_a_theorem @ X1))),
% 16.89/3.41 inference('cnf', [status(esa)], [condensed_detachment])).
% 16.89/3.41 thf(zip_derived_cl130, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 16.89/3.41 (~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ (equivalent @ X4 @ X3) @ X1) @ X0))
% 16.89/3.41 | (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X4 @ X2) @ (equivalent @ X3 @ X2)) @
% 16.89/3.41 X1) @
% 16.89/3.41 X0)))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl3427, plain,
% 16.89/3.41 (![X0 : $i]:
% 16.89/3.41 (~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ (equivalent @ X0 @ c) @ b) @ a))
% 16.89/3.41 | ~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ (equivalent @ X0 @ c) @ b) @ a)))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl356, zip_derived_cl130])).
% 16.89/3.41 thf(zip_derived_cl3431, plain,
% 16.89/3.41 (![X0 : $i]:
% 16.89/3.41 ~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ (equivalent @ X0 @ c) @ b) @ a))),
% 16.89/3.41 inference('simplify', [status(thm)], [zip_derived_cl3427])).
% 16.89/3.41 thf(zip_derived_cl0, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 16.89/3.41 | ~ (is_a_theorem @ X0)
% 16.89/3.41 | (is_a_theorem @ X1))),
% 16.89/3.41 inference('cnf', [status(esa)], [condensed_detachment])).
% 16.89/3.41 thf(zip_derived_cl3434, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 (~ (is_a_theorem @
% 16.89/3.41 (equivalent @ X1 @
% 16.89/3.41 (equivalent @ (equivalent @ (equivalent @ X0 @ c) @ b) @ a)))
% 16.89/3.41 | ~ (is_a_theorem @ X1))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl3431, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl3452, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 ~ (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ (equivalent @ X0 @ c) @ b) @ X1) @
% 16.89/3.41 (equivalent @ a @ X1)))),
% 16.89/3.41 inference('s_sup-', [status(thm)],
% 16.89/3.41 [zip_derived_cl561, zip_derived_cl3434])).
% 16.89/3.41 thf(zip_derived_cl24, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 16.89/3.41 | (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 16.89/3.41 X0)))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl3533, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 ~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ (equivalent @ X1 @ c) @ X0) @
% 16.89/3.41 (equivalent @ a @ (equivalent @ X0 @ b))))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl3452, zip_derived_cl24])).
% 16.89/3.41 thf(zip_derived_cl24, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 16.89/3.41 | (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 16.89/3.41 X0)))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 16.89/3.41 thf(zip_derived_cl3630, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 ~ (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X1 @ X0) @
% 16.89/3.41 (equivalent @ a @ (equivalent @ (equivalent @ X0 @ c) @ b))))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl3533, zip_derived_cl24])).
% 16.89/3.41 thf(zip_derived_cl527, plain,
% 16.89/3.41 (![X1 : $i, X2 : $i]:
% 16.89/3.41 (~ (is_a_theorem @ (equivalent @ (equivalent @ X1 @ X1) @ X2))
% 16.89/3.41 | (is_a_theorem @ X2))),
% 16.89/3.41 inference('s_sup-', [status(thm)], [zip_derived_cl486, zip_derived_cl26])).
% 16.89/3.41 thf(zip_derived_cl18, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.89/3.41 ( (is_a_theorem @
% 16.89/3.41 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 16.89/3.41 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 16.89/3.41 thf(zip_derived_cl558, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 16.89/3.41 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl527, zip_derived_cl18])).
% 16.89/3.41 thf(zip_derived_cl3895, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i]:
% 16.89/3.41 ~ (is_a_theorem @
% 16.89/3.41 (equivalent @
% 16.89/3.41 (equivalent @ a @ (equivalent @ (equivalent @ X0 @ c) @ b)) @
% 16.89/3.41 (equivalent @ X1 @ X0)))),
% 16.89/3.41 inference('s_sup+', [status(thm)],
% 16.89/3.41 [zip_derived_cl3630, zip_derived_cl558])).
% 16.89/3.41 thf(zip_derived_cl1, plain,
% 16.89/3.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.89/3.41 (is_a_theorem @
% 16.89/3.41 (equivalent @ X0 @
% 16.89/3.41 (equivalent @ X0 @
% 16.89/3.41 (equivalent @ (equivalent @ X1 @ X2) @
% 16.89/3.41 (equivalent @ (equivalent @ X1 @ X3) @ (equivalent @ X2 @ X3))))))),
% 16.89/3.41 inference('cnf', [status(esa)], [lg_2])).
% 16.89/3.41 thf(zip_derived_cl3935, plain, ($false),
% 16.89/3.41 inference('s_sup+', [status(thm)], [zip_derived_cl3895, zip_derived_cl1])).
% 16.89/3.41
% 16.89/3.41 % SZS output end Refutation
% 16.89/3.41
% 16.89/3.41
% 16.89/3.41 % Terminating...
% 16.89/3.46 % Runner terminated.
% 16.89/3.48 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------