%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL124-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.YnlzeRdv1s true
% Computer : n027.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 36.88s 6.00s
% Output : Refutation 36.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL124-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.YnlzeRdv1s true
% 0.10/0.36 % Computer : n027.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 4 14:14:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Running portfolio for 300 s
% 0.10/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Number of cores: 8
% 0.10/0.37 % Python version: Python 3.12.3
% 0.10/0.37 % 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
% 0.48/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.48/0.80 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.49/0.80 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.49/0.80 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.49/0.80 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.49/0.80 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.49/0.80 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 36.88/6.00 % Solved by fo/fo13.sh.
% 36.88/6.00 % done 1132 iterations in 5.167s
% 36.88/6.00 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 36.88/6.00 % SZS output start Refutation
% 36.88/6.00 thf(c_type, type, c: $i).
% 36.88/6.00 thf(is_a_theorem_type, type, is_a_theorem: $i > $o).
% 36.88/6.00 thf(equivalent_type, type, equivalent: $i > $i > $i).
% 36.88/6.00 thf(f_type, type, f: $i).
% 36.88/6.00 thf(b_type, type, b: $i).
% 36.88/6.00 thf(e_type, type, e: $i).
% 36.88/6.00 thf(a_type, type, a: $i).
% 36.88/6.00 thf(lg_2, axiom,
% 36.88/6.00 (is_a_theorem @
% 36.88/6.00 ( equivalent @
% 36.88/6.00 X @
% 36.88/6.00 ( equivalent @
% 36.88/6.00 X @
% 36.88/6.00 ( equivalent @
% 36.88/6.00 ( equivalent @ Y @ Z ) @
% 36.88/6.00 ( equivalent @ ( equivalent @ Y @ U ) @ ( equivalent @ Z @ U ) ) ) ) ))).
% 36.88/6.00 thf(zip_derived_cl1, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (is_a_theorem @
% 36.88/6.00 (equivalent @ X0 @
% 36.88/6.00 (equivalent @ X0 @
% 36.88/6.00 (equivalent @ (equivalent @ X1 @ X2) @
% 36.88/6.00 (equivalent @ (equivalent @ X1 @ X3) @ (equivalent @ X2 @ X3))))))),
% 36.88/6.00 inference('cnf', [status(esa)], [lg_2])).
% 36.88/6.00 thf(condensed_detachment, axiom,
% 36.88/6.00 (( ~( is_a_theorem @ ( equivalent @ X @ Y ) ) ) |
% 36.88/6.00 ( ~( is_a_theorem @ X ) ) | ( is_a_theorem @ Y ))).
% 36.88/6.00 thf(zip_derived_cl0, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 36.88/6.00 | ~ (is_a_theorem @ X0)
% 36.88/6.00 | (is_a_theorem @ X1))),
% 36.88/6.00 inference('cnf', [status(esa)], [condensed_detachment])).
% 36.88/6.00 thf(zip_derived_cl4, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ X3)
% 36.88/6.00 | (is_a_theorem @
% 36.88/6.00 (equivalent @ X3 @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X1) @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl0, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 36.88/6.00 | ~ (is_a_theorem @ X0)
% 36.88/6.00 | (is_a_theorem @ X1))),
% 36.88/6.00 inference('cnf', [status(esa)], [condensed_detachment])).
% 36.88/6.00 thf(zip_derived_cl5, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ X3)
% 36.88/6.00 | ~ (is_a_theorem @ X3)
% 36.88/6.00 | (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X1) @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl6, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 ( (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X1) @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))
% 36.88/6.00 | ~ (is_a_theorem @ X3))),
% 36.88/6.00 inference('simplify', [status(thm)], [zip_derived_cl5])).
% 36.88/6.00 thf(zip_derived_cl1, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (is_a_theorem @
% 36.88/6.00 (equivalent @ X0 @
% 36.88/6.00 (equivalent @ X0 @
% 36.88/6.00 (equivalent @ (equivalent @ X1 @ X2) @
% 36.88/6.00 (equivalent @ (equivalent @ X1 @ X3) @ (equivalent @ X2 @ X3))))))),
% 36.88/6.00 inference('cnf', [status(esa)], [lg_2])).
% 36.88/6.00 thf(zip_derived_cl10, plain,
% 36.88/6.00 (![X4 : $i, X5 : $i, X6 : $i]:
% 36.88/6.00 (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X6 @ X5) @
% 36.88/6.00 (equivalent @ (equivalent @ X6 @ X4) @ (equivalent @ X5 @ X4))))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 36.88/6.00 thf(zip_derived_cl6, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 ( (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X1) @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))
% 36.88/6.00 | ~ (is_a_theorem @ X3))),
% 36.88/6.00 inference('simplify', [status(thm)], [zip_derived_cl5])).
% 36.88/6.00 thf(zip_derived_cl0, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 36.88/6.00 | ~ (is_a_theorem @ X0)
% 36.88/6.00 | (is_a_theorem @ X1))),
% 36.88/6.00 inference('cnf', [status(esa)], [condensed_detachment])).
% 36.88/6.00 thf(zip_derived_cl8, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ X3)
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ X2 @ X1))
% 36.88/6.00 | (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl18, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.88/6.00 ( (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 36.88/6.00 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 36.88/6.00 thf(zip_derived_cl23, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ (equivalent @ X2 @ X1) @ X3) @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)) @
% 36.88/6.00 X3)))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl18])).
% 36.88/6.00 thf(zip_derived_cl0, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 36.88/6.00 | ~ (is_a_theorem @ X0)
% 36.88/6.00 | (is_a_theorem @ X1))),
% 36.88/6.00 inference('cnf', [status(esa)], [condensed_detachment])).
% 36.88/6.00 thf(zip_derived_cl24, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.00 | (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 36.88/6.00 X0)))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl18, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.88/6.00 ( (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 36.88/6.00 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 36.88/6.00 thf(zip_derived_cl27, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.00 | (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 36.88/6.00 X4) @
% 36.88/6.00 (equivalent @ X0 @ X4))))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl18])).
% 36.88/6.00 thf(zip_derived_cl24, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.00 | (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 36.88/6.00 X0)))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl0, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 36.88/6.00 | ~ (is_a_theorem @ X0)
% 36.88/6.00 | (is_a_theorem @ X1))),
% 36.88/6.00 inference('cnf', [status(esa)], [condensed_detachment])).
% 36.88/6.00 thf(zip_derived_cl26, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.00 | ~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 36.88/6.00 | (is_a_theorem @ X0))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl73, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 36.88/6.00 | ~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ X0 @ X0))))),
% 36.88/6.00 inference('eq_fact', [status(thm)], [zip_derived_cl26])).
% 36.88/6.00 thf(zip_derived_cl18, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.88/6.00 ( (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 36.88/6.00 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 36.88/6.00 thf(zip_derived_cl104, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl18])).
% 36.88/6.00 thf(zip_derived_cl160, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X4 @ X3) @ X1))
% 36.88/6.00 | (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ X1 @ X0))))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl104])).
% 36.88/6.00 thf(zip_derived_cl26, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.00 | ~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 36.88/6.00 | (is_a_theorem @ X0))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl411, plain,
% 36.88/6.00 (![X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X1))
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X1 @ X1) @ X4))
% 36.88/6.00 | (is_a_theorem @ X4))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl160, zip_derived_cl26])).
% 36.88/6.00 thf(zip_derived_cl538, plain,
% 36.88/6.00 (![X0 : $i]:
% 36.88/6.00 ( (is_a_theorem @ X0)
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X0 @ X0) @ X0)))),
% 36.88/6.00 inference('eq_fact', [status(thm)], [zip_derived_cl411])).
% 36.88/6.00 thf(zip_derived_cl24, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.00 | (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 36.88/6.00 X0)))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl565, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 36.88/6.00 | ~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X1 @ X1) @ (equivalent @ X1 @ X0))))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl538, zip_derived_cl24])).
% 36.88/6.00 thf(zip_derived_cl104, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl18])).
% 36.88/6.00 thf(zip_derived_cl574, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ X1 @ (equivalent @ X0 @ X0))))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl565, zip_derived_cl104])).
% 36.88/6.00 thf(zip_derived_cl10, plain,
% 36.88/6.00 (![X4 : $i, X5 : $i, X6 : $i]:
% 36.88/6.00 (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X6 @ X5) @
% 36.88/6.00 (equivalent @ (equivalent @ X6 @ X4) @ (equivalent @ X5 @ X4))))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 36.88/6.00 thf(zip_derived_cl618, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ X1 @ X0)))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl574, zip_derived_cl10])).
% 36.88/6.00 thf(zip_derived_cl574, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ X1 @ (equivalent @ X0 @ X0))))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl565, zip_derived_cl104])).
% 36.88/6.00 thf(zip_derived_cl680, plain,
% 36.88/6.00 (![X0 : $i]: (is_a_theorem @ (equivalent @ X0 @ X0))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl618, zip_derived_cl574])).
% 36.88/6.00 thf(zip_derived_cl26, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.00 | ~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 36.88/6.00 | (is_a_theorem @ X0))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl732, plain,
% 36.88/6.00 (![X1 : $i, X2 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X1 @ X1) @ X2))
% 36.88/6.00 | (is_a_theorem @ X2))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl680, zip_derived_cl26])).
% 36.88/6.00 thf(zip_derived_cl23, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ (equivalent @ X2 @ X1) @ X3) @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)) @
% 36.88/6.00 X3)))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl18])).
% 36.88/6.00 thf(zip_derived_cl799, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.88/6.00 (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)) @
% 36.88/6.00 (equivalent @ X1 @ X0)))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl732, zip_derived_cl23])).
% 36.88/6.00 thf(zip_derived_cl24, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.00 | (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 36.88/6.00 X0)))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl680, plain,
% 36.88/6.00 (![X0 : $i]: (is_a_theorem @ (equivalent @ X0 @ X0))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl618, zip_derived_cl574])).
% 36.88/6.00 thf(zip_derived_cl23, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ (equivalent @ X2 @ X1) @ X3) @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)) @
% 36.88/6.00 X3)))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl18])).
% 36.88/6.00 thf(zip_derived_cl18, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.88/6.00 ( (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 36.88/6.00 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 36.88/6.00 thf(zip_derived_cl25, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 36.88/6.00 (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ (equivalent @ X3 @ X2) @ X0) @ X4) @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 36.88/6.00 X0) @
% 36.88/6.00 X4)))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl18])).
% 36.88/6.00 thf(zip_derived_cl0, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 36.88/6.00 | ~ (is_a_theorem @ X0)
% 36.88/6.00 | (is_a_theorem @ X1))),
% 36.88/6.00 inference('cnf', [status(esa)], [condensed_detachment])).
% 36.88/6.00 thf(zip_derived_cl132, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 36.88/6.00 (~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ (equivalent @ X4 @ X3) @ X1) @ X0))
% 36.88/6.00 | (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X4 @ X2) @ (equivalent @ X3 @ X2)) @
% 36.88/6.00 X1) @
% 36.88/6.00 X0)))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl26, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.00 | ~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 36.88/6.00 | (is_a_theorem @ X0))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl23, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ (equivalent @ X2 @ X1) @ X3) @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)) @
% 36.88/6.00 X3)))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl18])).
% 36.88/6.00 thf(zip_derived_cl54, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 36.88/6.00 ( (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 36.88/6.00 X0))
% 36.88/6.00 | ~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ (equivalent @ X3 @ X2) @ X4) @
% 36.88/6.00 (equivalent @ X0 @ X4))))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl23])).
% 36.88/6.00 thf(zip_derived_cl24, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.00 | (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 36.88/6.00 X0)))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 36.88/6.00 thf(prove_lg_5, conjecture,
% 36.88/6.00 (is_a_theorem @
% 36.88/6.00 ( equivalent @
% 36.88/6.00 ( equivalent @
% 36.88/6.00 a @ ( equivalent @ b @ ( equivalent @ c @ ( equivalent @ e @ f ) ) ) ) @
% 36.88/6.00 ( equivalent @
% 36.88/6.00 ( equivalent @ a @ ( equivalent @ f @ c ) ) @
% 36.88/6.00 ( equivalent @ ( equivalent @ b @ ( equivalent @ f @ e ) ) @ f ) ) ))).
% 36.88/6.00 thf(zf_stmt_0, negated_conjecture,
% 36.88/6.00 (~( is_a_theorem @
% 36.88/6.00 ( equivalent @
% 36.88/6.00 ( equivalent @
% 36.88/6.00 a @
% 36.88/6.00 ( equivalent @ b @ ( equivalent @ c @ ( equivalent @ e @ f ) ) ) ) @
% 36.88/6.00 ( equivalent @
% 36.88/6.00 ( equivalent @ a @ ( equivalent @ f @ c ) ) @
% 36.88/6.00 ( equivalent @ ( equivalent @ b @ ( equivalent @ f @ e ) ) @ f ) ) ) )),
% 36.88/6.00 inference('cnf.neg', [status(esa)], [prove_lg_5])).
% 36.88/6.00 thf(zip_derived_cl2, plain,
% 36.88/6.00 (~ (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ a @
% 36.88/6.00 (equivalent @ b @ (equivalent @ c @ (equivalent @ e @ f)))) @
% 36.88/6.00 (equivalent @ (equivalent @ a @ (equivalent @ f @ c)) @
% 36.88/6.00 (equivalent @ (equivalent @ b @ (equivalent @ f @ e)) @ f))))),
% 36.88/6.00 inference('cnf', [status(esa)], [zf_stmt_0])).
% 36.88/6.00 thf(zip_derived_cl0, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 36.88/6.00 | ~ (is_a_theorem @ X0)
% 36.88/6.00 | (is_a_theorem @ X1))),
% 36.88/6.00 inference('cnf', [status(esa)], [condensed_detachment])).
% 36.88/6.00 thf(zip_derived_cl3, plain,
% 36.88/6.00 (![X0 : $i]:
% 36.88/6.00 (~ (is_a_theorem @
% 36.88/6.00 (equivalent @ X0 @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ a @
% 36.88/6.00 (equivalent @ b @ (equivalent @ c @ (equivalent @ e @ f)))) @
% 36.88/6.00 (equivalent @ (equivalent @ a @ (equivalent @ f @ c)) @
% 36.88/6.00 (equivalent @ (equivalent @ b @ (equivalent @ f @ e)) @ f)))))
% 36.88/6.00 | ~ (is_a_theorem @ X0))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl28, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.88/6.00 (~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X1) @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ a @
% 36.88/6.00 (equivalent @ b @ (equivalent @ c @ (equivalent @ e @ f)))) @
% 36.88/6.00 (equivalent @ (equivalent @ a @ (equivalent @ f @ c)) @
% 36.88/6.00 (equivalent @ (equivalent @ b @ (equivalent @ f @ e)) @ f)))))
% 36.88/6.00 | ~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl3])).
% 36.88/6.00 thf(zip_derived_cl18, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.88/6.00 ( (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 36.88/6.00 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 36.88/6.00 thf(zip_derived_cl31, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 (~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X0 @ X1) @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ a @ (equivalent @ f @ c)) @
% 36.88/6.00 (equivalent @ (equivalent @ b @ (equivalent @ f @ e)) @ f)) @
% 36.88/6.00 X1)))
% 36.88/6.00 | ~ (is_a_theorem @
% 36.88/6.00 (equivalent @ X0 @
% 36.88/6.00 (equivalent @ a @
% 36.88/6.00 (equivalent @ b @ (equivalent @ c @ (equivalent @ e @ f)))))))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl18])).
% 36.88/6.00 thf(zip_derived_cl4, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ X3)
% 36.88/6.00 | (is_a_theorem @
% 36.88/6.00 (equivalent @ X3 @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X1) @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl76, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 (~ (is_a_theorem @
% 36.88/6.00 (equivalent @ X1 @
% 36.88/6.00 (equivalent @ a @
% 36.88/6.00 (equivalent @ b @ (equivalent @ c @ (equivalent @ e @ f))))))
% 36.88/6.00 | ~ (is_a_theorem @
% 36.88/6.00 (equivalent @ X1 @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ a @ (equivalent @ f @ c)) @ X0) @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ b @ (equivalent @ f @ e)) @ f) @
% 36.88/6.00 X0)))))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl31, zip_derived_cl4])).
% 36.88/6.00 thf(zip_derived_cl1, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (is_a_theorem @
% 36.88/6.00 (equivalent @ X0 @
% 36.88/6.00 (equivalent @ X0 @
% 36.88/6.00 (equivalent @ (equivalent @ X1 @ X2) @
% 36.88/6.00 (equivalent @ (equivalent @ X1 @ X3) @ (equivalent @ X2 @ X3))))))),
% 36.88/6.00 inference('cnf', [status(esa)], [lg_2])).
% 36.88/6.00 thf(zip_derived_cl114, plain,
% 36.88/6.00 (![X0 : $i]:
% 36.88/6.00 ~ (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ a @ (equivalent @ f @ c)) @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ b @ (equivalent @ f @ e)) @ X0) @
% 36.88/6.00 (equivalent @ f @ X0))) @
% 36.88/6.00 (equivalent @ a @
% 36.88/6.00 (equivalent @ b @ (equivalent @ c @ (equivalent @ e @ f))))))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl1])).
% 36.88/6.00 thf(zip_derived_cl24, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.00 | (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 36.88/6.00 X0)))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl129, plain,
% 36.88/6.00 (~ (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ a @
% 36.88/6.00 (equivalent @ (equivalent @ b @ (equivalent @ f @ e)) @ c)) @
% 36.88/6.00 (equivalent @ a @
% 36.88/6.00 (equivalent @ b @ (equivalent @ c @ (equivalent @ e @ f))))))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl24])).
% 36.88/6.00 thf(zip_derived_cl26, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.00 | ~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 36.88/6.00 | (is_a_theorem @ X0))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 36.88/6.00 thf(zip_derived_cl18, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.88/6.00 ( (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 36.88/6.00 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 36.88/6.00 thf(zip_derived_cl52, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 36.88/6.00 | ~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X3) @ (equivalent @ X0 @ X3)))
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl18])).
% 36.88/6.00 thf(zip_derived_cl309, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 (~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X1 @ X0) @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ a @
% 36.88/6.00 (equivalent @ b @ (equivalent @ c @ (equivalent @ e @ f)))) @
% 36.88/6.00 X0)))
% 36.88/6.00 | ~ (is_a_theorem @
% 36.88/6.00 (equivalent @ X1 @
% 36.88/6.00 (equivalent @ a @
% 36.88/6.00 (equivalent @ (equivalent @ b @ (equivalent @ f @ e)) @ c)))))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl129, zip_derived_cl52])).
% 36.88/6.00 thf(zip_derived_cl27, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.00 | (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 36.88/6.00 X4) @
% 36.88/6.00 (equivalent @ X0 @ X4))))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl18])).
% 36.88/6.00 thf(zip_derived_cl331, plain,
% 36.88/6.00 (![X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.00 (~ (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 36.88/6.00 (equivalent @ a @
% 36.88/6.00 (equivalent @ (equivalent @ b @ (equivalent @ f @ e)) @ c))))
% 36.88/6.00 | ~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X3 @ X2) @
% 36.88/6.00 (equivalent @ a @
% 36.88/6.00 (equivalent @ b @ (equivalent @ c @ (equivalent @ e @ f)))))))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl309, zip_derived_cl27])).
% 36.88/6.00 thf(zip_derived_cl18, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.88/6.00 ( (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 36.88/6.00 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 36.88/6.00 thf(zip_derived_cl1096, plain,
% 36.88/6.00 (![X0 : $i]:
% 36.88/6.00 (~ (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ X0 @ (equivalent @ b @ (equivalent @ f @ e))) @
% 36.88/6.00 (equivalent @ a @
% 36.88/6.00 (equivalent @ b @ (equivalent @ c @ (equivalent @ e @ f))))))
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X0 @ c) @ a)))),
% 36.88/6.00 inference('s_sup+', [status(thm)], [zip_derived_cl331, zip_derived_cl18])).
% 36.88/6.00 thf(zip_derived_cl1577, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i]:
% 36.88/6.00 (~ (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ (equivalent @ X0 @ b) @ X1) @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ a @
% 36.88/6.00 (equivalent @ b @ (equivalent @ c @ (equivalent @ e @ f)))) @
% 36.88/6.00 X1)))
% 36.88/6.00 | ~ (is_a_theorem @
% 36.88/6.00 (equivalent @
% 36.88/6.00 (equivalent @ (equivalent @ X0 @ (equivalent @ f @ e)) @ c) @ a)))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl1096])).
% 36.88/6.00 thf(zip_derived_cl732, plain,
% 36.88/6.00 (![X1 : $i, X2 : $i]:
% 36.88/6.00 (~ (is_a_theorem @ (equivalent @ (equivalent @ X1 @ X1) @ X2))
% 36.88/6.00 | (is_a_theorem @ X2))),
% 36.88/6.00 inference('s_sup-', [status(thm)], [zip_derived_cl680, zip_derived_cl26])).
% 36.88/6.00 thf(zip_derived_cl18, plain,
% 36.88/6.00 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.88/6.00 ( (is_a_theorem @
% 36.88/6.00 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 36.88/6.00 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 36.88/6.00 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 36.88/6.01 thf(zip_derived_cl796, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 36.88/6.01 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 36.88/6.01 inference('s_sup+', [status(thm)], [zip_derived_cl732, zip_derived_cl18])).
% 36.88/6.01 thf(zip_derived_cl2008, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 (~ (is_a_theorem @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ (equivalent @ X1 @ (equivalent @ f @ e)) @ c) @ a))
% 36.88/6.01 | ~ (is_a_theorem @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ a @
% 36.88/6.01 (equivalent @ b @ (equivalent @ c @ (equivalent @ e @ f)))) @
% 36.88/6.01 X0) @
% 36.88/6.01 (equivalent @ (equivalent @ X1 @ b) @ X0))))),
% 36.88/6.01 inference('s_sup+', [status(thm)],
% 36.88/6.01 [zip_derived_cl1577, zip_derived_cl796])).
% 36.88/6.01 thf(zip_derived_cl4, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.01 (~ (is_a_theorem @ X3)
% 36.88/6.01 | (is_a_theorem @
% 36.88/6.01 (equivalent @ X3 @
% 36.88/6.01 (equivalent @ (equivalent @ X2 @ X1) @
% 36.88/6.01 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))))),
% 36.88/6.01 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 36.88/6.01 thf(zip_derived_cl2028, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 (~ (is_a_theorem @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ (equivalent @ X1 @ (equivalent @ f @ e)) @ c) @ a))
% 36.88/6.01 | ~ (is_a_theorem @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ a @
% 36.88/6.01 (equivalent @ b @ (equivalent @ c @ (equivalent @ e @ f)))) @
% 36.88/6.01 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ b @ X0)))))),
% 36.88/6.01 inference('s_sup+', [status(thm)], [zip_derived_cl2008, zip_derived_cl4])).
% 36.88/6.01 thf(zip_derived_cl18, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.88/6.01 ( (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 36.88/6.01 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 36.88/6.01 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 36.88/6.01 thf(zip_derived_cl2131, plain,
% 36.88/6.01 (![X0 : $i]:
% 36.88/6.01 (~ (is_a_theorem @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ (equivalent @ X0 @ (equivalent @ f @ e)) @ c) @ a))
% 36.88/6.01 | ~ (is_a_theorem @
% 36.88/6.01 (equivalent @ a @
% 36.88/6.01 (equivalent @ X0 @ (equivalent @ c @ (equivalent @ e @ f))))))),
% 36.88/6.01 inference('s_sup+', [status(thm)], [zip_derived_cl2028, zip_derived_cl18])).
% 36.88/6.01 thf(zip_derived_cl3446, plain,
% 36.88/6.01 (![X0 : $i]:
% 36.88/6.01 (~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ (equivalent @ X0 @ f) @ c) @ a))
% 36.88/6.01 | ~ (is_a_theorem @
% 36.88/6.01 (equivalent @ a @
% 36.88/6.01 (equivalent @ (equivalent @ X0 @ e) @
% 36.88/6.01 (equivalent @ c @ (equivalent @ e @ f))))))),
% 36.88/6.01 inference('s_sup-', [status(thm)],
% 36.88/6.01 [zip_derived_cl132, zip_derived_cl2131])).
% 36.88/6.01 thf(zip_derived_cl52, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.01 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 36.88/6.01 | ~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ X2 @ X3) @ (equivalent @ X0 @ X3)))
% 36.88/6.01 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 36.88/6.01 inference('s_sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl18])).
% 36.88/6.01 thf(zip_derived_cl3543, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 36.88/6.01 (~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ (equivalent @ X0 @ f) @ c) @ a))
% 36.88/6.01 | ~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ X2 @ X1) @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ (equivalent @ X0 @ e) @
% 36.88/6.01 (equivalent @ c @ (equivalent @ e @ f))) @
% 36.88/6.01 X1)))
% 36.88/6.01 | ~ (is_a_theorem @ (equivalent @ X2 @ a)))),
% 36.88/6.01 inference('s_sup+', [status(thm)], [zip_derived_cl3446, zip_derived_cl52])).
% 36.88/6.01 thf(zip_derived_cl3921, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 (~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ (equivalent @ X0 @ f) @ c) @ a))
% 36.88/6.01 | ~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ a @ X1) @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ (equivalent @ X0 @ e) @
% 36.88/6.01 (equivalent @ c @ (equivalent @ e @ f))) @
% 36.88/6.01 X1))))),
% 36.88/6.01 inference('s_sup-', [status(thm)],
% 36.88/6.01 [zip_derived_cl680, zip_derived_cl3543])).
% 36.88/6.01 thf(zip_derived_cl796, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 36.88/6.01 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 36.88/6.01 inference('s_sup+', [status(thm)], [zip_derived_cl732, zip_derived_cl18])).
% 36.88/6.01 thf(zip_derived_cl5071, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 (~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ (equivalent @ X1 @ f) @ c) @ a))
% 36.88/6.01 | ~ (is_a_theorem @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ (equivalent @ X1 @ e) @
% 36.88/6.01 (equivalent @ c @ (equivalent @ e @ f))) @
% 36.88/6.01 X0) @
% 36.88/6.01 (equivalent @ a @ X0))))),
% 36.88/6.01 inference('s_sup+', [status(thm)],
% 36.88/6.01 [zip_derived_cl3921, zip_derived_cl796])).
% 36.88/6.01 thf(zip_derived_cl24, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.01 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.01 | (is_a_theorem @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 36.88/6.01 X0)))),
% 36.88/6.01 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 36.88/6.01 thf(zip_derived_cl5196, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 (~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ (equivalent @ X1 @ f) @ c) @ a))
% 36.88/6.01 | ~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ (equivalent @ X1 @ e) @ X0) @
% 36.88/6.01 (equivalent @ a @
% 36.88/6.01 (equivalent @ X0 @ (equivalent @ c @ (equivalent @ e @ f)))))))),
% 36.88/6.01 inference('s_sup+', [status(thm)], [zip_derived_cl5071, zip_derived_cl24])).
% 36.88/6.01 thf(zip_derived_cl796, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 36.88/6.01 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 36.88/6.01 inference('s_sup+', [status(thm)], [zip_derived_cl732, zip_derived_cl18])).
% 36.88/6.01 thf(zip_derived_cl5880, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 (~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ (equivalent @ X1 @ f) @ c) @ a))
% 36.88/6.01 | ~ (is_a_theorem @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ a @
% 36.88/6.01 (equivalent @ X0 @ (equivalent @ c @ (equivalent @ e @ f)))) @
% 36.88/6.01 (equivalent @ (equivalent @ X1 @ e) @ X0))))),
% 36.88/6.01 inference('s_sup+', [status(thm)],
% 36.88/6.01 [zip_derived_cl5196, zip_derived_cl796])).
% 36.88/6.01 thf(zip_derived_cl4, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.01 (~ (is_a_theorem @ X3)
% 36.88/6.01 | (is_a_theorem @
% 36.88/6.01 (equivalent @ X3 @
% 36.88/6.01 (equivalent @ (equivalent @ X2 @ X1) @
% 36.88/6.01 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))))),
% 36.88/6.01 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 36.88/6.01 thf(zip_derived_cl5983, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 (~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ (equivalent @ X1 @ f) @ c) @ a))
% 36.88/6.01 | ~ (is_a_theorem @
% 36.88/6.01 (equivalent @ a @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ e @ X0)) @
% 36.88/6.01 (equivalent @ c @ (equivalent @ e @ f))))))),
% 36.88/6.01 inference('s_sup+', [status(thm)], [zip_derived_cl5880, zip_derived_cl4])).
% 36.88/6.01 thf(zip_derived_cl796, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 36.88/6.01 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 36.88/6.01 inference('s_sup+', [status(thm)], [zip_derived_cl732, zip_derived_cl18])).
% 36.88/6.01 thf(zip_derived_cl6148, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 (~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ (equivalent @ X1 @ f) @ c) @ a))
% 36.88/6.01 | ~ (is_a_theorem @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ e @ X0)) @
% 36.88/6.01 (equivalent @ c @ (equivalent @ e @ f))) @
% 36.88/6.01 a)))),
% 36.88/6.01 inference('s_sup+', [status(thm)],
% 36.88/6.01 [zip_derived_cl5983, zip_derived_cl796])).
% 36.88/6.01 thf(zip_derived_cl6232, plain,
% 36.88/6.01 (![X0 : $i]:
% 36.88/6.01 (~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ (equivalent @ X0 @ f) @ c) @ a))
% 36.88/6.01 | ~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ (equivalent @ X0 @ f) @ c) @ a)))),
% 36.88/6.01 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl6148])).
% 36.88/6.01 thf(zip_derived_cl6236, plain,
% 36.88/6.01 (![X0 : $i]:
% 36.88/6.01 ~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ (equivalent @ X0 @ f) @ c) @ a))),
% 36.88/6.01 inference('simplify', [status(thm)], [zip_derived_cl6232])).
% 36.88/6.01 thf(zip_derived_cl0, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 36.88/6.01 | ~ (is_a_theorem @ X0)
% 36.88/6.01 | (is_a_theorem @ X1))),
% 36.88/6.01 inference('cnf', [status(esa)], [condensed_detachment])).
% 36.88/6.01 thf(zip_derived_cl6239, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 (~ (is_a_theorem @
% 36.88/6.01 (equivalent @ X1 @
% 36.88/6.01 (equivalent @ (equivalent @ (equivalent @ X0 @ f) @ c) @ a)))
% 36.88/6.01 | ~ (is_a_theorem @ X1))),
% 36.88/6.01 inference('s_sup+', [status(thm)], [zip_derived_cl6236, zip_derived_cl0])).
% 36.88/6.01 thf(zip_derived_cl6281, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 ~ (is_a_theorem @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ (equivalent @ (equivalent @ X0 @ f) @ c) @ X1) @
% 36.88/6.01 (equivalent @ a @ X1)))),
% 36.88/6.01 inference('s_sup-', [status(thm)],
% 36.88/6.01 [zip_derived_cl799, zip_derived_cl6239])).
% 36.88/6.01 thf(zip_derived_cl24, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.01 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.01 | (is_a_theorem @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 36.88/6.01 X0)))),
% 36.88/6.01 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 36.88/6.01 thf(zip_derived_cl6290, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 ~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ (equivalent @ X1 @ f) @ X0) @
% 36.88/6.01 (equivalent @ a @ (equivalent @ X0 @ c))))),
% 36.88/6.01 inference('s_sup+', [status(thm)], [zip_derived_cl6281, zip_derived_cl24])).
% 36.88/6.01 thf(zip_derived_cl24, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.01 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 36.88/6.01 | (is_a_theorem @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 36.88/6.01 X0)))),
% 36.88/6.01 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 36.88/6.01 thf(zip_derived_cl6366, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 ~ (is_a_theorem @
% 36.88/6.01 (equivalent @ (equivalent @ X1 @ X0) @
% 36.88/6.01 (equivalent @ a @ (equivalent @ (equivalent @ X0 @ f) @ c))))),
% 36.88/6.01 inference('s_sup+', [status(thm)], [zip_derived_cl6290, zip_derived_cl24])).
% 36.88/6.01 thf(zip_derived_cl796, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 36.88/6.01 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 36.88/6.01 inference('s_sup+', [status(thm)], [zip_derived_cl732, zip_derived_cl18])).
% 36.88/6.01 thf(zip_derived_cl6422, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i]:
% 36.88/6.01 ~ (is_a_theorem @
% 36.88/6.01 (equivalent @
% 36.88/6.01 (equivalent @ a @ (equivalent @ (equivalent @ X0 @ f) @ c)) @
% 36.88/6.01 (equivalent @ X1 @ X0)))),
% 36.88/6.01 inference('s_sup+', [status(thm)],
% 36.88/6.01 [zip_derived_cl6366, zip_derived_cl796])).
% 36.88/6.01 thf(zip_derived_cl1, plain,
% 36.88/6.01 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 36.88/6.01 (is_a_theorem @
% 36.88/6.01 (equivalent @ X0 @
% 36.88/6.01 (equivalent @ X0 @
% 36.88/6.01 (equivalent @ (equivalent @ X1 @ X2) @
% 36.88/6.01 (equivalent @ (equivalent @ X1 @ X3) @ (equivalent @ X2 @ X3))))))),
% 36.88/6.01 inference('cnf', [status(esa)], [lg_2])).
% 36.88/6.01 thf(zip_derived_cl6489, plain, ($false),
% 36.88/6.01 inference('s_sup+', [status(thm)], [zip_derived_cl6422, zip_derived_cl1])).
% 36.88/6.01
% 36.88/6.01 % SZS output end Refutation
% 36.88/6.01
% 36.88/6.01
% 36.88/6.01 % Terminating...
% 37.80/6.05 % Runner terminated.
% 37.80/6.08 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------