%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL123-1 : 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.YUD6RRY0hB 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 9.86s 2.10s
% Output : Refutation 9.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL123-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.05 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.YUD6RRY0hB true
% 0.11/0.37 % Computer : n027.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 : Fri Sep 4 22:31:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Running portfolio for 300 s
% 0.11/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Number of cores: 8
% 0.11/0.38 % Python version: Python 3.12.3
% 0.11/0.38 % Running in FO mode
% 0.42/0.66 % Total configuration time : 435
% 0.42/0.66 % Estimated wc time : 1092
% 0.42/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.46/0.74 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.46/0.80 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.46/0.80 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.46/0.80 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.46/0.81 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.46/0.81 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.46/0.81 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 9.86/2.10 % Solved by fo/fo13.sh.
% 9.86/2.10 % done 357 iterations in 1.264s
% 9.86/2.10 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 9.86/2.10 % SZS output start Refutation
% 9.86/2.10 thf(c_type, type, c: $i).
% 9.86/2.10 thf(is_a_theorem_type, type, is_a_theorem: $i > $o).
% 9.86/2.10 thf(equivalent_type, type, equivalent: $i > $i > $i).
% 9.86/2.10 thf(f_type, type, f: $i).
% 9.86/2.10 thf(b_type, type, b: $i).
% 9.86/2.10 thf(e_type, type, e: $i).
% 9.86/2.10 thf(a_type, type, a: $i).
% 9.86/2.10 thf(lg_2, axiom,
% 9.86/2.10 (is_a_theorem @
% 9.86/2.10 ( equivalent @
% 9.86/2.10 X @
% 9.86/2.10 ( equivalent @
% 9.86/2.10 X @
% 9.86/2.10 ( equivalent @
% 9.86/2.10 ( equivalent @ Y @ Z ) @
% 9.86/2.10 ( equivalent @ ( equivalent @ Y @ U ) @ ( equivalent @ Z @ U ) ) ) ) ))).
% 9.86/2.10 thf(zip_derived_cl1, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (is_a_theorem @
% 9.86/2.10 (equivalent @ X0 @
% 9.86/2.10 (equivalent @ X0 @
% 9.86/2.10 (equivalent @ (equivalent @ X1 @ X2) @
% 9.86/2.10 (equivalent @ (equivalent @ X1 @ X3) @ (equivalent @ X2 @ X3))))))),
% 9.86/2.10 inference('cnf', [status(esa)], [lg_2])).
% 9.86/2.10 thf(condensed_detachment, axiom,
% 9.86/2.10 (( ~( is_a_theorem @ ( equivalent @ X @ Y ) ) ) |
% 9.86/2.10 ( ~( is_a_theorem @ X ) ) | ( is_a_theorem @ Y ))).
% 9.86/2.10 thf(zip_derived_cl0, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 9.86/2.10 | ~ (is_a_theorem @ X0)
% 9.86/2.10 | (is_a_theorem @ X1))),
% 9.86/2.10 inference('cnf', [status(esa)], [condensed_detachment])).
% 9.86/2.10 thf(zip_derived_cl4, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ X3)
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @ X3 @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X1) @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl0, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 9.86/2.10 | ~ (is_a_theorem @ X0)
% 9.86/2.10 | (is_a_theorem @ X1))),
% 9.86/2.10 inference('cnf', [status(esa)], [condensed_detachment])).
% 9.86/2.10 thf(zip_derived_cl5, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ X3)
% 9.86/2.10 | ~ (is_a_theorem @ X3)
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X1) @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl6, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 ( (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X1) @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))
% 9.86/2.10 | ~ (is_a_theorem @ X3))),
% 9.86/2.10 inference('simplify', [status(thm)], [zip_derived_cl5])).
% 9.86/2.10 thf(zip_derived_cl1, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (is_a_theorem @
% 9.86/2.10 (equivalent @ X0 @
% 9.86/2.10 (equivalent @ X0 @
% 9.86/2.10 (equivalent @ (equivalent @ X1 @ X2) @
% 9.86/2.10 (equivalent @ (equivalent @ X1 @ X3) @ (equivalent @ X2 @ X3))))))),
% 9.86/2.10 inference('cnf', [status(esa)], [lg_2])).
% 9.86/2.10 thf(zip_derived_cl10, plain,
% 9.86/2.10 (![X4 : $i, X5 : $i, X6 : $i]:
% 9.86/2.10 (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X6 @ X5) @
% 9.86/2.10 (equivalent @ (equivalent @ X6 @ X4) @ (equivalent @ X5 @ X4))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 9.86/2.10 thf(zip_derived_cl6, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 ( (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X1) @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))
% 9.86/2.10 | ~ (is_a_theorem @ X3))),
% 9.86/2.10 inference('simplify', [status(thm)], [zip_derived_cl5])).
% 9.86/2.10 thf(zip_derived_cl0, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 9.86/2.10 | ~ (is_a_theorem @ X0)
% 9.86/2.10 | (is_a_theorem @ X1))),
% 9.86/2.10 inference('cnf', [status(esa)], [condensed_detachment])).
% 9.86/2.10 thf(zip_derived_cl8, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ X3)
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X2 @ X1))
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl18, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.86/2.10 ( (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 9.86/2.10 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 9.86/2.10 thf(zip_derived_cl23, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ (equivalent @ X2 @ X1) @ X3) @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)) @
% 9.86/2.10 X3)))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl18])).
% 9.86/2.10 thf(zip_derived_cl0, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 9.86/2.10 | ~ (is_a_theorem @ X0)
% 9.86/2.10 | (is_a_theorem @ X1))),
% 9.86/2.10 inference('cnf', [status(esa)], [condensed_detachment])).
% 9.86/2.10 thf(zip_derived_cl24, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 9.86/2.10 X0)))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl18, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.86/2.10 ( (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 9.86/2.10 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 9.86/2.10 thf(zip_derived_cl27, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 9.86/2.10 X4) @
% 9.86/2.10 (equivalent @ X0 @ X4))))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl18])).
% 9.86/2.10 thf(zip_derived_cl24, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 9.86/2.10 X0)))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl0, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 9.86/2.10 | ~ (is_a_theorem @ X0)
% 9.86/2.10 | (is_a_theorem @ X1))),
% 9.86/2.10 inference('cnf', [status(esa)], [condensed_detachment])).
% 9.86/2.10 thf(zip_derived_cl26, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 9.86/2.10 | (is_a_theorem @ X0))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl73, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ X0 @ X0))))),
% 9.86/2.10 inference('eq_fact', [status(thm)], [zip_derived_cl26])).
% 9.86/2.10 thf(zip_derived_cl18, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.86/2.10 ( (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 9.86/2.10 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 9.86/2.10 thf(zip_derived_cl104, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl18])).
% 9.86/2.10 thf(zip_derived_cl169, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ (equivalent @ X4 @ X3) @ X1))
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ X1 @ X0))))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl104])).
% 9.86/2.10 thf(zip_derived_cl26, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 9.86/2.10 | (is_a_theorem @ X0))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl451, plain,
% 9.86/2.10 (![X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X1))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X1 @ X1) @ X4))
% 9.86/2.10 | (is_a_theorem @ X4))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl169, zip_derived_cl26])).
% 9.86/2.10 thf(zip_derived_cl524, plain,
% 9.86/2.10 (![X0 : $i]:
% 9.86/2.10 ( (is_a_theorem @ X0)
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X0 @ X0) @ X0)))),
% 9.86/2.10 inference('eq_fact', [status(thm)], [zip_derived_cl451])).
% 9.86/2.10 thf(zip_derived_cl24, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 9.86/2.10 X0)))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl539, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X1 @ X1) @ (equivalent @ X1 @ X0))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl524, zip_derived_cl24])).
% 9.86/2.10 thf(zip_derived_cl104, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl18])).
% 9.86/2.10 thf(zip_derived_cl548, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X1 @ (equivalent @ X0 @ X0))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl539, zip_derived_cl104])).
% 9.86/2.10 thf(zip_derived_cl10, plain,
% 9.86/2.10 (![X4 : $i, X5 : $i, X6 : $i]:
% 9.86/2.10 (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X6 @ X5) @
% 9.86/2.10 (equivalent @ (equivalent @ X6 @ X4) @ (equivalent @ X5 @ X4))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 9.86/2.10 thf(zip_derived_cl585, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ X1 @ X0)))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl548, zip_derived_cl10])).
% 9.86/2.10 thf(zip_derived_cl548, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X1 @ (equivalent @ X0 @ X0))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl539, zip_derived_cl104])).
% 9.86/2.10 thf(zip_derived_cl631, plain,
% 9.86/2.10 (![X0 : $i]: (is_a_theorem @ (equivalent @ X0 @ X0))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl585, zip_derived_cl548])).
% 9.86/2.10 thf(zip_derived_cl24, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 9.86/2.10 X0)))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 9.86/2.10 thf(prove_lg_4, conjecture,
% 9.86/2.10 (is_a_theorem @
% 9.86/2.10 ( equivalent @
% 9.86/2.10 ( equivalent @
% 9.86/2.10 ( equivalent @ a @ ( equivalent @ b @ c ) ) @
% 9.86/2.10 ( equivalent @ e @ ( equivalent @ b @ f ) ) ) @
% 9.86/2.10 ( equivalent @ a @ ( equivalent @ e @ ( equivalent @ c @ f ) ) ) ))).
% 9.86/2.10 thf(zf_stmt_0, negated_conjecture,
% 9.86/2.10 (~( is_a_theorem @
% 9.86/2.10 ( equivalent @
% 9.86/2.10 ( equivalent @
% 9.86/2.10 ( equivalent @ a @ ( equivalent @ b @ c ) ) @
% 9.86/2.10 ( equivalent @ e @ ( equivalent @ b @ f ) ) ) @
% 9.86/2.10 ( equivalent @ a @ ( equivalent @ e @ ( equivalent @ c @ f ) ) ) ) )),
% 9.86/2.10 inference('cnf.neg', [status(esa)], [prove_lg_4])).
% 9.86/2.10 thf(zip_derived_cl2, plain,
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @
% 9.86/2.10 (equivalent @ e @ (equivalent @ b @ f))) @
% 9.86/2.10 (equivalent @ a @ (equivalent @ e @ (equivalent @ c @ f)))))),
% 9.86/2.10 inference('cnf', [status(esa)], [zf_stmt_0])).
% 9.86/2.10 thf(zip_derived_cl0, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 9.86/2.10 | ~ (is_a_theorem @ X0)
% 9.86/2.10 | (is_a_theorem @ X1))),
% 9.86/2.10 inference('cnf', [status(esa)], [condensed_detachment])).
% 9.86/2.10 thf(zip_derived_cl3, plain,
% 9.86/2.10 (![X0 : $i]:
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @ X0 @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @
% 9.86/2.10 (equivalent @ e @ (equivalent @ b @ f))) @
% 9.86/2.10 (equivalent @ a @ (equivalent @ e @ (equivalent @ c @ f))))))
% 9.86/2.10 | ~ (is_a_theorem @ X0))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl28, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X1) @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @
% 9.86/2.10 (equivalent @ e @ (equivalent @ b @ f))) @
% 9.86/2.10 (equivalent @ a @ (equivalent @ e @ (equivalent @ c @ f))))))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl3])).
% 9.86/2.10 thf(zip_derived_cl18, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.86/2.10 ( (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 9.86/2.10 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 9.86/2.10 thf(zip_derived_cl31, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X0 @ X1) @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ a @ (equivalent @ e @ (equivalent @ c @ f))) @ X1)))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ X0 @
% 9.86/2.10 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @
% 9.86/2.10 (equivalent @ e @ (equivalent @ b @ f))))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl18])).
% 9.86/2.10 thf(zip_derived_cl4, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ X3)
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @ X3 @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X1) @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl76, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @ X1 @
% 9.86/2.10 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @
% 9.86/2.10 (equivalent @ e @ (equivalent @ b @ f)))))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ X1 @
% 9.86/2.10 (equivalent @ (equivalent @ a @ X0) @
% 9.86/2.10 (equivalent @ (equivalent @ e @ (equivalent @ c @ f)) @ X0)))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl31, zip_derived_cl4])).
% 9.86/2.10 thf(zip_derived_cl10, plain,
% 9.86/2.10 (![X4 : $i, X5 : $i, X6 : $i]:
% 9.86/2.10 (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X6 @ X5) @
% 9.86/2.10 (equivalent @ (equivalent @ X6 @ X4) @ (equivalent @ X5 @ X4))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 9.86/2.10 thf(zip_derived_cl157, plain,
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ a @ (equivalent @ e @ (equivalent @ c @ f))) @
% 9.86/2.10 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @
% 9.86/2.10 (equivalent @ e @ (equivalent @ b @ f)))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl10])).
% 9.86/2.10 thf(zip_derived_cl26, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 9.86/2.10 | (is_a_theorem @ X0))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl18, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.86/2.10 ( (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 9.86/2.10 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 9.86/2.10 thf(zip_derived_cl52, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X3) @ (equivalent @ X0 @ X3)))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl18])).
% 9.86/2.10 thf(zip_derived_cl343, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X1 @ X0) @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @
% 9.86/2.10 (equivalent @ e @ (equivalent @ b @ f))) @
% 9.86/2.10 X0)))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ X1 @
% 9.86/2.10 (equivalent @ a @ (equivalent @ e @ (equivalent @ c @ f))))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl157, zip_derived_cl52])).
% 9.86/2.10 thf(zip_derived_cl4, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ X3)
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @ X3 @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X1) @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl391, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @ X1 @
% 9.86/2.10 (equivalent @ a @ (equivalent @ e @ (equivalent @ c @ f)))))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ X1 @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ X0) @
% 9.86/2.10 (equivalent @ (equivalent @ e @ (equivalent @ b @ f)) @ X0)))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl343, zip_derived_cl4])).
% 9.86/2.10 thf(zip_derived_cl18, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.86/2.10 ( (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 9.86/2.10 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 9.86/2.10 thf(zip_derived_cl405, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ X1 @
% 9.86/2.10 (equivalent @ (equivalent @ e @ (equivalent @ b @ f)) @ X0)) @
% 9.86/2.10 (equivalent @ a @ (equivalent @ e @ (equivalent @ c @ f)))))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ X1 @
% 9.86/2.10 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ X0))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl391, zip_derived_cl18])).
% 9.86/2.10 thf(zip_derived_cl1, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (is_a_theorem @
% 9.86/2.10 (equivalent @ X0 @
% 9.86/2.10 (equivalent @ X0 @
% 9.86/2.10 (equivalent @ (equivalent @ X1 @ X2) @
% 9.86/2.10 (equivalent @ (equivalent @ X1 @ X3) @ (equivalent @ X2 @ X3))))))),
% 9.86/2.10 inference('cnf', [status(esa)], [lg_2])).
% 9.86/2.10 thf(zip_derived_cl18, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.86/2.10 ( (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 9.86/2.10 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 9.86/2.10 thf(zip_derived_cl19, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 9.86/2.10 (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X3 @ X4) @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ X3 @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X1) @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))) @
% 9.86/2.10 X4)))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl18])).
% 9.86/2.10 thf(zip_derived_cl0, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 9.86/2.10 | ~ (is_a_theorem @ X0)
% 9.86/2.10 | (is_a_theorem @ X1))),
% 9.86/2.10 inference('cnf', [status(esa)], [condensed_detachment])).
% 9.86/2.10 thf(zip_derived_cl43, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ X4 @ X0))
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ X4 @
% 9.86/2.10 (equivalent @ (equivalent @ X3 @ X2) @
% 9.86/2.10 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))) @
% 9.86/2.10 X0)))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl714, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @ X1 @
% 9.86/2.10 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @
% 9.86/2.10 (equivalent @ (equivalent @ e @ X0) @
% 9.86/2.10 (equivalent @ (equivalent @ b @ f) @ X0)))))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ X1 @
% 9.86/2.10 (equivalent @ a @ (equivalent @ e @ (equivalent @ c @ f))))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl405, zip_derived_cl43])).
% 9.86/2.10 thf(zip_derived_cl18, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.86/2.10 ( (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 9.86/2.10 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 9.86/2.10 thf(zip_derived_cl797, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ X1 @
% 9.86/2.10 (equivalent @ (equivalent @ e @ X0) @
% 9.86/2.10 (equivalent @ (equivalent @ b @ f) @ X0))) @
% 9.86/2.10 (equivalent @ a @ (equivalent @ e @ (equivalent @ c @ f)))))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ X1 @ (equivalent @ a @ (equivalent @ b @ c)))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl714, zip_derived_cl18])).
% 9.86/2.10 thf(zip_derived_cl24, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 9.86/2.10 X0)))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl861, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ X1 @ (equivalent @ (equivalent @ b @ f) @ X0)) @
% 9.86/2.10 (equivalent @ a @ (equivalent @ b @ c))))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X1 @ (equivalent @ e @ X0)) @
% 9.86/2.10 (equivalent @ a @ (equivalent @ e @ (equivalent @ c @ f))))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl797, zip_derived_cl24])).
% 9.86/2.10 thf(zip_derived_cl24, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 9.86/2.10 X0)))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl866, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i]:
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ e @ X0)) @
% 9.86/2.10 (equivalent @ a @ (equivalent @ e @ (equivalent @ c @ f)))))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X1 @ (equivalent @ b @ f)) @
% 9.86/2.10 (equivalent @ a @ (equivalent @ b @ c)))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl861, zip_derived_cl24])).
% 9.86/2.10 thf(zip_derived_cl18, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.86/2.10 ( (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 9.86/2.10 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 9.86/2.10 thf(zip_derived_cl873, plain,
% 9.86/2.10 (![X0 : $i]:
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X0 @ (equivalent @ b @ f)) @
% 9.86/2.10 (equivalent @ a @ (equivalent @ b @ c))))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X0 @ (equivalent @ c @ f)) @ a)))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl866, zip_derived_cl18])).
% 9.86/2.10 thf(zip_derived_cl24, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 9.86/2.10 X0)))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl880, plain,
% 9.86/2.10 (![X0 : $i]:
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ X0 @ f) @ (equivalent @ c @ f)) @ a))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X0 @ b) @
% 9.86/2.10 (equivalent @ a @ (equivalent @ b @ c)))))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl873, zip_derived_cl24])).
% 9.86/2.10 thf(zip_derived_cl24, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 9.86/2.10 | (is_a_theorem @
% 9.86/2.10 (equivalent @
% 9.86/2.10 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 9.86/2.10 X0)))),
% 9.86/2.10 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 9.86/2.10 thf(zip_derived_cl938, plain,
% 9.86/2.10 (![X0 : $i]:
% 9.86/2.10 (~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X0 @ b) @
% 9.86/2.10 (equivalent @ a @ (equivalent @ b @ c))))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X0 @ c) @ a)))),
% 9.86/2.10 inference('s_sup+', [status(thm)], [zip_derived_cl880, zip_derived_cl24])).
% 9.86/2.10 thf(zip_derived_cl52, plain,
% 9.86/2.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.10 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 9.86/2.10 | ~ (is_a_theorem @
% 9.86/2.10 (equivalent @ (equivalent @ X2 @ X3) @ (equivalent @ X0 @ X3)))
% 9.86/2.10 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 9.86/2.11 inference('s_sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl18])).
% 9.86/2.11 thf(zip_derived_cl942, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.86/2.11 (~ (is_a_theorem @ (equivalent @ (equivalent @ X0 @ c) @ a))
% 9.86/2.11 | ~ (is_a_theorem @
% 9.86/2.11 (equivalent @ (equivalent @ X2 @ X1) @
% 9.86/2.11 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ X1)))
% 9.86/2.11 | ~ (is_a_theorem @ (equivalent @ X2 @ (equivalent @ X0 @ b))))),
% 9.86/2.11 inference('s_sup+', [status(thm)], [zip_derived_cl938, zip_derived_cl52])).
% 9.86/2.11 thf(zip_derived_cl631, plain,
% 9.86/2.11 (![X0 : $i]: (is_a_theorem @ (equivalent @ X0 @ X0))),
% 9.86/2.11 inference('s_sup-', [status(thm)], [zip_derived_cl585, zip_derived_cl548])).
% 9.86/2.11 thf(zip_derived_cl1027, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i]:
% 9.86/2.11 (~ (is_a_theorem @
% 9.86/2.11 (equivalent @ (equivalent @ (equivalent @ X0 @ b) @ X1) @
% 9.86/2.11 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ X1)))
% 9.86/2.11 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X0 @ c) @ a)))),
% 9.86/2.11 inference('s_sup+', [status(thm)], [zip_derived_cl942, zip_derived_cl631])).
% 9.86/2.11 thf(zip_derived_cl631, plain,
% 9.86/2.11 (![X0 : $i]: (is_a_theorem @ (equivalent @ X0 @ X0))),
% 9.86/2.11 inference('s_sup-', [status(thm)], [zip_derived_cl585, zip_derived_cl548])).
% 9.86/2.11 thf(zip_derived_cl26, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.11 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 9.86/2.11 | ~ (is_a_theorem @
% 9.86/2.11 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 9.86/2.11 | (is_a_theorem @ X0))),
% 9.86/2.11 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 9.86/2.11 thf(zip_derived_cl679, plain,
% 9.86/2.11 (![X1 : $i, X2 : $i]:
% 9.86/2.11 (~ (is_a_theorem @ (equivalent @ (equivalent @ X1 @ X1) @ X2))
% 9.86/2.11 | (is_a_theorem @ X2))),
% 9.86/2.11 inference('s_sup-', [status(thm)], [zip_derived_cl631, zip_derived_cl26])).
% 9.86/2.11 thf(zip_derived_cl18, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.86/2.11 ( (is_a_theorem @
% 9.86/2.11 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 9.86/2.11 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 9.86/2.11 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 9.86/2.11 thf(zip_derived_cl751, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i]:
% 9.86/2.11 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 9.86/2.11 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 9.86/2.11 inference('s_sup+', [status(thm)], [zip_derived_cl679, zip_derived_cl18])).
% 9.86/2.11 thf(zip_derived_cl1350, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i]:
% 9.86/2.11 (~ (is_a_theorem @ (equivalent @ (equivalent @ X1 @ c) @ a))
% 9.86/2.11 | ~ (is_a_theorem @
% 9.86/2.11 (equivalent @
% 9.86/2.11 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ X0) @
% 9.86/2.11 (equivalent @ (equivalent @ X1 @ b) @ X0))))),
% 9.86/2.11 inference('s_sup+', [status(thm)],
% 9.86/2.11 [zip_derived_cl1027, zip_derived_cl751])).
% 9.86/2.11 thf(zip_derived_cl4, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.11 (~ (is_a_theorem @ X3)
% 9.86/2.11 | (is_a_theorem @
% 9.86/2.11 (equivalent @ X3 @
% 9.86/2.11 (equivalent @ (equivalent @ X2 @ X1) @
% 9.86/2.11 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))))),
% 9.86/2.11 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 9.86/2.11 thf(zip_derived_cl1755, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i]:
% 9.86/2.11 (~ (is_a_theorem @ (equivalent @ (equivalent @ X1 @ c) @ a))
% 9.86/2.11 | ~ (is_a_theorem @
% 9.86/2.11 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @
% 9.86/2.11 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ b @ X0)))))),
% 9.86/2.11 inference('s_sup+', [status(thm)], [zip_derived_cl1350, zip_derived_cl4])).
% 9.86/2.11 thf(zip_derived_cl18, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.86/2.11 ( (is_a_theorem @
% 9.86/2.11 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 9.86/2.11 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 9.86/2.11 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 9.86/2.11 thf(zip_derived_cl1922, plain,
% 9.86/2.11 (![X0 : $i]:
% 9.86/2.11 (~ (is_a_theorem @ (equivalent @ (equivalent @ X0 @ c) @ a))
% 9.86/2.11 | ~ (is_a_theorem @ (equivalent @ a @ (equivalent @ X0 @ c))))),
% 9.86/2.11 inference('s_sup+', [status(thm)], [zip_derived_cl1755, zip_derived_cl18])).
% 9.86/2.11 thf(zip_derived_cl751, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i]:
% 9.86/2.11 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 9.86/2.11 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 9.86/2.11 inference('s_sup+', [status(thm)], [zip_derived_cl679, zip_derived_cl18])).
% 9.86/2.11 thf(zip_derived_cl1925, plain,
% 9.86/2.11 (![X0 : $i]: ~ (is_a_theorem @ (equivalent @ a @ (equivalent @ X0 @ c)))),
% 9.86/2.11 inference('clc', [status(thm)], [zip_derived_cl1922, zip_derived_cl751])).
% 9.86/2.11 thf(zip_derived_cl52, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.11 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 9.86/2.11 | ~ (is_a_theorem @
% 9.86/2.11 (equivalent @ (equivalent @ X2 @ X3) @ (equivalent @ X0 @ X3)))
% 9.86/2.11 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 9.86/2.11 inference('s_sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl18])).
% 9.86/2.11 thf(zip_derived_cl1929, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i, X2 : $i]:
% 9.86/2.11 (~ (is_a_theorem @
% 9.86/2.11 (equivalent @ (equivalent @ X2 @ X1) @
% 9.86/2.11 (equivalent @ (equivalent @ X0 @ c) @ X1)))
% 9.86/2.11 | ~ (is_a_theorem @ (equivalent @ X2 @ a)))),
% 9.86/2.11 inference('s_sup+', [status(thm)], [zip_derived_cl1925, zip_derived_cl52])).
% 9.86/2.11 thf(zip_derived_cl1950, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i]:
% 9.86/2.11 ~ (is_a_theorem @
% 9.86/2.11 (equivalent @ (equivalent @ a @ X0) @
% 9.86/2.11 (equivalent @ (equivalent @ X1 @ c) @ X0)))),
% 9.86/2.11 inference('s_sup-', [status(thm)],
% 9.86/2.11 [zip_derived_cl631, zip_derived_cl1929])).
% 9.86/2.11 thf(zip_derived_cl751, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i]:
% 9.86/2.11 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 9.86/2.11 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 9.86/2.11 inference('s_sup+', [status(thm)], [zip_derived_cl679, zip_derived_cl18])).
% 9.86/2.11 thf(zip_derived_cl1958, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i]:
% 9.86/2.11 ~ (is_a_theorem @
% 9.86/2.11 (equivalent @ (equivalent @ (equivalent @ X1 @ c) @ X0) @
% 9.86/2.11 (equivalent @ a @ X0)))),
% 9.86/2.11 inference('s_sup+', [status(thm)],
% 9.86/2.11 [zip_derived_cl1950, zip_derived_cl751])).
% 9.86/2.11 thf(zip_derived_cl24, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.11 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 9.86/2.11 | (is_a_theorem @
% 9.86/2.11 (equivalent @
% 9.86/2.11 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 9.86/2.11 X0)))),
% 9.86/2.11 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 9.86/2.11 thf(zip_derived_cl1974, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i]:
% 9.86/2.11 ~ (is_a_theorem @
% 9.86/2.11 (equivalent @ (equivalent @ X1 @ X0) @
% 9.86/2.11 (equivalent @ a @ (equivalent @ X0 @ c))))),
% 9.86/2.11 inference('s_sup+', [status(thm)], [zip_derived_cl1958, zip_derived_cl24])).
% 9.86/2.11 thf(zip_derived_cl751, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i]:
% 9.86/2.11 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 9.86/2.11 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 9.86/2.11 inference('s_sup+', [status(thm)], [zip_derived_cl679, zip_derived_cl18])).
% 9.86/2.11 thf(zip_derived_cl2025, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i]:
% 9.86/2.11 ~ (is_a_theorem @
% 9.86/2.11 (equivalent @ (equivalent @ a @ (equivalent @ X0 @ c)) @
% 9.86/2.11 (equivalent @ X1 @ X0)))),
% 9.86/2.11 inference('s_sup+', [status(thm)],
% 9.86/2.11 [zip_derived_cl1974, zip_derived_cl751])).
% 9.86/2.11 thf(zip_derived_cl1, plain,
% 9.86/2.11 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 9.86/2.11 (is_a_theorem @
% 9.86/2.11 (equivalent @ X0 @
% 9.86/2.11 (equivalent @ X0 @
% 9.86/2.11 (equivalent @ (equivalent @ X1 @ X2) @
% 9.86/2.11 (equivalent @ (equivalent @ X1 @ X3) @ (equivalent @ X2 @ X3))))))),
% 9.86/2.11 inference('cnf', [status(esa)], [lg_2])).
% 9.86/2.11 thf(zip_derived_cl2047, plain, ($false),
% 9.86/2.11 inference('s_sup+', [status(thm)], [zip_derived_cl2025, zip_derived_cl1])).
% 9.86/2.11
% 9.86/2.11 % SZS output end Refutation
% 9.86/2.11
% 9.86/2.11
% 9.86/2.11 % Terminating...
% 2.72/2.15 % Runner terminated.
% 2.72/2.17 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------