TSTP Solution File: LCL122-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL122-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.bIFT2wrBBZ true
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 08:58:18 EDT 2023
% Result : Unsatisfiable 21.17s 3.49s
% Output : Refutation 21.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LCL122-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.00/0.09 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.bIFT2wrBBZ true
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Fri Aug 25 04:44:12 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.09/0.29 % Running portfolio for 300 s
% 0.09/0.29 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.29 % Number of cores: 8
% 0.09/0.29 % Python version: Python 3.6.8
% 0.09/0.29 % Running in FO mode
% 0.14/0.48 % Total configuration time : 435
% 0.14/0.48 % Estimated wc time : 1092
% 0.14/0.48 % Estimated cpu time (7 cpus) : 156.0
% 0.14/0.54 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.14/0.56 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.14/0.56 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.14/0.56 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.14/0.56 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.14/0.56 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.14/0.56 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 21.17/3.49 % Solved by fo/fo13.sh.
% 21.17/3.49 % done 1101 iterations in 2.906s
% 21.17/3.49 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 21.17/3.49 % SZS output start Refutation
% 21.17/3.49 thf(c_type, type, c: $i).
% 21.17/3.49 thf(is_a_theorem_type, type, is_a_theorem: $i > $o).
% 21.17/3.49 thf(equivalent_type, type, equivalent: $i > $i > $i).
% 21.17/3.49 thf(f_type, type, f: $i).
% 21.17/3.49 thf(b_type, type, b: $i).
% 21.17/3.49 thf(e_type, type, e: $i).
% 21.17/3.49 thf(a_type, type, a: $i).
% 21.17/3.49 thf(lg_2, axiom,
% 21.17/3.49 (is_a_theorem @
% 21.17/3.49 ( equivalent @
% 21.17/3.49 X @
% 21.17/3.49 ( equivalent @
% 21.17/3.49 X @
% 21.17/3.49 ( equivalent @
% 21.17/3.49 ( equivalent @ Y @ Z ) @
% 21.17/3.49 ( equivalent @ ( equivalent @ Y @ U ) @ ( equivalent @ Z @ U ) ) ) ) ))).
% 21.17/3.49 thf(zip_derived_cl1, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (is_a_theorem @
% 21.17/3.49 (equivalent @ X0 @
% 21.17/3.49 (equivalent @ X0 @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ X2) @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ X3) @ (equivalent @ X2 @ X3))))))),
% 21.17/3.49 inference('cnf', [status(esa)], [lg_2])).
% 21.17/3.49 thf(condensed_detachment, axiom,
% 21.17/3.49 (( ~( is_a_theorem @ ( equivalent @ X @ Y ) ) ) |
% 21.17/3.49 ( ~( is_a_theorem @ X ) ) | ( is_a_theorem @ Y ))).
% 21.17/3.49 thf(zip_derived_cl0, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 21.17/3.49 | ~ (is_a_theorem @ X0)
% 21.17/3.49 | (is_a_theorem @ X1))),
% 21.17/3.49 inference('cnf', [status(esa)], [condensed_detachment])).
% 21.17/3.49 thf(zip_derived_cl4, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ X3)
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @ X3 @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X1) @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl0, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 21.17/3.49 | ~ (is_a_theorem @ X0)
% 21.17/3.49 | (is_a_theorem @ X1))),
% 21.17/3.49 inference('cnf', [status(esa)], [condensed_detachment])).
% 21.17/3.49 thf(zip_derived_cl5, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ X3)
% 21.17/3.49 | ~ (is_a_theorem @ X3)
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X1) @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl6, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 ( (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X1) @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))
% 21.17/3.49 | ~ (is_a_theorem @ X3))),
% 21.17/3.49 inference('simplify', [status(thm)], [zip_derived_cl5])).
% 21.17/3.49 thf(zip_derived_cl1, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (is_a_theorem @
% 21.17/3.49 (equivalent @ X0 @
% 21.17/3.49 (equivalent @ X0 @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ X2) @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ X3) @ (equivalent @ X2 @ X3))))))),
% 21.17/3.49 inference('cnf', [status(esa)], [lg_2])).
% 21.17/3.49 thf(zip_derived_cl10, plain,
% 21.17/3.49 (![X4 : $i, X5 : $i, X6 : $i]:
% 21.17/3.49 (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X6 @ X5) @
% 21.17/3.49 (equivalent @ (equivalent @ X6 @ X4) @ (equivalent @ X5 @ X4))))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 21.17/3.49 thf(zip_derived_cl6, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 ( (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X1) @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))
% 21.17/3.49 | ~ (is_a_theorem @ X3))),
% 21.17/3.49 inference('simplify', [status(thm)], [zip_derived_cl5])).
% 21.17/3.49 thf(zip_derived_cl0, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 21.17/3.49 | ~ (is_a_theorem @ X0)
% 21.17/3.49 | (is_a_theorem @ X1))),
% 21.17/3.49 inference('cnf', [status(esa)], [condensed_detachment])).
% 21.17/3.49 thf(zip_derived_cl8, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ X3)
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X2 @ X1))
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl18, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.17/3.49 ( (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 21.17/3.49 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 21.17/3.49 thf(zip_derived_cl23, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X2 @ X1) @ X3) @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)) @
% 21.17/3.49 X3)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl0, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 21.17/3.49 | ~ (is_a_theorem @ X0)
% 21.17/3.49 | (is_a_theorem @ X1))),
% 21.17/3.49 inference('cnf', [status(esa)], [condensed_detachment])).
% 21.17/3.49 thf(zip_derived_cl24, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 21.17/3.49 X0)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl18, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.17/3.49 ( (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 21.17/3.49 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 21.17/3.49 thf(zip_derived_cl27, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 21.17/3.49 X4) @
% 21.17/3.49 (equivalent @ X0 @ X4))))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl24, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 21.17/3.49 X0)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl0, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 21.17/3.49 | ~ (is_a_theorem @ X0)
% 21.17/3.49 | (is_a_theorem @ X1))),
% 21.17/3.49 inference('cnf', [status(esa)], [condensed_detachment])).
% 21.17/3.49 thf(zip_derived_cl26, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 21.17/3.49 | (is_a_theorem @ X0))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl74, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ X0 @ X0))))),
% 21.17/3.49 inference('eq_fact', [status(thm)], [zip_derived_cl26])).
% 21.17/3.49 thf(zip_derived_cl18, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.17/3.49 ( (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 21.17/3.49 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 21.17/3.49 thf(zip_derived_cl89, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl199, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X4 @ X3) @ X1))
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ X1 @ X0))))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl89])).
% 21.17/3.49 thf(zip_derived_cl26, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 21.17/3.49 | (is_a_theorem @ X0))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl307, plain,
% 21.17/3.49 (![X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X1))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X1 @ X1) @ X4))
% 21.17/3.49 | (is_a_theorem @ X4))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl199, zip_derived_cl26])).
% 21.17/3.49 thf(zip_derived_cl414, plain,
% 21.17/3.49 (![X0 : $i]:
% 21.17/3.49 ( (is_a_theorem @ X0)
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X0 @ X0) @ X0)))),
% 21.17/3.49 inference('eq_fact', [status(thm)], [zip_derived_cl307])).
% 21.17/3.49 thf(zip_derived_cl24, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 21.17/3.49 X0)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl430, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ X1) @ (equivalent @ X1 @ X0))))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl414, zip_derived_cl24])).
% 21.17/3.49 thf(zip_derived_cl89, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl453, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X1 @ (equivalent @ X0 @ X0))))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl430, zip_derived_cl89])).
% 21.17/3.49 thf(zip_derived_cl10, plain,
% 21.17/3.49 (![X4 : $i, X5 : $i, X6 : $i]:
% 21.17/3.49 (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X6 @ X5) @
% 21.17/3.49 (equivalent @ (equivalent @ X6 @ X4) @ (equivalent @ X5 @ X4))))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 21.17/3.49 thf(zip_derived_cl480, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ X1 @ X0)))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl453, zip_derived_cl10])).
% 21.17/3.49 thf(zip_derived_cl453, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ( (is_a_theorem @ (equivalent @ X0 @ X0))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X1 @ (equivalent @ X0 @ X0))))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl430, zip_derived_cl89])).
% 21.17/3.49 thf(zip_derived_cl515, plain,
% 21.17/3.49 (![X0 : $i]: (is_a_theorem @ (equivalent @ X0 @ X0))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl480, zip_derived_cl453])).
% 21.17/3.49 thf(zip_derived_cl26, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 21.17/3.49 | (is_a_theorem @ X0))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl557, plain,
% 21.17/3.49 (![X1 : $i, X2 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X1 @ X1) @ X2))
% 21.17/3.49 | (is_a_theorem @ X2))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl515, zip_derived_cl26])).
% 21.17/3.49 thf(zip_derived_cl23, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X2 @ X1) @ X3) @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)) @
% 21.17/3.49 X3)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl581, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.17/3.49 (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ X2) @ (equivalent @ X0 @ X2)) @
% 21.17/3.49 (equivalent @ X1 @ X0)))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl557, zip_derived_cl23])).
% 21.17/3.49 thf(zip_derived_cl24, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 21.17/3.49 X0)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl515, plain,
% 21.17/3.49 (![X0 : $i]: (is_a_theorem @ (equivalent @ X0 @ X0))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl480, zip_derived_cl453])).
% 21.17/3.49 thf(zip_derived_cl23, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X2 @ X1) @ X3) @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)) @
% 21.17/3.49 X3)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl18, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.17/3.49 ( (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 21.17/3.49 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 21.17/3.49 thf(zip_derived_cl25, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 21.17/3.49 (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X3 @ X2) @ X0) @ X4) @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 21.17/3.49 X0) @
% 21.17/3.49 X4)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl0, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 21.17/3.49 | ~ (is_a_theorem @ X0)
% 21.17/3.49 | (is_a_theorem @ X1))),
% 21.17/3.49 inference('cnf', [status(esa)], [condensed_detachment])).
% 21.17/3.49 thf(zip_derived_cl148, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X4 @ X3) @ X1) @ X0))
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X4 @ X2) @ (equivalent @ X3 @ X2)) @
% 21.17/3.49 X1) @
% 21.17/3.49 X0)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl10, plain,
% 21.17/3.49 (![X4 : $i, X5 : $i, X6 : $i]:
% 21.17/3.49 (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X6 @ X5) @
% 21.17/3.49 (equivalent @ (equivalent @ X6 @ X4) @ (equivalent @ X5 @ X4))))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 21.17/3.49 thf(zip_derived_cl4, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ X3)
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @ X3 @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X1) @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl18, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.17/3.49 ( (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 21.17/3.49 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 21.17/3.49 thf(zip_derived_cl20, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ X3)
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X4) @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X1) @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))) @
% 21.17/3.49 X4))))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl24, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 21.17/3.49 X0)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 21.17/3.49 thf(prove_lg_3, conjecture,
% 21.17/3.49 (is_a_theorem @
% 21.17/3.49 ( equivalent @
% 21.17/3.49 a @
% 21.17/3.49 ( equivalent @
% 21.17/3.49 a @
% 21.17/3.49 ( equivalent @
% 21.17/3.49 ( equivalent @ b @ ( equivalent @ c @ e ) ) @
% 21.17/3.49 ( equivalent @
% 21.17/3.49 b @
% 21.17/3.49 ( equivalent @ ( equivalent @ c @ f ) @ ( equivalent @ e @ f ) ) ) ) ) ))).
% 21.17/3.49 thf(zf_stmt_0, negated_conjecture,
% 21.17/3.49 (~( is_a_theorem @
% 21.17/3.49 ( equivalent @
% 21.17/3.49 a @
% 21.17/3.49 ( equivalent @
% 21.17/3.49 a @
% 21.17/3.49 ( equivalent @
% 21.17/3.49 ( equivalent @ b @ ( equivalent @ c @ e ) ) @
% 21.17/3.49 ( equivalent @
% 21.17/3.49 b @
% 21.17/3.49 ( equivalent @ ( equivalent @ c @ f ) @ ( equivalent @ e @ f ) ) ) ) ) ) )),
% 21.17/3.49 inference('cnf.neg', [status(esa)], [prove_lg_3])).
% 21.17/3.49 thf(zip_derived_cl2, plain,
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ (equivalent @ b @ (equivalent @ c @ e)) @
% 21.17/3.49 (equivalent @ b @
% 21.17/3.49 (equivalent @ (equivalent @ c @ f) @ (equivalent @ e @ f)))))))),
% 21.17/3.49 inference('cnf', [status(esa)], [zf_stmt_0])).
% 21.17/3.49 thf(zip_derived_cl0, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 21.17/3.49 | ~ (is_a_theorem @ X0)
% 21.17/3.49 | (is_a_theorem @ X1))),
% 21.17/3.49 inference('cnf', [status(esa)], [condensed_detachment])).
% 21.17/3.49 thf(zip_derived_cl3, plain,
% 21.17/3.49 (![X0 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ X0 @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ (equivalent @ b @ (equivalent @ c @ e)) @
% 21.17/3.49 (equivalent @ b @
% 21.17/3.49 (equivalent @ (equivalent @ c @ f) @ (equivalent @ e @ f))))))))
% 21.17/3.49 | ~ (is_a_theorem @ X0))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl28, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X1) @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ (equivalent @ b @ (equivalent @ c @ e)) @
% 21.17/3.49 (equivalent @ b @
% 21.17/3.49 (equivalent @ (equivalent @ c @ f) @ (equivalent @ e @ f))))))))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl3])).
% 21.17/3.49 thf(zip_derived_cl0, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 21.17/3.49 | ~ (is_a_theorem @ X0)
% 21.17/3.49 | (is_a_theorem @ X1))),
% 21.17/3.49 inference('cnf', [status(esa)], [condensed_detachment])).
% 21.17/3.49 thf(zip_derived_cl32, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X1) @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ (equivalent @ b @ (equivalent @ c @ e)) @
% 21.17/3.49 (equivalent @ b @
% 21.17/3.49 (equivalent @ (equivalent @ c @ f) @ (equivalent @ e @ f))))))))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ X3 @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))
% 21.17/3.49 | ~ (is_a_theorem @ X3))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl104, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ X4)
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X2 @ X1) @ X3) @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ (equivalent @ b @ (equivalent @ c @ e)) @
% 21.17/3.49 (equivalent @ b @
% 21.17/3.49 (equivalent @ (equivalent @ c @ f) @ (equivalent @ e @ f))))))))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ X4 @
% 21.17/3.49 (equivalent @ X3 @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl32])).
% 21.17/3.49 thf(zip_derived_cl133, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ X3 @ (equivalent @ X2 @ X0)))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X1) @
% 21.17/3.49 (equivalent @ X3 @ (equivalent @ X1 @ X0))) @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ (equivalent @ b @ (equivalent @ c @ e)) @
% 21.17/3.49 (equivalent @ b @
% 21.17/3.49 (equivalent @ (equivalent @ c @ f) @ (equivalent @ e @ f)))))))))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl104])).
% 21.17/3.49 thf(zip_derived_cl18, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.17/3.49 ( (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 21.17/3.49 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 21.17/3.49 thf(zip_derived_cl3849, plain,
% 21.17/3.49 (![X0 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ X0 @
% 21.17/3.49 (equivalent @ b @
% 21.17/3.49 (equivalent @ (equivalent @ c @ f) @ (equivalent @ e @ f))))))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ X0 @ (equivalent @ b @ (equivalent @ c @ e))) @ a)))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl133, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl557, plain,
% 21.17/3.49 (![X1 : $i, X2 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X1 @ X1) @ X2))
% 21.17/3.49 | (is_a_theorem @ X2))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl515, zip_derived_cl26])).
% 21.17/3.49 thf(zip_derived_cl18, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.17/3.49 ( (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 21.17/3.49 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 21.17/3.49 thf(zip_derived_cl578, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl557, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl3862, plain,
% 21.17/3.49 (![X0 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ X0 @ (equivalent @ b @ (equivalent @ c @ e))) @ a))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ X0 @
% 21.17/3.49 (equivalent @ b @
% 21.17/3.49 (equivalent @ (equivalent @ c @ f) @ (equivalent @ e @ f)))) @
% 21.17/3.49 a)))),
% 21.17/3.49 inference('s_sup+', [status(thm)],
% 21.17/3.49 [zip_derived_cl3849, zip_derived_cl578])).
% 21.17/3.49 thf(zip_derived_cl24, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 21.17/3.49 X0)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl3869, plain,
% 21.17/3.49 (![X0 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ X0 @
% 21.17/3.49 (equivalent @ (equivalent @ c @ f) @ (equivalent @ e @ f))) @
% 21.17/3.49 (equivalent @ b @ (equivalent @ c @ e))) @
% 21.17/3.49 a))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X0 @ b) @ a)))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl3862, zip_derived_cl24])).
% 21.17/3.49 thf(zip_derived_cl4269, plain,
% 21.17/3.49 (![X0 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X0 @ (equivalent @ c @ f)) @
% 21.17/3.49 (equivalent @ b @ (equivalent @ c @ e))) @
% 21.17/3.49 a))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X0 @ (equivalent @ e @ f)) @ b) @ a)))),
% 21.17/3.49 inference('s_sup-', [status(thm)],
% 21.17/3.49 [zip_derived_cl148, zip_derived_cl3869])).
% 21.17/3.49 thf(zip_derived_cl148, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X4 @ X3) @ X1) @ X0))
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X4 @ X2) @ (equivalent @ X3 @ X2)) @
% 21.17/3.49 X1) @
% 21.17/3.49 X0)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl4318, plain,
% 21.17/3.49 (![X0 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X0 @ f) @ (equivalent @ e @ f)) @ b) @
% 21.17/3.49 a))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X0 @ c) @
% 21.17/3.49 (equivalent @ b @ (equivalent @ c @ e))) @
% 21.17/3.49 a)))),
% 21.17/3.49 inference('s_sup+', [status(thm)],
% 21.17/3.49 [zip_derived_cl4269, zip_derived_cl148])).
% 21.17/3.49 thf(zip_derived_cl148, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X4 @ X3) @ X1) @ X0))
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X4 @ X2) @ (equivalent @ X3 @ X2)) @
% 21.17/3.49 X1) @
% 21.17/3.49 X0)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl4326, plain,
% 21.17/3.49 (![X0 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X0 @ c) @
% 21.17/3.49 (equivalent @ b @ (equivalent @ c @ e))) @
% 21.17/3.49 a))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X0 @ e) @ b) @ a)))),
% 21.17/3.49 inference('s_sup+', [status(thm)],
% 21.17/3.49 [zip_derived_cl4318, zip_derived_cl148])).
% 21.17/3.49 thf(zip_derived_cl578, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl557, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl4333, plain,
% 21.17/3.49 (![X0 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X0 @ e) @ b) @ a))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ (equivalent @ X0 @ c) @
% 21.17/3.49 (equivalent @ b @ (equivalent @ c @ e))))))),
% 21.17/3.49 inference('s_sup+', [status(thm)],
% 21.17/3.49 [zip_derived_cl4326, zip_derived_cl578])).
% 21.17/3.49 thf(zip_derived_cl26, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)))
% 21.17/3.49 | (is_a_theorem @ X0))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl18, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.17/3.49 ( (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0)))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 21.17/3.49 inference('condensation', [status(thm)], [zip_derived_cl8])).
% 21.17/3.49 thf(zip_derived_cl53, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X3) @ (equivalent @ X0 @ X3)))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl4338, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X0 @ e) @ b) @ a))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X1) @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X0 @ c) @
% 21.17/3.49 (equivalent @ b @ (equivalent @ c @ e))) @
% 21.17/3.49 X1)))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X2 @ a)))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl4333, zip_derived_cl53])).
% 21.17/3.49 thf(zip_derived_cl4431, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X0 @ e) @ b) @ a))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ a @ X1) @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X0 @ c) @
% 21.17/3.49 (equivalent @ b @ (equivalent @ c @ e))) @
% 21.17/3.49 X1))))),
% 21.17/3.49 inference('s_sup-', [status(thm)],
% 21.17/3.49 [zip_derived_cl515, zip_derived_cl4338])).
% 21.17/3.49 thf(zip_derived_cl578, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl557, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl4518, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X1 @ e) @ b) @ a))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ c) @
% 21.17/3.49 (equivalent @ b @ (equivalent @ c @ e))) @
% 21.17/3.49 X0) @
% 21.17/3.49 (equivalent @ a @ X0))))),
% 21.17/3.49 inference('s_sup+', [status(thm)],
% 21.17/3.49 [zip_derived_cl4431, zip_derived_cl578])).
% 21.17/3.49 thf(zip_derived_cl24, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 21.17/3.49 X0)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl4547, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X1 @ e) @ b) @ a))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X1 @ c) @ X0) @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ X0 @ (equivalent @ b @ (equivalent @ c @ e)))))))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl4518, zip_derived_cl24])).
% 21.17/3.49 thf(zip_derived_cl578, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl557, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl4640, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X1 @ e) @ b) @ a))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @ X0 @ (equivalent @ b @ (equivalent @ c @ e)))) @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ c) @ X0))))),
% 21.17/3.49 inference('s_sup+', [status(thm)],
% 21.17/3.49 [zip_derived_cl4547, zip_derived_cl578])).
% 21.17/3.49 thf(zip_derived_cl4, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ X3)
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @ X3 @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X1) @
% 21.17/3.49 (equivalent @ (equivalent @ X2 @ X0) @ (equivalent @ X1 @ X0))))))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl5200, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X1 @ e) @ b) @ a))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ a @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ c @ X0)) @
% 21.17/3.49 (equivalent @ b @ (equivalent @ c @ e))))))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl4640, zip_derived_cl4])).
% 21.17/3.49 thf(zip_derived_cl578, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl557, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl5260, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X1 @ e) @ b) @ a))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ c @ X0)) @
% 21.17/3.49 (equivalent @ b @ (equivalent @ c @ e))) @
% 21.17/3.49 a)))),
% 21.17/3.49 inference('s_sup+', [status(thm)],
% 21.17/3.49 [zip_derived_cl5200, zip_derived_cl578])).
% 21.17/3.49 thf(zip_derived_cl5390, plain,
% 21.17/3.49 (![X0 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X0 @ e) @ b) @ a))
% 21.17/3.49 | ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X0 @ e) @ b) @ a)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl5260])).
% 21.17/3.49 thf(zip_derived_cl5394, plain,
% 21.17/3.49 (![X0 : $i]:
% 21.17/3.49 ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X0 @ e) @ b) @ a))),
% 21.17/3.49 inference('simplify', [status(thm)], [zip_derived_cl5390])).
% 21.17/3.49 thf(zip_derived_cl0, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 21.17/3.49 | ~ (is_a_theorem @ X0)
% 21.17/3.49 | (is_a_theorem @ X1))),
% 21.17/3.49 inference('cnf', [status(esa)], [condensed_detachment])).
% 21.17/3.49 thf(zip_derived_cl5397, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 (~ (is_a_theorem @
% 21.17/3.49 (equivalent @ X1 @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X0 @ e) @ b) @ a)))
% 21.17/3.49 | ~ (is_a_theorem @ X1))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl5394, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl5417, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ~ (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X0 @ e) @ b) @ X1) @
% 21.17/3.49 (equivalent @ a @ X1)))),
% 21.17/3.49 inference('s_sup-', [status(thm)],
% 21.17/3.49 [zip_derived_cl581, zip_derived_cl5397])).
% 21.17/3.49 thf(zip_derived_cl24, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 21.17/3.49 X0)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl5424, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ (equivalent @ X1 @ e) @ X0) @
% 21.17/3.49 (equivalent @ a @ (equivalent @ X0 @ b))))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl5417, zip_derived_cl24])).
% 21.17/3.49 thf(zip_derived_cl24, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (~ (is_a_theorem @ (equivalent @ (equivalent @ X3 @ X2) @ X0))
% 21.17/3.49 | (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ (equivalent @ X3 @ X1) @ (equivalent @ X2 @ X1)) @
% 21.17/3.49 X0)))),
% 21.17/3.49 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 21.17/3.49 thf(zip_derived_cl5898, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ~ (is_a_theorem @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ X0) @
% 21.17/3.49 (equivalent @ a @ (equivalent @ (equivalent @ X0 @ e) @ b))))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl5424, zip_derived_cl24])).
% 21.17/3.49 thf(zip_derived_cl578, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 21.17/3.49 | ~ (is_a_theorem @ (equivalent @ X0 @ X1)))),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl557, zip_derived_cl18])).
% 21.17/3.49 thf(zip_derived_cl6253, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i]:
% 21.17/3.49 ~ (is_a_theorem @
% 21.17/3.49 (equivalent @
% 21.17/3.49 (equivalent @ a @ (equivalent @ (equivalent @ X0 @ e) @ b)) @
% 21.17/3.49 (equivalent @ X1 @ X0)))),
% 21.17/3.49 inference('s_sup+', [status(thm)],
% 21.17/3.49 [zip_derived_cl5898, zip_derived_cl578])).
% 21.17/3.49 thf(zip_derived_cl1, plain,
% 21.17/3.49 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 21.17/3.49 (is_a_theorem @
% 21.17/3.49 (equivalent @ X0 @
% 21.17/3.49 (equivalent @ X0 @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ X2) @
% 21.17/3.49 (equivalent @ (equivalent @ X1 @ X3) @ (equivalent @ X2 @ X3))))))),
% 21.17/3.49 inference('cnf', [status(esa)], [lg_2])).
% 21.17/3.49 thf(zip_derived_cl6300, plain, ($false),
% 21.17/3.49 inference('s_sup+', [status(thm)], [zip_derived_cl6253, zip_derived_cl1])).
% 21.17/3.49
% 21.17/3.49 % SZS output end Refutation
% 21.17/3.49
% 21.17/3.49
% 21.17/3.49 % Terminating...
% 21.46/3.60 % Runner terminated.
% 21.46/3.61 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------