%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL144-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.V4fUvTPwsi true
% Computer : n006.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 01:35:17 PM UTC 2026
% Result : Unsatisfiable 14.44s 2.79s
% Output : Refutation 14.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL144-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.V4fUvTPwsi true
% 0.09/0.38 % Computer : n006.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 5 03:30:46 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Running portfolio for 300 s
% 0.09/0.38 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.38 % Number of cores: 8
% 0.09/0.39 % Python version: Python 3.12.3
% 0.09/0.39 % Running in FO mode
% 0.39/0.67 % Total configuration time : 435
% 0.39/0.67 % Estimated wc time : 1092
% 0.39/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.43/0.74 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.44/0.80 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.44/0.80 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.44/0.81 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.44/0.81 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.44/0.81 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.44/0.81 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 14.44/2.79 % Solved by fo/fo3_bce.sh.
% 14.44/2.79 % BCE start: 10
% 14.44/2.79 % BCE eliminated: 0
% 14.44/2.79 % PE start: 10
% 14.44/2.79 logic: eq
% 14.44/2.79 % PE eliminated: 0
% 14.44/2.79 % done 701 iterations in 1.957s
% 14.44/2.79 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 14.44/2.79 % SZS output start Refutation
% 14.44/2.79 thf(x_type, type, x: $i).
% 14.44/2.79 thf(z_type, type, z: $i).
% 14.44/2.79 thf(y_type, type, y: $i).
% 14.44/2.79 thf(truth_type, type, truth: $i).
% 14.44/2.79 thf(implies_type, type, implies: $i > $i > $i).
% 14.44/2.79 thf(ordered_type, type, ordered: $i > $i > $o).
% 14.44/2.79 thf(wajsberg_1, axiom, (( implies @ truth @ X ) = ( X ))).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(partial_order_definition1, axiom,
% 14.44/2.79 (( ~( ordered @ X @ Y ) ) | ( ( implies @ X @ Y ) = ( truth ) ))).
% 14.44/2.79 thf(zip_derived_cl6, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i]:
% 14.44/2.79 (~ (ordered @ X0 @ X1) | ((implies @ X0 @ X1) = (truth)))),
% 14.44/2.79 inference('cnf', [status(esa)], [partial_order_definition1])).
% 14.44/2.79 thf(antecedent, conjecture,
% 14.44/2.79 (~( ( ordered @ y @ ( implies @ x @ z ) ) |
% 14.44/2.79 ( ordered @ x @ ( implies @ y @ z ) ) ))).
% 14.44/2.79 thf(zf_stmt_0, negated_conjecture,
% 14.44/2.79 (( ordered @ y @ ( implies @ x @ z ) ) |
% 14.44/2.79 ( ordered @ x @ ( implies @ y @ z ) )),
% 14.44/2.79 inference('cnf.neg', [status(esa)], [antecedent])).
% 14.44/2.79 thf(zip_derived_cl8, plain,
% 14.44/2.79 (( (ordered @ y @ (implies @ x @ z)) | (ordered @ x @ (implies @ y @ z)))),
% 14.44/2.79 inference('cnf', [status(esa)], [zf_stmt_0])).
% 14.44/2.79 thf(zip_derived_cl28, plain,
% 14.44/2.79 ((((implies @ y @ (implies @ x @ z)) = (truth))
% 14.44/2.79 | (ordered @ x @ (implies @ y @ z)))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl8])).
% 14.44/2.79 thf(zip_derived_cl6, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i]:
% 14.44/2.79 (~ (ordered @ X0 @ X1) | ((implies @ X0 @ X1) = (truth)))),
% 14.44/2.79 inference('cnf', [status(esa)], [partial_order_definition1])).
% 14.44/2.79 thf(zip_derived_cl30, plain,
% 14.44/2.79 ((((implies @ y @ (implies @ x @ z)) = (truth))
% 14.44/2.79 | ((implies @ x @ (implies @ y @ z)) = (truth)))),
% 14.44/2.79 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl6])).
% 14.44/2.79 thf(wajsberg_2, axiom,
% 14.44/2.79 (( implies @
% 14.44/2.79 ( implies @ X @ Y ) @
% 14.44/2.79 ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) =
% 14.44/2.79 ( truth ))).
% 14.44/2.79 thf(zip_derived_cl1, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.44/2.79 ((implies @ (implies @ X0 @ X1) @
% 14.44/2.79 (implies @ (implies @ X1 @ X2) @ (implies @ X0 @ X2))) = (truth))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_2])).
% 14.44/2.79 thf(zip_derived_cl59, plain,
% 14.44/2.79 (![X0 : $i]:
% 14.44/2.79 (((implies @ truth @
% 14.44/2.79 (implies @ (implies @ (implies @ x @ z) @ X0) @ (implies @ y @ X0)))
% 14.44/2.79 = (truth))
% 14.44/2.79 | ((implies @ x @ (implies @ y @ z)) = (truth)))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl1])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl1815, plain,
% 14.44/2.79 (![X0 : $i]:
% 14.44/2.79 (((truth)
% 14.44/2.79 = (implies @ (implies @ (implies @ x @ z) @ X0) @
% 14.44/2.79 (implies @ y @ X0)))
% 14.44/2.79 | ((implies @ x @ (implies @ y @ z)) = (truth)))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl59, zip_derived_cl0])).
% 14.44/2.79 thf(zip_derived_cl1, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.44/2.79 ((implies @ (implies @ X0 @ X1) @
% 14.44/2.79 (implies @ (implies @ X1 @ X2) @ (implies @ X0 @ X2))) = (truth))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_2])).
% 14.44/2.79 thf(zip_derived_cl1, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.44/2.79 ((implies @ (implies @ X0 @ X1) @
% 14.44/2.79 (implies @ (implies @ X1 @ X2) @ (implies @ X0 @ X2))) = (truth))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_2])).
% 14.44/2.79 thf(zip_derived_cl32, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 14.44/2.79 ((implies @ truth @
% 14.44/2.79 (implies @
% 14.44/2.79 (implies @ (implies @ (implies @ X1 @ X3) @ (implies @ X2 @ X3)) @
% 14.44/2.79 X0) @
% 14.44/2.79 (implies @ (implies @ X2 @ X1) @ X0)))
% 14.44/2.79 = (truth))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl1])).
% 14.44/2.79 thf(zip_derived_cl3952, plain,
% 14.44/2.79 (![X0 : $i]:
% 14.44/2.79 (((implies @ truth @
% 14.44/2.79 (implies @ truth @
% 14.44/2.79 (implies @ (implies @ X0 @ x) @ (implies @ y @ (implies @ X0 @ z)))))
% 14.44/2.79 = (truth))
% 14.44/2.79 | ((implies @ x @ (implies @ y @ z)) = (truth)))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl1815, zip_derived_cl32])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl4016, plain,
% 14.44/2.79 (![X0 : $i]:
% 14.44/2.79 (((implies @ (implies @ X0 @ x) @ (implies @ y @ (implies @ X0 @ z)))
% 14.44/2.79 = (truth))
% 14.44/2.79 | ((implies @ x @ (implies @ y @ z)) = (truth)))),
% 14.44/2.79 inference('demod', [status(thm)],
% 14.44/2.79 [zip_derived_cl3952, zip_derived_cl0, zip_derived_cl0])).
% 14.44/2.79 thf(zip_derived_cl7063, plain,
% 14.44/2.79 ((((implies @ (implies @ truth @ x) @ (implies @ y @ z)) = (truth))
% 14.44/2.79 | ((implies @ x @ (implies @ y @ z)) = (truth)))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl4016])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl7083, plain,
% 14.44/2.79 ((((implies @ x @ (implies @ y @ z)) = (truth))
% 14.44/2.79 | ((implies @ x @ (implies @ y @ z)) = (truth)))),
% 14.44/2.79 inference('demod', [status(thm)], [zip_derived_cl7063, zip_derived_cl0])).
% 14.44/2.79 thf(zip_derived_cl7084, plain,
% 14.44/2.79 (((implies @ x @ (implies @ y @ z)) = (truth))),
% 14.44/2.79 inference('simplify', [status(thm)], [zip_derived_cl7083])).
% 14.44/2.79 thf(zip_derived_cl1, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.44/2.79 ((implies @ (implies @ X0 @ X1) @
% 14.44/2.79 (implies @ (implies @ X1 @ X2) @ (implies @ X0 @ X2))) = (truth))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_2])).
% 14.44/2.79 thf(wajsberg_3, axiom,
% 14.44/2.79 (( implies @ ( implies @ X @ Y ) @ Y ) =
% 14.44/2.79 ( implies @ ( implies @ Y @ X ) @ X ))).
% 14.44/2.79 thf(zip_derived_cl2, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i]:
% 14.44/2.79 ((implies @ (implies @ X1 @ X0) @ X0)
% 14.44/2.79 = (implies @ (implies @ X0 @ X1) @ X1))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_3])).
% 14.44/2.79 thf(zip_derived_cl92, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.44/2.79 ((implies @ truth @
% 14.44/2.79 (implies @ (implies @ X0 @ X2) @ (implies @ X1 @ X2)))
% 14.44/2.79 = (implies @
% 14.44/2.79 (implies @
% 14.44/2.79 (implies @ (implies @ X0 @ X2) @ (implies @ X1 @ X2)) @
% 14.44/2.79 (implies @ X1 @ X0)) @
% 14.44/2.79 (implies @ X1 @ X0)))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl98, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.44/2.79 ((implies @ (implies @ X0 @ X2) @ (implies @ X1 @ X2))
% 14.44/2.79 = (implies @
% 14.44/2.79 (implies @
% 14.44/2.79 (implies @ (implies @ X0 @ X2) @ (implies @ X1 @ X2)) @
% 14.44/2.79 (implies @ X1 @ X0)) @
% 14.44/2.79 (implies @ X1 @ X0)))),
% 14.44/2.79 inference('demod', [status(thm)], [zip_derived_cl92, zip_derived_cl0])).
% 14.44/2.79 thf(zip_derived_cl7147, plain,
% 14.44/2.79 (![X0 : $i]:
% 14.44/2.79 ((implies @ (implies @ (implies @ y @ z) @ X0) @ (implies @ x @ X0))
% 14.44/2.79 = (implies @
% 14.44/2.79 (implies @
% 14.44/2.79 (implies @ (implies @ (implies @ y @ z) @ X0) @
% 14.44/2.79 (implies @ x @ X0)) @
% 14.44/2.79 (implies @ x @ (implies @ y @ z))) @
% 14.44/2.79 truth))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl7084, zip_derived_cl98])).
% 14.44/2.79 thf(zip_derived_cl7084, plain,
% 14.44/2.79 (((implies @ x @ (implies @ y @ z)) = (truth))),
% 14.44/2.79 inference('simplify', [status(thm)], [zip_derived_cl7083])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl2, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i]:
% 14.44/2.79 ((implies @ (implies @ X1 @ X0) @ X0)
% 14.44/2.79 = (implies @ (implies @ X0 @ X1) @ X1))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_3])).
% 14.44/2.79 thf(zip_derived_cl93, plain,
% 14.44/2.79 (![X0 : $i]:
% 14.44/2.79 ((implies @ X0 @ X0) = (implies @ (implies @ X0 @ truth) @ truth))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl1, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.44/2.79 ((implies @ (implies @ X0 @ X1) @
% 14.44/2.79 (implies @ (implies @ X1 @ X2) @ (implies @ X0 @ X2))) = (truth))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_2])).
% 14.44/2.79 thf(zip_derived_cl40, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i]:
% 14.44/2.79 ((implies @ (implies @ X1 @ truth) @
% 14.44/2.79 (implies @ X0 @ (implies @ X1 @ X0))) = (truth))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 14.44/2.79 thf(zip_derived_cl1254, plain,
% 14.44/2.79 (![X0 : $i]:
% 14.44/2.79 ((implies @ (implies @ truth @ truth) @ (implies @ X0 @ X0)) = (truth))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl40])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl1288, plain, (![X0 : $i]: ((implies @ X0 @ X0) = (truth))),
% 14.44/2.79 inference('demod', [status(thm)],
% 14.44/2.79 [zip_derived_cl1254, zip_derived_cl0, zip_derived_cl0])).
% 14.44/2.79 thf(zip_derived_cl1307, plain,
% 14.44/2.79 (![X0 : $i]: ((truth) = (implies @ (implies @ X0 @ truth) @ truth))),
% 14.44/2.79 inference('demod', [status(thm)], [zip_derived_cl93, zip_derived_cl1288])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl1, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.44/2.79 ((implies @ (implies @ X0 @ X1) @
% 14.44/2.79 (implies @ (implies @ X1 @ X2) @ (implies @ X0 @ X2))) = (truth))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_2])).
% 14.44/2.79 thf(zip_derived_cl38, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i]:
% 14.44/2.79 ((implies @ (implies @ truth @ X1) @
% 14.44/2.79 (implies @ (implies @ X1 @ X0) @ X0)) = (truth))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl43, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i]:
% 14.44/2.79 ((implies @ X1 @ (implies @ (implies @ X1 @ X0) @ X0)) = (truth))),
% 14.44/2.79 inference('demod', [status(thm)], [zip_derived_cl38, zip_derived_cl0])).
% 14.44/2.79 thf(zip_derived_cl1655, plain,
% 14.44/2.79 (![X0 : $i]: ((implies @ X0 @ truth) = (truth))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl1307, zip_derived_cl43])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl7179, plain,
% 14.44/2.79 (![X0 : $i]:
% 14.44/2.79 ((implies @ (implies @ (implies @ y @ z) @ X0) @ (implies @ x @ X0))
% 14.44/2.79 = (truth))),
% 14.44/2.79 inference('demod', [status(thm)],
% 14.44/2.79 [zip_derived_cl7147, zip_derived_cl7084, zip_derived_cl1655,
% 14.44/2.79 zip_derived_cl0])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl32, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 14.44/2.79 ((implies @ truth @
% 14.44/2.79 (implies @
% 14.44/2.79 (implies @ (implies @ (implies @ X1 @ X3) @ (implies @ X2 @ X3)) @
% 14.44/2.79 X0) @
% 14.44/2.79 (implies @ (implies @ X2 @ X1) @ X0)))
% 14.44/2.79 = (truth))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl1])).
% 14.44/2.79 thf(zip_derived_cl176, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.44/2.79 ((implies @ truth @
% 14.44/2.79 (implies @
% 14.44/2.79 (implies @
% 14.44/2.79 (implies @ (implies @ X0 @ X2) @ (implies @ truth @ X2)) @ X1) @
% 14.44/2.79 (implies @ X0 @ X1)))
% 14.44/2.79 = (truth))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl32])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl215, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.44/2.79 ((implies @ (implies @ (implies @ (implies @ X0 @ X2) @ X2) @ X1) @
% 14.44/2.79 (implies @ X0 @ X1)) = (truth))),
% 14.44/2.79 inference('demod', [status(thm)],
% 14.44/2.79 [zip_derived_cl176, zip_derived_cl0, zip_derived_cl0])).
% 14.44/2.79 thf(zip_derived_cl9516, plain,
% 14.44/2.79 (((implies @ truth @ (implies @ y @ (implies @ x @ z))) = (truth))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl7179, zip_derived_cl215])).
% 14.44/2.79 thf(zip_derived_cl0, plain, (![X0 : $i]: ((implies @ truth @ X0) = (X0))),
% 14.44/2.79 inference('cnf', [status(esa)], [wajsberg_1])).
% 14.44/2.79 thf(zip_derived_cl9705, plain,
% 14.44/2.79 (((truth) = (implies @ y @ (implies @ x @ z)))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl9516, zip_derived_cl0])).
% 14.44/2.79 thf(partial_order_definition2, axiom,
% 14.44/2.79 (( ( implies @ X @ Y ) != ( truth ) ) | ( ordered @ X @ Y ))).
% 14.44/2.79 thf(zip_derived_cl7, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i]:
% 14.44/2.79 (((implies @ X0 @ X1) != (truth)) | (ordered @ X0 @ X1))),
% 14.44/2.79 inference('cnf', [status(esa)], [partial_order_definition2])).
% 14.44/2.79 thf(prove_wajsberg_theorem, conjecture,
% 14.44/2.79 (~( ( ~( ordered @ y @ ( implies @ x @ z ) ) ) |
% 14.44/2.79 ( ~( ordered @ x @ ( implies @ y @ z ) ) ) ))).
% 14.44/2.79 thf(zf_stmt_1, negated_conjecture,
% 14.44/2.79 (( ~( ordered @ y @ ( implies @ x @ z ) ) ) |
% 14.44/2.79 ( ~( ordered @ x @ ( implies @ y @ z ) ) )),
% 14.44/2.79 inference('cnf.neg', [status(esa)], [prove_wajsberg_theorem])).
% 14.44/2.79 thf(zip_derived_cl9, plain,
% 14.44/2.79 ((~ (ordered @ y @ (implies @ x @ z))
% 14.44/2.79 | ~ (ordered @ x @ (implies @ y @ z)))),
% 14.44/2.79 inference('cnf', [status(esa)], [zf_stmt_1])).
% 14.44/2.79 thf(zip_derived_cl48, plain,
% 14.44/2.79 ((((implies @ y @ (implies @ x @ z)) != (truth))
% 14.44/2.79 | ~ (ordered @ x @ (implies @ y @ z)))),
% 14.44/2.79 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 14.44/2.79 thf(zip_derived_cl7, plain,
% 14.44/2.79 (![X0 : $i, X1 : $i]:
% 14.44/2.79 (((implies @ X0 @ X1) != (truth)) | (ordered @ X0 @ X1))),
% 14.44/2.79 inference('cnf', [status(esa)], [partial_order_definition2])).
% 14.44/2.79 thf(zip_derived_cl53, plain,
% 14.44/2.79 ((((implies @ y @ (implies @ x @ z)) != (truth))
% 14.44/2.79 | ((implies @ x @ (implies @ y @ z)) != (truth)))),
% 14.44/2.79 inference('sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl7])).
% 14.44/2.79 thf(zip_derived_cl7084, plain,
% 14.44/2.79 (((implies @ x @ (implies @ y @ z)) = (truth))),
% 14.44/2.79 inference('simplify', [status(thm)], [zip_derived_cl7083])).
% 14.44/2.79 thf(zip_derived_cl7127, plain,
% 14.44/2.79 ((((implies @ y @ (implies @ x @ z)) != (truth)) | ((truth) != (truth)))),
% 14.44/2.79 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl7084])).
% 14.44/2.79 thf(zip_derived_cl7128, plain,
% 14.44/2.79 (((implies @ y @ (implies @ x @ z)) != (truth))),
% 14.44/2.79 inference('simplify', [status(thm)], [zip_derived_cl7127])).
% 14.44/2.79 thf(zip_derived_cl9741, plain, ($false),
% 14.44/2.79 inference('simplify_reflect-', [status(thm)],
% 14.44/2.79 [zip_derived_cl9705, zip_derived_cl7128])).
% 14.44/2.79
% 14.44/2.79 % SZS output end Refutation
% 14.44/2.79
% 14.44/2.79
% 14.44/2.80 % Terminating...
% 15.15/2.85 % Runner terminated.
% 15.15/2.88 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------