%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : COL081-1 : TPTP v9.2.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.DZTN6yURaa true
% Computer : n020.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 Oct 2 04:30:21 PM UTC 2025
% Result : Unsatisfiable 18.15s 3.23s
% Output : Refutation 18.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : COL081-1 : TPTP v9.2.0. Released v1.2.0.
% 0.07/0.16 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.DZTN6yURaa true
% 0.14/0.38 % Computer : n020.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Wed Oct 1 11:00:53 EDT 2025
% 0.14/0.39 % CPUTime :
% 0.14/0.39 % Running portfolio for 300 s
% 0.14/0.39 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.39 % Number of cores: 8
% 0.14/0.39 % Python version: Python 3.6.8
% 0.14/0.39 % Running in FO mode
% 0.56/0.72 % Total configuration time : 435
% 0.56/0.72 % Estimated wc time : 1092
% 0.56/0.72 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.82 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.83 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.83 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.84 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.84 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 18.15/3.23 % Solved by fo/fo5.sh.
% 18.15/3.23 % done 1049 iterations in 2.363s
% 18.15/3.23 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 18.15/3.23 % SZS output start Refutation
% 18.15/3.23 thf(n_type, type, n: $i > $i > $i).
% 18.15/3.23 thf(pair_type, type, pair: $i > $i > $i).
% 18.15/3.23 thf(k_type, type, k: $i > $i).
% 18.15/3.23 thf(b_type, type, b: $i).
% 18.15/3.23 thf(abstraction_type, type, abstraction: $i).
% 18.15/3.23 thf(apply_type, type, apply: $i > $i > $i).
% 18.15/3.23 thf(projection2_type, type, projection2: $i).
% 18.15/3.23 thf(projection1_type, type, projection1: $i).
% 18.15/3.23 thf(prove_TRC2c, conjecture,
% 18.15/3.23 (( k @ ( k @ b ) ) = ( apply @ abstraction @ ( k @ ( k @ b ) ) ))).
% 18.15/3.23 thf(zf_stmt_0, negated_conjecture,
% 18.15/3.23 (( k @ ( k @ b ) ) != ( apply @ abstraction @ ( k @ ( k @ b ) ) )),
% 18.15/3.23 inference('cnf.neg', [status(esa)], [prove_TRC2c])).
% 18.15/3.23 thf(zip_derived_cl11, plain,
% 18.15/3.23 (((k @ (k @ b)) != (apply @ abstraction @ (k @ (k @ b))))),
% 18.15/3.23 inference('cnf', [status(esa)], [zf_stmt_0])).
% 18.15/3.23 thf(projection1, axiom, (( apply @ projection1 @ ( pair @ X @ Y ) ) = ( X ))).
% 18.15/3.23 thf(zip_derived_cl1, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]: ((apply @ projection1 @ (pair @ X0 @ X1)) = (X0))),
% 18.15/3.23 inference('cnf', [status(esa)], [projection1])).
% 18.15/3.23 thf(k_definition, axiom, (( apply @ ( k @ X ) @ Y ) = ( X ))).
% 18.15/3.23 thf(zip_derived_cl0, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]: ((apply @ (k @ X0) @ X1) = (X0))),
% 18.15/3.23 inference('cnf', [status(esa)], [k_definition])).
% 18.15/3.23 thf(pairing, axiom,
% 18.15/3.23 (( pair @ ( apply @ projection1 @ X ) @ ( apply @ projection2 @ X ) ) =
% 18.15/3.23 ( X ))).
% 18.15/3.23 thf(zip_derived_cl3, plain,
% 18.15/3.23 (![X0 : $i]:
% 18.15/3.23 ((pair @ (apply @ projection1 @ X0) @ (apply @ projection2 @ X0))
% 18.15/3.23 = (X0))),
% 18.15/3.23 inference('cnf', [status(esa)], [pairing])).
% 18.15/3.23 thf(pairwise_application, axiom,
% 18.15/3.23 (( apply @ ( pair @ X @ Y ) @ Z ) =
% 18.15/3.23 ( pair @ ( apply @ X @ Z ) @ ( apply @ Y @ Z ) ))).
% 18.15/3.23 thf(zip_derived_cl4, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.15/3.23 ((apply @ (pair @ X0 @ X2) @ X1)
% 18.15/3.23 = (pair @ (apply @ X0 @ X1) @ (apply @ X2 @ X1)))),
% 18.15/3.23 inference('cnf', [status(esa)], [pairwise_application])).
% 18.15/3.23 thf(zip_derived_cl1, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]: ((apply @ projection1 @ (pair @ X0 @ X1)) = (X0))),
% 18.15/3.23 inference('cnf', [status(esa)], [projection1])).
% 18.15/3.23 thf(zip_derived_cl24, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.15/3.23 ((apply @ projection1 @ (apply @ (pair @ X2 @ X1) @ X0))
% 18.15/3.23 = (apply @ X2 @ X0))),
% 18.15/3.23 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl1])).
% 18.15/3.23 thf(zip_derived_cl55, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]:
% 18.15/3.23 ((apply @ projection1 @ (apply @ X0 @ X1))
% 18.15/3.23 = (apply @ (apply @ projection1 @ X0) @ X1))),
% 18.15/3.23 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl24])).
% 18.15/3.23 thf(zip_derived_cl0, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]: ((apply @ (k @ X0) @ X1) = (X0))),
% 18.15/3.23 inference('cnf', [status(esa)], [k_definition])).
% 18.15/3.23 thf(extensionality2, axiom,
% 18.15/3.23 (( ( X ) = ( Y ) ) |
% 18.15/3.23 ( ( apply @ X @ ( n @ X @ Y ) ) != ( apply @ Y @ ( n @ X @ Y ) ) ))).
% 18.15/3.23 thf(zip_derived_cl8, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]:
% 18.15/3.23 (((X1) = (X0))
% 18.15/3.23 | ((apply @ X1 @ (n @ X1 @ X0)) != (apply @ X0 @ (n @ X1 @ X0))))),
% 18.15/3.23 inference('cnf', [status(esa)], [extensionality2])).
% 18.15/3.23 thf(zip_derived_cl73, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]:
% 18.15/3.23 (((X0) != (apply @ X1 @ (n @ (k @ X0) @ X1))) | ((k @ X0) = (X1)))),
% 18.15/3.23 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl8])).
% 18.15/3.23 thf(zip_derived_cl121, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]:
% 18.15/3.23 (((X1)
% 18.15/3.23 != (apply @ projection1 @
% 18.15/3.23 (apply @ X0 @ (n @ (k @ X1) @ (apply @ projection1 @ X0)))))
% 18.15/3.23 | ((k @ X1) = (apply @ projection1 @ X0)))),
% 18.15/3.23 inference('sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl73])).
% 18.15/3.23 thf(zip_derived_cl334, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]:
% 18.15/3.23 (((X1) != (apply @ projection1 @ X0))
% 18.15/3.23 | ((k @ X1) = (apply @ projection1 @ (k @ X0))))),
% 18.15/3.23 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl121])).
% 18.15/3.23 thf(zip_derived_cl352, plain,
% 18.15/3.23 (![X0 : $i]:
% 18.15/3.23 ((k @ (apply @ projection1 @ X0)) = (apply @ projection1 @ (k @ X0)))),
% 18.15/3.23 inference('eq_res', [status(thm)], [zip_derived_cl334])).
% 18.15/3.23 thf(zip_derived_cl389, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]:
% 18.15/3.23 ((k @ X0) = (apply @ projection1 @ (k @ (pair @ X0 @ X1))))),
% 18.15/3.23 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl352])).
% 18.15/3.23 thf(zip_derived_cl352, plain,
% 18.15/3.23 (![X0 : $i]:
% 18.15/3.23 ((k @ (apply @ projection1 @ X0)) = (apply @ projection1 @ (k @ X0)))),
% 18.15/3.23 inference('eq_res', [status(thm)], [zip_derived_cl334])).
% 18.15/3.23 thf(zip_derived_cl493, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]:
% 18.15/3.23 ((k @ (k @ X0)) = (apply @ projection1 @ (k @ (k @ (pair @ X0 @ X1)))))),
% 18.15/3.23 inference('sup+', [status(thm)], [zip_derived_cl389, zip_derived_cl352])).
% 18.15/3.23 thf(zip_derived_cl55, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]:
% 18.15/3.23 ((apply @ projection1 @ (apply @ X0 @ X1))
% 18.15/3.23 = (apply @ (apply @ projection1 @ X0) @ X1))),
% 18.15/3.23 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl24])).
% 18.15/3.23 thf(abstraction, axiom,
% 18.15/3.23 (( apply @ ( apply @ ( apply @ abstraction @ X ) @ Y ) @ Z ) =
% 18.15/3.23 ( apply @ ( apply @ X @ ( k @ Z ) ) @ ( apply @ Y @ Z ) ))).
% 18.15/3.23 thf(zip_derived_cl5, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.15/3.23 ((apply @ (apply @ (apply @ abstraction @ X0) @ X2) @ X1)
% 18.15/3.23 = (apply @ (apply @ X0 @ (k @ X1)) @ (apply @ X2 @ X1)))),
% 18.15/3.23 inference('cnf', [status(esa)], [abstraction])).
% 18.15/3.23 thf(zip_derived_cl109, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.15/3.23 ((apply @
% 18.15/3.23 (apply @ (apply @ abstraction @ (apply @ projection1 @ X1)) @ X2) @
% 18.15/3.23 X0)
% 18.15/3.23 = (apply @ (apply @ projection1 @ (apply @ X1 @ (k @ X0))) @
% 18.15/3.23 (apply @ X2 @ X0)))),
% 18.15/3.23 inference('sup+', [status(thm)], [zip_derived_cl55, zip_derived_cl5])).
% 18.15/3.23 thf(zip_derived_cl17132, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 18.15/3.23 ((apply @ (apply @ (apply @ abstraction @ (k @ (k @ X0))) @ X2) @ X1)
% 18.15/3.23 = (apply @
% 18.15/3.23 (apply @ projection1 @
% 18.15/3.23 (apply @ (k @ (k @ (pair @ X0 @ X3))) @ (k @ X1))) @
% 18.15/3.23 (apply @ X2 @ X1)))),
% 18.15/3.23 inference('sup+', [status(thm)], [zip_derived_cl493, zip_derived_cl109])).
% 18.15/3.23 thf(zip_derived_cl0, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]: ((apply @ (k @ X0) @ X1) = (X0))),
% 18.15/3.23 inference('cnf', [status(esa)], [k_definition])).
% 18.15/3.23 thf(zip_derived_cl389, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]:
% 18.15/3.23 ((k @ X0) = (apply @ projection1 @ (k @ (pair @ X0 @ X1))))),
% 18.15/3.23 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl352])).
% 18.15/3.23 thf(zip_derived_cl0, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]: ((apply @ (k @ X0) @ X1) = (X0))),
% 18.15/3.23 inference('cnf', [status(esa)], [k_definition])).
% 18.15/3.23 thf(zip_derived_cl17389, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.15/3.23 ((apply @ (apply @ (apply @ abstraction @ (k @ (k @ X0))) @ X2) @ X1)
% 18.15/3.23 = (X0))),
% 18.15/3.23 inference('demod', [status(thm)],
% 18.15/3.23 [zip_derived_cl17132, zip_derived_cl0, zip_derived_cl389,
% 18.15/3.23 zip_derived_cl0])).
% 18.15/3.23 thf(zip_derived_cl73, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]:
% 18.15/3.23 (((X0) != (apply @ X1 @ (n @ (k @ X0) @ X1))) | ((k @ X0) = (X1)))),
% 18.15/3.23 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl8])).
% 18.15/3.23 thf(zip_derived_cl17649, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 18.15/3.23 (((X2) != (X0))
% 18.15/3.23 | ((k @ X2) = (apply @ (apply @ abstraction @ (k @ (k @ X0))) @ X1)))),
% 18.15/3.23 inference('sup-', [status(thm)], [zip_derived_cl17389, zip_derived_cl73])).
% 18.15/3.23 thf(zip_derived_cl17742, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]:
% 18.15/3.23 ((k @ X0) = (apply @ (apply @ abstraction @ (k @ (k @ X0))) @ X1))),
% 18.15/3.23 inference('eq_res', [status(thm)], [zip_derived_cl17649])).
% 18.15/3.23 thf(zip_derived_cl73, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]:
% 18.15/3.23 (((X0) != (apply @ X1 @ (n @ (k @ X0) @ X1))) | ((k @ X0) = (X1)))),
% 18.15/3.23 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl8])).
% 18.15/3.23 thf(zip_derived_cl17806, plain,
% 18.15/3.23 (![X0 : $i, X1 : $i]:
% 18.15/3.23 (((X1) != (k @ X0))
% 18.15/3.23 | ((k @ X1) = (apply @ abstraction @ (k @ (k @ X0)))))),
% 18.15/3.23 inference('sup-', [status(thm)], [zip_derived_cl17742, zip_derived_cl73])).
% 18.15/3.23 thf(zip_derived_cl17909, plain,
% 18.15/3.23 (![X0 : $i]: ((k @ (k @ X0)) = (apply @ abstraction @ (k @ (k @ X0))))),
% 18.15/3.23 inference('eq_res', [status(thm)], [zip_derived_cl17806])).
% 18.15/3.23 thf(zip_derived_cl17913, plain, (((k @ (k @ b)) != (k @ (k @ b)))),
% 18.15/3.23 inference('demod', [status(thm)], [zip_derived_cl11, zip_derived_cl17909])).
% 18.15/3.23 thf(zip_derived_cl17914, plain, ($false),
% 18.15/3.23 inference('simplify', [status(thm)], [zip_derived_cl17913])).
% 18.15/3.23
% 18.15/3.23 % SZS output end Refutation
% 18.15/3.23
% 18.15/3.23
% 18.15/3.23 % Terminating...
% 18.74/3.32 % Runner terminated.
% 18.74/3.34 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------