TSTP Solution File: COL078-2 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : COL078-2 : TPTP v8.1.2. Released v1.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.CjS9M0h9yL true
% Computer : n029.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 : Wed Aug 30 18:34:46 EDT 2023
% Result : Unsatisfiable 3.72s 1.19s
% Output : Refutation 3.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL078-2 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.CjS9M0h9yL true
% 0.17/0.34 % Computer : n029.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Sun Aug 27 04:34:40 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.17/0.34 % Running portfolio for 300 s
% 0.17/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.34 % Number of cores: 8
% 0.17/0.34 % Python version: Python 3.6.8
% 0.17/0.34 % Running in FO mode
% 0.20/0.64 % Total configuration time : 435
% 0.20/0.64 % Estimated wc time : 1092
% 0.20/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.71 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.73 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 3.72/1.19 % Solved by fo/fo5.sh.
% 3.72/1.19 % done 246 iterations in 0.402s
% 3.72/1.19 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 3.72/1.19 % SZS output start Refutation
% 3.72/1.19 thf(k_type, type, k: $i > $i).
% 3.72/1.19 thf(identity_type, type, identity: $i).
% 3.72/1.19 thf(apply_type, type, apply: $i > $i > $i).
% 3.72/1.19 thf(n_type, type, n: $i > $i > $i).
% 3.72/1.19 thf(abstraction_type, type, abstraction: $i).
% 3.72/1.19 thf(abstraction, axiom,
% 3.72/1.19 (( apply @ ( apply @ ( apply @ abstraction @ X ) @ Y ) @ Z ) =
% 3.72/1.19 ( apply @ ( apply @ X @ ( k @ Z ) ) @ ( apply @ Y @ Z ) ))).
% 3.72/1.19 thf(zip_derived_cl1, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.72/1.19 ((apply @ (apply @ (apply @ abstraction @ X0) @ X2) @ X1)
% 3.72/1.19 = (apply @ (apply @ X0 @ (k @ X1)) @ (apply @ X2 @ X1)))),
% 3.72/1.19 inference('cnf', [status(esa)], [abstraction])).
% 3.72/1.19 thf(zip_derived_cl1, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.72/1.19 ((apply @ (apply @ (apply @ abstraction @ X0) @ X2) @ X1)
% 3.72/1.19 = (apply @ (apply @ X0 @ (k @ X1)) @ (apply @ X2 @ X1)))),
% 3.72/1.19 inference('cnf', [status(esa)], [abstraction])).
% 3.72/1.19 thf(zip_derived_cl13, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.72/1.19 ((apply @
% 3.72/1.19 (apply @ (apply @ (apply @ abstraction @ abstraction) @ X1) @ X0) @
% 3.72/1.19 X2)
% 3.72/1.19 = (apply @ (apply @ (k @ X0) @ (k @ X2)) @
% 3.72/1.19 (apply @ (apply @ X1 @ X0) @ X2)))),
% 3.72/1.19 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl1])).
% 3.72/1.19 thf(k_definition, axiom, (( apply @ ( k @ X ) @ Y ) = ( X ))).
% 3.72/1.19 thf(zip_derived_cl0, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i]: ((apply @ (k @ X0) @ X1) = (X0))),
% 3.72/1.19 inference('cnf', [status(esa)], [k_definition])).
% 3.72/1.19 thf(zip_derived_cl20, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.72/1.19 ((apply @
% 3.72/1.19 (apply @ (apply @ (apply @ abstraction @ abstraction) @ X1) @ X0) @
% 3.72/1.19 X2) = (apply @ X0 @ (apply @ (apply @ X1 @ X0) @ X2)))),
% 3.72/1.19 inference('demod', [status(thm)], [zip_derived_cl13, zip_derived_cl0])).
% 3.72/1.19 thf(zip_derived_cl1, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.72/1.19 ((apply @ (apply @ (apply @ abstraction @ X0) @ X2) @ X1)
% 3.72/1.19 = (apply @ (apply @ X0 @ (k @ X1)) @ (apply @ X2 @ X1)))),
% 3.72/1.19 inference('cnf', [status(esa)], [abstraction])).
% 3.72/1.19 thf(zip_derived_cl954, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.72/1.19 ((apply @
% 3.72/1.19 (apply @
% 3.72/1.19 (apply @ abstraction @
% 3.72/1.19 (apply @ (apply @ abstraction @ abstraction) @ X2)) @
% 3.72/1.19 X1) @
% 3.72/1.19 X0)
% 3.72/1.19 = (apply @ (k @ X0) @
% 3.72/1.19 (apply @ (apply @ X2 @ (k @ X0)) @ (apply @ X1 @ X0))))),
% 3.72/1.19 inference('sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl1])).
% 3.72/1.19 thf(zip_derived_cl0, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i]: ((apply @ (k @ X0) @ X1) = (X0))),
% 3.72/1.19 inference('cnf', [status(esa)], [k_definition])).
% 3.72/1.19 thf(zip_derived_cl1035, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.72/1.19 ((apply @
% 3.72/1.19 (apply @
% 3.72/1.19 (apply @ abstraction @
% 3.72/1.19 (apply @ (apply @ abstraction @ abstraction) @ X2)) @
% 3.72/1.19 X1) @
% 3.72/1.19 X0) = (X0))),
% 3.72/1.19 inference('demod', [status(thm)], [zip_derived_cl954, zip_derived_cl0])).
% 3.72/1.19 thf(identity_definition, axiom, (( apply @ identity @ X ) = ( X ))).
% 3.72/1.19 thf(zip_derived_cl3, plain, (![X0 : $i]: ((apply @ identity @ X0) = (X0))),
% 3.72/1.19 inference('cnf', [status(esa)], [identity_definition])).
% 3.72/1.19 thf(extensionality2, axiom,
% 3.72/1.19 (( ( X ) = ( Y ) ) |
% 3.72/1.19 ( ( apply @ X @ ( n @ X @ Y ) ) != ( apply @ Y @ ( n @ X @ Y ) ) ))).
% 3.72/1.19 thf(zip_derived_cl2, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i]:
% 3.72/1.19 (((X1) = (X0))
% 3.72/1.19 | ((apply @ X1 @ (n @ X1 @ X0)) != (apply @ X0 @ (n @ X1 @ X0))))),
% 3.72/1.19 inference('cnf', [status(esa)], [extensionality2])).
% 3.72/1.19 thf(zip_derived_cl6, plain,
% 3.72/1.19 (![X0 : $i]:
% 3.72/1.19 (((n @ identity @ X0) != (apply @ X0 @ (n @ identity @ X0)))
% 3.72/1.19 | ((identity) = (X0)))),
% 3.72/1.19 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl2])).
% 3.72/1.19 thf(zip_derived_cl1640, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i]:
% 3.72/1.19 (((n @ identity @
% 3.72/1.19 (apply @
% 3.72/1.19 (apply @ abstraction @
% 3.72/1.19 (apply @ (apply @ abstraction @ abstraction) @ X1)) @
% 3.72/1.19 X0))
% 3.72/1.19 != (n @ identity @
% 3.72/1.19 (apply @
% 3.72/1.19 (apply @ abstraction @
% 3.72/1.19 (apply @ (apply @ abstraction @ abstraction) @ X1)) @
% 3.72/1.19 X0)))
% 3.72/1.19 | ((identity)
% 3.72/1.19 = (apply @
% 3.72/1.19 (apply @ abstraction @
% 3.72/1.19 (apply @ (apply @ abstraction @ abstraction) @ X1)) @
% 3.72/1.19 X0)))),
% 3.72/1.19 inference('sup-', [status(thm)], [zip_derived_cl1035, zip_derived_cl6])).
% 3.72/1.19 thf(zip_derived_cl1670, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i]:
% 3.72/1.19 ((identity)
% 3.72/1.19 = (apply @
% 3.72/1.19 (apply @ abstraction @
% 3.72/1.19 (apply @ (apply @ abstraction @ abstraction) @ X1)) @
% 3.72/1.19 X0))),
% 3.72/1.19 inference('simplify', [status(thm)], [zip_derived_cl1640])).
% 3.72/1.19 thf(zip_derived_cl0, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i]: ((apply @ (k @ X0) @ X1) = (X0))),
% 3.72/1.19 inference('cnf', [status(esa)], [k_definition])).
% 3.72/1.19 thf(zip_derived_cl2, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i]:
% 3.72/1.19 (((X1) = (X0))
% 3.72/1.19 | ((apply @ X1 @ (n @ X1 @ X0)) != (apply @ X0 @ (n @ X1 @ X0))))),
% 3.72/1.19 inference('cnf', [status(esa)], [extensionality2])).
% 3.72/1.19 thf(zip_derived_cl5, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i]:
% 3.72/1.19 (((X0) != (apply @ X1 @ (n @ (k @ X0) @ X1))) | ((k @ X0) = (X1)))),
% 3.72/1.19 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.72/1.19 thf(zip_derived_cl1872, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i]:
% 3.72/1.19 (((X1) != (identity))
% 3.72/1.19 | ((k @ X1)
% 3.72/1.19 = (apply @ abstraction @
% 3.72/1.19 (apply @ (apply @ abstraction @ abstraction) @ X0))))),
% 3.72/1.19 inference('sup-', [status(thm)], [zip_derived_cl1670, zip_derived_cl5])).
% 3.72/1.19 thf(zip_derived_cl1905, plain,
% 3.72/1.19 (![X0 : $i]:
% 3.72/1.19 ((k @ identity)
% 3.72/1.19 = (apply @ abstraction @
% 3.72/1.19 (apply @ (apply @ abstraction @ abstraction) @ X0)))),
% 3.72/1.19 inference('eq_res', [status(thm)], [zip_derived_cl1872])).
% 3.72/1.19 thf(zip_derived_cl0, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i]: ((apply @ (k @ X0) @ X1) = (X0))),
% 3.72/1.19 inference('cnf', [status(esa)], [k_definition])).
% 3.72/1.19 thf(zip_derived_cl1, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.72/1.19 ((apply @ (apply @ (apply @ abstraction @ X0) @ X2) @ X1)
% 3.72/1.19 = (apply @ (apply @ X0 @ (k @ X1)) @ (apply @ X2 @ X1)))),
% 3.72/1.19 inference('cnf', [status(esa)], [abstraction])).
% 3.72/1.19 thf(zip_derived_cl18, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.72/1.19 ((apply @ (apply @ (apply @ abstraction @ (k @ X0)) @ X2) @ X1)
% 3.72/1.19 = (apply @ X0 @ (apply @ X2 @ X1)))),
% 3.72/1.19 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 3.72/1.19 thf(zip_derived_cl5, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i]:
% 3.72/1.19 (((X0) != (apply @ X1 @ (n @ (k @ X0) @ X1))) | ((k @ X0) = (X1)))),
% 3.72/1.19 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.72/1.19 thf(zip_derived_cl55, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.72/1.19 (((X2)
% 3.72/1.19 != (apply @ X1 @
% 3.72/1.19 (apply @ X0 @
% 3.72/1.19 (n @ (k @ X2) @
% 3.72/1.19 (apply @ (apply @ abstraction @ (k @ X1)) @ X0)))))
% 3.72/1.19 | ((k @ X2) = (apply @ (apply @ abstraction @ (k @ X1)) @ X0)))),
% 3.72/1.19 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl5])).
% 3.72/1.19 thf(zip_derived_cl2286, plain,
% 3.72/1.19 (![X0 : $i]:
% 3.72/1.19 (((X0) != (k @ identity))
% 3.72/1.19 | ((k @ X0)
% 3.72/1.19 = (apply @ (apply @ abstraction @ (k @ abstraction)) @
% 3.72/1.19 (apply @ abstraction @ abstraction))))),
% 3.72/1.19 inference('sup-', [status(thm)], [zip_derived_cl1905, zip_derived_cl55])).
% 3.72/1.19 thf(zip_derived_cl2324, plain,
% 3.72/1.19 (((k @ (k @ identity))
% 3.72/1.19 = (apply @ (apply @ abstraction @ (k @ abstraction)) @
% 3.72/1.19 (apply @ abstraction @ abstraction)))),
% 3.72/1.19 inference('eq_res', [status(thm)], [zip_derived_cl2286])).
% 3.72/1.19 thf(zip_derived_cl1, plain,
% 3.72/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.72/1.19 ((apply @ (apply @ (apply @ abstraction @ X0) @ X2) @ X1)
% 3.72/1.19 = (apply @ (apply @ X0 @ (k @ X1)) @ (apply @ X2 @ X1)))),
% 3.72/1.19 inference('cnf', [status(esa)], [abstraction])).
% 3.72/1.19 thf(zip_derived_cl2341, plain,
% 3.72/1.19 (((apply @ (apply @ (apply @ abstraction @ abstraction) @ abstraction) @
% 3.72/1.19 abstraction) = (k @ (k @ identity)))),
% 3.72/1.19 inference('sup+', [status(thm)], [zip_derived_cl2324, zip_derived_cl1])).
% 3.72/1.19 thf(prove_TRC1b, conjecture,
% 3.72/1.19 (( apply @
% 3.72/1.19 ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @
% 3.72/1.19 abstraction ) =
% 3.72/1.19 ( k @ ( k @ identity ) ))).
% 3.72/1.19 thf(zf_stmt_0, negated_conjecture,
% 3.72/1.19 (( apply @
% 3.72/1.19 ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @
% 3.72/1.19 abstraction ) !=
% 3.72/1.19 ( k @ ( k @ identity ) )),
% 3.72/1.19 inference('cnf.neg', [status(esa)], [prove_TRC1b])).
% 3.72/1.19 thf(zip_derived_cl4, plain,
% 3.72/1.19 (((apply @ (apply @ (apply @ abstraction @ abstraction) @ abstraction) @
% 3.72/1.19 abstraction) != (k @ (k @ identity)))),
% 3.72/1.19 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.72/1.19 thf(zip_derived_cl2356, plain, ($false),
% 3.72/1.19 inference('simplify_reflect-', [status(thm)],
% 3.72/1.19 [zip_derived_cl2341, zip_derived_cl4])).
% 3.72/1.19
% 3.72/1.19 % SZS output end Refutation
% 3.72/1.19
% 3.72/1.19
% 3.72/1.19 % Terminating...
% 4.69/1.28 % Runner terminated.
% 4.69/1.29 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------