TSTP Solution File: COL077-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : COL077-1 : TPTP v8.1.2. Released v1.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.47has1ZfbX 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 : Wed Aug 30 18:34:46 EDT 2023
% Result : Unsatisfiable 3.66s 1.04s
% Output : Refutation 3.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : COL077-1 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.47has1ZfbX true
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Sun Aug 27 05:15:29 EDT 2023
% 0.11/0.30 % CPUTime :
% 0.11/0.30 % Running portfolio for 300 s
% 0.11/0.30 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.30 % Number of cores: 8
% 0.11/0.31 % Python version: Python 3.6.8
% 0.11/0.31 % Running in FO mode
% 0.16/0.53 % Total configuration time : 435
% 0.16/0.53 % Estimated wc time : 1092
% 0.16/0.53 % Estimated cpu time (7 cpus) : 156.0
% 0.16/0.60 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.16/0.60 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.16/0.60 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.16/0.60 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.16/0.60 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.16/0.61 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.16/0.61 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 3.66/1.04 % Solved by fo/fo7.sh.
% 3.66/1.04 % done 580 iterations in 0.418s
% 3.66/1.04 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 3.66/1.04 % SZS output start Refutation
% 3.66/1.04 thf(n_type, type, n: $i > $i > $i).
% 3.66/1.04 thf(pair_type, type, pair: $i > $i > $i).
% 3.66/1.04 thf(k_type, type, k: $i > $i).
% 3.66/1.04 thf(abstraction_type, type, abstraction: $i).
% 3.66/1.04 thf(identity_type, type, identity: $i).
% 3.66/1.04 thf(apply_type, type, apply: $i > $i > $i).
% 3.66/1.04 thf(projection2_type, type, projection2: $i).
% 3.66/1.04 thf(projection1_type, type, projection1: $i).
% 3.66/1.04 thf(prove_TRC1a, conjecture,
% 3.66/1.04 (( apply @
% 3.66/1.04 ( apply @
% 3.66/1.04 ( apply @
% 3.66/1.04 ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @
% 3.66/1.04 abstraction ) @
% 3.66/1.04 abstraction ) @
% 3.66/1.04 abstraction ) =
% 3.66/1.04 ( identity ))).
% 3.66/1.04 thf(zf_stmt_0, negated_conjecture,
% 3.66/1.04 (( apply @
% 3.66/1.04 ( apply @
% 3.66/1.04 ( apply @
% 3.66/1.04 ( apply @ ( apply @ abstraction @ abstraction ) @ abstraction ) @
% 3.66/1.04 abstraction ) @
% 3.66/1.04 abstraction ) @
% 3.66/1.04 abstraction ) !=
% 3.66/1.04 ( identity )),
% 3.66/1.04 inference('cnf.neg', [status(esa)], [prove_TRC1a])).
% 3.66/1.04 thf(zip_derived_cl11, plain,
% 3.66/1.04 (((apply @
% 3.66/1.04 (apply @
% 3.66/1.04 (apply @
% 3.66/1.04 (apply @ (apply @ abstraction @ abstraction) @ abstraction) @
% 3.66/1.04 abstraction) @
% 3.66/1.04 abstraction) @
% 3.66/1.04 abstraction) != (identity))),
% 3.66/1.04 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.66/1.04 thf(identity_definition, axiom, (( apply @ identity @ X ) = ( X ))).
% 3.66/1.04 thf(zip_derived_cl10, plain, (![X0 : $i]: ((apply @ identity @ X0) = (X0))),
% 3.66/1.04 inference('cnf', [status(esa)], [identity_definition])).
% 3.66/1.04 thf(pairing, axiom,
% 3.66/1.04 (( pair @ ( apply @ projection1 @ X ) @ ( apply @ projection2 @ X ) ) =
% 3.66/1.04 ( X ))).
% 3.66/1.04 thf(zip_derived_cl3, plain,
% 3.66/1.04 (![X0 : $i]:
% 3.66/1.04 ((pair @ (apply @ projection1 @ X0) @ (apply @ projection2 @ X0))
% 3.66/1.04 = (X0))),
% 3.66/1.04 inference('cnf', [status(esa)], [pairing])).
% 3.66/1.04 thf(pairwise_application, axiom,
% 3.66/1.04 (( apply @ ( pair @ X @ Y ) @ Z ) =
% 3.66/1.04 ( pair @ ( apply @ X @ Z ) @ ( apply @ Y @ Z ) ))).
% 3.66/1.04 thf(zip_derived_cl4, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.66/1.04 ((apply @ (pair @ X0 @ X2) @ X1)
% 3.66/1.04 = (pair @ (apply @ X0 @ X1) @ (apply @ X2 @ X1)))),
% 3.66/1.04 inference('cnf', [status(esa)], [pairwise_application])).
% 3.66/1.04 thf(zip_derived_cl53, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]:
% 3.66/1.04 ((apply @ X0 @ X1)
% 3.66/1.04 = (pair @ (apply @ (apply @ projection1 @ X0) @ X1) @
% 3.66/1.04 (apply @ (apply @ projection2 @ X0) @ X1)))),
% 3.66/1.04 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 3.66/1.04 thf(projection1, axiom, (( apply @ projection1 @ ( pair @ X @ Y ) ) = ( X ))).
% 3.66/1.04 thf(zip_derived_cl1, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]: ((apply @ projection1 @ (pair @ X0 @ X1)) = (X0))),
% 3.66/1.04 inference('cnf', [status(esa)], [projection1])).
% 3.66/1.04 thf(zip_derived_cl56, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]:
% 3.66/1.04 ((apply @ projection1 @ (apply @ X1 @ X0))
% 3.66/1.04 = (apply @ (apply @ projection1 @ X1) @ X0))),
% 3.66/1.04 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl1])).
% 3.66/1.04 thf(extensionality2, axiom,
% 3.66/1.04 (( ( X ) = ( Y ) ) |
% 3.66/1.04 ( ( apply @ X @ ( n @ X @ Y ) ) != ( apply @ Y @ ( n @ X @ Y ) ) ))).
% 3.66/1.04 thf(zip_derived_cl8, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]:
% 3.66/1.04 (((X1) = (X0))
% 3.66/1.04 | ((apply @ X1 @ (n @ X1 @ X0)) != (apply @ X0 @ (n @ X1 @ X0))))),
% 3.66/1.04 inference('cnf', [status(esa)], [extensionality2])).
% 3.66/1.04 thf(zip_derived_cl67, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]:
% 3.66/1.04 (((apply @ X1 @ (n @ X1 @ (apply @ projection1 @ X0)))
% 3.66/1.04 != (apply @ projection1 @
% 3.66/1.04 (apply @ X0 @ (n @ X1 @ (apply @ projection1 @ X0)))))
% 3.66/1.04 | ((X1) = (apply @ projection1 @ X0)))),
% 3.66/1.04 inference('sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl8])).
% 3.66/1.04 thf(zip_derived_cl769, plain,
% 3.66/1.04 (![X0 : $i]:
% 3.66/1.04 (((apply @ X0 @ (n @ X0 @ (apply @ projection1 @ identity)))
% 3.66/1.04 != (apply @ projection1 @
% 3.66/1.04 (n @ X0 @ (apply @ projection1 @ identity))))
% 3.66/1.04 | ((X0) = (apply @ projection1 @ identity)))),
% 3.66/1.04 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl67])).
% 3.66/1.04 thf(zip_derived_cl835, plain,
% 3.66/1.04 (((projection1) = (apply @ projection1 @ identity))),
% 3.66/1.04 inference('eq_res', [status(thm)], [zip_derived_cl769])).
% 3.66/1.04 thf(zip_derived_cl3, plain,
% 3.66/1.04 (![X0 : $i]:
% 3.66/1.04 ((pair @ (apply @ projection1 @ X0) @ (apply @ projection2 @ X0))
% 3.66/1.04 = (X0))),
% 3.66/1.04 inference('cnf', [status(esa)], [pairing])).
% 3.66/1.04 thf(zip_derived_cl842, plain,
% 3.66/1.04 (((pair @ projection1 @ (apply @ projection2 @ identity)) = (identity))),
% 3.66/1.04 inference('sup+', [status(thm)], [zip_derived_cl835, zip_derived_cl3])).
% 3.66/1.04 thf(zip_derived_cl10, plain, (![X0 : $i]: ((apply @ identity @ X0) = (X0))),
% 3.66/1.04 inference('cnf', [status(esa)], [identity_definition])).
% 3.66/1.04 thf(zip_derived_cl53, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]:
% 3.66/1.04 ((apply @ X0 @ X1)
% 3.66/1.04 = (pair @ (apply @ (apply @ projection1 @ X0) @ X1) @
% 3.66/1.04 (apply @ (apply @ projection2 @ X0) @ X1)))),
% 3.66/1.04 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl4])).
% 3.66/1.04 thf(zip_derived_cl56, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]:
% 3.66/1.04 ((apply @ projection1 @ (apply @ X1 @ X0))
% 3.66/1.04 = (apply @ (apply @ projection1 @ X1) @ X0))),
% 3.66/1.04 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl1])).
% 3.66/1.04 thf(zip_derived_cl66, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]:
% 3.66/1.04 ((apply @ X0 @ X1)
% 3.66/1.04 = (pair @ (apply @ projection1 @ (apply @ X0 @ X1)) @
% 3.66/1.04 (apply @ (apply @ projection2 @ X0) @ X1)))),
% 3.66/1.04 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl56])).
% 3.66/1.04 thf(projection2, axiom, (( apply @ projection2 @ ( pair @ X @ Y ) ) = ( Y ))).
% 3.66/1.04 thf(zip_derived_cl2, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]: ((apply @ projection2 @ (pair @ X1 @ X0)) = (X0))),
% 3.66/1.04 inference('cnf', [status(esa)], [projection2])).
% 3.66/1.04 thf(zip_derived_cl76, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]:
% 3.66/1.04 ((apply @ projection2 @ (apply @ X1 @ X0))
% 3.66/1.04 = (apply @ (apply @ projection2 @ X1) @ X0))),
% 3.66/1.04 inference('sup+', [status(thm)], [zip_derived_cl66, zip_derived_cl2])).
% 3.66/1.04 thf(zip_derived_cl8, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]:
% 3.66/1.04 (((X1) = (X0))
% 3.66/1.04 | ((apply @ X1 @ (n @ X1 @ X0)) != (apply @ X0 @ (n @ X1 @ X0))))),
% 3.66/1.04 inference('cnf', [status(esa)], [extensionality2])).
% 3.66/1.04 thf(zip_derived_cl105, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]:
% 3.66/1.04 (((apply @ X1 @ (n @ X1 @ (apply @ projection2 @ X0)))
% 3.66/1.04 != (apply @ projection2 @
% 3.66/1.04 (apply @ X0 @ (n @ X1 @ (apply @ projection2 @ X0)))))
% 3.66/1.04 | ((X1) = (apply @ projection2 @ X0)))),
% 3.66/1.04 inference('sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl8])).
% 3.66/1.04 thf(zip_derived_cl1465, plain,
% 3.66/1.04 (![X0 : $i]:
% 3.66/1.04 (((apply @ X0 @ (n @ X0 @ (apply @ projection2 @ identity)))
% 3.66/1.04 != (apply @ projection2 @
% 3.66/1.04 (n @ X0 @ (apply @ projection2 @ identity))))
% 3.66/1.04 | ((X0) = (apply @ projection2 @ identity)))),
% 3.66/1.04 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl105])).
% 3.66/1.04 thf(zip_derived_cl1556, plain,
% 3.66/1.04 (((projection2) = (apply @ projection2 @ identity))),
% 3.66/1.04 inference('eq_res', [status(thm)], [zip_derived_cl1465])).
% 3.66/1.04 thf(zip_derived_cl1562, plain,
% 3.66/1.04 (((pair @ projection1 @ projection2) = (identity))),
% 3.66/1.04 inference('demod', [status(thm)], [zip_derived_cl842, zip_derived_cl1556])).
% 3.66/1.04 thf(zip_derived_cl1597, plain,
% 3.66/1.04 (((apply @
% 3.66/1.04 (apply @
% 3.66/1.04 (apply @
% 3.66/1.04 (apply @ (apply @ abstraction @ abstraction) @ abstraction) @
% 3.66/1.04 abstraction) @
% 3.66/1.04 abstraction) @
% 3.66/1.04 abstraction) != (pair @ projection1 @ projection2))),
% 3.66/1.04 inference('demod', [status(thm)], [zip_derived_cl11, zip_derived_cl1562])).
% 3.66/1.04 thf(abstraction, axiom,
% 3.66/1.04 (( apply @ ( apply @ ( apply @ abstraction @ X ) @ Y ) @ Z ) =
% 3.66/1.04 ( apply @ ( apply @ X @ ( k @ Z ) ) @ ( apply @ Y @ Z ) ))).
% 3.66/1.04 thf(zip_derived_cl5, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.66/1.04 ((apply @ (apply @ (apply @ abstraction @ X0) @ X2) @ X1)
% 3.66/1.04 = (apply @ (apply @ X0 @ (k @ X1)) @ (apply @ X2 @ X1)))),
% 3.66/1.04 inference('cnf', [status(esa)], [abstraction])).
% 3.66/1.04 thf(zip_derived_cl5, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.66/1.04 ((apply @ (apply @ (apply @ abstraction @ X0) @ X2) @ X1)
% 3.66/1.04 = (apply @ (apply @ X0 @ (k @ X1)) @ (apply @ X2 @ X1)))),
% 3.66/1.04 inference('cnf', [status(esa)], [abstraction])).
% 3.66/1.04 thf(k_definition, axiom, (( apply @ ( k @ X ) @ Y ) = ( X ))).
% 3.66/1.04 thf(zip_derived_cl0, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]: ((apply @ (k @ X0) @ X1) = (X0))),
% 3.66/1.04 inference('cnf', [status(esa)], [k_definition])).
% 3.66/1.04 thf(zip_derived_cl2012, plain,
% 3.66/1.04 (((apply @
% 3.66/1.04 (apply @ abstraction @
% 3.66/1.04 (apply @ (apply @ abstraction @ abstraction) @ abstraction)) @
% 3.66/1.04 abstraction) != (pair @ projection1 @ projection2))),
% 3.66/1.04 inference('demod', [status(thm)],
% 3.66/1.04 [zip_derived_cl1597, zip_derived_cl5, zip_derived_cl5,
% 3.66/1.04 zip_derived_cl0])).
% 3.66/1.04 thf(zip_derived_cl5, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.66/1.04 ((apply @ (apply @ (apply @ abstraction @ X0) @ X2) @ X1)
% 3.66/1.04 = (apply @ (apply @ X0 @ (k @ X1)) @ (apply @ X2 @ X1)))),
% 3.66/1.04 inference('cnf', [status(esa)], [abstraction])).
% 3.66/1.04 thf(zip_derived_cl5, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.66/1.04 ((apply @ (apply @ (apply @ abstraction @ X0) @ X2) @ X1)
% 3.66/1.04 = (apply @ (apply @ X0 @ (k @ X1)) @ (apply @ X2 @ X1)))),
% 3.66/1.04 inference('cnf', [status(esa)], [abstraction])).
% 3.66/1.04 thf(zip_derived_cl2020, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.66/1.04 ((apply @
% 3.66/1.04 (apply @ (apply @ (apply @ abstraction @ abstraction) @ X1) @ X0) @
% 3.66/1.04 X2)
% 3.66/1.04 = (apply @ (apply @ (k @ X0) @ (k @ X2)) @
% 3.66/1.04 (apply @ (apply @ X1 @ X0) @ X2)))),
% 3.66/1.04 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl5])).
% 3.66/1.04 thf(zip_derived_cl0, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]: ((apply @ (k @ X0) @ X1) = (X0))),
% 3.66/1.04 inference('cnf', [status(esa)], [k_definition])).
% 3.66/1.04 thf(zip_derived_cl2130, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.66/1.04 ((apply @
% 3.66/1.04 (apply @ (apply @ (apply @ abstraction @ abstraction) @ X1) @ X0) @
% 3.66/1.04 X2) = (apply @ X0 @ (apply @ (apply @ X1 @ X0) @ X2)))),
% 3.66/1.04 inference('demod', [status(thm)], [zip_derived_cl2020, zip_derived_cl0])).
% 3.66/1.04 thf(zip_derived_cl5, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.66/1.04 ((apply @ (apply @ (apply @ abstraction @ X0) @ X2) @ X1)
% 3.66/1.04 = (apply @ (apply @ X0 @ (k @ X1)) @ (apply @ X2 @ X1)))),
% 3.66/1.04 inference('cnf', [status(esa)], [abstraction])).
% 3.66/1.04 thf(zip_derived_cl2887, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.66/1.04 ((apply @
% 3.66/1.04 (apply @
% 3.66/1.04 (apply @ abstraction @
% 3.66/1.04 (apply @ (apply @ abstraction @ abstraction) @ X2)) @
% 3.66/1.04 X1) @
% 3.66/1.04 X0)
% 3.66/1.04 = (apply @ (k @ X0) @
% 3.66/1.04 (apply @ (apply @ X2 @ (k @ X0)) @ (apply @ X1 @ X0))))),
% 3.66/1.04 inference('sup+', [status(thm)], [zip_derived_cl2130, zip_derived_cl5])).
% 3.66/1.04 thf(zip_derived_cl0, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]: ((apply @ (k @ X0) @ X1) = (X0))),
% 3.66/1.04 inference('cnf', [status(esa)], [k_definition])).
% 3.66/1.04 thf(zip_derived_cl2891, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.66/1.04 ((apply @
% 3.66/1.04 (apply @
% 3.66/1.04 (apply @ abstraction @
% 3.66/1.04 (apply @ (apply @ abstraction @ abstraction) @ X2)) @
% 3.66/1.04 X1) @
% 3.66/1.04 X0) = (X0))),
% 3.66/1.04 inference('demod', [status(thm)], [zip_derived_cl2887, zip_derived_cl0])).
% 3.66/1.04 thf(zip_derived_cl10, plain, (![X0 : $i]: ((apply @ identity @ X0) = (X0))),
% 3.66/1.04 inference('cnf', [status(esa)], [identity_definition])).
% 3.66/1.04 thf(zip_derived_cl8, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]:
% 3.66/1.04 (((X1) = (X0))
% 3.66/1.04 | ((apply @ X1 @ (n @ X1 @ X0)) != (apply @ X0 @ (n @ X1 @ X0))))),
% 3.66/1.04 inference('cnf', [status(esa)], [extensionality2])).
% 3.66/1.04 thf(zip_derived_cl13, plain,
% 3.66/1.04 (![X0 : $i]:
% 3.66/1.04 (((n @ identity @ X0) != (apply @ X0 @ (n @ identity @ X0)))
% 3.66/1.04 | ((identity) = (X0)))),
% 3.66/1.04 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl8])).
% 3.66/1.04 thf(zip_derived_cl1562, plain,
% 3.66/1.04 (((pair @ projection1 @ projection2) = (identity))),
% 3.66/1.04 inference('demod', [status(thm)], [zip_derived_cl842, zip_derived_cl1556])).
% 3.66/1.04 thf(zip_derived_cl1562, plain,
% 3.66/1.04 (((pair @ projection1 @ projection2) = (identity))),
% 3.66/1.04 inference('demod', [status(thm)], [zip_derived_cl842, zip_derived_cl1556])).
% 3.66/1.04 thf(zip_derived_cl1562, plain,
% 3.66/1.04 (((pair @ projection1 @ projection2) = (identity))),
% 3.66/1.04 inference('demod', [status(thm)], [zip_derived_cl842, zip_derived_cl1556])).
% 3.66/1.04 thf(zip_derived_cl1598, plain,
% 3.66/1.04 (![X0 : $i]:
% 3.66/1.04 (((n @ (pair @ projection1 @ projection2) @ X0)
% 3.66/1.04 != (apply @ X0 @ (n @ (pair @ projection1 @ projection2) @ X0)))
% 3.66/1.04 | ((pair @ projection1 @ projection2) = (X0)))),
% 3.66/1.04 inference('demod', [status(thm)],
% 3.66/1.04 [zip_derived_cl13, zip_derived_cl1562, zip_derived_cl1562,
% 3.66/1.04 zip_derived_cl1562])).
% 3.66/1.04 thf(zip_derived_cl2916, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]:
% 3.66/1.04 (((n @ (pair @ projection1 @ projection2) @
% 3.66/1.04 (apply @
% 3.66/1.04 (apply @ abstraction @
% 3.66/1.04 (apply @ (apply @ abstraction @ abstraction) @ X1)) @
% 3.66/1.04 X0))
% 3.66/1.04 != (n @ (pair @ projection1 @ projection2) @
% 3.66/1.04 (apply @
% 3.66/1.04 (apply @ abstraction @
% 3.66/1.04 (apply @ (apply @ abstraction @ abstraction) @ X1)) @
% 3.66/1.04 X0)))
% 3.66/1.04 | ((pair @ projection1 @ projection2)
% 3.66/1.04 = (apply @
% 3.66/1.04 (apply @ abstraction @
% 3.66/1.04 (apply @ (apply @ abstraction @ abstraction) @ X1)) @
% 3.66/1.04 X0)))),
% 3.66/1.04 inference('sup-', [status(thm)], [zip_derived_cl2891, zip_derived_cl1598])).
% 3.66/1.04 thf(zip_derived_cl2927, plain,
% 3.66/1.04 (![X0 : $i, X1 : $i]:
% 3.66/1.04 ((pair @ projection1 @ projection2)
% 3.66/1.04 = (apply @
% 3.66/1.04 (apply @ abstraction @
% 3.66/1.04 (apply @ (apply @ abstraction @ abstraction) @ X1)) @
% 3.66/1.04 X0))),
% 3.66/1.04 inference('simplify', [status(thm)], [zip_derived_cl2916])).
% 3.66/1.04 thf(zip_derived_cl2929, plain,
% 3.66/1.04 (((pair @ projection1 @ projection2)
% 3.66/1.04 != (pair @ projection1 @ projection2))),
% 3.66/1.04 inference('demod', [status(thm)],
% 3.66/1.04 [zip_derived_cl2012, zip_derived_cl2927])).
% 3.66/1.04 thf(zip_derived_cl2930, plain, ($false),
% 3.66/1.04 inference('simplify', [status(thm)], [zip_derived_cl2929])).
% 3.66/1.04
% 3.66/1.04 % SZS output end Refutation
% 3.66/1.04
% 3.66/1.04
% 3.66/1.04 % Terminating...
% 4.25/1.14 % Runner terminated.
% 4.25/1.15 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------