TSTP Solution File: CAT010-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : CAT010-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.jORdD2VNhf true
% Computer : n009.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 18:20:56 EDT 2023
% Result : Unsatisfiable 3.57s 1.08s
% Output : Refutation 3.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT010-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.jORdD2VNhf true
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 00:08:20 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.41/0.62 % Total configuration time : 435
% 0.41/0.62 % Estimated wc time : 1092
% 0.41/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.52/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.52/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.52/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.52/0.74 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 3.57/1.08 % Solved by fo/fo6_bce.sh.
% 3.57/1.08 % BCE start: 20
% 3.57/1.08 % BCE eliminated: 0
% 3.57/1.08 % PE start: 20
% 3.57/1.08 logic: eq
% 3.57/1.08 % PE eliminated: 0
% 3.57/1.08 % done 468 iterations in 0.366s
% 3.57/1.08 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 3.57/1.08 % SZS output start Refutation
% 3.57/1.08 thf(a_type, type, a: $i).
% 3.57/1.08 thf(compose_type, type, compose: $i > $i > $i).
% 3.57/1.08 thf(codomain_type, type, codomain: $i > $i).
% 3.57/1.08 thf(domain_type, type, domain: $i > $i).
% 3.57/1.08 thf(identity_map_type, type, identity_map: $i > $o).
% 3.57/1.08 thf(defined_type, type, defined: $i > $i > $o).
% 3.57/1.08 thf(product_type, type, product: $i > $i > $i > $o).
% 3.57/1.08 thf(b_type, type, b: $i).
% 3.57/1.08 thf(closure_of_composition, axiom,
% 3.57/1.08 (( ~( defined @ X @ Y ) ) | ( product @ X @ Y @ ( compose @ X @ Y ) ))).
% 3.57/1.08 thf(zip_derived_cl0, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X0 @ X1) | (product @ X0 @ X1 @ (compose @ X0 @ X1)))),
% 3.57/1.08 inference('cnf', [status(esa)], [closure_of_composition])).
% 3.57/1.08 thf(product_on_codomain, axiom, (product @ ( codomain @ X ) @ X @ X)).
% 3.57/1.08 thf(zip_derived_cl14, plain,
% 3.57/1.08 (![X0 : $i]: (product @ (codomain @ X0) @ X0 @ X0)),
% 3.57/1.08 inference('cnf', [status(esa)], [product_on_codomain])).
% 3.57/1.08 thf(category_theory_axiom1, axiom,
% 3.57/1.08 (( ~( product @ X @ Y @ Xy ) ) | ( ~( product @ Y @ Z @ Yz ) ) |
% 3.57/1.08 ( ~( defined @ Xy @ Z ) ) | ( defined @ X @ Yz ))).
% 3.57/1.08 thf(zip_derived_cl3, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 3.57/1.08 (~ (product @ X0 @ X1 @ X2)
% 3.57/1.08 | ~ (product @ X1 @ X3 @ X4)
% 3.57/1.08 | ~ (defined @ X2 @ X3)
% 3.57/1.08 | (defined @ X0 @ X4))),
% 3.57/1.08 inference('cnf', [status(esa)], [category_theory_axiom1])).
% 3.57/1.08 thf(zip_derived_cl136, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.57/1.08 (~ (product @ X0 @ X2 @ X1)
% 3.57/1.08 | ~ (defined @ X0 @ X2)
% 3.57/1.08 | (defined @ (codomain @ X0) @ X1))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl3])).
% 3.57/1.08 thf(associative_property1, axiom,
% 3.57/1.08 (( ~( product @ X @ Y @ Z ) ) | ( defined @ X @ Y ))).
% 3.57/1.08 thf(zip_derived_cl1, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.57/1.08 (~ (product @ X0 @ X1 @ X2) | (defined @ X0 @ X1))),
% 3.57/1.08 inference('cnf', [status(esa)], [associative_property1])).
% 3.57/1.08 thf(zip_derived_cl265, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.57/1.08 ( (defined @ (codomain @ X0) @ X1) | ~ (product @ X0 @ X2 @ X1))),
% 3.57/1.08 inference('clc', [status(thm)], [zip_derived_cl136, zip_derived_cl1])).
% 3.57/1.08 thf(zip_derived_cl266, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ X0)
% 3.57/1.08 | (defined @ (codomain @ X1) @ (compose @ X1 @ X0)))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl265])).
% 3.57/1.08 thf(zip_derived_cl14, plain,
% 3.57/1.08 (![X0 : $i]: (product @ (codomain @ X0) @ X0 @ X0)),
% 3.57/1.08 inference('cnf', [status(esa)], [product_on_codomain])).
% 3.57/1.08 thf(category_theory_axiom3, axiom,
% 3.57/1.08 (( ~( product @ Y @ Z @ Yz ) ) | ( ~( defined @ X @ Yz ) ) |
% 3.57/1.08 ( defined @ X @ Y ))).
% 3.57/1.08 thf(zip_derived_cl5, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.57/1.08 (~ (product @ X0 @ X1 @ X2)
% 3.57/1.08 | ~ (defined @ X3 @ X2)
% 3.57/1.08 | (defined @ X3 @ X0))),
% 3.57/1.08 inference('cnf', [status(esa)], [category_theory_axiom3])).
% 3.57/1.08 thf(zip_derived_cl156, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ X0) | (defined @ X1 @ (codomain @ X0)))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl5])).
% 3.57/1.08 thf(product_on_domain, axiom, (product @ X @ ( domain @ X ) @ X)).
% 3.57/1.08 thf(zip_derived_cl13, plain,
% 3.57/1.08 (![X0 : $i]: (product @ X0 @ (domain @ X0) @ X0)),
% 3.57/1.08 inference('cnf', [status(esa)], [product_on_domain])).
% 3.57/1.08 thf(associative_property2, axiom,
% 3.57/1.08 (( ~( product @ X @ Y @ Xy ) ) | ( ~( defined @ Xy @ Z ) ) |
% 3.57/1.08 ( defined @ Y @ Z ))).
% 3.57/1.08 thf(zip_derived_cl2, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.57/1.08 (~ (product @ X0 @ X1 @ X2)
% 3.57/1.08 | ~ (defined @ X2 @ X3)
% 3.57/1.08 | (defined @ X1 @ X3))),
% 3.57/1.08 inference('cnf', [status(esa)], [associative_property2])).
% 3.57/1.08 thf(zip_derived_cl120, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X0 @ X1) | (defined @ (domain @ X0) @ X1))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl2])).
% 3.57/1.08 thf(identity1, axiom,
% 3.57/1.08 (( ~( defined @ X @ Y ) ) | ( ~( identity_map @ X ) ) |
% 3.57/1.08 ( product @ X @ Y @ Y ))).
% 3.57/1.08 thf(zip_derived_cl15, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X0 @ X1)
% 3.57/1.08 | ~ (identity_map @ X0)
% 3.57/1.08 | (product @ X0 @ X1 @ X1))),
% 3.57/1.08 inference('cnf', [status(esa)], [identity1])).
% 3.57/1.08 thf(zip_derived_cl214, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ X0)
% 3.57/1.08 | ~ (identity_map @ (domain @ X1))
% 3.57/1.08 | (product @ (domain @ X1) @ X0 @ X0))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl120, zip_derived_cl15])).
% 3.57/1.08 thf(domain_is_an_identity_map, axiom, (identity_map @ ( domain @ X ))).
% 3.57/1.08 thf(zip_derived_cl9, plain, (![X0 : $i]: (identity_map @ (domain @ X0))),
% 3.57/1.08 inference('cnf', [status(esa)], [domain_is_an_identity_map])).
% 3.57/1.08 thf(zip_derived_cl216, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ X0) | (product @ (domain @ X1) @ X0 @ X0))),
% 3.57/1.08 inference('demod', [status(thm)], [zip_derived_cl214, zip_derived_cl9])).
% 3.57/1.08 thf(zip_derived_cl156, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ X0) | (defined @ X1 @ (codomain @ X0)))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl5])).
% 3.57/1.08 thf(zip_derived_cl15, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X0 @ X1)
% 3.57/1.08 | ~ (identity_map @ X0)
% 3.57/1.08 | (product @ X0 @ X1 @ X1))),
% 3.57/1.08 inference('cnf', [status(esa)], [identity1])).
% 3.57/1.08 thf(zip_derived_cl165, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ X0)
% 3.57/1.08 | ~ (identity_map @ X1)
% 3.57/1.08 | (product @ X1 @ (codomain @ X0) @ (codomain @ X0)))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl156, zip_derived_cl15])).
% 3.57/1.08 thf(mapping_from_codomain_of_x_to_x, axiom, (defined @ ( codomain @ X ) @ X)).
% 3.57/1.08 thf(zip_derived_cl12, plain, (![X0 : $i]: (defined @ (codomain @ X0) @ X0)),
% 3.57/1.08 inference('cnf', [status(esa)], [mapping_from_codomain_of_x_to_x])).
% 3.57/1.08 thf(identity2, axiom,
% 3.57/1.08 (( ~( defined @ X @ Y ) ) | ( ~( identity_map @ Y ) ) |
% 3.57/1.08 ( product @ X @ Y @ X ))).
% 3.57/1.08 thf(zip_derived_cl16, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X0 @ X1)
% 3.57/1.08 | ~ (identity_map @ X1)
% 3.57/1.08 | (product @ X0 @ X1 @ X0))),
% 3.57/1.08 inference('cnf', [status(esa)], [identity2])).
% 3.57/1.08 thf(zip_derived_cl158, plain,
% 3.57/1.08 (![X0 : $i]:
% 3.57/1.08 (~ (identity_map @ X0)
% 3.57/1.08 | (product @ (codomain @ X0) @ X0 @ (codomain @ X0)))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl16])).
% 3.57/1.08 thf(composition_is_well_defined, axiom,
% 3.57/1.08 (( ~( product @ X @ Y @ Z ) ) | ( ~( product @ X @ Y @ W ) ) |
% 3.57/1.08 ( ( Z ) = ( W ) ))).
% 3.57/1.08 thf(zip_derived_cl17, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.57/1.08 (~ (product @ X0 @ X1 @ X2)
% 3.57/1.08 | ~ (product @ X0 @ X1 @ X3)
% 3.57/1.08 | ((X2) = (X3)))),
% 3.57/1.08 inference('cnf', [status(esa)], [composition_is_well_defined])).
% 3.57/1.08 thf(zip_derived_cl174, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (identity_map @ X0)
% 3.57/1.08 | ~ (product @ (codomain @ X0) @ X0 @ X1)
% 3.57/1.08 | ((codomain @ X0) = (X1)))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl158, zip_derived_cl17])).
% 3.57/1.08 thf(zip_derived_cl528, plain,
% 3.57/1.08 (![X0 : $i]:
% 3.57/1.08 (~ (identity_map @ (codomain @ (codomain @ X0)))
% 3.57/1.08 | ~ (defined @ (codomain @ (codomain @ X0)) @ X0)
% 3.57/1.08 | ~ (identity_map @ (codomain @ X0))
% 3.57/1.08 | ((codomain @ (codomain @ X0)) = (codomain @ X0)))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl165, zip_derived_cl174])).
% 3.57/1.08 thf(codomain_is_an_identity_map, axiom, (identity_map @ ( codomain @ X ))).
% 3.57/1.08 thf(zip_derived_cl10, plain, (![X0 : $i]: (identity_map @ (codomain @ X0))),
% 3.57/1.08 inference('cnf', [status(esa)], [codomain_is_an_identity_map])).
% 3.57/1.08 thf(zip_derived_cl14, plain,
% 3.57/1.08 (![X0 : $i]: (product @ (codomain @ X0) @ X0 @ X0)),
% 3.57/1.08 inference('cnf', [status(esa)], [product_on_codomain])).
% 3.57/1.08 thf(zip_derived_cl265, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.57/1.08 ( (defined @ (codomain @ X0) @ X1) | ~ (product @ X0 @ X2 @ X1))),
% 3.57/1.08 inference('clc', [status(thm)], [zip_derived_cl136, zip_derived_cl1])).
% 3.57/1.08 thf(zip_derived_cl269, plain,
% 3.57/1.08 (![X0 : $i]: (defined @ (codomain @ (codomain @ X0)) @ X0)),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl265])).
% 3.57/1.08 thf(zip_derived_cl10, plain, (![X0 : $i]: (identity_map @ (codomain @ X0))),
% 3.57/1.08 inference('cnf', [status(esa)], [codomain_is_an_identity_map])).
% 3.57/1.08 thf(zip_derived_cl541, plain,
% 3.57/1.08 (![X0 : $i]: ((codomain @ (codomain @ X0)) = (codomain @ X0))),
% 3.57/1.08 inference('demod', [status(thm)],
% 3.57/1.08 [zip_derived_cl528, zip_derived_cl10, zip_derived_cl269,
% 3.57/1.08 zip_derived_cl10])).
% 3.57/1.08 thf(zip_derived_cl156, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ X0) | (defined @ X1 @ (codomain @ X0)))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl5])).
% 3.57/1.08 thf(zip_derived_cl16, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X0 @ X1)
% 3.57/1.08 | ~ (identity_map @ X1)
% 3.57/1.08 | (product @ X0 @ X1 @ X0))),
% 3.57/1.08 inference('cnf', [status(esa)], [identity2])).
% 3.57/1.08 thf(zip_derived_cl166, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ X0)
% 3.57/1.08 | ~ (identity_map @ (codomain @ X0))
% 3.57/1.08 | (product @ X1 @ (codomain @ X0) @ X1))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl156, zip_derived_cl16])).
% 3.57/1.08 thf(zip_derived_cl10, plain, (![X0 : $i]: (identity_map @ (codomain @ X0))),
% 3.57/1.08 inference('cnf', [status(esa)], [codomain_is_an_identity_map])).
% 3.57/1.08 thf(zip_derived_cl167, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ X0) | (product @ X1 @ (codomain @ X0) @ X1))),
% 3.57/1.08 inference('demod', [status(thm)], [zip_derived_cl166, zip_derived_cl10])).
% 3.57/1.08 thf(zip_derived_cl0, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X0 @ X1) | (product @ X0 @ X1 @ (compose @ X0 @ X1)))),
% 3.57/1.08 inference('cnf', [status(esa)], [closure_of_composition])).
% 3.57/1.08 thf(zip_derived_cl17, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.57/1.08 (~ (product @ X0 @ X1 @ X2)
% 3.57/1.08 | ~ (product @ X0 @ X1 @ X3)
% 3.57/1.08 | ((X2) = (X3)))),
% 3.57/1.08 inference('cnf', [status(esa)], [composition_is_well_defined])).
% 3.57/1.08 thf(zip_derived_cl122, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ X0)
% 3.57/1.08 | ~ (product @ X1 @ X0 @ X2)
% 3.57/1.08 | ((compose @ X1 @ X0) = (X2)))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl17])).
% 3.57/1.08 thf(zip_derived_cl1, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.57/1.08 (~ (product @ X0 @ X1 @ X2) | (defined @ X0 @ X1))),
% 3.57/1.08 inference('cnf', [status(esa)], [associative_property1])).
% 3.57/1.08 thf(zip_derived_cl150, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.57/1.08 (((compose @ X1 @ X0) = (X2)) | ~ (product @ X1 @ X0 @ X2))),
% 3.57/1.08 inference('clc', [status(thm)], [zip_derived_cl122, zip_derived_cl1])).
% 3.57/1.08 thf(zip_derived_cl577, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X0 @ X1) | ((compose @ X0 @ (codomain @ X1)) = (X0)))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl167, zip_derived_cl150])).
% 3.57/1.08 thf(zip_derived_cl744, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ (codomain @ X0))
% 3.57/1.08 | ((compose @ X1 @ (codomain @ X0)) = (X1)))),
% 3.57/1.08 inference('s_sup+', [status(thm)], [zip_derived_cl541, zip_derived_cl577])).
% 3.57/1.08 thf(zip_derived_cl0, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X0 @ X1) | (product @ X0 @ X1 @ (compose @ X0 @ X1)))),
% 3.57/1.08 inference('cnf', [status(esa)], [closure_of_composition])).
% 3.57/1.08 thf(zip_derived_cl746, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X0 @ (codomain @ X1))
% 3.57/1.08 | ~ (defined @ X0 @ (codomain @ X1))
% 3.57/1.08 | (product @ X0 @ (codomain @ X1) @ X0))),
% 3.57/1.08 inference('s_sup+', [status(thm)], [zip_derived_cl744, zip_derived_cl0])).
% 3.57/1.08 thf(zip_derived_cl756, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 ( (product @ X0 @ (codomain @ X1) @ X0)
% 3.57/1.08 | ~ (defined @ X0 @ (codomain @ X1)))),
% 3.57/1.08 inference('simplify', [status(thm)], [zip_derived_cl746])).
% 3.57/1.08 thf(zip_derived_cl17, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.57/1.08 (~ (product @ X0 @ X1 @ X2)
% 3.57/1.08 | ~ (product @ X0 @ X1 @ X3)
% 3.57/1.08 | ((X2) = (X3)))),
% 3.57/1.08 inference('cnf', [status(esa)], [composition_is_well_defined])).
% 3.57/1.08 thf(zip_derived_cl778, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.57/1.08 (~ (defined @ X0 @ (codomain @ X1))
% 3.57/1.08 | ~ (product @ X0 @ (codomain @ X1) @ X2)
% 3.57/1.08 | ((X0) = (X2)))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl756, zip_derived_cl17])).
% 3.57/1.08 thf(zip_derived_cl1, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.57/1.08 (~ (product @ X0 @ X1 @ X2) | (defined @ X0 @ X1))),
% 3.57/1.08 inference('cnf', [status(esa)], [associative_property1])).
% 3.57/1.08 thf(zip_derived_cl1971, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.57/1.08 (((X0) = (X2)) | ~ (product @ X0 @ (codomain @ X1) @ X2))),
% 3.57/1.08 inference('clc', [status(thm)], [zip_derived_cl778, zip_derived_cl1])).
% 3.57/1.08 thf(zip_derived_cl1978, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ (codomain @ X0))
% 3.57/1.08 | ((domain @ X1) = (codomain @ X0)))),
% 3.57/1.08 inference('s_sup-', [status(thm)],
% 3.57/1.08 [zip_derived_cl216, zip_derived_cl1971])).
% 3.57/1.08 thf(zip_derived_cl2050, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ X0) | ((domain @ X1) = (codomain @ X0)))),
% 3.57/1.08 inference('s_sup-', [status(thm)],
% 3.57/1.08 [zip_derived_cl156, zip_derived_cl1978])).
% 3.57/1.08 thf(zip_derived_cl2274, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ X0)
% 3.57/1.08 | ((domain @ (codomain @ X1)) = (codomain @ (compose @ X1 @ X0))))),
% 3.57/1.08 inference('s_sup-', [status(thm)],
% 3.57/1.08 [zip_derived_cl266, zip_derived_cl2050])).
% 3.57/1.08 thf(zip_derived_cl541, plain,
% 3.57/1.08 (![X0 : $i]: ((codomain @ (codomain @ X0)) = (codomain @ X0))),
% 3.57/1.08 inference('demod', [status(thm)],
% 3.57/1.08 [zip_derived_cl528, zip_derived_cl10, zip_derived_cl269,
% 3.57/1.08 zip_derived_cl10])).
% 3.57/1.08 thf(zip_derived_cl12, plain, (![X0 : $i]: (defined @ (codomain @ X0) @ X0)),
% 3.57/1.08 inference('cnf', [status(esa)], [mapping_from_codomain_of_x_to_x])).
% 3.57/1.08 thf(zip_derived_cl552, plain,
% 3.57/1.08 (![X0 : $i]: (defined @ (codomain @ X0) @ (codomain @ X0))),
% 3.57/1.08 inference('s_sup+', [status(thm)], [zip_derived_cl541, zip_derived_cl12])).
% 3.57/1.08 thf(zip_derived_cl1978, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ (codomain @ X0))
% 3.57/1.08 | ((domain @ X1) = (codomain @ X0)))),
% 3.57/1.08 inference('s_sup-', [status(thm)],
% 3.57/1.08 [zip_derived_cl216, zip_derived_cl1971])).
% 3.57/1.08 thf(zip_derived_cl2056, plain,
% 3.57/1.08 (![X0 : $i]: ((domain @ (codomain @ X0)) = (codomain @ X0))),
% 3.57/1.08 inference('s_sup-', [status(thm)],
% 3.57/1.08 [zip_derived_cl552, zip_derived_cl1978])).
% 3.57/1.08 thf(zip_derived_cl2281, plain,
% 3.57/1.08 (![X0 : $i, X1 : $i]:
% 3.57/1.08 (~ (defined @ X1 @ X0)
% 3.57/1.08 | ((codomain @ X1) = (codomain @ (compose @ X1 @ X0))))),
% 3.57/1.08 inference('demod', [status(thm)],
% 3.57/1.08 [zip_derived_cl2274, zip_derived_cl2056])).
% 3.57/1.08 thf(prove_codomain_of_ba_equals_codomain_of_b, conjecture,
% 3.57/1.08 (( codomain @ ( compose @ b @ a ) ) = ( codomain @ b ))).
% 3.57/1.08 thf(zf_stmt_0, negated_conjecture,
% 3.57/1.08 (( codomain @ ( compose @ b @ a ) ) != ( codomain @ b )),
% 3.57/1.08 inference('cnf.neg', [status(esa)],
% 3.57/1.08 [prove_codomain_of_ba_equals_codomain_of_b])).
% 3.57/1.08 thf(zip_derived_cl19, plain,
% 3.57/1.08 (((codomain @ (compose @ b @ a)) != (codomain @ b))),
% 3.57/1.08 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.57/1.08 thf(zip_derived_cl2802, plain,
% 3.57/1.08 ((~ (defined @ b @ a) | ((codomain @ b) != (codomain @ b)))),
% 3.57/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl2281, zip_derived_cl19])).
% 3.57/1.08 thf(ba_defined, axiom, (defined @ b @ a)).
% 3.57/1.08 thf(zip_derived_cl18, plain, ( (defined @ b @ a)),
% 3.57/1.08 inference('cnf', [status(esa)], [ba_defined])).
% 3.57/1.08 thf(zip_derived_cl2821, plain, (((codomain @ b) != (codomain @ b))),
% 3.57/1.08 inference('demod', [status(thm)], [zip_derived_cl2802, zip_derived_cl18])).
% 3.57/1.08 thf(zip_derived_cl2822, plain, ($false),
% 3.57/1.08 inference('simplify', [status(thm)], [zip_derived_cl2821])).
% 3.57/1.08
% 3.57/1.08 % SZS output end Refutation
% 3.57/1.08
% 3.57/1.08
% 3.57/1.08 % Terminating...
% 3.87/1.13 % Runner terminated.
% 3.87/1.14 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------