TSTP Solution File: CAT001-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : CAT001-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.84opqZAHtO 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 18:20:49 EDT 2023
% Result : Unsatisfiable 1.28s 1.34s
% Output : Refutation 1.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT001-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.84opqZAHtO true
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 01:06:10 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.21/0.66 % Total configuration time : 435
% 0.21/0.66 % Estimated wc time : 1092
% 0.21/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.28/1.34 % Solved by fo/fo3_bce.sh.
% 1.28/1.34 % BCE start: 23
% 1.28/1.34 % BCE eliminated: 0
% 1.28/1.34 % PE start: 23
% 1.28/1.34 logic: eq
% 1.28/1.34 % PE eliminated: -1
% 1.28/1.34 % done 1515 iterations in 0.568s
% 1.28/1.34 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.28/1.34 % SZS output start Refutation
% 1.28/1.34 thf(g_type, type, g: $i).
% 1.28/1.34 thf(b_type, type, b: $i).
% 1.28/1.34 thf(h_type, type, h: $i).
% 1.28/1.34 thf(compose_type, type, compose: $i > $i > $i).
% 1.28/1.34 thf(c_type, type, c: $i).
% 1.28/1.34 thf(codomain_type, type, codomain: $i > $i).
% 1.28/1.34 thf(d_type, type, d: $i).
% 1.28/1.34 thf(domain_type, type, domain: $i > $i).
% 1.28/1.34 thf(identity_map_type, type, identity_map: $i > $o).
% 1.28/1.34 thf(defined_type, type, defined: $i > $i > $o).
% 1.28/1.34 thf(product_type, type, product: $i > $i > $i > $o).
% 1.28/1.34 thf(a_type, type, a: $i).
% 1.28/1.34 thf(closure_of_composition, axiom,
% 1.28/1.34 (( ~( defined @ X @ Y ) ) | ( product @ X @ Y @ ( compose @ X @ Y ) ))).
% 1.28/1.34 thf(zip_derived_cl0, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 (~ (defined @ X0 @ X1) | (product @ X0 @ X1 @ (compose @ X0 @ X1)))),
% 1.28/1.34 inference('cnf', [status(esa)], [closure_of_composition])).
% 1.28/1.34 thf(bh_equals_d, axiom, (product @ b @ h @ d)).
% 1.28/1.34 thf(zip_derived_cl20, plain, ( (product @ b @ h @ d)),
% 1.28/1.34 inference('cnf', [status(esa)], [bh_equals_d])).
% 1.28/1.34 thf(ab_equals_c, axiom, (product @ a @ b @ c)).
% 1.28/1.34 thf(zip_derived_cl18, plain, ( (product @ a @ b @ c)),
% 1.28/1.34 inference('cnf', [status(esa)], [ab_equals_c])).
% 1.28/1.34 thf(category_theory_axiom2, axiom,
% 1.28/1.34 (( ~( product @ X @ Y @ Xy ) ) | ( ~( product @ Xy @ Z @ Xyz ) ) |
% 1.28/1.34 ( ~( product @ Y @ Z @ Yz ) ) | ( product @ X @ Yz @ Xyz ))).
% 1.28/1.34 thf(zip_derived_cl4, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.28/1.34 (~ (product @ X0 @ X1 @ X2)
% 1.28/1.34 | ~ (product @ X2 @ X3 @ X4)
% 1.28/1.34 | ~ (product @ X1 @ X3 @ X5)
% 1.28/1.34 | (product @ X0 @ X5 @ X4))),
% 1.28/1.34 inference('cnf', [status(esa)], [category_theory_axiom2])).
% 1.28/1.34 thf(zip_derived_cl199, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 ( (product @ a @ X1 @ X0)
% 1.28/1.34 | ~ (product @ b @ X2 @ X1)
% 1.28/1.34 | ~ (product @ c @ X2 @ X0))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl4])).
% 1.28/1.34 thf(zip_derived_cl1103, plain,
% 1.28/1.34 (![X0 : $i]: (~ (product @ c @ h @ X0) | (product @ a @ d @ X0))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl199])).
% 1.28/1.34 thf(zip_derived_cl5390, plain,
% 1.28/1.34 ((~ (defined @ c @ h) | (product @ a @ d @ (compose @ c @ h)))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl1103])).
% 1.28/1.34 thf(domain_is_an_identity_map, axiom, (identity_map @ ( domain @ X ))).
% 1.28/1.34 thf(zip_derived_cl9, plain, (![X0 : $i]: (identity_map @ (domain @ X0))),
% 1.28/1.34 inference('cnf', [status(esa)], [domain_is_an_identity_map])).
% 1.28/1.34 thf(identity1, axiom,
% 1.28/1.34 (( ~( defined @ X @ Y ) ) | ( ~( identity_map @ X ) ) |
% 1.28/1.34 ( product @ X @ Y @ Y ))).
% 1.28/1.34 thf(zip_derived_cl15, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 (~ (defined @ X0 @ X1)
% 1.28/1.34 | ~ (identity_map @ X0)
% 1.28/1.34 | (product @ X0 @ X1 @ X1))),
% 1.28/1.34 inference('cnf', [status(esa)], [identity1])).
% 1.28/1.34 thf(zip_derived_cl122, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 ( (product @ (domain @ X0) @ X1 @ X1)
% 1.28/1.34 | ~ (defined @ (domain @ X0) @ X1))),
% 1.28/1.34 inference('dp-resolution', [status(thm)],
% 1.28/1.34 [zip_derived_cl9, zip_derived_cl15])).
% 1.28/1.34 thf(composition_is_well_defined, axiom,
% 1.28/1.34 (( ~( product @ X @ Y @ Z ) ) | ( ~( product @ X @ Y @ W ) ) |
% 1.28/1.34 ( ( Z ) = ( W ) ))).
% 1.28/1.34 thf(zip_derived_cl17, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.28/1.34 (~ (product @ X0 @ X1 @ X2)
% 1.28/1.34 | ~ (product @ X0 @ X1 @ X3)
% 1.28/1.34 | ((X2) = (X3)))),
% 1.28/1.34 inference('cnf', [status(esa)], [composition_is_well_defined])).
% 1.28/1.34 thf(zip_derived_cl179, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 (~ (defined @ (domain @ X1) @ X0)
% 1.28/1.34 | ((X0) = (X2))
% 1.28/1.34 | ~ (product @ (domain @ X1) @ X0 @ X2))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl17])).
% 1.28/1.34 thf(associative_property1, axiom,
% 1.28/1.34 (( ~( product @ X @ Y @ Z ) ) | ( defined @ X @ Y ))).
% 1.28/1.34 thf(zip_derived_cl1, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 (~ (product @ X0 @ X1 @ X2) | (defined @ X0 @ X1))),
% 1.28/1.34 inference('cnf', [status(esa)], [associative_property1])).
% 1.28/1.34 thf(zip_derived_cl817, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 (~ (product @ (domain @ X1) @ X0 @ X2) | ((X0) = (X2)))),
% 1.28/1.34 inference('clc', [status(thm)], [zip_derived_cl179, zip_derived_cl1])).
% 1.28/1.34 thf(zip_derived_cl9, plain, (![X0 : $i]: (identity_map @ (domain @ X0))),
% 1.28/1.34 inference('cnf', [status(esa)], [domain_is_an_identity_map])).
% 1.28/1.34 thf(identity2, axiom,
% 1.28/1.34 (( ~( defined @ X @ Y ) ) | ( ~( identity_map @ Y ) ) |
% 1.28/1.34 ( product @ X @ Y @ X ))).
% 1.28/1.34 thf(zip_derived_cl16, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 (~ (defined @ X0 @ X1)
% 1.28/1.34 | ~ (identity_map @ X1)
% 1.28/1.34 | (product @ X0 @ X1 @ X0))),
% 1.28/1.34 inference('cnf', [status(esa)], [identity2])).
% 1.28/1.34 thf(zip_derived_cl123, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 ( (product @ X1 @ (domain @ X0) @ X1)
% 1.28/1.34 | ~ (defined @ X1 @ (domain @ X0)))),
% 1.28/1.34 inference('dp-resolution', [status(thm)],
% 1.28/1.34 [zip_derived_cl9, zip_derived_cl16])).
% 1.28/1.34 thf(zip_derived_cl820, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 (((domain @ X1) = (domain @ X0))
% 1.28/1.34 | ~ (defined @ (domain @ X0) @ (domain @ X1)))),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl817, zip_derived_cl123])).
% 1.28/1.34 thf(product_on_domain, axiom, (product @ X @ ( domain @ X ) @ X)).
% 1.28/1.34 thf(zip_derived_cl13, plain,
% 1.28/1.34 (![X0 : $i]: (product @ X0 @ (domain @ X0) @ X0)),
% 1.28/1.34 inference('cnf', [status(esa)], [product_on_domain])).
% 1.28/1.34 thf(associative_property2, axiom,
% 1.28/1.34 (( ~( product @ X @ Y @ Xy ) ) | ( ~( defined @ Xy @ Z ) ) |
% 1.28/1.34 ( defined @ Y @ Z ))).
% 1.28/1.34 thf(zip_derived_cl2, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.28/1.34 (~ (product @ X0 @ X1 @ X2)
% 1.28/1.34 | ~ (defined @ X2 @ X3)
% 1.28/1.34 | (defined @ X1 @ X3))),
% 1.28/1.34 inference('cnf', [status(esa)], [associative_property2])).
% 1.28/1.34 thf(zip_derived_cl149, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 ( (defined @ (domain @ X0) @ X1) | ~ (defined @ X0 @ X1))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl2])).
% 1.28/1.34 thf(zip_derived_cl954, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 (((domain @ X0) = (domain @ X1)) | ~ (defined @ X1 @ (domain @ X0)))),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl820, zip_derived_cl149])).
% 1.28/1.34 thf(zip_derived_cl18, plain, ( (product @ a @ b @ c)),
% 1.28/1.34 inference('cnf', [status(esa)], [ab_equals_c])).
% 1.28/1.34 thf(zip_derived_cl2, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.28/1.34 (~ (product @ X0 @ X1 @ X2)
% 1.28/1.34 | ~ (defined @ X2 @ X3)
% 1.28/1.34 | (defined @ X1 @ X3))),
% 1.28/1.34 inference('cnf', [status(esa)], [associative_property2])).
% 1.28/1.34 thf(zip_derived_cl141, plain,
% 1.28/1.34 (![X0 : $i]: ( (defined @ b @ X0) | ~ (defined @ c @ X0))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl2])).
% 1.28/1.34 thf(mapping_from_x_to_its_domain, axiom, (defined @ X @ ( domain @ X ))).
% 1.28/1.34 thf(zip_derived_cl11, plain, (![X0 : $i]: (defined @ X0 @ (domain @ X0))),
% 1.28/1.34 inference('cnf', [status(esa)], [mapping_from_x_to_its_domain])).
% 1.28/1.34 thf(zip_derived_cl275, plain, ( (defined @ b @ (domain @ c))),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl141, zip_derived_cl11])).
% 1.28/1.34 thf(zip_derived_cl971, plain, (((domain @ c) = (domain @ b))),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl954, zip_derived_cl275])).
% 1.28/1.34 thf(zip_derived_cl11, plain, (![X0 : $i]: (defined @ X0 @ (domain @ X0))),
% 1.28/1.34 inference('cnf', [status(esa)], [mapping_from_x_to_its_domain])).
% 1.28/1.34 thf(zip_derived_cl1051, plain, ( (defined @ c @ (domain @ b))),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl971, zip_derived_cl11])).
% 1.28/1.34 thf(zip_derived_cl149, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 ( (defined @ (domain @ X0) @ X1) | ~ (defined @ X0 @ X1))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl2])).
% 1.28/1.34 thf(zip_derived_cl9, plain, (![X0 : $i]: (identity_map @ (domain @ X0))),
% 1.28/1.34 inference('cnf', [status(esa)], [domain_is_an_identity_map])).
% 1.28/1.34 thf(category_theory_axiom6, axiom,
% 1.28/1.34 (( ~( defined @ X @ Y ) ) | ( ~( defined @ Y @ Z ) ) |
% 1.28/1.34 ( ~( identity_map @ Y ) ) | ( defined @ X @ Z ))).
% 1.28/1.34 thf(zip_derived_cl8, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 (~ (defined @ X0 @ X1)
% 1.28/1.34 | ~ (defined @ X1 @ X2)
% 1.28/1.34 | ~ (identity_map @ X1)
% 1.28/1.34 | (defined @ X0 @ X2))),
% 1.28/1.34 inference('cnf', [status(esa)], [category_theory_axiom6])).
% 1.28/1.34 thf(zip_derived_cl121, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 ( (defined @ X1 @ X2)
% 1.28/1.34 | ~ (defined @ (domain @ X0) @ X2)
% 1.28/1.34 | ~ (defined @ X1 @ (domain @ X0)))),
% 1.28/1.34 inference('dp-resolution', [status(thm)],
% 1.28/1.34 [zip_derived_cl9, zip_derived_cl8])).
% 1.28/1.34 thf(zip_derived_cl442, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 (~ (defined @ X1 @ X0)
% 1.28/1.34 | ~ (defined @ X2 @ (domain @ X1))
% 1.28/1.34 | (defined @ X2 @ X0))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl149, zip_derived_cl121])).
% 1.28/1.34 thf(zip_derived_cl1180, plain,
% 1.28/1.34 (![X0 : $i]: ( (defined @ c @ X0) | ~ (defined @ b @ X0))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl1051, zip_derived_cl442])).
% 1.28/1.34 thf(product_on_codomain, axiom, (product @ ( codomain @ X ) @ X @ X)).
% 1.28/1.34 thf(zip_derived_cl14, plain,
% 1.28/1.34 (![X0 : $i]: (product @ (codomain @ X0) @ X0 @ X0)),
% 1.28/1.34 inference('cnf', [status(esa)], [product_on_codomain])).
% 1.28/1.34 thf(category_theory_axiom3, axiom,
% 1.28/1.34 (( ~( product @ Y @ Z @ Yz ) ) | ( ~( defined @ X @ Yz ) ) |
% 1.28/1.34 ( defined @ X @ Y ))).
% 1.28/1.34 thf(zip_derived_cl5, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.28/1.34 (~ (product @ X0 @ X1 @ X2)
% 1.28/1.34 | ~ (defined @ X3 @ X2)
% 1.28/1.34 | (defined @ X3 @ X0))),
% 1.28/1.34 inference('cnf', [status(esa)], [category_theory_axiom3])).
% 1.28/1.34 thf(zip_derived_cl165, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 ( (defined @ X1 @ (codomain @ X0)) | ~ (defined @ X1 @ X0))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl5])).
% 1.28/1.34 thf(zip_derived_cl13, plain,
% 1.28/1.34 (![X0 : $i]: (product @ X0 @ (domain @ X0) @ X0)),
% 1.28/1.34 inference('cnf', [status(esa)], [product_on_domain])).
% 1.28/1.34 thf(cancellation_for_product, axiom,
% 1.28/1.34 (( ~( product @ c @ X1 @ X2 ) ) | ( ~( product @ c @ X3 @ X2 ) ) |
% 1.28/1.34 ( ( X1 ) = ( X3 ) ))).
% 1.28/1.34 thf(zip_derived_cl19, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 (~ (product @ c @ X0 @ X1) | ~ (product @ c @ X2 @ X1) | ((X0) = (X2)))),
% 1.28/1.34 inference('cnf', [status(esa)], [cancellation_for_product])).
% 1.28/1.34 thf(zip_derived_cl160, plain,
% 1.28/1.34 (![X0 : $i]: (((domain @ c) = (X0)) | ~ (product @ c @ X0 @ c))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl19])).
% 1.28/1.34 thf(codomain_is_an_identity_map, axiom, (identity_map @ ( codomain @ X ))).
% 1.28/1.34 thf(zip_derived_cl10, plain, (![X0 : $i]: (identity_map @ (codomain @ X0))),
% 1.28/1.34 inference('cnf', [status(esa)], [codomain_is_an_identity_map])).
% 1.28/1.34 thf(zip_derived_cl16, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 (~ (defined @ X0 @ X1)
% 1.28/1.34 | ~ (identity_map @ X1)
% 1.28/1.34 | (product @ X0 @ X1 @ X0))),
% 1.28/1.34 inference('cnf', [status(esa)], [identity2])).
% 1.28/1.34 thf(zip_derived_cl126, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 ( (product @ X1 @ (codomain @ X0) @ X1)
% 1.28/1.34 | ~ (defined @ X1 @ (codomain @ X0)))),
% 1.28/1.34 inference('dp-resolution', [status(thm)],
% 1.28/1.34 [zip_derived_cl10, zip_derived_cl16])).
% 1.28/1.34 thf(zip_derived_cl403, plain,
% 1.28/1.34 (![X0 : $i]:
% 1.28/1.34 (((domain @ c) = (codomain @ X0)) | ~ (defined @ c @ (codomain @ X0)))),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl160, zip_derived_cl126])).
% 1.28/1.34 thf(zip_derived_cl649, plain,
% 1.28/1.34 (![X0 : $i]: (~ (defined @ c @ X0) | ((domain @ c) = (codomain @ X0)))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl165, zip_derived_cl403])).
% 1.28/1.34 thf(zip_derived_cl971, plain, (((domain @ c) = (domain @ b))),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl954, zip_derived_cl275])).
% 1.28/1.34 thf(zip_derived_cl1048, plain,
% 1.28/1.34 (![X0 : $i]: (~ (defined @ c @ X0) | ((domain @ b) = (codomain @ X0)))),
% 1.28/1.34 inference('demod', [status(thm)], [zip_derived_cl649, zip_derived_cl971])).
% 1.28/1.34 thf(zip_derived_cl1208, plain,
% 1.28/1.34 (![X0 : $i]: (~ (defined @ b @ X0) | ((domain @ b) = (codomain @ X0)))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl1180, zip_derived_cl1048])).
% 1.28/1.34 thf(zip_derived_cl1, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 (~ (product @ X0 @ X1 @ X2) | (defined @ X0 @ X1))),
% 1.28/1.34 inference('cnf', [status(esa)], [associative_property1])).
% 1.28/1.34 thf(zip_derived_cl20, plain, ( (product @ b @ h @ d)),
% 1.28/1.34 inference('cnf', [status(esa)], [bh_equals_d])).
% 1.28/1.34 thf(zip_derived_cl129, plain, ( (defined @ b @ h)),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl20])).
% 1.28/1.34 thf(zip_derived_cl1262, plain, (((domain @ b) = (codomain @ h))),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl1208, zip_derived_cl129])).
% 1.28/1.34 thf(mapping_from_codomain_of_x_to_x, axiom, (defined @ ( codomain @ X ) @ X)).
% 1.28/1.34 thf(zip_derived_cl12, plain, (![X0 : $i]: (defined @ (codomain @ X0) @ X0)),
% 1.28/1.34 inference('cnf', [status(esa)], [mapping_from_codomain_of_x_to_x])).
% 1.28/1.34 thf(zip_derived_cl10, plain, (![X0 : $i]: (identity_map @ (codomain @ X0))),
% 1.28/1.34 inference('cnf', [status(esa)], [codomain_is_an_identity_map])).
% 1.28/1.34 thf(zip_derived_cl8, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 (~ (defined @ X0 @ X1)
% 1.28/1.34 | ~ (defined @ X1 @ X2)
% 1.28/1.34 | ~ (identity_map @ X1)
% 1.28/1.34 | (defined @ X0 @ X2))),
% 1.28/1.34 inference('cnf', [status(esa)], [category_theory_axiom6])).
% 1.28/1.34 thf(zip_derived_cl124, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 ( (defined @ X1 @ X2)
% 1.28/1.34 | ~ (defined @ (codomain @ X0) @ X2)
% 1.28/1.34 | ~ (defined @ X1 @ (codomain @ X0)))),
% 1.28/1.34 inference('dp-resolution', [status(thm)],
% 1.28/1.34 [zip_derived_cl10, zip_derived_cl8])).
% 1.28/1.34 thf(zip_derived_cl172, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 (~ (defined @ X1 @ (codomain @ X0)) | (defined @ X1 @ X0))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl124])).
% 1.28/1.34 thf(zip_derived_cl1278, plain,
% 1.28/1.34 (![X0 : $i]: (~ (defined @ X0 @ (domain @ b)) | (defined @ X0 @ h))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl1262, zip_derived_cl172])).
% 1.28/1.34 thf(zip_derived_cl1051, plain, ( (defined @ c @ (domain @ b))),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl971, zip_derived_cl11])).
% 1.28/1.34 thf(zip_derived_cl1351, plain, ( (defined @ c @ h)),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl1278, zip_derived_cl1051])).
% 1.28/1.34 thf(zip_derived_cl5391, plain, ( (product @ a @ d @ (compose @ c @ h))),
% 1.28/1.34 inference('demod', [status(thm)],
% 1.28/1.34 [zip_derived_cl5390, zip_derived_cl1351])).
% 1.28/1.34 thf(zip_derived_cl0, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 (~ (defined @ X0 @ X1) | (product @ X0 @ X1 @ (compose @ X0 @ X1)))),
% 1.28/1.34 inference('cnf', [status(esa)], [closure_of_composition])).
% 1.28/1.34 thf(zip_derived_cl17, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.28/1.34 (~ (product @ X0 @ X1 @ X2)
% 1.28/1.34 | ~ (product @ X0 @ X1 @ X3)
% 1.28/1.34 | ((X2) = (X3)))),
% 1.28/1.34 inference('cnf', [status(esa)], [composition_is_well_defined])).
% 1.28/1.34 thf(zip_derived_cl135, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 (~ (defined @ X1 @ X0)
% 1.28/1.34 | ((compose @ X1 @ X0) = (X2))
% 1.28/1.34 | ~ (product @ X1 @ X0 @ X2))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl17])).
% 1.28/1.34 thf(zip_derived_cl1, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 (~ (product @ X0 @ X1 @ X2) | (defined @ X0 @ X1))),
% 1.28/1.34 inference('cnf', [status(esa)], [associative_property1])).
% 1.28/1.34 thf(zip_derived_cl254, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 (~ (product @ X1 @ X0 @ X2) | ((compose @ X1 @ X0) = (X2)))),
% 1.28/1.34 inference('clc', [status(thm)], [zip_derived_cl135, zip_derived_cl1])).
% 1.28/1.34 thf(zip_derived_cl5408, plain, (((compose @ a @ d) = (compose @ c @ h))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl5391, zip_derived_cl254])).
% 1.28/1.34 thf(zip_derived_cl0, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 (~ (defined @ X0 @ X1) | (product @ X0 @ X1 @ (compose @ X0 @ X1)))),
% 1.28/1.34 inference('cnf', [status(esa)], [closure_of_composition])).
% 1.28/1.34 thf(zip_derived_cl5426, plain,
% 1.28/1.34 (( (product @ c @ h @ (compose @ a @ d)) | ~ (defined @ c @ h))),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl5408, zip_derived_cl0])).
% 1.28/1.34 thf(zip_derived_cl1351, plain, ( (defined @ c @ h)),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl1278, zip_derived_cl1051])).
% 1.28/1.34 thf(zip_derived_cl5440, plain, ( (product @ c @ h @ (compose @ a @ d))),
% 1.28/1.34 inference('demod', [status(thm)],
% 1.28/1.34 [zip_derived_cl5426, zip_derived_cl1351])).
% 1.28/1.34 thf(zip_derived_cl0, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 (~ (defined @ X0 @ X1) | (product @ X0 @ X1 @ (compose @ X0 @ X1)))),
% 1.28/1.34 inference('cnf', [status(esa)], [closure_of_composition])).
% 1.28/1.34 thf(bg_equals_d, axiom, (product @ b @ g @ d)).
% 1.28/1.34 thf(zip_derived_cl21, plain, ( (product @ b @ g @ d)),
% 1.28/1.34 inference('cnf', [status(esa)], [bg_equals_d])).
% 1.28/1.34 thf(zip_derived_cl199, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 ( (product @ a @ X1 @ X0)
% 1.28/1.34 | ~ (product @ b @ X2 @ X1)
% 1.28/1.34 | ~ (product @ c @ X2 @ X0))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl4])).
% 1.28/1.34 thf(zip_derived_cl1104, plain,
% 1.28/1.34 (![X0 : $i]: (~ (product @ c @ g @ X0) | (product @ a @ d @ X0))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl199])).
% 1.28/1.34 thf(zip_derived_cl5394, plain,
% 1.28/1.34 ((~ (defined @ c @ g) | (product @ a @ d @ (compose @ c @ g)))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl1104])).
% 1.28/1.34 thf(zip_derived_cl1208, plain,
% 1.28/1.34 (![X0 : $i]: (~ (defined @ b @ X0) | ((domain @ b) = (codomain @ X0)))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl1180, zip_derived_cl1048])).
% 1.28/1.34 thf(zip_derived_cl1, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 (~ (product @ X0 @ X1 @ X2) | (defined @ X0 @ X1))),
% 1.28/1.34 inference('cnf', [status(esa)], [associative_property1])).
% 1.28/1.34 thf(zip_derived_cl21, plain, ( (product @ b @ g @ d)),
% 1.28/1.34 inference('cnf', [status(esa)], [bg_equals_d])).
% 1.28/1.34 thf(zip_derived_cl130, plain, ( (defined @ b @ g)),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 1.28/1.34 thf(zip_derived_cl1263, plain, (((domain @ b) = (codomain @ g))),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl1208, zip_derived_cl130])).
% 1.28/1.34 thf(zip_derived_cl172, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 (~ (defined @ X1 @ (codomain @ X0)) | (defined @ X1 @ X0))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl124])).
% 1.28/1.34 thf(zip_derived_cl1302, plain,
% 1.28/1.34 (![X0 : $i]: (~ (defined @ X0 @ (domain @ b)) | (defined @ X0 @ g))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl1263, zip_derived_cl172])).
% 1.28/1.34 thf(zip_derived_cl1051, plain, ( (defined @ c @ (domain @ b))),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl971, zip_derived_cl11])).
% 1.28/1.34 thf(zip_derived_cl1469, plain, ( (defined @ c @ g)),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl1302, zip_derived_cl1051])).
% 1.28/1.34 thf(zip_derived_cl5395, plain, ( (product @ a @ d @ (compose @ c @ g))),
% 1.28/1.34 inference('demod', [status(thm)],
% 1.28/1.34 [zip_derived_cl5394, zip_derived_cl1469])).
% 1.28/1.34 thf(zip_derived_cl254, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 (~ (product @ X1 @ X0 @ X2) | ((compose @ X1 @ X0) = (X2)))),
% 1.28/1.34 inference('clc', [status(thm)], [zip_derived_cl135, zip_derived_cl1])).
% 1.28/1.34 thf(zip_derived_cl5735, plain, (((compose @ a @ d) = (compose @ c @ g))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl5395, zip_derived_cl254])).
% 1.28/1.34 thf(zip_derived_cl0, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 (~ (defined @ X0 @ X1) | (product @ X0 @ X1 @ (compose @ X0 @ X1)))),
% 1.28/1.34 inference('cnf', [status(esa)], [closure_of_composition])).
% 1.28/1.34 thf(zip_derived_cl19, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.28/1.34 (~ (product @ c @ X0 @ X1) | ~ (product @ c @ X2 @ X1) | ((X0) = (X2)))),
% 1.28/1.34 inference('cnf', [status(esa)], [cancellation_for_product])).
% 1.28/1.34 thf(zip_derived_cl159, plain,
% 1.28/1.34 (![X0 : $i, X1 : $i]:
% 1.28/1.34 (~ (defined @ c @ X0)
% 1.28/1.34 | ((X0) = (X1))
% 1.28/1.34 | ~ (product @ c @ X1 @ (compose @ c @ X0)))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl19])).
% 1.28/1.34 thf(zip_derived_cl5767, plain,
% 1.28/1.34 (![X0 : $i]:
% 1.28/1.34 (~ (product @ c @ X0 @ (compose @ a @ d))
% 1.28/1.34 | ((g) = (X0))
% 1.28/1.34 | ~ (defined @ c @ g))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl5735, zip_derived_cl159])).
% 1.28/1.34 thf(zip_derived_cl1469, plain, ( (defined @ c @ g)),
% 1.28/1.34 inference('sup+', [status(thm)], [zip_derived_cl1302, zip_derived_cl1051])).
% 1.28/1.34 thf(zip_derived_cl5782, plain,
% 1.28/1.34 (![X0 : $i]: (~ (product @ c @ X0 @ (compose @ a @ d)) | ((g) = (X0)))),
% 1.28/1.34 inference('demod', [status(thm)],
% 1.28/1.34 [zip_derived_cl5767, zip_derived_cl1469])).
% 1.28/1.34 thf(zip_derived_cl6075, plain, (((g) = (h))),
% 1.28/1.34 inference('sup-', [status(thm)], [zip_derived_cl5440, zip_derived_cl5782])).
% 1.28/1.34 thf(prove_h_equals_g, conjecture, (( h ) = ( g ))).
% 1.28/1.34 thf(zf_stmt_0, negated_conjecture, (( h ) != ( g )),
% 1.28/1.34 inference('cnf.neg', [status(esa)], [prove_h_equals_g])).
% 1.28/1.34 thf(zip_derived_cl22, plain, (((h) != (g))),
% 1.28/1.34 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.28/1.34 thf(zip_derived_cl6076, plain, ($false),
% 1.28/1.34 inference('simplify_reflect-', [status(thm)],
% 1.28/1.34 [zip_derived_cl6075, zip_derived_cl22])).
% 1.28/1.34
% 1.28/1.34 % SZS output end Refutation
% 1.28/1.34
% 1.28/1.34
% 1.28/1.35 % Terminating...
% 1.28/1.47 % Runner terminated.
% 1.28/1.48 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------