%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP124-7.004 : 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.ch2ryCq0Hp 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 04:35:42 PM UTC 2025
% Result : Unsatisfiable 4.42s 1.23s
% Output : Refutation 4.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP124-7.004 : TPTP v9.2.0. Released v1.2.0.
% 0.08/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.ch2ryCq0Hp true
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 1 14:04:08 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.37 % Python version: Python 3.6.8
% 0.14/0.37 % Running in FO mode
% 0.57/0.68 % Total configuration time : 435
% 0.57/0.68 % Estimated wc time : 1092
% 0.57/0.68 % Estimated cpu time (7 cpus) : 156.0
% 0.61/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.61/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.61/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.62/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.62/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.62/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.62/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 4.42/1.23 % Solved by fo/fo4.sh.
% 4.42/1.23 % done 532 iterations in 0.398s
% 4.42/1.23 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 4.42/1.23 % SZS output start Refutation
% 4.42/1.23 thf(group_element_type, type, group_element: $i > $o).
% 4.42/1.23 thf(e_4_type, type, e_4: $i).
% 4.42/1.23 thf(equalish_type, type, equalish: $i > $i > $o).
% 4.42/1.23 thf(e_3_type, type, e_3: $i).
% 4.42/1.23 thf(e_2_type, type, e_2: $i).
% 4.42/1.23 thf(product2_type, type, product2: $i > $i > $i > $o).
% 4.42/1.23 thf(e_1_type, type, e_1: $i).
% 4.42/1.23 thf(product1_type, type, product1: $i > $i > $i > $o).
% 4.42/1.23 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 4.42/1.23 thf(zip_derived_cl20, plain, (~ (equalish @ e_3 @ e_1)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 4.42/1.23 thf(product1_idempotence, axiom, (product1 @ X @ X @ X)).
% 4.42/1.23 thf(zip_derived_cl30, plain, (![X0 : $i]: (product1 @ X0 @ X0 @ X0)),
% 4.42/1.23 inference('cnf', [status(esa)], [product1_idempotence])).
% 4.42/1.23 thf(product1_left_cancellation, axiom,
% 4.42/1.23 (( ~( product1 @ W @ Y @ X ) ) | ( ~( product1 @ Z @ Y @ X ) ) |
% 4.42/1.23 ( equalish @ W @ Z ))).
% 4.42/1.23 thf(zip_derived_cl29, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.42/1.23 (~ (product1 @ X0 @ X1 @ X2)
% 4.42/1.23 | ~ (product1 @ X3 @ X1 @ X2)
% 4.42/1.23 | (equalish @ X0 @ X3))),
% 4.42/1.23 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 4.42/1.23 thf(zip_derived_cl41, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 4.42/1.23 thf(zip_derived_cl30, plain, (![X0 : $i]: (product1 @ X0 @ X0 @ X0)),
% 4.42/1.23 inference('cnf', [status(esa)], [product1_idempotence])).
% 4.42/1.23 thf(product1_right_cancellation, axiom,
% 4.42/1.23 (( ~( product1 @ X @ W @ Y ) ) | ( ~( product1 @ X @ Z @ Y ) ) |
% 4.42/1.23 ( equalish @ W @ Z ))).
% 4.42/1.23 thf(zip_derived_cl28, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.42/1.23 (~ (product1 @ X0 @ X1 @ X2)
% 4.42/1.23 | ~ (product1 @ X0 @ X3 @ X2)
% 4.42/1.23 | (equalish @ X1 @ X3))),
% 4.42/1.23 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 4.42/1.23 thf(zip_derived_cl39, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 4.42/1.23 thf(zip_derived_cl41, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 4.42/1.23 thf(zip_derived_cl39, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 4.42/1.23 thf(element_3, axiom, (group_element @ e_3)).
% 4.42/1.23 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 4.42/1.23 inference('cnf', [status(esa)], [element_3])).
% 4.42/1.23 thf(element_1, axiom, (group_element @ e_1)).
% 4.42/1.23 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 4.42/1.23 inference('cnf', [status(esa)], [element_1])).
% 4.42/1.23 thf(product1_total_function1, axiom,
% 4.42/1.23 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 4.42/1.23 ( product1 @ X @ Y @ e_1 ) | ( product1 @ X @ Y @ e_2 ) |
% 4.42/1.23 ( product1 @ X @ Y @ e_3 ) | ( product1 @ X @ Y @ e_4 ))).
% 4.42/1.23 thf(zip_derived_cl26, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 (~ (group_element @ X0)
% 4.42/1.23 | ~ (group_element @ X1)
% 4.42/1.23 | (product1 @ X0 @ X1 @ e_1)
% 4.42/1.23 | (product1 @ X0 @ X1 @ e_2)
% 4.42/1.23 | (product1 @ X0 @ X1 @ e_3)
% 4.42/1.23 | (product1 @ X0 @ X1 @ e_4))),
% 4.42/1.23 inference('cnf', [status(esa)], [product1_total_function1])).
% 4.42/1.23 thf(zip_derived_cl51, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_1 @ X0 @ e_4)
% 4.42/1.23 | (product1 @ e_1 @ X0 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ X0 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ X0 @ e_1)
% 4.42/1.23 | ~ (group_element @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl26])).
% 4.42/1.23 thf(zip_derived_cl94, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_3 @ e_1)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_4))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl51])).
% 4.42/1.23 thf(element_2, axiom, (group_element @ e_2)).
% 4.42/1.23 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 4.42/1.23 inference('cnf', [status(esa)], [element_2])).
% 4.42/1.23 thf(zip_derived_cl51, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_1 @ X0 @ e_4)
% 4.42/1.23 | (product1 @ e_1 @ X0 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ X0 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ X0 @ e_1)
% 4.42/1.23 | ~ (group_element @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl26])).
% 4.42/1.23 thf(zip_derived_cl93, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_2 @ e_1)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_4))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl51])).
% 4.42/1.23 thf(zip_derived_cl28, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.42/1.23 (~ (product1 @ X0 @ X1 @ X2)
% 4.42/1.23 | ~ (product1 @ X0 @ X3 @ X2)
% 4.42/1.23 | (equalish @ X1 @ X3))),
% 4.42/1.23 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 4.42/1.23 thf(zip_derived_cl131, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_1 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_1)
% 4.42/1.23 | (equalish @ e_2 @ X0)
% 4.42/1.23 | ~ (product1 @ e_1 @ X0 @ e_4))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl28])).
% 4.42/1.23 thf(zip_derived_cl145, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_1)
% 4.42/1.23 | (equalish @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_1)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_3))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl94, zip_derived_cl131])).
% 4.42/1.23 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 4.42/1.23 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 4.42/1.23 thf(zip_derived_cl146, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_1)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_1)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl145, zip_derived_cl18])).
% 4.42/1.23 thf(zip_derived_cl1121, plain,
% 4.42/1.23 (( (equalish @ e_1 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_1)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_3))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl146])).
% 4.42/1.23 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 4.42/1.23 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 4.42/1.23 thf(zip_derived_cl1122, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_1)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl1121, zip_derived_cl14])).
% 4.42/1.23 thf(zip_derived_cl1903, plain,
% 4.42/1.23 (( (equalish @ e_2 @ e_1)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_1)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_3))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl1122])).
% 4.42/1.23 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 4.42/1.23 thf(zip_derived_cl17, plain, (~ (equalish @ e_2 @ e_1)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 4.42/1.23 thf(zip_derived_cl1904, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_1)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl1903, zip_derived_cl17])).
% 4.42/1.23 thf(zip_derived_cl1921, plain,
% 4.42/1.23 (( (equalish @ e_1 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_3))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl1904])).
% 4.42/1.23 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 4.42/1.23 thf(zip_derived_cl15, plain, (~ (equalish @ e_1 @ e_3)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 4.42/1.23 thf(zip_derived_cl1922, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl1921, zip_derived_cl15])).
% 4.42/1.23 thf(zip_derived_cl41, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 4.42/1.23 thf(product2_idempotence, axiom, (product2 @ X @ X @ X)).
% 4.42/1.23 thf(zip_derived_cl35, plain, (![X0 : $i]: (product2 @ X0 @ X0 @ X0)),
% 4.42/1.23 inference('cnf', [status(esa)], [product2_idempotence])).
% 4.42/1.23 thf(product2_total_function2, axiom,
% 4.42/1.23 (( ~( product2 @ X @ Y @ W ) ) | ( ~( product2 @ X @ Y @ Z ) ) |
% 4.42/1.23 ( equalish @ W @ Z ))).
% 4.42/1.23 thf(zip_derived_cl32, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.42/1.23 (~ (product2 @ X0 @ X1 @ X2)
% 4.42/1.23 | ~ (product2 @ X0 @ X1 @ X3)
% 4.42/1.23 | (equalish @ X2 @ X3))),
% 4.42/1.23 inference('cnf', [status(esa)], [product2_total_function2])).
% 4.42/1.23 thf(zip_derived_cl43, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product2 @ X0 @ X0 @ X1))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl32])).
% 4.42/1.23 thf(zip_derived_cl39, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 4.42/1.23 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 4.42/1.23 inference('cnf', [status(esa)], [element_2])).
% 4.42/1.23 thf(element_4, axiom, (group_element @ e_4)).
% 4.42/1.23 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 4.42/1.23 inference('cnf', [status(esa)], [element_4])).
% 4.42/1.23 thf(zip_derived_cl26, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 (~ (group_element @ X0)
% 4.42/1.23 | ~ (group_element @ X1)
% 4.42/1.23 | (product1 @ X0 @ X1 @ e_1)
% 4.42/1.23 | (product1 @ X0 @ X1 @ e_2)
% 4.42/1.23 | (product1 @ X0 @ X1 @ e_3)
% 4.42/1.23 | (product1 @ X0 @ X1 @ e_4))),
% 4.42/1.23 inference('cnf', [status(esa)], [product1_total_function1])).
% 4.42/1.23 thf(zip_derived_cl54, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_4 @ X0 @ e_4)
% 4.42/1.23 | (product1 @ e_4 @ X0 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ X0 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ X0 @ e_1)
% 4.42/1.23 | ~ (group_element @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl26])).
% 4.42/1.23 thf(zip_derived_cl108, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_2 @ e_1)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_4))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl54])).
% 4.42/1.23 thf(zip_derived_cl279, plain,
% 4.42/1.23 (( (equalish @ e_4 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_1))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl108])).
% 4.42/1.23 thf(e_4_is_not_e_2, axiom, (~( equalish @ e_4 @ e_2 ))).
% 4.42/1.23 thf(zip_derived_cl24, plain, (~ (equalish @ e_4 @ e_2)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 4.42/1.23 thf(zip_derived_cl280, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_1))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl279, zip_derived_cl24])).
% 4.42/1.23 thf(zip_derived_cl39, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 4.42/1.23 thf(zip_derived_cl41, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 4.42/1.23 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 4.42/1.23 inference('cnf', [status(esa)], [element_4])).
% 4.42/1.23 thf(zip_derived_cl51, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_1 @ X0 @ e_4)
% 4.42/1.23 | (product1 @ e_1 @ X0 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ X0 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ X0 @ e_1)
% 4.42/1.23 | ~ (group_element @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl26])).
% 4.42/1.23 thf(zip_derived_cl95, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_4 @ e_1)
% 4.42/1.23 | (product1 @ e_1 @ e_4 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_4 @ e_4))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl51])).
% 4.42/1.23 thf(zip_derived_cl153, plain,
% 4.42/1.23 (( (equalish @ e_4 @ e_1)
% 4.42/1.23 | (product1 @ e_1 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_4 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_4 @ e_1))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl95])).
% 4.42/1.23 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 4.42/1.23 thf(zip_derived_cl23, plain, (~ (equalish @ e_4 @ e_1)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 4.42/1.23 thf(zip_derived_cl154, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_4 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_4 @ e_1))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl153, zip_derived_cl23])).
% 4.42/1.23 thf(zip_derived_cl165, plain,
% 4.42/1.23 (( (equalish @ e_1 @ e_4)
% 4.42/1.23 | (product1 @ e_1 @ e_4 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_4 @ e_3))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl154])).
% 4.42/1.23 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 4.42/1.23 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 4.42/1.23 thf(zip_derived_cl166, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_4 @ e_2) | (product1 @ e_1 @ e_4 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl165, zip_derived_cl16])).
% 4.42/1.23 thf(qg2a, conjecture,
% 4.42/1.23 (~( ( product2 @ Z2 @ Y @ X ) | ( ~( product1 @ Z1 @ X @ Z2 ) ) |
% 4.42/1.23 ( ~( product1 @ X @ Y @ Z1 ) ) ))).
% 4.42/1.23 thf(zf_stmt_0, negated_conjecture,
% 4.42/1.23 (( product2 @ Z2 @ Y @ X ) | ( ~( product1 @ Z1 @ X @ Z2 ) ) |
% 4.42/1.23 ( ~( product1 @ X @ Y @ Z1 ) )),
% 4.42/1.23 inference('cnf.neg', [status(esa)], [qg2a])).
% 4.42/1.23 thf(zip_derived_cl36, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.42/1.23 ( (product2 @ X0 @ X1 @ X2)
% 4.42/1.23 | ~ (product1 @ X3 @ X2 @ X0)
% 4.42/1.23 | ~ (product1 @ X2 @ X1 @ X3))),
% 4.42/1.23 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.42/1.23 thf(zip_derived_cl171, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_1 @ e_4 @ e_3)
% 4.42/1.23 | ~ (product1 @ e_4 @ X0 @ e_1)
% 4.42/1.23 | (product2 @ e_2 @ X0 @ e_4))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl166, zip_derived_cl36])).
% 4.42/1.23 thf(zip_derived_cl286, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_2 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_3)
% 4.42/1.23 | (product2 @ e_2 @ e_2 @ e_4)
% 4.42/1.23 | (product1 @ e_1 @ e_4 @ e_3))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl280, zip_derived_cl171])).
% 4.42/1.23 thf(zip_derived_cl648, plain,
% 4.42/1.23 (( (equalish @ e_2 @ e_4)
% 4.42/1.23 | (product1 @ e_1 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_2))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl43, zip_derived_cl286])).
% 4.42/1.23 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 4.42/1.23 thf(zip_derived_cl19, plain, (~ (equalish @ e_2 @ e_4)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 4.42/1.23 thf(zip_derived_cl649, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_2))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl648, zip_derived_cl19])).
% 4.42/1.23 thf(zip_derived_cl702, plain,
% 4.42/1.23 (( (equalish @ e_2 @ e_4)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_4 @ e_3))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl649])).
% 4.42/1.23 thf(zip_derived_cl19, plain, (~ (equalish @ e_2 @ e_4)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 4.42/1.23 thf(zip_derived_cl703, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_2 @ e_3) | (product1 @ e_1 @ e_4 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl702, zip_derived_cl19])).
% 4.42/1.23 thf(zip_derived_cl28, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.42/1.23 (~ (product1 @ X0 @ X1 @ X2)
% 4.42/1.23 | ~ (product1 @ X0 @ X3 @ X2)
% 4.42/1.23 | (equalish @ X1 @ X3))),
% 4.42/1.23 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 4.42/1.23 thf(zip_derived_cl709, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_4 @ e_2 @ e_3)
% 4.42/1.23 | (equalish @ e_4 @ X0)
% 4.42/1.23 | ~ (product1 @ e_1 @ X0 @ e_3))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl703, zip_derived_cl28])).
% 4.42/1.23 thf(zip_derived_cl1935, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (equalish @ e_4 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_3))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl1922, zip_derived_cl709])).
% 4.42/1.23 thf(zip_derived_cl24, plain, (~ (equalish @ e_4 @ e_2)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 4.42/1.23 thf(zip_derived_cl1941, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl1935, zip_derived_cl24])).
% 4.42/1.23 thf(zip_derived_cl1922, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl1921, zip_derived_cl15])).
% 4.42/1.23 thf(zip_derived_cl29, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.42/1.23 (~ (product1 @ X0 @ X1 @ X2)
% 4.42/1.23 | ~ (product1 @ X3 @ X1 @ X2)
% 4.42/1.23 | (equalish @ X0 @ X3))),
% 4.42/1.23 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 4.42/1.23 thf(zip_derived_cl1929, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (equalish @ e_1 @ X0)
% 4.42/1.23 | ~ (product1 @ X0 @ e_2 @ e_3))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl1922, zip_derived_cl29])).
% 4.42/1.23 thf(zip_derived_cl2095, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (equalish @ e_1 @ e_4)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_3))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl1941, zip_derived_cl1929])).
% 4.42/1.23 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 4.42/1.23 thf(zip_derived_cl2101, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl2095, zip_derived_cl16])).
% 4.42/1.23 thf(zip_derived_cl2102, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_3 @ e_3) | (product1 @ e_1 @ e_3 @ e_2))),
% 4.42/1.23 inference('simplify', [status(thm)], [zip_derived_cl2101])).
% 4.42/1.23 thf(zip_derived_cl39, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 4.42/1.23 thf(zip_derived_cl41, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 4.42/1.23 thf(zip_derived_cl39, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 4.42/1.23 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 4.42/1.23 inference('cnf', [status(esa)], [element_3])).
% 4.42/1.23 thf(zip_derived_cl54, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_4 @ X0 @ e_4)
% 4.42/1.23 | (product1 @ e_4 @ X0 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ X0 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ X0 @ e_1)
% 4.42/1.23 | ~ (group_element @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl26])).
% 4.42/1.23 thf(zip_derived_cl109, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_3 @ e_1)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_4))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl54])).
% 4.42/1.23 thf(zip_derived_cl346, plain,
% 4.42/1.23 (( (equalish @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_1))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl109])).
% 4.42/1.23 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 4.42/1.23 thf(zip_derived_cl25, plain, (~ (equalish @ e_4 @ e_3)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 4.42/1.23 thf(zip_derived_cl347, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_1))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl346, zip_derived_cl25])).
% 4.42/1.23 thf(zip_derived_cl280, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_1))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl279, zip_derived_cl24])).
% 4.42/1.23 thf(zip_derived_cl28, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.42/1.23 (~ (product1 @ X0 @ X1 @ X2)
% 4.42/1.23 | ~ (product1 @ X0 @ X3 @ X2)
% 4.42/1.23 | (equalish @ X1 @ X3))),
% 4.42/1.23 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 4.42/1.23 thf(zip_derived_cl283, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_4 @ e_2 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_3)
% 4.42/1.23 | (equalish @ e_2 @ X0)
% 4.42/1.23 | ~ (product1 @ e_4 @ X0 @ e_1))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl280, zip_derived_cl28])).
% 4.42/1.23 thf(zip_derived_cl357, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_3)
% 4.42/1.23 | (equalish @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_2))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl347, zip_derived_cl283])).
% 4.42/1.23 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 4.42/1.23 thf(zip_derived_cl358, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_2))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl357, zip_derived_cl18])).
% 4.42/1.23 thf(zip_derived_cl753, plain,
% 4.42/1.23 (( (equalish @ e_2 @ e_4)
% 4.42/1.23 | (product1 @ e_4 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_2))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl358])).
% 4.42/1.23 thf(zip_derived_cl19, plain, (~ (equalish @ e_2 @ e_4)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 4.42/1.23 thf(zip_derived_cl754, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_2 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_2))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl753, zip_derived_cl19])).
% 4.42/1.23 thf(zip_derived_cl43, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product2 @ X0 @ X0 @ X1))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl32])).
% 4.42/1.23 thf(zip_derived_cl41, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 4.42/1.23 thf(zip_derived_cl39, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 4.42/1.23 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 4.42/1.23 inference('cnf', [status(esa)], [element_1])).
% 4.42/1.23 thf(zip_derived_cl54, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_4 @ X0 @ e_4)
% 4.42/1.23 | (product1 @ e_4 @ X0 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ X0 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ X0 @ e_1)
% 4.42/1.23 | ~ (group_element @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl26])).
% 4.42/1.23 thf(zip_derived_cl107, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_1 @ e_1)
% 4.42/1.23 | (product1 @ e_4 @ e_1 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_1 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_1 @ e_4))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl54])).
% 4.42/1.23 thf(zip_derived_cl253, plain,
% 4.42/1.23 (( (equalish @ e_4 @ e_1)
% 4.42/1.23 | (product1 @ e_4 @ e_1 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_1 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_1 @ e_1))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl107])).
% 4.42/1.23 thf(zip_derived_cl23, plain, (~ (equalish @ e_4 @ e_1)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 4.42/1.23 thf(zip_derived_cl254, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_1 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_1 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_1 @ e_1))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl253, zip_derived_cl23])).
% 4.42/1.23 thf(zip_derived_cl262, plain,
% 4.42/1.23 (( (equalish @ e_1 @ e_4)
% 4.42/1.23 | (product1 @ e_4 @ e_1 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_1 @ e_3))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl254])).
% 4.42/1.23 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 4.42/1.23 thf(zip_derived_cl263, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_1 @ e_2) | (product1 @ e_4 @ e_1 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl262, zip_derived_cl16])).
% 4.42/1.23 thf(zip_derived_cl41, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 4.42/1.23 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 4.42/1.23 inference('cnf', [status(esa)], [element_4])).
% 4.42/1.23 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 4.42/1.23 inference('cnf', [status(esa)], [element_2])).
% 4.42/1.23 thf(zip_derived_cl26, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 (~ (group_element @ X0)
% 4.42/1.23 | ~ (group_element @ X1)
% 4.42/1.23 | (product1 @ X0 @ X1 @ e_1)
% 4.42/1.23 | (product1 @ X0 @ X1 @ e_2)
% 4.42/1.23 | (product1 @ X0 @ X1 @ e_3)
% 4.42/1.23 | (product1 @ X0 @ X1 @ e_4))),
% 4.42/1.23 inference('cnf', [status(esa)], [product1_total_function1])).
% 4.42/1.23 thf(zip_derived_cl52, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_2 @ X0 @ e_4)
% 4.42/1.23 | (product1 @ e_2 @ X0 @ e_3)
% 4.42/1.23 | (product1 @ e_2 @ X0 @ e_2)
% 4.42/1.23 | (product1 @ e_2 @ X0 @ e_1)
% 4.42/1.23 | ~ (group_element @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl26])).
% 4.42/1.23 thf(zip_derived_cl100, plain,
% 4.42/1.23 (( (product1 @ e_2 @ e_4 @ e_1)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_2)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_4))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl52])).
% 4.42/1.23 thf(zip_derived_cl186, plain,
% 4.42/1.23 (( (equalish @ e_4 @ e_2)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_2)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_1))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl100])).
% 4.42/1.23 thf(zip_derived_cl24, plain, (~ (equalish @ e_4 @ e_2)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 4.42/1.23 thf(zip_derived_cl187, plain,
% 4.42/1.23 (( (product1 @ e_2 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_2)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_1))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl186, zip_derived_cl24])).
% 4.42/1.23 thf(zip_derived_cl36, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.42/1.23 ( (product2 @ X0 @ X1 @ X2)
% 4.42/1.23 | ~ (product1 @ X3 @ X2 @ X0)
% 4.42/1.23 | ~ (product1 @ X2 @ X1 @ X3))),
% 4.42/1.23 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.42/1.23 thf(zip_derived_cl192, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_2 @ e_4 @ e_2)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_3)
% 4.42/1.23 | ~ (product1 @ e_4 @ X0 @ e_2)
% 4.42/1.23 | (product2 @ e_1 @ X0 @ e_4))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl187, zip_derived_cl36])).
% 4.42/1.23 thf(zip_derived_cl269, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_1 @ e_3)
% 4.42/1.23 | (product2 @ e_1 @ e_1 @ e_4)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_2))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl263, zip_derived_cl192])).
% 4.42/1.23 thf(zip_derived_cl500, plain,
% 4.42/1.23 (( (equalish @ e_1 @ e_4)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_2)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_1 @ e_3))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl43, zip_derived_cl269])).
% 4.42/1.23 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 4.42/1.23 thf(zip_derived_cl501, plain,
% 4.42/1.23 (( (product1 @ e_2 @ e_4 @ e_2)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_1 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl500, zip_derived_cl16])).
% 4.42/1.23 thf(zip_derived_cl28, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.42/1.23 (~ (product1 @ X0 @ X1 @ X2)
% 4.42/1.23 | ~ (product1 @ X0 @ X3 @ X2)
% 4.42/1.23 | (equalish @ X1 @ X3))),
% 4.42/1.23 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 4.42/1.23 thf(zip_derived_cl504, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_2 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_2)
% 4.42/1.23 | (equalish @ e_1 @ X0)
% 4.42/1.23 | ~ (product1 @ e_4 @ X0 @ e_3))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl501, zip_derived_cl28])).
% 4.42/1.23 thf(zip_derived_cl764, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_3)
% 4.42/1.23 | (equalish @ e_1 @ e_2)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_2)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_3))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl754, zip_derived_cl504])).
% 4.42/1.23 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 4.42/1.23 thf(zip_derived_cl766, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_3 @ e_2)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_2)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl764, zip_derived_cl14])).
% 4.42/1.23 thf(zip_derived_cl1019, plain,
% 4.42/1.23 (( (equalish @ e_2 @ e_4)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_2))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl766])).
% 4.42/1.23 thf(zip_derived_cl19, plain, (~ (equalish @ e_2 @ e_4)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 4.42/1.23 thf(zip_derived_cl1023, plain,
% 4.42/1.23 (( (product1 @ e_2 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_2))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl1019, zip_derived_cl19])).
% 4.42/1.23 thf(zip_derived_cl29, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.42/1.23 (~ (product1 @ X0 @ X1 @ X2)
% 4.42/1.23 | ~ (product1 @ X3 @ X1 @ X2)
% 4.42/1.23 | (equalish @ X0 @ X3))),
% 4.42/1.23 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 4.42/1.23 thf(zip_derived_cl1031, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_4 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_3)
% 4.42/1.23 | (equalish @ e_4 @ X0)
% 4.42/1.23 | ~ (product1 @ X0 @ e_3 @ e_2))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl1023, zip_derived_cl29])).
% 4.42/1.23 thf(zip_derived_cl2143, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (equalish @ e_4 @ e_1)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_3))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl2102, zip_derived_cl1031])).
% 4.42/1.23 thf(zip_derived_cl23, plain, (~ (equalish @ e_4 @ e_1)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 4.42/1.23 thf(zip_derived_cl2146, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_2 @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_4 @ e_3 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl2143, zip_derived_cl23])).
% 4.42/1.23 thf(zip_derived_cl2102, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_3 @ e_3) | (product1 @ e_1 @ e_3 @ e_2))),
% 4.42/1.23 inference('simplify', [status(thm)], [zip_derived_cl2101])).
% 4.42/1.23 thf(zip_derived_cl166, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_4 @ e_2) | (product1 @ e_1 @ e_4 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl165, zip_derived_cl16])).
% 4.42/1.23 thf(zip_derived_cl28, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.42/1.23 (~ (product1 @ X0 @ X1 @ X2)
% 4.42/1.23 | ~ (product1 @ X0 @ X3 @ X2)
% 4.42/1.23 | (equalish @ X1 @ X3))),
% 4.42/1.23 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 4.42/1.23 thf(zip_derived_cl169, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_1 @ e_4 @ e_3)
% 4.42/1.23 | (equalish @ e_4 @ X0)
% 4.42/1.23 | ~ (product1 @ e_1 @ X0 @ e_2))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl166, zip_derived_cl28])).
% 4.42/1.23 thf(zip_derived_cl2144, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (equalish @ e_4 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_4 @ e_3))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl2102, zip_derived_cl169])).
% 4.42/1.23 thf(zip_derived_cl25, plain, (~ (equalish @ e_4 @ e_3)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 4.42/1.23 thf(zip_derived_cl2147, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_3 @ e_3) | (product1 @ e_1 @ e_4 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl2144, zip_derived_cl25])).
% 4.42/1.23 thf(zip_derived_cl29, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.42/1.23 (~ (product1 @ X0 @ X1 @ X2)
% 4.42/1.23 | ~ (product1 @ X3 @ X1 @ X2)
% 4.42/1.23 | (equalish @ X0 @ X3))),
% 4.42/1.23 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 4.42/1.23 thf(zip_derived_cl2165, plain,
% 4.42/1.23 (![X0 : $i]:
% 4.42/1.23 ( (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (equalish @ e_1 @ X0)
% 4.42/1.23 | ~ (product1 @ X0 @ e_4 @ e_3))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl2147, zip_derived_cl29])).
% 4.42/1.23 thf(zip_derived_cl2321, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (equalish @ e_1 @ e_2)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_3))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl2146, zip_derived_cl2165])).
% 4.42/1.23 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 4.42/1.23 thf(zip_derived_cl2328, plain,
% 4.42/1.23 (( (product1 @ e_4 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_3)
% 4.42/1.23 | (product1 @ e_1 @ e_3 @ e_3))),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl2321, zip_derived_cl14])).
% 4.42/1.23 thf(zip_derived_cl2329, plain,
% 4.42/1.23 (( (product1 @ e_1 @ e_3 @ e_3) | (product1 @ e_4 @ e_3 @ e_3))),
% 4.42/1.23 inference('simplify', [status(thm)], [zip_derived_cl2328])).
% 4.42/1.23 thf(zip_derived_cl2347, plain,
% 4.42/1.23 (( (equalish @ e_3 @ e_4) | (product1 @ e_1 @ e_3 @ e_3))),
% 4.42/1.23 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl2329])).
% 4.42/1.23 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 4.42/1.23 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 4.42/1.23 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 4.42/1.23 thf(zip_derived_cl2348, plain, ( (product1 @ e_1 @ e_3 @ e_3)),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl2347, zip_derived_cl22])).
% 4.42/1.23 thf(zip_derived_cl41, plain,
% 4.42/1.23 (![X0 : $i, X1 : $i]:
% 4.42/1.23 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 4.42/1.23 thf(zip_derived_cl2362, plain, ( (equalish @ e_3 @ e_1)),
% 4.42/1.23 inference('sup-', [status(thm)], [zip_derived_cl2348, zip_derived_cl41])).
% 4.42/1.23 thf(zip_derived_cl2391, plain, ($false),
% 4.42/1.23 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl2362])).
% 4.42/1.23
% 4.42/1.23 % SZS output end Refutation
% 4.42/1.23
% 4.42/1.23
% 4.42/1.23 % Terminating...
% 4.49/1.28 % Runner terminated.
% 4.49/1.29 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------