TSTP Solution File: GRP127-4.004 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP127-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.mvQkRYtdUy 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 Aug 31 01:50:11 EDT 2023
% Result : Unsatisfiable 1.35s 1.14s
% Output : Refutation 1.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP127-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.mvQkRYtdUy true
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 02:11:43 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.35 % Python version: Python 3.6.8
% 0.12/0.35 % Running in FO mode
% 0.20/0.65 % Total configuration time : 435
% 0.20/0.65 % Estimated wc time : 1092
% 0.20/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.58/0.74 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.58/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 1.32/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 1.32/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.32/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.32/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.32/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.35/1.14 % Solved by fo/fo7.sh.
% 1.35/1.14 % done 281 iterations in 0.365s
% 1.35/1.14 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.35/1.14 % SZS output start Refutation
% 1.35/1.14 thf(e_1_type, type, e_1: $i).
% 1.35/1.14 thf(product_type, type, product: $i > $i > $i > $o).
% 1.35/1.14 thf(e_2_type, type, e_2: $i).
% 1.35/1.14 thf(group_element_type, type, group_element: $i > $o).
% 1.35/1.14 thf(e_4_type, type, e_4: $i).
% 1.35/1.14 thf(equalish_type, type, equalish: $i > $i > $o).
% 1.35/1.14 thf(e_3_type, type, e_3: $i).
% 1.35/1.14 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 1.35/1.14 thf(zip_derived_cl10, plain, (~ (equalish @ e_1 @ e_4)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 1.35/1.14 thf(row_surjectivity, axiom,
% 1.35/1.14 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 1.35/1.14 ( product @ e_1 @ X @ Y ) | ( product @ e_2 @ X @ Y ) |
% 1.35/1.14 ( product @ e_3 @ X @ Y ) | ( product @ e_4 @ X @ Y ))).
% 1.35/1.14 thf(zip_derived_cl0, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i]:
% 1.35/1.14 (~ (group_element @ X0)
% 1.35/1.14 | ~ (group_element @ X1)
% 1.35/1.14 | (product @ e_1 @ X0 @ X1)
% 1.35/1.14 | (product @ e_2 @ X0 @ X1)
% 1.35/1.14 | (product @ e_3 @ X0 @ X1)
% 1.35/1.14 | (product @ e_4 @ X0 @ X1))),
% 1.35/1.14 inference('cnf', [status(esa)], [row_surjectivity])).
% 1.35/1.14 thf(product_idempotence, axiom, (product @ X @ X @ X)).
% 1.35/1.14 thf(zip_derived_cl24, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 1.35/1.14 inference('cnf', [status(esa)], [product_idempotence])).
% 1.35/1.14 thf(product_total_function2, axiom,
% 1.35/1.14 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 1.35/1.14 ( equalish @ W @ Z ))).
% 1.35/1.14 thf(zip_derived_cl21, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.35/1.14 (~ (product @ X0 @ X1 @ X2)
% 1.35/1.14 | ~ (product @ X0 @ X1 @ X3)
% 1.35/1.14 | (equalish @ X2 @ X3))),
% 1.35/1.14 inference('cnf', [status(esa)], [product_total_function2])).
% 1.35/1.14 thf(zip_derived_cl26, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i]:
% 1.35/1.14 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X0 @ X1))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl21])).
% 1.35/1.14 thf(zip_derived_cl36, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_3 @ e_4 @ X0)
% 1.35/1.14 | (product @ e_2 @ e_4 @ X0)
% 1.35/1.14 | (product @ e_1 @ e_4 @ X0)
% 1.35/1.14 | ~ (group_element @ X0)
% 1.35/1.14 | ~ (group_element @ e_4)
% 1.35/1.14 | (equalish @ e_4 @ X0))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl26])).
% 1.35/1.14 thf(element_4, axiom, (group_element @ e_4)).
% 1.35/1.14 thf(zip_derived_cl7, plain, ( (group_element @ e_4)),
% 1.35/1.14 inference('cnf', [status(esa)], [element_4])).
% 1.35/1.14 thf(zip_derived_cl38, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_3 @ e_4 @ X0)
% 1.35/1.14 | (product @ e_2 @ e_4 @ X0)
% 1.35/1.14 | (product @ e_1 @ e_4 @ X0)
% 1.35/1.14 | ~ (group_element @ X0)
% 1.35/1.14 | (equalish @ e_4 @ X0))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl7])).
% 1.35/1.14 thf(zip_derived_cl0, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i]:
% 1.35/1.14 (~ (group_element @ X0)
% 1.35/1.14 | ~ (group_element @ X1)
% 1.35/1.14 | (product @ e_1 @ X0 @ X1)
% 1.35/1.14 | (product @ e_2 @ X0 @ X1)
% 1.35/1.14 | (product @ e_3 @ X0 @ X1)
% 1.35/1.14 | (product @ e_4 @ X0 @ X1))),
% 1.35/1.14 inference('cnf', [status(esa)], [row_surjectivity])).
% 1.35/1.14 thf(zip_derived_cl24, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 1.35/1.14 inference('cnf', [status(esa)], [product_idempotence])).
% 1.35/1.14 thf(product_right_cancellation, axiom,
% 1.35/1.14 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 1.35/1.14 ( equalish @ W @ Z ))).
% 1.35/1.14 thf(zip_derived_cl22, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.35/1.14 (~ (product @ X0 @ X1 @ X2)
% 1.35/1.14 | ~ (product @ X0 @ X3 @ X2)
% 1.35/1.14 | (equalish @ X1 @ X3))),
% 1.35/1.14 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.35/1.14 thf(zip_derived_cl30, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i]:
% 1.35/1.14 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 1.35/1.14 thf(zip_derived_cl37, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_3 @ X0 @ e_4)
% 1.35/1.14 | (product @ e_2 @ X0 @ e_4)
% 1.35/1.14 | (product @ e_1 @ X0 @ e_4)
% 1.35/1.14 | ~ (group_element @ e_4)
% 1.35/1.14 | ~ (group_element @ X0)
% 1.35/1.14 | (equalish @ e_4 @ X0))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl30])).
% 1.35/1.14 thf(zip_derived_cl7, plain, ( (group_element @ e_4)),
% 1.35/1.14 inference('cnf', [status(esa)], [element_4])).
% 1.35/1.14 thf(zip_derived_cl39, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_3 @ X0 @ e_4)
% 1.35/1.14 | (product @ e_2 @ X0 @ e_4)
% 1.35/1.14 | (product @ e_1 @ X0 @ e_4)
% 1.35/1.14 | ~ (group_element @ X0)
% 1.35/1.14 | (equalish @ e_4 @ X0))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl7])).
% 1.35/1.14 thf(zip_derived_cl38, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_3 @ e_4 @ X0)
% 1.35/1.14 | (product @ e_2 @ e_4 @ X0)
% 1.35/1.14 | (product @ e_1 @ e_4 @ X0)
% 1.35/1.14 | ~ (group_element @ X0)
% 1.35/1.14 | (equalish @ e_4 @ X0))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl7])).
% 1.35/1.14 thf(zip_derived_cl39, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_3 @ X0 @ e_4)
% 1.35/1.14 | (product @ e_2 @ X0 @ e_4)
% 1.35/1.14 | (product @ e_1 @ X0 @ e_4)
% 1.35/1.14 | ~ (group_element @ X0)
% 1.35/1.14 | (equalish @ e_4 @ X0))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl7])).
% 1.35/1.14 thf(zip_derived_cl38, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_3 @ e_4 @ X0)
% 1.35/1.14 | (product @ e_2 @ e_4 @ X0)
% 1.35/1.14 | (product @ e_1 @ e_4 @ X0)
% 1.35/1.14 | ~ (group_element @ X0)
% 1.35/1.14 | (equalish @ e_4 @ X0))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl7])).
% 1.35/1.14 thf(zip_derived_cl39, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_3 @ X0 @ e_4)
% 1.35/1.14 | (product @ e_2 @ X0 @ e_4)
% 1.35/1.14 | (product @ e_1 @ X0 @ e_4)
% 1.35/1.14 | ~ (group_element @ X0)
% 1.35/1.14 | (equalish @ e_4 @ X0))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl7])).
% 1.35/1.14 thf(zip_derived_cl26, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i]:
% 1.35/1.14 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X0 @ X1))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl21])).
% 1.35/1.14 thf(zip_derived_cl48, plain,
% 1.35/1.14 (( (equalish @ e_4 @ e_3)
% 1.35/1.14 | ~ (group_element @ e_3)
% 1.35/1.14 | (product @ e_1 @ e_3 @ e_4)
% 1.35/1.14 | (product @ e_2 @ e_3 @ e_4)
% 1.35/1.14 | (equalish @ e_3 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl26])).
% 1.35/1.14 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 1.35/1.14 thf(zip_derived_cl19, plain, (~ (equalish @ e_4 @ e_3)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 1.35/1.14 thf(element_3, axiom, (group_element @ e_3)).
% 1.35/1.14 thf(zip_derived_cl6, plain, ( (group_element @ e_3)),
% 1.35/1.14 inference('cnf', [status(esa)], [element_3])).
% 1.35/1.14 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 1.35/1.14 thf(zip_derived_cl16, plain, (~ (equalish @ e_3 @ e_4)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 1.35/1.14 thf(zip_derived_cl49, plain,
% 1.35/1.14 (( (product @ e_1 @ e_3 @ e_4) | (product @ e_2 @ e_3 @ e_4))),
% 1.35/1.14 inference('demod', [status(thm)],
% 1.35/1.14 [zip_derived_cl48, zip_derived_cl19, zip_derived_cl6,
% 1.35/1.14 zip_derived_cl16])).
% 1.35/1.14 thf(qg3, conjecture,
% 1.35/1.14 (~( ( product @ Z2 @ Y @ X ) | ( ~( product @ Z1 @ Y @ Z2 ) ) |
% 1.35/1.14 ( ~( product @ Y @ X @ Z1 ) ) ))).
% 1.35/1.14 thf(zf_stmt_0, negated_conjecture,
% 1.35/1.14 (( product @ Z2 @ Y @ X ) | ( ~( product @ Z1 @ Y @ Z2 ) ) |
% 1.35/1.14 ( ~( product @ Y @ X @ Z1 ) )),
% 1.35/1.14 inference('cnf.neg', [status(esa)], [qg3])).
% 1.35/1.14 thf(zip_derived_cl25, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.35/1.14 ( (product @ X0 @ X1 @ X2)
% 1.35/1.14 | ~ (product @ X3 @ X1 @ X0)
% 1.35/1.14 | ~ (product @ X1 @ X2 @ X3))),
% 1.35/1.14 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.35/1.14 thf(zip_derived_cl151, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_1 @ e_3 @ e_4)
% 1.35/1.14 | ~ (product @ e_3 @ X0 @ e_2)
% 1.35/1.14 | (product @ e_4 @ e_3 @ X0))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl25])).
% 1.35/1.14 thf(zip_derived_cl30, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i]:
% 1.35/1.14 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 1.35/1.14 thf(zip_derived_cl196, plain,
% 1.35/1.14 ((~ (product @ e_3 @ e_4 @ e_2)
% 1.35/1.14 | (product @ e_1 @ e_3 @ e_4)
% 1.35/1.14 | (equalish @ e_4 @ e_3))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl30])).
% 1.35/1.14 thf(zip_derived_cl19, plain, (~ (equalish @ e_4 @ e_3)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 1.35/1.14 thf(zip_derived_cl204, plain,
% 1.35/1.14 ((~ (product @ e_3 @ e_4 @ e_2) | (product @ e_1 @ e_3 @ e_4))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl196, zip_derived_cl19])).
% 1.35/1.14 thf(zip_derived_cl209, plain,
% 1.35/1.14 (( (equalish @ e_4 @ e_2)
% 1.35/1.14 | ~ (group_element @ e_2)
% 1.35/1.14 | (product @ e_1 @ e_4 @ e_2)
% 1.35/1.14 | (product @ e_2 @ e_4 @ e_2)
% 1.35/1.14 | (product @ e_1 @ e_3 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl204])).
% 1.35/1.14 thf(e_4_is_not_e_2, axiom, (~( equalish @ e_4 @ e_2 ))).
% 1.35/1.14 thf(zip_derived_cl18, plain, (~ (equalish @ e_4 @ e_2)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 1.35/1.14 thf(element_2, axiom, (group_element @ e_2)).
% 1.35/1.14 thf(zip_derived_cl5, plain, ( (group_element @ e_2)),
% 1.35/1.14 inference('cnf', [status(esa)], [element_2])).
% 1.35/1.14 thf(zip_derived_cl210, plain,
% 1.35/1.14 (( (product @ e_1 @ e_4 @ e_2)
% 1.35/1.14 | (product @ e_2 @ e_4 @ e_2)
% 1.35/1.14 | (product @ e_1 @ e_3 @ e_4))),
% 1.35/1.14 inference('demod', [status(thm)],
% 1.35/1.14 [zip_derived_cl209, zip_derived_cl18, zip_derived_cl5])).
% 1.35/1.14 thf(zip_derived_cl30, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i]:
% 1.35/1.14 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 1.35/1.14 thf(zip_derived_cl239, plain,
% 1.35/1.14 (( (product @ e_1 @ e_3 @ e_4)
% 1.35/1.14 | (product @ e_1 @ e_4 @ e_2)
% 1.35/1.14 | (equalish @ e_2 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl210, zip_derived_cl30])).
% 1.35/1.14 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 1.35/1.14 thf(zip_derived_cl13, plain, (~ (equalish @ e_2 @ e_4)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 1.35/1.14 thf(zip_derived_cl243, plain,
% 1.35/1.14 (( (product @ e_1 @ e_3 @ e_4) | (product @ e_1 @ e_4 @ e_2))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl239, zip_derived_cl13])).
% 1.35/1.14 thf(qg3_2, conjecture,
% 1.35/1.14 (~( ( ~( product @ Y @ X @ Z1 ) ) | ( ~( product @ Z2 @ Y @ X ) ) |
% 1.35/1.14 ( product @ Z1 @ Y @ Z2 ) ))).
% 1.35/1.14 thf(zf_stmt_1, negated_conjecture,
% 1.35/1.14 (( ~( product @ Y @ X @ Z1 ) ) | ( ~( product @ Z2 @ Y @ X ) ) |
% 1.35/1.14 ( product @ Z1 @ Y @ Z2 )),
% 1.35/1.14 inference('cnf.neg', [status(esa)], [qg3_2])).
% 1.35/1.14 thf(zip_derived_cl3, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.35/1.14 (~ (product @ X0 @ X1 @ X2)
% 1.35/1.14 | ~ (product @ X3 @ X0 @ X1)
% 1.35/1.14 | (product @ X2 @ X0 @ X3))),
% 1.35/1.14 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.35/1.14 thf(zip_derived_cl246, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_1 @ e_3 @ e_4)
% 1.35/1.14 | (product @ e_2 @ e_1 @ X0)
% 1.35/1.14 | ~ (product @ X0 @ e_1 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl243, zip_derived_cl3])).
% 1.35/1.14 thf(zip_derived_cl297, plain,
% 1.35/1.14 (( (equalish @ e_4 @ e_1)
% 1.35/1.14 | ~ (group_element @ e_1)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_2 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_2 @ e_1 @ e_3)
% 1.35/1.14 | (product @ e_1 @ e_3 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl246])).
% 1.35/1.14 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 1.35/1.14 thf(zip_derived_cl17, plain, (~ (equalish @ e_4 @ e_1)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 1.35/1.14 thf(element_1, axiom, (group_element @ e_1)).
% 1.35/1.14 thf(zip_derived_cl4, plain, ( (group_element @ e_1)),
% 1.35/1.14 inference('cnf', [status(esa)], [element_1])).
% 1.35/1.14 thf(zip_derived_cl299, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_2 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_2 @ e_1 @ e_3)
% 1.35/1.14 | (product @ e_1 @ e_3 @ e_4))),
% 1.35/1.14 inference('demod', [status(thm)],
% 1.35/1.14 [zip_derived_cl297, zip_derived_cl17, zip_derived_cl4])).
% 1.35/1.14 thf(zip_derived_cl49, plain,
% 1.35/1.14 (( (product @ e_1 @ e_3 @ e_4) | (product @ e_2 @ e_3 @ e_4))),
% 1.35/1.14 inference('demod', [status(thm)],
% 1.35/1.14 [zip_derived_cl48, zip_derived_cl19, zip_derived_cl6,
% 1.35/1.14 zip_derived_cl16])).
% 1.35/1.14 thf(zip_derived_cl22, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.35/1.14 (~ (product @ X0 @ X1 @ X2)
% 1.35/1.14 | ~ (product @ X0 @ X3 @ X2)
% 1.35/1.14 | (equalish @ X1 @ X3))),
% 1.35/1.14 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.35/1.14 thf(zip_derived_cl51, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_1 @ e_3 @ e_4)
% 1.35/1.14 | (equalish @ e_3 @ X0)
% 1.35/1.14 | ~ (product @ e_2 @ X0 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl22])).
% 1.35/1.14 thf(zip_derived_cl712, plain,
% 1.35/1.14 (( (product @ e_1 @ e_3 @ e_4)
% 1.35/1.14 | (product @ e_2 @ e_1 @ e_3)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (equalish @ e_3 @ e_1)
% 1.35/1.14 | (product @ e_1 @ e_3 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl299, zip_derived_cl51])).
% 1.35/1.14 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 1.35/1.14 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_1)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 1.35/1.14 thf(zip_derived_cl714, plain,
% 1.35/1.14 (( (product @ e_1 @ e_3 @ e_4)
% 1.35/1.14 | (product @ e_2 @ e_1 @ e_3)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_1 @ e_3 @ e_4))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl712, zip_derived_cl14])).
% 1.35/1.14 thf(zip_derived_cl715, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_2 @ e_1 @ e_3)
% 1.35/1.14 | (product @ e_1 @ e_3 @ e_4))),
% 1.35/1.14 inference('simplify', [status(thm)], [zip_derived_cl714])).
% 1.35/1.14 thf(zip_derived_cl38, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_3 @ e_4 @ X0)
% 1.35/1.14 | (product @ e_2 @ e_4 @ X0)
% 1.35/1.14 | (product @ e_1 @ e_4 @ X0)
% 1.35/1.14 | ~ (group_element @ X0)
% 1.35/1.14 | (equalish @ e_4 @ X0))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl7])).
% 1.35/1.14 thf(zip_derived_cl30, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i]:
% 1.35/1.14 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 1.35/1.14 thf(zip_derived_cl42, plain,
% 1.35/1.14 (( (equalish @ e_4 @ e_3)
% 1.35/1.14 | ~ (group_element @ e_3)
% 1.35/1.14 | (product @ e_1 @ e_4 @ e_3)
% 1.35/1.14 | (product @ e_2 @ e_4 @ e_3)
% 1.35/1.14 | (equalish @ e_3 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl30])).
% 1.35/1.14 thf(zip_derived_cl19, plain, (~ (equalish @ e_4 @ e_3)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 1.35/1.14 thf(zip_derived_cl6, plain, ( (group_element @ e_3)),
% 1.35/1.14 inference('cnf', [status(esa)], [element_3])).
% 1.35/1.14 thf(zip_derived_cl16, plain, (~ (equalish @ e_3 @ e_4)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 1.35/1.14 thf(zip_derived_cl43, plain,
% 1.35/1.14 (( (product @ e_1 @ e_4 @ e_3) | (product @ e_2 @ e_4 @ e_3))),
% 1.35/1.14 inference('demod', [status(thm)],
% 1.35/1.14 [zip_derived_cl42, zip_derived_cl19, zip_derived_cl6,
% 1.35/1.14 zip_derived_cl16])).
% 1.35/1.14 thf(zip_derived_cl22, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.35/1.14 (~ (product @ X0 @ X1 @ X2)
% 1.35/1.14 | ~ (product @ X0 @ X3 @ X2)
% 1.35/1.14 | (equalish @ X1 @ X3))),
% 1.35/1.14 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.35/1.14 thf(zip_derived_cl45, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_1 @ e_4 @ e_3)
% 1.35/1.14 | (equalish @ e_4 @ X0)
% 1.35/1.14 | ~ (product @ e_2 @ X0 @ e_3))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl22])).
% 1.35/1.14 thf(zip_derived_cl723, plain,
% 1.35/1.14 (( (product @ e_1 @ e_3 @ e_4)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (equalish @ e_4 @ e_1)
% 1.35/1.14 | (product @ e_1 @ e_4 @ e_3))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl715, zip_derived_cl45])).
% 1.35/1.14 thf(zip_derived_cl17, plain, (~ (equalish @ e_4 @ e_1)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 1.35/1.14 thf(zip_derived_cl724, plain,
% 1.35/1.14 (( (product @ e_1 @ e_3 @ e_4)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_1 @ e_4 @ e_3))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl723, zip_derived_cl17])).
% 1.35/1.14 thf(zip_derived_cl243, plain,
% 1.35/1.14 (( (product @ e_1 @ e_3 @ e_4) | (product @ e_1 @ e_4 @ e_2))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl239, zip_derived_cl13])).
% 1.35/1.14 thf(zip_derived_cl21, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.35/1.14 (~ (product @ X0 @ X1 @ X2)
% 1.35/1.14 | ~ (product @ X0 @ X1 @ X3)
% 1.35/1.14 | (equalish @ X2 @ X3))),
% 1.35/1.14 inference('cnf', [status(esa)], [product_total_function2])).
% 1.35/1.14 thf(zip_derived_cl247, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_1 @ e_3 @ e_4)
% 1.35/1.14 | (equalish @ e_2 @ X0)
% 1.35/1.14 | ~ (product @ e_1 @ e_4 @ X0))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl243, zip_derived_cl21])).
% 1.35/1.14 thf(zip_derived_cl737, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_1 @ e_3 @ e_4)
% 1.35/1.14 | (equalish @ e_2 @ e_3)
% 1.35/1.14 | (product @ e_1 @ e_3 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl724, zip_derived_cl247])).
% 1.35/1.14 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 1.35/1.14 thf(zip_derived_cl12, plain, (~ (equalish @ e_2 @ e_3)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 1.35/1.14 thf(zip_derived_cl745, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_1 @ e_3 @ e_4)
% 1.35/1.14 | (product @ e_1 @ e_3 @ e_4))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl737, zip_derived_cl12])).
% 1.35/1.14 thf(zip_derived_cl746, plain,
% 1.35/1.14 (( (product @ e_1 @ e_3 @ e_4) | (product @ e_1 @ e_1 @ e_4))),
% 1.35/1.14 inference('simplify', [status(thm)], [zip_derived_cl745])).
% 1.35/1.14 thf(zip_derived_cl25, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.35/1.14 ( (product @ X0 @ X1 @ X2)
% 1.35/1.14 | ~ (product @ X3 @ X1 @ X0)
% 1.35/1.14 | ~ (product @ X1 @ X2 @ X3))),
% 1.35/1.14 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.35/1.14 thf(zip_derived_cl753, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | ~ (product @ e_3 @ X0 @ e_1)
% 1.35/1.14 | (product @ e_4 @ e_3 @ X0))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl746, zip_derived_cl25])).
% 1.35/1.14 thf(zip_derived_cl30, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i]:
% 1.35/1.14 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 1.35/1.14 thf(zip_derived_cl815, plain,
% 1.35/1.14 ((~ (product @ e_3 @ e_4 @ e_1)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (equalish @ e_4 @ e_3))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl753, zip_derived_cl30])).
% 1.35/1.14 thf(zip_derived_cl19, plain, (~ (equalish @ e_4 @ e_3)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 1.35/1.14 thf(zip_derived_cl830, plain,
% 1.35/1.14 ((~ (product @ e_3 @ e_4 @ e_1) | (product @ e_1 @ e_1 @ e_4))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl815, zip_derived_cl19])).
% 1.35/1.14 thf(zip_derived_cl837, plain,
% 1.35/1.14 (( (equalish @ e_4 @ e_1)
% 1.35/1.14 | ~ (group_element @ e_1)
% 1.35/1.14 | (product @ e_1 @ e_4 @ e_1)
% 1.35/1.14 | (product @ e_2 @ e_4 @ e_1)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl830])).
% 1.35/1.14 thf(zip_derived_cl17, plain, (~ (equalish @ e_4 @ e_1)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 1.35/1.14 thf(zip_derived_cl4, plain, ( (group_element @ e_1)),
% 1.35/1.14 inference('cnf', [status(esa)], [element_1])).
% 1.35/1.14 thf(zip_derived_cl838, plain,
% 1.35/1.14 (( (product @ e_1 @ e_4 @ e_1)
% 1.35/1.14 | (product @ e_2 @ e_4 @ e_1)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4))),
% 1.35/1.14 inference('demod', [status(thm)],
% 1.35/1.14 [zip_derived_cl837, zip_derived_cl17, zip_derived_cl4])).
% 1.35/1.14 thf(zip_derived_cl24, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 1.35/1.14 inference('cnf', [status(esa)], [product_idempotence])).
% 1.35/1.14 thf(zip_derived_cl25, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.35/1.14 ( (product @ X0 @ X1 @ X2)
% 1.35/1.14 | ~ (product @ X3 @ X1 @ X0)
% 1.35/1.14 | ~ (product @ X1 @ X2 @ X3))),
% 1.35/1.14 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.35/1.14 thf(zip_derived_cl150, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i]:
% 1.35/1.14 (~ (product @ X0 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl25])).
% 1.35/1.14 thf(zip_derived_cl842, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4) | (product @ e_2 @ e_4 @ e_1))),
% 1.35/1.14 inference('clc', [status(thm)], [zip_derived_cl838, zip_derived_cl150])).
% 1.35/1.14 thf(zip_derived_cl43, plain,
% 1.35/1.14 (( (product @ e_1 @ e_4 @ e_3) | (product @ e_2 @ e_4 @ e_3))),
% 1.35/1.14 inference('demod', [status(thm)],
% 1.35/1.14 [zip_derived_cl42, zip_derived_cl19, zip_derived_cl6,
% 1.35/1.14 zip_derived_cl16])).
% 1.35/1.14 thf(zip_derived_cl21, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.35/1.14 (~ (product @ X0 @ X1 @ X2)
% 1.35/1.14 | ~ (product @ X0 @ X1 @ X3)
% 1.35/1.14 | (equalish @ X2 @ X3))),
% 1.35/1.14 inference('cnf', [status(esa)], [product_total_function2])).
% 1.35/1.14 thf(zip_derived_cl44, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_1 @ e_4 @ e_3)
% 1.35/1.14 | (equalish @ e_3 @ X0)
% 1.35/1.14 | ~ (product @ e_2 @ e_4 @ X0))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl21])).
% 1.35/1.14 thf(zip_derived_cl849, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (equalish @ e_3 @ e_1)
% 1.35/1.14 | (product @ e_1 @ e_4 @ e_3))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl842, zip_derived_cl44])).
% 1.35/1.14 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_1)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 1.35/1.14 thf(zip_derived_cl856, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4) | (product @ e_1 @ e_4 @ e_3))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl849, zip_derived_cl14])).
% 1.35/1.14 thf(zip_derived_cl3, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.35/1.14 (~ (product @ X0 @ X1 @ X2)
% 1.35/1.14 | ~ (product @ X3 @ X0 @ X1)
% 1.35/1.14 | (product @ X2 @ X0 @ X3))),
% 1.35/1.14 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.35/1.14 thf(zip_derived_cl858, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_3 @ e_1 @ X0)
% 1.35/1.14 | ~ (product @ X0 @ e_1 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl856, zip_derived_cl3])).
% 1.35/1.14 thf(zip_derived_cl956, plain,
% 1.35/1.14 (( (equalish @ e_4 @ e_1)
% 1.35/1.14 | ~ (group_element @ e_1)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_2 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_3 @ e_1 @ e_3)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl858])).
% 1.35/1.14 thf(zip_derived_cl17, plain, (~ (equalish @ e_4 @ e_1)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 1.35/1.14 thf(zip_derived_cl4, plain, ( (group_element @ e_1)),
% 1.35/1.14 inference('cnf', [status(esa)], [element_1])).
% 1.35/1.14 thf(zip_derived_cl959, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_2 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_3 @ e_1 @ e_3)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4))),
% 1.35/1.14 inference('demod', [status(thm)],
% 1.35/1.14 [zip_derived_cl956, zip_derived_cl17, zip_derived_cl4])).
% 1.35/1.14 thf(zip_derived_cl960, plain,
% 1.35/1.14 (( (product @ e_3 @ e_1 @ e_3)
% 1.35/1.14 | (product @ e_2 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4))),
% 1.35/1.14 inference('simplify', [status(thm)], [zip_derived_cl959])).
% 1.35/1.14 thf(zip_derived_cl30, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i]:
% 1.35/1.14 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 1.35/1.14 thf(zip_derived_cl976, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_2 @ e_1 @ e_4)
% 1.35/1.14 | (equalish @ e_3 @ e_1))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl960, zip_derived_cl30])).
% 1.35/1.14 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_1)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 1.35/1.14 thf(zip_derived_cl982, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4) | (product @ e_2 @ e_1 @ e_4))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl976, zip_derived_cl14])).
% 1.35/1.14 thf(zip_derived_cl858, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_3 @ e_1 @ X0)
% 1.35/1.14 | ~ (product @ X0 @ e_1 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl856, zip_derived_cl3])).
% 1.35/1.14 thf(zip_derived_cl994, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_3 @ e_1 @ e_2)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl982, zip_derived_cl858])).
% 1.35/1.14 thf(zip_derived_cl996, plain,
% 1.35/1.14 (( (product @ e_3 @ e_1 @ e_2) | (product @ e_1 @ e_1 @ e_4))),
% 1.35/1.14 inference('simplify', [status(thm)], [zip_derived_cl994])).
% 1.35/1.14 thf(zip_derived_cl22, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.35/1.14 (~ (product @ X0 @ X1 @ X2)
% 1.35/1.14 | ~ (product @ X0 @ X3 @ X2)
% 1.35/1.14 | (equalish @ X1 @ X3))),
% 1.35/1.14 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.35/1.14 thf(zip_derived_cl1001, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (equalish @ e_1 @ X0)
% 1.35/1.14 | ~ (product @ e_3 @ X0 @ e_2))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl996, zip_derived_cl22])).
% 1.35/1.14 thf(zip_derived_cl1044, plain,
% 1.35/1.14 (( (equalish @ e_4 @ e_2)
% 1.35/1.14 | ~ (group_element @ e_2)
% 1.35/1.14 | (product @ e_1 @ e_4 @ e_2)
% 1.35/1.14 | (product @ e_2 @ e_4 @ e_2)
% 1.35/1.14 | (equalish @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl1001])).
% 1.35/1.14 thf(zip_derived_cl18, plain, (~ (equalish @ e_4 @ e_2)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 1.35/1.14 thf(zip_derived_cl5, plain, ( (group_element @ e_2)),
% 1.35/1.14 inference('cnf', [status(esa)], [element_2])).
% 1.35/1.14 thf(zip_derived_cl10, plain, (~ (equalish @ e_1 @ e_4)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 1.35/1.14 thf(zip_derived_cl1048, plain,
% 1.35/1.14 (( (product @ e_1 @ e_4 @ e_2)
% 1.35/1.14 | (product @ e_2 @ e_4 @ e_2)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4))),
% 1.35/1.14 inference('demod', [status(thm)],
% 1.35/1.14 [zip_derived_cl1044, zip_derived_cl18, zip_derived_cl5,
% 1.35/1.14 zip_derived_cl10])).
% 1.35/1.14 thf(zip_derived_cl30, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i]:
% 1.35/1.14 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 1.35/1.14 thf(zip_derived_cl1094, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (product @ e_1 @ e_4 @ e_2)
% 1.35/1.14 | (equalish @ e_2 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl1048, zip_derived_cl30])).
% 1.35/1.14 thf(zip_derived_cl13, plain, (~ (equalish @ e_2 @ e_4)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 1.35/1.14 thf(zip_derived_cl1105, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4) | (product @ e_1 @ e_4 @ e_2))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl1094, zip_derived_cl13])).
% 1.35/1.14 thf(zip_derived_cl856, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4) | (product @ e_1 @ e_4 @ e_3))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl849, zip_derived_cl14])).
% 1.35/1.14 thf(zip_derived_cl21, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.35/1.14 (~ (product @ X0 @ X1 @ X2)
% 1.35/1.14 | ~ (product @ X0 @ X1 @ X3)
% 1.35/1.14 | (equalish @ X2 @ X3))),
% 1.35/1.14 inference('cnf', [status(esa)], [product_total_function2])).
% 1.35/1.14 thf(zip_derived_cl859, plain,
% 1.35/1.14 (![X0 : $i]:
% 1.35/1.14 ( (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (equalish @ e_3 @ X0)
% 1.35/1.14 | ~ (product @ e_1 @ e_4 @ X0))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl856, zip_derived_cl21])).
% 1.35/1.14 thf(zip_derived_cl1142, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4)
% 1.35/1.14 | (equalish @ e_3 @ e_2)
% 1.35/1.14 | (product @ e_1 @ e_1 @ e_4))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl1105, zip_derived_cl859])).
% 1.35/1.14 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 1.35/1.14 thf(zip_derived_cl15, plain, (~ (equalish @ e_3 @ e_2)),
% 1.35/1.14 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 1.35/1.14 thf(zip_derived_cl1148, plain,
% 1.35/1.14 (( (product @ e_1 @ e_1 @ e_4) | (product @ e_1 @ e_1 @ e_4))),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl1142, zip_derived_cl15])).
% 1.35/1.14 thf(zip_derived_cl1149, plain, ( (product @ e_1 @ e_1 @ e_4)),
% 1.35/1.14 inference('simplify', [status(thm)], [zip_derived_cl1148])).
% 1.35/1.14 thf(zip_derived_cl26, plain,
% 1.35/1.14 (![X0 : $i, X1 : $i]:
% 1.35/1.14 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X0 @ X1))),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl21])).
% 1.35/1.14 thf(zip_derived_cl1156, plain, ( (equalish @ e_1 @ e_4)),
% 1.35/1.14 inference('sup-', [status(thm)], [zip_derived_cl1149, zip_derived_cl26])).
% 1.35/1.14 thf(zip_derived_cl1163, plain, ($false),
% 1.35/1.14 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1156])).
% 1.35/1.14
% 1.35/1.14 % SZS output end Refutation
% 1.35/1.14
% 1.35/1.14
% 1.35/1.14 % Terminating...
% 1.76/1.28 % Runner terminated.
% 1.76/1.29 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------