%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP124-3.004 : 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.MFuWEVT426 true
% Computer : n027.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 0.61s 1.15s
% Output : Refutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP124-3.004 : TPTP v9.2.0. Released v1.2.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.MFuWEVT426 true
% 0.12/0.34 % Computer : n027.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 : Wed Oct 1 14:20:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox2/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
% 0.57/0.66 % Total configuration time : 435
% 0.57/0.66 % Estimated wc time : 1092
% 0.57/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.60/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.60/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.60/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.60/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.60/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.60/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.61/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.61/0.87 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 0.61/1.15 % Solved by fo/fo7.sh.
% 0.61/1.15 % done 354 iterations in 0.379s
% 0.61/1.15 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.61/1.15 % SZS output start Refutation
% 0.61/1.15 thf(e_4_type, type, e_4: $i).
% 0.61/1.15 thf(e_3_type, type, e_3: $i).
% 0.61/1.15 thf(e_2_type, type, e_2: $i).
% 0.61/1.15 thf(e_1_type, type, e_1: $i).
% 0.61/1.15 thf(product_type, type, product: $i > $i > $i > $o).
% 0.61/1.15 thf(group_element_type, type, group_element: $i > $o).
% 0.61/1.15 thf(equalish_type, type, equalish: $i > $i > $o).
% 0.61/1.15 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 0.61/1.15 thf(zip_derived_cl26, plain, (~ (equalish @ e_1 @ e_3)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.61/1.15 thf(product_total_function1, axiom,
% 0.61/1.15 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 0.61/1.15 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 0.61/1.15 ( product @ X @ Y @ e_3 ) | ( product @ X @ Y @ e_4 ))).
% 0.61/1.15 thf(zip_derived_cl37, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 (~ (group_element @ X0)
% 0.61/1.15 | ~ (group_element @ X1)
% 0.61/1.15 | (product @ X0 @ X1 @ e_1)
% 0.61/1.15 | (product @ X0 @ X1 @ e_2)
% 0.61/1.15 | (product @ X0 @ X1 @ e_3)
% 0.61/1.15 | (product @ X0 @ X1 @ e_4))),
% 0.61/1.15 inference('cnf', [status(esa)], [product_total_function1])).
% 0.61/1.15 thf(zip_derived_cl37, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 (~ (group_element @ X0)
% 0.61/1.15 | ~ (group_element @ X1)
% 0.61/1.15 | (product @ X0 @ X1 @ e_1)
% 0.61/1.15 | (product @ X0 @ X1 @ e_2)
% 0.61/1.15 | (product @ X0 @ X1 @ e_3)
% 0.61/1.15 | (product @ X0 @ X1 @ e_4))),
% 0.61/1.15 inference('cnf', [status(esa)], [product_total_function1])).
% 0.61/1.15 thf(product_idempotence, axiom, (product @ X @ X @ X)).
% 0.61/1.15 thf(zip_derived_cl41, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.61/1.15 inference('cnf', [status(esa)], [product_idempotence])).
% 0.61/1.15 thf(product_left_cancellation, axiom,
% 0.61/1.15 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 0.61/1.15 ( equalish @ W @ Z ))).
% 0.61/1.15 thf(zip_derived_cl40, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.61/1.15 (~ (product @ X0 @ X1 @ X2)
% 0.61/1.15 | ~ (product @ X3 @ X1 @ X2)
% 0.61/1.15 | (equalish @ X0 @ X3))),
% 0.61/1.15 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.61/1.15 thf(zip_derived_cl55, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 ( (equalish @ X0 @ X1) | ~ (product @ X1 @ X0 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.61/1.15 thf(zip_derived_cl163, plain,
% 0.61/1.15 (![X0 : $i]:
% 0.61/1.15 ( (product @ X0 @ e_4 @ e_3)
% 0.61/1.15 | (product @ X0 @ e_4 @ e_2)
% 0.61/1.15 | (product @ X0 @ e_4 @ e_1)
% 0.61/1.15 | ~ (group_element @ e_4)
% 0.61/1.15 | ~ (group_element @ X0)
% 0.61/1.15 | (equalish @ e_4 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl55])).
% 0.61/1.15 thf(element_4, axiom, (group_element @ e_4)).
% 0.61/1.15 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 0.61/1.15 inference('cnf', [status(esa)], [element_4])).
% 0.61/1.15 thf(zip_derived_cl167, plain,
% 0.61/1.15 (![X0 : $i]:
% 0.61/1.15 ( (product @ X0 @ e_4 @ e_3)
% 0.61/1.15 | (product @ X0 @ e_4 @ e_2)
% 0.61/1.15 | (product @ X0 @ e_4 @ e_1)
% 0.61/1.15 | ~ (group_element @ X0)
% 0.61/1.15 | (equalish @ e_4 @ X0))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl163, zip_derived_cl24])).
% 0.61/1.15 thf(zip_derived_cl41, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.61/1.15 inference('cnf', [status(esa)], [product_idempotence])).
% 0.61/1.15 thf(product_right_cancellation, axiom,
% 0.61/1.15 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 0.61/1.15 ( equalish @ W @ Z ))).
% 0.61/1.15 thf(zip_derived_cl39, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.61/1.15 (~ (product @ X0 @ X1 @ X2)
% 0.61/1.15 | ~ (product @ X0 @ X3 @ X2)
% 0.61/1.15 | (equalish @ X1 @ X3))),
% 0.61/1.15 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.61/1.15 thf(zip_derived_cl51, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.61/1.15 thf(zip_derived_cl293, plain,
% 0.61/1.15 (( (equalish @ e_4 @ e_3)
% 0.61/1.15 | ~ (group_element @ e_3)
% 0.61/1.15 | (product @ e_3 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_3 @ e_4 @ e_2)
% 0.61/1.15 | (equalish @ e_3 @ e_4))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl167, zip_derived_cl51])).
% 0.61/1.15 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 0.61/1.15 thf(zip_derived_cl36, plain, (~ (equalish @ e_4 @ e_3)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 0.61/1.15 thf(element_3, axiom, (group_element @ e_3)).
% 0.61/1.15 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 0.61/1.15 inference('cnf', [status(esa)], [element_3])).
% 0.61/1.15 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 0.61/1.15 thf(zip_derived_cl33, plain, (~ (equalish @ e_3 @ e_4)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 0.61/1.15 thf(zip_derived_cl300, plain,
% 0.61/1.15 (( (product @ e_3 @ e_4 @ e_1) | (product @ e_3 @ e_4 @ e_2))),
% 0.61/1.15 inference('demod', [status(thm)],
% 0.61/1.15 [zip_derived_cl293, zip_derived_cl36, zip_derived_cl23,
% 0.61/1.15 zip_derived_cl33])).
% 0.61/1.15 thf(qg2_1, conjecture,
% 0.61/1.15 (~( ( equalish @ X1 @ X2 ) | ( ~( product @ Z2 @ X2 @ Y2 ) ) |
% 0.61/1.15 ( ~( product @ Z2 @ X1 @ Y1 ) ) | ( ~( product @ X2 @ Y2 @ Z1 ) ) |
% 0.61/1.15 ( ~( product @ X1 @ Y1 @ Z1 ) ) ))).
% 0.61/1.15 thf(zf_stmt_0, negated_conjecture,
% 0.61/1.15 (( equalish @ X1 @ X2 ) | ( ~( product @ Z2 @ X2 @ Y2 ) ) |
% 0.61/1.15 ( ~( product @ Z2 @ X1 @ Y1 ) ) | ( ~( product @ X2 @ Y2 @ Z1 ) ) |
% 0.61/1.15 ( ~( product @ X1 @ Y1 @ Z1 ) )),
% 0.61/1.15 inference('cnf.neg', [status(esa)], [qg2_1])).
% 0.61/1.15 thf(zip_derived_cl42, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.61/1.15 ( (equalish @ X0 @ X1)
% 0.61/1.15 | ~ (product @ X2 @ X1 @ X3)
% 0.61/1.15 | ~ (product @ X2 @ X0 @ X4)
% 0.61/1.15 | ~ (product @ X1 @ X3 @ X5)
% 0.61/1.15 | ~ (product @ X0 @ X4 @ X5))),
% 0.61/1.15 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.61/1.15 thf(zip_derived_cl116, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.61/1.15 (~ (product @ X2 @ X1 @ X0)
% 0.61/1.15 | ~ (product @ X0 @ X0 @ X0)
% 0.61/1.15 | ~ (product @ X0 @ X2 @ X1)
% 0.61/1.15 | (equalish @ X2 @ X0))),
% 0.61/1.15 inference('eq_fact', [status(thm)], [zip_derived_cl42])).
% 0.61/1.15 thf(zip_derived_cl41, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.61/1.15 inference('cnf', [status(esa)], [product_idempotence])).
% 0.61/1.15 thf(zip_derived_cl119, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.61/1.15 (~ (product @ X2 @ X1 @ X0)
% 0.61/1.15 | ~ (product @ X0 @ X2 @ X1)
% 0.61/1.15 | (equalish @ X2 @ X0))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl116, zip_derived_cl41])).
% 0.61/1.15 thf(zip_derived_cl354, plain,
% 0.61/1.15 (( (product @ e_3 @ e_4 @ e_1)
% 0.61/1.15 | (equalish @ e_3 @ e_2)
% 0.61/1.15 | ~ (product @ e_2 @ e_3 @ e_4))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl300, zip_derived_cl119])).
% 0.61/1.15 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 0.61/1.15 thf(zip_derived_cl32, plain, (~ (equalish @ e_3 @ e_2)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 0.61/1.15 thf(zip_derived_cl359, plain,
% 0.61/1.15 (( (product @ e_3 @ e_4 @ e_1) | ~ (product @ e_2 @ e_3 @ e_4))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl354, zip_derived_cl32])).
% 0.61/1.15 thf(zip_derived_cl362, plain,
% 0.61/1.15 (( (product @ e_2 @ e_3 @ e_3)
% 0.61/1.15 | (product @ e_2 @ e_3 @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_3 @ e_1)
% 0.61/1.15 | ~ (group_element @ e_3)
% 0.61/1.15 | ~ (group_element @ e_2)
% 0.61/1.15 | (product @ e_3 @ e_4 @ e_1))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl359])).
% 0.61/1.15 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 0.61/1.15 inference('cnf', [status(esa)], [element_3])).
% 0.61/1.15 thf(element_2, axiom, (group_element @ e_2)).
% 0.61/1.15 thf(zip_derived_cl22, plain, ( (group_element @ e_2)),
% 0.61/1.15 inference('cnf', [status(esa)], [element_2])).
% 0.61/1.15 thf(zip_derived_cl363, plain,
% 0.61/1.15 (( (product @ e_2 @ e_3 @ e_3)
% 0.61/1.15 | (product @ e_2 @ e_3 @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_3 @ e_1)
% 0.61/1.15 | (product @ e_3 @ e_4 @ e_1))),
% 0.61/1.15 inference('demod', [status(thm)],
% 0.61/1.15 [zip_derived_cl362, zip_derived_cl23, zip_derived_cl22])).
% 0.61/1.15 thf(zip_derived_cl167, plain,
% 0.61/1.15 (![X0 : $i]:
% 0.61/1.15 ( (product @ X0 @ e_4 @ e_3)
% 0.61/1.15 | (product @ X0 @ e_4 @ e_2)
% 0.61/1.15 | (product @ X0 @ e_4 @ e_1)
% 0.61/1.15 | ~ (group_element @ X0)
% 0.61/1.15 | (equalish @ e_4 @ X0))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl163, zip_derived_cl24])).
% 0.61/1.15 thf(zip_derived_cl167, plain,
% 0.61/1.15 (![X0 : $i]:
% 0.61/1.15 ( (product @ X0 @ e_4 @ e_3)
% 0.61/1.15 | (product @ X0 @ e_4 @ e_2)
% 0.61/1.15 | (product @ X0 @ e_4 @ e_1)
% 0.61/1.15 | ~ (group_element @ X0)
% 0.61/1.15 | (equalish @ e_4 @ X0))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl163, zip_derived_cl24])).
% 0.61/1.15 thf(zip_derived_cl37, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 (~ (group_element @ X0)
% 0.61/1.15 | ~ (group_element @ X1)
% 0.61/1.15 | (product @ X0 @ X1 @ e_1)
% 0.61/1.15 | (product @ X0 @ X1 @ e_2)
% 0.61/1.15 | (product @ X0 @ X1 @ e_3)
% 0.61/1.15 | (product @ X0 @ X1 @ e_4))),
% 0.61/1.15 inference('cnf', [status(esa)], [product_total_function1])).
% 0.61/1.15 thf(zip_derived_cl51, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.61/1.15 thf(zip_derived_cl162, plain,
% 0.61/1.15 (![X0 : $i]:
% 0.61/1.15 ( (product @ e_4 @ X0 @ e_3)
% 0.61/1.15 | (product @ e_4 @ X0 @ e_2)
% 0.61/1.15 | (product @ e_4 @ X0 @ e_1)
% 0.61/1.15 | ~ (group_element @ X0)
% 0.61/1.15 | ~ (group_element @ e_4)
% 0.61/1.15 | (equalish @ e_4 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl51])).
% 0.61/1.15 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 0.61/1.15 inference('cnf', [status(esa)], [element_4])).
% 0.61/1.15 thf(zip_derived_cl166, plain,
% 0.61/1.15 (![X0 : $i]:
% 0.61/1.15 ( (product @ e_4 @ X0 @ e_3)
% 0.61/1.15 | (product @ e_4 @ X0 @ e_2)
% 0.61/1.15 | (product @ e_4 @ X0 @ e_1)
% 0.61/1.15 | ~ (group_element @ X0)
% 0.61/1.15 | (equalish @ e_4 @ X0))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl162, zip_derived_cl24])).
% 0.61/1.15 thf(zip_derived_cl55, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 ( (equalish @ X0 @ X1) | ~ (product @ X1 @ X0 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.61/1.15 thf(zip_derived_cl265, plain,
% 0.61/1.15 (( (equalish @ e_4 @ e_3)
% 0.61/1.15 | ~ (group_element @ e_3)
% 0.61/1.15 | (product @ e_4 @ e_3 @ e_1)
% 0.61/1.15 | (product @ e_4 @ e_3 @ e_2)
% 0.61/1.15 | (equalish @ e_3 @ e_4))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl166, zip_derived_cl55])).
% 0.61/1.15 thf(zip_derived_cl36, plain, (~ (equalish @ e_4 @ e_3)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 0.61/1.15 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 0.61/1.15 inference('cnf', [status(esa)], [element_3])).
% 0.61/1.15 thf(zip_derived_cl33, plain, (~ (equalish @ e_3 @ e_4)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 0.61/1.15 thf(zip_derived_cl270, plain,
% 0.61/1.15 (( (product @ e_4 @ e_3 @ e_1) | (product @ e_4 @ e_3 @ e_2))),
% 0.61/1.15 inference('demod', [status(thm)],
% 0.61/1.15 [zip_derived_cl265, zip_derived_cl36, zip_derived_cl23,
% 0.61/1.15 zip_derived_cl33])).
% 0.61/1.15 thf(zip_derived_cl119, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.61/1.15 (~ (product @ X2 @ X1 @ X0)
% 0.61/1.15 | ~ (product @ X0 @ X2 @ X1)
% 0.61/1.15 | (equalish @ X2 @ X0))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl116, zip_derived_cl41])).
% 0.61/1.15 thf(zip_derived_cl276, plain,
% 0.61/1.15 (( (product @ e_4 @ e_3 @ e_1)
% 0.61/1.15 | (equalish @ e_4 @ e_2)
% 0.61/1.15 | ~ (product @ e_2 @ e_4 @ e_3))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl270, zip_derived_cl119])).
% 0.61/1.15 thf(e_4_is_not_e_2, axiom, (~( equalish @ e_4 @ e_2 ))).
% 0.61/1.15 thf(zip_derived_cl35, plain, (~ (equalish @ e_4 @ e_2)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 0.61/1.15 thf(zip_derived_cl281, plain,
% 0.61/1.15 (( (product @ e_4 @ e_3 @ e_1) | ~ (product @ e_2 @ e_4 @ e_3))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl276, zip_derived_cl35])).
% 0.61/1.15 thf(zip_derived_cl296, plain,
% 0.61/1.15 (( (equalish @ e_4 @ e_2)
% 0.61/1.15 | ~ (group_element @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_4 @ e_3 @ e_1))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl167, zip_derived_cl281])).
% 0.61/1.15 thf(zip_derived_cl35, plain, (~ (equalish @ e_4 @ e_2)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 0.61/1.15 thf(zip_derived_cl22, plain, ( (group_element @ e_2)),
% 0.61/1.15 inference('cnf', [status(esa)], [element_2])).
% 0.61/1.15 thf(zip_derived_cl301, plain,
% 0.61/1.15 (( (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_4 @ e_3 @ e_1))),
% 0.61/1.15 inference('demod', [status(thm)],
% 0.61/1.15 [zip_derived_cl296, zip_derived_cl35, zip_derived_cl22])).
% 0.61/1.15 thf(zip_derived_cl119, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.61/1.15 (~ (product @ X2 @ X1 @ X0)
% 0.61/1.15 | ~ (product @ X0 @ X2 @ X1)
% 0.61/1.15 | (equalish @ X2 @ X0))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl116, zip_derived_cl41])).
% 0.61/1.15 thf(zip_derived_cl391, plain,
% 0.61/1.15 (( (product @ e_2 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (equalish @ e_4 @ e_1)
% 0.61/1.15 | ~ (product @ e_1 @ e_4 @ e_3))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl301, zip_derived_cl119])).
% 0.61/1.15 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 0.61/1.15 thf(zip_derived_cl34, plain, (~ (equalish @ e_4 @ e_1)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.61/1.15 thf(zip_derived_cl397, plain,
% 0.61/1.15 (( (product @ e_2 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | ~ (product @ e_1 @ e_4 @ e_3))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl391, zip_derived_cl34])).
% 0.61/1.15 thf(zip_derived_cl422, plain,
% 0.61/1.15 (( (equalish @ e_4 @ e_1)
% 0.61/1.15 | ~ (group_element @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_2))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl167, zip_derived_cl397])).
% 0.61/1.15 thf(zip_derived_cl34, plain, (~ (equalish @ e_4 @ e_1)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.61/1.15 thf(element_1, axiom, (group_element @ e_1)).
% 0.61/1.15 thf(zip_derived_cl21, plain, ( (group_element @ e_1)),
% 0.61/1.15 inference('cnf', [status(esa)], [element_1])).
% 0.61/1.15 thf(zip_derived_cl423, plain,
% 0.61/1.15 (( (product @ e_1 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_2))),
% 0.61/1.15 inference('demod', [status(thm)],
% 0.61/1.15 [zip_derived_cl422, zip_derived_cl34, zip_derived_cl21])).
% 0.61/1.15 thf(zip_derived_cl51, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.61/1.15 thf(zip_derived_cl544, plain,
% 0.61/1.15 (( (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_1)
% 0.61/1.15 | (equalish @ e_2 @ e_4))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl423, zip_derived_cl51])).
% 0.61/1.15 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 0.61/1.15 thf(zip_derived_cl30, plain, (~ (equalish @ e_2 @ e_4)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 0.61/1.15 thf(zip_derived_cl551, plain,
% 0.61/1.15 (( (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_1))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl544, zip_derived_cl30])).
% 0.61/1.15 thf(zip_derived_cl166, plain,
% 0.61/1.15 (![X0 : $i]:
% 0.61/1.15 ( (product @ e_4 @ X0 @ e_3)
% 0.61/1.15 | (product @ e_4 @ X0 @ e_2)
% 0.61/1.15 | (product @ e_4 @ X0 @ e_1)
% 0.61/1.15 | ~ (group_element @ X0)
% 0.61/1.15 | (equalish @ e_4 @ X0))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl162, zip_derived_cl24])).
% 0.61/1.15 thf(zip_derived_cl119, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.61/1.15 (~ (product @ X2 @ X1 @ X0)
% 0.61/1.15 | ~ (product @ X0 @ X2 @ X1)
% 0.61/1.15 | (equalish @ X2 @ X0))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl116, zip_derived_cl41])).
% 0.61/1.15 thf(zip_derived_cl262, plain,
% 0.61/1.15 (![X0 : $i]:
% 0.61/1.15 ( (equalish @ e_4 @ X0)
% 0.61/1.15 | ~ (group_element @ X0)
% 0.61/1.15 | (product @ e_4 @ X0 @ e_1)
% 0.61/1.15 | (product @ e_4 @ X0 @ e_2)
% 0.61/1.15 | (equalish @ e_4 @ e_3)
% 0.61/1.15 | ~ (product @ e_3 @ e_4 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl166, zip_derived_cl119])).
% 0.61/1.15 thf(zip_derived_cl36, plain, (~ (equalish @ e_4 @ e_3)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 0.61/1.15 thf(zip_derived_cl269, plain,
% 0.61/1.15 (![X0 : $i]:
% 0.61/1.15 ( (equalish @ e_4 @ X0)
% 0.61/1.15 | ~ (group_element @ X0)
% 0.61/1.15 | (product @ e_4 @ X0 @ e_1)
% 0.61/1.15 | (product @ e_4 @ X0 @ e_2)
% 0.61/1.15 | ~ (product @ e_3 @ e_4 @ X0))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl262, zip_derived_cl36])).
% 0.61/1.15 thf(zip_derived_cl119, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.61/1.15 (~ (product @ X2 @ X1 @ X0)
% 0.61/1.15 | ~ (product @ X0 @ X2 @ X1)
% 0.61/1.15 | (equalish @ X2 @ X0))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl116, zip_derived_cl41])).
% 0.61/1.15 thf(zip_derived_cl477, plain,
% 0.61/1.15 (![X0 : $i]:
% 0.61/1.15 (~ (product @ e_3 @ e_4 @ X0)
% 0.61/1.15 | (product @ e_4 @ X0 @ e_1)
% 0.61/1.15 | ~ (group_element @ X0)
% 0.61/1.15 | (equalish @ e_4 @ X0)
% 0.61/1.15 | (equalish @ e_4 @ e_2)
% 0.61/1.15 | ~ (product @ e_2 @ e_4 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl269, zip_derived_cl119])).
% 0.61/1.15 thf(zip_derived_cl35, plain, (~ (equalish @ e_4 @ e_2)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 0.61/1.15 thf(zip_derived_cl491, plain,
% 0.61/1.15 (![X0 : $i]:
% 0.61/1.15 (~ (product @ e_3 @ e_4 @ X0)
% 0.61/1.15 | (product @ e_4 @ X0 @ e_1)
% 0.61/1.15 | ~ (group_element @ X0)
% 0.61/1.15 | (equalish @ e_4 @ X0)
% 0.61/1.15 | ~ (product @ e_2 @ e_4 @ X0))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl477, zip_derived_cl35])).
% 0.61/1.15 thf(zip_derived_cl55, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 ( (equalish @ X0 @ X1) | ~ (product @ X1 @ X0 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.61/1.15 thf(zip_derived_cl828, plain,
% 0.61/1.15 ((~ (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (equalish @ e_4 @ e_1)
% 0.61/1.15 | ~ (group_element @ e_1)
% 0.61/1.15 | ~ (product @ e_3 @ e_4 @ e_1)
% 0.61/1.15 | (equalish @ e_1 @ e_4))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl491, zip_derived_cl55])).
% 0.61/1.15 thf(zip_derived_cl34, plain, (~ (equalish @ e_4 @ e_1)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.61/1.15 thf(zip_derived_cl21, plain, ( (group_element @ e_1)),
% 0.61/1.15 inference('cnf', [status(esa)], [element_1])).
% 0.61/1.15 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 0.61/1.15 thf(zip_derived_cl27, plain, (~ (equalish @ e_1 @ e_4)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 0.61/1.15 thf(zip_derived_cl845, plain,
% 0.61/1.15 ((~ (product @ e_2 @ e_4 @ e_1) | ~ (product @ e_3 @ e_4 @ e_1))),
% 0.61/1.15 inference('demod', [status(thm)],
% 0.61/1.15 [zip_derived_cl828, zip_derived_cl34, zip_derived_cl21,
% 0.61/1.15 zip_derived_cl27])).
% 0.61/1.15 thf(zip_derived_cl904, plain,
% 0.61/1.15 (( (product @ e_1 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | ~ (product @ e_3 @ e_4 @ e_1))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl551, zip_derived_cl845])).
% 0.61/1.15 thf(zip_derived_cl906, plain,
% 0.61/1.15 (( (product @ e_2 @ e_3 @ e_1)
% 0.61/1.15 | (product @ e_2 @ e_3 @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_3 @ e_3)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_1))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl363, zip_derived_cl904])).
% 0.61/1.15 thf(zip_derived_cl55, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 ( (equalish @ X0 @ X1) | ~ (product @ X1 @ X0 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.61/1.15 thf(zip_derived_cl1294, plain,
% 0.61/1.15 (( (product @ e_1 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_3 @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_3 @ e_1)
% 0.61/1.15 | (equalish @ e_3 @ e_2))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl906, zip_derived_cl55])).
% 0.61/1.15 thf(zip_derived_cl32, plain, (~ (equalish @ e_3 @ e_2)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 0.61/1.15 thf(zip_derived_cl1300, plain,
% 0.61/1.15 (( (product @ e_1 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_3 @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_3 @ e_1))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl1294, zip_derived_cl32])).
% 0.61/1.15 thf(zip_derived_cl51, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.61/1.15 thf(zip_derived_cl1395, plain,
% 0.61/1.15 (( (product @ e_2 @ e_3 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_1)
% 0.61/1.15 | (equalish @ e_2 @ e_3))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl1300, zip_derived_cl51])).
% 0.61/1.15 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 0.61/1.15 thf(zip_derived_cl29, plain, (~ (equalish @ e_2 @ e_3)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.61/1.15 thf(zip_derived_cl1404, plain,
% 0.61/1.15 (( (product @ e_2 @ e_3 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_1))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl1395, zip_derived_cl29])).
% 0.61/1.15 thf(zip_derived_cl551, plain,
% 0.61/1.15 (( (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_1))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl544, zip_derived_cl30])).
% 0.61/1.15 thf(zip_derived_cl39, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.61/1.15 (~ (product @ X0 @ X1 @ X2)
% 0.61/1.15 | ~ (product @ X0 @ X3 @ X2)
% 0.61/1.15 | (equalish @ X1 @ X3))),
% 0.61/1.15 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.61/1.15 thf(zip_derived_cl554, plain,
% 0.61/1.15 (![X0 : $i]:
% 0.61/1.15 ( (product @ e_1 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | (equalish @ e_4 @ X0)
% 0.61/1.15 | ~ (product @ e_2 @ X0 @ e_1))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl551, zip_derived_cl39])).
% 0.61/1.15 thf(zip_derived_cl1423, plain,
% 0.61/1.15 (( (product @ e_1 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | (equalish @ e_4 @ e_3)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_1))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl1404, zip_derived_cl554])).
% 0.61/1.15 thf(zip_derived_cl36, plain, (~ (equalish @ e_4 @ e_3)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 0.61/1.15 thf(zip_derived_cl1432, plain,
% 0.61/1.15 (( (product @ e_1 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_1))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl1423, zip_derived_cl36])).
% 0.61/1.15 thf(zip_derived_cl1433, plain,
% 0.61/1.15 (( (product @ e_1 @ e_4 @ e_2) | (product @ e_1 @ e_4 @ e_1))),
% 0.61/1.15 inference('simplify', [status(thm)], [zip_derived_cl1432])).
% 0.61/1.15 thf(zip_derived_cl300, plain,
% 0.61/1.15 (( (product @ e_3 @ e_4 @ e_1) | (product @ e_3 @ e_4 @ e_2))),
% 0.61/1.15 inference('demod', [status(thm)],
% 0.61/1.15 [zip_derived_cl293, zip_derived_cl36, zip_derived_cl23,
% 0.61/1.15 zip_derived_cl33])).
% 0.61/1.15 thf(zip_derived_cl269, plain,
% 0.61/1.15 (![X0 : $i]:
% 0.61/1.15 ( (equalish @ e_4 @ X0)
% 0.61/1.15 | ~ (group_element @ X0)
% 0.61/1.15 | (product @ e_4 @ X0 @ e_1)
% 0.61/1.15 | (product @ e_4 @ X0 @ e_2)
% 0.61/1.15 | ~ (product @ e_3 @ e_4 @ X0))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl262, zip_derived_cl36])).
% 0.61/1.15 thf(zip_derived_cl55, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 ( (equalish @ X0 @ X1) | ~ (product @ X1 @ X0 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.61/1.15 thf(zip_derived_cl480, plain,
% 0.61/1.15 ((~ (product @ e_3 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_4 @ e_2 @ e_1)
% 0.61/1.15 | ~ (group_element @ e_2)
% 0.61/1.15 | (equalish @ e_4 @ e_2)
% 0.61/1.15 | (equalish @ e_2 @ e_4))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl269, zip_derived_cl55])).
% 0.61/1.15 thf(zip_derived_cl22, plain, ( (group_element @ e_2)),
% 0.61/1.15 inference('cnf', [status(esa)], [element_2])).
% 0.61/1.15 thf(zip_derived_cl35, plain, (~ (equalish @ e_4 @ e_2)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 0.61/1.15 thf(zip_derived_cl30, plain, (~ (equalish @ e_2 @ e_4)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 0.61/1.15 thf(zip_derived_cl492, plain,
% 0.61/1.15 ((~ (product @ e_3 @ e_4 @ e_2) | (product @ e_4 @ e_2 @ e_1))),
% 0.61/1.15 inference('demod', [status(thm)],
% 0.61/1.15 [zip_derived_cl480, zip_derived_cl22, zip_derived_cl35,
% 0.61/1.15 zip_derived_cl30])).
% 0.61/1.15 thf(zip_derived_cl501, plain,
% 0.61/1.15 (( (product @ e_3 @ e_4 @ e_1) | (product @ e_4 @ e_2 @ e_1))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl300, zip_derived_cl492])).
% 0.61/1.15 thf(zip_derived_cl119, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.61/1.15 (~ (product @ X2 @ X1 @ X0)
% 0.61/1.15 | ~ (product @ X0 @ X2 @ X1)
% 0.61/1.15 | (equalish @ X2 @ X0))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl116, zip_derived_cl41])).
% 0.61/1.15 thf(zip_derived_cl507, plain,
% 0.61/1.15 (( (product @ e_3 @ e_4 @ e_1)
% 0.61/1.15 | (equalish @ e_4 @ e_1)
% 0.61/1.15 | ~ (product @ e_1 @ e_4 @ e_2))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl501, zip_derived_cl119])).
% 0.61/1.15 thf(zip_derived_cl34, plain, (~ (equalish @ e_4 @ e_1)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.61/1.15 thf(zip_derived_cl515, plain,
% 0.61/1.15 (( (product @ e_3 @ e_4 @ e_1) | ~ (product @ e_1 @ e_4 @ e_2))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl507, zip_derived_cl34])).
% 0.61/1.15 thf(zip_derived_cl1449, plain,
% 0.61/1.15 (( (product @ e_1 @ e_4 @ e_1) | (product @ e_3 @ e_4 @ e_1))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl1433, zip_derived_cl515])).
% 0.61/1.15 thf(zip_derived_cl37, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 (~ (group_element @ X0)
% 0.61/1.15 | ~ (group_element @ X1)
% 0.61/1.15 | (product @ X0 @ X1 @ e_1)
% 0.61/1.15 | (product @ X0 @ X1 @ e_2)
% 0.61/1.15 | (product @ X0 @ X1 @ e_3)
% 0.61/1.15 | (product @ X0 @ X1 @ e_4))),
% 0.61/1.15 inference('cnf', [status(esa)], [product_total_function1])).
% 0.61/1.15 thf(zip_derived_cl501, plain,
% 0.61/1.15 (( (product @ e_3 @ e_4 @ e_1) | (product @ e_4 @ e_2 @ e_1))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl300, zip_derived_cl492])).
% 0.61/1.15 thf(zip_derived_cl301, plain,
% 0.61/1.15 (( (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_4 @ e_3 @ e_1))),
% 0.61/1.15 inference('demod', [status(thm)],
% 0.61/1.15 [zip_derived_cl296, zip_derived_cl35, zip_derived_cl22])).
% 0.61/1.15 thf(zip_derived_cl39, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.61/1.15 (~ (product @ X0 @ X1 @ X2)
% 0.61/1.15 | ~ (product @ X0 @ X3 @ X2)
% 0.61/1.15 | (equalish @ X1 @ X3))),
% 0.61/1.15 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.61/1.15 thf(zip_derived_cl387, plain,
% 0.61/1.15 (![X0 : $i]:
% 0.61/1.15 ( (product @ e_2 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (equalish @ e_3 @ X0)
% 0.61/1.15 | ~ (product @ e_4 @ X0 @ e_1))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl301, zip_derived_cl39])).
% 0.61/1.15 thf(zip_derived_cl512, plain,
% 0.61/1.15 (( (product @ e_3 @ e_4 @ e_1)
% 0.61/1.15 | (equalish @ e_3 @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_2))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl501, zip_derived_cl387])).
% 0.61/1.15 thf(zip_derived_cl32, plain, (~ (equalish @ e_3 @ e_2)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 0.61/1.15 thf(zip_derived_cl518, plain,
% 0.61/1.15 (( (product @ e_3 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_2))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl512, zip_derived_cl32])).
% 0.61/1.15 thf(zip_derived_cl119, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.61/1.15 (~ (product @ X2 @ X1 @ X0)
% 0.61/1.15 | ~ (product @ X0 @ X2 @ X1)
% 0.61/1.15 | (equalish @ X2 @ X0))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl116, zip_derived_cl41])).
% 0.61/1.15 thf(zip_derived_cl526, plain,
% 0.61/1.15 (( (product @ e_2 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (equalish @ e_3 @ e_1)
% 0.61/1.15 | ~ (product @ e_1 @ e_3 @ e_4))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl518, zip_derived_cl119])).
% 0.61/1.15 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 0.61/1.15 thf(zip_derived_cl31, plain, (~ (equalish @ e_3 @ e_1)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.61/1.15 thf(zip_derived_cl532, plain,
% 0.61/1.15 (( (product @ e_2 @ e_4 @ e_2)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | ~ (product @ e_1 @ e_3 @ e_4))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl526, zip_derived_cl31])).
% 0.61/1.15 thf(zip_derived_cl609, plain,
% 0.61/1.15 (( (product @ e_1 @ e_3 @ e_3)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_1)
% 0.61/1.15 | ~ (group_element @ e_3)
% 0.61/1.15 | ~ (group_element @ e_1)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_2))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl532])).
% 0.61/1.15 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 0.61/1.15 inference('cnf', [status(esa)], [element_3])).
% 0.61/1.15 thf(zip_derived_cl21, plain, ( (group_element @ e_1)),
% 0.61/1.15 inference('cnf', [status(esa)], [element_1])).
% 0.61/1.15 thf(zip_derived_cl610, plain,
% 0.61/1.15 (( (product @ e_1 @ e_3 @ e_3)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_1)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_2 @ e_4 @ e_2))),
% 0.61/1.15 inference('demod', [status(thm)],
% 0.61/1.15 [zip_derived_cl609, zip_derived_cl23, zip_derived_cl21])).
% 0.61/1.15 thf(zip_derived_cl51, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.61/1.15 thf(zip_derived_cl755, plain,
% 0.61/1.15 (( (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_3)
% 0.61/1.15 | (equalish @ e_2 @ e_4))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl610, zip_derived_cl51])).
% 0.61/1.15 thf(zip_derived_cl30, plain, (~ (equalish @ e_2 @ e_4)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 0.61/1.15 thf(zip_derived_cl764, plain,
% 0.61/1.15 (( (product @ e_2 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_3))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl755, zip_derived_cl30])).
% 0.61/1.15 thf(zip_derived_cl845, plain,
% 0.61/1.15 ((~ (product @ e_2 @ e_4 @ e_1) | ~ (product @ e_3 @ e_4 @ e_1))),
% 0.61/1.15 inference('demod', [status(thm)],
% 0.61/1.15 [zip_derived_cl828, zip_derived_cl34, zip_derived_cl21,
% 0.61/1.15 zip_derived_cl27])).
% 0.61/1.15 thf(zip_derived_cl905, plain,
% 0.61/1.15 (( (product @ e_1 @ e_3 @ e_3)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_1)
% 0.61/1.15 | ~ (product @ e_3 @ e_4 @ e_1))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl764, zip_derived_cl845])).
% 0.61/1.15 thf(zip_derived_cl1486, plain,
% 0.61/1.15 (( (product @ e_1 @ e_4 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_3))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl1449, zip_derived_cl905])).
% 0.61/1.15 thf(zip_derived_cl51, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.61/1.15 thf(zip_derived_cl1614, plain,
% 0.61/1.15 (( (product @ e_1 @ e_3 @ e_3)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_1)
% 0.61/1.15 | (equalish @ e_1 @ e_4))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl1486, zip_derived_cl51])).
% 0.61/1.15 thf(zip_derived_cl27, plain, (~ (equalish @ e_1 @ e_4)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 0.61/1.15 thf(zip_derived_cl1627, plain,
% 0.61/1.15 (( (product @ e_1 @ e_3 @ e_3)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_2)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_1))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl1614, zip_derived_cl27])).
% 0.61/1.15 thf(zip_derived_cl55, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 ( (equalish @ X0 @ X1) | ~ (product @ X1 @ X0 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.61/1.15 thf(zip_derived_cl1643, plain,
% 0.61/1.15 (( (product @ e_1 @ e_3 @ e_1)
% 0.61/1.15 | (product @ e_1 @ e_3 @ e_2)
% 0.61/1.15 | (equalish @ e_3 @ e_1))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl1627, zip_derived_cl55])).
% 0.61/1.15 thf(zip_derived_cl31, plain, (~ (equalish @ e_3 @ e_1)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.61/1.15 thf(zip_derived_cl1651, plain,
% 0.61/1.15 (( (product @ e_1 @ e_3 @ e_1) | (product @ e_1 @ e_3 @ e_2))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl1643, zip_derived_cl31])).
% 0.61/1.15 thf(zip_derived_cl1433, plain,
% 0.61/1.15 (( (product @ e_1 @ e_4 @ e_2) | (product @ e_1 @ e_4 @ e_1))),
% 0.61/1.15 inference('simplify', [status(thm)], [zip_derived_cl1432])).
% 0.61/1.15 thf(zip_derived_cl39, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.61/1.15 (~ (product @ X0 @ X1 @ X2)
% 0.61/1.15 | ~ (product @ X0 @ X3 @ X2)
% 0.61/1.15 | (equalish @ X1 @ X3))),
% 0.61/1.15 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.61/1.15 thf(zip_derived_cl1435, plain,
% 0.61/1.15 (![X0 : $i]:
% 0.61/1.15 ( (product @ e_1 @ e_4 @ e_1)
% 0.61/1.15 | (equalish @ e_4 @ X0)
% 0.61/1.15 | ~ (product @ e_1 @ X0 @ e_2))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl1433, zip_derived_cl39])).
% 0.61/1.15 thf(zip_derived_cl1667, plain,
% 0.61/1.15 (( (product @ e_1 @ e_3 @ e_1)
% 0.61/1.15 | (equalish @ e_4 @ e_3)
% 0.61/1.15 | (product @ e_1 @ e_4 @ e_1))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl1651, zip_derived_cl1435])).
% 0.61/1.15 thf(zip_derived_cl36, plain, (~ (equalish @ e_4 @ e_3)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 0.61/1.15 thf(zip_derived_cl1674, plain,
% 0.61/1.15 (( (product @ e_1 @ e_3 @ e_1) | (product @ e_1 @ e_4 @ e_1))),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl1667, zip_derived_cl36])).
% 0.61/1.15 thf(zip_derived_cl51, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.61/1.15 thf(zip_derived_cl1763, plain,
% 0.61/1.15 (( (product @ e_1 @ e_3 @ e_1) | (equalish @ e_1 @ e_4))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl1674, zip_derived_cl51])).
% 0.61/1.15 thf(zip_derived_cl27, plain, (~ (equalish @ e_1 @ e_4)),
% 0.61/1.15 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 0.61/1.15 thf(zip_derived_cl1776, plain, ( (product @ e_1 @ e_3 @ e_1)),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl1763, zip_derived_cl27])).
% 0.61/1.15 thf(zip_derived_cl51, plain,
% 0.61/1.15 (![X0 : $i, X1 : $i]:
% 0.61/1.15 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.61/1.15 thf(zip_derived_cl1792, plain, ( (equalish @ e_1 @ e_3)),
% 0.61/1.15 inference('sup-', [status(thm)], [zip_derived_cl1776, zip_derived_cl51])).
% 0.61/1.15 thf(zip_derived_cl1810, plain, ($false),
% 0.61/1.15 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl1792])).
% 0.61/1.15
% 0.61/1.15 % SZS output end Refutation
% 0.61/1.15
% 0.61/1.15
% 0.61/1.15 % Terminating...
% 4.30/1.28 % Runner terminated.
% 4.30/1.29 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------