%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP124-8.004 : TPTP v9.2.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.3fPoqAlmxR true
% Computer : n010.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 3.89s 1.16s
% Output : Refutation 4.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.10 % Problem : GRP124-8.004 : TPTP v9.2.0. Released v1.2.0.
% 0.04/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.3fPoqAlmxR true
% 0.10/0.31 % Computer : n010.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Oct 1 14:15:23 EDT 2025
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % Running portfolio for 300 s
% 0.10/0.31 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.31 % Number of cores: 8
% 0.15/0.31 % Python version: Python 3.6.8
% 0.15/0.31 % Running in FO mode
% 0.46/0.56 % Total configuration time : 435
% 0.46/0.56 % Estimated wc time : 1092
% 0.46/0.56 % Estimated cpu time (7 cpus) : 156.0
% 0.47/0.67 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.47/0.67 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.47/0.67 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.47/0.68 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.47/0.68 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.47/0.68 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.47/0.68 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.48/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 3.89/1.16 % Solved by fo/fo7.sh.
% 3.89/1.16 % done 408 iterations in 0.452s
% 3.89/1.16 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 3.89/1.16 % SZS output start Refutation
% 3.89/1.16 thf(e_4_type, type, e_4: $i).
% 3.89/1.16 thf(e_3_type, type, e_3: $i).
% 3.89/1.16 thf(e_2_type, type, e_2: $i).
% 3.89/1.16 thf(e_1_type, type, e_1: $i).
% 3.89/1.16 thf(product2_type, type, product2: $i > $i > $i > $o).
% 3.89/1.16 thf(group_element_type, type, group_element: $i > $o).
% 3.89/1.16 thf(product1_type, type, product1: $i > $i > $i > $o).
% 3.89/1.16 thf(equalish_type, type, equalish: $i > $i > $o).
% 3.89/1.16 thf(product1_total_function1, axiom,
% 3.89/1.16 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 3.89/1.16 ( product1 @ X @ Y @ e_1 ) | ( product1 @ X @ Y @ e_2 ) |
% 3.89/1.16 ( product1 @ X @ Y @ e_3 ) | ( product1 @ X @ Y @ e_4 ))).
% 3.89/1.16 thf(zip_derived_cl37, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 (~ (group_element @ X0)
% 3.89/1.16 | ~ (group_element @ X1)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_1)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_2)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_3)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_4))),
% 3.89/1.16 inference('cnf', [status(esa)], [product1_total_function1])).
% 3.89/1.16 thf(product1_idempotence, axiom, (product1 @ X @ X @ X)).
% 3.89/1.16 thf(zip_derived_cl41, plain, (![X0 : $i]: (product1 @ X0 @ X0 @ X0)),
% 3.89/1.16 inference('cnf', [status(esa)], [product1_idempotence])).
% 3.89/1.16 thf(product1_right_cancellation, axiom,
% 3.89/1.16 (( ~( product1 @ X @ W @ Y ) ) | ( ~( product1 @ X @ Z @ Y ) ) |
% 3.89/1.16 ( equalish @ W @ Z ))).
% 3.89/1.16 thf(zip_derived_cl39, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.89/1.16 (~ (product1 @ X0 @ X1 @ X2)
% 3.89/1.16 | ~ (product1 @ X0 @ X3 @ X2)
% 3.89/1.16 | (equalish @ X1 @ X3))),
% 3.89/1.16 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 3.89/1.16 thf(zip_derived_cl55, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 3.89/1.16 thf(zip_derived_cl168, plain,
% 3.89/1.16 (![X0 : $i]:
% 3.89/1.16 ( (product1 @ e_4 @ X0 @ e_3)
% 3.89/1.16 | (product1 @ e_4 @ X0 @ e_2)
% 3.89/1.16 | (product1 @ e_4 @ X0 @ e_1)
% 3.89/1.16 | ~ (group_element @ X0)
% 3.89/1.16 | ~ (group_element @ e_4)
% 3.89/1.16 | (equalish @ e_4 @ X0))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl55])).
% 3.89/1.16 thf(element_4, axiom, (group_element @ e_4)).
% 3.89/1.16 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 3.89/1.16 inference('cnf', [status(esa)], [element_4])).
% 3.89/1.16 thf(zip_derived_cl174, plain,
% 3.89/1.16 (![X0 : $i]:
% 3.89/1.16 ( (product1 @ e_4 @ X0 @ e_3)
% 3.89/1.16 | (product1 @ e_4 @ X0 @ e_2)
% 3.89/1.16 | (product1 @ e_4 @ X0 @ e_1)
% 3.89/1.16 | ~ (group_element @ X0)
% 3.89/1.16 | (equalish @ e_4 @ X0))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl168, zip_derived_cl24])).
% 3.89/1.16 thf(zip_derived_cl37, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 (~ (group_element @ X0)
% 3.89/1.16 | ~ (group_element @ X1)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_1)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_2)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_3)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_4))),
% 3.89/1.16 inference('cnf', [status(esa)], [product1_total_function1])).
% 3.89/1.16 thf(zip_derived_cl37, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 (~ (group_element @ X0)
% 3.89/1.16 | ~ (group_element @ X1)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_1)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_2)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_3)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_4))),
% 3.89/1.16 inference('cnf', [status(esa)], [product1_total_function1])).
% 3.89/1.16 thf(zip_derived_cl174, plain,
% 3.89/1.16 (![X0 : $i]:
% 3.89/1.16 ( (product1 @ e_4 @ X0 @ e_3)
% 3.89/1.16 | (product1 @ e_4 @ X0 @ e_2)
% 3.89/1.16 | (product1 @ e_4 @ X0 @ e_1)
% 3.89/1.16 | ~ (group_element @ X0)
% 3.89/1.16 | (equalish @ e_4 @ X0))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl168, zip_derived_cl24])).
% 3.89/1.16 thf(zip_derived_cl41, plain, (![X0 : $i]: (product1 @ X0 @ X0 @ X0)),
% 3.89/1.16 inference('cnf', [status(esa)], [product1_idempotence])).
% 3.89/1.16 thf(product1_left_cancellation, axiom,
% 3.89/1.16 (( ~( product1 @ W @ Y @ X ) ) | ( ~( product1 @ Z @ Y @ X ) ) |
% 3.89/1.16 ( equalish @ W @ Z ))).
% 3.89/1.16 thf(zip_derived_cl40, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.89/1.16 (~ (product1 @ X0 @ X1 @ X2)
% 3.89/1.16 | ~ (product1 @ X3 @ X1 @ X2)
% 3.89/1.16 | (equalish @ X0 @ X3))),
% 3.89/1.16 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 3.89/1.16 thf(zip_derived_cl59, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 3.89/1.16 thf(zip_derived_cl259, plain,
% 3.89/1.16 (( (equalish @ e_4 @ e_3)
% 3.89/1.16 | ~ (group_element @ e_3)
% 3.89/1.16 | (product1 @ e_4 @ e_3 @ e_1)
% 3.89/1.16 | (product1 @ e_4 @ e_3 @ e_2)
% 3.89/1.16 | (equalish @ e_3 @ e_4))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl174, zip_derived_cl59])).
% 3.89/1.16 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 3.89/1.16 thf(zip_derived_cl36, plain, (~ (equalish @ e_4 @ e_3)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 3.89/1.16 thf(element_3, axiom, (group_element @ e_3)).
% 3.89/1.16 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 3.89/1.16 inference('cnf', [status(esa)], [element_3])).
% 3.89/1.16 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 3.89/1.16 thf(zip_derived_cl33, plain, (~ (equalish @ e_3 @ e_4)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 3.89/1.16 thf(zip_derived_cl261, plain,
% 3.89/1.16 (( (product1 @ e_4 @ e_3 @ e_1) | (product1 @ e_4 @ e_3 @ e_2))),
% 3.89/1.16 inference('demod', [status(thm)],
% 3.89/1.16 [zip_derived_cl259, zip_derived_cl36, zip_derived_cl23,
% 3.89/1.16 zip_derived_cl33])).
% 3.89/1.16 thf(qg2a, conjecture,
% 3.89/1.16 (~( ( product2 @ Z2 @ Y @ X ) | ( ~( product1 @ Z1 @ X @ Z2 ) ) |
% 3.89/1.16 ( ~( product1 @ X @ Y @ Z1 ) ) ))).
% 3.89/1.16 thf(zf_stmt_0, negated_conjecture,
% 3.89/1.16 (( product2 @ Z2 @ Y @ X ) | ( ~( product1 @ Z1 @ X @ Z2 ) ) |
% 3.89/1.16 ( ~( product1 @ X @ Y @ Z1 ) )),
% 3.89/1.16 inference('cnf.neg', [status(esa)], [qg2a])).
% 3.89/1.16 thf(zip_derived_cl47, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.89/1.16 ( (product2 @ X0 @ X1 @ X2)
% 3.89/1.16 | ~ (product1 @ X3 @ X2 @ X0)
% 3.89/1.16 | ~ (product1 @ X2 @ X1 @ X3))),
% 3.89/1.16 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.89/1.16 thf(zip_derived_cl265, plain,
% 3.89/1.16 (![X0 : $i]:
% 3.89/1.16 ( (product1 @ e_4 @ e_3 @ e_1)
% 3.89/1.16 | ~ (product1 @ e_3 @ X0 @ e_4)
% 3.89/1.16 | (product2 @ e_2 @ X0 @ e_3))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl261, zip_derived_cl47])).
% 3.89/1.16 thf(product2_idempotence, axiom, (product2 @ X @ X @ X)).
% 3.89/1.16 thf(zip_derived_cl46, plain, (![X0 : $i]: (product2 @ X0 @ X0 @ X0)),
% 3.89/1.16 inference('cnf', [status(esa)], [product2_idempotence])).
% 3.89/1.16 thf(product2_total_function2, axiom,
% 3.89/1.16 (( ~( product2 @ X @ Y @ W ) ) | ( ~( product2 @ X @ Y @ Z ) ) |
% 3.89/1.16 ( equalish @ W @ Z ))).
% 3.89/1.16 thf(zip_derived_cl43, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.89/1.16 (~ (product2 @ X0 @ X1 @ X2)
% 3.89/1.16 | ~ (product2 @ X0 @ X1 @ X3)
% 3.89/1.16 | (equalish @ X2 @ X3))),
% 3.89/1.16 inference('cnf', [status(esa)], [product2_total_function2])).
% 3.89/1.16 thf(zip_derived_cl63, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 ( (equalish @ X0 @ X1) | ~ (product2 @ X0 @ X0 @ X1))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl43])).
% 3.89/1.16 thf(zip_derived_cl280, plain,
% 3.89/1.16 ((~ (product1 @ e_3 @ e_2 @ e_4)
% 3.89/1.16 | (product1 @ e_4 @ e_3 @ e_1)
% 3.89/1.16 | (equalish @ e_2 @ e_3))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl265, zip_derived_cl63])).
% 3.89/1.16 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 3.89/1.16 thf(zip_derived_cl29, plain, (~ (equalish @ e_2 @ e_3)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 3.89/1.16 thf(zip_derived_cl282, plain,
% 3.89/1.16 ((~ (product1 @ e_3 @ e_2 @ e_4) | (product1 @ e_4 @ e_3 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl280, zip_derived_cl29])).
% 3.89/1.16 thf(zip_derived_cl284, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_2 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_1)
% 3.89/1.16 | ~ (group_element @ e_2)
% 3.89/1.16 | ~ (group_element @ e_3)
% 3.89/1.16 | (product1 @ e_4 @ e_3 @ e_1))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl282])).
% 3.89/1.16 thf(element_2, axiom, (group_element @ e_2)).
% 3.89/1.16 thf(zip_derived_cl22, plain, ( (group_element @ e_2)),
% 3.89/1.16 inference('cnf', [status(esa)], [element_2])).
% 3.89/1.16 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 3.89/1.16 inference('cnf', [status(esa)], [element_3])).
% 3.89/1.16 thf(zip_derived_cl285, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_2 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_1)
% 3.89/1.16 | (product1 @ e_4 @ e_3 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)],
% 3.89/1.16 [zip_derived_cl284, zip_derived_cl22, zip_derived_cl23])).
% 3.89/1.16 thf(zip_derived_cl47, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.89/1.16 ( (product2 @ X0 @ X1 @ X2)
% 3.89/1.16 | ~ (product1 @ X3 @ X2 @ X0)
% 3.89/1.16 | ~ (product1 @ X2 @ X1 @ X3))),
% 3.89/1.16 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.89/1.16 thf(zip_derived_cl291, plain,
% 3.89/1.16 (![X0 : $i]:
% 3.89/1.16 ( (product1 @ e_3 @ e_2 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_3)
% 3.89/1.16 | ~ (product1 @ e_3 @ X0 @ e_4)
% 3.89/1.16 | (product2 @ e_1 @ X0 @ e_3))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl285, zip_derived_cl47])).
% 3.89/1.16 thf(zip_derived_cl63, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 ( (equalish @ X0 @ X1) | ~ (product2 @ X0 @ X0 @ X1))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl43])).
% 3.89/1.16 thf(zip_derived_cl512, plain,
% 3.89/1.16 ((~ (product1 @ e_3 @ e_1 @ e_4)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_1)
% 3.89/1.16 | (equalish @ e_1 @ e_3))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl291, zip_derived_cl63])).
% 3.89/1.16 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 3.89/1.16 thf(zip_derived_cl26, plain, (~ (equalish @ e_1 @ e_3)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 3.89/1.16 thf(zip_derived_cl516, plain,
% 3.89/1.16 ((~ (product1 @ e_3 @ e_1 @ e_4)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl512, zip_derived_cl26])).
% 3.89/1.16 thf(zip_derived_cl521, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | ~ (group_element @ e_1)
% 3.89/1.16 | ~ (group_element @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_3))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl516])).
% 3.89/1.16 thf(element_1, axiom, (group_element @ e_1)).
% 3.89/1.16 thf(zip_derived_cl21, plain, ( (group_element @ e_1)),
% 3.89/1.16 inference('cnf', [status(esa)], [element_1])).
% 3.89/1.16 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 3.89/1.16 inference('cnf', [status(esa)], [element_3])).
% 3.89/1.16 thf(zip_derived_cl522, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_3))),
% 3.89/1.16 inference('demod', [status(thm)],
% 3.89/1.16 [zip_derived_cl521, zip_derived_cl21, zip_derived_cl23])).
% 3.89/1.16 thf(zip_derived_cl55, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 3.89/1.16 thf(zip_derived_cl621, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_2 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_3)
% 3.89/1.16 | (equalish @ e_3 @ e_2))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl522, zip_derived_cl55])).
% 3.89/1.16 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 3.89/1.16 thf(zip_derived_cl32, plain, (~ (equalish @ e_3 @ e_2)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 3.89/1.16 thf(zip_derived_cl626, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_2 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_3))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl621, zip_derived_cl32])).
% 3.89/1.16 thf(zip_derived_cl59, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 3.89/1.16 thf(zip_derived_cl631, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_1)
% 3.89/1.16 | (equalish @ e_2 @ e_3))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl626, zip_derived_cl59])).
% 3.89/1.16 thf(zip_derived_cl29, plain, (~ (equalish @ e_2 @ e_3)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 3.89/1.16 thf(zip_derived_cl635, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl631, zip_derived_cl29])).
% 3.89/1.16 thf(zip_derived_cl174, plain,
% 3.89/1.16 (![X0 : $i]:
% 3.89/1.16 ( (product1 @ e_4 @ X0 @ e_3)
% 3.89/1.16 | (product1 @ e_4 @ X0 @ e_2)
% 3.89/1.16 | (product1 @ e_4 @ X0 @ e_1)
% 3.89/1.16 | ~ (group_element @ X0)
% 3.89/1.16 | (equalish @ e_4 @ X0))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl168, zip_derived_cl24])).
% 3.89/1.16 thf(zip_derived_cl37, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 (~ (group_element @ X0)
% 3.89/1.16 | ~ (group_element @ X1)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_1)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_2)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_3)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_4))),
% 3.89/1.16 inference('cnf', [status(esa)], [product1_total_function1])).
% 3.89/1.16 thf(zip_derived_cl59, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 3.89/1.16 thf(zip_derived_cl172, plain,
% 3.89/1.16 (![X0 : $i]:
% 3.89/1.16 ( (product1 @ X0 @ e_4 @ e_3)
% 3.89/1.16 | (product1 @ X0 @ e_4 @ e_2)
% 3.89/1.16 | (product1 @ X0 @ e_4 @ e_1)
% 3.89/1.16 | ~ (group_element @ e_4)
% 3.89/1.16 | ~ (group_element @ X0)
% 3.89/1.16 | (equalish @ e_4 @ X0))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl59])).
% 3.89/1.16 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 3.89/1.16 inference('cnf', [status(esa)], [element_4])).
% 3.89/1.16 thf(zip_derived_cl178, plain,
% 3.89/1.16 (![X0 : $i]:
% 3.89/1.16 ( (product1 @ X0 @ e_4 @ e_3)
% 3.89/1.16 | (product1 @ X0 @ e_4 @ e_2)
% 3.89/1.16 | (product1 @ X0 @ e_4 @ e_1)
% 3.89/1.16 | ~ (group_element @ X0)
% 3.89/1.16 | (equalish @ e_4 @ X0))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl172, zip_derived_cl24])).
% 3.89/1.16 thf(zip_derived_cl55, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 3.89/1.16 thf(zip_derived_cl339, plain,
% 3.89/1.16 (( (equalish @ e_4 @ e_3)
% 3.89/1.16 | ~ (group_element @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_4 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_4 @ e_2)
% 3.89/1.16 | (equalish @ e_3 @ e_4))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl178, zip_derived_cl55])).
% 3.89/1.16 thf(zip_derived_cl36, plain, (~ (equalish @ e_4 @ e_3)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 3.89/1.16 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 3.89/1.16 inference('cnf', [status(esa)], [element_3])).
% 3.89/1.16 thf(zip_derived_cl33, plain, (~ (equalish @ e_3 @ e_4)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 3.89/1.16 thf(zip_derived_cl345, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_4 @ e_1) | (product1 @ e_3 @ e_4 @ e_2))),
% 3.89/1.16 inference('demod', [status(thm)],
% 3.89/1.16 [zip_derived_cl339, zip_derived_cl36, zip_derived_cl23,
% 3.89/1.16 zip_derived_cl33])).
% 3.89/1.16 thf(zip_derived_cl47, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.89/1.16 ( (product2 @ X0 @ X1 @ X2)
% 3.89/1.16 | ~ (product1 @ X3 @ X2 @ X0)
% 3.89/1.16 | ~ (product1 @ X2 @ X1 @ X3))),
% 3.89/1.16 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.89/1.16 thf(zip_derived_cl353, plain,
% 3.89/1.16 (![X0 : $i]:
% 3.89/1.16 ( (product1 @ e_3 @ e_4 @ e_1)
% 3.89/1.16 | ~ (product1 @ e_4 @ X0 @ e_3)
% 3.89/1.16 | (product2 @ e_2 @ X0 @ e_4))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl345, zip_derived_cl47])).
% 3.89/1.16 thf(zip_derived_cl63, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 ( (equalish @ X0 @ X1) | ~ (product2 @ X0 @ X0 @ X1))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl43])).
% 3.89/1.16 thf(zip_derived_cl357, plain,
% 3.89/1.16 ((~ (product1 @ e_4 @ e_2 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_4 @ e_1)
% 3.89/1.16 | (equalish @ e_2 @ e_4))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl353, zip_derived_cl63])).
% 3.89/1.16 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 3.89/1.16 thf(zip_derived_cl30, plain, (~ (equalish @ e_2 @ e_4)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 3.89/1.16 thf(zip_derived_cl360, plain,
% 3.89/1.16 ((~ (product1 @ e_4 @ e_2 @ e_3) | (product1 @ e_3 @ e_4 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl357, zip_derived_cl30])).
% 3.89/1.16 thf(zip_derived_cl363, plain,
% 3.89/1.16 (( (equalish @ e_4 @ e_2)
% 3.89/1.16 | ~ (group_element @ e_2)
% 3.89/1.16 | (product1 @ e_4 @ e_2 @ e_1)
% 3.89/1.16 | (product1 @ e_4 @ e_2 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_4 @ e_1))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl174, zip_derived_cl360])).
% 3.89/1.16 thf(e_4_is_not_e_2, axiom, (~( equalish @ e_4 @ e_2 ))).
% 3.89/1.16 thf(zip_derived_cl35, plain, (~ (equalish @ e_4 @ e_2)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 3.89/1.16 thf(zip_derived_cl22, plain, ( (group_element @ e_2)),
% 3.89/1.16 inference('cnf', [status(esa)], [element_2])).
% 3.89/1.16 thf(zip_derived_cl364, plain,
% 3.89/1.16 (( (product1 @ e_4 @ e_2 @ e_1)
% 3.89/1.16 | (product1 @ e_4 @ e_2 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_4 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)],
% 3.89/1.16 [zip_derived_cl363, zip_derived_cl35, zip_derived_cl22])).
% 3.89/1.16 thf(zip_derived_cl59, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 3.89/1.16 thf(zip_derived_cl369, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_4 @ e_1)
% 3.89/1.16 | (product1 @ e_4 @ e_2 @ e_1)
% 3.89/1.16 | (equalish @ e_2 @ e_4))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl364, zip_derived_cl59])).
% 3.89/1.16 thf(zip_derived_cl30, plain, (~ (equalish @ e_2 @ e_4)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 3.89/1.16 thf(zip_derived_cl371, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_4 @ e_1) | (product1 @ e_4 @ e_2 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl369, zip_derived_cl30])).
% 3.89/1.16 thf(zip_derived_cl40, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.89/1.16 (~ (product1 @ X0 @ X1 @ X2)
% 3.89/1.16 | ~ (product1 @ X3 @ X1 @ X2)
% 3.89/1.16 | (equalish @ X0 @ X3))),
% 3.89/1.16 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 3.89/1.16 thf(zip_derived_cl375, plain,
% 3.89/1.16 (![X0 : $i]:
% 3.89/1.16 ( (product1 @ e_3 @ e_4 @ e_1)
% 3.89/1.16 | (equalish @ e_4 @ X0)
% 3.89/1.16 | ~ (product1 @ X0 @ e_2 @ e_1))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl371, zip_derived_cl40])).
% 3.89/1.16 thf(zip_derived_cl754, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_3)
% 3.89/1.16 | (equalish @ e_4 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_4 @ e_1))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl635, zip_derived_cl375])).
% 3.89/1.16 thf(zip_derived_cl36, plain, (~ (equalish @ e_4 @ e_3)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 3.89/1.16 thf(zip_derived_cl757, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_4 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl754, zip_derived_cl36])).
% 3.89/1.16 thf(zip_derived_cl635, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_2 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl631, zip_derived_cl29])).
% 3.89/1.16 thf(zip_derived_cl39, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.89/1.16 (~ (product1 @ X0 @ X1 @ X2)
% 3.89/1.16 | ~ (product1 @ X0 @ X3 @ X2)
% 3.89/1.16 | (equalish @ X1 @ X3))),
% 3.89/1.16 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 3.89/1.16 thf(zip_derived_cl749, plain,
% 3.89/1.16 (![X0 : $i]:
% 3.89/1.16 ( (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_3)
% 3.89/1.16 | (equalish @ e_2 @ X0)
% 3.89/1.16 | ~ (product1 @ e_3 @ X0 @ e_1))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl635, zip_derived_cl39])).
% 3.89/1.16 thf(zip_derived_cl1772, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (equalish @ e_2 @ e_4)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl757, zip_derived_cl749])).
% 3.89/1.16 thf(zip_derived_cl30, plain, (~ (equalish @ e_2 @ e_4)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 3.89/1.16 thf(zip_derived_cl1781, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl1772, zip_derived_cl30])).
% 3.89/1.16 thf(zip_derived_cl1782, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_3))),
% 3.89/1.16 inference('simplify', [status(thm)], [zip_derived_cl1781])).
% 3.89/1.16 thf(zip_derived_cl55, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 3.89/1.16 thf(zip_derived_cl1787, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (equalish @ e_3 @ e_1))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl1782, zip_derived_cl55])).
% 3.89/1.16 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 3.89/1.16 thf(zip_derived_cl31, plain, (~ (equalish @ e_3 @ e_1)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 3.89/1.16 thf(zip_derived_cl1797, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_2) | (product1 @ e_3 @ e_1 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl1787, zip_derived_cl31])).
% 3.89/1.16 thf(zip_derived_cl345, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_4 @ e_1) | (product1 @ e_3 @ e_4 @ e_2))),
% 3.89/1.16 inference('demod', [status(thm)],
% 3.89/1.16 [zip_derived_cl339, zip_derived_cl36, zip_derived_cl23,
% 3.89/1.16 zip_derived_cl33])).
% 3.89/1.16 thf(zip_derived_cl39, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.89/1.16 (~ (product1 @ X0 @ X1 @ X2)
% 3.89/1.16 | ~ (product1 @ X0 @ X3 @ X2)
% 3.89/1.16 | (equalish @ X1 @ X3))),
% 3.89/1.16 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 3.89/1.16 thf(zip_derived_cl351, plain,
% 3.89/1.16 (![X0 : $i]:
% 3.89/1.16 ( (product1 @ e_3 @ e_4 @ e_1)
% 3.89/1.16 | (equalish @ e_4 @ X0)
% 3.89/1.16 | ~ (product1 @ e_3 @ X0 @ e_2))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl345, zip_derived_cl39])).
% 3.89/1.16 thf(zip_derived_cl1811, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (equalish @ e_4 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_4 @ e_1))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl1797, zip_derived_cl351])).
% 3.89/1.16 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 3.89/1.16 thf(zip_derived_cl34, plain, (~ (equalish @ e_4 @ e_1)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 3.89/1.16 thf(zip_derived_cl1816, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_1) | (product1 @ e_3 @ e_4 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl1811, zip_derived_cl34])).
% 3.89/1.16 thf(zip_derived_cl47, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.89/1.16 ( (product2 @ X0 @ X1 @ X2)
% 3.89/1.16 | ~ (product1 @ X3 @ X2 @ X0)
% 3.89/1.16 | ~ (product1 @ X2 @ X1 @ X3))),
% 3.89/1.16 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.89/1.16 thf(zip_derived_cl1820, plain,
% 3.89/1.16 (![X0 : $i]:
% 3.89/1.16 ( (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | ~ (product1 @ e_4 @ X0 @ e_3)
% 3.89/1.16 | (product2 @ e_1 @ X0 @ e_4))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl1816, zip_derived_cl47])).
% 3.89/1.16 thf(zip_derived_cl63, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 ( (equalish @ X0 @ X1) | ~ (product2 @ X0 @ X0 @ X1))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl43])).
% 3.89/1.16 thf(zip_derived_cl1947, plain,
% 3.89/1.16 ((~ (product1 @ e_4 @ e_1 @ e_3)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (equalish @ e_1 @ e_4))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl1820, zip_derived_cl63])).
% 3.89/1.16 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 3.89/1.16 thf(zip_derived_cl27, plain, (~ (equalish @ e_1 @ e_4)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 3.89/1.16 thf(zip_derived_cl1951, plain,
% 3.89/1.16 ((~ (product1 @ e_4 @ e_1 @ e_3) | (product1 @ e_3 @ e_1 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl1947, zip_derived_cl27])).
% 3.89/1.16 thf(zip_derived_cl1956, plain,
% 3.89/1.16 (( (equalish @ e_4 @ e_1)
% 3.89/1.16 | ~ (group_element @ e_1)
% 3.89/1.16 | (product1 @ e_4 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_4 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl174, zip_derived_cl1951])).
% 3.89/1.16 thf(zip_derived_cl34, plain, (~ (equalish @ e_4 @ e_1)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 3.89/1.16 thf(zip_derived_cl21, plain, ( (group_element @ e_1)),
% 3.89/1.16 inference('cnf', [status(esa)], [element_1])).
% 3.89/1.16 thf(zip_derived_cl1958, plain,
% 3.89/1.16 (( (product1 @ e_4 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_4 @ e_1 @ e_2)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)],
% 3.89/1.16 [zip_derived_cl1956, zip_derived_cl34, zip_derived_cl21])).
% 3.89/1.16 thf(zip_derived_cl1797, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_2) | (product1 @ e_3 @ e_1 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl1787, zip_derived_cl31])).
% 3.89/1.16 thf(zip_derived_cl40, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.89/1.16 (~ (product1 @ X0 @ X1 @ X2)
% 3.89/1.16 | ~ (product1 @ X3 @ X1 @ X2)
% 3.89/1.16 | (equalish @ X0 @ X3))),
% 3.89/1.16 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 3.89/1.16 thf(zip_derived_cl1805, plain,
% 3.89/1.16 (![X0 : $i]:
% 3.89/1.16 ( (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (equalish @ e_3 @ X0)
% 3.89/1.16 | ~ (product1 @ X0 @ e_1 @ e_2))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl1797, zip_derived_cl40])).
% 3.89/1.16 thf(zip_derived_cl1981, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_4 @ e_1 @ e_1)
% 3.89/1.16 | (equalish @ e_3 @ e_4)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl1958, zip_derived_cl1805])).
% 3.89/1.16 thf(zip_derived_cl33, plain, (~ (equalish @ e_3 @ e_4)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 3.89/1.16 thf(zip_derived_cl1989, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_4 @ e_1 @ e_1)
% 3.89/1.16 | (product1 @ e_3 @ e_1 @ e_1))),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl1981, zip_derived_cl33])).
% 3.89/1.16 thf(zip_derived_cl1990, plain,
% 3.89/1.16 (( (product1 @ e_4 @ e_1 @ e_1) | (product1 @ e_3 @ e_1 @ e_1))),
% 3.89/1.16 inference('simplify', [status(thm)], [zip_derived_cl1989])).
% 3.89/1.16 thf(zip_derived_cl59, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 3.89/1.16 thf(zip_derived_cl2000, plain,
% 3.89/1.16 (( (product1 @ e_3 @ e_1 @ e_1) | (equalish @ e_1 @ e_4))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl1990, zip_derived_cl59])).
% 3.89/1.16 thf(zip_derived_cl27, plain, (~ (equalish @ e_1 @ e_4)),
% 3.89/1.16 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 3.89/1.16 thf(zip_derived_cl2013, plain, ( (product1 @ e_3 @ e_1 @ e_1)),
% 3.89/1.16 inference('demod', [status(thm)], [zip_derived_cl2000, zip_derived_cl27])).
% 3.89/1.16 thf(zip_derived_cl37, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 (~ (group_element @ X0)
% 3.89/1.16 | ~ (group_element @ X1)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_1)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_2)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_3)
% 3.89/1.16 | (product1 @ X0 @ X1 @ e_4))),
% 3.89/1.16 inference('cnf', [status(esa)], [product1_total_function1])).
% 3.89/1.16 thf(zip_derived_cl41, plain, (![X0 : $i]: (product1 @ X0 @ X0 @ X0)),
% 3.89/1.16 inference('cnf', [status(esa)], [product1_idempotence])).
% 3.89/1.16 thf(product1_total_function2, axiom,
% 3.89/1.16 (( ~( product1 @ X @ Y @ W ) ) | ( ~( product1 @ X @ Y @ Z ) ) |
% 3.89/1.16 ( equalish @ W @ Z ))).
% 3.89/1.16 thf(zip_derived_cl38, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.89/1.16 (~ (product1 @ X0 @ X1 @ X2)
% 3.89/1.16 | ~ (product1 @ X0 @ X1 @ X3)
% 3.89/1.16 | (equalish @ X2 @ X3))),
% 3.89/1.16 inference('cnf', [status(esa)], [product1_total_function2])).
% 3.89/1.16 thf(zip_derived_cl49, plain,
% 3.89/1.16 (![X0 : $i, X1 : $i]:
% 3.89/1.16 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X0 @ X1))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl38])).
% 3.89/1.16 thf(zip_derived_cl167, plain,
% 3.89/1.16 (![X0 : $i]:
% 3.89/1.16 ( (product1 @ X0 @ X0 @ e_3)
% 3.89/1.16 | (product1 @ X0 @ X0 @ e_2)
% 3.89/1.16 | (product1 @ X0 @ X0 @ e_1)
% 3.89/1.16 | ~ (group_element @ X0)
% 3.89/1.16 | ~ (group_element @ X0)
% 3.89/1.16 | (equalish @ X0 @ e_4))),
% 3.89/1.16 inference('sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl49])).
% 4.45/1.16 thf(zip_derived_cl173, plain,
% 4.45/1.16 (![X0 : $i]:
% 4.45/1.16 ( (equalish @ X0 @ e_4)
% 4.45/1.16 | ~ (group_element @ X0)
% 4.45/1.16 | (product1 @ X0 @ X0 @ e_1)
% 4.45/1.16 | (product1 @ X0 @ X0 @ e_2)
% 4.45/1.16 | (product1 @ X0 @ X0 @ e_3))),
% 4.45/1.16 inference('simplify', [status(thm)], [zip_derived_cl167])).
% 4.45/1.16 thf(zip_derived_cl49, plain,
% 4.45/1.16 (![X0 : $i, X1 : $i]:
% 4.45/1.16 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X0 @ X1))),
% 4.45/1.16 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl38])).
% 4.45/1.16 thf(zip_derived_cl183, plain,
% 4.45/1.16 (![X0 : $i]:
% 4.45/1.16 ( (product1 @ X0 @ X0 @ e_2)
% 4.45/1.16 | (product1 @ X0 @ X0 @ e_1)
% 4.45/1.16 | ~ (group_element @ X0)
% 4.45/1.16 | (equalish @ X0 @ e_4)
% 4.45/1.16 | (equalish @ X0 @ e_3))),
% 4.45/1.16 inference('sup-', [status(thm)], [zip_derived_cl173, zip_derived_cl49])).
% 4.45/1.16 thf(zip_derived_cl49, plain,
% 4.45/1.16 (![X0 : $i, X1 : $i]:
% 4.45/1.16 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X0 @ X1))),
% 4.45/1.16 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl38])).
% 4.45/1.16 thf(zip_derived_cl198, plain,
% 4.45/1.16 (![X0 : $i]:
% 4.45/1.16 ( (equalish @ X0 @ e_3)
% 4.45/1.16 | (equalish @ X0 @ e_4)
% 4.45/1.16 | ~ (group_element @ X0)
% 4.45/1.16 | (product1 @ X0 @ X0 @ e_1)
% 4.45/1.16 | (equalish @ X0 @ e_2))),
% 4.45/1.16 inference('sup-', [status(thm)], [zip_derived_cl183, zip_derived_cl49])).
% 4.45/1.16 thf(zip_derived_cl40, plain,
% 4.45/1.16 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.45/1.16 (~ (product1 @ X0 @ X1 @ X2)
% 4.45/1.16 | ~ (product1 @ X3 @ X1 @ X2)
% 4.45/1.16 | (equalish @ X0 @ X3))),
% 4.45/1.16 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 4.45/1.16 thf(zip_derived_cl211, plain,
% 4.45/1.16 (![X0 : $i, X1 : $i]:
% 4.45/1.16 ( (equalish @ X0 @ e_2)
% 4.45/1.16 | ~ (group_element @ X0)
% 4.45/1.16 | (equalish @ X0 @ e_4)
% 4.45/1.16 | (equalish @ X0 @ e_3)
% 4.45/1.16 | (equalish @ X0 @ X1)
% 4.45/1.16 | ~ (product1 @ X1 @ X0 @ e_1))),
% 4.45/1.16 inference('sup-', [status(thm)], [zip_derived_cl198, zip_derived_cl40])).
% 4.45/1.16 thf(zip_derived_cl2035, plain,
% 4.45/1.16 (( (equalish @ e_1 @ e_3)
% 4.45/1.16 | (equalish @ e_1 @ e_3)
% 4.45/1.16 | (equalish @ e_1 @ e_4)
% 4.45/1.16 | ~ (group_element @ e_1)
% 4.45/1.16 | (equalish @ e_1 @ e_2))),
% 4.45/1.16 inference('sup-', [status(thm)], [zip_derived_cl2013, zip_derived_cl211])).
% 4.45/1.16 thf(zip_derived_cl26, plain, (~ (equalish @ e_1 @ e_3)),
% 4.45/1.16 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 4.45/1.16 thf(zip_derived_cl26, plain, (~ (equalish @ e_1 @ e_3)),
% 4.45/1.16 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 4.45/1.16 thf(zip_derived_cl27, plain, (~ (equalish @ e_1 @ e_4)),
% 4.45/1.16 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 4.45/1.16 thf(zip_derived_cl21, plain, ( (group_element @ e_1)),
% 4.45/1.16 inference('cnf', [status(esa)], [element_1])).
% 4.45/1.16 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 4.45/1.16 thf(zip_derived_cl25, plain, (~ (equalish @ e_1 @ e_2)),
% 4.45/1.16 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 4.45/1.16 thf(zip_derived_cl2045, plain, ($false),
% 4.45/1.16 inference('demod', [status(thm)],
% 4.45/1.16 [zip_derived_cl2035, zip_derived_cl26, zip_derived_cl26,
% 4.45/1.16 zip_derived_cl27, zip_derived_cl21, zip_derived_cl25])).
% 4.45/1.16
% 4.45/1.16 % SZS output end Refutation
% 4.45/1.16
% 4.45/1.16
% 4.45/1.16 % Terminating...
% 4.45/1.18 % Runner terminated.
% 4.45/1.21 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------