TSTP Solution File: GRP124-9.004 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP124-9.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.FusKQJP2an true
% Computer : n021.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 01:50:06 EDT 2023
% Result : Unsatisfiable 3.61s 1.21s
% Output : Refutation 3.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP124-9.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.FusKQJP2an true
% 0.11/0.32 % Computer : n021.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 21:07:43 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % Running portfolio for 300 s
% 0.11/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.33 % Number of cores: 8
% 0.11/0.33 % Python version: Python 3.6.8
% 0.11/0.33 % Running in FO mode
% 0.18/0.59 % Total configuration time : 435
% 0.18/0.59 % Estimated wc time : 1092
% 0.18/0.59 % Estimated cpu time (7 cpus) : 156.0
% 0.18/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.18/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.18/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.18/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.18/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.18/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.18/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 3.61/1.21 % Solved by fo/fo4.sh.
% 3.61/1.21 % done 509 iterations in 0.464s
% 3.61/1.21 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 3.61/1.21 % SZS output start Refutation
% 3.61/1.21 thf(e_1_type, type, e_1: $i).
% 3.61/1.21 thf(e_2_type, type, e_2: $i).
% 3.61/1.21 thf(group_element_type, type, group_element: $i > $o).
% 3.61/1.21 thf(e_4_type, type, e_4: $i).
% 3.61/1.21 thf(product1_type, type, product1: $i > $i > $i > $o).
% 3.61/1.21 thf(product2_type, type, product2: $i > $i > $i > $o).
% 3.61/1.21 thf(equalish_type, type, equalish: $i > $i > $o).
% 3.61/1.21 thf(e_3_type, type, e_3: $i).
% 3.61/1.21 thf(e_4_is_not_e_2, axiom, (~( equalish @ e_4 @ e_2 ))).
% 3.61/1.21 thf(zip_derived_cl16, plain, (~ (equalish @ e_4 @ e_2)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 3.61/1.21 thf(product1_idempotence, axiom, (product1 @ X @ X @ X)).
% 3.61/1.21 thf(zip_derived_cl22, plain, (![X0 : $i]: (product1 @ X0 @ X0 @ X0)),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_idempotence])).
% 3.61/1.21 thf(product1_left_cancellation, axiom,
% 3.61/1.21 (( ~( product1 @ W @ Y @ X ) ) | ( ~( product1 @ Z @ Y @ X ) ) |
% 3.61/1.21 ( equalish @ W @ Z ))).
% 3.61/1.21 thf(zip_derived_cl21, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.61/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.61/1.21 | ~ (product1 @ X3 @ X1 @ X2)
% 3.61/1.21 | (equalish @ X0 @ X3))),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 3.61/1.21 thf(zip_derived_cl53, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl21])).
% 3.61/1.21 thf(zip_derived_cl22, plain, (![X0 : $i]: (product1 @ X0 @ X0 @ X0)),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_idempotence])).
% 3.61/1.21 thf(product1_right_cancellation, axiom,
% 3.61/1.21 (( ~( product1 @ X @ W @ Y ) ) | ( ~( product1 @ X @ Z @ Y ) ) |
% 3.61/1.21 ( equalish @ W @ Z ))).
% 3.61/1.21 thf(zip_derived_cl20, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.61/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.61/1.21 | ~ (product1 @ X0 @ X3 @ X2)
% 3.61/1.21 | (equalish @ X1 @ X3))),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 3.61/1.21 thf(zip_derived_cl51, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl20])).
% 3.61/1.21 thf(zip_derived_cl53, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl21])).
% 3.61/1.21 thf(zip_derived_cl51, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl20])).
% 3.61/1.21 thf(element_4, axiom, (group_element @ e_4)).
% 3.61/1.21 thf(zip_derived_cl5, plain, ( (group_element @ e_4)),
% 3.61/1.21 inference('cnf', [status(esa)], [element_4])).
% 3.61/1.21 thf(element_2, axiom, (group_element @ e_2)).
% 3.61/1.21 thf(zip_derived_cl3, plain, ( (group_element @ e_2)),
% 3.61/1.21 inference('cnf', [status(esa)], [element_2])).
% 3.61/1.21 thf(product1_total_function1, axiom,
% 3.61/1.21 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 3.61/1.21 ( product1 @ X @ Y @ e_1 ) | ( product1 @ X @ Y @ e_2 ) |
% 3.61/1.21 ( product1 @ X @ Y @ e_3 ) | ( product1 @ X @ Y @ e_4 ))).
% 3.61/1.21 thf(zip_derived_cl18, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 (~ (group_element @ X0)
% 3.61/1.21 | ~ (group_element @ X1)
% 3.61/1.21 | (product1 @ X0 @ X1 @ e_1)
% 3.61/1.21 | (product1 @ X0 @ X1 @ e_2)
% 3.61/1.21 | (product1 @ X0 @ X1 @ e_3)
% 3.61/1.21 | (product1 @ X0 @ X1 @ e_4))),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_total_function1])).
% 3.61/1.21 thf(zip_derived_cl91, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_2 @ X0 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ X0 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ X0 @ e_2)
% 3.61/1.21 | (product1 @ e_2 @ X0 @ e_1)
% 3.61/1.21 | ~ (group_element @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl18])).
% 3.61/1.21 thf(zip_derived_cl126, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_4 @ e_1)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_2)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl91])).
% 3.61/1.21 thf(element_3, axiom, (group_element @ e_3)).
% 3.61/1.21 thf(zip_derived_cl4, plain, ( (group_element @ e_3)),
% 3.61/1.21 inference('cnf', [status(esa)], [element_3])).
% 3.61/1.21 thf(zip_derived_cl91, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_2 @ X0 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ X0 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ X0 @ e_2)
% 3.61/1.21 | (product1 @ e_2 @ X0 @ e_1)
% 3.61/1.21 | ~ (group_element @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl18])).
% 3.61/1.21 thf(zip_derived_cl125, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_3 @ e_1)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_2)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl91])).
% 3.61/1.21 thf(zip_derived_cl20, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.61/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.61/1.21 | ~ (product1 @ X0 @ X3 @ X2)
% 3.61/1.21 | (equalish @ X1 @ X3))),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 3.61/1.21 thf(zip_derived_cl293, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_2 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_2)
% 3.61/1.21 | (equalish @ e_3 @ X0)
% 3.61/1.21 | ~ (product1 @ e_2 @ X0 @ e_1))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl125, zip_derived_cl20])).
% 3.61/1.21 thf(zip_derived_cl959, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_2)
% 3.61/1.21 | (equalish @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_2)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl126, zip_derived_cl293])).
% 3.61/1.21 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 3.61/1.21 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_4)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 3.61/1.21 thf(zip_derived_cl962, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_2)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_2)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl959, zip_derived_cl14])).
% 3.61/1.21 thf(zip_derived_cl1569, plain,
% 3.61/1.21 (( (equalish @ e_2 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_2)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_4))),
% 3.61/1.21 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl962])).
% 3.61/1.21 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 3.61/1.21 thf(zip_derived_cl10, plain, (~ (equalish @ e_2 @ e_3)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 3.61/1.21 thf(zip_derived_cl1570, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_2)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl1569, zip_derived_cl10])).
% 3.61/1.21 thf(zip_derived_cl1583, plain,
% 3.61/1.21 (( (equalish @ e_3 @ e_2)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_2)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_4))),
% 3.61/1.21 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl1570])).
% 3.61/1.21 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 3.61/1.21 thf(zip_derived_cl13, plain, (~ (equalish @ e_3 @ e_2)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 3.61/1.21 thf(zip_derived_cl1584, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_2)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl1583, zip_derived_cl13])).
% 3.61/1.21 thf(zip_derived_cl1668, plain,
% 3.61/1.21 (( (equalish @ e_2 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_4))),
% 3.61/1.21 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl1584])).
% 3.61/1.21 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 3.61/1.21 thf(zip_derived_cl11, plain, (~ (equalish @ e_2 @ e_4)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 3.61/1.21 thf(zip_derived_cl1669, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl1668, zip_derived_cl11])).
% 3.61/1.21 thf(zip_derived_cl53, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl21])).
% 3.61/1.21 thf(zip_derived_cl22, plain, (![X0 : $i]: (product1 @ X0 @ X0 @ X0)),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_idempotence])).
% 3.61/1.21 thf(zip_derived_cl22, plain, (![X0 : $i]: (product1 @ X0 @ X0 @ X0)),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_idempotence])).
% 3.61/1.21 thf(qg2a, conjecture,
% 3.61/1.21 (~( ( product2 @ Z2 @ Y @ X ) | ( ~( product1 @ Z1 @ X @ Z2 ) ) |
% 3.61/1.21 ( ~( product1 @ X @ Y @ Z1 ) ) ))).
% 3.61/1.21 thf(zf_stmt_0, negated_conjecture,
% 3.61/1.21 (( product2 @ Z2 @ Y @ X ) | ( ~( product1 @ Z1 @ X @ Z2 ) ) |
% 3.61/1.21 ( ~( product1 @ X @ Y @ Z1 ) )),
% 3.61/1.21 inference('cnf.neg', [status(esa)], [qg2a])).
% 3.61/1.21 thf(zip_derived_cl28, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.61/1.21 ( (product2 @ X0 @ X1 @ X2)
% 3.61/1.21 | ~ (product1 @ X3 @ X2 @ X0)
% 3.61/1.21 | ~ (product1 @ X2 @ X1 @ X3))),
% 3.61/1.21 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.61/1.21 thf(zip_derived_cl61, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 (~ (product1 @ X0 @ X1 @ X0) | (product2 @ X0 @ X1 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl28])).
% 3.61/1.21 thf(product2_total_function2, axiom,
% 3.61/1.21 (( ~( product2 @ X @ Y @ W ) ) | ( ~( product2 @ X @ Y @ Z ) ) |
% 3.61/1.21 ( equalish @ W @ Z ))).
% 3.61/1.21 thf(zip_derived_cl24, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.61/1.21 (~ (product2 @ X0 @ X1 @ X2)
% 3.61/1.21 | ~ (product2 @ X0 @ X1 @ X3)
% 3.61/1.21 | (equalish @ X2 @ X3))),
% 3.61/1.21 inference('cnf', [status(esa)], [product2_total_function2])).
% 3.61/1.21 thf(zip_derived_cl73, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.61/1.21 (~ (product1 @ X0 @ X1 @ X0)
% 3.61/1.21 | (equalish @ X0 @ X2)
% 3.61/1.21 | ~ (product2 @ X0 @ X1 @ X2))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl24])).
% 3.61/1.21 thf(zip_derived_cl76, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 (~ (product2 @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl73])).
% 3.61/1.21 thf(zip_derived_cl51, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl20])).
% 3.61/1.21 thf(zip_derived_cl4, plain, ( (group_element @ e_3)),
% 3.61/1.21 inference('cnf', [status(esa)], [element_3])).
% 3.61/1.21 thf(element_1, axiom, (group_element @ e_1)).
% 3.61/1.21 thf(zip_derived_cl2, plain, ( (group_element @ e_1)),
% 3.61/1.21 inference('cnf', [status(esa)], [element_1])).
% 3.61/1.21 thf(zip_derived_cl18, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 (~ (group_element @ X0)
% 3.61/1.21 | ~ (group_element @ X1)
% 3.61/1.21 | (product1 @ X0 @ X1 @ e_1)
% 3.61/1.21 | (product1 @ X0 @ X1 @ e_2)
% 3.61/1.21 | (product1 @ X0 @ X1 @ e_3)
% 3.61/1.21 | (product1 @ X0 @ X1 @ e_4))),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_total_function1])).
% 3.61/1.21 thf(zip_derived_cl90, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_1 @ X0 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ X0 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ X0 @ e_2)
% 3.61/1.21 | (product1 @ e_1 @ X0 @ e_1)
% 3.61/1.21 | ~ (group_element @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl18])).
% 3.61/1.21 thf(zip_derived_cl118, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_3 @ e_1)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_2)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl90])).
% 3.61/1.21 thf(zip_derived_cl208, plain,
% 3.61/1.21 (( (equalish @ e_1 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_2))),
% 3.61/1.21 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl118])).
% 3.61/1.21 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 3.61/1.21 thf(zip_derived_cl7, plain, (~ (equalish @ e_1 @ e_3)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 3.61/1.21 thf(zip_derived_cl209, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_2))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl208, zip_derived_cl7])).
% 3.61/1.21 thf(zip_derived_cl51, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl20])).
% 3.61/1.21 thf(zip_derived_cl53, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl21])).
% 3.61/1.21 thf(zip_derived_cl2, plain, ( (group_element @ e_1)),
% 3.61/1.21 inference('cnf', [status(esa)], [element_1])).
% 3.61/1.21 thf(zip_derived_cl91, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_2 @ X0 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ X0 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ X0 @ e_2)
% 3.61/1.21 | (product1 @ e_2 @ X0 @ e_1)
% 3.61/1.21 | ~ (group_element @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl18])).
% 3.61/1.21 thf(zip_derived_cl123, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_1 @ e_1)
% 3.61/1.21 | (product1 @ e_2 @ e_1 @ e_2)
% 3.61/1.21 | (product1 @ e_2 @ e_1 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_1 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl91])).
% 3.61/1.21 thf(zip_derived_cl265, plain,
% 3.61/1.21 (( (equalish @ e_1 @ e_2)
% 3.61/1.21 | (product1 @ e_2 @ e_1 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_1 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_1 @ e_2))),
% 3.61/1.21 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl123])).
% 3.61/1.21 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 3.61/1.21 thf(zip_derived_cl6, plain, (~ (equalish @ e_1 @ e_2)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 3.61/1.21 thf(zip_derived_cl266, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_1 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_1 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_1 @ e_2))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl265, zip_derived_cl6])).
% 3.61/1.21 thf(zip_derived_cl281, plain,
% 3.61/1.21 (( (equalish @ e_2 @ e_1)
% 3.61/1.21 | (product1 @ e_2 @ e_1 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_1 @ e_4))),
% 3.61/1.21 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl266])).
% 3.61/1.21 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 3.61/1.21 thf(zip_derived_cl9, plain, (~ (equalish @ e_2 @ e_1)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 3.61/1.21 thf(zip_derived_cl282, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_1 @ e_3) | (product1 @ e_2 @ e_1 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl281, zip_derived_cl9])).
% 3.61/1.21 thf(zip_derived_cl28, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.61/1.21 ( (product2 @ X0 @ X1 @ X2)
% 3.61/1.21 | ~ (product1 @ X3 @ X2 @ X0)
% 3.61/1.21 | ~ (product1 @ X2 @ X1 @ X3))),
% 3.61/1.21 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.61/1.21 thf(zip_derived_cl287, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_2 @ e_1 @ e_4)
% 3.61/1.21 | ~ (product1 @ e_1 @ X0 @ e_2)
% 3.61/1.21 | (product2 @ e_3 @ X0 @ e_1))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl282, zip_derived_cl28])).
% 3.61/1.21 thf(zip_derived_cl351, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_3 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_4)
% 3.61/1.21 | (product2 @ e_3 @ e_3 @ e_1)
% 3.61/1.21 | (product1 @ e_2 @ e_1 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl209, zip_derived_cl287])).
% 3.61/1.21 thf(zip_derived_cl652, plain,
% 3.61/1.21 (( (equalish @ e_3 @ e_1)
% 3.61/1.21 | (product1 @ e_2 @ e_1 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_3))),
% 3.61/1.21 inference('sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl351])).
% 3.61/1.21 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 3.61/1.21 thf(zip_derived_cl12, plain, (~ (equalish @ e_3 @ e_1)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 3.61/1.21 thf(zip_derived_cl653, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_1 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_3))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl652, zip_derived_cl12])).
% 3.61/1.21 thf(zip_derived_cl663, plain,
% 3.61/1.21 (( (equalish @ e_3 @ e_1)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_1 @ e_4))),
% 3.61/1.21 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl653])).
% 3.61/1.21 thf(zip_derived_cl12, plain, (~ (equalish @ e_3 @ e_1)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 3.61/1.21 thf(zip_derived_cl664, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_3 @ e_4) | (product1 @ e_2 @ e_1 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl663, zip_derived_cl12])).
% 3.61/1.21 thf(zip_derived_cl20, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.61/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.61/1.21 | ~ (product1 @ X0 @ X3 @ X2)
% 3.61/1.21 | (equalish @ X1 @ X3))),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 3.61/1.21 thf(zip_derived_cl670, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_1 @ e_3 @ e_4)
% 3.61/1.21 | (equalish @ e_1 @ X0)
% 3.61/1.21 | ~ (product1 @ e_2 @ X0 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl664, zip_derived_cl20])).
% 3.61/1.21 thf(zip_derived_cl1680, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (equalish @ e_1 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl1669, zip_derived_cl670])).
% 3.61/1.21 thf(zip_derived_cl7, plain, (~ (equalish @ e_1 @ e_3)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 3.61/1.21 thf(zip_derived_cl1684, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl1680, zip_derived_cl7])).
% 3.61/1.21 thf(zip_derived_cl1669, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl1668, zip_derived_cl11])).
% 3.61/1.21 thf(zip_derived_cl21, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.61/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.61/1.21 | ~ (product1 @ X3 @ X1 @ X2)
% 3.61/1.21 | (equalish @ X0 @ X3))),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 3.61/1.21 thf(zip_derived_cl1676, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_2 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (equalish @ e_2 @ X0)
% 3.61/1.21 | ~ (product1 @ X0 @ e_3 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl1669, zip_derived_cl21])).
% 3.61/1.21 thf(zip_derived_cl1729, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_4)
% 3.61/1.21 | (equalish @ e_2 @ e_1)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl1684, zip_derived_cl1676])).
% 3.61/1.21 thf(zip_derived_cl9, plain, (~ (equalish @ e_2 @ e_1)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 3.61/1.21 thf(zip_derived_cl1740, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl1729, zip_derived_cl9])).
% 3.61/1.21 thf(zip_derived_cl1741, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_4 @ e_4) | (product1 @ e_2 @ e_4 @ e_3))),
% 3.61/1.21 inference('simplify', [status(thm)], [zip_derived_cl1740])).
% 3.61/1.21 thf(zip_derived_cl51, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl20])).
% 3.61/1.21 thf(zip_derived_cl76, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 (~ (product2 @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl73])).
% 3.61/1.21 thf(zip_derived_cl53, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl21])).
% 3.61/1.21 thf(product2_idempotence, axiom, (product2 @ X @ X @ X)).
% 3.61/1.21 thf(zip_derived_cl27, plain, (![X0 : $i]: (product2 @ X0 @ X0 @ X0)),
% 3.61/1.21 inference('cnf', [status(esa)], [product2_idempotence])).
% 3.61/1.21 thf(zip_derived_cl3, plain, ( (group_element @ e_2)),
% 3.61/1.21 inference('cnf', [status(esa)], [element_2])).
% 3.61/1.21 thf(zip_derived_cl90, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_1 @ X0 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ X0 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ X0 @ e_2)
% 3.61/1.21 | (product1 @ e_1 @ X0 @ e_1)
% 3.61/1.21 | ~ (group_element @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl18])).
% 3.61/1.21 thf(zip_derived_cl117, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_2 @ e_1)
% 3.61/1.21 | (product1 @ e_1 @ e_2 @ e_2)
% 3.61/1.21 | (product1 @ e_1 @ e_2 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_2 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl90])).
% 3.61/1.21 thf(zip_derived_cl61, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 (~ (product1 @ X0 @ X1 @ X0) | (product2 @ X0 @ X1 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl28])).
% 3.61/1.21 thf(product2_right_cancellation, axiom,
% 3.61/1.21 (( ~( product2 @ X @ W @ Y ) ) | ( ~( product2 @ X @ Z @ Y ) ) |
% 3.61/1.21 ( equalish @ W @ Z ))).
% 3.61/1.21 thf(zip_derived_cl25, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.61/1.21 (~ (product2 @ X0 @ X1 @ X2)
% 3.61/1.21 | ~ (product2 @ X0 @ X3 @ X2)
% 3.61/1.21 | (equalish @ X1 @ X3))),
% 3.61/1.21 inference('cnf', [status(esa)], [product2_right_cancellation])).
% 3.61/1.21 thf(zip_derived_cl74, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.61/1.21 (~ (product1 @ X0 @ X1 @ X0)
% 3.61/1.21 | (equalish @ X1 @ X2)
% 3.61/1.21 | ~ (product2 @ X0 @ X2 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl25])).
% 3.61/1.21 thf(zip_derived_cl171, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_1 @ e_2 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_2 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_2 @ e_2)
% 3.61/1.21 | ~ (product2 @ e_1 @ X0 @ e_1)
% 3.61/1.21 | (equalish @ e_2 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl117, zip_derived_cl74])).
% 3.61/1.21 thf(zip_derived_cl178, plain,
% 3.61/1.21 (( (equalish @ e_2 @ e_1)
% 3.61/1.21 | (product1 @ e_1 @ e_2 @ e_2)
% 3.61/1.21 | (product1 @ e_1 @ e_2 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_2 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl171])).
% 3.61/1.21 thf(zip_derived_cl9, plain, (~ (equalish @ e_2 @ e_1)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 3.61/1.21 thf(zip_derived_cl180, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_2 @ e_2)
% 3.61/1.21 | (product1 @ e_1 @ e_2 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_2 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl178, zip_derived_cl9])).
% 3.61/1.21 thf(zip_derived_cl186, plain,
% 3.61/1.21 (( (equalish @ e_2 @ e_1)
% 3.61/1.21 | (product1 @ e_1 @ e_2 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_2 @ e_3))),
% 3.61/1.21 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl180])).
% 3.61/1.21 thf(zip_derived_cl9, plain, (~ (equalish @ e_2 @ e_1)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 3.61/1.21 thf(zip_derived_cl187, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_2 @ e_4) | (product1 @ e_1 @ e_2 @ e_3))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl186, zip_derived_cl9])).
% 3.61/1.21 thf(zip_derived_cl53, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl21])).
% 3.61/1.21 thf(zip_derived_cl2, plain, ( (group_element @ e_1)),
% 3.61/1.21 inference('cnf', [status(esa)], [element_1])).
% 3.61/1.21 thf(zip_derived_cl4, plain, ( (group_element @ e_3)),
% 3.61/1.21 inference('cnf', [status(esa)], [element_3])).
% 3.61/1.21 thf(zip_derived_cl18, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 (~ (group_element @ X0)
% 3.61/1.21 | ~ (group_element @ X1)
% 3.61/1.21 | (product1 @ X0 @ X1 @ e_1)
% 3.61/1.21 | (product1 @ X0 @ X1 @ e_2)
% 3.61/1.21 | (product1 @ X0 @ X1 @ e_3)
% 3.61/1.21 | (product1 @ X0 @ X1 @ e_4))),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_total_function1])).
% 3.61/1.21 thf(zip_derived_cl92, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_3 @ X0 @ e_4)
% 3.61/1.21 | (product1 @ e_3 @ X0 @ e_3)
% 3.61/1.21 | (product1 @ e_3 @ X0 @ e_2)
% 3.61/1.21 | (product1 @ e_3 @ X0 @ e_1)
% 3.61/1.21 | ~ (group_element @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl18])).
% 3.61/1.21 thf(zip_derived_cl128, plain,
% 3.61/1.21 (( (product1 @ e_3 @ e_1 @ e_1)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_2)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_3)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl92])).
% 3.61/1.21 thf(zip_derived_cl309, plain,
% 3.61/1.21 (( (equalish @ e_1 @ e_3)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_4)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_3)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_2))),
% 3.61/1.21 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl128])).
% 3.61/1.21 thf(zip_derived_cl7, plain, (~ (equalish @ e_1 @ e_3)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 3.61/1.21 thf(zip_derived_cl310, plain,
% 3.61/1.21 (( (product1 @ e_3 @ e_1 @ e_4)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_3)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_2))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl309, zip_derived_cl7])).
% 3.61/1.21 thf(zip_derived_cl28, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.61/1.21 ( (product2 @ X0 @ X1 @ X2)
% 3.61/1.21 | ~ (product1 @ X3 @ X2 @ X0)
% 3.61/1.21 | ~ (product1 @ X2 @ X1 @ X3))),
% 3.61/1.21 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.61/1.21 thf(zip_derived_cl315, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_3 @ e_1 @ e_3)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_4)
% 3.61/1.21 | ~ (product1 @ e_1 @ X0 @ e_3)
% 3.61/1.21 | (product2 @ e_2 @ X0 @ e_1))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl310, zip_derived_cl28])).
% 3.61/1.21 thf(zip_derived_cl353, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_2 @ e_4)
% 3.61/1.21 | (product2 @ e_2 @ e_2 @ e_1)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_4)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_3))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl187, zip_derived_cl315])).
% 3.61/1.21 thf(zip_derived_cl755, plain,
% 3.61/1.21 (( (equalish @ e_2 @ e_1)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_3)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_2 @ e_4))),
% 3.61/1.21 inference('sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl353])).
% 3.61/1.21 thf(zip_derived_cl9, plain, (~ (equalish @ e_2 @ e_1)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 3.61/1.21 thf(zip_derived_cl756, plain,
% 3.61/1.21 (( (product1 @ e_3 @ e_1 @ e_3)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_2 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl755, zip_derived_cl9])).
% 3.61/1.21 thf(zip_derived_cl53, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl21])).
% 3.61/1.21 thf(zip_derived_cl51, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 ( (equalish @ X0 @ X1) | ~ (product1 @ X0 @ X1 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl20])).
% 3.61/1.21 thf(zip_derived_cl5, plain, ( (group_element @ e_4)),
% 3.61/1.21 inference('cnf', [status(esa)], [element_4])).
% 3.61/1.21 thf(zip_derived_cl90, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_1 @ X0 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ X0 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ X0 @ e_2)
% 3.61/1.21 | (product1 @ e_1 @ X0 @ e_1)
% 3.61/1.21 | ~ (group_element @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl18])).
% 3.61/1.21 thf(zip_derived_cl119, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_4 @ e_1)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_2)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl90])).
% 3.61/1.21 thf(zip_derived_cl225, plain,
% 3.61/1.21 (( (equalish @ e_1 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_2))),
% 3.61/1.21 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl119])).
% 3.61/1.21 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 3.61/1.21 thf(zip_derived_cl8, plain, (~ (equalish @ e_1 @ e_4)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 3.61/1.21 thf(zip_derived_cl226, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_2))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl225, zip_derived_cl8])).
% 3.61/1.21 thf(zip_derived_cl209, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_2))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl208, zip_derived_cl7])).
% 3.61/1.21 thf(zip_derived_cl20, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.61/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.61/1.21 | ~ (product1 @ X0 @ X3 @ X2)
% 3.61/1.21 | (equalish @ X1 @ X3))),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 3.61/1.21 thf(zip_derived_cl214, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_1 @ e_3 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_4)
% 3.61/1.21 | (equalish @ e_3 @ X0)
% 3.61/1.21 | ~ (product1 @ e_1 @ X0 @ e_2))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl209, zip_derived_cl20])).
% 3.61/1.21 thf(zip_derived_cl237, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (equalish @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_3))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl226, zip_derived_cl214])).
% 3.61/1.21 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_4)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 3.61/1.21 thf(zip_derived_cl240, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_3))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl237, zip_derived_cl14])).
% 3.61/1.21 thf(zip_derived_cl635, plain,
% 3.61/1.21 (( (equalish @ e_3 @ e_1)
% 3.61/1.21 | (product1 @ e_1 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_3))),
% 3.61/1.21 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl240])).
% 3.61/1.21 thf(zip_derived_cl12, plain, (~ (equalish @ e_3 @ e_1)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 3.61/1.21 thf(zip_derived_cl636, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_3 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_3))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl635, zip_derived_cl12])).
% 3.61/1.21 thf(zip_derived_cl20, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.61/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.61/1.21 | ~ (product1 @ X0 @ X3 @ X2)
% 3.61/1.21 | (equalish @ X1 @ X3))),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 3.61/1.21 thf(zip_derived_cl642, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_1 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (equalish @ e_3 @ X0)
% 3.61/1.21 | ~ (product1 @ e_1 @ X0 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl636, zip_derived_cl20])).
% 3.61/1.21 thf(zip_derived_cl762, plain,
% 3.61/1.21 (( (product1 @ e_3 @ e_1 @ e_4)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_3)
% 3.61/1.21 | (equalish @ e_3 @ e_2)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_3))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl756, zip_derived_cl642])).
% 3.61/1.21 thf(zip_derived_cl13, plain, (~ (equalish @ e_3 @ e_2)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 3.61/1.21 thf(zip_derived_cl764, plain,
% 3.61/1.21 (( (product1 @ e_3 @ e_1 @ e_4)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_3))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl762, zip_derived_cl13])).
% 3.61/1.21 thf(zip_derived_cl932, plain,
% 3.61/1.21 (( (equalish @ e_3 @ e_1)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_4))),
% 3.61/1.21 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl764])).
% 3.61/1.21 thf(zip_derived_cl12, plain, (~ (equalish @ e_3 @ e_1)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 3.61/1.21 thf(zip_derived_cl936, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_4 @ e_3)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl932, zip_derived_cl12])).
% 3.61/1.21 thf(zip_derived_cl21, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.61/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.61/1.21 | ~ (product1 @ X3 @ X1 @ X2)
% 3.61/1.21 | (equalish @ X0 @ X3))),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 3.61/1.21 thf(zip_derived_cl944, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_3 @ e_1 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (equalish @ e_1 @ X0)
% 3.61/1.21 | ~ (product1 @ X0 @ e_4 @ e_3))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl936, zip_derived_cl21])).
% 3.61/1.21 thf(zip_derived_cl1753, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_4 @ e_4)
% 3.61/1.21 | (equalish @ e_1 @ e_2)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl1741, zip_derived_cl944])).
% 3.61/1.21 thf(zip_derived_cl6, plain, (~ (equalish @ e_1 @ e_2)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 3.61/1.21 thf(zip_derived_cl1756, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_3 @ e_1 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl1753, zip_derived_cl6])).
% 3.61/1.21 thf(zip_derived_cl1741, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_4 @ e_4) | (product1 @ e_2 @ e_4 @ e_3))),
% 3.61/1.21 inference('simplify', [status(thm)], [zip_derived_cl1740])).
% 3.61/1.21 thf(zip_derived_cl282, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_1 @ e_3) | (product1 @ e_2 @ e_1 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl281, zip_derived_cl9])).
% 3.61/1.21 thf(zip_derived_cl20, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.61/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.61/1.21 | ~ (product1 @ X0 @ X3 @ X2)
% 3.61/1.21 | (equalish @ X1 @ X3))),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 3.61/1.21 thf(zip_derived_cl285, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_2 @ e_1 @ e_4)
% 3.61/1.21 | (equalish @ e_1 @ X0)
% 3.61/1.21 | ~ (product1 @ e_2 @ X0 @ e_3))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl282, zip_derived_cl20])).
% 3.61/1.21 thf(zip_derived_cl1754, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_4 @ e_4)
% 3.61/1.21 | (equalish @ e_1 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_1 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl1741, zip_derived_cl285])).
% 3.61/1.21 thf(zip_derived_cl8, plain, (~ (equalish @ e_1 @ e_4)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 3.61/1.21 thf(zip_derived_cl1757, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_4 @ e_4) | (product1 @ e_2 @ e_1 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl1754, zip_derived_cl8])).
% 3.61/1.21 thf(zip_derived_cl21, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.61/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.61/1.21 | ~ (product1 @ X3 @ X1 @ X2)
% 3.61/1.21 | (equalish @ X0 @ X3))),
% 3.61/1.21 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 3.61/1.21 thf(zip_derived_cl1764, plain,
% 3.61/1.21 (![X0 : $i]:
% 3.61/1.21 ( (product1 @ e_2 @ e_4 @ e_4)
% 3.61/1.21 | (equalish @ e_2 @ X0)
% 3.61/1.21 | ~ (product1 @ X0 @ e_1 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl1757, zip_derived_cl21])).
% 3.61/1.21 thf(zip_derived_cl1887, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_4)
% 3.61/1.21 | (equalish @ e_2 @ e_3)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_4))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl1756, zip_derived_cl1764])).
% 3.61/1.21 thf(zip_derived_cl10, plain, (~ (equalish @ e_2 @ e_3)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 3.61/1.21 thf(zip_derived_cl1893, plain,
% 3.61/1.21 (( (product1 @ e_1 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_4)
% 3.61/1.21 | (product1 @ e_2 @ e_4 @ e_4))),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl1887, zip_derived_cl10])).
% 3.61/1.21 thf(zip_derived_cl1894, plain,
% 3.61/1.21 (( (product1 @ e_2 @ e_4 @ e_4) | (product1 @ e_1 @ e_4 @ e_4))),
% 3.61/1.21 inference('simplify', [status(thm)], [zip_derived_cl1893])).
% 3.61/1.21 thf(zip_derived_cl1910, plain,
% 3.61/1.21 (( (equalish @ e_4 @ e_1) | (product1 @ e_2 @ e_4 @ e_4))),
% 3.61/1.21 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl1894])).
% 3.61/1.21 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 3.61/1.21 thf(zip_derived_cl15, plain, (~ (equalish @ e_4 @ e_1)),
% 3.61/1.21 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 3.61/1.21 thf(zip_derived_cl1911, plain, ( (product1 @ e_2 @ e_4 @ e_4)),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl1910, zip_derived_cl15])).
% 3.61/1.21 thf(zip_derived_cl53, plain,
% 3.61/1.21 (![X0 : $i, X1 : $i]:
% 3.61/1.21 ( (equalish @ X0 @ X1) | ~ (product1 @ X1 @ X0 @ X0))),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl21])).
% 3.61/1.21 thf(zip_derived_cl1923, plain, ( (equalish @ e_4 @ e_2)),
% 3.61/1.21 inference('sup-', [status(thm)], [zip_derived_cl1911, zip_derived_cl53])).
% 3.61/1.21 thf(zip_derived_cl1927, plain, ($false),
% 3.61/1.21 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl1923])).
% 3.61/1.21
% 3.61/1.21 % SZS output end Refutation
% 3.61/1.21
% 3.61/1.21
% 3.61/1.21 % Terminating...
% 4.60/1.30 % Runner terminated.
% 4.65/1.32 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------