TSTP Solution File: GRP124-4.004 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP124-4.004 : 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.L1IrKAzzZc true
% Computer : n001.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 01:50:05 EDT 2023
% Result : Unsatisfiable 2.45s 0.94s
% Output : Refutation 2.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP124-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.L1IrKAzzZc true
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 01:51:51 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.20/0.64 % Total configuration time : 435
% 0.20/0.64 % Estimated wc time : 1092
% 0.20/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.20/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 2.45/0.94 % Solved by fo/fo7.sh.
% 2.45/0.94 % done 388 iterations in 0.162s
% 2.45/0.94 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 2.45/0.94 % SZS output start Refutation
% 2.45/0.94 thf(e_1_type, type, e_1: $i).
% 2.45/0.94 thf(product_type, type, product: $i > $i > $i > $o).
% 2.45/0.94 thf(e_2_type, type, e_2: $i).
% 2.45/0.94 thf(group_element_type, type, group_element: $i > $o).
% 2.45/0.94 thf(e_4_type, type, e_4: $i).
% 2.45/0.94 thf(equalish_type, type, equalish: $i > $i > $o).
% 2.45/0.94 thf(e_3_type, type, e_3: $i).
% 2.45/0.94 thf(product_idempotence, axiom, (product @ X @ X @ X)).
% 2.45/0.94 thf(zip_derived_cl22, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 2.45/0.94 inference('cnf', [status(esa)], [product_idempotence])).
% 2.45/0.94 thf(product_total_function2, axiom,
% 2.45/0.94 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 2.45/0.94 ( equalish @ W @ Z ))).
% 2.45/0.94 thf(zip_derived_cl19, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.45/0.94 (~ (product @ X0 @ X1 @ X2)
% 2.45/0.94 | ~ (product @ X0 @ X1 @ X3)
% 2.45/0.94 | (equalish @ X2 @ X3))),
% 2.45/0.94 inference('cnf', [status(esa)], [product_total_function2])).
% 2.45/0.94 thf(zip_derived_cl25, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X0 @ X1))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl19])).
% 2.45/0.94 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 2.45/0.94 thf(zip_derived_cl13, plain, (~ (equalish @ e_3 @ e_2)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 2.45/0.94 thf(zip_derived_cl38, plain, (~ (product @ e_3 @ e_3 @ e_2)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl13])).
% 2.45/0.94 thf(row_surjectivity, axiom,
% 2.45/0.94 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 2.45/0.94 ( product @ e_1 @ X @ Y ) | ( product @ e_2 @ X @ Y ) |
% 2.45/0.94 ( product @ e_3 @ X @ Y ) | ( product @ e_4 @ X @ Y ))).
% 2.45/0.94 thf(zip_derived_cl0, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 (~ (group_element @ X0)
% 2.45/0.94 | ~ (group_element @ X1)
% 2.45/0.94 | (product @ e_1 @ X0 @ X1)
% 2.45/0.94 | (product @ e_2 @ X0 @ X1)
% 2.45/0.94 | (product @ e_3 @ X0 @ X1)
% 2.45/0.94 | (product @ e_4 @ X0 @ X1))),
% 2.45/0.94 inference('cnf', [status(esa)], [row_surjectivity])).
% 2.45/0.94 thf(zip_derived_cl0, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 (~ (group_element @ X0)
% 2.45/0.94 | ~ (group_element @ X1)
% 2.45/0.94 | (product @ e_1 @ X0 @ X1)
% 2.45/0.94 | (product @ e_2 @ X0 @ X1)
% 2.45/0.94 | (product @ e_3 @ X0 @ X1)
% 2.45/0.94 | (product @ e_4 @ X0 @ X1))),
% 2.45/0.94 inference('cnf', [status(esa)], [row_surjectivity])).
% 2.45/0.94 thf(zip_derived_cl25, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X0 @ X1))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl19])).
% 2.45/0.94 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 2.45/0.94 thf(zip_derived_cl17, plain, (~ (equalish @ e_4 @ e_3)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 2.45/0.94 thf(zip_derived_cl42, plain, (~ (product @ e_4 @ e_4 @ e_3)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl17])).
% 2.45/0.94 thf(zip_derived_cl106, plain,
% 2.45/0.94 (( (product @ e_3 @ e_4 @ e_3)
% 2.45/0.94 | (product @ e_2 @ e_4 @ e_3)
% 2.45/0.94 | (product @ e_1 @ e_4 @ e_3)
% 2.45/0.94 | ~ (group_element @ e_3)
% 2.45/0.94 | ~ (group_element @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl42])).
% 2.45/0.94 thf(element_3, axiom, (group_element @ e_3)).
% 2.45/0.94 thf(zip_derived_cl4, plain, ( (group_element @ e_3)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_3])).
% 2.45/0.94 thf(element_4, axiom, (group_element @ e_4)).
% 2.45/0.94 thf(zip_derived_cl5, plain, ( (group_element @ e_4)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_4])).
% 2.45/0.94 thf(zip_derived_cl109, plain,
% 2.45/0.94 (( (product @ e_3 @ e_4 @ e_3)
% 2.45/0.94 | (product @ e_2 @ e_4 @ e_3)
% 2.45/0.94 | (product @ e_1 @ e_4 @ e_3))),
% 2.45/0.94 inference('demod', [status(thm)],
% 2.45/0.94 [zip_derived_cl106, zip_derived_cl4, zip_derived_cl5])).
% 2.45/0.94 thf(zip_derived_cl22, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 2.45/0.94 inference('cnf', [status(esa)], [product_idempotence])).
% 2.45/0.94 thf(product_right_cancellation, axiom,
% 2.45/0.94 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 2.45/0.94 ( equalish @ W @ Z ))).
% 2.45/0.94 thf(zip_derived_cl20, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.45/0.94 (~ (product @ X0 @ X1 @ X2)
% 2.45/0.94 | ~ (product @ X0 @ X3 @ X2)
% 2.45/0.94 | (equalish @ X1 @ X3))),
% 2.45/0.94 inference('cnf', [status(esa)], [product_right_cancellation])).
% 2.45/0.94 thf(zip_derived_cl28, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl20])).
% 2.45/0.94 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 2.45/0.94 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_4)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 2.45/0.94 thf(zip_derived_cl54, plain, (~ (product @ e_3 @ e_4 @ e_3)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl14])).
% 2.45/0.94 thf(zip_derived_cl191, plain,
% 2.45/0.94 (( (product @ e_1 @ e_4 @ e_3) | (product @ e_2 @ e_4 @ e_3))),
% 2.45/0.94 inference('clc', [status(thm)], [zip_derived_cl109, zip_derived_cl54])).
% 2.45/0.94 thf(zip_derived_cl19, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.45/0.94 (~ (product @ X0 @ X1 @ X2)
% 2.45/0.94 | ~ (product @ X0 @ X1 @ X3)
% 2.45/0.94 | (equalish @ X2 @ X3))),
% 2.45/0.94 inference('cnf', [status(esa)], [product_total_function2])).
% 2.45/0.94 thf(zip_derived_cl192, plain,
% 2.45/0.94 (![X0 : $i]:
% 2.45/0.94 ( (product @ e_1 @ e_4 @ e_3)
% 2.45/0.94 | (equalish @ e_3 @ X0)
% 2.45/0.94 | ~ (product @ e_2 @ e_4 @ X0))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl191, zip_derived_cl19])).
% 2.45/0.94 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 2.45/0.94 thf(zip_derived_cl12, plain, (~ (equalish @ e_3 @ e_1)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 2.45/0.94 thf(zip_derived_cl292, plain,
% 2.45/0.94 ((~ (product @ e_2 @ e_4 @ e_1) | (product @ e_1 @ e_4 @ e_3))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl192, zip_derived_cl12])).
% 2.45/0.94 thf(zip_derived_cl0, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 (~ (group_element @ X0)
% 2.45/0.94 | ~ (group_element @ X1)
% 2.45/0.94 | (product @ e_1 @ X0 @ X1)
% 2.45/0.94 | (product @ e_2 @ X0 @ X1)
% 2.45/0.94 | (product @ e_3 @ X0 @ X1)
% 2.45/0.94 | (product @ e_4 @ X0 @ X1))),
% 2.45/0.94 inference('cnf', [status(esa)], [row_surjectivity])).
% 2.45/0.94 thf(zip_derived_cl25, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X0 @ X1))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl19])).
% 2.45/0.94 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 2.45/0.94 thf(zip_derived_cl15, plain, (~ (equalish @ e_4 @ e_1)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 2.45/0.94 thf(zip_derived_cl40, plain, (~ (product @ e_4 @ e_4 @ e_1)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl15])).
% 2.45/0.94 thf(zip_derived_cl104, plain,
% 2.45/0.94 (( (product @ e_3 @ e_4 @ e_1)
% 2.45/0.94 | (product @ e_2 @ e_4 @ e_1)
% 2.45/0.94 | (product @ e_1 @ e_4 @ e_1)
% 2.45/0.94 | ~ (group_element @ e_1)
% 2.45/0.94 | ~ (group_element @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl40])).
% 2.45/0.94 thf(zip_derived_cl28, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl20])).
% 2.45/0.94 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 2.45/0.94 thf(zip_derived_cl8, plain, (~ (equalish @ e_1 @ e_4)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 2.45/0.94 thf(zip_derived_cl48, plain, (~ (product @ e_1 @ e_4 @ e_1)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl8])).
% 2.45/0.94 thf(element_1, axiom, (group_element @ e_1)).
% 2.45/0.94 thf(zip_derived_cl2, plain, ( (group_element @ e_1)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_1])).
% 2.45/0.94 thf(zip_derived_cl5, plain, ( (group_element @ e_4)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_4])).
% 2.45/0.94 thf(zip_derived_cl107, plain,
% 2.45/0.94 (( (product @ e_3 @ e_4 @ e_1) | (product @ e_2 @ e_4 @ e_1))),
% 2.45/0.94 inference('demod', [status(thm)],
% 2.45/0.94 [zip_derived_cl104, zip_derived_cl48, zip_derived_cl2,
% 2.45/0.94 zip_derived_cl5])).
% 2.45/0.94 thf(zip_derived_cl22, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 2.45/0.94 inference('cnf', [status(esa)], [product_idempotence])).
% 2.45/0.94 thf(qg2_1, conjecture,
% 2.45/0.94 (~( ( equalish @ X1 @ X2 ) | ( ~( product @ Z2 @ X2 @ Y2 ) ) |
% 2.45/0.94 ( ~( product @ Z2 @ X1 @ Y1 ) ) | ( ~( product @ X2 @ Y2 @ Z1 ) ) |
% 2.45/0.94 ( ~( product @ X1 @ Y1 @ Z1 ) ) ))).
% 2.45/0.94 thf(zf_stmt_0, negated_conjecture,
% 2.45/0.94 (( equalish @ X1 @ X2 ) | ( ~( product @ Z2 @ X2 @ Y2 ) ) |
% 2.45/0.94 ( ~( product @ Z2 @ X1 @ Y1 ) ) | ( ~( product @ X2 @ Y2 @ Z1 ) ) |
% 2.45/0.94 ( ~( product @ X1 @ Y1 @ Z1 ) )),
% 2.45/0.94 inference('cnf.neg', [status(esa)], [qg2_1])).
% 2.45/0.94 thf(zip_derived_cl23, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1)
% 2.45/0.94 | ~ (product @ X2 @ X1 @ X3)
% 2.45/0.94 | ~ (product @ X2 @ X0 @ X4)
% 2.45/0.94 | ~ (product @ X1 @ X3 @ X5)
% 2.45/0.94 | ~ (product @ X0 @ X4 @ X5))),
% 2.45/0.94 inference('cnf', [status(esa)], [zf_stmt_0])).
% 2.45/0.94 thf(zip_derived_cl70, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.45/0.94 (~ (product @ X3 @ X2 @ X1)
% 2.45/0.94 | ~ (product @ X0 @ X0 @ X1)
% 2.45/0.94 | ~ (product @ X0 @ X3 @ X2)
% 2.45/0.94 | (equalish @ X3 @ X0))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl23])).
% 2.45/0.94 thf(zip_derived_cl116, plain,
% 2.45/0.94 (![X0 : $i]:
% 2.45/0.94 ( (product @ e_2 @ e_4 @ e_1)
% 2.45/0.94 | (equalish @ e_3 @ X0)
% 2.45/0.94 | ~ (product @ X0 @ e_3 @ e_4)
% 2.45/0.94 | ~ (product @ X0 @ X0 @ e_1))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl107, zip_derived_cl70])).
% 2.45/0.94 thf(zip_derived_cl12, plain, (~ (equalish @ e_3 @ e_1)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 2.45/0.94 thf(zip_derived_cl380, plain,
% 2.45/0.94 ((~ (product @ e_1 @ e_1 @ e_1)
% 2.45/0.94 | ~ (product @ e_1 @ e_3 @ e_4)
% 2.45/0.94 | (product @ e_2 @ e_4 @ e_1))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl12])).
% 2.45/0.94 thf(zip_derived_cl22, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 2.45/0.94 inference('cnf', [status(esa)], [product_idempotence])).
% 2.45/0.94 thf(zip_derived_cl383, plain,
% 2.45/0.94 ((~ (product @ e_1 @ e_3 @ e_4) | (product @ e_2 @ e_4 @ e_1))),
% 2.45/0.94 inference('demod', [status(thm)], [zip_derived_cl380, zip_derived_cl22])).
% 2.45/0.94 thf(zip_derived_cl0, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 (~ (group_element @ X0)
% 2.45/0.94 | ~ (group_element @ X1)
% 2.45/0.94 | (product @ e_1 @ X0 @ X1)
% 2.45/0.94 | (product @ e_2 @ X0 @ X1)
% 2.45/0.94 | (product @ e_3 @ X0 @ X1)
% 2.45/0.94 | (product @ e_4 @ X0 @ X1))),
% 2.45/0.94 inference('cnf', [status(esa)], [row_surjectivity])).
% 2.45/0.94 thf(zip_derived_cl0, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 (~ (group_element @ X0)
% 2.45/0.94 | ~ (group_element @ X1)
% 2.45/0.94 | (product @ e_1 @ X0 @ X1)
% 2.45/0.94 | (product @ e_2 @ X0 @ X1)
% 2.45/0.94 | (product @ e_3 @ X0 @ X1)
% 2.45/0.94 | (product @ e_4 @ X0 @ X1))),
% 2.45/0.94 inference('cnf', [status(esa)], [row_surjectivity])).
% 2.45/0.94 thf(zip_derived_cl28, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl20])).
% 2.45/0.94 thf(zip_derived_cl15, plain, (~ (equalish @ e_4 @ e_1)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 2.45/0.94 thf(zip_derived_cl55, plain, (~ (product @ e_4 @ e_1 @ e_4)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl15])).
% 2.45/0.94 thf(zip_derived_cl122, plain,
% 2.45/0.94 (( (product @ e_3 @ e_1 @ e_4)
% 2.45/0.94 | (product @ e_2 @ e_1 @ e_4)
% 2.45/0.94 | (product @ e_1 @ e_1 @ e_4)
% 2.45/0.94 | ~ (group_element @ e_4)
% 2.45/0.94 | ~ (group_element @ e_1))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl55])).
% 2.45/0.94 thf(zip_derived_cl25, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X0 @ X1))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl19])).
% 2.45/0.94 thf(zip_derived_cl8, plain, (~ (equalish @ e_1 @ e_4)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 2.45/0.94 thf(zip_derived_cl33, plain, (~ (product @ e_1 @ e_1 @ e_4)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl8])).
% 2.45/0.94 thf(zip_derived_cl5, plain, ( (group_element @ e_4)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_4])).
% 2.45/0.94 thf(zip_derived_cl2, plain, ( (group_element @ e_1)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_1])).
% 2.45/0.94 thf(zip_derived_cl123, plain,
% 2.45/0.94 (( (product @ e_3 @ e_1 @ e_4) | (product @ e_2 @ e_1 @ e_4))),
% 2.45/0.94 inference('demod', [status(thm)],
% 2.45/0.94 [zip_derived_cl122, zip_derived_cl33, zip_derived_cl5,
% 2.45/0.94 zip_derived_cl2])).
% 2.45/0.94 thf(zip_derived_cl70, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.45/0.94 (~ (product @ X3 @ X2 @ X1)
% 2.45/0.94 | ~ (product @ X0 @ X0 @ X1)
% 2.45/0.94 | ~ (product @ X0 @ X3 @ X2)
% 2.45/0.94 | (equalish @ X3 @ X0))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl23])).
% 2.45/0.94 thf(zip_derived_cl162, plain,
% 2.45/0.94 (![X0 : $i]:
% 2.45/0.94 ( (product @ e_2 @ e_1 @ e_4)
% 2.45/0.94 | (equalish @ e_3 @ X0)
% 2.45/0.94 | ~ (product @ X0 @ e_3 @ e_1)
% 2.45/0.94 | ~ (product @ X0 @ X0 @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl123, zip_derived_cl70])).
% 2.45/0.94 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_4)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 2.45/0.94 thf(zip_derived_cl550, plain,
% 2.45/0.94 ((~ (product @ e_4 @ e_4 @ e_4)
% 2.45/0.94 | ~ (product @ e_4 @ e_3 @ e_1)
% 2.45/0.94 | (product @ e_2 @ e_1 @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl162, zip_derived_cl14])).
% 2.45/0.94 thf(zip_derived_cl22, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 2.45/0.94 inference('cnf', [status(esa)], [product_idempotence])).
% 2.45/0.94 thf(zip_derived_cl554, plain,
% 2.45/0.94 ((~ (product @ e_4 @ e_3 @ e_1) | (product @ e_2 @ e_1 @ e_4))),
% 2.45/0.94 inference('demod', [status(thm)], [zip_derived_cl550, zip_derived_cl22])).
% 2.45/0.94 thf(zip_derived_cl555, plain,
% 2.45/0.94 (( (product @ e_3 @ e_3 @ e_1)
% 2.45/0.94 | (product @ e_2 @ e_3 @ e_1)
% 2.45/0.94 | (product @ e_1 @ e_3 @ e_1)
% 2.45/0.94 | ~ (group_element @ e_1)
% 2.45/0.94 | ~ (group_element @ e_3)
% 2.45/0.94 | (product @ e_2 @ e_1 @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl554])).
% 2.45/0.94 thf(zip_derived_cl28, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl20])).
% 2.45/0.94 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 2.45/0.94 thf(zip_derived_cl7, plain, (~ (equalish @ e_1 @ e_3)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 2.45/0.94 thf(zip_derived_cl47, plain, (~ (product @ e_1 @ e_3 @ e_1)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl7])).
% 2.45/0.94 thf(zip_derived_cl2, plain, ( (group_element @ e_1)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_1])).
% 2.45/0.94 thf(zip_derived_cl4, plain, ( (group_element @ e_3)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_3])).
% 2.45/0.94 thf(zip_derived_cl556, plain,
% 2.45/0.94 (( (product @ e_3 @ e_3 @ e_1)
% 2.45/0.94 | (product @ e_2 @ e_3 @ e_1)
% 2.45/0.94 | (product @ e_2 @ e_1 @ e_4))),
% 2.45/0.94 inference('demod', [status(thm)],
% 2.45/0.94 [zip_derived_cl555, zip_derived_cl47, zip_derived_cl2,
% 2.45/0.94 zip_derived_cl4])).
% 2.45/0.94 thf(zip_derived_cl25, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X0 @ X1))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl19])).
% 2.45/0.94 thf(zip_derived_cl12, plain, (~ (equalish @ e_3 @ e_1)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 2.45/0.94 thf(zip_derived_cl37, plain, (~ (product @ e_3 @ e_3 @ e_1)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl12])).
% 2.45/0.94 thf(zip_derived_cl557, plain,
% 2.45/0.94 (( (product @ e_2 @ e_1 @ e_4) | (product @ e_2 @ e_3 @ e_1))),
% 2.45/0.94 inference('clc', [status(thm)], [zip_derived_cl556, zip_derived_cl37])).
% 2.45/0.94 thf(zip_derived_cl0, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 (~ (group_element @ X0)
% 2.45/0.94 | ~ (group_element @ X1)
% 2.45/0.94 | (product @ e_1 @ X0 @ X1)
% 2.45/0.94 | (product @ e_2 @ X0 @ X1)
% 2.45/0.94 | (product @ e_3 @ X0 @ X1)
% 2.45/0.94 | (product @ e_4 @ X0 @ X1))),
% 2.45/0.94 inference('cnf', [status(esa)], [row_surjectivity])).
% 2.45/0.94 thf(zip_derived_cl28, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl20])).
% 2.45/0.94 thf(zip_derived_cl17, plain, (~ (equalish @ e_4 @ e_3)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 2.45/0.94 thf(zip_derived_cl57, plain, (~ (product @ e_4 @ e_3 @ e_4)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl17])).
% 2.45/0.94 thf(zip_derived_cl126, plain,
% 2.45/0.94 (( (product @ e_3 @ e_3 @ e_4)
% 2.45/0.94 | (product @ e_2 @ e_3 @ e_4)
% 2.45/0.94 | (product @ e_1 @ e_3 @ e_4)
% 2.45/0.94 | ~ (group_element @ e_4)
% 2.45/0.94 | ~ (group_element @ e_3))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl57])).
% 2.45/0.94 thf(zip_derived_cl5, plain, ( (group_element @ e_4)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_4])).
% 2.45/0.94 thf(zip_derived_cl4, plain, ( (group_element @ e_3)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_3])).
% 2.45/0.94 thf(zip_derived_cl127, plain,
% 2.45/0.94 (( (product @ e_3 @ e_3 @ e_4)
% 2.45/0.94 | (product @ e_2 @ e_3 @ e_4)
% 2.45/0.94 | (product @ e_1 @ e_3 @ e_4))),
% 2.45/0.94 inference('demod', [status(thm)],
% 2.45/0.94 [zip_derived_cl126, zip_derived_cl5, zip_derived_cl4])).
% 2.45/0.94 thf(zip_derived_cl25, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X0 @ X1))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl19])).
% 2.45/0.94 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_4)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 2.45/0.94 thf(zip_derived_cl39, plain, (~ (product @ e_3 @ e_3 @ e_4)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl14])).
% 2.45/0.94 thf(zip_derived_cl202, plain,
% 2.45/0.94 (( (product @ e_1 @ e_3 @ e_4) | (product @ e_2 @ e_3 @ e_4))),
% 2.45/0.94 inference('clc', [status(thm)], [zip_derived_cl127, zip_derived_cl39])).
% 2.45/0.94 thf(zip_derived_cl19, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.45/0.94 (~ (product @ X0 @ X1 @ X2)
% 2.45/0.94 | ~ (product @ X0 @ X1 @ X3)
% 2.45/0.94 | (equalish @ X2 @ X3))),
% 2.45/0.94 inference('cnf', [status(esa)], [product_total_function2])).
% 2.45/0.94 thf(zip_derived_cl203, plain,
% 2.45/0.94 (![X0 : $i]:
% 2.45/0.94 ( (product @ e_1 @ e_3 @ e_4)
% 2.45/0.94 | (equalish @ e_4 @ X0)
% 2.45/0.94 | ~ (product @ e_2 @ e_3 @ X0))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl202, zip_derived_cl19])).
% 2.45/0.94 thf(zip_derived_cl15, plain, (~ (equalish @ e_4 @ e_1)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 2.45/0.94 thf(zip_derived_cl302, plain,
% 2.45/0.94 ((~ (product @ e_2 @ e_3 @ e_1) | (product @ e_1 @ e_3 @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl203, zip_derived_cl15])).
% 2.45/0.94 thf(zip_derived_cl568, plain,
% 2.45/0.94 (( (product @ e_2 @ e_1 @ e_4) | (product @ e_1 @ e_3 @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl557, zip_derived_cl302])).
% 2.45/0.94 thf(zip_derived_cl202, plain,
% 2.45/0.94 (( (product @ e_1 @ e_3 @ e_4) | (product @ e_2 @ e_3 @ e_4))),
% 2.45/0.94 inference('clc', [status(thm)], [zip_derived_cl127, zip_derived_cl39])).
% 2.45/0.94 thf(zip_derived_cl20, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.45/0.94 (~ (product @ X0 @ X1 @ X2)
% 2.45/0.94 | ~ (product @ X0 @ X3 @ X2)
% 2.45/0.94 | (equalish @ X1 @ X3))),
% 2.45/0.94 inference('cnf', [status(esa)], [product_right_cancellation])).
% 2.45/0.94 thf(zip_derived_cl204, plain,
% 2.45/0.94 (![X0 : $i]:
% 2.45/0.94 ( (product @ e_1 @ e_3 @ e_4)
% 2.45/0.94 | (equalish @ e_3 @ X0)
% 2.45/0.94 | ~ (product @ e_2 @ X0 @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl202, zip_derived_cl20])).
% 2.45/0.94 thf(zip_derived_cl12, plain, (~ (equalish @ e_3 @ e_1)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 2.45/0.94 thf(zip_derived_cl305, plain,
% 2.45/0.94 ((~ (product @ e_2 @ e_1 @ e_4) | (product @ e_1 @ e_3 @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl204, zip_derived_cl12])).
% 2.45/0.94 thf(zip_derived_cl584, plain, ( (product @ e_1 @ e_3 @ e_4)),
% 2.45/0.94 inference('clc', [status(thm)], [zip_derived_cl568, zip_derived_cl305])).
% 2.45/0.94 thf(zip_derived_cl585, plain, ( (product @ e_2 @ e_4 @ e_1)),
% 2.45/0.94 inference('demod', [status(thm)], [zip_derived_cl383, zip_derived_cl584])).
% 2.45/0.94 thf(zip_derived_cl596, plain, ( (product @ e_1 @ e_4 @ e_3)),
% 2.45/0.94 inference('demod', [status(thm)], [zip_derived_cl292, zip_derived_cl585])).
% 2.45/0.94 thf(zip_derived_cl0, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 (~ (group_element @ X0)
% 2.45/0.94 | ~ (group_element @ X1)
% 2.45/0.94 | (product @ e_1 @ X0 @ X1)
% 2.45/0.94 | (product @ e_2 @ X0 @ X1)
% 2.45/0.94 | (product @ e_3 @ X0 @ X1)
% 2.45/0.94 | (product @ e_4 @ X0 @ X1))),
% 2.45/0.94 inference('cnf', [status(esa)], [row_surjectivity])).
% 2.45/0.94 thf(zip_derived_cl25, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X0 @ X1))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl19])).
% 2.45/0.94 thf(e_4_is_not_e_2, axiom, (~( equalish @ e_4 @ e_2 ))).
% 2.45/0.94 thf(zip_derived_cl16, plain, (~ (equalish @ e_4 @ e_2)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 2.45/0.94 thf(zip_derived_cl41, plain, (~ (product @ e_4 @ e_4 @ e_2)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl16])).
% 2.45/0.94 thf(zip_derived_cl105, plain,
% 2.45/0.94 (( (product @ e_3 @ e_4 @ e_2)
% 2.45/0.94 | (product @ e_2 @ e_4 @ e_2)
% 2.45/0.94 | (product @ e_1 @ e_4 @ e_2)
% 2.45/0.94 | ~ (group_element @ e_2)
% 2.45/0.94 | ~ (group_element @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl41])).
% 2.45/0.94 thf(zip_derived_cl28, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl20])).
% 2.45/0.94 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 2.45/0.94 thf(zip_derived_cl11, plain, (~ (equalish @ e_2 @ e_4)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 2.45/0.94 thf(zip_derived_cl51, plain, (~ (product @ e_2 @ e_4 @ e_2)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl11])).
% 2.45/0.94 thf(element_2, axiom, (group_element @ e_2)).
% 2.45/0.94 thf(zip_derived_cl3, plain, ( (group_element @ e_2)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_2])).
% 2.45/0.94 thf(zip_derived_cl5, plain, ( (group_element @ e_4)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_4])).
% 2.45/0.94 thf(zip_derived_cl108, plain,
% 2.45/0.94 (( (product @ e_3 @ e_4 @ e_2) | (product @ e_1 @ e_4 @ e_2))),
% 2.45/0.94 inference('demod', [status(thm)],
% 2.45/0.94 [zip_derived_cl105, zip_derived_cl51, zip_derived_cl3,
% 2.45/0.94 zip_derived_cl5])).
% 2.45/0.94 thf(zip_derived_cl0, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 (~ (group_element @ X0)
% 2.45/0.94 | ~ (group_element @ X1)
% 2.45/0.94 | (product @ e_1 @ X0 @ X1)
% 2.45/0.94 | (product @ e_2 @ X0 @ X1)
% 2.45/0.94 | (product @ e_3 @ X0 @ X1)
% 2.45/0.94 | (product @ e_4 @ X0 @ X1))),
% 2.45/0.94 inference('cnf', [status(esa)], [row_surjectivity])).
% 2.45/0.94 thf(zip_derived_cl28, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl20])).
% 2.45/0.94 thf(zip_derived_cl16, plain, (~ (equalish @ e_4 @ e_2)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 2.45/0.94 thf(zip_derived_cl56, plain, (~ (product @ e_4 @ e_2 @ e_4)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl16])).
% 2.45/0.94 thf(zip_derived_cl124, plain,
% 2.45/0.94 (( (product @ e_3 @ e_2 @ e_4)
% 2.45/0.94 | (product @ e_2 @ e_2 @ e_4)
% 2.45/0.94 | (product @ e_1 @ e_2 @ e_4)
% 2.45/0.94 | ~ (group_element @ e_4)
% 2.45/0.94 | ~ (group_element @ e_2))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl56])).
% 2.45/0.94 thf(zip_derived_cl25, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X0 @ X1))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl19])).
% 2.45/0.94 thf(zip_derived_cl11, plain, (~ (equalish @ e_2 @ e_4)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 2.45/0.94 thf(zip_derived_cl36, plain, (~ (product @ e_2 @ e_2 @ e_4)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl11])).
% 2.45/0.94 thf(zip_derived_cl5, plain, ( (group_element @ e_4)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_4])).
% 2.45/0.94 thf(zip_derived_cl3, plain, ( (group_element @ e_2)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_2])).
% 2.45/0.94 thf(zip_derived_cl125, plain,
% 2.45/0.94 (( (product @ e_3 @ e_2 @ e_4) | (product @ e_1 @ e_2 @ e_4))),
% 2.45/0.94 inference('demod', [status(thm)],
% 2.45/0.94 [zip_derived_cl124, zip_derived_cl36, zip_derived_cl5,
% 2.45/0.94 zip_derived_cl3])).
% 2.45/0.94 thf(zip_derived_cl123, plain,
% 2.45/0.94 (( (product @ e_3 @ e_1 @ e_4) | (product @ e_2 @ e_1 @ e_4))),
% 2.45/0.94 inference('demod', [status(thm)],
% 2.45/0.94 [zip_derived_cl122, zip_derived_cl33, zip_derived_cl5,
% 2.45/0.94 zip_derived_cl2])).
% 2.45/0.94 thf(zip_derived_cl20, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.45/0.94 (~ (product @ X0 @ X1 @ X2)
% 2.45/0.94 | ~ (product @ X0 @ X3 @ X2)
% 2.45/0.94 | (equalish @ X1 @ X3))),
% 2.45/0.94 inference('cnf', [status(esa)], [product_right_cancellation])).
% 2.45/0.94 thf(zip_derived_cl157, plain,
% 2.45/0.94 (![X0 : $i]:
% 2.45/0.94 ( (product @ e_2 @ e_1 @ e_4)
% 2.45/0.94 | (equalish @ e_1 @ X0)
% 2.45/0.94 | ~ (product @ e_3 @ X0 @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl123, zip_derived_cl20])).
% 2.45/0.94 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 2.45/0.94 thf(zip_derived_cl6, plain, (~ (equalish @ e_1 @ e_2)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 2.45/0.94 thf(zip_derived_cl229, plain,
% 2.45/0.94 ((~ (product @ e_3 @ e_2 @ e_4) | (product @ e_2 @ e_1 @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl157, zip_derived_cl6])).
% 2.45/0.94 thf(zip_derived_cl232, plain,
% 2.45/0.94 (( (product @ e_1 @ e_2 @ e_4) | (product @ e_2 @ e_1 @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl125, zip_derived_cl229])).
% 2.45/0.94 thf(zip_derived_cl305, plain,
% 2.45/0.94 ((~ (product @ e_2 @ e_1 @ e_4) | (product @ e_1 @ e_3 @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl204, zip_derived_cl12])).
% 2.45/0.94 thf(zip_derived_cl316, plain,
% 2.45/0.94 (( (product @ e_1 @ e_2 @ e_4) | (product @ e_1 @ e_3 @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl232, zip_derived_cl305])).
% 2.45/0.94 thf(zip_derived_cl383, plain,
% 2.45/0.94 ((~ (product @ e_1 @ e_3 @ e_4) | (product @ e_2 @ e_4 @ e_1))),
% 2.45/0.94 inference('demod', [status(thm)], [zip_derived_cl380, zip_derived_cl22])).
% 2.45/0.94 thf(zip_derived_cl386, plain,
% 2.45/0.94 (( (product @ e_1 @ e_2 @ e_4) | (product @ e_2 @ e_4 @ e_1))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl316, zip_derived_cl383])).
% 2.45/0.94 thf(zip_derived_cl292, plain,
% 2.45/0.94 ((~ (product @ e_2 @ e_4 @ e_1) | (product @ e_1 @ e_4 @ e_3))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl192, zip_derived_cl12])).
% 2.45/0.94 thf(zip_derived_cl421, plain,
% 2.45/0.94 (( (product @ e_1 @ e_2 @ e_4) | (product @ e_1 @ e_4 @ e_3))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl386, zip_derived_cl292])).
% 2.45/0.94 thf(zip_derived_cl19, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.45/0.94 (~ (product @ X0 @ X1 @ X2)
% 2.45/0.94 | ~ (product @ X0 @ X1 @ X3)
% 2.45/0.94 | (equalish @ X2 @ X3))),
% 2.45/0.94 inference('cnf', [status(esa)], [product_total_function2])).
% 2.45/0.94 thf(zip_derived_cl424, plain,
% 2.45/0.94 (![X0 : $i]:
% 2.45/0.94 ( (product @ e_1 @ e_2 @ e_4)
% 2.45/0.94 | (equalish @ e_3 @ X0)
% 2.45/0.94 | ~ (product @ e_1 @ e_4 @ X0))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl421, zip_derived_cl19])).
% 2.45/0.94 thf(zip_derived_cl13, plain, (~ (equalish @ e_3 @ e_2)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 2.45/0.94 thf(zip_derived_cl442, plain,
% 2.45/0.94 ((~ (product @ e_1 @ e_4 @ e_2) | (product @ e_1 @ e_2 @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl424, zip_derived_cl13])).
% 2.45/0.94 thf(zip_derived_cl584, plain, ( (product @ e_1 @ e_3 @ e_4)),
% 2.45/0.94 inference('clc', [status(thm)], [zip_derived_cl568, zip_derived_cl305])).
% 2.45/0.94 thf(zip_derived_cl20, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.45/0.94 (~ (product @ X0 @ X1 @ X2)
% 2.45/0.94 | ~ (product @ X0 @ X3 @ X2)
% 2.45/0.94 | (equalish @ X1 @ X3))),
% 2.45/0.94 inference('cnf', [status(esa)], [product_right_cancellation])).
% 2.45/0.94 thf(zip_derived_cl587, plain,
% 2.45/0.94 (![X0 : $i]: ( (equalish @ e_3 @ X0) | ~ (product @ e_1 @ X0 @ e_4))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl584, zip_derived_cl20])).
% 2.45/0.94 thf(zip_derived_cl13, plain, (~ (equalish @ e_3 @ e_2)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 2.45/0.94 thf(zip_derived_cl613, plain, (~ (product @ e_1 @ e_2 @ e_4)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl587, zip_derived_cl13])).
% 2.45/0.94 thf(zip_derived_cl653, plain, (~ (product @ e_1 @ e_4 @ e_2)),
% 2.45/0.94 inference('demod', [status(thm)], [zip_derived_cl442, zip_derived_cl613])).
% 2.45/0.94 thf(zip_derived_cl723, plain, ( (product @ e_3 @ e_4 @ e_2)),
% 2.45/0.94 inference('demod', [status(thm)], [zip_derived_cl108, zip_derived_cl653])).
% 2.45/0.94 thf(zip_derived_cl584, plain, ( (product @ e_1 @ e_3 @ e_4)),
% 2.45/0.94 inference('clc', [status(thm)], [zip_derived_cl568, zip_derived_cl305])).
% 2.45/0.94 thf(zip_derived_cl23, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1)
% 2.45/0.94 | ~ (product @ X2 @ X1 @ X3)
% 2.45/0.94 | ~ (product @ X2 @ X0 @ X4)
% 2.45/0.94 | ~ (product @ X1 @ X3 @ X5)
% 2.45/0.94 | ~ (product @ X0 @ X4 @ X5))),
% 2.45/0.94 inference('cnf', [status(esa)], [zf_stmt_0])).
% 2.45/0.94 thf(zip_derived_cl589, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.45/0.94 (~ (product @ X2 @ X1 @ X0)
% 2.45/0.94 | ~ (product @ e_3 @ e_4 @ X0)
% 2.45/0.94 | ~ (product @ e_1 @ X2 @ X1)
% 2.45/0.94 | (equalish @ X2 @ e_3))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl584, zip_derived_cl23])).
% 2.45/0.94 thf(zip_derived_cl767, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ e_3)
% 2.45/0.94 | ~ (product @ e_1 @ X0 @ X1)
% 2.45/0.94 | ~ (product @ X0 @ X1 @ e_2))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl723, zip_derived_cl589])).
% 2.45/0.94 thf(zip_derived_cl773, plain,
% 2.45/0.94 ((~ (product @ e_4 @ e_3 @ e_2) | (equalish @ e_4 @ e_3))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl596, zip_derived_cl767])).
% 2.45/0.94 thf(zip_derived_cl17, plain, (~ (equalish @ e_4 @ e_3)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 2.45/0.94 thf(zip_derived_cl776, plain, (~ (product @ e_4 @ e_3 @ e_2)),
% 2.45/0.94 inference('clc', [status(thm)], [zip_derived_cl773, zip_derived_cl17])).
% 2.45/0.94 thf(zip_derived_cl777, plain,
% 2.45/0.94 (( (product @ e_3 @ e_3 @ e_2)
% 2.45/0.94 | (product @ e_2 @ e_3 @ e_2)
% 2.45/0.94 | (product @ e_1 @ e_3 @ e_2)
% 2.45/0.94 | ~ (group_element @ e_2)
% 2.45/0.94 | ~ (group_element @ e_3))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl776])).
% 2.45/0.94 thf(zip_derived_cl28, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i]:
% 2.45/0.94 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl20])).
% 2.45/0.94 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 2.45/0.94 thf(zip_derived_cl10, plain, (~ (equalish @ e_2 @ e_3)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 2.45/0.94 thf(zip_derived_cl50, plain, (~ (product @ e_2 @ e_3 @ e_2)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl28, zip_derived_cl10])).
% 2.45/0.94 thf(zip_derived_cl584, plain, ( (product @ e_1 @ e_3 @ e_4)),
% 2.45/0.94 inference('clc', [status(thm)], [zip_derived_cl568, zip_derived_cl305])).
% 2.45/0.94 thf(zip_derived_cl19, plain,
% 2.45/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 2.45/0.94 (~ (product @ X0 @ X1 @ X2)
% 2.45/0.94 | ~ (product @ X0 @ X1 @ X3)
% 2.45/0.94 | (equalish @ X2 @ X3))),
% 2.45/0.94 inference('cnf', [status(esa)], [product_total_function2])).
% 2.45/0.94 thf(zip_derived_cl586, plain,
% 2.45/0.94 (![X0 : $i]: ( (equalish @ e_4 @ X0) | ~ (product @ e_1 @ e_3 @ X0))),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl584, zip_derived_cl19])).
% 2.45/0.94 thf(zip_derived_cl16, plain, (~ (equalish @ e_4 @ e_2)),
% 2.45/0.94 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 2.45/0.94 thf(zip_derived_cl610, plain, (~ (product @ e_1 @ e_3 @ e_2)),
% 2.45/0.94 inference('sup-', [status(thm)], [zip_derived_cl586, zip_derived_cl16])).
% 2.45/0.94 thf(zip_derived_cl3, plain, ( (group_element @ e_2)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_2])).
% 2.45/0.94 thf(zip_derived_cl4, plain, ( (group_element @ e_3)),
% 2.45/0.94 inference('cnf', [status(esa)], [element_3])).
% 2.45/0.94 thf(zip_derived_cl778, plain, ( (product @ e_3 @ e_3 @ e_2)),
% 2.45/0.94 inference('demod', [status(thm)],
% 2.45/0.94 [zip_derived_cl777, zip_derived_cl50, zip_derived_cl610,
% 2.45/0.94 zip_derived_cl3, zip_derived_cl4])).
% 2.45/0.94 thf(zip_derived_cl789, plain, ($false),
% 2.45/0.94 inference('demod', [status(thm)], [zip_derived_cl38, zip_derived_cl778])).
% 2.45/0.94
% 2.45/0.94 % SZS output end Refutation
% 2.45/0.94
% 2.45/0.94
% 2.45/0.94 % Terminating...
% 3.04/1.05 % Runner terminated.
% 3.04/1.06 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------