%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP126-4.004 : TPTP v9.2.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.xhlhAvnQys true
% Computer : n028.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 04:35:44 PM UTC 2025
% Result : Unsatisfiable 3.42s 1.34s
% Output : Refutation 3.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.15 % Problem : GRP126-4.004 : TPTP v9.2.0. Bugfixed v1.2.1.
% 0.10/0.16 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.xhlhAvnQys true
% 0.12/0.37 % Computer : n028.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8042.1875MB
% 0.12/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Oct 1 14:24:38 EDT 2025
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Running portfolio for 300 s
% 0.12/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Number of cores: 8
% 0.12/0.37 % Python version: Python 3.6.8
% 0.12/0.38 % Running in FO mode
% 0.42/0.62 % Total configuration time : 435
% 0.42/0.62 % Estimated wc time : 1092
% 0.42/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.43/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.43/0.77 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.43/0.82 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.43/0.82 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.43/0.83 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.43/0.83 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.43/0.84 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 3.42/1.34 % Solved by fo/fo7.sh.
% 3.42/1.34 % done 195 iterations in 0.359s
% 3.42/1.34 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 3.42/1.34 % SZS output start Refutation
% 3.42/1.34 thf(e_1_type, type, e_1: $i).
% 3.42/1.34 thf(product_type, type, product: $i > $i > $i > $o).
% 3.42/1.34 thf(e_2_type, type, e_2: $i).
% 3.42/1.34 thf(group_element_type, type, group_element: $i > $o).
% 3.42/1.34 thf(e_4_type, type, e_4: $i).
% 3.42/1.34 thf(equalish_type, type, equalish: $i > $i > $o).
% 3.42/1.34 thf(e_3_type, type, e_3: $i).
% 3.42/1.34 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 3.42/1.34 thf(zip_derived_cl10, plain, (~ (equalish @ e_1 @ e_4)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 3.42/1.34 thf(row_surjectivity, axiom,
% 3.42/1.34 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 3.42/1.34 ( product @ e_1 @ X @ Y ) | ( product @ e_2 @ X @ Y ) |
% 3.42/1.34 ( product @ e_3 @ X @ Y ) | ( product @ e_4 @ X @ Y ))).
% 3.42/1.34 thf(zip_derived_cl0, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i]:
% 3.42/1.34 (~ (group_element @ X0)
% 3.42/1.34 | ~ (group_element @ X1)
% 3.42/1.34 | (product @ e_1 @ X0 @ X1)
% 3.42/1.34 | (product @ e_2 @ X0 @ X1)
% 3.42/1.34 | (product @ e_3 @ X0 @ X1)
% 3.42/1.34 | (product @ e_4 @ X0 @ X1))),
% 3.42/1.34 inference('cnf', [status(esa)], [row_surjectivity])).
% 3.42/1.34 thf(product_idempotence, axiom, (product @ X @ X @ X)).
% 3.42/1.34 thf(zip_derived_cl24, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 3.42/1.34 inference('cnf', [status(esa)], [product_idempotence])).
% 3.42/1.34 thf(product_total_function2, axiom,
% 3.42/1.34 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 3.42/1.34 ( equalish @ W @ Z ))).
% 3.42/1.34 thf(zip_derived_cl21, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.42/1.34 (~ (product @ X0 @ X1 @ X2)
% 3.42/1.34 | ~ (product @ X0 @ X1 @ X3)
% 3.42/1.34 | (equalish @ X2 @ X3))),
% 3.42/1.34 inference('cnf', [status(esa)], [product_total_function2])).
% 3.42/1.34 thf(zip_derived_cl26, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i]:
% 3.42/1.34 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X0 @ X1))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl21])).
% 3.42/1.34 thf(zip_derived_cl36, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_3 @ e_4 @ X0)
% 3.42/1.34 | (product @ e_2 @ e_4 @ X0)
% 3.42/1.34 | (product @ e_1 @ e_4 @ X0)
% 3.42/1.34 | ~ (group_element @ X0)
% 3.42/1.34 | ~ (group_element @ e_4)
% 3.42/1.34 | (equalish @ e_4 @ X0))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl26])).
% 3.42/1.34 thf(element_4, axiom, (group_element @ e_4)).
% 3.42/1.34 thf(zip_derived_cl7, plain, ( (group_element @ e_4)),
% 3.42/1.34 inference('cnf', [status(esa)], [element_4])).
% 3.42/1.34 thf(zip_derived_cl38, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_3 @ e_4 @ X0)
% 3.42/1.34 | (product @ e_2 @ e_4 @ X0)
% 3.42/1.34 | (product @ e_1 @ e_4 @ X0)
% 3.42/1.34 | ~ (group_element @ X0)
% 3.42/1.34 | (equalish @ e_4 @ X0))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl7])).
% 3.42/1.34 thf(zip_derived_cl38, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_3 @ e_4 @ X0)
% 3.42/1.34 | (product @ e_2 @ e_4 @ X0)
% 3.42/1.34 | (product @ e_1 @ e_4 @ X0)
% 3.42/1.34 | ~ (group_element @ X0)
% 3.42/1.34 | (equalish @ e_4 @ X0))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl7])).
% 3.42/1.34 thf(zip_derived_cl38, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_3 @ e_4 @ X0)
% 3.42/1.34 | (product @ e_2 @ e_4 @ X0)
% 3.42/1.34 | (product @ e_1 @ e_4 @ X0)
% 3.42/1.34 | ~ (group_element @ X0)
% 3.42/1.34 | (equalish @ e_4 @ X0))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl7])).
% 3.42/1.34 thf(zip_derived_cl38, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_3 @ e_4 @ X0)
% 3.42/1.34 | (product @ e_2 @ e_4 @ X0)
% 3.42/1.34 | (product @ e_1 @ e_4 @ X0)
% 3.42/1.34 | ~ (group_element @ X0)
% 3.42/1.34 | (equalish @ e_4 @ X0))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl7])).
% 3.42/1.34 thf(zip_derived_cl0, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i]:
% 3.42/1.34 (~ (group_element @ X0)
% 3.42/1.34 | ~ (group_element @ X1)
% 3.42/1.34 | (product @ e_1 @ X0 @ X1)
% 3.42/1.34 | (product @ e_2 @ X0 @ X1)
% 3.42/1.34 | (product @ e_3 @ X0 @ X1)
% 3.42/1.34 | (product @ e_4 @ X0 @ X1))),
% 3.42/1.34 inference('cnf', [status(esa)], [row_surjectivity])).
% 3.42/1.34 thf(zip_derived_cl24, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 3.42/1.34 inference('cnf', [status(esa)], [product_idempotence])).
% 3.42/1.34 thf(product_right_cancellation, axiom,
% 3.42/1.34 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 3.42/1.34 ( equalish @ W @ Z ))).
% 3.42/1.34 thf(zip_derived_cl22, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.42/1.34 (~ (product @ X0 @ X1 @ X2)
% 3.42/1.34 | ~ (product @ X0 @ X3 @ X2)
% 3.42/1.34 | (equalish @ X1 @ X3))),
% 3.42/1.34 inference('cnf', [status(esa)], [product_right_cancellation])).
% 3.42/1.34 thf(zip_derived_cl30, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i]:
% 3.42/1.34 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 3.42/1.34 thf(zip_derived_cl37, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_3 @ X0 @ e_4)
% 3.42/1.34 | (product @ e_2 @ X0 @ e_4)
% 3.42/1.34 | (product @ e_1 @ X0 @ e_4)
% 3.42/1.34 | ~ (group_element @ e_4)
% 3.42/1.34 | ~ (group_element @ X0)
% 3.42/1.34 | (equalish @ e_4 @ X0))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl30])).
% 3.42/1.34 thf(zip_derived_cl7, plain, ( (group_element @ e_4)),
% 3.42/1.34 inference('cnf', [status(esa)], [element_4])).
% 3.42/1.34 thf(zip_derived_cl39, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_3 @ X0 @ e_4)
% 3.42/1.34 | (product @ e_2 @ X0 @ e_4)
% 3.42/1.34 | (product @ e_1 @ X0 @ e_4)
% 3.42/1.34 | ~ (group_element @ X0)
% 3.42/1.34 | (equalish @ e_4 @ X0))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl7])).
% 3.42/1.34 thf(zip_derived_cl26, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i]:
% 3.42/1.34 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X0 @ X1))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl21])).
% 3.42/1.34 thf(zip_derived_cl48, plain,
% 3.42/1.34 (( (equalish @ e_4 @ e_3)
% 3.42/1.34 | ~ (group_element @ e_3)
% 3.42/1.34 | (product @ e_1 @ e_3 @ e_4)
% 3.42/1.34 | (product @ e_2 @ e_3 @ e_4)
% 3.42/1.34 | (equalish @ e_3 @ e_4))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl39, zip_derived_cl26])).
% 3.42/1.34 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 3.42/1.34 thf(zip_derived_cl19, plain, (~ (equalish @ e_4 @ e_3)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 3.42/1.34 thf(element_3, axiom, (group_element @ e_3)).
% 3.42/1.34 thf(zip_derived_cl6, plain, ( (group_element @ e_3)),
% 3.42/1.34 inference('cnf', [status(esa)], [element_3])).
% 3.42/1.34 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 3.42/1.34 thf(zip_derived_cl16, plain, (~ (equalish @ e_3 @ e_4)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 3.42/1.34 thf(zip_derived_cl49, plain,
% 3.42/1.34 (( (product @ e_1 @ e_3 @ e_4) | (product @ e_2 @ e_3 @ e_4))),
% 3.42/1.34 inference('demod', [status(thm)],
% 3.42/1.34 [zip_derived_cl48, zip_derived_cl19, zip_derived_cl6,
% 3.42/1.34 zip_derived_cl16])).
% 3.42/1.34 thf(qg4_1, conjecture,
% 3.42/1.34 (~( ( ~( product @ Y @ X @ Z2 ) ) | ( ~( product @ Z1 @ Z2 @ Y ) ) |
% 3.42/1.34 ( product @ X @ Y @ Z1 ) ))).
% 3.42/1.34 thf(zf_stmt_0, negated_conjecture,
% 3.42/1.34 (( ~( product @ Y @ X @ Z2 ) ) | ( ~( product @ Z1 @ Z2 @ Y ) ) |
% 3.42/1.34 ( product @ X @ Y @ Z1 )),
% 3.42/1.34 inference('cnf.neg', [status(esa)], [qg4_1])).
% 3.42/1.34 thf(zip_derived_cl2, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.42/1.34 (~ (product @ X0 @ X1 @ X2)
% 3.42/1.34 | ~ (product @ X3 @ X2 @ X0)
% 3.42/1.34 | (product @ X1 @ X0 @ X3))),
% 3.42/1.34 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.42/1.34 thf(zip_derived_cl68, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_1 @ e_3 @ e_4)
% 3.42/1.34 | (product @ e_3 @ e_2 @ X0)
% 3.42/1.34 | ~ (product @ X0 @ e_4 @ e_2))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl2])).
% 3.42/1.34 thf(zip_derived_cl153, plain,
% 3.42/1.34 (( (equalish @ e_4 @ e_2)
% 3.42/1.34 | ~ (group_element @ e_2)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_2)
% 3.42/1.34 | (product @ e_2 @ e_4 @ e_2)
% 3.42/1.34 | (product @ e_3 @ e_2 @ e_3)
% 3.42/1.34 | (product @ e_1 @ e_3 @ e_4))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl68])).
% 3.42/1.34 thf(e_4_is_not_e_2, axiom, (~( equalish @ e_4 @ e_2 ))).
% 3.42/1.34 thf(zip_derived_cl18, plain, (~ (equalish @ e_4 @ e_2)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 3.42/1.34 thf(element_2, axiom, (group_element @ e_2)).
% 3.42/1.34 thf(zip_derived_cl5, plain, ( (group_element @ e_2)),
% 3.42/1.34 inference('cnf', [status(esa)], [element_2])).
% 3.42/1.34 thf(zip_derived_cl155, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_2)
% 3.42/1.34 | (product @ e_2 @ e_4 @ e_2)
% 3.42/1.34 | (product @ e_3 @ e_2 @ e_3)
% 3.42/1.34 | (product @ e_1 @ e_3 @ e_4))),
% 3.42/1.34 inference('demod', [status(thm)],
% 3.42/1.34 [zip_derived_cl153, zip_derived_cl18, zip_derived_cl5])).
% 3.42/1.34 thf(zip_derived_cl30, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i]:
% 3.42/1.34 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 3.42/1.34 thf(zip_derived_cl225, plain,
% 3.42/1.34 (( (product @ e_1 @ e_3 @ e_4)
% 3.42/1.34 | (product @ e_2 @ e_4 @ e_2)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_2)
% 3.42/1.34 | (equalish @ e_3 @ e_2))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl155, zip_derived_cl30])).
% 3.42/1.34 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 3.42/1.34 thf(zip_derived_cl15, plain, (~ (equalish @ e_3 @ e_2)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 3.42/1.34 thf(zip_derived_cl228, plain,
% 3.42/1.34 (( (product @ e_1 @ e_3 @ e_4)
% 3.42/1.34 | (product @ e_2 @ e_4 @ e_2)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_2))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl225, zip_derived_cl15])).
% 3.42/1.34 thf(zip_derived_cl30, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i]:
% 3.42/1.34 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 3.42/1.34 thf(zip_derived_cl236, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_2)
% 3.42/1.34 | (product @ e_1 @ e_3 @ e_4)
% 3.42/1.34 | (equalish @ e_2 @ e_4))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl228, zip_derived_cl30])).
% 3.42/1.34 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 3.42/1.34 thf(zip_derived_cl13, plain, (~ (equalish @ e_2 @ e_4)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 3.42/1.34 thf(zip_derived_cl240, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_2) | (product @ e_1 @ e_3 @ e_4))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl236, zip_derived_cl13])).
% 3.42/1.34 thf(zip_derived_cl68, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_1 @ e_3 @ e_4)
% 3.42/1.34 | (product @ e_3 @ e_2 @ X0)
% 3.42/1.34 | ~ (product @ X0 @ e_4 @ e_2))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl2])).
% 3.42/1.34 thf(zip_derived_cl249, plain,
% 3.42/1.34 (( (product @ e_1 @ e_3 @ e_4)
% 3.42/1.34 | (product @ e_3 @ e_2 @ e_1)
% 3.42/1.34 | (product @ e_1 @ e_3 @ e_4))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl240, zip_derived_cl68])).
% 3.42/1.34 thf(zip_derived_cl251, plain,
% 3.42/1.34 (( (product @ e_3 @ e_2 @ e_1) | (product @ e_1 @ e_3 @ e_4))),
% 3.42/1.34 inference('simplify', [status(thm)], [zip_derived_cl249])).
% 3.42/1.34 thf(zip_derived_cl22, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.42/1.34 (~ (product @ X0 @ X1 @ X2)
% 3.42/1.34 | ~ (product @ X0 @ X3 @ X2)
% 3.42/1.34 | (equalish @ X1 @ X3))),
% 3.42/1.34 inference('cnf', [status(esa)], [product_right_cancellation])).
% 3.42/1.34 thf(zip_derived_cl256, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_1 @ e_3 @ e_4)
% 3.42/1.34 | (equalish @ e_2 @ X0)
% 3.42/1.34 | ~ (product @ e_3 @ X0 @ e_1))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl251, zip_derived_cl22])).
% 3.42/1.34 thf(zip_derived_cl291, plain,
% 3.42/1.34 (( (equalish @ e_4 @ e_1)
% 3.42/1.34 | ~ (group_element @ e_1)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_1)
% 3.42/1.34 | (product @ e_2 @ e_4 @ e_1)
% 3.42/1.34 | (equalish @ e_2 @ e_4)
% 3.42/1.34 | (product @ e_1 @ e_3 @ e_4))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl256])).
% 3.42/1.34 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 3.42/1.34 thf(zip_derived_cl17, plain, (~ (equalish @ e_4 @ e_1)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 3.42/1.34 thf(element_1, axiom, (group_element @ e_1)).
% 3.42/1.34 thf(zip_derived_cl4, plain, ( (group_element @ e_1)),
% 3.42/1.34 inference('cnf', [status(esa)], [element_1])).
% 3.42/1.34 thf(zip_derived_cl13, plain, (~ (equalish @ e_2 @ e_4)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 3.42/1.34 thf(zip_derived_cl294, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_1)
% 3.42/1.34 | (product @ e_2 @ e_4 @ e_1)
% 3.42/1.34 | (product @ e_1 @ e_3 @ e_4))),
% 3.42/1.34 inference('demod', [status(thm)],
% 3.42/1.34 [zip_derived_cl291, zip_derived_cl17, zip_derived_cl4,
% 3.42/1.34 zip_derived_cl13])).
% 3.42/1.34 thf(zip_derived_cl38, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_3 @ e_4 @ X0)
% 3.42/1.34 | (product @ e_2 @ e_4 @ X0)
% 3.42/1.34 | (product @ e_1 @ e_4 @ X0)
% 3.42/1.34 | ~ (group_element @ X0)
% 3.42/1.34 | (equalish @ e_4 @ X0))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl7])).
% 3.42/1.34 thf(zip_derived_cl30, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i]:
% 3.42/1.34 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 3.42/1.34 thf(zip_derived_cl42, plain,
% 3.42/1.34 (( (equalish @ e_4 @ e_3)
% 3.42/1.34 | ~ (group_element @ e_3)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_3)
% 3.42/1.34 | (product @ e_2 @ e_4 @ e_3)
% 3.42/1.34 | (equalish @ e_3 @ e_4))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl30])).
% 3.42/1.34 thf(zip_derived_cl19, plain, (~ (equalish @ e_4 @ e_3)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 3.42/1.34 thf(zip_derived_cl6, plain, ( (group_element @ e_3)),
% 3.42/1.34 inference('cnf', [status(esa)], [element_3])).
% 3.42/1.34 thf(zip_derived_cl16, plain, (~ (equalish @ e_3 @ e_4)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 3.42/1.34 thf(zip_derived_cl43, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_3) | (product @ e_2 @ e_4 @ e_3))),
% 3.42/1.34 inference('demod', [status(thm)],
% 3.42/1.34 [zip_derived_cl42, zip_derived_cl19, zip_derived_cl6,
% 3.42/1.34 zip_derived_cl16])).
% 3.42/1.34 thf(zip_derived_cl21, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.42/1.34 (~ (product @ X0 @ X1 @ X2)
% 3.42/1.34 | ~ (product @ X0 @ X1 @ X3)
% 3.42/1.34 | (equalish @ X2 @ X3))),
% 3.42/1.34 inference('cnf', [status(esa)], [product_total_function2])).
% 3.42/1.34 thf(zip_derived_cl44, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_1 @ e_4 @ e_3)
% 3.42/1.34 | (equalish @ e_3 @ X0)
% 3.42/1.34 | ~ (product @ e_2 @ e_4 @ X0))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl21])).
% 3.42/1.34 thf(zip_derived_cl404, plain,
% 3.42/1.34 (( (product @ e_1 @ e_3 @ e_4)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_1)
% 3.42/1.34 | (equalish @ e_3 @ e_1)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_3))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl294, zip_derived_cl44])).
% 3.42/1.34 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 3.42/1.34 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_1)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 3.42/1.34 thf(zip_derived_cl405, plain,
% 3.42/1.34 (( (product @ e_1 @ e_3 @ e_4)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_1)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_3))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl404, zip_derived_cl14])).
% 3.42/1.34 thf(zip_derived_cl240, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_2) | (product @ e_1 @ e_3 @ e_4))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl236, zip_derived_cl13])).
% 3.42/1.34 thf(zip_derived_cl21, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.42/1.34 (~ (product @ X0 @ X1 @ X2)
% 3.42/1.34 | ~ (product @ X0 @ X1 @ X3)
% 3.42/1.34 | (equalish @ X2 @ X3))),
% 3.42/1.34 inference('cnf', [status(esa)], [product_total_function2])).
% 3.42/1.34 thf(zip_derived_cl245, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_1 @ e_3 @ e_4)
% 3.42/1.34 | (equalish @ e_2 @ X0)
% 3.42/1.34 | ~ (product @ e_1 @ e_4 @ X0))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl240, zip_derived_cl21])).
% 3.42/1.34 thf(zip_derived_cl419, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_1)
% 3.42/1.34 | (product @ e_1 @ e_3 @ e_4)
% 3.42/1.34 | (equalish @ e_2 @ e_3)
% 3.42/1.34 | (product @ e_1 @ e_3 @ e_4))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl405, zip_derived_cl245])).
% 3.42/1.34 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 3.42/1.34 thf(zip_derived_cl12, plain, (~ (equalish @ e_2 @ e_3)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 3.42/1.34 thf(zip_derived_cl424, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_1)
% 3.42/1.34 | (product @ e_1 @ e_3 @ e_4)
% 3.42/1.34 | (product @ e_1 @ e_3 @ e_4))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl419, zip_derived_cl12])).
% 3.42/1.34 thf(zip_derived_cl425, plain,
% 3.42/1.34 (( (product @ e_1 @ e_3 @ e_4) | (product @ e_1 @ e_4 @ e_1))),
% 3.42/1.34 inference('simplify', [status(thm)], [zip_derived_cl424])).
% 3.42/1.34 thf(zip_derived_cl30, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i]:
% 3.42/1.34 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 3.42/1.34 thf(zip_derived_cl432, plain,
% 3.42/1.34 (( (product @ e_1 @ e_3 @ e_4) | (equalish @ e_1 @ e_4))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl425, zip_derived_cl30])).
% 3.42/1.34 thf(zip_derived_cl10, plain, (~ (equalish @ e_1 @ e_4)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 3.42/1.34 thf(zip_derived_cl437, plain, ( (product @ e_1 @ e_3 @ e_4)),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl432, zip_derived_cl10])).
% 3.42/1.34 thf(zip_derived_cl2, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.42/1.34 (~ (product @ X0 @ X1 @ X2)
% 3.42/1.34 | ~ (product @ X3 @ X2 @ X0)
% 3.42/1.34 | (product @ X1 @ X0 @ X3))),
% 3.42/1.34 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.42/1.34 thf(zip_derived_cl441, plain,
% 3.42/1.34 (![X0 : $i]: ( (product @ e_3 @ e_1 @ X0) | ~ (product @ X0 @ e_4 @ e_1))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl437, zip_derived_cl2])).
% 3.42/1.34 thf(zip_derived_cl460, plain,
% 3.42/1.34 (( (equalish @ e_4 @ e_1)
% 3.42/1.34 | ~ (group_element @ e_1)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_1)
% 3.42/1.34 | (product @ e_2 @ e_4 @ e_1)
% 3.42/1.34 | (product @ e_3 @ e_1 @ e_3))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl441])).
% 3.42/1.34 thf(zip_derived_cl17, plain, (~ (equalish @ e_4 @ e_1)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 3.42/1.34 thf(zip_derived_cl4, plain, ( (group_element @ e_1)),
% 3.42/1.34 inference('cnf', [status(esa)], [element_1])).
% 3.42/1.34 thf(zip_derived_cl462, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_1)
% 3.42/1.34 | (product @ e_2 @ e_4 @ e_1)
% 3.42/1.34 | (product @ e_3 @ e_1 @ e_3))),
% 3.42/1.34 inference('demod', [status(thm)],
% 3.42/1.34 [zip_derived_cl460, zip_derived_cl17, zip_derived_cl4])).
% 3.42/1.34 thf(zip_derived_cl30, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i]:
% 3.42/1.34 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 3.42/1.34 thf(zip_derived_cl500, plain,
% 3.42/1.34 (( (product @ e_2 @ e_4 @ e_1)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_1)
% 3.42/1.34 | (equalish @ e_3 @ e_1))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl462, zip_derived_cl30])).
% 3.42/1.34 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_1)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 3.42/1.34 thf(zip_derived_cl503, plain,
% 3.42/1.34 (( (product @ e_2 @ e_4 @ e_1) | (product @ e_1 @ e_4 @ e_1))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl500, zip_derived_cl14])).
% 3.42/1.34 thf(zip_derived_cl441, plain,
% 3.42/1.34 (![X0 : $i]: ( (product @ e_3 @ e_1 @ X0) | ~ (product @ X0 @ e_4 @ e_1))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl437, zip_derived_cl2])).
% 3.42/1.34 thf(zip_derived_cl510, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_1) | (product @ e_3 @ e_1 @ e_2))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl503, zip_derived_cl441])).
% 3.42/1.34 thf(zip_derived_cl22, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.42/1.34 (~ (product @ X0 @ X1 @ X2)
% 3.42/1.34 | ~ (product @ X0 @ X3 @ X2)
% 3.42/1.34 | (equalish @ X1 @ X3))),
% 3.42/1.34 inference('cnf', [status(esa)], [product_right_cancellation])).
% 3.42/1.34 thf(zip_derived_cl516, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_1 @ e_4 @ e_1)
% 3.42/1.34 | (equalish @ e_1 @ X0)
% 3.42/1.34 | ~ (product @ e_3 @ X0 @ e_2))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl510, zip_derived_cl22])).
% 3.42/1.34 thf(zip_derived_cl560, plain,
% 3.42/1.34 (( (equalish @ e_4 @ e_2)
% 3.42/1.34 | ~ (group_element @ e_2)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_2)
% 3.42/1.34 | (product @ e_2 @ e_4 @ e_2)
% 3.42/1.34 | (equalish @ e_1 @ e_4)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_1))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl516])).
% 3.42/1.34 thf(zip_derived_cl18, plain, (~ (equalish @ e_4 @ e_2)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 3.42/1.34 thf(zip_derived_cl5, plain, ( (group_element @ e_2)),
% 3.42/1.34 inference('cnf', [status(esa)], [element_2])).
% 3.42/1.34 thf(zip_derived_cl10, plain, (~ (equalish @ e_1 @ e_4)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 3.42/1.34 thf(zip_derived_cl563, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_2)
% 3.42/1.34 | (product @ e_2 @ e_4 @ e_2)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_1))),
% 3.42/1.34 inference('demod', [status(thm)],
% 3.42/1.34 [zip_derived_cl560, zip_derived_cl18, zip_derived_cl5,
% 3.42/1.34 zip_derived_cl10])).
% 3.42/1.34 thf(zip_derived_cl30, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i]:
% 3.42/1.34 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 3.42/1.34 thf(zip_derived_cl688, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_1)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_2)
% 3.42/1.34 | (equalish @ e_2 @ e_4))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl563, zip_derived_cl30])).
% 3.42/1.34 thf(zip_derived_cl13, plain, (~ (equalish @ e_2 @ e_4)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 3.42/1.34 thf(zip_derived_cl693, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_1) | (product @ e_1 @ e_4 @ e_2))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl688, zip_derived_cl13])).
% 3.42/1.34 thf(zip_derived_cl503, plain,
% 3.42/1.34 (( (product @ e_2 @ e_4 @ e_1) | (product @ e_1 @ e_4 @ e_1))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl500, zip_derived_cl14])).
% 3.42/1.34 thf(zip_derived_cl44, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_1 @ e_4 @ e_3)
% 3.42/1.34 | (equalish @ e_3 @ X0)
% 3.42/1.34 | ~ (product @ e_2 @ e_4 @ X0))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl21])).
% 3.42/1.34 thf(zip_derived_cl511, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_1)
% 3.42/1.34 | (equalish @ e_3 @ e_1)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_3))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl503, zip_derived_cl44])).
% 3.42/1.34 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_1)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 3.42/1.34 thf(zip_derived_cl512, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_1) | (product @ e_1 @ e_4 @ e_3))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl511, zip_derived_cl14])).
% 3.42/1.34 thf(zip_derived_cl21, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.42/1.34 (~ (product @ X0 @ X1 @ X2)
% 3.42/1.34 | ~ (product @ X0 @ X1 @ X3)
% 3.42/1.34 | (equalish @ X2 @ X3))),
% 3.42/1.34 inference('cnf', [status(esa)], [product_total_function2])).
% 3.42/1.34 thf(zip_derived_cl522, plain,
% 3.42/1.34 (![X0 : $i]:
% 3.42/1.34 ( (product @ e_1 @ e_4 @ e_1)
% 3.42/1.34 | (equalish @ e_3 @ X0)
% 3.42/1.34 | ~ (product @ e_1 @ e_4 @ X0))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl512, zip_derived_cl21])).
% 3.42/1.34 thf(zip_derived_cl705, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_1)
% 3.42/1.34 | (equalish @ e_3 @ e_2)
% 3.42/1.34 | (product @ e_1 @ e_4 @ e_1))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl693, zip_derived_cl522])).
% 3.42/1.34 thf(zip_derived_cl15, plain, (~ (equalish @ e_3 @ e_2)),
% 3.42/1.34 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 3.42/1.34 thf(zip_derived_cl707, plain,
% 3.42/1.34 (( (product @ e_1 @ e_4 @ e_1) | (product @ e_1 @ e_4 @ e_1))),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl705, zip_derived_cl15])).
% 3.42/1.34 thf(zip_derived_cl708, plain, ( (product @ e_1 @ e_4 @ e_1)),
% 3.42/1.34 inference('simplify', [status(thm)], [zip_derived_cl707])).
% 3.42/1.34 thf(zip_derived_cl30, plain,
% 3.42/1.34 (![X0 : $i, X1 : $i]:
% 3.42/1.34 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 3.42/1.34 thf(zip_derived_cl715, plain, ( (equalish @ e_1 @ e_4)),
% 3.42/1.34 inference('sup-', [status(thm)], [zip_derived_cl708, zip_derived_cl30])).
% 3.42/1.34 thf(zip_derived_cl720, plain, ($false),
% 3.42/1.34 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl715])).
% 3.42/1.34
% 3.42/1.34 % SZS output end Refutation
% 3.42/1.34
% 3.42/1.34
% 3.42/1.34 % Terminating...
% 3.81/1.53 % Runner terminated.
% 3.81/1.56 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------