%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP124-2.004 : TPTP v9.2.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Xysl3ogWmg true
% Computer : n009.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 04:35:41 PM UTC 2025
% Result : Unsatisfiable 0.47s 0.91s
% Output : Refutation 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : GRP124-2.004 : TPTP v9.2.0. Released v1.2.0.
% 0.03/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Xysl3ogWmg true
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 1 14:13:23 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running portfolio for 300 s
% 0.14/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.34 % Number of cores: 8
% 0.14/0.34 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.42/0.61 % Total configuration time : 435
% 0.42/0.61 % Estimated wc time : 1092
% 0.42/0.61 % Estimated cpu time (7 cpus) : 156.0
% 0.46/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.46/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.46/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.47/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.47/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.47/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.47/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.47/0.91 % Solved by fo/fo7.sh.
% 0.47/0.91 % done 284 iterations in 0.146s
% 0.47/0.91 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.47/0.91 % SZS output start Refutation
% 0.47/0.91 thf(group_element_type, type, group_element: $i > $o).
% 0.47/0.91 thf(e_4_type, type, e_4: $i).
% 0.47/0.91 thf(equalish_type, type, equalish: $i > $i > $o).
% 0.47/0.91 thf(e_3_type, type, e_3: $i).
% 0.47/0.91 thf(e_2_type, type, e_2: $i).
% 0.47/0.91 thf(e_1_type, type, e_1: $i).
% 0.47/0.91 thf(product_type, type, product: $i > $i > $i > $o).
% 0.47/0.91 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 0.47/0.91 thf(zip_derived_cl25, plain, (~ (equalish @ e_4 @ e_3)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 0.47/0.91 thf(product_idempotence, axiom, (product @ X @ X @ X)).
% 0.47/0.91 thf(zip_derived_cl30, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.47/0.91 inference('cnf', [status(esa)], [product_idempotence])).
% 0.47/0.91 thf(product_total_function1, axiom,
% 0.47/0.91 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 0.47/0.91 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 0.47/0.91 ( product @ X @ Y @ e_3 ) | ( product @ X @ Y @ e_4 ))).
% 0.47/0.91 thf(zip_derived_cl26, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 (~ (group_element @ X0)
% 0.47/0.91 | ~ (group_element @ X1)
% 0.47/0.91 | (product @ X0 @ X1 @ e_1)
% 0.47/0.91 | (product @ X0 @ X1 @ e_2)
% 0.47/0.91 | (product @ X0 @ X1 @ e_3)
% 0.47/0.91 | (product @ X0 @ X1 @ e_4))),
% 0.47/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.47/0.91 thf(zip_derived_cl26, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 (~ (group_element @ X0)
% 0.47/0.91 | ~ (group_element @ X1)
% 0.47/0.91 | (product @ X0 @ X1 @ e_1)
% 0.47/0.91 | (product @ X0 @ X1 @ e_2)
% 0.47/0.91 | (product @ X0 @ X1 @ e_3)
% 0.47/0.91 | (product @ X0 @ X1 @ e_4))),
% 0.47/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.47/0.91 thf(zip_derived_cl30, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.47/0.91 inference('cnf', [status(esa)], [product_idempotence])).
% 0.47/0.91 thf(product_right_cancellation, axiom,
% 0.47/0.91 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 0.47/0.91 ( equalish @ W @ Z ))).
% 0.47/0.91 thf(zip_derived_cl28, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.47/0.91 (~ (product @ X0 @ X1 @ X2)
% 0.47/0.91 | ~ (product @ X0 @ X3 @ X2)
% 0.47/0.91 | (equalish @ X1 @ X3))),
% 0.47/0.91 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.47/0.91 thf(zip_derived_cl36, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 0.47/0.91 thf(zip_derived_cl25, plain, (~ (equalish @ e_4 @ e_3)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 0.47/0.91 thf(zip_derived_cl66, plain, (~ (product @ e_4 @ e_3 @ e_4)),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl25])).
% 0.47/0.91 thf(zip_derived_cl119, plain,
% 0.47/0.91 (( (product @ e_4 @ e_3 @ e_3)
% 0.47/0.91 | (product @ e_4 @ e_3 @ e_2)
% 0.47/0.91 | (product @ e_4 @ e_3 @ e_1)
% 0.47/0.91 | ~ (group_element @ e_3)
% 0.47/0.91 | ~ (group_element @ e_4))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl66])).
% 0.47/0.91 thf(element_3, axiom, (group_element @ e_3)).
% 0.47/0.91 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 0.47/0.91 inference('cnf', [status(esa)], [element_3])).
% 0.47/0.91 thf(element_4, axiom, (group_element @ e_4)).
% 0.47/0.91 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 0.47/0.91 inference('cnf', [status(esa)], [element_4])).
% 0.47/0.91 thf(zip_derived_cl126, plain,
% 0.47/0.91 (( (product @ e_4 @ e_3 @ e_3)
% 0.47/0.91 | (product @ e_4 @ e_3 @ e_2)
% 0.47/0.91 | (product @ e_4 @ e_3 @ e_1))),
% 0.47/0.91 inference('demod', [status(thm)],
% 0.47/0.91 [zip_derived_cl119, zip_derived_cl12, zip_derived_cl13])).
% 0.47/0.91 thf(zip_derived_cl30, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.47/0.91 inference('cnf', [status(esa)], [product_idempotence])).
% 0.47/0.91 thf(product_left_cancellation, axiom,
% 0.47/0.91 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 0.47/0.91 ( equalish @ W @ Z ))).
% 0.47/0.91 thf(zip_derived_cl29, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.47/0.91 (~ (product @ X0 @ X1 @ X2)
% 0.47/0.91 | ~ (product @ X3 @ X1 @ X2)
% 0.47/0.91 | (equalish @ X0 @ X3))),
% 0.47/0.91 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.47/0.91 thf(zip_derived_cl40, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 ( (equalish @ X0 @ X1) | ~ (product @ X1 @ X0 @ X0))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 0.47/0.91 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 0.47/0.91 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 0.47/0.91 thf(zip_derived_cl75, plain, (~ (product @ e_4 @ e_3 @ e_3)),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl22])).
% 0.47/0.91 thf(zip_derived_cl181, plain,
% 0.47/0.91 (( (product @ e_4 @ e_3 @ e_1) | (product @ e_4 @ e_3 @ e_2))),
% 0.47/0.91 inference('clc', [status(thm)], [zip_derived_cl126, zip_derived_cl75])).
% 0.47/0.91 thf(zip_derived_cl28, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.47/0.91 (~ (product @ X0 @ X1 @ X2)
% 0.47/0.91 | ~ (product @ X0 @ X3 @ X2)
% 0.47/0.91 | (equalish @ X1 @ X3))),
% 0.47/0.91 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.47/0.91 thf(zip_derived_cl183, plain,
% 0.47/0.91 (![X0 : $i]:
% 0.47/0.91 ( (product @ e_4 @ e_3 @ e_1)
% 0.47/0.91 | (equalish @ e_3 @ X0)
% 0.47/0.91 | ~ (product @ e_4 @ X0 @ e_2))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl181, zip_derived_cl28])).
% 0.47/0.91 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 0.47/0.91 thf(zip_derived_cl20, plain, (~ (equalish @ e_3 @ e_1)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.47/0.91 thf(zip_derived_cl287, plain,
% 0.47/0.91 ((~ (product @ e_4 @ e_1 @ e_2) | (product @ e_4 @ e_3 @ e_1))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl183, zip_derived_cl20])).
% 0.47/0.91 thf(zip_derived_cl26, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 (~ (group_element @ X0)
% 0.47/0.91 | ~ (group_element @ X1)
% 0.47/0.91 | (product @ X0 @ X1 @ e_1)
% 0.47/0.91 | (product @ X0 @ X1 @ e_2)
% 0.47/0.91 | (product @ X0 @ X1 @ e_3)
% 0.47/0.91 | (product @ X0 @ X1 @ e_4))),
% 0.47/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.47/0.91 thf(zip_derived_cl36, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 0.47/0.91 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 0.47/0.91 thf(zip_derived_cl23, plain, (~ (equalish @ e_4 @ e_1)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.47/0.91 thf(zip_derived_cl64, plain, (~ (product @ e_4 @ e_1 @ e_4)),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl23])).
% 0.47/0.91 thf(zip_derived_cl117, plain,
% 0.47/0.91 (( (product @ e_4 @ e_1 @ e_3)
% 0.47/0.91 | (product @ e_4 @ e_1 @ e_2)
% 0.47/0.91 | (product @ e_4 @ e_1 @ e_1)
% 0.47/0.91 | ~ (group_element @ e_1)
% 0.47/0.91 | ~ (group_element @ e_4))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl64])).
% 0.47/0.91 thf(zip_derived_cl40, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 ( (equalish @ X0 @ X1) | ~ (product @ X1 @ X0 @ X0))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 0.47/0.91 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 0.47/0.91 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 0.47/0.91 thf(zip_derived_cl69, plain, (~ (product @ e_4 @ e_1 @ e_1)),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl16])).
% 0.47/0.91 thf(element_1, axiom, (group_element @ e_1)).
% 0.47/0.91 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 0.47/0.91 inference('cnf', [status(esa)], [element_1])).
% 0.47/0.91 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 0.47/0.91 inference('cnf', [status(esa)], [element_4])).
% 0.47/0.91 thf(zip_derived_cl124, plain,
% 0.47/0.91 (( (product @ e_4 @ e_1 @ e_3) | (product @ e_4 @ e_1 @ e_2))),
% 0.47/0.91 inference('demod', [status(thm)],
% 0.47/0.91 [zip_derived_cl117, zip_derived_cl69, zip_derived_cl10,
% 0.47/0.91 zip_derived_cl13])).
% 0.47/0.91 thf(zip_derived_cl30, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.47/0.91 inference('cnf', [status(esa)], [product_idempotence])).
% 0.47/0.91 thf(qg2_1, conjecture,
% 0.47/0.91 (~( ( equalish @ X1 @ X2 ) | ( ~( product @ Z2 @ X2 @ Y2 ) ) |
% 0.47/0.91 ( ~( product @ Z2 @ X1 @ Y1 ) ) | ( ~( product @ X2 @ Y2 @ Z1 ) ) |
% 0.47/0.91 ( ~( product @ X1 @ Y1 @ Z1 ) ) ))).
% 0.47/0.91 thf(zf_stmt_0, negated_conjecture,
% 0.47/0.91 (( equalish @ X1 @ X2 ) | ( ~( product @ Z2 @ X2 @ Y2 ) ) |
% 0.47/0.91 ( ~( product @ Z2 @ X1 @ Y1 ) ) | ( ~( product @ X2 @ Y2 @ Z1 ) ) |
% 0.47/0.91 ( ~( product @ X1 @ Y1 @ Z1 ) )),
% 0.47/0.91 inference('cnf.neg', [status(esa)], [qg2_1])).
% 0.47/0.91 thf(zip_derived_cl31, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.47/0.91 ( (equalish @ X0 @ X1)
% 0.47/0.91 | ~ (product @ X2 @ X1 @ X3)
% 0.47/0.91 | ~ (product @ X2 @ X0 @ X4)
% 0.47/0.91 | ~ (product @ X1 @ X3 @ X5)
% 0.47/0.91 | ~ (product @ X0 @ X4 @ X5))),
% 0.47/0.91 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.47/0.91 thf(zip_derived_cl79, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.47/0.91 (~ (product @ X3 @ X2 @ X1)
% 0.47/0.91 | ~ (product @ X0 @ X0 @ X1)
% 0.47/0.91 | ~ (product @ X0 @ X3 @ X2)
% 0.47/0.91 | (equalish @ X3 @ X0))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl31])).
% 0.47/0.91 thf(zip_derived_cl133, plain,
% 0.47/0.91 (![X0 : $i]:
% 0.47/0.91 ( (product @ e_4 @ e_1 @ e_2)
% 0.47/0.91 | (equalish @ e_4 @ X0)
% 0.47/0.91 | ~ (product @ X0 @ e_4 @ e_1)
% 0.47/0.91 | ~ (product @ X0 @ X0 @ e_3))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl124, zip_derived_cl79])).
% 0.47/0.91 thf(zip_derived_cl25, plain, (~ (equalish @ e_4 @ e_3)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 0.47/0.91 thf(zip_derived_cl344, plain,
% 0.47/0.91 ((~ (product @ e_3 @ e_3 @ e_3)
% 0.47/0.91 | ~ (product @ e_3 @ e_4 @ e_1)
% 0.47/0.91 | (product @ e_4 @ e_1 @ e_2))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl25])).
% 0.47/0.91 thf(zip_derived_cl30, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.47/0.91 inference('cnf', [status(esa)], [product_idempotence])).
% 0.47/0.91 thf(zip_derived_cl348, plain,
% 0.47/0.91 ((~ (product @ e_3 @ e_4 @ e_1) | (product @ e_4 @ e_1 @ e_2))),
% 0.47/0.91 inference('demod', [status(thm)], [zip_derived_cl344, zip_derived_cl30])).
% 0.47/0.91 thf(zip_derived_cl26, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 (~ (group_element @ X0)
% 0.47/0.91 | ~ (group_element @ X1)
% 0.47/0.91 | (product @ X0 @ X1 @ e_1)
% 0.47/0.91 | (product @ X0 @ X1 @ e_2)
% 0.47/0.91 | (product @ X0 @ X1 @ e_3)
% 0.47/0.91 | (product @ X0 @ X1 @ e_4))),
% 0.47/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.47/0.91 thf(zip_derived_cl26, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 (~ (group_element @ X0)
% 0.47/0.91 | ~ (group_element @ X1)
% 0.47/0.91 | (product @ X0 @ X1 @ e_1)
% 0.47/0.91 | (product @ X0 @ X1 @ e_2)
% 0.47/0.91 | (product @ X0 @ X1 @ e_3)
% 0.47/0.91 | (product @ X0 @ X1 @ e_4))),
% 0.47/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.47/0.91 thf(zip_derived_cl40, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 ( (equalish @ X0 @ X1) | ~ (product @ X1 @ X0 @ X0))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 0.47/0.91 thf(zip_derived_cl23, plain, (~ (equalish @ e_4 @ e_1)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.47/0.91 thf(zip_derived_cl76, plain, (~ (product @ e_1 @ e_4 @ e_4)),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl23])).
% 0.47/0.91 thf(zip_derived_cl144, plain,
% 0.47/0.91 (( (product @ e_1 @ e_4 @ e_3)
% 0.47/0.91 | (product @ e_1 @ e_4 @ e_2)
% 0.47/0.91 | (product @ e_1 @ e_4 @ e_1)
% 0.47/0.91 | ~ (group_element @ e_4)
% 0.47/0.91 | ~ (group_element @ e_1))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl76])).
% 0.47/0.91 thf(zip_derived_cl36, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 0.47/0.91 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 0.47/0.91 thf(zip_derived_cl57, plain, (~ (product @ e_1 @ e_4 @ e_1)),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl16])).
% 0.47/0.91 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 0.47/0.91 inference('cnf', [status(esa)], [element_4])).
% 0.47/0.91 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 0.47/0.91 inference('cnf', [status(esa)], [element_1])).
% 0.47/0.91 thf(zip_derived_cl145, plain,
% 0.47/0.91 (( (product @ e_1 @ e_4 @ e_3) | (product @ e_1 @ e_4 @ e_2))),
% 0.47/0.91 inference('demod', [status(thm)],
% 0.47/0.91 [zip_derived_cl144, zip_derived_cl57, zip_derived_cl13,
% 0.47/0.91 zip_derived_cl10])).
% 0.47/0.91 thf(zip_derived_cl79, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.47/0.91 (~ (product @ X3 @ X2 @ X1)
% 0.47/0.91 | ~ (product @ X0 @ X0 @ X1)
% 0.47/0.91 | ~ (product @ X0 @ X3 @ X2)
% 0.47/0.91 | (equalish @ X3 @ X0))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl31])).
% 0.47/0.91 thf(zip_derived_cl156, plain,
% 0.47/0.91 (![X0 : $i]:
% 0.47/0.91 ( (product @ e_1 @ e_4 @ e_2)
% 0.47/0.91 | (equalish @ e_1 @ X0)
% 0.47/0.91 | ~ (product @ X0 @ e_1 @ e_4)
% 0.47/0.91 | ~ (product @ X0 @ X0 @ e_3))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl79])).
% 0.47/0.91 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 0.47/0.91 thf(zip_derived_cl15, plain, (~ (equalish @ e_1 @ e_3)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.47/0.91 thf(zip_derived_cl389, plain,
% 0.47/0.91 ((~ (product @ e_3 @ e_3 @ e_3)
% 0.47/0.91 | ~ (product @ e_3 @ e_1 @ e_4)
% 0.47/0.91 | (product @ e_1 @ e_4 @ e_2))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl156, zip_derived_cl15])).
% 0.47/0.91 thf(zip_derived_cl30, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.47/0.91 inference('cnf', [status(esa)], [product_idempotence])).
% 0.47/0.91 thf(zip_derived_cl391, plain,
% 0.47/0.91 ((~ (product @ e_3 @ e_1 @ e_4) | (product @ e_1 @ e_4 @ e_2))),
% 0.47/0.91 inference('demod', [status(thm)], [zip_derived_cl389, zip_derived_cl30])).
% 0.47/0.91 thf(zip_derived_cl393, plain,
% 0.47/0.91 (( (product @ e_3 @ e_1 @ e_3)
% 0.47/0.91 | (product @ e_3 @ e_1 @ e_2)
% 0.47/0.91 | (product @ e_3 @ e_1 @ e_1)
% 0.47/0.91 | ~ (group_element @ e_1)
% 0.47/0.91 | ~ (group_element @ e_3)
% 0.47/0.91 | (product @ e_1 @ e_4 @ e_2))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl391])).
% 0.47/0.91 thf(zip_derived_cl40, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 ( (equalish @ X0 @ X1) | ~ (product @ X1 @ X0 @ X0))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 0.47/0.91 thf(zip_derived_cl15, plain, (~ (equalish @ e_1 @ e_3)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.47/0.91 thf(zip_derived_cl68, plain, (~ (product @ e_3 @ e_1 @ e_1)),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl15])).
% 0.47/0.91 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 0.47/0.91 inference('cnf', [status(esa)], [element_1])).
% 0.47/0.91 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 0.47/0.91 inference('cnf', [status(esa)], [element_3])).
% 0.47/0.91 thf(zip_derived_cl394, plain,
% 0.47/0.91 (( (product @ e_3 @ e_1 @ e_3)
% 0.47/0.91 | (product @ e_3 @ e_1 @ e_2)
% 0.47/0.91 | (product @ e_1 @ e_4 @ e_2))),
% 0.47/0.91 inference('demod', [status(thm)],
% 0.47/0.91 [zip_derived_cl393, zip_derived_cl68, zip_derived_cl10,
% 0.47/0.91 zip_derived_cl12])).
% 0.47/0.91 thf(zip_derived_cl36, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 0.47/0.91 thf(zip_derived_cl20, plain, (~ (equalish @ e_3 @ e_1)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.47/0.91 thf(zip_derived_cl61, plain, (~ (product @ e_3 @ e_1 @ e_3)),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl20])).
% 0.47/0.91 thf(zip_derived_cl397, plain,
% 0.47/0.91 (( (product @ e_1 @ e_4 @ e_2) | (product @ e_3 @ e_1 @ e_2))),
% 0.47/0.91 inference('clc', [status(thm)], [zip_derived_cl394, zip_derived_cl61])).
% 0.47/0.91 thf(zip_derived_cl26, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 (~ (group_element @ X0)
% 0.47/0.91 | ~ (group_element @ X1)
% 0.47/0.91 | (product @ X0 @ X1 @ e_1)
% 0.47/0.91 | (product @ X0 @ X1 @ e_2)
% 0.47/0.91 | (product @ X0 @ X1 @ e_3)
% 0.47/0.91 | (product @ X0 @ X1 @ e_4))),
% 0.47/0.91 inference('cnf', [status(esa)], [product_total_function1])).
% 0.47/0.91 thf(zip_derived_cl40, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 ( (equalish @ X0 @ X1) | ~ (product @ X1 @ X0 @ X0))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 0.47/0.91 thf(zip_derived_cl25, plain, (~ (equalish @ e_4 @ e_3)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 0.47/0.91 thf(zip_derived_cl78, plain, (~ (product @ e_3 @ e_4 @ e_4)),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl25])).
% 0.47/0.91 thf(zip_derived_cl148, plain,
% 0.47/0.91 (( (product @ e_3 @ e_4 @ e_3)
% 0.47/0.91 | (product @ e_3 @ e_4 @ e_2)
% 0.47/0.91 | (product @ e_3 @ e_4 @ e_1)
% 0.47/0.91 | ~ (group_element @ e_4)
% 0.47/0.91 | ~ (group_element @ e_3))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl78])).
% 0.47/0.91 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 0.47/0.91 inference('cnf', [status(esa)], [element_4])).
% 0.47/0.91 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 0.47/0.91 inference('cnf', [status(esa)], [element_3])).
% 0.47/0.91 thf(zip_derived_cl149, plain,
% 0.47/0.91 (( (product @ e_3 @ e_4 @ e_3)
% 0.47/0.91 | (product @ e_3 @ e_4 @ e_2)
% 0.47/0.91 | (product @ e_3 @ e_4 @ e_1))),
% 0.47/0.91 inference('demod', [status(thm)],
% 0.47/0.91 [zip_derived_cl148, zip_derived_cl13, zip_derived_cl12])).
% 0.47/0.91 thf(zip_derived_cl36, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 ( (equalish @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 0.47/0.91 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 0.47/0.91 thf(zip_derived_cl63, plain, (~ (product @ e_3 @ e_4 @ e_3)),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl22])).
% 0.47/0.91 thf(zip_derived_cl192, plain,
% 0.47/0.91 (( (product @ e_3 @ e_4 @ e_1) | (product @ e_3 @ e_4 @ e_2))),
% 0.47/0.91 inference('clc', [status(thm)], [zip_derived_cl149, zip_derived_cl63])).
% 0.47/0.91 thf(zip_derived_cl28, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.47/0.91 (~ (product @ X0 @ X1 @ X2)
% 0.47/0.91 | ~ (product @ X0 @ X3 @ X2)
% 0.47/0.91 | (equalish @ X1 @ X3))),
% 0.47/0.91 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.47/0.91 thf(zip_derived_cl194, plain,
% 0.47/0.91 (![X0 : $i]:
% 0.47/0.91 ( (product @ e_3 @ e_4 @ e_1)
% 0.47/0.91 | (equalish @ e_4 @ X0)
% 0.47/0.91 | ~ (product @ e_3 @ X0 @ e_2))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl192, zip_derived_cl28])).
% 0.47/0.91 thf(zip_derived_cl23, plain, (~ (equalish @ e_4 @ e_1)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.47/0.91 thf(zip_derived_cl300, plain,
% 0.47/0.91 ((~ (product @ e_3 @ e_1 @ e_2) | (product @ e_3 @ e_4 @ e_1))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl194, zip_derived_cl23])).
% 0.47/0.91 thf(zip_derived_cl407, plain,
% 0.47/0.91 (( (product @ e_1 @ e_4 @ e_2) | (product @ e_3 @ e_4 @ e_1))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl397, zip_derived_cl300])).
% 0.47/0.91 thf(zip_derived_cl192, plain,
% 0.47/0.91 (( (product @ e_3 @ e_4 @ e_1) | (product @ e_3 @ e_4 @ e_2))),
% 0.47/0.91 inference('clc', [status(thm)], [zip_derived_cl149, zip_derived_cl63])).
% 0.47/0.91 thf(zip_derived_cl29, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.47/0.91 (~ (product @ X0 @ X1 @ X2)
% 0.47/0.91 | ~ (product @ X3 @ X1 @ X2)
% 0.47/0.91 | (equalish @ X0 @ X3))),
% 0.47/0.91 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.47/0.91 thf(zip_derived_cl195, plain,
% 0.47/0.91 (![X0 : $i]:
% 0.47/0.91 ( (product @ e_3 @ e_4 @ e_1)
% 0.47/0.91 | (equalish @ e_3 @ X0)
% 0.47/0.91 | ~ (product @ X0 @ e_4 @ e_2))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl192, zip_derived_cl29])).
% 0.47/0.91 thf(zip_derived_cl20, plain, (~ (equalish @ e_3 @ e_1)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.47/0.91 thf(zip_derived_cl305, plain,
% 0.47/0.91 ((~ (product @ e_1 @ e_4 @ e_2) | (product @ e_3 @ e_4 @ e_1))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl195, zip_derived_cl20])).
% 0.47/0.91 thf(zip_derived_cl410, plain, ( (product @ e_3 @ e_4 @ e_1)),
% 0.47/0.91 inference('clc', [status(thm)], [zip_derived_cl407, zip_derived_cl305])).
% 0.47/0.91 thf(zip_derived_cl412, plain, ( (product @ e_4 @ e_1 @ e_2)),
% 0.47/0.91 inference('demod', [status(thm)], [zip_derived_cl348, zip_derived_cl410])).
% 0.47/0.91 thf(zip_derived_cl433, plain, ( (product @ e_4 @ e_3 @ e_1)),
% 0.47/0.91 inference('demod', [status(thm)], [zip_derived_cl287, zip_derived_cl412])).
% 0.47/0.91 thf(zip_derived_cl31, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.47/0.91 ( (equalish @ X0 @ X1)
% 0.47/0.91 | ~ (product @ X2 @ X1 @ X3)
% 0.47/0.91 | ~ (product @ X2 @ X0 @ X4)
% 0.47/0.91 | ~ (product @ X1 @ X3 @ X5)
% 0.47/0.91 | ~ (product @ X0 @ X4 @ X5))),
% 0.47/0.91 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.47/0.91 thf(zip_derived_cl449, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.47/0.91 (~ (product @ X2 @ X1 @ X0)
% 0.47/0.91 | ~ (product @ e_3 @ e_1 @ X0)
% 0.47/0.91 | ~ (product @ e_4 @ X2 @ X1)
% 0.47/0.91 | (equalish @ X2 @ e_3))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl433, zip_derived_cl31])).
% 0.47/0.91 thf(zip_derived_cl576, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 ( (product @ e_3 @ e_1 @ e_3)
% 0.47/0.91 | (product @ e_3 @ e_1 @ e_2)
% 0.47/0.91 | (product @ e_3 @ e_1 @ e_1)
% 0.47/0.91 | ~ (group_element @ e_1)
% 0.47/0.91 | ~ (group_element @ e_3)
% 0.47/0.91 | (equalish @ X0 @ e_3)
% 0.47/0.91 | ~ (product @ e_4 @ X0 @ X1)
% 0.47/0.91 | ~ (product @ X0 @ X1 @ e_4))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl449])).
% 0.47/0.91 thf(zip_derived_cl61, plain, (~ (product @ e_3 @ e_1 @ e_3)),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl20])).
% 0.47/0.91 thf(zip_derived_cl412, plain, ( (product @ e_4 @ e_1 @ e_2)),
% 0.47/0.91 inference('demod', [status(thm)], [zip_derived_cl348, zip_derived_cl410])).
% 0.47/0.91 thf(zip_derived_cl29, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.47/0.91 (~ (product @ X0 @ X1 @ X2)
% 0.47/0.91 | ~ (product @ X3 @ X1 @ X2)
% 0.47/0.91 | (equalish @ X0 @ X3))),
% 0.47/0.91 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.47/0.91 thf(zip_derived_cl436, plain,
% 0.47/0.91 (![X0 : $i]: ( (equalish @ e_4 @ X0) | ~ (product @ X0 @ e_1 @ e_2))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl412, zip_derived_cl29])).
% 0.47/0.91 thf(zip_derived_cl25, plain, (~ (equalish @ e_4 @ e_3)),
% 0.47/0.91 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 0.47/0.91 thf(zip_derived_cl483, plain, (~ (product @ e_3 @ e_1 @ e_2)),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl436, zip_derived_cl25])).
% 0.47/0.91 thf(zip_derived_cl68, plain, (~ (product @ e_3 @ e_1 @ e_1)),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl15])).
% 0.47/0.91 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 0.47/0.91 inference('cnf', [status(esa)], [element_1])).
% 0.47/0.91 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 0.47/0.91 inference('cnf', [status(esa)], [element_3])).
% 0.47/0.91 thf(zip_derived_cl579, plain,
% 0.47/0.91 (![X0 : $i, X1 : $i]:
% 0.47/0.91 ( (equalish @ X0 @ e_3)
% 0.47/0.91 | ~ (product @ e_4 @ X0 @ X1)
% 0.47/0.91 | ~ (product @ X0 @ X1 @ e_4))),
% 0.47/0.91 inference('demod', [status(thm)],
% 0.47/0.91 [zip_derived_cl576, zip_derived_cl61, zip_derived_cl483,
% 0.47/0.91 zip_derived_cl68, zip_derived_cl10, zip_derived_cl12])).
% 0.47/0.91 thf(zip_derived_cl581, plain,
% 0.47/0.91 ((~ (product @ e_4 @ e_4 @ e_4) | (equalish @ e_4 @ e_3))),
% 0.47/0.91 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl579])).
% 0.47/0.91 thf(zip_derived_cl30, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.47/0.91 inference('cnf', [status(esa)], [product_idempotence])).
% 0.47/0.91 thf(zip_derived_cl585, plain, ( (equalish @ e_4 @ e_3)),
% 0.47/0.91 inference('demod', [status(thm)], [zip_derived_cl581, zip_derived_cl30])).
% 0.47/0.91 thf(zip_derived_cl590, plain, ($false),
% 0.47/0.91 inference('demod', [status(thm)], [zip_derived_cl25, zip_derived_cl585])).
% 0.47/0.91
% 0.47/0.91 % SZS output end Refutation
% 0.47/0.91
% 0.47/0.91
% 0.47/0.91 % Terminating...
% 0.51/1.02 % Runner terminated.
% 2.01/1.04 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------