%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP130-3.003 : 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.HwxpX8dqyp true
% Computer : n008.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 04:35:47 PM UTC 2025
% Result : Unsatisfiable 3.73s 1.55s
% Output : Refutation 3.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : GRP130-3.003 : TPTP v9.2.0. Released v1.2.0.
% 0.10/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HwxpX8dqyp true
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Wed Oct 1 14:23:08 EDT 2025
% 0.18/0.35 % CPUTime :
% 0.18/0.35 % Running portfolio for 300 s
% 0.18/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.35 % Number of cores: 8
% 0.18/0.35 % Python version: Python 3.6.8
% 0.18/0.35 % Running in FO mode
% 0.53/0.65 % Total configuration time : 435
% 0.53/0.65 % Estimated wc time : 1092
% 0.53/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.88 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.53/0.89 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.92 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.53/0.93 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.54/0.95 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.54/0.98 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 3.73/1.55 % Solved by fo/fo7.sh.
% 3.73/1.55 % done 332 iterations in 0.538s
% 3.73/1.55 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 3.73/1.55 % SZS output start Refutation
% 3.73/1.55 thf(equalish_type, type, equalish: $i > $i > $o).
% 3.73/1.55 thf(group_element_type, type, group_element: $i > $o).
% 3.73/1.55 thf(product_type, type, product: $i > $i > $i > $o).
% 3.73/1.55 thf(e_3_type, type, e_3: $i).
% 3.73/1.55 thf(greater_type, type, greater: $i > $i > $o).
% 3.73/1.55 thf(e_2_type, type, e_2: $i).
% 3.73/1.55 thf(cycle_type, type, cycle: $i > $i > $o).
% 3.73/1.55 thf(e_1_type, type, e_1: $i).
% 3.73/1.55 thf(e_0_type, type, e_0: $i).
% 3.73/1.55 thf(next_type, type, next: $i > $i > $o).
% 3.73/1.55 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 3.73/1.55 thf(zip_derived_cl19, plain, (~ (equalish @ e_1 @ e_2)),
% 3.73/1.55 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 3.73/1.55 thf(product_total_function1, axiom,
% 3.73/1.55 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 3.73/1.55 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 3.73/1.55 ( product @ X @ Y @ e_3 ))).
% 3.73/1.55 thf(zip_derived_cl25, plain,
% 3.73/1.55 (![X0 : $i, X1 : $i]:
% 3.73/1.55 (~ (group_element @ X0)
% 3.73/1.55 | ~ (group_element @ X1)
% 3.73/1.55 | (product @ X0 @ X1 @ e_1)
% 3.73/1.55 | (product @ X0 @ X1 @ e_2)
% 3.73/1.55 | (product @ X0 @ X1 @ e_3))),
% 3.73/1.55 inference('cnf', [status(esa)], [product_total_function1])).
% 3.73/1.55 thf(e_3_greater_e_1, axiom, (greater @ e_3 @ e_1)).
% 3.73/1.55 thf(zip_derived_cl7, plain, ( (greater @ e_3 @ e_1)),
% 3.73/1.55 inference('cnf', [status(esa)], [e_3_greater_e_1])).
% 3.73/1.55 thf(zip_derived_cl25, plain,
% 3.73/1.55 (![X0 : $i, X1 : $i]:
% 3.73/1.55 (~ (group_element @ X0)
% 3.73/1.55 | ~ (group_element @ X1)
% 3.73/1.55 | (product @ X0 @ X1 @ e_1)
% 3.73/1.55 | (product @ X0 @ X1 @ e_2)
% 3.73/1.55 | (product @ X0 @ X1 @ e_3))),
% 3.73/1.55 inference('cnf', [status(esa)], [product_total_function1])).
% 3.73/1.55 thf(e_1_then_e_2, axiom, (next @ e_1 @ e_2)).
% 3.73/1.55 thf(zip_derived_cl1, plain, ( (next @ e_1 @ e_2)),
% 3.73/1.55 inference('cnf', [status(esa)], [e_1_then_e_2])).
% 3.73/1.55 thf(cycle2, axiom,
% 3.73/1.55 (( ~( group_element @ X ) ) | ( cycle @ X @ e_0 ) | ( cycle @ X @ e_1 ) |
% 3.73/1.55 ( cycle @ X @ e_2 ))).
% 3.73/1.55 thf(zip_derived_cl10, plain,
% 3.73/1.55 (![X0 : $i]:
% 3.73/1.55 (~ (group_element @ X0)
% 3.73/1.55 | (cycle @ X0 @ e_0)
% 3.73/1.56 | (cycle @ X0 @ e_1)
% 3.73/1.56 | (cycle @ X0 @ e_2))),
% 3.73/1.56 inference('cnf', [status(esa)], [cycle2])).
% 3.73/1.56 thf(element_1, axiom, (group_element @ e_1)).
% 3.73/1.56 thf(zip_derived_cl16, plain, ( (group_element @ e_1)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_1])).
% 3.73/1.56 thf(zip_derived_cl53, plain,
% 3.73/1.56 (( (cycle @ e_1 @ e_2) | (cycle @ e_1 @ e_1) | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl16])).
% 3.73/1.56 thf(e_2_greater_e_0, axiom, (greater @ e_2 @ e_0)).
% 3.73/1.56 thf(zip_derived_cl4, plain, ( (greater @ e_2 @ e_0)),
% 3.73/1.56 inference('cnf', [status(esa)], [e_2_greater_e_0])).
% 3.73/1.56 thf(cycle7, axiom,
% 3.73/1.56 (( ~( cycle @ X @ Y ) ) | ( ~( product @ X @ e_1 @ Z ) ) |
% 3.73/1.56 ( ~( greater @ Y @ e_0 ) ) | ( ~( next @ X @ X1 ) ) |
% 3.73/1.56 ( equalish @ Z @ X1 ))).
% 3.73/1.56 thf(zip_derived_cl15, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 (~ (cycle @ X0 @ X1)
% 3.73/1.56 | ~ (product @ X0 @ e_1 @ X2)
% 3.73/1.56 | ~ (greater @ X1 @ e_0)
% 3.73/1.56 | ~ (next @ X0 @ X3)
% 3.73/1.56 | (equalish @ X2 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [cycle7])).
% 3.73/1.56 thf(zip_derived_cl47, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.73/1.56 ( (equalish @ X1 @ X0)
% 3.73/1.56 | ~ (next @ X2 @ X0)
% 3.73/1.56 | ~ (product @ X2 @ e_1 @ X1)
% 3.73/1.56 | ~ (cycle @ X2 @ e_2))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl15])).
% 3.73/1.56 thf(zip_derived_cl64, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i]:
% 3.73/1.56 ( (cycle @ e_1 @ e_0)
% 3.73/1.56 | (cycle @ e_1 @ e_1)
% 3.73/1.56 | ~ (product @ e_1 @ e_1 @ X0)
% 3.73/1.56 | ~ (next @ e_1 @ X1)
% 3.73/1.56 | (equalish @ X0 @ X1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl47])).
% 3.73/1.56 thf(e_1_greater_e_0, axiom, (greater @ e_1 @ e_0)).
% 3.73/1.56 thf(zip_derived_cl3, plain, ( (greater @ e_1 @ e_0)),
% 3.73/1.56 inference('cnf', [status(esa)], [e_1_greater_e_0])).
% 3.73/1.56 thf(zip_derived_cl15, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 (~ (cycle @ X0 @ X1)
% 3.73/1.56 | ~ (product @ X0 @ e_1 @ X2)
% 3.73/1.56 | ~ (greater @ X1 @ e_0)
% 3.73/1.56 | ~ (next @ X0 @ X3)
% 3.73/1.56 | (equalish @ X2 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [cycle7])).
% 3.73/1.56 thf(zip_derived_cl46, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.73/1.56 ( (equalish @ X1 @ X0)
% 3.73/1.56 | ~ (next @ X2 @ X0)
% 3.73/1.56 | ~ (product @ X2 @ e_1 @ X1)
% 3.73/1.56 | ~ (cycle @ X2 @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl15])).
% 3.73/1.56 thf(zip_derived_cl134, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i]:
% 3.73/1.56 ( (equalish @ X0 @ X1)
% 3.73/1.56 | ~ (next @ e_1 @ X1)
% 3.73/1.56 | ~ (product @ e_1 @ e_1 @ X0)
% 3.73/1.56 | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('clc', [status(thm)], [zip_derived_cl64, zip_derived_cl46])).
% 3.73/1.56 thf(zip_derived_cl135, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (cycle @ e_1 @ e_0)
% 3.73/1.56 | ~ (product @ e_1 @ e_1 @ X0)
% 3.73/1.56 | (equalish @ X0 @ e_2))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl134])).
% 3.73/1.56 thf(zip_derived_cl136, plain,
% 3.73/1.56 (( (product @ e_1 @ e_1 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | ~ (group_element @ e_1)
% 3.73/1.56 | ~ (group_element @ e_1)
% 3.73/1.56 | (equalish @ e_3 @ e_2)
% 3.73/1.56 | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl135])).
% 3.73/1.56 thf(zip_derived_cl16, plain, ( (group_element @ e_1)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_1])).
% 3.73/1.56 thf(zip_derived_cl16, plain, ( (group_element @ e_1)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_1])).
% 3.73/1.56 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 3.73/1.56 thf(zip_derived_cl24, plain, (~ (equalish @ e_3 @ e_2)),
% 3.73/1.56 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 3.73/1.56 thf(zip_derived_cl137, plain,
% 3.73/1.56 (( (product @ e_1 @ e_1 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('demod', [status(thm)],
% 3.73/1.56 [zip_derived_cl136, zip_derived_cl16, zip_derived_cl16,
% 3.73/1.56 zip_derived_cl24])).
% 3.73/1.56 thf(zip_derived_cl25, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i]:
% 3.73/1.56 (~ (group_element @ X0)
% 3.73/1.56 | ~ (group_element @ X1)
% 3.73/1.56 | (product @ X0 @ X1 @ e_1)
% 3.73/1.56 | (product @ X0 @ X1 @ e_2)
% 3.73/1.56 | (product @ X0 @ X1 @ e_3))),
% 3.73/1.56 inference('cnf', [status(esa)], [product_total_function1])).
% 3.73/1.56 thf(qg3, conjecture,
% 3.73/1.56 (~( ( product @ Z2 @ Y @ X ) | ( ~( product @ X @ Z1 @ Z2 ) ) |
% 3.73/1.56 ( ~( product @ X @ Y @ Z1 ) ) ))).
% 3.73/1.56 thf(zf_stmt_0, negated_conjecture,
% 3.73/1.56 (( product @ Z2 @ Y @ X ) | ( ~( product @ X @ Z1 @ Z2 ) ) |
% 3.73/1.56 ( ~( product @ X @ Y @ Z1 ) )),
% 3.73/1.56 inference('cnf.neg', [status(esa)], [qg3])).
% 3.73/1.56 thf(zip_derived_cl29, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 ( (product @ X0 @ X1 @ X2)
% 3.73/1.56 | ~ (product @ X2 @ X3 @ X0)
% 3.73/1.56 | ~ (product @ X2 @ X1 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.73/1.56 thf(zip_derived_cl96, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.73/1.56 ( (product @ X1 @ X0 @ e_2)
% 3.73/1.56 | (product @ X1 @ X0 @ e_1)
% 3.73/1.56 | ~ (group_element @ X0)
% 3.73/1.56 | ~ (group_element @ X1)
% 3.73/1.56 | ~ (product @ X1 @ X2 @ X0)
% 3.73/1.56 | (product @ e_3 @ X2 @ X1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl29])).
% 3.73/1.56 thf(zip_derived_cl524, plain,
% 3.73/1.56 (( (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_1 @ e_1)
% 3.73/1.56 | ~ (group_element @ e_1)
% 3.73/1.56 | ~ (group_element @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl96])).
% 3.73/1.56 thf(zip_derived_cl16, plain, ( (group_element @ e_1)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_1])).
% 3.73/1.56 thf(element_2, axiom, (group_element @ e_2)).
% 3.73/1.56 thf(zip_derived_cl17, plain, ( (group_element @ e_2)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_2])).
% 3.73/1.56 thf(zip_derived_cl537, plain,
% 3.73/1.56 (( (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2))),
% 3.73/1.56 inference('demod', [status(thm)],
% 3.73/1.56 [zip_derived_cl524, zip_derived_cl16, zip_derived_cl17])).
% 3.73/1.56 thf(zip_derived_cl137, plain,
% 3.73/1.56 (( (product @ e_1 @ e_1 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('demod', [status(thm)],
% 3.73/1.56 [zip_derived_cl136, zip_derived_cl16, zip_derived_cl16,
% 3.73/1.56 zip_derived_cl24])).
% 3.73/1.56 thf(zip_derived_cl29, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 ( (product @ X0 @ X1 @ X2)
% 3.73/1.56 | ~ (product @ X2 @ X3 @ X0)
% 3.73/1.56 | ~ (product @ X2 @ X1 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.73/1.56 thf(zip_derived_cl146, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | ~ (product @ e_1 @ X0 @ e_1)
% 3.73/1.56 | (product @ e_2 @ X0 @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl29])).
% 3.73/1.56 thf(product_left_cancellation, axiom,
% 3.73/1.56 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 3.73/1.56 ( equalish @ W @ Z ))).
% 3.73/1.56 thf(zip_derived_cl28, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 (~ (product @ X0 @ X1 @ X2)
% 3.73/1.56 | ~ (product @ X3 @ X1 @ X2)
% 3.73/1.56 | (equalish @ X0 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [product_left_cancellation])).
% 3.73/1.56 thf(zip_derived_cl235, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i]:
% 3.73/1.56 (~ (product @ e_1 @ X0 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0)
% 3.73/1.56 | (equalish @ e_2 @ X1)
% 3.73/1.56 | ~ (product @ X1 @ X0 @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl146, zip_derived_cl28])).
% 3.73/1.56 thf(zip_derived_cl434, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 (~ (product @ e_1 @ X0 @ e_1)
% 3.73/1.56 | (equalish @ e_2 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1))),
% 3.73/1.56 inference('eq_fact', [status(thm)], [zip_derived_cl235])).
% 3.73/1.56 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 3.73/1.56 thf(zip_derived_cl21, plain, (~ (equalish @ e_2 @ e_1)),
% 3.73/1.56 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 3.73/1.56 thf(zip_derived_cl435, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 (~ (product @ e_1 @ X0 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1))),
% 3.73/1.56 inference('demod', [status(thm)], [zip_derived_cl434, zip_derived_cl21])).
% 3.73/1.56 thf(zip_derived_cl599, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_3 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('clc', [status(thm)], [zip_derived_cl537, zip_derived_cl435])).
% 3.73/1.56 thf(zip_derived_cl25, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i]:
% 3.73/1.56 (~ (group_element @ X0)
% 3.73/1.56 | ~ (group_element @ X1)
% 3.73/1.56 | (product @ X0 @ X1 @ e_1)
% 3.73/1.56 | (product @ X0 @ X1 @ e_2)
% 3.73/1.56 | (product @ X0 @ X1 @ e_3))),
% 3.73/1.56 inference('cnf', [status(esa)], [product_total_function1])).
% 3.73/1.56 thf(zip_derived_cl137, plain,
% 3.73/1.56 (( (product @ e_1 @ e_1 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('demod', [status(thm)],
% 3.73/1.56 [zip_derived_cl136, zip_derived_cl16, zip_derived_cl16,
% 3.73/1.56 zip_derived_cl24])).
% 3.73/1.56 thf(zip_derived_cl25, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i]:
% 3.73/1.56 (~ (group_element @ X0)
% 3.73/1.56 | ~ (group_element @ X1)
% 3.73/1.56 | (product @ X0 @ X1 @ e_1)
% 3.73/1.56 | (product @ X0 @ X1 @ e_2)
% 3.73/1.56 | (product @ X0 @ X1 @ e_3))),
% 3.73/1.56 inference('cnf', [status(esa)], [product_total_function1])).
% 3.73/1.56 thf(zip_derived_cl29, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 ( (product @ X0 @ X1 @ X2)
% 3.73/1.56 | ~ (product @ X2 @ X3 @ X0)
% 3.73/1.56 | ~ (product @ X2 @ X1 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.73/1.56 thf(zip_derived_cl40, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i]:
% 3.73/1.56 (~ (product @ X1 @ X0 @ X0) | (product @ X0 @ X0 @ X1))),
% 3.73/1.56 inference('eq_fact', [status(thm)], [zip_derived_cl29])).
% 3.73/1.56 thf(zip_derived_cl100, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (product @ X0 @ e_3 @ e_2)
% 3.73/1.56 | (product @ X0 @ e_3 @ e_1)
% 3.73/1.56 | ~ (group_element @ e_3)
% 3.73/1.56 | ~ (group_element @ X0)
% 3.73/1.56 | (product @ e_3 @ e_3 @ X0))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl40])).
% 3.73/1.56 thf(element_3, axiom, (group_element @ e_3)).
% 3.73/1.56 thf(zip_derived_cl18, plain, ( (group_element @ e_3)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_3])).
% 3.73/1.56 thf(zip_derived_cl101, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (product @ X0 @ e_3 @ e_2)
% 3.73/1.56 | (product @ X0 @ e_3 @ e_1)
% 3.73/1.56 | ~ (group_element @ X0)
% 3.73/1.56 | (product @ e_3 @ e_3 @ X0))),
% 3.73/1.56 inference('demod', [status(thm)], [zip_derived_cl100, zip_derived_cl18])).
% 3.73/1.56 thf(product_right_cancellation, axiom,
% 3.73/1.56 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 3.73/1.56 ( equalish @ W @ Z ))).
% 3.73/1.56 thf(zip_derived_cl27, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 (~ (product @ X0 @ X1 @ X2)
% 3.73/1.56 | ~ (product @ X0 @ X3 @ X2)
% 3.73/1.56 | (equalish @ X1 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [product_right_cancellation])).
% 3.73/1.56 thf(zip_derived_cl103, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i]:
% 3.73/1.56 ( (product @ e_3 @ e_3 @ X0)
% 3.73/1.56 | ~ (group_element @ X0)
% 3.73/1.56 | (product @ X0 @ e_3 @ e_1)
% 3.73/1.56 | (equalish @ e_3 @ X1)
% 3.73/1.56 | ~ (product @ X0 @ X1 @ e_2))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl101, zip_derived_cl27])).
% 3.73/1.56 thf(zip_derived_cl368, plain,
% 3.73/1.56 (( (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (equalish @ e_3 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_3 @ e_1)
% 3.73/1.56 | ~ (group_element @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_3 @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl103])).
% 3.73/1.56 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 3.73/1.56 thf(zip_derived_cl23, plain, (~ (equalish @ e_3 @ e_1)),
% 3.73/1.56 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 3.73/1.56 thf(zip_derived_cl16, plain, ( (group_element @ e_1)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_1])).
% 3.73/1.56 thf(zip_derived_cl374, plain,
% 3.73/1.56 (( (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_3 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_3 @ e_1))),
% 3.73/1.56 inference('demod', [status(thm)],
% 3.73/1.56 [zip_derived_cl368, zip_derived_cl23, zip_derived_cl16])).
% 3.73/1.56 thf(product_total_function2, axiom,
% 3.73/1.56 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 3.73/1.56 ( equalish @ W @ Z ))).
% 3.73/1.56 thf(zip_derived_cl26, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 (~ (product @ X0 @ X1 @ X2)
% 3.73/1.56 | ~ (product @ X0 @ X1 @ X3)
% 3.73/1.56 | (equalish @ X2 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [product_total_function2])).
% 3.73/1.56 thf(zip_derived_cl410, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (product @ e_1 @ e_3 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0)
% 3.73/1.56 | (equalish @ e_1 @ X0)
% 3.73/1.56 | ~ (product @ e_3 @ e_3 @ X0))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl374, zip_derived_cl26])).
% 3.73/1.56 thf(zip_derived_cl435, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 (~ (product @ e_1 @ X0 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1))),
% 3.73/1.56 inference('demod', [status(thm)], [zip_derived_cl434, zip_derived_cl21])).
% 3.73/1.56 thf(zip_derived_cl439, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 (~ (product @ e_3 @ e_3 @ X0)
% 3.73/1.56 | (equalish @ e_1 @ X0)
% 3.73/1.56 | (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1))),
% 3.73/1.56 inference('clc', [status(thm)], [zip_derived_cl410, zip_derived_cl435])).
% 3.73/1.56 thf(zip_derived_cl440, plain,
% 3.73/1.56 (( (product @ e_3 @ e_3 @ e_2)
% 3.73/1.56 | (product @ e_3 @ e_3 @ e_1)
% 3.73/1.56 | ~ (group_element @ e_3)
% 3.73/1.56 | ~ (group_element @ e_3)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0)
% 3.73/1.56 | (equalish @ e_1 @ e_3))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl439])).
% 3.73/1.56 thf(zip_derived_cl18, plain, ( (group_element @ e_3)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_3])).
% 3.73/1.56 thf(zip_derived_cl18, plain, ( (group_element @ e_3)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_3])).
% 3.73/1.56 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 3.73/1.56 thf(zip_derived_cl20, plain, (~ (equalish @ e_1 @ e_3)),
% 3.73/1.56 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 3.73/1.56 thf(zip_derived_cl446, plain,
% 3.73/1.56 (( (product @ e_3 @ e_3 @ e_2)
% 3.73/1.56 | (product @ e_3 @ e_3 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('demod', [status(thm)],
% 3.73/1.56 [zip_derived_cl440, zip_derived_cl18, zip_derived_cl18,
% 3.73/1.56 zip_derived_cl20])).
% 3.73/1.56 thf(zip_derived_cl439, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 (~ (product @ e_3 @ e_3 @ X0)
% 3.73/1.56 | (equalish @ e_1 @ X0)
% 3.73/1.56 | (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1))),
% 3.73/1.56 inference('clc', [status(thm)], [zip_derived_cl410, zip_derived_cl435])).
% 3.73/1.56 thf(zip_derived_cl467, plain,
% 3.73/1.56 (( (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_3 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0)
% 3.73/1.56 | (equalish @ e_1 @ e_2))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl446, zip_derived_cl439])).
% 3.73/1.56 thf(zip_derived_cl19, plain, (~ (equalish @ e_1 @ e_2)),
% 3.73/1.56 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 3.73/1.56 thf(zip_derived_cl482, plain,
% 3.73/1.56 (( (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_3 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('demod', [status(thm)], [zip_derived_cl467, zip_derived_cl19])).
% 3.73/1.56 thf(zip_derived_cl483, plain,
% 3.73/1.56 (( (product @ e_3 @ e_3 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('simplify', [status(thm)], [zip_derived_cl482])).
% 3.73/1.56 thf(zip_derived_cl27, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 (~ (product @ X0 @ X1 @ X2)
% 3.73/1.56 | ~ (product @ X0 @ X3 @ X2)
% 3.73/1.56 | (equalish @ X1 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [product_right_cancellation])).
% 3.73/1.56 thf(zip_derived_cl485, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (equalish @ e_3 @ X0)
% 3.73/1.56 | ~ (product @ e_3 @ X0 @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl483, zip_derived_cl27])).
% 3.73/1.56 thf(zip_derived_cl611, plain,
% 3.73/1.56 (( (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (equalish @ e_3 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl599, zip_derived_cl485])).
% 3.73/1.56 thf(zip_derived_cl23, plain, (~ (equalish @ e_3 @ e_1)),
% 3.73/1.56 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 3.73/1.56 thf(zip_derived_cl618, plain,
% 3.73/1.56 (( (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('demod', [status(thm)], [zip_derived_cl611, zip_derived_cl23])).
% 3.73/1.56 thf(zip_derived_cl619, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('simplify', [status(thm)], [zip_derived_cl618])).
% 3.73/1.56 thf(zip_derived_cl137, plain,
% 3.73/1.56 (( (product @ e_1 @ e_1 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('demod', [status(thm)],
% 3.73/1.56 [zip_derived_cl136, zip_derived_cl16, zip_derived_cl16,
% 3.73/1.56 zip_derived_cl24])).
% 3.73/1.56 thf(zip_derived_cl27, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 (~ (product @ X0 @ X1 @ X2)
% 3.73/1.56 | ~ (product @ X0 @ X3 @ X2)
% 3.73/1.56 | (equalish @ X1 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [product_right_cancellation])).
% 3.73/1.56 thf(zip_derived_cl144, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (equalish @ e_1 @ X0)
% 3.73/1.56 | ~ (product @ e_1 @ X0 @ e_2))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl27])).
% 3.73/1.56 thf(zip_derived_cl631, plain,
% 3.73/1.56 (( (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (equalish @ e_1 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl619, zip_derived_cl144])).
% 3.73/1.56 thf(zip_derived_cl19, plain, (~ (equalish @ e_1 @ e_2)),
% 3.73/1.56 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 3.73/1.56 thf(zip_derived_cl638, plain,
% 3.73/1.56 (( (cycle @ e_1 @ e_0)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('demod', [status(thm)], [zip_derived_cl631, zip_derived_cl19])).
% 3.73/1.56 thf(zip_derived_cl639, plain,
% 3.73/1.56 (( (product @ e_1 @ e_1 @ e_1) | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('simplify', [status(thm)], [zip_derived_cl638])).
% 3.73/1.56 thf(zip_derived_cl135, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (cycle @ e_1 @ e_0)
% 3.73/1.56 | ~ (product @ e_1 @ e_1 @ X0)
% 3.73/1.56 | (equalish @ X0 @ e_2))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl134])).
% 3.73/1.56 thf(zip_derived_cl650, plain,
% 3.73/1.56 (( (cycle @ e_1 @ e_0) | (equalish @ e_1 @ e_2) | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl639, zip_derived_cl135])).
% 3.73/1.56 thf(zip_derived_cl653, plain,
% 3.73/1.56 (( (equalish @ e_1 @ e_2) | (cycle @ e_1 @ e_0))),
% 3.73/1.56 inference('simplify', [status(thm)], [zip_derived_cl650])).
% 3.73/1.56 thf(zip_derived_cl19, plain, (~ (equalish @ e_1 @ e_2)),
% 3.73/1.56 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 3.73/1.56 thf(zip_derived_cl657, plain, ( (cycle @ e_1 @ e_0)),
% 3.73/1.56 inference('clc', [status(thm)], [zip_derived_cl653, zip_derived_cl19])).
% 3.73/1.56 thf(cycle6, axiom,
% 3.73/1.56 (( ~( cycle @ X @ e_0 ) ) | ( ~( product @ X @ e_1 @ Y ) ) |
% 3.73/1.56 ( ~( greater @ Y @ X ) ))).
% 3.73/1.56 thf(zip_derived_cl14, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i]:
% 3.73/1.56 (~ (cycle @ X0 @ e_0)
% 3.73/1.56 | ~ (product @ X0 @ e_1 @ X1)
% 3.73/1.56 | ~ (greater @ X1 @ X0))),
% 3.73/1.56 inference('cnf', [status(esa)], [cycle6])).
% 3.73/1.56 thf(zip_derived_cl660, plain,
% 3.73/1.56 (![X0 : $i]: (~ (greater @ X0 @ e_1) | ~ (product @ e_1 @ e_1 @ X0))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl657, zip_derived_cl14])).
% 3.73/1.56 thf(zip_derived_cl664, plain, (~ (product @ e_1 @ e_1 @ e_3)),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl660])).
% 3.73/1.56 thf(zip_derived_cl708, plain,
% 3.73/1.56 (( (product @ e_1 @ e_1 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_1)
% 3.73/1.56 | ~ (group_element @ e_1)
% 3.73/1.56 | ~ (group_element @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl664])).
% 3.73/1.56 thf(zip_derived_cl16, plain, ( (group_element @ e_1)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_1])).
% 3.73/1.56 thf(zip_derived_cl16, plain, ( (group_element @ e_1)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_1])).
% 3.73/1.56 thf(zip_derived_cl709, plain,
% 3.73/1.56 (( (product @ e_1 @ e_1 @ e_2) | (product @ e_1 @ e_1 @ e_1))),
% 3.73/1.56 inference('demod', [status(thm)],
% 3.73/1.56 [zip_derived_cl708, zip_derived_cl16, zip_derived_cl16])).
% 3.73/1.56 thf(e_2_greater_e_1, axiom, (greater @ e_2 @ e_1)).
% 3.73/1.56 thf(zip_derived_cl6, plain, ( (greater @ e_2 @ e_1)),
% 3.73/1.56 inference('cnf', [status(esa)], [e_2_greater_e_1])).
% 3.73/1.56 thf(zip_derived_cl660, plain,
% 3.73/1.56 (![X0 : $i]: (~ (greater @ X0 @ e_1) | ~ (product @ e_1 @ e_1 @ X0))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl657, zip_derived_cl14])).
% 3.73/1.56 thf(zip_derived_cl663, plain, (~ (product @ e_1 @ e_1 @ e_2)),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl660])).
% 3.73/1.56 thf(zip_derived_cl710, plain, ( (product @ e_1 @ e_1 @ e_1)),
% 3.73/1.56 inference('clc', [status(thm)], [zip_derived_cl709, zip_derived_cl663])).
% 3.73/1.56 thf(zip_derived_cl101, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (product @ X0 @ e_3 @ e_2)
% 3.73/1.56 | (product @ X0 @ e_3 @ e_1)
% 3.73/1.56 | ~ (group_element @ X0)
% 3.73/1.56 | (product @ e_3 @ e_3 @ X0))),
% 3.73/1.56 inference('demod', [status(thm)], [zip_derived_cl100, zip_derived_cl18])).
% 3.73/1.56 thf(zip_derived_cl96, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.73/1.56 ( (product @ X1 @ X0 @ e_2)
% 3.73/1.56 | (product @ X1 @ X0 @ e_1)
% 3.73/1.56 | ~ (group_element @ X0)
% 3.73/1.56 | ~ (group_element @ X1)
% 3.73/1.56 | ~ (product @ X1 @ X2 @ X0)
% 3.73/1.56 | (product @ e_3 @ X2 @ X1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl29])).
% 3.73/1.56 thf(zip_derived_cl523, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (product @ e_3 @ e_3 @ X0)
% 3.73/1.56 | ~ (group_element @ X0)
% 3.73/1.56 | (product @ X0 @ e_3 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_3 @ X0)
% 3.73/1.56 | ~ (group_element @ X0)
% 3.73/1.56 | ~ (group_element @ e_2)
% 3.73/1.56 | (product @ X0 @ e_2 @ e_1)
% 3.73/1.56 | (product @ X0 @ e_2 @ e_2))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl101, zip_derived_cl96])).
% 3.73/1.56 thf(zip_derived_cl17, plain, ( (group_element @ e_2)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_2])).
% 3.73/1.56 thf(zip_derived_cl535, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (product @ e_3 @ e_3 @ X0)
% 3.73/1.56 | ~ (group_element @ X0)
% 3.73/1.56 | (product @ X0 @ e_3 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_3 @ X0)
% 3.73/1.56 | ~ (group_element @ X0)
% 3.73/1.56 | (product @ X0 @ e_2 @ e_1)
% 3.73/1.56 | (product @ X0 @ e_2 @ e_2))),
% 3.73/1.56 inference('demod', [status(thm)], [zip_derived_cl523, zip_derived_cl17])).
% 3.73/1.56 thf(zip_derived_cl536, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (product @ X0 @ e_2 @ e_2)
% 3.73/1.56 | (product @ X0 @ e_2 @ e_1)
% 3.73/1.56 | (product @ X0 @ e_3 @ e_1)
% 3.73/1.56 | ~ (group_element @ X0)
% 3.73/1.56 | (product @ e_3 @ e_3 @ X0))),
% 3.73/1.56 inference('simplify', [status(thm)], [zip_derived_cl535])).
% 3.73/1.56 thf(zip_derived_cl27, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 (~ (product @ X0 @ X1 @ X2)
% 3.73/1.56 | ~ (product @ X0 @ X3 @ X2)
% 3.73/1.56 | (equalish @ X1 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [product_right_cancellation])).
% 3.73/1.56 thf(zip_derived_cl767, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i]:
% 3.73/1.56 ( (product @ e_3 @ e_3 @ X0)
% 3.73/1.56 | ~ (group_element @ X0)
% 3.73/1.56 | (product @ X0 @ e_2 @ e_1)
% 3.73/1.56 | (product @ X0 @ e_2 @ e_2)
% 3.73/1.56 | (equalish @ e_3 @ X1)
% 3.73/1.56 | ~ (product @ X0 @ X1 @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl536, zip_derived_cl27])).
% 3.73/1.56 thf(zip_derived_cl984, plain,
% 3.73/1.56 (( (equalish @ e_3 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | ~ (group_element @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_3 @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl710, zip_derived_cl767])).
% 3.73/1.56 thf(zip_derived_cl23, plain, (~ (equalish @ e_3 @ e_1)),
% 3.73/1.56 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 3.73/1.56 thf(zip_derived_cl16, plain, ( (group_element @ e_1)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_1])).
% 3.73/1.56 thf(zip_derived_cl989, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_3 @ e_1))),
% 3.73/1.56 inference('demod', [status(thm)],
% 3.73/1.56 [zip_derived_cl984, zip_derived_cl23, zip_derived_cl16])).
% 3.73/1.56 thf(zip_derived_cl989, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_3 @ e_1))),
% 3.73/1.56 inference('demod', [status(thm)],
% 3.73/1.56 [zip_derived_cl984, zip_derived_cl23, zip_derived_cl16])).
% 3.73/1.56 thf(zip_derived_cl96, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.73/1.56 ( (product @ X1 @ X0 @ e_2)
% 3.73/1.56 | (product @ X1 @ X0 @ e_1)
% 3.73/1.56 | ~ (group_element @ X0)
% 3.73/1.56 | ~ (group_element @ X1)
% 3.73/1.56 | ~ (product @ X1 @ X2 @ X0)
% 3.73/1.56 | (product @ e_3 @ X2 @ X1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl29])).
% 3.73/1.56 thf(zip_derived_cl1042, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_3 @ e_3 @ e_3)
% 3.73/1.56 | ~ (group_element @ e_3)
% 3.73/1.56 | ~ (group_element @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_1 @ e_2))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl989, zip_derived_cl96])).
% 3.73/1.56 thf(zip_derived_cl18, plain, ( (group_element @ e_3)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_3])).
% 3.73/1.56 thf(zip_derived_cl16, plain, ( (group_element @ e_1)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_1])).
% 3.73/1.56 thf(zip_derived_cl1062, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_3 @ e_3 @ e_3)
% 3.73/1.56 | (product @ e_3 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_1 @ e_2))),
% 3.73/1.56 inference('demod', [status(thm)],
% 3.73/1.56 [zip_derived_cl1042, zip_derived_cl18, zip_derived_cl16])).
% 3.73/1.56 thf(zip_derived_cl989, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_3 @ e_1))),
% 3.73/1.56 inference('demod', [status(thm)],
% 3.73/1.56 [zip_derived_cl984, zip_derived_cl23, zip_derived_cl16])).
% 3.73/1.56 thf(zip_derived_cl26, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 (~ (product @ X0 @ X1 @ X2)
% 3.73/1.56 | ~ (product @ X0 @ X1 @ X3)
% 3.73/1.56 | (equalish @ X2 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [product_total_function2])).
% 3.73/1.56 thf(zip_derived_cl1034, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (equalish @ e_1 @ X0)
% 3.73/1.56 | ~ (product @ e_3 @ e_3 @ X0))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl989, zip_derived_cl26])).
% 3.73/1.56 thf(zip_derived_cl1210, plain,
% 3.73/1.56 (( (product @ e_3 @ e_1 @ e_2)
% 3.73/1.56 | (product @ e_3 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (equalish @ e_1 @ e_3)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1062, zip_derived_cl1034])).
% 3.73/1.56 thf(zip_derived_cl20, plain, (~ (equalish @ e_1 @ e_3)),
% 3.73/1.56 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 3.73/1.56 thf(zip_derived_cl1240, plain,
% 3.73/1.56 (( (product @ e_3 @ e_1 @ e_2)
% 3.73/1.56 | (product @ e_3 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1))),
% 3.73/1.56 inference('demod', [status(thm)], [zip_derived_cl1210, zip_derived_cl20])).
% 3.73/1.56 thf(zip_derived_cl1241, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_3 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_1 @ e_2))),
% 3.73/1.56 inference('simplify', [status(thm)], [zip_derived_cl1240])).
% 3.73/1.56 thf(zip_derived_cl29, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 ( (product @ X0 @ X1 @ X2)
% 3.73/1.56 | ~ (product @ X2 @ X3 @ X0)
% 3.73/1.56 | ~ (product @ X2 @ X1 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.73/1.56 thf(zip_derived_cl1245, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (product @ e_3 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | ~ (product @ e_3 @ X0 @ e_1)
% 3.73/1.56 | (product @ e_2 @ X0 @ e_3))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1241, zip_derived_cl29])).
% 3.73/1.56 thf(zip_derived_cl1296, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_2 @ e_3 @ e_3)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_3 @ e_1 @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl989, zip_derived_cl1245])).
% 3.73/1.56 thf(zip_derived_cl1301, plain,
% 3.73/1.56 (( (product @ e_3 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_2 @ e_3 @ e_3)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1))),
% 3.73/1.56 inference('simplify', [status(thm)], [zip_derived_cl1296])).
% 3.73/1.56 thf(zip_derived_cl40, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i]:
% 3.73/1.56 (~ (product @ X1 @ X0 @ X0) | (product @ X0 @ X0 @ X1))),
% 3.73/1.56 inference('eq_fact', [status(thm)], [zip_derived_cl29])).
% 3.73/1.56 thf(zip_derived_cl1309, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_2 @ e_3 @ e_3)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_3))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1301, zip_derived_cl40])).
% 3.73/1.56 thf(zip_derived_cl664, plain, (~ (product @ e_1 @ e_1 @ e_3)),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl660])).
% 3.73/1.56 thf(zip_derived_cl1324, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_2 @ e_3 @ e_3))),
% 3.73/1.56 inference('demod', [status(thm)], [zip_derived_cl1309, zip_derived_cl664])).
% 3.73/1.56 thf(zip_derived_cl40, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i]:
% 3.73/1.56 (~ (product @ X1 @ X0 @ X0) | (product @ X0 @ X0 @ X1))),
% 3.73/1.56 inference('eq_fact', [status(thm)], [zip_derived_cl29])).
% 3.73/1.56 thf(zip_derived_cl1346, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_3 @ e_2))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1324, zip_derived_cl40])).
% 3.73/1.56 thf(zip_derived_cl1034, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (equalish @ e_1 @ X0)
% 3.73/1.56 | ~ (product @ e_3 @ e_3 @ X0))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl989, zip_derived_cl26])).
% 3.73/1.56 thf(zip_derived_cl1411, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (equalish @ e_1 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1346, zip_derived_cl1034])).
% 3.73/1.56 thf(zip_derived_cl19, plain, (~ (equalish @ e_1 @ e_2)),
% 3.73/1.56 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 3.73/1.56 thf(zip_derived_cl1439, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1))),
% 3.73/1.56 inference('demod', [status(thm)], [zip_derived_cl1411, zip_derived_cl19])).
% 3.73/1.56 thf(zip_derived_cl1440, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_2) | (product @ e_1 @ e_2 @ e_1))),
% 3.73/1.56 inference('simplify', [status(thm)], [zip_derived_cl1439])).
% 3.73/1.56 thf(zip_derived_cl40, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i]:
% 3.73/1.56 (~ (product @ X1 @ X0 @ X0) | (product @ X0 @ X0 @ X1))),
% 3.73/1.56 inference('eq_fact', [status(thm)], [zip_derived_cl29])).
% 3.73/1.56 thf(zip_derived_cl1448, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_1) | (product @ e_2 @ e_2 @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1440, zip_derived_cl40])).
% 3.73/1.56 thf(zip_derived_cl96, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.73/1.56 ( (product @ X1 @ X0 @ e_2)
% 3.73/1.56 | (product @ X1 @ X0 @ e_1)
% 3.73/1.56 | ~ (group_element @ X0)
% 3.73/1.56 | ~ (group_element @ X1)
% 3.73/1.56 | ~ (product @ X1 @ X2 @ X0)
% 3.73/1.56 | (product @ e_3 @ X2 @ X1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl29])).
% 3.73/1.56 thf(zip_derived_cl1470, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_2 @ e_2)
% 3.73/1.56 | ~ (group_element @ e_2)
% 3.73/1.56 | ~ (group_element @ e_1)
% 3.73/1.56 | (product @ e_2 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_2 @ e_1 @ e_2))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1448, zip_derived_cl96])).
% 3.73/1.56 thf(zip_derived_cl17, plain, ( (group_element @ e_2)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_2])).
% 3.73/1.56 thf(zip_derived_cl16, plain, ( (group_element @ e_1)),
% 3.73/1.56 inference('cnf', [status(esa)], [element_1])).
% 3.73/1.56 thf(zip_derived_cl1476, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_3 @ e_2 @ e_2)
% 3.73/1.56 | (product @ e_2 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_2 @ e_1 @ e_2))),
% 3.73/1.56 inference('demod', [status(thm)],
% 3.73/1.56 [zip_derived_cl1470, zip_derived_cl17, zip_derived_cl16])).
% 3.73/1.56 thf(zip_derived_cl1440, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_2) | (product @ e_1 @ e_2 @ e_1))),
% 3.73/1.56 inference('simplify', [status(thm)], [zip_derived_cl1439])).
% 3.73/1.56 thf(zip_derived_cl28, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 (~ (product @ X0 @ X1 @ X2)
% 3.73/1.56 | ~ (product @ X3 @ X1 @ X2)
% 3.73/1.56 | (equalish @ X0 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [product_left_cancellation])).
% 3.73/1.56 thf(zip_derived_cl1443, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (equalish @ e_1 @ X0)
% 3.73/1.56 | ~ (product @ X0 @ e_2 @ e_2))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1440, zip_derived_cl28])).
% 3.73/1.56 thf(zip_derived_cl1769, plain,
% 3.73/1.56 (( (product @ e_2 @ e_1 @ e_2)
% 3.73/1.56 | (product @ e_2 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (equalish @ e_1 @ e_3)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1476, zip_derived_cl1443])).
% 3.73/1.56 thf(zip_derived_cl20, plain, (~ (equalish @ e_1 @ e_3)),
% 3.73/1.56 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 3.73/1.56 thf(zip_derived_cl1783, plain,
% 3.73/1.56 (( (product @ e_2 @ e_1 @ e_2)
% 3.73/1.56 | (product @ e_2 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1))),
% 3.73/1.56 inference('demod', [status(thm)], [zip_derived_cl1769, zip_derived_cl20])).
% 3.73/1.56 thf(zip_derived_cl1784, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_2 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_2 @ e_1 @ e_2))),
% 3.73/1.56 inference('simplify', [status(thm)], [zip_derived_cl1783])).
% 3.73/1.56 thf(zip_derived_cl1448, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_1) | (product @ e_2 @ e_2 @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1440, zip_derived_cl40])).
% 3.73/1.56 thf(zip_derived_cl29, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 ( (product @ X0 @ X1 @ X2)
% 3.73/1.56 | ~ (product @ X2 @ X3 @ X0)
% 3.73/1.56 | ~ (product @ X2 @ X1 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.73/1.56 thf(zip_derived_cl1465, plain,
% 3.73/1.56 (![X0 : $i]:
% 3.73/1.56 ( (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | ~ (product @ e_2 @ X0 @ e_2)
% 3.73/1.56 | (product @ e_1 @ X0 @ e_2))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1448, zip_derived_cl29])).
% 3.73/1.56 thf(zip_derived_cl1801, plain,
% 3.73/1.56 (( (product @ e_2 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_1 @ e_2)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1784, zip_derived_cl1465])).
% 3.73/1.56 thf(zip_derived_cl663, plain, (~ (product @ e_1 @ e_1 @ e_2)),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl660])).
% 3.73/1.56 thf(zip_derived_cl1811, plain,
% 3.73/1.56 (( (product @ e_2 @ e_1 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1)
% 3.73/1.56 | (product @ e_1 @ e_2 @ e_1))),
% 3.73/1.56 inference('demod', [status(thm)], [zip_derived_cl1801, zip_derived_cl663])).
% 3.73/1.56 thf(zip_derived_cl1812, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_1) | (product @ e_2 @ e_1 @ e_1))),
% 3.73/1.56 inference('simplify', [status(thm)], [zip_derived_cl1811])).
% 3.73/1.56 thf(zip_derived_cl40, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i]:
% 3.73/1.56 (~ (product @ X1 @ X0 @ X0) | (product @ X0 @ X0 @ X1))),
% 3.73/1.56 inference('eq_fact', [status(thm)], [zip_derived_cl29])).
% 3.73/1.56 thf(zip_derived_cl1821, plain,
% 3.73/1.56 (( (product @ e_1 @ e_2 @ e_1) | (product @ e_1 @ e_1 @ e_2))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1812, zip_derived_cl40])).
% 3.73/1.56 thf(zip_derived_cl663, plain, (~ (product @ e_1 @ e_1 @ e_2)),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl660])).
% 3.73/1.56 thf(zip_derived_cl1831, plain, ( (product @ e_1 @ e_2 @ e_1)),
% 3.73/1.56 inference('demod', [status(thm)], [zip_derived_cl1821, zip_derived_cl663])).
% 3.73/1.56 thf(zip_derived_cl710, plain, ( (product @ e_1 @ e_1 @ e_1)),
% 3.73/1.56 inference('clc', [status(thm)], [zip_derived_cl709, zip_derived_cl663])).
% 3.73/1.56 thf(zip_derived_cl27, plain,
% 3.73/1.56 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.73/1.56 (~ (product @ X0 @ X1 @ X2)
% 3.73/1.56 | ~ (product @ X0 @ X3 @ X2)
% 3.73/1.56 | (equalish @ X1 @ X3))),
% 3.73/1.56 inference('cnf', [status(esa)], [product_right_cancellation])).
% 3.73/1.56 thf(zip_derived_cl712, plain,
% 3.73/1.56 (![X0 : $i]: ( (equalish @ e_1 @ X0) | ~ (product @ e_1 @ X0 @ e_1))),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl710, zip_derived_cl27])).
% 3.73/1.56 thf(zip_derived_cl1849, plain, ( (equalish @ e_1 @ e_2)),
% 3.73/1.56 inference('sup-', [status(thm)], [zip_derived_cl1831, zip_derived_cl712])).
% 3.73/1.56 thf(zip_derived_cl1853, plain, ($false),
% 3.73/1.56 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl1849])).
% 3.73/1.56
% 3.73/1.56 % SZS output end Refutation
% 3.73/1.56
% 3.73/1.56
% 3.73/1.56 % Terminating...
% 4.33/1.81 % Runner terminated.
% 4.37/1.84 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------