%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP133-2.003 : 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.DoswGT1ebA true
% Computer : n027.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 04:35:48 PM UTC 2025
% Result : Unsatisfiable 0.45s 0.76s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP133-2.003 : TPTP v9.2.0. Released v1.2.0.
% 0.09/0.10 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.DoswGT1ebA true
% 0.09/0.28 % Computer : n027.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Wed Oct 1 14:06:38 EDT 2025
% 0.09/0.28 % CPUTime :
% 0.09/0.28 % Running portfolio for 300 s
% 0.09/0.28 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.28 % Number of cores: 8
% 0.09/0.29 % Python version: Python 3.6.8
% 0.09/0.29 % Running in FO mode
% 0.42/0.55 % Total configuration time : 435
% 0.42/0.55 % Estimated wc time : 1092
% 0.42/0.55 % Estimated cpu time (7 cpus) : 156.0
% 0.42/0.61 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.42/0.62 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.44/0.63 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.44/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.44/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.44/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.44/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.45/0.76 % Solved by fo/fo3_bce.sh.
% 0.45/0.76 % BCE start: 20
% 0.45/0.76 % BCE eliminated: 0
% 0.45/0.76 % PE start: 20
% 0.45/0.76 logic: neq
% 0.45/0.76 % PE eliminated: -4
% 0.45/0.76 % done 237 iterations in 0.118s
% 0.45/0.76 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.45/0.76 % SZS output start Refutation
% 0.45/0.76 thf(greater_type, type, greater: $i > $i > $o).
% 0.45/0.76 thf(product_type, type, product: $i > $i > $i > $o).
% 0.45/0.76 thf(e_3_type, type, e_3: $i).
% 0.45/0.76 thf(e_2_type, type, e_2: $i).
% 0.45/0.76 thf(e_1_type, type, e_1: $i).
% 0.45/0.76 thf(next_type, type, next: $i > $i > $o).
% 0.45/0.76 thf(group_element_type, type, group_element: $i > $o).
% 0.45/0.76 thf(equalish_type, type, equalish: $i > $i > $o).
% 0.45/0.76 thf(product_total_function1, axiom,
% 0.45/0.76 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 0.45/0.76 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 0.45/0.76 ( product @ X @ Y @ e_3 ))).
% 0.45/0.76 thf(zip_derived_cl15, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (group_element @ X0)
% 0.45/0.76 | ~ (group_element @ X1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_2)
% 0.45/0.76 | (product @ X0 @ X1 @ e_3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_total_function1])).
% 0.45/0.76 thf(zip_derived_cl15, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (group_element @ X0)
% 0.45/0.76 | ~ (group_element @ X1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_2)
% 0.45/0.76 | (product @ X0 @ X1 @ e_3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_total_function1])).
% 0.45/0.76 thf(product_right_cancellation, axiom,
% 0.45/0.76 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 0.45/0.76 ( equalish @ W @ Z ))).
% 0.45/0.76 thf(zip_derived_cl17, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.45/0.76 (~ (product @ X0 @ X1 @ X2)
% 0.45/0.76 | ~ (product @ X0 @ X3 @ X2)
% 0.45/0.76 | (equalish @ X1 @ X3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.45/0.76 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 0.45/0.76 thf(zip_derived_cl12, plain, (~ (equalish @ e_2 @ e_3)),
% 0.45/0.76 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.45/0.76 thf(zip_derived_cl32, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ X1 @ e_3 @ X0) | ~ (product @ X1 @ e_2 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl17, zip_derived_cl12])).
% 0.45/0.76 thf(zip_derived_cl60, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 ( (product @ X0 @ e_3 @ e_2)
% 0.45/0.76 | (product @ X0 @ e_3 @ e_1)
% 0.45/0.76 | ~ (group_element @ e_3)
% 0.45/0.76 | ~ (group_element @ X0)
% 0.45/0.76 | ~ (product @ X0 @ e_2 @ e_3))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl32])).
% 0.45/0.76 thf(element_3, axiom, (group_element @ e_3)).
% 0.45/0.76 thf(zip_derived_cl8, plain, ( (group_element @ e_3)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_3])).
% 0.45/0.76 thf(zip_derived_cl61, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 ( (product @ X0 @ e_3 @ e_2)
% 0.45/0.76 | (product @ X0 @ e_3 @ e_1)
% 0.45/0.76 | ~ (group_element @ X0)
% 0.45/0.76 | ~ (product @ X0 @ e_2 @ e_3))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl8])).
% 0.45/0.76 thf(qg3, conjecture,
% 0.45/0.76 (~( ( product @ Z1 @ Z2 @ X ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 0.45/0.76 ( ~( product @ X @ Y @ Z1 ) ) ))).
% 0.45/0.76 thf(zf_stmt_0, negated_conjecture,
% 0.45/0.76 (( product @ Z1 @ Z2 @ X ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 0.45/0.76 ( ~( product @ X @ Y @ Z1 ) )),
% 0.45/0.76 inference('cnf.neg', [status(esa)], [qg3])).
% 0.45/0.76 thf(zip_derived_cl19, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.45/0.76 ( (product @ X0 @ X1 @ X2)
% 0.45/0.76 | ~ (product @ X3 @ X2 @ X1)
% 0.45/0.76 | ~ (product @ X2 @ X3 @ X0))),
% 0.45/0.76 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.45/0.76 thf(zip_derived_cl66, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 0.45/0.76 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 0.45/0.76 thf(zip_derived_cl216, plain,
% 0.45/0.76 ((~ (product @ e_3 @ e_2 @ e_3)
% 0.45/0.76 | ~ (group_element @ e_3)
% 0.45/0.76 | (product @ e_3 @ e_3 @ e_1)
% 0.45/0.76 | (product @ e_2 @ e_2 @ e_3))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl66])).
% 0.45/0.76 thf(zip_derived_cl8, plain, ( (group_element @ e_3)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_3])).
% 0.45/0.76 thf(zip_derived_cl232, plain,
% 0.45/0.76 ((~ (product @ e_3 @ e_2 @ e_3)
% 0.45/0.76 | (product @ e_3 @ e_3 @ e_1)
% 0.45/0.76 | (product @ e_2 @ e_2 @ e_3))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl216, zip_derived_cl8])).
% 0.45/0.76 thf(product_left_cancellation, axiom,
% 0.45/0.76 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 0.45/0.76 ( equalish @ W @ Z ))).
% 0.45/0.76 thf(zip_derived_cl18, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.45/0.76 (~ (product @ X0 @ X1 @ X2)
% 0.45/0.76 | ~ (product @ X3 @ X1 @ X2)
% 0.45/0.76 | (equalish @ X0 @ X3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.45/0.76 thf(zip_derived_cl12, plain, (~ (equalish @ e_2 @ e_3)),
% 0.45/0.76 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.45/0.76 thf(zip_derived_cl38, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_2 @ X1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl18, zip_derived_cl12])).
% 0.45/0.76 thf(zip_derived_cl297, plain,
% 0.45/0.76 (( (product @ e_3 @ e_3 @ e_1) | ~ (product @ e_3 @ e_2 @ e_3))),
% 0.45/0.76 inference('clc', [status(thm)], [zip_derived_cl232, zip_derived_cl38])).
% 0.45/0.76 thf(zip_derived_cl66, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 0.45/0.76 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 0.45/0.76 thf(zip_derived_cl299, plain,
% 0.45/0.76 ((~ (product @ e_3 @ e_2 @ e_3) | (product @ e_1 @ e_1 @ e_3))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl297, zip_derived_cl66])).
% 0.45/0.76 thf(e_3_greater_e_2, axiom, (greater @ e_3 @ e_2)).
% 0.45/0.76 thf(zip_derived_cl4, plain, ( (greater @ e_3 @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [e_3_greater_e_2])).
% 0.45/0.76 thf(e_1_then_e_2, axiom, (next @ e_1 @ e_2)).
% 0.45/0.76 thf(zip_derived_cl0, plain, ( (next @ e_1 @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [e_1_then_e_2])).
% 0.45/0.76 thf(no_redundancy, axiom,
% 0.45/0.76 (( ~( product @ X @ e_1 @ Y ) ) | ( ~( next @ X @ X1 ) ) |
% 0.45/0.76 ( ~( greater @ Y @ X1 ) ))).
% 0.45/0.76 thf(zip_derived_cl5, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.45/0.76 (~ (product @ X0 @ e_1 @ X1)
% 0.45/0.76 | ~ (next @ X0 @ X2)
% 0.45/0.76 | ~ (greater @ X1 @ X2))),
% 0.45/0.76 inference('cnf', [status(esa)], [no_redundancy])).
% 0.45/0.76 thf(zip_derived_cl20, plain,
% 0.45/0.76 (![X0 : $i]: (~ (greater @ X0 @ e_2) | ~ (product @ e_1 @ e_1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl0, zip_derived_cl5])).
% 0.45/0.76 thf(zip_derived_cl22, plain, (~ (product @ e_1 @ e_1 @ e_3)),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl4, zip_derived_cl20])).
% 0.45/0.76 thf(zip_derived_cl308, plain, (~ (product @ e_3 @ e_2 @ e_3)),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl299, zip_derived_cl22])).
% 0.45/0.76 thf(zip_derived_cl310, plain,
% 0.45/0.76 (( (product @ e_3 @ e_2 @ e_2)
% 0.45/0.76 | (product @ e_3 @ e_2 @ e_1)
% 0.45/0.76 | ~ (group_element @ e_2)
% 0.45/0.76 | ~ (group_element @ e_3))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl308])).
% 0.45/0.76 thf(element_2, axiom, (group_element @ e_2)).
% 0.45/0.76 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_2])).
% 0.45/0.76 thf(zip_derived_cl8, plain, ( (group_element @ e_3)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_3])).
% 0.45/0.76 thf(zip_derived_cl311, plain,
% 0.45/0.76 (( (product @ e_3 @ e_2 @ e_2) | (product @ e_3 @ e_2 @ e_1))),
% 0.45/0.76 inference('demod', [status(thm)],
% 0.45/0.76 [zip_derived_cl310, zip_derived_cl7, zip_derived_cl8])).
% 0.45/0.76 thf(zip_derived_cl18, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.45/0.76 (~ (product @ X0 @ X1 @ X2)
% 0.45/0.76 | ~ (product @ X3 @ X1 @ X2)
% 0.45/0.76 | (equalish @ X0 @ X3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.45/0.76 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 0.45/0.76 thf(zip_derived_cl10, plain, (~ (equalish @ e_1 @ e_3)),
% 0.45/0.76 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.45/0.76 thf(zip_derived_cl36, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl18, zip_derived_cl10])).
% 0.45/0.76 thf(zip_derived_cl317, plain,
% 0.45/0.76 (( (product @ e_3 @ e_2 @ e_1) | ~ (product @ e_1 @ e_2 @ e_2))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl311, zip_derived_cl36])).
% 0.45/0.76 thf(zip_derived_cl38, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_2 @ X1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl18, zip_derived_cl12])).
% 0.45/0.76 thf(zip_derived_cl373, plain,
% 0.45/0.76 ((~ (product @ e_1 @ e_2 @ e_2) | ~ (product @ e_2 @ e_2 @ e_1))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl317, zip_derived_cl38])).
% 0.45/0.76 thf(zip_derived_cl15, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (group_element @ X0)
% 0.45/0.76 | ~ (group_element @ X1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_2)
% 0.45/0.76 | (product @ X0 @ X1 @ e_3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_total_function1])).
% 0.45/0.76 thf(zip_derived_cl61, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 ( (product @ X0 @ e_3 @ e_2)
% 0.45/0.76 | (product @ X0 @ e_3 @ e_1)
% 0.45/0.76 | ~ (group_element @ X0)
% 0.45/0.76 | ~ (product @ X0 @ e_2 @ e_3))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl60, zip_derived_cl8])).
% 0.45/0.76 thf(zip_derived_cl17, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.45/0.76 (~ (product @ X0 @ X1 @ X2)
% 0.45/0.76 | ~ (product @ X0 @ X3 @ X2)
% 0.45/0.76 | (equalish @ X1 @ X3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.45/0.76 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 0.45/0.76 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.45/0.76 thf(zip_derived_cl29, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ X1 @ e_2 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl17, zip_derived_cl9])).
% 0.45/0.76 thf(zip_derived_cl15, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (group_element @ X0)
% 0.45/0.76 | ~ (group_element @ X1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_2)
% 0.45/0.76 | (product @ X0 @ X1 @ e_3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_total_function1])).
% 0.45/0.76 thf(zip_derived_cl18, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.45/0.76 (~ (product @ X0 @ X1 @ X2)
% 0.45/0.76 | ~ (product @ X3 @ X1 @ X2)
% 0.45/0.76 | (equalish @ X0 @ X3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.45/0.76 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.45/0.76 thf(zip_derived_cl35, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ e_2 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl18, zip_derived_cl9])).
% 0.45/0.76 thf(zip_derived_cl68, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 ( (product @ e_2 @ X0 @ e_2)
% 0.45/0.76 | (product @ e_2 @ X0 @ e_1)
% 0.45/0.76 | ~ (group_element @ X0)
% 0.45/0.76 | ~ (group_element @ e_2)
% 0.45/0.76 | ~ (product @ e_1 @ X0 @ e_3))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl35])).
% 0.45/0.76 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_2])).
% 0.45/0.76 thf(zip_derived_cl69, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 ( (product @ e_2 @ X0 @ e_2)
% 0.45/0.76 | (product @ e_2 @ X0 @ e_1)
% 0.45/0.76 | ~ (group_element @ X0)
% 0.45/0.76 | ~ (product @ e_1 @ X0 @ e_3))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl7])).
% 0.45/0.76 thf(zip_derived_cl394, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_1 @ e_2)
% 0.45/0.76 | ~ (product @ e_1 @ e_2 @ e_3)
% 0.45/0.76 | ~ (group_element @ e_2)
% 0.45/0.76 | (product @ e_2 @ e_2 @ e_1))),
% 0.45/0.76 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl69])).
% 0.45/0.76 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_2])).
% 0.45/0.76 thf(zip_derived_cl398, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_1 @ e_2)
% 0.45/0.76 | ~ (product @ e_1 @ e_2 @ e_3)
% 0.45/0.76 | (product @ e_2 @ e_2 @ e_1))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl394, zip_derived_cl7])).
% 0.45/0.76 thf(zip_derived_cl66, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 0.45/0.76 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 0.45/0.76 thf(zip_derived_cl691, plain,
% 0.45/0.76 ((~ (product @ e_1 @ e_2 @ e_3)
% 0.45/0.76 | ~ (product @ e_2 @ e_1 @ e_2)
% 0.45/0.76 | (product @ e_1 @ e_1 @ e_2))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl398, zip_derived_cl66])).
% 0.45/0.76 thf(zip_derived_cl35, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ e_2 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl18, zip_derived_cl9])).
% 0.45/0.76 thf(zip_derived_cl735, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_1 @ e_2) | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.45/0.76 inference('clc', [status(thm)], [zip_derived_cl691, zip_derived_cl35])).
% 0.45/0.76 thf(zip_derived_cl15, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (group_element @ X0)
% 0.45/0.76 | ~ (group_element @ X1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_2)
% 0.45/0.76 | (product @ X0 @ X1 @ e_3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_total_function1])).
% 0.45/0.76 thf(zip_derived_cl15, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (group_element @ X0)
% 0.45/0.76 | ~ (group_element @ X1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_2)
% 0.45/0.76 | (product @ X0 @ X1 @ e_3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_total_function1])).
% 0.45/0.76 thf(zip_derived_cl29, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ X1 @ e_2 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl17, zip_derived_cl9])).
% 0.45/0.76 thf(zip_derived_cl52, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 ( (product @ X0 @ e_2 @ e_2)
% 0.45/0.76 | (product @ X0 @ e_2 @ e_1)
% 0.45/0.76 | ~ (group_element @ e_2)
% 0.45/0.76 | ~ (group_element @ X0)
% 0.45/0.76 | ~ (product @ X0 @ e_1 @ e_3))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl29])).
% 0.45/0.76 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_2])).
% 0.45/0.76 thf(zip_derived_cl53, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 ( (product @ X0 @ e_2 @ e_2)
% 0.45/0.76 | (product @ X0 @ e_2 @ e_1)
% 0.45/0.76 | ~ (group_element @ X0)
% 0.45/0.76 | ~ (product @ X0 @ e_1 @ e_3))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl7])).
% 0.45/0.76 thf(zip_derived_cl311, plain,
% 0.45/0.76 (( (product @ e_3 @ e_2 @ e_2) | (product @ e_3 @ e_2 @ e_1))),
% 0.45/0.76 inference('demod', [status(thm)],
% 0.45/0.76 [zip_derived_cl310, zip_derived_cl7, zip_derived_cl8])).
% 0.45/0.76 thf(zip_derived_cl38, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_2 @ X1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl18, zip_derived_cl12])).
% 0.45/0.76 thf(zip_derived_cl318, plain,
% 0.45/0.76 (( (product @ e_3 @ e_2 @ e_1) | ~ (product @ e_2 @ e_2 @ e_2))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl311, zip_derived_cl38])).
% 0.45/0.76 thf(zip_derived_cl35, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ e_2 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl18, zip_derived_cl9])).
% 0.45/0.76 thf(zip_derived_cl15, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (group_element @ X0)
% 0.45/0.76 | ~ (group_element @ X1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_2)
% 0.45/0.76 | (product @ X0 @ X1 @ e_3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_total_function1])).
% 0.45/0.76 thf(zip_derived_cl17, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.45/0.76 (~ (product @ X0 @ X1 @ X2)
% 0.45/0.76 | ~ (product @ X0 @ X3 @ X2)
% 0.45/0.76 | (equalish @ X1 @ X3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.45/0.76 thf(zip_derived_cl10, plain, (~ (equalish @ e_1 @ e_3)),
% 0.45/0.76 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.45/0.76 thf(zip_derived_cl30, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ X1 @ e_3 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl17, zip_derived_cl10])).
% 0.45/0.76 thf(zip_derived_cl56, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 ( (product @ X0 @ e_3 @ e_2)
% 0.45/0.76 | (product @ X0 @ e_3 @ e_1)
% 0.45/0.76 | ~ (group_element @ e_3)
% 0.45/0.76 | ~ (group_element @ X0)
% 0.45/0.76 | ~ (product @ X0 @ e_1 @ e_3))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl30])).
% 0.45/0.76 thf(zip_derived_cl8, plain, ( (group_element @ e_3)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_3])).
% 0.45/0.76 thf(zip_derived_cl57, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 ( (product @ X0 @ e_3 @ e_2)
% 0.45/0.76 | (product @ X0 @ e_3 @ e_1)
% 0.45/0.76 | ~ (group_element @ X0)
% 0.45/0.76 | ~ (product @ X0 @ e_1 @ e_3))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl56, zip_derived_cl8])).
% 0.45/0.76 thf(zip_derived_cl166, plain,
% 0.45/0.76 ((~ (product @ e_1 @ e_3 @ e_2)
% 0.45/0.76 | ~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | ~ (group_element @ e_2)
% 0.45/0.76 | (product @ e_2 @ e_3 @ e_1))),
% 0.45/0.76 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl57])).
% 0.45/0.76 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_2])).
% 0.45/0.76 thf(zip_derived_cl169, plain,
% 0.45/0.76 ((~ (product @ e_1 @ e_3 @ e_2)
% 0.45/0.76 | ~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | (product @ e_2 @ e_3 @ e_1))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl166, zip_derived_cl7])).
% 0.45/0.76 thf(zip_derived_cl19, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.45/0.76 ( (product @ X0 @ X1 @ X2)
% 0.45/0.76 | ~ (product @ X3 @ X2 @ X1)
% 0.45/0.76 | ~ (product @ X2 @ X3 @ X0))),
% 0.45/0.76 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.45/0.76 thf(zip_derived_cl236, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 (~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | ~ (product @ e_1 @ e_3 @ e_2)
% 0.45/0.76 | ~ (product @ e_3 @ e_2 @ X0)
% 0.45/0.76 | (product @ X0 @ e_1 @ e_3))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl169, zip_derived_cl19])).
% 0.45/0.76 thf(zip_derived_cl413, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_2 @ e_2)
% 0.45/0.76 | (product @ e_1 @ e_1 @ e_3)
% 0.45/0.76 | ~ (product @ e_1 @ e_3 @ e_2)
% 0.45/0.76 | ~ (product @ e_2 @ e_1 @ e_3))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl318, zip_derived_cl236])).
% 0.45/0.76 thf(zip_derived_cl22, plain, (~ (product @ e_1 @ e_1 @ e_3)),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl4, zip_derived_cl20])).
% 0.45/0.76 thf(zip_derived_cl420, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_2 @ e_2)
% 0.45/0.76 | ~ (product @ e_1 @ e_3 @ e_2)
% 0.45/0.76 | ~ (product @ e_2 @ e_1 @ e_3))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl413, zip_derived_cl22])).
% 0.45/0.76 thf(zip_derived_cl446, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | ~ (group_element @ e_2)
% 0.45/0.76 | (product @ e_2 @ e_2 @ e_1)
% 0.45/0.76 | ~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | ~ (product @ e_1 @ e_3 @ e_2))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl420])).
% 0.45/0.76 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_2])).
% 0.45/0.76 thf(zip_derived_cl449, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | (product @ e_2 @ e_2 @ e_1)
% 0.45/0.76 | ~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | ~ (product @ e_1 @ e_3 @ e_2))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl446, zip_derived_cl7])).
% 0.45/0.76 thf(zip_derived_cl450, plain,
% 0.45/0.76 ((~ (product @ e_1 @ e_3 @ e_2)
% 0.45/0.76 | (product @ e_2 @ e_2 @ e_1)
% 0.45/0.76 | ~ (product @ e_2 @ e_1 @ e_3))),
% 0.45/0.76 inference('simplify', [status(thm)], [zip_derived_cl449])).
% 0.45/0.76 thf(zip_derived_cl169, plain,
% 0.45/0.76 ((~ (product @ e_1 @ e_3 @ e_2)
% 0.45/0.76 | ~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | (product @ e_2 @ e_3 @ e_1))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl166, zip_derived_cl7])).
% 0.45/0.76 thf(zip_derived_cl32, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ X1 @ e_3 @ X0) | ~ (product @ X1 @ e_2 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl17, zip_derived_cl12])).
% 0.45/0.76 thf(zip_derived_cl238, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | ~ (product @ e_1 @ e_3 @ e_2)
% 0.45/0.76 | ~ (product @ e_2 @ e_2 @ e_1))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl169, zip_derived_cl32])).
% 0.45/0.76 thf(zip_derived_cl514, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_1 @ e_3) | ~ (product @ e_1 @ e_3 @ e_2))),
% 0.45/0.76 inference('clc', [status(thm)], [zip_derived_cl450, zip_derived_cl238])).
% 0.45/0.76 thf(zip_derived_cl516, plain,
% 0.45/0.76 (( (product @ e_2 @ e_1 @ e_2)
% 0.45/0.76 | (product @ e_2 @ e_1 @ e_1)
% 0.45/0.76 | ~ (group_element @ e_1)
% 0.45/0.76 | ~ (group_element @ e_2)
% 0.45/0.76 | ~ (product @ e_1 @ e_3 @ e_2))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl514])).
% 0.45/0.76 thf(zip_derived_cl22, plain, (~ (product @ e_1 @ e_1 @ e_3)),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl4, zip_derived_cl20])).
% 0.45/0.76 thf(zip_derived_cl15, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (group_element @ X0)
% 0.45/0.76 | ~ (group_element @ X1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_2)
% 0.45/0.76 | (product @ X0 @ X1 @ e_3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_total_function1])).
% 0.45/0.76 thf(zip_derived_cl42, plain,
% 0.45/0.76 (( (product @ e_1 @ e_1 @ e_2)
% 0.45/0.76 | (product @ e_1 @ e_1 @ e_1)
% 0.45/0.76 | ~ (group_element @ e_1)
% 0.45/0.76 | ~ (group_element @ e_1))),
% 0.45/0.76 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl15])).
% 0.45/0.76 thf(element_1, axiom, (group_element @ e_1)).
% 0.45/0.76 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_1])).
% 0.45/0.76 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_1])).
% 0.45/0.76 thf(zip_derived_cl43, plain,
% 0.45/0.76 (( (product @ e_1 @ e_1 @ e_2) | (product @ e_1 @ e_1 @ e_1))),
% 0.45/0.76 inference('demod', [status(thm)],
% 0.45/0.76 [zip_derived_cl42, zip_derived_cl6, zip_derived_cl6])).
% 0.45/0.76 thf(zip_derived_cl66, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 0.45/0.76 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 0.45/0.76 thf(zip_derived_cl80, plain,
% 0.45/0.76 (( (product @ e_1 @ e_1 @ e_1) | (product @ e_2 @ e_2 @ e_1))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl66])).
% 0.45/0.76 thf(zip_derived_cl29, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ X1 @ e_2 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl17, zip_derived_cl9])).
% 0.45/0.76 thf(zip_derived_cl104, plain,
% 0.45/0.76 (( (product @ e_1 @ e_1 @ e_1) | ~ (product @ e_2 @ e_1 @ e_1))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl29])).
% 0.45/0.76 thf(zip_derived_cl35, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ e_2 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl18, zip_derived_cl9])).
% 0.45/0.76 thf(zip_derived_cl108, plain, (~ (product @ e_2 @ e_1 @ e_1)),
% 0.45/0.76 inference('clc', [status(thm)], [zip_derived_cl104, zip_derived_cl35])).
% 0.45/0.76 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_1])).
% 0.45/0.76 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_2])).
% 0.45/0.76 thf(zip_derived_cl517, plain,
% 0.45/0.76 (( (product @ e_2 @ e_1 @ e_2) | ~ (product @ e_1 @ e_3 @ e_2))),
% 0.45/0.76 inference('demod', [status(thm)],
% 0.45/0.76 [zip_derived_cl516, zip_derived_cl108, zip_derived_cl6,
% 0.45/0.76 zip_derived_cl7])).
% 0.45/0.76 thf(zip_derived_cl738, plain,
% 0.45/0.76 ((~ (product @ e_1 @ e_2 @ e_3) | ~ (product @ e_1 @ e_3 @ e_2))),
% 0.45/0.76 inference('sup+', [status(thm)], [zip_derived_cl735, zip_derived_cl517])).
% 0.45/0.76 thf(zip_derived_cl747, plain,
% 0.45/0.76 ((~ (product @ e_1 @ e_2 @ e_3)
% 0.45/0.76 | ~ (group_element @ e_1)
% 0.45/0.76 | (product @ e_1 @ e_3 @ e_1)
% 0.45/0.76 | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl738])).
% 0.45/0.76 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_1])).
% 0.45/0.76 thf(zip_derived_cl749, plain,
% 0.45/0.76 ((~ (product @ e_1 @ e_2 @ e_3)
% 0.45/0.76 | (product @ e_1 @ e_3 @ e_1)
% 0.45/0.76 | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl747, zip_derived_cl6])).
% 0.45/0.76 thf(zip_derived_cl750, plain,
% 0.45/0.76 (( (product @ e_1 @ e_3 @ e_1) | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.45/0.76 inference('simplify', [status(thm)], [zip_derived_cl749])).
% 0.45/0.76 thf(zip_derived_cl30, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ X1 @ e_3 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl17, zip_derived_cl10])).
% 0.45/0.76 thf(zip_derived_cl756, plain,
% 0.45/0.76 ((~ (product @ e_1 @ e_2 @ e_3) | ~ (product @ e_1 @ e_1 @ e_1))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl750, zip_derived_cl30])).
% 0.45/0.76 thf(zip_derived_cl764, plain,
% 0.45/0.76 (( (product @ e_1 @ e_2 @ e_2)
% 0.45/0.76 | (product @ e_1 @ e_2 @ e_1)
% 0.45/0.76 | ~ (group_element @ e_2)
% 0.45/0.76 | ~ (group_element @ e_1)
% 0.45/0.76 | ~ (product @ e_1 @ e_1 @ e_1))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl756])).
% 0.45/0.76 thf(zip_derived_cl80, plain,
% 0.45/0.76 (( (product @ e_1 @ e_1 @ e_1) | (product @ e_2 @ e_2 @ e_1))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl66])).
% 0.45/0.76 thf(zip_derived_cl35, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ e_2 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl18, zip_derived_cl9])).
% 0.45/0.76 thf(zip_derived_cl105, plain,
% 0.45/0.76 (( (product @ e_1 @ e_1 @ e_1) | ~ (product @ e_1 @ e_2 @ e_1))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl35])).
% 0.45/0.76 thf(zip_derived_cl29, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ X1 @ e_2 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl17, zip_derived_cl9])).
% 0.45/0.76 thf(zip_derived_cl109, plain, (~ (product @ e_1 @ e_2 @ e_1)),
% 0.45/0.76 inference('clc', [status(thm)], [zip_derived_cl105, zip_derived_cl29])).
% 0.45/0.76 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_2])).
% 0.45/0.76 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_1])).
% 0.45/0.76 thf(zip_derived_cl765, plain,
% 0.45/0.76 (( (product @ e_1 @ e_2 @ e_2) | ~ (product @ e_1 @ e_1 @ e_1))),
% 0.45/0.76 inference('demod', [status(thm)],
% 0.45/0.76 [zip_derived_cl764, zip_derived_cl109, zip_derived_cl7,
% 0.45/0.76 zip_derived_cl6])).
% 0.45/0.76 thf(zip_derived_cl765, plain,
% 0.45/0.76 (( (product @ e_1 @ e_2 @ e_2) | ~ (product @ e_1 @ e_1 @ e_1))),
% 0.45/0.76 inference('demod', [status(thm)],
% 0.45/0.76 [zip_derived_cl764, zip_derived_cl109, zip_derived_cl7,
% 0.45/0.76 zip_derived_cl6])).
% 0.45/0.76 thf(zip_derived_cl15, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (group_element @ X0)
% 0.45/0.76 | ~ (group_element @ X1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_2)
% 0.45/0.76 | (product @ X0 @ X1 @ e_3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_total_function1])).
% 0.45/0.76 thf(zip_derived_cl35, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ e_2 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl18, zip_derived_cl9])).
% 0.45/0.76 thf(zip_derived_cl53, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 ( (product @ X0 @ e_2 @ e_2)
% 0.45/0.76 | (product @ X0 @ e_2 @ e_1)
% 0.45/0.76 | ~ (group_element @ X0)
% 0.45/0.76 | ~ (product @ X0 @ e_1 @ e_3))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl7])).
% 0.45/0.76 thf(zip_derived_cl92, plain,
% 0.45/0.76 ((~ (product @ e_1 @ e_2 @ e_2)
% 0.45/0.76 | ~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | ~ (group_element @ e_2)
% 0.45/0.76 | (product @ e_2 @ e_2 @ e_1))),
% 0.45/0.76 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl53])).
% 0.45/0.76 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_2])).
% 0.45/0.76 thf(zip_derived_cl95, plain,
% 0.45/0.76 ((~ (product @ e_1 @ e_2 @ e_2)
% 0.45/0.76 | ~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | (product @ e_2 @ e_2 @ e_1))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl92, zip_derived_cl7])).
% 0.45/0.76 thf(zip_derived_cl66, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 0.45/0.76 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 0.45/0.76 thf(zip_derived_cl113, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | ~ (product @ e_1 @ e_2 @ e_2)
% 0.45/0.76 | (product @ e_1 @ e_1 @ e_2))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl95, zip_derived_cl66])).
% 0.45/0.76 thf(zip_derived_cl29, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ X1 @ e_2 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl17, zip_derived_cl9])).
% 0.45/0.76 thf(zip_derived_cl122, plain,
% 0.45/0.76 ((~ (product @ e_1 @ e_2 @ e_2) | ~ (product @ e_2 @ e_1 @ e_3))),
% 0.45/0.76 inference('clc', [status(thm)], [zip_derived_cl113, zip_derived_cl29])).
% 0.45/0.76 thf(zip_derived_cl124, plain,
% 0.45/0.76 (( (product @ e_2 @ e_1 @ e_2)
% 0.45/0.76 | (product @ e_2 @ e_1 @ e_1)
% 0.45/0.76 | ~ (group_element @ e_1)
% 0.45/0.76 | ~ (group_element @ e_2)
% 0.45/0.76 | ~ (product @ e_1 @ e_2 @ e_2))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl122])).
% 0.45/0.76 thf(zip_derived_cl108, plain, (~ (product @ e_2 @ e_1 @ e_1)),
% 0.45/0.76 inference('clc', [status(thm)], [zip_derived_cl104, zip_derived_cl35])).
% 0.45/0.76 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_1])).
% 0.45/0.76 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_2])).
% 0.45/0.76 thf(zip_derived_cl125, plain,
% 0.45/0.76 (( (product @ e_2 @ e_1 @ e_2) | ~ (product @ e_1 @ e_2 @ e_2))),
% 0.45/0.76 inference('demod', [status(thm)],
% 0.45/0.76 [zip_derived_cl124, zip_derived_cl108, zip_derived_cl6,
% 0.45/0.76 zip_derived_cl7])).
% 0.45/0.76 thf(zip_derived_cl19, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.45/0.76 ( (product @ X0 @ X1 @ X2)
% 0.45/0.76 | ~ (product @ X3 @ X2 @ X1)
% 0.45/0.76 | ~ (product @ X2 @ X3 @ X0))),
% 0.45/0.76 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.45/0.76 thf(zip_derived_cl127, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 (~ (product @ e_1 @ e_2 @ e_2)
% 0.45/0.76 | ~ (product @ e_1 @ e_2 @ X0)
% 0.45/0.76 | (product @ X0 @ e_2 @ e_1))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl125, zip_derived_cl19])).
% 0.45/0.76 thf(zip_derived_cl773, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 (~ (product @ e_1 @ e_1 @ e_1)
% 0.45/0.76 | (product @ X0 @ e_2 @ e_1)
% 0.45/0.76 | ~ (product @ e_1 @ e_2 @ X0))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl765, zip_derived_cl127])).
% 0.45/0.76 thf(zip_derived_cl840, plain,
% 0.45/0.76 ((~ (product @ e_1 @ e_1 @ e_1)
% 0.45/0.76 | (product @ e_2 @ e_2 @ e_1)
% 0.45/0.76 | ~ (product @ e_1 @ e_1 @ e_1))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl765, zip_derived_cl773])).
% 0.45/0.76 thf(zip_derived_cl844, plain,
% 0.45/0.76 (( (product @ e_2 @ e_2 @ e_1) | ~ (product @ e_1 @ e_1 @ e_1))),
% 0.45/0.76 inference('simplify', [status(thm)], [zip_derived_cl840])).
% 0.45/0.76 thf(zip_derived_cl80, plain,
% 0.45/0.76 (( (product @ e_1 @ e_1 @ e_1) | (product @ e_2 @ e_2 @ e_1))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl66])).
% 0.45/0.76 thf(zip_derived_cl845, plain, ( (product @ e_2 @ e_2 @ e_1)),
% 0.45/0.76 inference('clc', [status(thm)], [zip_derived_cl844, zip_derived_cl80])).
% 0.45/0.76 thf(zip_derived_cl847, plain, (~ (product @ e_1 @ e_2 @ e_2)),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl373, zip_derived_cl845])).
% 0.45/0.76 thf(zip_derived_cl15, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (group_element @ X0)
% 0.45/0.76 | ~ (group_element @ X1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_2)
% 0.45/0.76 | (product @ X0 @ X1 @ e_3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_total_function1])).
% 0.45/0.76 thf(zip_derived_cl15, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (group_element @ X0)
% 0.45/0.76 | ~ (group_element @ X1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_2)
% 0.45/0.76 | (product @ X0 @ X1 @ e_3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_total_function1])).
% 0.45/0.76 thf(zip_derived_cl311, plain,
% 0.45/0.76 (( (product @ e_3 @ e_2 @ e_2) | (product @ e_3 @ e_2 @ e_1))),
% 0.45/0.76 inference('demod', [status(thm)],
% 0.45/0.76 [zip_derived_cl310, zip_derived_cl7, zip_derived_cl8])).
% 0.45/0.76 thf(zip_derived_cl29, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ X1 @ e_2 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl17, zip_derived_cl9])).
% 0.45/0.76 thf(zip_derived_cl316, plain,
% 0.45/0.76 (( (product @ e_3 @ e_2 @ e_1) | ~ (product @ e_3 @ e_1 @ e_2))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl311, zip_derived_cl29])).
% 0.45/0.76 thf(zip_derived_cl38, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_2 @ X1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl18, zip_derived_cl12])).
% 0.45/0.76 thf(zip_derived_cl327, plain,
% 0.45/0.76 ((~ (product @ e_3 @ e_1 @ e_2) | ~ (product @ e_2 @ e_2 @ e_1))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl316, zip_derived_cl38])).
% 0.45/0.76 thf(zip_derived_cl15, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (group_element @ X0)
% 0.45/0.76 | ~ (group_element @ X1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_1)
% 0.45/0.76 | (product @ X0 @ X1 @ e_2)
% 0.45/0.76 | (product @ X0 @ X1 @ e_3))),
% 0.45/0.76 inference('cnf', [status(esa)], [product_total_function1])).
% 0.45/0.76 thf(zip_derived_cl38, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i]:
% 0.45/0.76 (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_2 @ X1 @ X0))),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl18, zip_derived_cl12])).
% 0.45/0.76 thf(zip_derived_cl76, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 ( (product @ e_3 @ X0 @ e_2)
% 0.45/0.76 | (product @ e_3 @ X0 @ e_1)
% 0.45/0.76 | ~ (group_element @ X0)
% 0.45/0.76 | ~ (group_element @ e_3)
% 0.45/0.76 | ~ (product @ e_2 @ X0 @ e_3))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl38])).
% 0.45/0.76 thf(zip_derived_cl8, plain, ( (group_element @ e_3)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_3])).
% 0.45/0.76 thf(zip_derived_cl77, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 ( (product @ e_3 @ X0 @ e_2)
% 0.45/0.76 | (product @ e_3 @ X0 @ e_1)
% 0.45/0.76 | ~ (group_element @ X0)
% 0.45/0.76 | ~ (product @ e_2 @ X0 @ e_3))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl8])).
% 0.45/0.76 thf(zip_derived_cl593, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_2 @ e_1)
% 0.45/0.76 | ~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | ~ (group_element @ e_1)
% 0.45/0.76 | (product @ e_3 @ e_1 @ e_1))),
% 0.45/0.76 inference('sup+', [status(thm)], [zip_derived_cl327, zip_derived_cl77])).
% 0.45/0.76 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_1])).
% 0.45/0.76 thf(zip_derived_cl597, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_2 @ e_1)
% 0.45/0.76 | ~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | (product @ e_3 @ e_1 @ e_1))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl593, zip_derived_cl6])).
% 0.45/0.76 thf(zip_derived_cl750, plain,
% 0.45/0.76 (( (product @ e_1 @ e_3 @ e_1) | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.45/0.76 inference('simplify', [status(thm)], [zip_derived_cl749])).
% 0.45/0.76 thf(zip_derived_cl19, plain,
% 0.45/0.76 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.45/0.76 ( (product @ X0 @ X1 @ X2)
% 0.45/0.76 | ~ (product @ X3 @ X2 @ X1)
% 0.45/0.76 | ~ (product @ X2 @ X3 @ X0))),
% 0.45/0.76 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.45/0.76 thf(zip_derived_cl755, plain,
% 0.45/0.76 (![X0 : $i]:
% 0.45/0.76 (~ (product @ e_1 @ e_2 @ e_3)
% 0.45/0.76 | ~ (product @ e_3 @ e_1 @ X0)
% 0.45/0.76 | (product @ X0 @ e_1 @ e_3))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl750, zip_derived_cl19])).
% 0.45/0.76 thf(zip_derived_cl784, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | ~ (product @ e_2 @ e_2 @ e_1)
% 0.45/0.76 | (product @ e_1 @ e_1 @ e_3)
% 0.45/0.76 | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl597, zip_derived_cl755])).
% 0.45/0.76 thf(zip_derived_cl22, plain, (~ (product @ e_1 @ e_1 @ e_3)),
% 0.45/0.76 inference('dp-resolution', [status(thm)],
% 0.45/0.76 [zip_derived_cl4, zip_derived_cl20])).
% 0.45/0.76 thf(zip_derived_cl790, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_1 @ e_3)
% 0.45/0.76 | ~ (product @ e_2 @ e_2 @ e_1)
% 0.45/0.76 | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl784, zip_derived_cl22])).
% 0.45/0.76 thf(zip_derived_cl845, plain, ( (product @ e_2 @ e_2 @ e_1)),
% 0.45/0.76 inference('clc', [status(thm)], [zip_derived_cl844, zip_derived_cl80])).
% 0.45/0.76 thf(zip_derived_cl850, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_1 @ e_3) | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl790, zip_derived_cl845])).
% 0.45/0.76 thf(zip_derived_cl890, plain,
% 0.45/0.76 (( (product @ e_2 @ e_1 @ e_2)
% 0.45/0.76 | (product @ e_2 @ e_1 @ e_1)
% 0.45/0.76 | ~ (group_element @ e_1)
% 0.45/0.76 | ~ (group_element @ e_2)
% 0.45/0.76 | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl850])).
% 0.45/0.76 thf(zip_derived_cl108, plain, (~ (product @ e_2 @ e_1 @ e_1)),
% 0.45/0.76 inference('clc', [status(thm)], [zip_derived_cl104, zip_derived_cl35])).
% 0.45/0.76 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_1])).
% 0.45/0.76 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_2])).
% 0.45/0.76 thf(zip_derived_cl891, plain,
% 0.45/0.76 (( (product @ e_2 @ e_1 @ e_2) | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.45/0.76 inference('demod', [status(thm)],
% 0.45/0.76 [zip_derived_cl890, zip_derived_cl108, zip_derived_cl6,
% 0.45/0.76 zip_derived_cl7])).
% 0.45/0.76 thf(zip_derived_cl735, plain,
% 0.45/0.76 ((~ (product @ e_2 @ e_1 @ e_2) | ~ (product @ e_1 @ e_2 @ e_3))),
% 0.45/0.76 inference('clc', [status(thm)], [zip_derived_cl691, zip_derived_cl35])).
% 0.45/0.76 thf(zip_derived_cl976, plain, (~ (product @ e_1 @ e_2 @ e_3)),
% 0.45/0.76 inference('clc', [status(thm)], [zip_derived_cl891, zip_derived_cl735])).
% 0.45/0.76 thf(zip_derived_cl978, plain,
% 0.45/0.76 (( (product @ e_1 @ e_2 @ e_2)
% 0.45/0.76 | (product @ e_1 @ e_2 @ e_1)
% 0.45/0.76 | ~ (group_element @ e_2)
% 0.45/0.76 | ~ (group_element @ e_1))),
% 0.45/0.76 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl976])).
% 0.45/0.76 thf(zip_derived_cl109, plain, (~ (product @ e_1 @ e_2 @ e_1)),
% 0.45/0.76 inference('clc', [status(thm)], [zip_derived_cl105, zip_derived_cl29])).
% 0.45/0.76 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_2])).
% 0.45/0.76 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.45/0.76 inference('cnf', [status(esa)], [element_1])).
% 0.45/0.76 thf(zip_derived_cl979, plain, ( (product @ e_1 @ e_2 @ e_2)),
% 0.45/0.76 inference('demod', [status(thm)],
% 0.45/0.76 [zip_derived_cl978, zip_derived_cl109, zip_derived_cl7,
% 0.45/0.76 zip_derived_cl6])).
% 0.45/0.76 thf(zip_derived_cl983, plain, ($false),
% 0.45/0.76 inference('demod', [status(thm)], [zip_derived_cl847, zip_derived_cl979])).
% 0.45/0.76
% 0.45/0.76 % SZS output end Refutation
% 0.45/0.76
% 0.45/0.76
% 0.45/0.76 % Terminating...
% 0.48/0.86 % Runner terminated.
% 0.48/0.87 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------