TSTP Solution File: GRP128-1.003 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : GRP128-1.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.b3c3vXYjZK true

% Computer : n022.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 01:50:11 EDT 2023

% Result   : Unsatisfiable 0.55s 1.02s
% Output   : Refutation 0.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : GRP128-1.003 : TPTP v8.1.2. Released v1.2.0.
% 0.11/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.b3c3vXYjZK true
% 0.13/0.35  % Computer : n022.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue Aug 29 01:17:24 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36  % Number of cores: 8
% 0.21/0.36  % Python version: Python 3.6.8
% 0.21/0.36  % Running in FO mode
% 0.22/0.71  % Total configuration time : 435
% 0.22/0.71  % Estimated wc time : 1092
% 0.22/0.71  % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.81  % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.53/0.81  % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.81  % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.54/0.84  % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.54/0.84  % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.54/0.85  % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.54/0.86  % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.55/1.02  % Solved by fo/fo3_bce.sh.
% 0.55/1.02  % BCE start: 14
% 0.55/1.02  % BCE eliminated: 0
% 0.55/1.02  % PE start: 14
% 0.55/1.02  logic: neq
% 0.55/1.02  % PE eliminated: -9
% 0.55/1.02  % done 340 iterations in 0.185s
% 0.55/1.02  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.55/1.02  % SZS output start Refutation
% 0.55/1.02  thf(e_1_type, type, e_1: $i).
% 0.55/1.02  thf(e_3_type, type, e_3: $i).
% 0.55/1.02  thf(group_element_type, type, group_element: $i > $o).
% 0.55/1.02  thf(e_2_type, type, e_2: $i).
% 0.55/1.02  thf(product_type, type, product: $i > $i > $i > $o).
% 0.55/1.02  thf(equalish_type, type, equalish: $i > $i > $o).
% 0.55/1.02  thf(element_1, axiom, (group_element @ e_1)).
% 0.55/1.02  thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.55/1.02      inference('cnf', [status(esa)], [element_1])).
% 0.55/1.02  thf(product_total_function1, axiom,
% 0.55/1.02    (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) | 
% 0.55/1.02     ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) | 
% 0.55/1.02     ( product @ X @ Y @ e_3 ))).
% 0.55/1.02  thf(zip_derived_cl9, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (group_element @ X0)
% 0.55/1.02          | ~ (group_element @ X1)
% 0.55/1.02          |  (product @ X0 @ X1 @ e_1)
% 0.55/1.02          |  (product @ X0 @ X1 @ e_2)
% 0.55/1.02          |  (product @ X0 @ X1 @ e_3))),
% 0.55/1.02      inference('cnf', [status(esa)], [product_total_function1])).
% 0.55/1.02  thf(qg3, conjecture,
% 0.55/1.02    (~( ( product @ X @ Z1 @ Z2 ) | ( ~( product @ Z1 @ Y @ Z2 ) ) | 
% 0.55/1.02        ( ~( product @ X @ Y @ Z1 ) ) ))).
% 0.55/1.02  thf(zf_stmt_0, negated_conjecture,
% 0.55/1.02    (( product @ X @ Z1 @ Z2 ) | ( ~( product @ Z1 @ Y @ Z2 ) ) | 
% 0.55/1.02     ( ~( product @ X @ Y @ Z1 ) )),
% 0.55/1.02    inference('cnf.neg', [status(esa)], [qg3])).
% 0.55/1.02  thf(zip_derived_cl13, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.02         ( (product @ X0 @ X1 @ X2)
% 0.55/1.02          | ~ (product @ X1 @ X3 @ X2)
% 0.55/1.02          | ~ (product @ X0 @ X3 @ X1))),
% 0.55/1.02      inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.55/1.02  thf(zip_derived_cl36, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (product @ X0 @ X1 @ X0) |  (product @ X0 @ X0 @ X0))),
% 0.55/1.02      inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 0.55/1.02  thf(zip_derived_cl51, plain,
% 0.55/1.02      (![X0 : $i]:
% 0.55/1.02         ( (product @ e_3 @ X0 @ e_2)
% 0.55/1.02          |  (product @ e_3 @ X0 @ e_1)
% 0.55/1.02          | ~ (group_element @ X0)
% 0.55/1.02          | ~ (group_element @ e_3)
% 0.55/1.02          |  (product @ e_3 @ e_3 @ e_3))),
% 0.55/1.02      inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl36])).
% 0.55/1.02  thf(element_3, axiom, (group_element @ e_3)).
% 0.55/1.02  thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.55/1.02      inference('cnf', [status(esa)], [element_3])).
% 0.55/1.02  thf(zip_derived_cl53, plain,
% 0.55/1.02      (![X0 : $i]:
% 0.55/1.02         ( (product @ e_3 @ X0 @ e_2)
% 0.55/1.02          |  (product @ e_3 @ X0 @ e_1)
% 0.55/1.02          | ~ (group_element @ X0)
% 0.55/1.02          |  (product @ e_3 @ e_3 @ e_3))),
% 0.55/1.02      inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl2])).
% 0.55/1.02  thf(zip_derived_cl307, plain,
% 0.55/1.02      (( (product @ e_3 @ e_3 @ e_3)
% 0.55/1.02        |  (product @ e_3 @ e_1 @ e_1)
% 0.55/1.02        |  (product @ e_3 @ e_1 @ e_2))),
% 0.55/1.02      inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl53])).
% 0.55/1.02  thf(product_right_cancellation, axiom,
% 0.55/1.02    (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) | 
% 0.55/1.02     ( equalish @ W @ Z ))).
% 0.55/1.02  thf(zip_derived_cl11, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.02         (~ (product @ X0 @ X1 @ X2)
% 0.55/1.02          | ~ (product @ X0 @ X3 @ X2)
% 0.55/1.02          |  (equalish @ X1 @ X3))),
% 0.55/1.02      inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.55/1.02  thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 0.55/1.02  thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 0.55/1.02      inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.55/1.02  thf(zip_derived_cl21, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (product @ X1 @ e_3 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.55/1.02      inference('dp-resolution', [status(thm)],
% 0.55/1.02                [zip_derived_cl11, zip_derived_cl4])).
% 0.55/1.02  thf(zip_derived_cl364, plain,
% 0.55/1.02      (( (product @ e_3 @ e_1 @ e_2)
% 0.55/1.02        |  (product @ e_3 @ e_1 @ e_1)
% 0.55/1.02        | ~ (product @ e_3 @ e_1 @ e_3))),
% 0.55/1.02      inference('sup-', [status(thm)], [zip_derived_cl307, zip_derived_cl21])).
% 0.55/1.02  thf(product_total_function2, axiom,
% 0.55/1.02    (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) | 
% 0.55/1.02     ( equalish @ W @ Z ))).
% 0.55/1.02  thf(zip_derived_cl10, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.02         (~ (product @ X0 @ X1 @ X2)
% 0.55/1.02          | ~ (product @ X0 @ X1 @ X3)
% 0.55/1.02          |  (equalish @ X2 @ X3))),
% 0.55/1.02      inference('cnf', [status(esa)], [product_total_function2])).
% 0.55/1.02  thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 0.55/1.02  thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.55/1.02      inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.55/1.02  thf(zip_derived_cl17, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (product @ X1 @ X0 @ e_3) | ~ (product @ X1 @ X0 @ e_2))),
% 0.55/1.02      inference('dp-resolution', [status(thm)],
% 0.55/1.02                [zip_derived_cl10, zip_derived_cl6])).
% 0.55/1.02  thf(zip_derived_cl457, plain,
% 0.55/1.02      ((~ (product @ e_3 @ e_1 @ e_3) |  (product @ e_3 @ e_1 @ e_1))),
% 0.55/1.02      inference('clc', [status(thm)], [zip_derived_cl364, zip_derived_cl17])).
% 0.55/1.02  thf(zip_derived_cl10, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.02         (~ (product @ X0 @ X1 @ X2)
% 0.55/1.02          | ~ (product @ X0 @ X1 @ X3)
% 0.55/1.02          |  (equalish @ X2 @ X3))),
% 0.55/1.02      inference('cnf', [status(esa)], [product_total_function2])).
% 0.55/1.02  thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 0.55/1.02      inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.55/1.02  thf(zip_derived_cl15, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (product @ X1 @ X0 @ e_3) | ~ (product @ X1 @ X0 @ e_1))),
% 0.55/1.02      inference('dp-resolution', [status(thm)],
% 0.55/1.02                [zip_derived_cl10, zip_derived_cl4])).
% 0.55/1.02  thf(zip_derived_cl458, plain, (~ (product @ e_3 @ e_1 @ e_3)),
% 0.55/1.02      inference('clc', [status(thm)], [zip_derived_cl457, zip_derived_cl15])).
% 0.55/1.02  thf(zip_derived_cl9, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (group_element @ X0)
% 0.55/1.02          | ~ (group_element @ X1)
% 0.55/1.02          |  (product @ X0 @ X1 @ e_1)
% 0.55/1.02          |  (product @ X0 @ X1 @ e_2)
% 0.55/1.02          |  (product @ X0 @ X1 @ e_3))),
% 0.55/1.02      inference('cnf', [status(esa)], [product_total_function1])).
% 0.55/1.02  thf(element_2, axiom, (group_element @ e_2)).
% 0.55/1.02  thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.55/1.02      inference('cnf', [status(esa)], [element_2])).
% 0.55/1.02  thf(zip_derived_cl53, plain,
% 0.55/1.02      (![X0 : $i]:
% 0.55/1.02         ( (product @ e_3 @ X0 @ e_2)
% 0.55/1.02          |  (product @ e_3 @ X0 @ e_1)
% 0.55/1.02          | ~ (group_element @ X0)
% 0.55/1.02          |  (product @ e_3 @ e_3 @ e_3))),
% 0.55/1.02      inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl2])).
% 0.55/1.02  thf(zip_derived_cl308, plain,
% 0.55/1.02      (( (product @ e_3 @ e_3 @ e_3)
% 0.55/1.02        |  (product @ e_3 @ e_2 @ e_1)
% 0.55/1.02        |  (product @ e_3 @ e_2 @ e_2))),
% 0.55/1.02      inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl53])).
% 0.55/1.02  thf(zip_derived_cl11, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.02         (~ (product @ X0 @ X1 @ X2)
% 0.55/1.02          | ~ (product @ X0 @ X3 @ X2)
% 0.55/1.02          |  (equalish @ X1 @ X3))),
% 0.55/1.02      inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.55/1.02  thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.55/1.02      inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.55/1.02  thf(zip_derived_cl23, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (product @ X1 @ e_3 @ X0) | ~ (product @ X1 @ e_2 @ X0))),
% 0.55/1.02      inference('dp-resolution', [status(thm)],
% 0.55/1.02                [zip_derived_cl11, zip_derived_cl6])).
% 0.55/1.02  thf(zip_derived_cl416, plain,
% 0.55/1.02      (( (product @ e_3 @ e_2 @ e_2)
% 0.55/1.02        |  (product @ e_3 @ e_2 @ e_1)
% 0.55/1.02        | ~ (product @ e_3 @ e_2 @ e_3))),
% 0.55/1.02      inference('sup-', [status(thm)], [zip_derived_cl308, zip_derived_cl23])).
% 0.55/1.02  thf(zip_derived_cl17, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (product @ X1 @ X0 @ e_3) | ~ (product @ X1 @ X0 @ e_2))),
% 0.55/1.02      inference('dp-resolution', [status(thm)],
% 0.55/1.02                [zip_derived_cl10, zip_derived_cl6])).
% 0.55/1.02  thf(zip_derived_cl713, plain,
% 0.55/1.02      ((~ (product @ e_3 @ e_2 @ e_3) |  (product @ e_3 @ e_2 @ e_1))),
% 0.55/1.02      inference('clc', [status(thm)], [zip_derived_cl416, zip_derived_cl17])).
% 0.55/1.02  thf(zip_derived_cl15, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (product @ X1 @ X0 @ e_3) | ~ (product @ X1 @ X0 @ e_1))),
% 0.55/1.02      inference('dp-resolution', [status(thm)],
% 0.55/1.02                [zip_derived_cl10, zip_derived_cl4])).
% 0.55/1.02  thf(zip_derived_cl714, plain, (~ (product @ e_3 @ e_2 @ e_3)),
% 0.55/1.02      inference('clc', [status(thm)], [zip_derived_cl713, zip_derived_cl15])).
% 0.55/1.02  thf(zip_derived_cl716, plain,
% 0.55/1.02      (( (product @ e_3 @ e_2 @ e_2)
% 0.55/1.02        |  (product @ e_3 @ e_2 @ e_1)
% 0.55/1.02        | ~ (group_element @ e_2)
% 0.55/1.02        | ~ (group_element @ e_3))),
% 0.55/1.02      inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl714])).
% 0.55/1.02  thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.55/1.02      inference('cnf', [status(esa)], [element_2])).
% 0.55/1.02  thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.55/1.02      inference('cnf', [status(esa)], [element_3])).
% 0.55/1.02  thf(zip_derived_cl717, plain,
% 0.55/1.02      (( (product @ e_3 @ e_2 @ e_2) |  (product @ e_3 @ e_2 @ e_1))),
% 0.55/1.02      inference('demod', [status(thm)],
% 0.55/1.02                [zip_derived_cl716, zip_derived_cl1, zip_derived_cl2])).
% 0.55/1.02  thf(product_left_cancellation, axiom,
% 0.55/1.02    (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) | 
% 0.55/1.02     ( equalish @ W @ Z ))).
% 0.55/1.02  thf(zip_derived_cl12, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.02         (~ (product @ X0 @ X1 @ X2)
% 0.55/1.02          | ~ (product @ X3 @ X1 @ X2)
% 0.55/1.02          |  (equalish @ X0 @ X3))),
% 0.55/1.02      inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.55/1.02  thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.55/1.02      inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.55/1.02  thf(zip_derived_cl29, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_2 @ X1 @ X0))),
% 0.55/1.02      inference('dp-resolution', [status(thm)],
% 0.55/1.02                [zip_derived_cl12, zip_derived_cl6])).
% 0.55/1.02  thf(zip_derived_cl725, plain,
% 0.55/1.02      (( (product @ e_3 @ e_2 @ e_1) | ~ (product @ e_2 @ e_2 @ e_2))),
% 0.55/1.02      inference('sup-', [status(thm)], [zip_derived_cl717, zip_derived_cl29])).
% 0.55/1.02  thf(zip_derived_cl9, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (group_element @ X0)
% 0.55/1.02          | ~ (group_element @ X1)
% 0.55/1.02          |  (product @ X0 @ X1 @ e_1)
% 0.55/1.02          |  (product @ X0 @ X1 @ e_2)
% 0.55/1.02          |  (product @ X0 @ X1 @ e_3))),
% 0.55/1.02      inference('cnf', [status(esa)], [product_total_function1])).
% 0.55/1.02  thf(zip_derived_cl9, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (group_element @ X0)
% 0.55/1.02          | ~ (group_element @ X1)
% 0.55/1.02          |  (product @ X0 @ X1 @ e_1)
% 0.55/1.02          |  (product @ X0 @ X1 @ e_2)
% 0.55/1.02          |  (product @ X0 @ X1 @ e_3))),
% 0.55/1.02      inference('cnf', [status(esa)], [product_total_function1])).
% 0.55/1.02  thf(zip_derived_cl23, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (product @ X1 @ e_3 @ X0) | ~ (product @ X1 @ e_2 @ X0))),
% 0.55/1.02      inference('dp-resolution', [status(thm)],
% 0.55/1.02                [zip_derived_cl11, zip_derived_cl6])).
% 0.55/1.02  thf(zip_derived_cl48, plain,
% 0.55/1.02      (![X0 : $i]:
% 0.55/1.02         ( (product @ X0 @ e_3 @ e_2)
% 0.55/1.02          |  (product @ X0 @ e_3 @ e_1)
% 0.55/1.02          | ~ (group_element @ e_3)
% 0.55/1.02          | ~ (group_element @ X0)
% 0.55/1.02          | ~ (product @ X0 @ e_2 @ e_3))),
% 0.55/1.02      inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl23])).
% 0.55/1.02  thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.55/1.02      inference('cnf', [status(esa)], [element_3])).
% 0.55/1.02  thf(zip_derived_cl49, plain,
% 0.55/1.02      (![X0 : $i]:
% 0.55/1.02         ( (product @ X0 @ e_3 @ e_2)
% 0.55/1.02          |  (product @ X0 @ e_3 @ e_1)
% 0.55/1.02          | ~ (group_element @ X0)
% 0.55/1.02          | ~ (product @ X0 @ e_2 @ e_3))),
% 0.55/1.02      inference('demod', [status(thm)], [zip_derived_cl48, zip_derived_cl2])).
% 0.55/1.02  thf(zip_derived_cl36, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (product @ X0 @ X1 @ X0) |  (product @ X0 @ X0 @ X0))),
% 0.55/1.02      inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 0.55/1.02  thf(zip_derived_cl231, plain,
% 0.55/1.02      ((~ (product @ e_2 @ e_2 @ e_3)
% 0.55/1.02        | ~ (group_element @ e_2)
% 0.55/1.02        |  (product @ e_2 @ e_3 @ e_1)
% 0.55/1.02        |  (product @ e_2 @ e_2 @ e_2))),
% 0.55/1.02      inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl36])).
% 0.55/1.02  thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.55/1.02      inference('cnf', [status(esa)], [element_2])).
% 0.55/1.02  thf(zip_derived_cl248, plain,
% 0.55/1.02      ((~ (product @ e_2 @ e_2 @ e_3)
% 0.55/1.02        |  (product @ e_2 @ e_3 @ e_1)
% 0.55/1.02        |  (product @ e_2 @ e_2 @ e_2))),
% 0.55/1.02      inference('demod', [status(thm)], [zip_derived_cl231, zip_derived_cl1])).
% 0.55/1.02  thf(zip_derived_cl17, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (product @ X1 @ X0 @ e_3) | ~ (product @ X1 @ X0 @ e_2))),
% 0.55/1.02      inference('dp-resolution', [status(thm)],
% 0.55/1.02                [zip_derived_cl10, zip_derived_cl6])).
% 0.55/1.02  thf(zip_derived_cl315, plain,
% 0.55/1.02      (( (product @ e_2 @ e_3 @ e_1) | ~ (product @ e_2 @ e_2 @ e_3))),
% 0.55/1.02      inference('clc', [status(thm)], [zip_derived_cl248, zip_derived_cl17])).
% 0.55/1.02  thf(zip_derived_cl9, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (group_element @ X0)
% 0.55/1.02          | ~ (group_element @ X1)
% 0.55/1.02          |  (product @ X0 @ X1 @ e_1)
% 0.55/1.02          |  (product @ X0 @ X1 @ e_2)
% 0.55/1.02          |  (product @ X0 @ X1 @ e_3))),
% 0.55/1.02      inference('cnf', [status(esa)], [product_total_function1])).
% 0.55/1.02  thf(zip_derived_cl12, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.02         (~ (product @ X0 @ X1 @ X2)
% 0.55/1.02          | ~ (product @ X3 @ X1 @ X2)
% 0.55/1.02          |  (equalish @ X0 @ X3))),
% 0.55/1.02      inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.55/1.02  thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 0.55/1.02      inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.55/1.02  thf(zip_derived_cl27, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.55/1.02      inference('dp-resolution', [status(thm)],
% 0.55/1.02                [zip_derived_cl12, zip_derived_cl4])).
% 0.55/1.02  thf(zip_derived_cl21, plain,
% 0.55/1.02      (![X0 : $i, X1 : $i]:
% 0.55/1.02         (~ (product @ X1 @ e_3 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.55/1.02      inference('dp-resolution', [status(thm)],
% 0.55/1.02                [zip_derived_cl11, zip_derived_cl4])).
% 0.55/1.02  thf(zip_derived_cl9, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (group_element @ X0)
% 0.55/1.03          | ~ (group_element @ X1)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_1)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_2)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_3))),
% 0.55/1.03      inference('cnf', [status(esa)], [product_total_function1])).
% 0.55/1.03  thf(zip_derived_cl27, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl12, zip_derived_cl4])).
% 0.55/1.03  thf(zip_derived_cl59, plain,
% 0.55/1.03      (![X0 : $i]:
% 0.55/1.03         ( (product @ e_3 @ X0 @ e_2)
% 0.55/1.03          |  (product @ e_3 @ X0 @ e_1)
% 0.55/1.03          | ~ (group_element @ X0)
% 0.55/1.03          | ~ (group_element @ e_3)
% 0.55/1.03          | ~ (product @ e_1 @ X0 @ e_3))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl27])).
% 0.55/1.03  thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_3])).
% 0.55/1.03  thf(zip_derived_cl60, plain,
% 0.55/1.03      (![X0 : $i]:
% 0.55/1.03         ( (product @ e_3 @ X0 @ e_2)
% 0.55/1.03          |  (product @ e_3 @ X0 @ e_1)
% 0.55/1.03          | ~ (group_element @ X0)
% 0.55/1.03          | ~ (product @ e_1 @ X0 @ e_3))),
% 0.55/1.03      inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl2])).
% 0.55/1.03  thf(zip_derived_cl441, plain,
% 0.55/1.03      ((~ (product @ e_3 @ e_1 @ e_2)
% 0.55/1.03        | ~ (product @ e_1 @ e_3 @ e_3)
% 0.55/1.03        | ~ (group_element @ e_3)
% 0.55/1.03        |  (product @ e_3 @ e_3 @ e_1))),
% 0.55/1.03      inference('sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl60])).
% 0.55/1.03  thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_3])).
% 0.55/1.03  thf(zip_derived_cl447, plain,
% 0.55/1.03      ((~ (product @ e_3 @ e_1 @ e_2)
% 0.55/1.03        | ~ (product @ e_1 @ e_3 @ e_3)
% 0.55/1.03        |  (product @ e_3 @ e_3 @ e_1))),
% 0.55/1.03      inference('demod', [status(thm)], [zip_derived_cl441, zip_derived_cl2])).
% 0.55/1.03  thf(zip_derived_cl23, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ X1 @ e_3 @ X0) | ~ (product @ X1 @ e_2 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl11, zip_derived_cl6])).
% 0.55/1.03  thf(zip_derived_cl927, plain,
% 0.55/1.03      ((~ (product @ e_1 @ e_3 @ e_3)
% 0.55/1.03        | ~ (product @ e_3 @ e_1 @ e_2)
% 0.55/1.03        | ~ (product @ e_3 @ e_2 @ e_1))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl447, zip_derived_cl23])).
% 0.55/1.03  thf(zip_derived_cl717, plain,
% 0.55/1.03      (( (product @ e_3 @ e_2 @ e_2) |  (product @ e_3 @ e_2 @ e_1))),
% 0.55/1.03      inference('demod', [status(thm)],
% 0.55/1.03                [zip_derived_cl716, zip_derived_cl1, zip_derived_cl2])).
% 0.55/1.03  thf(zip_derived_cl11, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.03         (~ (product @ X0 @ X1 @ X2)
% 0.55/1.03          | ~ (product @ X0 @ X3 @ X2)
% 0.55/1.03          |  (equalish @ X1 @ X3))),
% 0.55/1.03      inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.55/1.03  thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 0.55/1.03  thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.55/1.03      inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.55/1.03  thf(zip_derived_cl20, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ X1 @ e_2 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl11, zip_derived_cl3])).
% 0.55/1.03  thf(zip_derived_cl722, plain,
% 0.55/1.03      (( (product @ e_3 @ e_2 @ e_1) | ~ (product @ e_3 @ e_1 @ e_2))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl717, zip_derived_cl20])).
% 0.55/1.03  thf(zip_derived_cl953, plain,
% 0.55/1.03      ((~ (product @ e_3 @ e_1 @ e_2) | ~ (product @ e_1 @ e_3 @ e_3))),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl927, zip_derived_cl722])).
% 0.55/1.03  thf(zip_derived_cl9, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (group_element @ X0)
% 0.55/1.03          | ~ (group_element @ X1)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_1)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_2)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_3))),
% 0.55/1.03      inference('cnf', [status(esa)], [product_total_function1])).
% 0.55/1.03  thf(zip_derived_cl458, plain, (~ (product @ e_3 @ e_1 @ e_3)),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl457, zip_derived_cl15])).
% 0.55/1.03  thf(zip_derived_cl460, plain,
% 0.55/1.03      (( (product @ e_3 @ e_1 @ e_2)
% 0.55/1.03        |  (product @ e_3 @ e_1 @ e_1)
% 0.55/1.03        | ~ (group_element @ e_1)
% 0.55/1.03        | ~ (group_element @ e_3))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl458])).
% 0.55/1.03  thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_1])).
% 0.55/1.03  thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_3])).
% 0.55/1.03  thf(zip_derived_cl461, plain,
% 0.55/1.03      (( (product @ e_3 @ e_1 @ e_2) |  (product @ e_3 @ e_1 @ e_1))),
% 0.55/1.03      inference('demod', [status(thm)],
% 0.55/1.03                [zip_derived_cl460, zip_derived_cl0, zip_derived_cl2])).
% 0.55/1.03  thf(zip_derived_cl956, plain,
% 0.55/1.03      ((~ (product @ e_1 @ e_3 @ e_3) |  (product @ e_3 @ e_1 @ e_1))),
% 0.55/1.03      inference('sup+', [status(thm)], [zip_derived_cl953, zip_derived_cl461])).
% 0.55/1.03  thf(zip_derived_cl969, plain,
% 0.55/1.03      ((~ (product @ e_1 @ e_1 @ e_1) | ~ (product @ e_1 @ e_3 @ e_3))),
% 0.55/1.03      inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl956])).
% 0.55/1.03  thf(zip_derived_cl461, plain,
% 0.55/1.03      (( (product @ e_3 @ e_1 @ e_2) |  (product @ e_3 @ e_1 @ e_1))),
% 0.55/1.03      inference('demod', [status(thm)],
% 0.55/1.03                [zip_derived_cl460, zip_derived_cl0, zip_derived_cl2])).
% 0.55/1.03  thf(zip_derived_cl27, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl12, zip_derived_cl4])).
% 0.55/1.03  thf(zip_derived_cl466, plain,
% 0.55/1.03      (( (product @ e_3 @ e_1 @ e_1) | ~ (product @ e_1 @ e_1 @ e_2))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl461, zip_derived_cl27])).
% 0.55/1.03  thf(zip_derived_cl9, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (group_element @ X0)
% 0.55/1.03          | ~ (group_element @ X1)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_1)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_2)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_3))),
% 0.55/1.03      inference('cnf', [status(esa)], [product_total_function1])).
% 0.55/1.03  thf(zip_derived_cl9, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (group_element @ X0)
% 0.55/1.03          | ~ (group_element @ X1)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_1)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_2)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_3))),
% 0.55/1.03      inference('cnf', [status(esa)], [product_total_function1])).
% 0.55/1.03  thf(zip_derived_cl20, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ X1 @ e_2 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl11, zip_derived_cl3])).
% 0.55/1.03  thf(zip_derived_cl40, plain,
% 0.55/1.03      (![X0 : $i]:
% 0.55/1.03         ( (product @ X0 @ e_2 @ e_2)
% 0.55/1.03          |  (product @ X0 @ e_2 @ e_1)
% 0.55/1.03          | ~ (group_element @ e_2)
% 0.55/1.03          | ~ (group_element @ X0)
% 0.55/1.03          | ~ (product @ X0 @ e_1 @ e_3))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl20])).
% 0.55/1.03  thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_2])).
% 0.55/1.03  thf(zip_derived_cl41, plain,
% 0.55/1.03      (![X0 : $i]:
% 0.55/1.03         ( (product @ X0 @ e_2 @ e_2)
% 0.55/1.03          |  (product @ X0 @ e_2 @ e_1)
% 0.55/1.03          | ~ (group_element @ X0)
% 0.55/1.03          | ~ (product @ X0 @ e_1 @ e_3))),
% 0.55/1.03      inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl1])).
% 0.55/1.03  thf(zip_derived_cl9, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (group_element @ X0)
% 0.55/1.03          | ~ (group_element @ X1)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_1)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_2)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_3))),
% 0.55/1.03      inference('cnf', [status(esa)], [product_total_function1])).
% 0.55/1.03  thf(zip_derived_cl315, plain,
% 0.55/1.03      (( (product @ e_2 @ e_3 @ e_1) | ~ (product @ e_2 @ e_2 @ e_3))),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl248, zip_derived_cl17])).
% 0.55/1.03  thf(zip_derived_cl21, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ X1 @ e_3 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl11, zip_derived_cl4])).
% 0.55/1.03  thf(zip_derived_cl318, plain,
% 0.55/1.03      ((~ (product @ e_2 @ e_2 @ e_3) | ~ (product @ e_2 @ e_1 @ e_1))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl315, zip_derived_cl21])).
% 0.55/1.03  thf(zip_derived_cl326, plain,
% 0.55/1.03      (( (product @ e_2 @ e_2 @ e_2)
% 0.55/1.03        |  (product @ e_2 @ e_2 @ e_1)
% 0.55/1.03        | ~ (group_element @ e_2)
% 0.55/1.03        | ~ (group_element @ e_2)
% 0.55/1.03        | ~ (product @ e_2 @ e_1 @ e_1))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl318])).
% 0.55/1.03  thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_2])).
% 0.55/1.03  thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_2])).
% 0.55/1.03  thf(zip_derived_cl327, plain,
% 0.55/1.03      (( (product @ e_2 @ e_2 @ e_2)
% 0.55/1.03        |  (product @ e_2 @ e_2 @ e_1)
% 0.55/1.03        | ~ (product @ e_2 @ e_1 @ e_1))),
% 0.55/1.03      inference('demod', [status(thm)],
% 0.55/1.03                [zip_derived_cl326, zip_derived_cl1, zip_derived_cl1])).
% 0.55/1.03  thf(zip_derived_cl20, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ X1 @ e_2 @ X0) | ~ (product @ X1 @ e_1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl11, zip_derived_cl3])).
% 0.55/1.03  thf(zip_derived_cl599, plain,
% 0.55/1.03      ((~ (product @ e_2 @ e_1 @ e_1) |  (product @ e_2 @ e_2 @ e_2))),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl327, zip_derived_cl20])).
% 0.55/1.03  thf(zip_derived_cl12, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.03         (~ (product @ X0 @ X1 @ X2)
% 0.55/1.03          | ~ (product @ X3 @ X1 @ X2)
% 0.55/1.03          |  (equalish @ X0 @ X3))),
% 0.55/1.03      inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.55/1.03  thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.55/1.03      inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.55/1.03  thf(zip_derived_cl26, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ e_2 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl12, zip_derived_cl3])).
% 0.55/1.03  thf(zip_derived_cl605, plain,
% 0.55/1.03      ((~ (product @ e_2 @ e_1 @ e_1) | ~ (product @ e_1 @ e_2 @ e_2))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl599, zip_derived_cl26])).
% 0.55/1.03  thf(zip_derived_cl9, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (group_element @ X0)
% 0.55/1.03          | ~ (group_element @ X1)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_1)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_2)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_3))),
% 0.55/1.03      inference('cnf', [status(esa)], [product_total_function1])).
% 0.55/1.03  thf(zip_derived_cl26, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ e_2 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl12, zip_derived_cl3])).
% 0.55/1.03  thf(zip_derived_cl41, plain,
% 0.55/1.03      (![X0 : $i]:
% 0.55/1.03         ( (product @ X0 @ e_2 @ e_2)
% 0.55/1.03          |  (product @ X0 @ e_2 @ e_1)
% 0.55/1.03          | ~ (group_element @ X0)
% 0.55/1.03          | ~ (product @ X0 @ e_1 @ e_3))),
% 0.55/1.03      inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl1])).
% 0.55/1.03  thf(zip_derived_cl75, plain,
% 0.55/1.03      ((~ (product @ e_1 @ e_2 @ e_2)
% 0.55/1.03        | ~ (product @ e_2 @ e_1 @ e_3)
% 0.55/1.03        | ~ (group_element @ e_2)
% 0.55/1.03        |  (product @ e_2 @ e_2 @ e_1))),
% 0.55/1.03      inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl41])).
% 0.55/1.03  thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_2])).
% 0.55/1.03  thf(zip_derived_cl78, plain,
% 0.55/1.03      ((~ (product @ e_1 @ e_2 @ e_2)
% 0.55/1.03        | ~ (product @ e_2 @ e_1 @ e_3)
% 0.55/1.03        |  (product @ e_2 @ e_2 @ e_1))),
% 0.55/1.03      inference('demod', [status(thm)], [zip_derived_cl75, zip_derived_cl1])).
% 0.55/1.03  thf(zip_derived_cl13, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.03         ( (product @ X0 @ X1 @ X2)
% 0.55/1.03          | ~ (product @ X1 @ X3 @ X2)
% 0.55/1.03          | ~ (product @ X0 @ X3 @ X1))),
% 0.55/1.03      inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.55/1.03  thf(zip_derived_cl85, plain,
% 0.55/1.03      (![X0 : $i]:
% 0.55/1.03         (~ (product @ e_2 @ e_1 @ e_3)
% 0.55/1.03          | ~ (product @ e_1 @ e_2 @ e_2)
% 0.55/1.03          | ~ (product @ X0 @ e_2 @ e_2)
% 0.55/1.03          |  (product @ X0 @ e_2 @ e_1))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl78, zip_derived_cl13])).
% 0.55/1.03  thf(zip_derived_cl10, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.03         (~ (product @ X0 @ X1 @ X2)
% 0.55/1.03          | ~ (product @ X0 @ X1 @ X3)
% 0.55/1.03          |  (equalish @ X2 @ X3))),
% 0.55/1.03      inference('cnf', [status(esa)], [product_total_function2])).
% 0.55/1.03  thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.55/1.03      inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.55/1.03  thf(zip_derived_cl14, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ X1 @ X0 @ e_2) | ~ (product @ X1 @ X0 @ e_1))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl10, zip_derived_cl3])).
% 0.55/1.03  thf(zip_derived_cl110, plain,
% 0.55/1.03      (![X0 : $i]:
% 0.55/1.03         (~ (product @ X0 @ e_2 @ e_2)
% 0.55/1.03          | ~ (product @ e_1 @ e_2 @ e_2)
% 0.55/1.03          | ~ (product @ e_2 @ e_1 @ e_3))),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl85, zip_derived_cl14])).
% 0.55/1.03  thf(zip_derived_cl111, plain,
% 0.55/1.03      ((~ (product @ e_2 @ e_1 @ e_3) | ~ (product @ e_1 @ e_2 @ e_2))),
% 0.55/1.03      inference('condensation', [status(thm)], [zip_derived_cl110])).
% 0.55/1.03  thf(zip_derived_cl113, plain,
% 0.55/1.03      (( (product @ e_2 @ e_1 @ e_2)
% 0.55/1.03        |  (product @ e_2 @ e_1 @ e_1)
% 0.55/1.03        | ~ (group_element @ e_1)
% 0.55/1.03        | ~ (group_element @ e_2)
% 0.55/1.03        | ~ (product @ e_1 @ e_2 @ e_2))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl111])).
% 0.55/1.03  thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_1])).
% 0.55/1.03  thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_2])).
% 0.55/1.03  thf(zip_derived_cl114, plain,
% 0.55/1.03      (( (product @ e_2 @ e_1 @ e_2)
% 0.55/1.03        |  (product @ e_2 @ e_1 @ e_1)
% 0.55/1.03        | ~ (product @ e_1 @ e_2 @ e_2))),
% 0.55/1.03      inference('demod', [status(thm)],
% 0.55/1.03                [zip_derived_cl113, zip_derived_cl0, zip_derived_cl1])).
% 0.55/1.03  thf(zip_derived_cl36, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ X0 @ X1 @ X0) |  (product @ X0 @ X0 @ X0))),
% 0.55/1.03      inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 0.55/1.03  thf(zip_derived_cl132, plain,
% 0.55/1.03      ((~ (product @ e_1 @ e_2 @ e_2)
% 0.55/1.03        |  (product @ e_2 @ e_1 @ e_1)
% 0.55/1.03        |  (product @ e_2 @ e_2 @ e_2))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl36])).
% 0.55/1.03  thf(zip_derived_cl26, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ e_2 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl12, zip_derived_cl3])).
% 0.55/1.03  thf(zip_derived_cl192, plain,
% 0.55/1.03      (( (product @ e_2 @ e_1 @ e_1) | ~ (product @ e_1 @ e_2 @ e_2))),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl132, zip_derived_cl26])).
% 0.55/1.03  thf(zip_derived_cl610, plain, (~ (product @ e_1 @ e_2 @ e_2)),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl605, zip_derived_cl192])).
% 0.55/1.03  thf(zip_derived_cl612, plain,
% 0.55/1.03      ((~ (product @ e_1 @ e_1 @ e_3)
% 0.55/1.03        | ~ (group_element @ e_1)
% 0.55/1.03        |  (product @ e_1 @ e_2 @ e_1))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl610])).
% 0.55/1.03  thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_1])).
% 0.55/1.03  thf(zip_derived_cl613, plain,
% 0.55/1.03      ((~ (product @ e_1 @ e_1 @ e_3) |  (product @ e_1 @ e_2 @ e_1))),
% 0.55/1.03      inference('demod', [status(thm)], [zip_derived_cl612, zip_derived_cl0])).
% 0.55/1.03  thf(zip_derived_cl36, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ X0 @ X1 @ X0) |  (product @ X0 @ X0 @ X0))),
% 0.55/1.03      inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 0.55/1.03  thf(zip_derived_cl636, plain,
% 0.55/1.03      ((~ (product @ e_1 @ e_1 @ e_3) |  (product @ e_1 @ e_1 @ e_1))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl613, zip_derived_cl36])).
% 0.55/1.03  thf(zip_derived_cl15, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ X1 @ X0 @ e_3) | ~ (product @ X1 @ X0 @ e_1))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl10, zip_derived_cl4])).
% 0.55/1.03  thf(zip_derived_cl643, plain, (~ (product @ e_1 @ e_1 @ e_3)),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl636, zip_derived_cl15])).
% 0.55/1.03  thf(zip_derived_cl645, plain,
% 0.55/1.03      (( (product @ e_1 @ e_1 @ e_2)
% 0.55/1.03        |  (product @ e_1 @ e_1 @ e_1)
% 0.55/1.03        | ~ (group_element @ e_1)
% 0.55/1.03        | ~ (group_element @ e_1))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl643])).
% 0.55/1.03  thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_1])).
% 0.55/1.03  thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_1])).
% 0.55/1.03  thf(zip_derived_cl646, plain,
% 0.55/1.03      (( (product @ e_1 @ e_1 @ e_2) |  (product @ e_1 @ e_1 @ e_1))),
% 0.55/1.03      inference('demod', [status(thm)],
% 0.55/1.03                [zip_derived_cl645, zip_derived_cl0, zip_derived_cl0])).
% 0.55/1.03  thf(zip_derived_cl13, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.03         ( (product @ X0 @ X1 @ X2)
% 0.55/1.03          | ~ (product @ X1 @ X3 @ X2)
% 0.55/1.03          | ~ (product @ X0 @ X3 @ X1))),
% 0.55/1.03      inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.55/1.03  thf(zip_derived_cl648, plain,
% 0.55/1.03      (![X0 : $i]:
% 0.55/1.03         ( (product @ e_1 @ e_1 @ e_1)
% 0.55/1.03          | ~ (product @ X0 @ e_1 @ e_1)
% 0.55/1.03          |  (product @ X0 @ e_1 @ e_2))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl646, zip_derived_cl13])).
% 0.55/1.03  thf(zip_derived_cl14, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ X1 @ X0 @ e_2) | ~ (product @ X1 @ X0 @ e_1))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl10, zip_derived_cl3])).
% 0.55/1.03  thf(zip_derived_cl657, plain,
% 0.55/1.03      (![X0 : $i]:
% 0.55/1.03         (~ (product @ X0 @ e_1 @ e_1) |  (product @ e_1 @ e_1 @ e_1))),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl648, zip_derived_cl14])).
% 0.55/1.03  thf(zip_derived_cl658, plain,
% 0.55/1.03      ((~ (product @ e_1 @ e_1 @ e_2) |  (product @ e_1 @ e_1 @ e_1))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl466, zip_derived_cl657])).
% 0.55/1.03  thf(zip_derived_cl646, plain,
% 0.55/1.03      (( (product @ e_1 @ e_1 @ e_2) |  (product @ e_1 @ e_1 @ e_1))),
% 0.55/1.03      inference('demod', [status(thm)],
% 0.55/1.03                [zip_derived_cl645, zip_derived_cl0, zip_derived_cl0])).
% 0.55/1.03  thf(zip_derived_cl661, plain, ( (product @ e_1 @ e_1 @ e_1)),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl658, zip_derived_cl646])).
% 0.55/1.03  thf(zip_derived_cl972, plain, (~ (product @ e_1 @ e_3 @ e_3)),
% 0.55/1.03      inference('demod', [status(thm)], [zip_derived_cl969, zip_derived_cl661])).
% 0.55/1.03  thf(zip_derived_cl976, plain,
% 0.55/1.03      (( (product @ e_1 @ e_3 @ e_2)
% 0.55/1.03        |  (product @ e_1 @ e_3 @ e_1)
% 0.55/1.03        | ~ (group_element @ e_3)
% 0.55/1.03        | ~ (group_element @ e_1))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl972])).
% 0.55/1.03  thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_3])).
% 0.55/1.03  thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_1])).
% 0.55/1.03  thf(zip_derived_cl977, plain,
% 0.55/1.03      (( (product @ e_1 @ e_3 @ e_2) |  (product @ e_1 @ e_3 @ e_1))),
% 0.55/1.03      inference('demod', [status(thm)],
% 0.55/1.03                [zip_derived_cl976, zip_derived_cl2, zip_derived_cl0])).
% 0.55/1.03  thf(zip_derived_cl13, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.03         ( (product @ X0 @ X1 @ X2)
% 0.55/1.03          | ~ (product @ X1 @ X3 @ X2)
% 0.55/1.03          | ~ (product @ X0 @ X3 @ X1))),
% 0.55/1.03      inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.55/1.03  thf(zip_derived_cl981, plain,
% 0.55/1.03      (![X0 : $i]:
% 0.55/1.03         ( (product @ e_1 @ e_3 @ e_1)
% 0.55/1.03          | ~ (product @ X0 @ e_3 @ e_1)
% 0.55/1.03          |  (product @ X0 @ e_1 @ e_2))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl977, zip_derived_cl13])).
% 0.55/1.03  thf(zip_derived_cl1064, plain,
% 0.55/1.03      ((~ (product @ e_2 @ e_2 @ e_3)
% 0.55/1.03        |  (product @ e_2 @ e_1 @ e_2)
% 0.55/1.03        |  (product @ e_1 @ e_3 @ e_1))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl315, zip_derived_cl981])).
% 0.55/1.03  thf(zip_derived_cl461, plain,
% 0.55/1.03      (( (product @ e_3 @ e_1 @ e_2) |  (product @ e_3 @ e_1 @ e_1))),
% 0.55/1.03      inference('demod', [status(thm)],
% 0.55/1.03                [zip_derived_cl460, zip_derived_cl0, zip_derived_cl2])).
% 0.55/1.03  thf(zip_derived_cl29, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_2 @ X1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl12, zip_derived_cl6])).
% 0.55/1.03  thf(zip_derived_cl467, plain,
% 0.55/1.03      (( (product @ e_3 @ e_1 @ e_1) | ~ (product @ e_2 @ e_1 @ e_2))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl461, zip_derived_cl29])).
% 0.55/1.03  thf(zip_derived_cl27, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl12, zip_derived_cl4])).
% 0.55/1.03  thf(zip_derived_cl483, plain,
% 0.55/1.03      ((~ (product @ e_2 @ e_1 @ e_2) | ~ (product @ e_1 @ e_1 @ e_1))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl467, zip_derived_cl27])).
% 0.55/1.03  thf(zip_derived_cl661, plain, ( (product @ e_1 @ e_1 @ e_1)),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl658, zip_derived_cl646])).
% 0.55/1.03  thf(zip_derived_cl662, plain, (~ (product @ e_2 @ e_1 @ e_2)),
% 0.55/1.03      inference('demod', [status(thm)], [zip_derived_cl483, zip_derived_cl661])).
% 0.55/1.03  thf(zip_derived_cl1067, plain,
% 0.55/1.03      ((~ (product @ e_2 @ e_2 @ e_3) |  (product @ e_1 @ e_3 @ e_1))),
% 0.55/1.03      inference('demod', [status(thm)], [zip_derived_cl1064, zip_derived_cl662])).
% 0.55/1.03  thf(zip_derived_cl315, plain,
% 0.55/1.03      (( (product @ e_2 @ e_3 @ e_1) | ~ (product @ e_2 @ e_2 @ e_3))),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl248, zip_derived_cl17])).
% 0.55/1.03  thf(zip_derived_cl26, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ e_2 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl12, zip_derived_cl3])).
% 0.55/1.03  thf(zip_derived_cl320, plain,
% 0.55/1.03      ((~ (product @ e_2 @ e_2 @ e_3) | ~ (product @ e_1 @ e_3 @ e_1))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl315, zip_derived_cl26])).
% 0.55/1.03  thf(zip_derived_cl1068, plain, (~ (product @ e_2 @ e_2 @ e_3)),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl1067, zip_derived_cl320])).
% 0.55/1.03  thf(zip_derived_cl1070, plain,
% 0.55/1.03      (( (product @ e_2 @ e_2 @ e_2)
% 0.55/1.03        |  (product @ e_2 @ e_2 @ e_1)
% 0.55/1.03        | ~ (group_element @ e_2)
% 0.55/1.03        | ~ (group_element @ e_2))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl1068])).
% 0.55/1.03  thf(zip_derived_cl27, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl12, zip_derived_cl4])).
% 0.55/1.03  thf(zip_derived_cl722, plain,
% 0.55/1.03      (( (product @ e_3 @ e_2 @ e_1) | ~ (product @ e_3 @ e_1 @ e_2))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl717, zip_derived_cl20])).
% 0.55/1.03  thf(zip_derived_cl29, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_2 @ X1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl12, zip_derived_cl6])).
% 0.55/1.03  thf(zip_derived_cl739, plain,
% 0.55/1.03      ((~ (product @ e_3 @ e_1 @ e_2) | ~ (product @ e_2 @ e_2 @ e_1))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl722, zip_derived_cl29])).
% 0.55/1.03  thf(zip_derived_cl461, plain,
% 0.55/1.03      (( (product @ e_3 @ e_1 @ e_2) |  (product @ e_3 @ e_1 @ e_1))),
% 0.55/1.03      inference('demod', [status(thm)],
% 0.55/1.03                [zip_derived_cl460, zip_derived_cl0, zip_derived_cl2])).
% 0.55/1.03  thf(zip_derived_cl757, plain,
% 0.55/1.03      ((~ (product @ e_2 @ e_2 @ e_1) |  (product @ e_3 @ e_1 @ e_1))),
% 0.55/1.03      inference('sup+', [status(thm)], [zip_derived_cl739, zip_derived_cl461])).
% 0.55/1.03  thf(zip_derived_cl842, plain,
% 0.55/1.03      ((~ (product @ e_1 @ e_1 @ e_1) | ~ (product @ e_2 @ e_2 @ e_1))),
% 0.55/1.03      inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl757])).
% 0.55/1.03  thf(zip_derived_cl661, plain, ( (product @ e_1 @ e_1 @ e_1)),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl658, zip_derived_cl646])).
% 0.55/1.03  thf(zip_derived_cl845, plain, (~ (product @ e_2 @ e_2 @ e_1)),
% 0.55/1.03      inference('demod', [status(thm)], [zip_derived_cl842, zip_derived_cl661])).
% 0.55/1.03  thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_2])).
% 0.55/1.03  thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_2])).
% 0.55/1.03  thf(zip_derived_cl1071, plain, ( (product @ e_2 @ e_2 @ e_2)),
% 0.55/1.03      inference('demod', [status(thm)],
% 0.55/1.03                [zip_derived_cl1070, zip_derived_cl845, zip_derived_cl1, 
% 0.55/1.03                 zip_derived_cl1])).
% 0.55/1.03  thf(zip_derived_cl1073, plain, ( (product @ e_3 @ e_2 @ e_1)),
% 0.55/1.03      inference('demod', [status(thm)], [zip_derived_cl725, zip_derived_cl1071])).
% 0.55/1.03  thf(zip_derived_cl9, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (group_element @ X0)
% 0.55/1.03          | ~ (group_element @ X1)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_1)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_2)
% 0.55/1.03          |  (product @ X0 @ X1 @ e_3))),
% 0.55/1.03      inference('cnf', [status(esa)], [product_total_function1])).
% 0.55/1.03  thf(zip_derived_cl13, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.03         ( (product @ X0 @ X1 @ X2)
% 0.55/1.03          | ~ (product @ X1 @ X3 @ X2)
% 0.55/1.03          | ~ (product @ X0 @ X3 @ X1))),
% 0.55/1.03      inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.55/1.03  thf(zip_derived_cl34, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.03         ( (product @ X1 @ X0 @ e_2)
% 0.55/1.03          |  (product @ X1 @ X0 @ e_1)
% 0.55/1.03          | ~ (group_element @ X0)
% 0.55/1.03          | ~ (group_element @ X1)
% 0.55/1.03          | ~ (product @ X2 @ X0 @ X1)
% 0.55/1.03          |  (product @ X2 @ X1 @ e_3))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl13])).
% 0.55/1.03  thf(zip_derived_cl1095, plain,
% 0.55/1.03      (( (product @ e_3 @ e_1 @ e_3)
% 0.55/1.03        | ~ (group_element @ e_1)
% 0.55/1.03        | ~ (group_element @ e_2)
% 0.55/1.03        |  (product @ e_1 @ e_2 @ e_1)
% 0.55/1.03        |  (product @ e_1 @ e_2 @ e_2))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl1073, zip_derived_cl34])).
% 0.55/1.03  thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_1])).
% 0.55/1.03  thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.55/1.03      inference('cnf', [status(esa)], [element_2])).
% 0.55/1.03  thf(zip_derived_cl27, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl12, zip_derived_cl4])).
% 0.55/1.03  thf(zip_derived_cl722, plain,
% 0.55/1.03      (( (product @ e_3 @ e_2 @ e_1) | ~ (product @ e_3 @ e_1 @ e_2))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl717, zip_derived_cl20])).
% 0.55/1.03  thf(zip_derived_cl27, plain,
% 0.55/1.03      (![X0 : $i, X1 : $i]:
% 0.55/1.03         (~ (product @ e_3 @ X1 @ X0) | ~ (product @ e_1 @ X1 @ X0))),
% 0.55/1.03      inference('dp-resolution', [status(thm)],
% 0.55/1.03                [zip_derived_cl12, zip_derived_cl4])).
% 0.55/1.03  thf(zip_derived_cl738, plain,
% 0.55/1.03      ((~ (product @ e_3 @ e_1 @ e_2) | ~ (product @ e_1 @ e_2 @ e_1))),
% 0.55/1.03      inference('sup-', [status(thm)], [zip_derived_cl722, zip_derived_cl27])).
% 0.55/1.03  thf(zip_derived_cl461, plain,
% 0.55/1.03      (( (product @ e_3 @ e_1 @ e_2) |  (product @ e_3 @ e_1 @ e_1))),
% 0.55/1.03      inference('demod', [status(thm)],
% 0.55/1.03                [zip_derived_cl460, zip_derived_cl0, zip_derived_cl2])).
% 0.55/1.03  thf(zip_derived_cl747, plain,
% 0.55/1.03      ((~ (product @ e_1 @ e_2 @ e_1) |  (product @ e_3 @ e_1 @ e_1))),
% 0.55/1.03      inference('sup+', [status(thm)], [zip_derived_cl738, zip_derived_cl461])).
% 0.55/1.03  thf(zip_derived_cl823, plain,
% 0.55/1.03      ((~ (product @ e_1 @ e_1 @ e_1) | ~ (product @ e_1 @ e_2 @ e_1))),
% 0.55/1.03      inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl747])).
% 0.55/1.03  thf(zip_derived_cl661, plain, ( (product @ e_1 @ e_1 @ e_1)),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl658, zip_derived_cl646])).
% 0.55/1.03  thf(zip_derived_cl826, plain, (~ (product @ e_1 @ e_2 @ e_1)),
% 0.55/1.03      inference('demod', [status(thm)], [zip_derived_cl823, zip_derived_cl661])).
% 0.55/1.03  thf(zip_derived_cl610, plain, (~ (product @ e_1 @ e_2 @ e_2)),
% 0.55/1.03      inference('clc', [status(thm)], [zip_derived_cl605, zip_derived_cl192])).
% 0.55/1.03  thf(zip_derived_cl1103, plain, ( (product @ e_3 @ e_1 @ e_3)),
% 0.55/1.03      inference('demod', [status(thm)],
% 0.55/1.03                [zip_derived_cl1095, zip_derived_cl0, zip_derived_cl1, 
% 0.55/1.03                 zip_derived_cl826, zip_derived_cl610])).
% 0.55/1.03  thf(zip_derived_cl1175, plain, ($false),
% 0.55/1.03      inference('demod', [status(thm)], [zip_derived_cl458, zip_derived_cl1103])).
% 0.55/1.03  
% 0.55/1.03  % SZS output end Refutation
% 0.55/1.03  
% 0.55/1.03  
% 0.55/1.03  % Terminating...
% 1.86/1.13  % Runner terminated.
% 1.86/1.15  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------