TSTP Solution File: GRP125-2.005 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP125-2.005 : TPTP v8.1.2. Released v1.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.BBdmudVubA true
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:50:07 EDT 2023
% Result : Unsatisfiable 4.10s 1.14s
% Output : Refutation 4.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP125-2.005 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.BBdmudVubA true
% 0.17/0.35 % Computer : n008.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Mon Aug 28 21:30:32 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.17/0.35 % Running portfolio for 300 s
% 0.17/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.35 % Number of cores: 8
% 0.17/0.35 % Python version: Python 3.6.8
% 0.17/0.36 % Running in FO mode
% 0.22/0.61 % Total configuration time : 435
% 0.22/0.61 % Estimated wc time : 1092
% 0.22/0.61 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.65 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.65 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.69 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.70 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.71 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.71 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.71 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 4.10/1.14 % Solved by fo/fo1_av.sh.
% 4.10/1.14 % done 1620 iterations in 0.410s
% 4.10/1.14 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 4.10/1.14 % SZS output start Refutation
% 4.10/1.14 thf(e_5_type, type, e_5: $i).
% 4.10/1.14 thf(e_4_type, type, e_4: $i).
% 4.10/1.14 thf(e_3_type, type, e_3: $i).
% 4.10/1.14 thf(e_2_type, type, e_2: $i).
% 4.10/1.14 thf(e_1_type, type, e_1: $i).
% 4.10/1.14 thf(next_type, type, next: $i > $i > $o).
% 4.10/1.14 thf(product_type, type, product: $i > $i > $i > $o).
% 4.10/1.14 thf(greater_type, type, greater: $i > $i > $o).
% 4.10/1.14 thf(equalish_type, type, equalish: $i > $i > $o).
% 4.10/1.14 thf(group_element_type, type, group_element: $i > $o).
% 4.10/1.14 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 4.10/1.14 thf(zip_derived_cl24, plain, (~ (equalish @ e_2 @ e_1)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 4.10/1.14 thf(element_4, axiom, (group_element @ e_4)).
% 4.10/1.14 thf(zip_derived_cl18, plain, ( (group_element @ e_4)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_4])).
% 4.10/1.14 thf(product_total_function1, axiom,
% 4.10/1.14 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 4.10/1.14 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 4.10/1.14 ( product @ X @ Y @ e_3 ) | ( product @ X @ Y @ e_4 ) |
% 4.10/1.14 ( product @ X @ Y @ e_5 ))).
% 4.10/1.14 thf(zip_derived_cl40, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | ~ (group_element @ X1)
% 4.10/1.14 | (product @ X0 @ X1 @ e_1)
% 4.10/1.14 | (product @ X0 @ X1 @ e_2)
% 4.10/1.14 | (product @ X0 @ X1 @ e_3)
% 4.10/1.14 | (product @ X0 @ X1 @ e_4)
% 4.10/1.14 | (product @ X0 @ X1 @ e_5))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_total_function1])).
% 4.10/1.14 thf(zip_derived_cl57, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_4 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_4 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_4 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_4 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_4 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl40])).
% 4.10/1.14 thf(element_2, axiom, (group_element @ e_2)).
% 4.10/1.14 thf(zip_derived_cl16, plain, ( (group_element @ e_2)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_2])).
% 4.10/1.14 thf(zip_derived_cl158, plain,
% 4.10/1.14 (( (product @ e_4 @ e_2 @ e_5)
% 4.10/1.14 | (product @ e_4 @ e_2 @ e_4)
% 4.10/1.14 | (product @ e_4 @ e_2 @ e_3)
% 4.10/1.14 | (product @ e_4 @ e_2 @ e_2)
% 4.10/1.14 | (product @ e_4 @ e_2 @ e_1))),
% 4.10/1.14 inference('s_sup+', [status(thm)], [zip_derived_cl57, zip_derived_cl16])).
% 4.10/1.14 thf(zip_derived_cl694, plain,
% 4.10/1.14 (( (product @ e_4 @ e_2 @ e_1)) <= (( (product @ e_4 @ e_2 @ e_1)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl158])).
% 4.10/1.14 thf(zip_derived_cl693, plain,
% 4.10/1.14 (( (product @ e_4 @ e_2 @ e_2)) <= (( (product @ e_4 @ e_2 @ e_2)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl158])).
% 4.10/1.14 thf(product_idempotence, axiom, (product @ X @ X @ X)).
% 4.10/1.14 thf(zip_derived_cl44, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 4.10/1.14 inference('cnf', [status(esa)], [product_idempotence])).
% 4.10/1.14 thf(product_left_cancellation, axiom,
% 4.10/1.14 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 4.10/1.14 ( equalish @ W @ Z ))).
% 4.10/1.14 thf(zip_derived_cl43, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X3 @ X1 @ X2)
% 4.10/1.14 | (equalish @ X0 @ X3))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_left_cancellation])).
% 4.10/1.14 thf(zip_derived_cl65, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl43])).
% 4.10/1.14 thf(zip_derived_cl2006, plain,
% 4.10/1.14 (( (equalish @ e_2 @ e_4)) <= (( (product @ e_4 @ e_2 @ e_2)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl693, zip_derived_cl65])).
% 4.10/1.14 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 4.10/1.14 thf(zip_derived_cl26, plain, (~ (equalish @ e_2 @ e_4)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 4.10/1.14 thf('0', plain, (~ ( (product @ e_4 @ e_2 @ e_2))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl2006, zip_derived_cl26])).
% 4.10/1.14 thf(zip_derived_cl16, plain, ( (group_element @ e_2)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_2])).
% 4.10/1.14 thf(element_3, axiom, (group_element @ e_3)).
% 4.10/1.14 thf(zip_derived_cl17, plain, ( (group_element @ e_3)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_3])).
% 4.10/1.14 thf(zip_derived_cl40, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | ~ (group_element @ X1)
% 4.10/1.14 | (product @ X0 @ X1 @ e_1)
% 4.10/1.14 | (product @ X0 @ X1 @ e_2)
% 4.10/1.14 | (product @ X0 @ X1 @ e_3)
% 4.10/1.14 | (product @ X0 @ X1 @ e_4)
% 4.10/1.14 | (product @ X0 @ X1 @ e_5))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_total_function1])).
% 4.10/1.14 thf(zip_derived_cl56, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl142, plain,
% 4.10/1.14 (( (product @ e_3 @ e_2 @ e_1)
% 4.10/1.14 | (product @ e_3 @ e_2 @ e_2)
% 4.10/1.14 | (product @ e_3 @ e_2 @ e_3)
% 4.10/1.14 | (product @ e_3 @ e_2 @ e_4)
% 4.10/1.14 | (product @ e_3 @ e_2 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl56])).
% 4.10/1.14 thf(zip_derived_cl601, plain,
% 4.10/1.14 (( (product @ e_3 @ e_2 @ e_4)) <= (( (product @ e_3 @ e_2 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl142])).
% 4.10/1.14 thf(element_1, axiom, (group_element @ e_1)).
% 4.10/1.14 thf(zip_derived_cl15, plain, ( (group_element @ e_1)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_1])).
% 4.10/1.14 thf(zip_derived_cl56, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl141, plain,
% 4.10/1.14 (( (product @ e_3 @ e_1 @ e_1)
% 4.10/1.14 | (product @ e_3 @ e_1 @ e_2)
% 4.10/1.14 | (product @ e_3 @ e_1 @ e_3)
% 4.10/1.14 | (product @ e_3 @ e_1 @ e_4)
% 4.10/1.14 | (product @ e_3 @ e_1 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl56])).
% 4.10/1.14 thf(zip_derived_cl568, plain,
% 4.10/1.14 (( (product @ e_3 @ e_1 @ e_4)) <= (( (product @ e_3 @ e_1 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl141])).
% 4.10/1.14 thf(product_right_cancellation, axiom,
% 4.10/1.14 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 4.10/1.14 ( equalish @ W @ Z ))).
% 4.10/1.14 thf(zip_derived_cl42, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.14 | (equalish @ X1 @ X3))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.14 thf(zip_derived_cl573, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (product @ e_3 @ X0 @ e_4) | (equalish @ e_1 @ X0)))
% 4.10/1.14 <= (( (product @ e_3 @ e_1 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl568, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl1063, plain,
% 4.10/1.14 (( (equalish @ e_1 @ e_2))
% 4.10/1.14 <= (( (product @ e_3 @ e_1 @ e_4)) & ( (product @ e_3 @ e_2 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl601, zip_derived_cl573])).
% 4.10/1.14 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 4.10/1.14 thf(zip_derived_cl20, plain, (~ (equalish @ e_1 @ e_2)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 4.10/1.14 thf('1', plain,
% 4.10/1.14 (~ ( (product @ e_3 @ e_2 @ e_4)) | ~ ( (product @ e_3 @ e_1 @ e_4))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1063, zip_derived_cl20])).
% 4.10/1.14 thf(zip_derived_cl15, plain, ( (group_element @ e_1)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_1])).
% 4.10/1.14 thf(zip_derived_cl40, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | ~ (group_element @ X1)
% 4.10/1.14 | (product @ X0 @ X1 @ e_1)
% 4.10/1.14 | (product @ X0 @ X1 @ e_2)
% 4.10/1.14 | (product @ X0 @ X1 @ e_3)
% 4.10/1.14 | (product @ X0 @ X1 @ e_4)
% 4.10/1.14 | (product @ X0 @ X1 @ e_5))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_total_function1])).
% 4.10/1.14 thf(zip_derived_cl54, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl17, plain, ( (group_element @ e_3)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_3])).
% 4.10/1.14 thf(zip_derived_cl88, plain,
% 4.10/1.14 (( (product @ e_1 @ e_3 @ e_5)
% 4.10/1.14 | (product @ e_1 @ e_3 @ e_4)
% 4.10/1.14 | (product @ e_1 @ e_3 @ e_3)
% 4.10/1.14 | (product @ e_1 @ e_3 @ e_2)
% 4.10/1.14 | (product @ e_1 @ e_3 @ e_1))),
% 4.10/1.14 inference('s_sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl17])).
% 4.10/1.14 thf(zip_derived_cl202, plain,
% 4.10/1.14 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl88])).
% 4.10/1.14 thf(zip_derived_cl44, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 4.10/1.14 inference('cnf', [status(esa)], [product_idempotence])).
% 4.10/1.14 thf(zip_derived_cl42, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.14 | (equalish @ X1 @ X3))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.14 thf(zip_derived_cl60, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl273, plain,
% 4.10/1.14 (( (equalish @ e_1 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl202, zip_derived_cl60])).
% 4.10/1.14 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 4.10/1.14 thf(zip_derived_cl21, plain, (~ (equalish @ e_1 @ e_3)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 4.10/1.14 thf('2', plain, (~ ( (product @ e_1 @ e_3 @ e_1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl273, zip_derived_cl21])).
% 4.10/1.14 thf(element_5, axiom, (group_element @ e_5)).
% 4.10/1.14 thf(zip_derived_cl19, plain, ( (group_element @ e_5)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_5])).
% 4.10/1.14 thf(zip_derived_cl16, plain, ( (group_element @ e_2)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_2])).
% 4.10/1.14 thf(zip_derived_cl40, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | ~ (group_element @ X1)
% 4.10/1.14 | (product @ X0 @ X1 @ e_1)
% 4.10/1.14 | (product @ X0 @ X1 @ e_2)
% 4.10/1.14 | (product @ X0 @ X1 @ e_3)
% 4.10/1.14 | (product @ X0 @ X1 @ e_4)
% 4.10/1.14 | (product @ X0 @ X1 @ e_5))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_total_function1])).
% 4.10/1.14 thf(zip_derived_cl55, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl107, plain,
% 4.10/1.14 (( (product @ e_2 @ e_5 @ e_1)
% 4.10/1.14 | (product @ e_2 @ e_5 @ e_2)
% 4.10/1.14 | (product @ e_2 @ e_5 @ e_3)
% 4.10/1.14 | (product @ e_2 @ e_5 @ e_4)
% 4.10/1.14 | (product @ e_2 @ e_5 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl55])).
% 4.10/1.14 thf(zip_derived_cl462, plain,
% 4.10/1.14 (( (product @ e_2 @ e_5 @ e_4)) <= (( (product @ e_2 @ e_5 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl107])).
% 4.10/1.14 thf(zip_derived_cl19, plain, ( (group_element @ e_5)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_5])).
% 4.10/1.14 thf(zip_derived_cl54, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl95, plain,
% 4.10/1.14 (( (product @ e_1 @ e_5 @ e_1)
% 4.10/1.14 | (product @ e_1 @ e_5 @ e_2)
% 4.10/1.14 | (product @ e_1 @ e_5 @ e_3)
% 4.10/1.14 | (product @ e_1 @ e_5 @ e_4)
% 4.10/1.14 | (product @ e_1 @ e_5 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl54])).
% 4.10/1.14 thf(zip_derived_cl307, plain,
% 4.10/1.14 (( (product @ e_1 @ e_5 @ e_4)) <= (( (product @ e_1 @ e_5 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl95])).
% 4.10/1.14 thf(zip_derived_cl43, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X3 @ X1 @ X2)
% 4.10/1.14 | (equalish @ X0 @ X3))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_left_cancellation])).
% 4.10/1.14 thf(zip_derived_cl313, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (product @ X0 @ e_5 @ e_4) | (equalish @ e_1 @ X0)))
% 4.10/1.14 <= (( (product @ e_1 @ e_5 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl307, zip_derived_cl43])).
% 4.10/1.14 thf(zip_derived_cl518, plain,
% 4.10/1.14 (( (equalish @ e_1 @ e_2))
% 4.10/1.14 <= (( (product @ e_1 @ e_5 @ e_4)) & ( (product @ e_2 @ e_5 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl462, zip_derived_cl313])).
% 4.10/1.14 thf(zip_derived_cl20, plain, (~ (equalish @ e_1 @ e_2)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 4.10/1.14 thf('3', plain,
% 4.10/1.14 (~ ( (product @ e_1 @ e_5 @ e_4)) | ~ ( (product @ e_2 @ e_5 @ e_4))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl518, zip_derived_cl20])).
% 4.10/1.14 thf(zip_derived_cl307, plain,
% 4.10/1.14 (( (product @ e_1 @ e_5 @ e_4)) <= (( (product @ e_1 @ e_5 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl95])).
% 4.10/1.14 thf(zip_derived_cl199, plain,
% 4.10/1.14 (( (product @ e_1 @ e_3 @ e_4)) <= (( (product @ e_1 @ e_3 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl88])).
% 4.10/1.14 thf(zip_derived_cl42, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.14 | (equalish @ X1 @ X3))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.14 thf(zip_derived_cl245, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_4) | (equalish @ e_3 @ X0)))
% 4.10/1.14 <= (( (product @ e_1 @ e_3 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl199, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl378, plain,
% 4.10/1.14 (( (equalish @ e_3 @ e_5))
% 4.10/1.14 <= (( (product @ e_1 @ e_3 @ e_4)) & ( (product @ e_1 @ e_5 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl307, zip_derived_cl245])).
% 4.10/1.14 thf(e_3_is_not_e_5, axiom, (~( equalish @ e_3 @ e_5 ))).
% 4.10/1.14 thf(zip_derived_cl31, plain, (~ (equalish @ e_3 @ e_5)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_3_is_not_e_5])).
% 4.10/1.14 thf('4', plain,
% 4.10/1.14 (~ ( (product @ e_1 @ e_3 @ e_4)) | ~ ( (product @ e_1 @ e_5 @ e_4))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl378, zip_derived_cl31])).
% 4.10/1.14 thf(zip_derived_cl307, plain,
% 4.10/1.14 (( (product @ e_1 @ e_5 @ e_4)) <= (( (product @ e_1 @ e_5 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl95])).
% 4.10/1.14 thf(zip_derived_cl54, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl16, plain, ( (group_element @ e_2)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_2])).
% 4.10/1.14 thf(zip_derived_cl87, plain,
% 4.10/1.14 (( (product @ e_1 @ e_2 @ e_5)
% 4.10/1.14 | (product @ e_1 @ e_2 @ e_4)
% 4.10/1.14 | (product @ e_1 @ e_2 @ e_3)
% 4.10/1.14 | (product @ e_1 @ e_2 @ e_2)
% 4.10/1.14 | (product @ e_1 @ e_2 @ e_1))),
% 4.10/1.14 inference('s_sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl16])).
% 4.10/1.14 thf(zip_derived_cl115, plain,
% 4.10/1.14 (( (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl87])).
% 4.10/1.14 thf(zip_derived_cl42, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.14 | (equalish @ X1 @ X3))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.14 thf(zip_derived_cl124, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_4) | (equalish @ e_2 @ X0)))
% 4.10/1.14 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl115, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl315, plain,
% 4.10/1.14 (( (equalish @ e_2 @ e_5))
% 4.10/1.14 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_1 @ e_5 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl307, zip_derived_cl124])).
% 4.10/1.14 thf(e_2_is_not_e_5, axiom, (~( equalish @ e_2 @ e_5 ))).
% 4.10/1.14 thf(zip_derived_cl27, plain, (~ (equalish @ e_2 @ e_5)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_2_is_not_e_5])).
% 4.10/1.14 thf('5', plain,
% 4.10/1.14 (~ ( (product @ e_1 @ e_5 @ e_4)) | ~ ( (product @ e_1 @ e_2 @ e_4))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl315, zip_derived_cl27])).
% 4.10/1.14 thf(zip_derived_cl568, plain,
% 4.10/1.14 (( (product @ e_3 @ e_1 @ e_4)) <= (( (product @ e_3 @ e_1 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl141])).
% 4.10/1.14 thf(zip_derived_cl201, plain,
% 4.10/1.14 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl88])).
% 4.10/1.14 thf(qg3, conjecture,
% 4.10/1.14 (~( ( product @ Z1 @ Z2 @ X ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 4.10/1.14 ( ~( product @ X @ Y @ Z1 ) ) ))).
% 4.10/1.14 thf(zf_stmt_0, negated_conjecture,
% 4.10/1.14 (( product @ Z1 @ Z2 @ X ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 4.10/1.14 ( ~( product @ X @ Y @ Z1 ) )),
% 4.10/1.14 inference('cnf.neg', [status(esa)], [qg3])).
% 4.10/1.14 thf(zip_derived_cl45, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 ( (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X3 @ X2 @ X1)
% 4.10/1.14 | ~ (product @ X2 @ X3 @ X0))),
% 4.10/1.14 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.10/1.14 thf(zip_derived_cl268, plain,
% 4.10/1.14 ((![X0 : $i]:
% 4.10/1.14 ( (product @ X0 @ e_2 @ e_3) | ~ (product @ e_3 @ e_1 @ X0)))
% 4.10/1.14 <= (( (product @ e_1 @ e_3 @ e_2)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl201, zip_derived_cl45])).
% 4.10/1.14 thf(zip_derived_cl579, plain,
% 4.10/1.14 (( (product @ e_4 @ e_2 @ e_3))
% 4.10/1.14 <= (( (product @ e_1 @ e_3 @ e_2)) & ( (product @ e_3 @ e_1 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl568, zip_derived_cl268])).
% 4.10/1.14 thf(zip_derived_cl55, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl18, plain, ( (group_element @ e_4)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_4])).
% 4.10/1.14 thf(zip_derived_cl101, plain,
% 4.10/1.14 (( (product @ e_2 @ e_4 @ e_5)
% 4.10/1.14 | (product @ e_2 @ e_4 @ e_4)
% 4.10/1.14 | (product @ e_2 @ e_4 @ e_3)
% 4.10/1.14 | (product @ e_2 @ e_4 @ e_2)
% 4.10/1.14 | (product @ e_2 @ e_4 @ e_1))),
% 4.10/1.14 inference('s_sup+', [status(thm)], [zip_derived_cl55, zip_derived_cl18])).
% 4.10/1.14 thf(zip_derived_cl364, plain,
% 4.10/1.14 (( (product @ e_2 @ e_4 @ e_5)) <= (( (product @ e_2 @ e_4 @ e_5)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl101])).
% 4.10/1.14 thf(zip_derived_cl45, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 ( (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X3 @ X2 @ X1)
% 4.10/1.14 | ~ (product @ X2 @ X3 @ X0))),
% 4.10/1.14 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.10/1.14 thf(zip_derived_cl372, plain,
% 4.10/1.14 ((![X0 : $i]:
% 4.10/1.14 ( (product @ X0 @ e_5 @ e_4) | ~ (product @ e_4 @ e_2 @ X0)))
% 4.10/1.14 <= (( (product @ e_2 @ e_4 @ e_5)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl364, zip_derived_cl45])).
% 4.10/1.14 thf(zip_derived_cl599, plain,
% 4.10/1.14 (( (product @ e_3 @ e_5 @ e_4))
% 4.10/1.14 <= (( (product @ e_1 @ e_3 @ e_2)) &
% 4.10/1.14 ( (product @ e_2 @ e_4 @ e_5)) &
% 4.10/1.14 ( (product @ e_3 @ e_1 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl579, zip_derived_cl372])).
% 4.10/1.14 thf(zip_derived_cl313, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (product @ X0 @ e_5 @ e_4) | (equalish @ e_1 @ X0)))
% 4.10/1.14 <= (( (product @ e_1 @ e_5 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl307, zip_derived_cl43])).
% 4.10/1.14 thf(zip_derived_cl623, plain,
% 4.10/1.14 (( (equalish @ e_1 @ e_3))
% 4.10/1.14 <= (( (product @ e_1 @ e_3 @ e_2)) &
% 4.10/1.14 ( (product @ e_1 @ e_5 @ e_4)) &
% 4.10/1.14 ( (product @ e_2 @ e_4 @ e_5)) &
% 4.10/1.14 ( (product @ e_3 @ e_1 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl599, zip_derived_cl313])).
% 4.10/1.14 thf(zip_derived_cl21, plain, (~ (equalish @ e_1 @ e_3)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 4.10/1.14 thf('6', plain,
% 4.10/1.14 (~ ( (product @ e_1 @ e_5 @ e_4)) | ~ ( (product @ e_2 @ e_4 @ e_5)) |
% 4.10/1.14 ~ ( (product @ e_1 @ e_3 @ e_2)) | ~ ( (product @ e_3 @ e_1 @ e_4))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl623, zip_derived_cl21])).
% 4.10/1.14 thf(zip_derived_cl56, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl16, plain, ( (group_element @ e_2)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_2])).
% 4.10/1.14 thf(zip_derived_cl137, plain,
% 4.10/1.14 (( (product @ e_3 @ e_2 @ e_5)
% 4.10/1.14 | (product @ e_3 @ e_2 @ e_4)
% 4.10/1.14 | (product @ e_3 @ e_2 @ e_3)
% 4.10/1.14 | (product @ e_3 @ e_2 @ e_2)
% 4.10/1.14 | (product @ e_3 @ e_2 @ e_1))),
% 4.10/1.14 inference('s_sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl16])).
% 4.10/1.14 thf(zip_derived_cl505, plain,
% 4.10/1.14 (( (product @ e_3 @ e_2 @ e_3)) <= (( (product @ e_3 @ e_2 @ e_3)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl137])).
% 4.10/1.14 thf(zip_derived_cl60, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl1560, plain,
% 4.10/1.14 (( (equalish @ e_3 @ e_2)) <= (( (product @ e_3 @ e_2 @ e_3)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl505, zip_derived_cl60])).
% 4.10/1.14 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 4.10/1.14 thf(zip_derived_cl29, plain, (~ (equalish @ e_3 @ e_2)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 4.10/1.14 thf('7', plain, (~ ( (product @ e_3 @ e_2 @ e_3))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1560, zip_derived_cl29])).
% 4.10/1.14 thf(zip_derived_cl506, plain,
% 4.10/1.14 (( (product @ e_3 @ e_2 @ e_2)) <= (( (product @ e_3 @ e_2 @ e_2)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl137])).
% 4.10/1.14 thf(zip_derived_cl65, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl43])).
% 4.10/1.14 thf(zip_derived_cl1583, plain,
% 4.10/1.14 (( (equalish @ e_2 @ e_3)) <= (( (product @ e_3 @ e_2 @ e_2)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl506, zip_derived_cl65])).
% 4.10/1.14 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 4.10/1.14 thf(zip_derived_cl25, plain, (~ (equalish @ e_2 @ e_3)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 4.10/1.14 thf('8', plain, (~ ( (product @ e_3 @ e_2 @ e_2))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1583, zip_derived_cl25])).
% 4.10/1.14 thf(zip_derived_cl503, plain,
% 4.10/1.14 (( (product @ e_3 @ e_2 @ e_5)) <= (( (product @ e_3 @ e_2 @ e_5)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl137])).
% 4.10/1.14 thf(zip_derived_cl55, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl17, plain, ( (group_element @ e_3)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_3])).
% 4.10/1.14 thf(zip_derived_cl100, plain,
% 4.10/1.14 (( (product @ e_2 @ e_3 @ e_5)
% 4.10/1.14 | (product @ e_2 @ e_3 @ e_4)
% 4.10/1.14 | (product @ e_2 @ e_3 @ e_3)
% 4.10/1.14 | (product @ e_2 @ e_3 @ e_2)
% 4.10/1.14 | (product @ e_2 @ e_3 @ e_1))),
% 4.10/1.14 inference('s_sup+', [status(thm)], [zip_derived_cl55, zip_derived_cl17])).
% 4.10/1.14 thf(zip_derived_cl344, plain,
% 4.10/1.14 (( (product @ e_2 @ e_3 @ e_5)) <= (( (product @ e_2 @ e_3 @ e_5)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl100])).
% 4.10/1.14 thf(zip_derived_cl45, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 ( (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X3 @ X2 @ X1)
% 4.10/1.14 | ~ (product @ X2 @ X3 @ X0))),
% 4.10/1.14 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.10/1.14 thf(zip_derived_cl352, plain,
% 4.10/1.14 ((![X0 : $i]:
% 4.10/1.14 ( (product @ X0 @ e_5 @ e_3) | ~ (product @ e_3 @ e_2 @ X0)))
% 4.10/1.14 <= (( (product @ e_2 @ e_3 @ e_5)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl344, zip_derived_cl45])).
% 4.10/1.14 thf(zip_derived_cl513, plain,
% 4.10/1.14 (( (product @ e_5 @ e_5 @ e_3))
% 4.10/1.14 <= (( (product @ e_2 @ e_3 @ e_5)) & ( (product @ e_3 @ e_2 @ e_5)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl503, zip_derived_cl352])).
% 4.10/1.14 thf(zip_derived_cl44, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 4.10/1.14 inference('cnf', [status(esa)], [product_idempotence])).
% 4.10/1.14 thf(product_total_function2, axiom,
% 4.10/1.14 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 4.10/1.14 ( equalish @ W @ Z ))).
% 4.10/1.14 thf(zip_derived_cl41, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X0 @ X1 @ X3)
% 4.10/1.14 | (equalish @ X2 @ X3))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_total_function2])).
% 4.10/1.14 thf(zip_derived_cl49, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl41])).
% 4.10/1.14 thf(zip_derived_cl523, plain,
% 4.10/1.14 (( (equalish @ e_5 @ e_3))
% 4.10/1.14 <= (( (product @ e_2 @ e_3 @ e_5)) & ( (product @ e_3 @ e_2 @ e_5)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl513, zip_derived_cl49])).
% 4.10/1.14 thf(e_5_is_not_e_3, axiom, (~( equalish @ e_5 @ e_3 ))).
% 4.10/1.14 thf(zip_derived_cl38, plain, (~ (equalish @ e_5 @ e_3)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_5_is_not_e_3])).
% 4.10/1.14 thf('9', plain,
% 4.10/1.14 (~ ( (product @ e_2 @ e_3 @ e_5)) | ~ ( (product @ e_3 @ e_2 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl523, zip_derived_cl38])).
% 4.10/1.14 thf('10', plain,
% 4.10/1.14 (( (product @ e_2 @ e_3 @ e_1)) | ( (product @ e_2 @ e_3 @ e_4)) |
% 4.10/1.14 ( (product @ e_2 @ e_3 @ e_3)) | ( (product @ e_2 @ e_3 @ e_2)) |
% 4.10/1.14 ( (product @ e_2 @ e_3 @ e_5))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl100])).
% 4.10/1.14 thf(zip_derived_cl346, plain,
% 4.10/1.14 (( (product @ e_2 @ e_3 @ e_3)) <= (( (product @ e_2 @ e_3 @ e_3)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl100])).
% 4.10/1.14 thf(zip_derived_cl65, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl43])).
% 4.10/1.14 thf(zip_derived_cl1223, plain,
% 4.10/1.14 (( (equalish @ e_3 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_3)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl346, zip_derived_cl65])).
% 4.10/1.14 thf(zip_derived_cl29, plain, (~ (equalish @ e_3 @ e_2)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 4.10/1.14 thf('11', plain, (~ ( (product @ e_2 @ e_3 @ e_3))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1223, zip_derived_cl29])).
% 4.10/1.14 thf(zip_derived_cl347, plain,
% 4.10/1.14 (( (product @ e_2 @ e_3 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl100])).
% 4.10/1.14 thf(zip_derived_cl60, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl1238, plain,
% 4.10/1.14 (( (equalish @ e_2 @ e_3)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl347, zip_derived_cl60])).
% 4.10/1.14 thf(zip_derived_cl25, plain, (~ (equalish @ e_2 @ e_3)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 4.10/1.14 thf('12', plain, (~ ( (product @ e_2 @ e_3 @ e_2))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1238, zip_derived_cl25])).
% 4.10/1.14 thf(zip_derived_cl56, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl19, plain, ( (group_element @ e_5)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_5])).
% 4.10/1.14 thf(zip_derived_cl140, plain,
% 4.10/1.14 (( (product @ e_3 @ e_5 @ e_5)
% 4.10/1.14 | (product @ e_3 @ e_5 @ e_4)
% 4.10/1.14 | (product @ e_3 @ e_5 @ e_3)
% 4.10/1.14 | (product @ e_3 @ e_5 @ e_2)
% 4.10/1.14 | (product @ e_3 @ e_5 @ e_1))),
% 4.10/1.14 inference('s_sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl19])).
% 4.10/1.14 thf(zip_derived_cl547, plain,
% 4.10/1.14 (( (product @ e_3 @ e_5 @ e_5)) <= (( (product @ e_3 @ e_5 @ e_5)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl140])).
% 4.10/1.14 thf(zip_derived_cl65, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl43])).
% 4.10/1.14 thf(zip_derived_cl556, plain,
% 4.10/1.14 (( (equalish @ e_5 @ e_3)) <= (( (product @ e_3 @ e_5 @ e_5)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl547, zip_derived_cl65])).
% 4.10/1.14 thf(zip_derived_cl38, plain, (~ (equalish @ e_5 @ e_3)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_5_is_not_e_3])).
% 4.10/1.14 thf('13', plain, (~ ( (product @ e_3 @ e_5 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl556, zip_derived_cl38])).
% 4.10/1.14 thf(zip_derived_cl549, plain,
% 4.10/1.14 (( (product @ e_3 @ e_5 @ e_3)) <= (( (product @ e_3 @ e_5 @ e_3)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl140])).
% 4.10/1.14 thf(zip_derived_cl60, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl1729, plain,
% 4.10/1.14 (( (equalish @ e_3 @ e_5)) <= (( (product @ e_3 @ e_5 @ e_3)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl549, zip_derived_cl60])).
% 4.10/1.14 thf(zip_derived_cl31, plain, (~ (equalish @ e_3 @ e_5)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_3_is_not_e_5])).
% 4.10/1.14 thf('14', plain, (~ ( (product @ e_3 @ e_5 @ e_3))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1729, zip_derived_cl31])).
% 4.10/1.14 thf(zip_derived_cl462, plain,
% 4.10/1.14 (( (product @ e_2 @ e_5 @ e_4)) <= (( (product @ e_2 @ e_5 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl107])).
% 4.10/1.14 thf(zip_derived_cl17, plain, ( (group_element @ e_3)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_3])).
% 4.10/1.14 thf(zip_derived_cl55, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl105, plain,
% 4.10/1.14 (( (product @ e_2 @ e_3 @ e_1)
% 4.10/1.14 | (product @ e_2 @ e_3 @ e_2)
% 4.10/1.14 | (product @ e_2 @ e_3 @ e_3)
% 4.10/1.14 | (product @ e_2 @ e_3 @ e_4)
% 4.10/1.14 | (product @ e_2 @ e_3 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl55])).
% 4.10/1.14 thf(zip_derived_cl427, plain,
% 4.10/1.14 (( (product @ e_2 @ e_3 @ e_4)) <= (( (product @ e_2 @ e_3 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl105])).
% 4.10/1.14 thf(zip_derived_cl42, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.14 | (equalish @ X1 @ X3))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.14 thf(zip_derived_cl432, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_4) | (equalish @ e_3 @ X0)))
% 4.10/1.14 <= (( (product @ e_2 @ e_3 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl427, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl748, plain,
% 4.10/1.14 (( (equalish @ e_3 @ e_5))
% 4.10/1.14 <= (( (product @ e_2 @ e_3 @ e_4)) & ( (product @ e_2 @ e_5 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl462, zip_derived_cl432])).
% 4.10/1.14 thf(zip_derived_cl31, plain, (~ (equalish @ e_3 @ e_5)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_3_is_not_e_5])).
% 4.10/1.14 thf('15', plain,
% 4.10/1.14 (~ ( (product @ e_2 @ e_3 @ e_4)) | ~ ( (product @ e_2 @ e_5 @ e_4))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl748, zip_derived_cl31])).
% 4.10/1.14 thf(zip_derived_cl19, plain, ( (group_element @ e_5)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_5])).
% 4.10/1.14 thf(zip_derived_cl56, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_3 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl145, plain,
% 4.10/1.14 (( (product @ e_3 @ e_5 @ e_1)
% 4.10/1.14 | (product @ e_3 @ e_5 @ e_2)
% 4.10/1.14 | (product @ e_3 @ e_5 @ e_3)
% 4.10/1.14 | (product @ e_3 @ e_5 @ e_4)
% 4.10/1.14 | (product @ e_3 @ e_5 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl56])).
% 4.10/1.14 thf(zip_derived_cl647, plain,
% 4.10/1.14 (( (product @ e_3 @ e_5 @ e_4)) <= (( (product @ e_3 @ e_5 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl145])).
% 4.10/1.14 thf(zip_derived_cl573, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (product @ e_3 @ X0 @ e_4) | (equalish @ e_1 @ X0)))
% 4.10/1.14 <= (( (product @ e_3 @ e_1 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl568, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl1064, plain,
% 4.10/1.14 (( (equalish @ e_1 @ e_5))
% 4.10/1.14 <= (( (product @ e_3 @ e_1 @ e_4)) & ( (product @ e_3 @ e_5 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl647, zip_derived_cl573])).
% 4.10/1.14 thf(e_1_is_not_e_5, axiom, (~( equalish @ e_1 @ e_5 ))).
% 4.10/1.14 thf(zip_derived_cl23, plain, (~ (equalish @ e_1 @ e_5)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_1_is_not_e_5])).
% 4.10/1.14 thf('16', plain,
% 4.10/1.14 (~ ( (product @ e_3 @ e_5 @ e_4)) | ~ ( (product @ e_3 @ e_1 @ e_4))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1064, zip_derived_cl23])).
% 4.10/1.14 thf(zip_derived_cl55, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl19, plain, ( (group_element @ e_5)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_5])).
% 4.10/1.14 thf(zip_derived_cl102, plain,
% 4.10/1.14 (( (product @ e_2 @ e_5 @ e_5)
% 4.10/1.14 | (product @ e_2 @ e_5 @ e_4)
% 4.10/1.14 | (product @ e_2 @ e_5 @ e_3)
% 4.10/1.14 | (product @ e_2 @ e_5 @ e_2)
% 4.10/1.14 | (product @ e_2 @ e_5 @ e_1))),
% 4.10/1.14 inference('s_sup+', [status(thm)], [zip_derived_cl55, zip_derived_cl19])).
% 4.10/1.14 thf('17', plain,
% 4.10/1.14 (( (product @ e_2 @ e_5 @ e_4)) | ( (product @ e_2 @ e_5 @ e_1)) |
% 4.10/1.14 ( (product @ e_2 @ e_5 @ e_5)) | ( (product @ e_2 @ e_5 @ e_2)) |
% 4.10/1.14 ( (product @ e_2 @ e_5 @ e_3))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl102])).
% 4.10/1.14 thf(zip_derived_cl380, plain,
% 4.10/1.14 (( (product @ e_2 @ e_5 @ e_5)) <= (( (product @ e_2 @ e_5 @ e_5)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl102])).
% 4.10/1.14 thf(zip_derived_cl65, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl43])).
% 4.10/1.14 thf(zip_derived_cl389, plain,
% 4.10/1.14 (( (equalish @ e_5 @ e_2)) <= (( (product @ e_2 @ e_5 @ e_5)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl380, zip_derived_cl65])).
% 4.10/1.14 thf(e_5_is_not_e_2, axiom, (~( equalish @ e_5 @ e_2 ))).
% 4.10/1.14 thf(zip_derived_cl37, plain, (~ (equalish @ e_5 @ e_2)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_5_is_not_e_2])).
% 4.10/1.14 thf('18', plain, (~ ( (product @ e_2 @ e_5 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl389, zip_derived_cl37])).
% 4.10/1.14 thf(zip_derived_cl383, plain,
% 4.10/1.14 (( (product @ e_2 @ e_5 @ e_2)) <= (( (product @ e_2 @ e_5 @ e_2)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl102])).
% 4.10/1.14 thf(zip_derived_cl60, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl1362, plain,
% 4.10/1.14 (( (equalish @ e_2 @ e_5)) <= (( (product @ e_2 @ e_5 @ e_2)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl383, zip_derived_cl60])).
% 4.10/1.14 thf(zip_derived_cl27, plain, (~ (equalish @ e_2 @ e_5)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_2_is_not_e_5])).
% 4.10/1.14 thf('19', plain, (~ ( (product @ e_2 @ e_5 @ e_2))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1362, zip_derived_cl27])).
% 4.10/1.14 thf(zip_derived_cl15, plain, ( (group_element @ e_1)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_1])).
% 4.10/1.14 thf(zip_derived_cl55, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl103, plain,
% 4.10/1.14 (( (product @ e_2 @ e_1 @ e_1)
% 4.10/1.14 | (product @ e_2 @ e_1 @ e_2)
% 4.10/1.14 | (product @ e_2 @ e_1 @ e_3)
% 4.10/1.14 | (product @ e_2 @ e_1 @ e_4)
% 4.10/1.14 | (product @ e_2 @ e_1 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl55])).
% 4.10/1.14 thf(zip_derived_cl403, plain,
% 4.10/1.14 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl103])).
% 4.10/1.14 thf(zip_derived_cl55, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl15, plain, ( (group_element @ e_1)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_1])).
% 4.10/1.14 thf(zip_derived_cl98, plain,
% 4.10/1.14 (( (product @ e_2 @ e_1 @ e_5)
% 4.10/1.14 | (product @ e_2 @ e_1 @ e_4)
% 4.10/1.14 | (product @ e_2 @ e_1 @ e_3)
% 4.10/1.14 | (product @ e_2 @ e_1 @ e_2)
% 4.10/1.14 | (product @ e_2 @ e_1 @ e_1))),
% 4.10/1.14 inference('s_sup+', [status(thm)], [zip_derived_cl55, zip_derived_cl15])).
% 4.10/1.14 thf(zip_derived_cl324, plain,
% 4.10/1.14 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl98])).
% 4.10/1.14 thf(zip_derived_cl60, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl1169, plain,
% 4.10/1.14 (( (equalish @ e_2 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl324, zip_derived_cl60])).
% 4.10/1.14 thf(zip_derived_cl24, plain, (~ (equalish @ e_2 @ e_1)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 4.10/1.14 thf('20', plain, (~ ( (product @ e_2 @ e_1 @ e_2))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1169, zip_derived_cl24])).
% 4.10/1.14 thf(e_2_then_e_3, axiom, (next @ e_2 @ e_3)).
% 4.10/1.14 thf(zip_derived_cl1, plain, ( (next @ e_2 @ e_3)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_2_then_e_3])).
% 4.10/1.14 thf(zip_derived_cl402, plain,
% 4.10/1.14 (( (product @ e_2 @ e_1 @ e_4)) <= (( (product @ e_2 @ e_1 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl103])).
% 4.10/1.14 thf(no_redundancy, axiom,
% 4.10/1.14 (( ~( product @ X @ e_1 @ Y ) ) | ( ~( next @ X @ X1 ) ) |
% 4.10/1.14 ( ~( greater @ Y @ X1 ) ))).
% 4.10/1.14 thf(zip_derived_cl14, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.10/1.14 (~ (product @ X0 @ e_1 @ X1)
% 4.10/1.14 | ~ (next @ X0 @ X2)
% 4.10/1.14 | ~ (greater @ X1 @ X2))),
% 4.10/1.14 inference('cnf', [status(esa)], [no_redundancy])).
% 4.10/1.14 thf(zip_derived_cl410, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (next @ e_2 @ X0) | ~ (greater @ e_4 @ X0)))
% 4.10/1.14 <= (( (product @ e_2 @ e_1 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl402, zip_derived_cl14])).
% 4.10/1.14 thf(zip_derived_cl415, plain,
% 4.10/1.14 ((~ (greater @ e_4 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl410])).
% 4.10/1.14 thf(e_4_greater_e_3, axiom, (greater @ e_4 @ e_3)).
% 4.10/1.14 thf(zip_derived_cl11, plain, ( (greater @ e_4 @ e_3)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_4_greater_e_3])).
% 4.10/1.14 thf('21', plain, (~ ( (product @ e_2 @ e_1 @ e_4))),
% 4.10/1.14 inference('demod', [status(thm)], [zip_derived_cl415, zip_derived_cl11])).
% 4.10/1.14 thf(zip_derived_cl1, plain, ( (next @ e_2 @ e_3)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_2_then_e_3])).
% 4.10/1.14 thf(zip_derived_cl321, plain,
% 4.10/1.14 (( (product @ e_2 @ e_1 @ e_5)) <= (( (product @ e_2 @ e_1 @ e_5)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl98])).
% 4.10/1.14 thf(zip_derived_cl14, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.10/1.14 (~ (product @ X0 @ e_1 @ X1)
% 4.10/1.14 | ~ (next @ X0 @ X2)
% 4.10/1.14 | ~ (greater @ X1 @ X2))),
% 4.10/1.14 inference('cnf', [status(esa)], [no_redundancy])).
% 4.10/1.14 thf(zip_derived_cl330, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (next @ e_2 @ X0) | ~ (greater @ e_5 @ X0)))
% 4.10/1.14 <= (( (product @ e_2 @ e_1 @ e_5)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl321, zip_derived_cl14])).
% 4.10/1.14 thf(zip_derived_cl335, plain,
% 4.10/1.14 ((~ (greater @ e_5 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_5)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl330])).
% 4.10/1.14 thf(e_5_greater_e_3, axiom, (greater @ e_5 @ e_3)).
% 4.10/1.14 thf(zip_derived_cl12, plain, ( (greater @ e_5 @ e_3)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_5_greater_e_3])).
% 4.10/1.14 thf('22', plain, (~ ( (product @ e_2 @ e_1 @ e_5))),
% 4.10/1.14 inference('demod', [status(thm)], [zip_derived_cl335, zip_derived_cl12])).
% 4.10/1.14 thf(zip_derived_cl325, plain,
% 4.10/1.14 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl98])).
% 4.10/1.14 thf(zip_derived_cl65, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl43])).
% 4.10/1.14 thf(zip_derived_cl1187, plain,
% 4.10/1.14 (( (equalish @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl325, zip_derived_cl65])).
% 4.10/1.14 thf(zip_derived_cl20, plain, (~ (equalish @ e_1 @ e_2)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 4.10/1.14 thf('23', plain, (~ ( (product @ e_2 @ e_1 @ e_1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1187, zip_derived_cl20])).
% 4.10/1.14 thf('24', plain,
% 4.10/1.14 (( (product @ e_2 @ e_1 @ e_3)) | ( (product @ e_2 @ e_1 @ e_1)) |
% 4.10/1.14 ( (product @ e_2 @ e_1 @ e_5)) | ( (product @ e_2 @ e_1 @ e_4)) |
% 4.10/1.14 ( (product @ e_2 @ e_1 @ e_2))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl98])).
% 4.10/1.14 thf('25', plain, (( (product @ e_2 @ e_1 @ e_3))),
% 4.10/1.14 inference('sat_resolution*', [status(thm)],
% 4.10/1.14 ['20', '21', '22', '23', '24'])).
% 4.10/1.14 thf(zip_derived_cl1391, plain, ( (product @ e_2 @ e_1 @ e_3)),
% 4.10/1.14 inference('simpl_trail', [status(thm)], [zip_derived_cl403, '25'])).
% 4.10/1.14 thf(zip_derived_cl382, plain,
% 4.10/1.14 (( (product @ e_2 @ e_5 @ e_3)) <= (( (product @ e_2 @ e_5 @ e_3)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl102])).
% 4.10/1.14 thf(zip_derived_cl42, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.14 | (equalish @ X1 @ X3))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.14 thf(zip_derived_cl1338, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_3) | (equalish @ e_5 @ X0)))
% 4.10/1.14 <= (( (product @ e_2 @ e_5 @ e_3)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl382, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl1630, plain,
% 4.10/1.14 (( (equalish @ e_5 @ e_1)) <= (( (product @ e_2 @ e_5 @ e_3)))),
% 4.10/1.14 inference('s_sup-', [status(thm)],
% 4.10/1.14 [zip_derived_cl1391, zip_derived_cl1338])).
% 4.10/1.14 thf(e_5_is_not_e_1, axiom, (~( equalish @ e_5 @ e_1 ))).
% 4.10/1.14 thf(zip_derived_cl36, plain, (~ (equalish @ e_5 @ e_1)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_5_is_not_e_1])).
% 4.10/1.14 thf('26', plain, (~ ( (product @ e_2 @ e_5 @ e_3))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1630, zip_derived_cl36])).
% 4.10/1.14 thf(zip_derived_cl368, plain,
% 4.10/1.14 (( (product @ e_2 @ e_4 @ e_1)) <= (( (product @ e_2 @ e_4 @ e_1)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl101])).
% 4.10/1.14 thf(zip_derived_cl42, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.14 | (equalish @ X1 @ X3))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.14 thf(zip_derived_cl1317, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_1) | (equalish @ e_4 @ X0)))
% 4.10/1.14 <= (( (product @ e_2 @ e_4 @ e_1)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl368, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl384, plain,
% 4.10/1.14 (( (product @ e_2 @ e_5 @ e_1)) <= (( (product @ e_2 @ e_5 @ e_1)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl102])).
% 4.10/1.14 thf(zip_derived_cl1551, plain,
% 4.10/1.14 (( (equalish @ e_4 @ e_5))
% 4.10/1.14 <= (( (product @ e_2 @ e_4 @ e_1)) & ( (product @ e_2 @ e_5 @ e_1)))),
% 4.10/1.14 inference('s_sup+', [status(thm)],
% 4.10/1.14 [zip_derived_cl1317, zip_derived_cl384])).
% 4.10/1.14 thf(e_4_is_not_e_5, axiom, (~( equalish @ e_4 @ e_5 ))).
% 4.10/1.14 thf(zip_derived_cl35, plain, (~ (equalish @ e_4 @ e_5)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_4_is_not_e_5])).
% 4.10/1.14 thf('27', plain,
% 4.10/1.14 (~ ( (product @ e_2 @ e_5 @ e_1)) | ~ ( (product @ e_2 @ e_4 @ e_1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1551, zip_derived_cl35])).
% 4.10/1.14 thf(zip_derived_cl348, plain,
% 4.10/1.14 (( (product @ e_2 @ e_3 @ e_1)) <= (( (product @ e_2 @ e_3 @ e_1)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl100])).
% 4.10/1.14 thf(zip_derived_cl42, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.14 | (equalish @ X1 @ X3))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.14 thf(zip_derived_cl1254, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_1) | (equalish @ e_3 @ X0)))
% 4.10/1.14 <= (( (product @ e_2 @ e_3 @ e_1)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl368, plain,
% 4.10/1.14 (( (product @ e_2 @ e_4 @ e_1)) <= (( (product @ e_2 @ e_4 @ e_1)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl101])).
% 4.10/1.14 thf(zip_derived_cl1477, plain,
% 4.10/1.14 (( (equalish @ e_3 @ e_4))
% 4.10/1.14 <= (( (product @ e_2 @ e_3 @ e_1)) & ( (product @ e_2 @ e_4 @ e_1)))),
% 4.10/1.14 inference('s_sup+', [status(thm)],
% 4.10/1.14 [zip_derived_cl1254, zip_derived_cl368])).
% 4.10/1.14 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 4.10/1.14 thf(zip_derived_cl30, plain, (~ (equalish @ e_3 @ e_4)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 4.10/1.14 thf('28', plain,
% 4.10/1.14 (~ ( (product @ e_2 @ e_4 @ e_1)) | ~ ( (product @ e_2 @ e_3 @ e_1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1477, zip_derived_cl30])).
% 4.10/1.14 thf(zip_derived_cl601, plain,
% 4.10/1.14 (( (product @ e_3 @ e_2 @ e_4)) <= (( (product @ e_3 @ e_2 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl142])).
% 4.10/1.14 thf(zip_derived_cl115, plain,
% 4.10/1.14 (( (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl87])).
% 4.10/1.14 thf(zip_derived_cl43, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X3 @ X1 @ X2)
% 4.10/1.14 | (equalish @ X0 @ X3))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_left_cancellation])).
% 4.10/1.14 thf(zip_derived_cl125, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_4) | (equalish @ e_1 @ X0)))
% 4.10/1.14 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl115, zip_derived_cl43])).
% 4.10/1.14 thf(zip_derived_cl609, plain,
% 4.10/1.14 (( (equalish @ e_1 @ e_3))
% 4.10/1.14 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_3 @ e_2 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl601, zip_derived_cl125])).
% 4.10/1.14 thf(zip_derived_cl21, plain, (~ (equalish @ e_1 @ e_3)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 4.10/1.14 thf('29', plain,
% 4.10/1.14 (~ ( (product @ e_3 @ e_2 @ e_4)) | ~ ( (product @ e_1 @ e_2 @ e_4))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl609, zip_derived_cl21])).
% 4.10/1.14 thf('30', plain,
% 4.10/1.14 (( (product @ e_2 @ e_4 @ e_5)) | ( (product @ e_2 @ e_4 @ e_1)) |
% 4.10/1.14 ( (product @ e_2 @ e_4 @ e_4)) | ( (product @ e_2 @ e_4 @ e_2)) |
% 4.10/1.14 ( (product @ e_2 @ e_4 @ e_3))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl101])).
% 4.10/1.14 thf(zip_derived_cl18, plain, ( (group_element @ e_4)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_4])).
% 4.10/1.14 thf(zip_derived_cl55, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_2 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl106, plain,
% 4.10/1.14 (( (product @ e_2 @ e_4 @ e_1)
% 4.10/1.14 | (product @ e_2 @ e_4 @ e_2)
% 4.10/1.14 | (product @ e_2 @ e_4 @ e_3)
% 4.10/1.14 | (product @ e_2 @ e_4 @ e_4)
% 4.10/1.14 | (product @ e_2 @ e_4 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl55])).
% 4.10/1.14 thf(zip_derived_cl439, plain,
% 4.10/1.14 (( (product @ e_2 @ e_4 @ e_4)) <= (( (product @ e_2 @ e_4 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl106])).
% 4.10/1.14 thf(zip_derived_cl65, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl43])).
% 4.10/1.14 thf(zip_derived_cl447, plain,
% 4.10/1.14 (( (equalish @ e_4 @ e_2)) <= (( (product @ e_2 @ e_4 @ e_4)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl439, zip_derived_cl65])).
% 4.10/1.14 thf(e_4_is_not_e_2, axiom, (~( equalish @ e_4 @ e_2 ))).
% 4.10/1.14 thf(zip_derived_cl33, plain, (~ (equalish @ e_4 @ e_2)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 4.10/1.14 thf('31', plain, (~ ( (product @ e_2 @ e_4 @ e_4))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl447, zip_derived_cl33])).
% 4.10/1.14 thf(zip_derived_cl367, plain,
% 4.10/1.14 (( (product @ e_2 @ e_4 @ e_2)) <= (( (product @ e_2 @ e_4 @ e_2)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl101])).
% 4.10/1.14 thf(zip_derived_cl60, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl1305, plain,
% 4.10/1.14 (( (equalish @ e_2 @ e_4)) <= (( (product @ e_2 @ e_4 @ e_2)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl367, zip_derived_cl60])).
% 4.10/1.14 thf(zip_derived_cl26, plain, (~ (equalish @ e_2 @ e_4)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 4.10/1.14 thf('32', plain, (~ ( (product @ e_2 @ e_4 @ e_2))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1305, zip_derived_cl26])).
% 4.10/1.14 thf(zip_derived_cl1391, plain, ( (product @ e_2 @ e_1 @ e_3)),
% 4.10/1.14 inference('simpl_trail', [status(thm)], [zip_derived_cl403, '25'])).
% 4.10/1.14 thf(zip_derived_cl366, plain,
% 4.10/1.14 (( (product @ e_2 @ e_4 @ e_3)) <= (( (product @ e_2 @ e_4 @ e_3)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl101])).
% 4.10/1.14 thf(zip_derived_cl42, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.14 | (equalish @ X1 @ X3))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.14 thf(zip_derived_cl1282, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_3) | (equalish @ e_4 @ X0)))
% 4.10/1.14 <= (( (product @ e_2 @ e_4 @ e_3)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl366, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl1493, plain,
% 4.10/1.14 (( (equalish @ e_4 @ e_1)) <= (( (product @ e_2 @ e_4 @ e_3)))),
% 4.10/1.14 inference('s_sup-', [status(thm)],
% 4.10/1.14 [zip_derived_cl1391, zip_derived_cl1282])).
% 4.10/1.14 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 4.10/1.14 thf(zip_derived_cl32, plain, (~ (equalish @ e_4 @ e_1)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 4.10/1.14 thf('33', plain, (~ ( (product @ e_2 @ e_4 @ e_3))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1493, zip_derived_cl32])).
% 4.10/1.14 thf(zip_derived_cl364, plain,
% 4.10/1.14 (( (product @ e_2 @ e_4 @ e_5)) <= (( (product @ e_2 @ e_4 @ e_5)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl101])).
% 4.10/1.14 thf(zip_derived_cl54, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl18, plain, ( (group_element @ e_4)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_4])).
% 4.10/1.14 thf(zip_derived_cl89, plain,
% 4.10/1.14 (( (product @ e_1 @ e_4 @ e_5)
% 4.10/1.14 | (product @ e_1 @ e_4 @ e_4)
% 4.10/1.14 | (product @ e_1 @ e_4 @ e_3)
% 4.10/1.14 | (product @ e_1 @ e_4 @ e_2)
% 4.10/1.14 | (product @ e_1 @ e_4 @ e_1))),
% 4.10/1.14 inference('s_sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl18])).
% 4.10/1.14 thf(zip_derived_cl213, plain,
% 4.10/1.14 (( (product @ e_1 @ e_4 @ e_5)) <= (( (product @ e_1 @ e_4 @ e_5)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl89])).
% 4.10/1.14 thf(zip_derived_cl43, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X3 @ X1 @ X2)
% 4.10/1.14 | (equalish @ X0 @ X3))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_left_cancellation])).
% 4.10/1.14 thf(zip_derived_cl220, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_5) | (equalish @ e_1 @ X0)))
% 4.10/1.14 <= (( (product @ e_1 @ e_4 @ e_5)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl213, zip_derived_cl43])).
% 4.10/1.14 thf(zip_derived_cl373, plain,
% 4.10/1.14 (( (equalish @ e_1 @ e_2))
% 4.10/1.14 <= (( (product @ e_1 @ e_4 @ e_5)) & ( (product @ e_2 @ e_4 @ e_5)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl364, zip_derived_cl220])).
% 4.10/1.14 thf(zip_derived_cl20, plain, (~ (equalish @ e_1 @ e_2)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 4.10/1.14 thf('34', plain,
% 4.10/1.14 (~ ( (product @ e_1 @ e_4 @ e_5)) | ~ ( (product @ e_2 @ e_4 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl373, zip_derived_cl20])).
% 4.10/1.14 thf(zip_derived_cl213, plain,
% 4.10/1.14 (( (product @ e_1 @ e_4 @ e_5)) <= (( (product @ e_1 @ e_4 @ e_5)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl89])).
% 4.10/1.14 thf(zip_derived_cl114, plain,
% 4.10/1.14 (( (product @ e_1 @ e_2 @ e_5)) <= (( (product @ e_1 @ e_2 @ e_5)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl87])).
% 4.10/1.14 thf(zip_derived_cl42, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.14 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.14 | (equalish @ X1 @ X3))),
% 4.10/1.14 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.14 thf(zip_derived_cl120, plain,
% 4.10/1.14 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_5) | (equalish @ e_2 @ X0)))
% 4.10/1.14 <= (( (product @ e_1 @ e_2 @ e_5)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl222, plain,
% 4.10/1.14 (( (equalish @ e_2 @ e_4))
% 4.10/1.14 <= (( (product @ e_1 @ e_2 @ e_5)) & ( (product @ e_1 @ e_4 @ e_5)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl213, zip_derived_cl120])).
% 4.10/1.14 thf(zip_derived_cl26, plain, (~ (equalish @ e_2 @ e_4)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 4.10/1.14 thf('35', plain,
% 4.10/1.14 (~ ( (product @ e_1 @ e_2 @ e_5)) | ~ ( (product @ e_1 @ e_4 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl222, zip_derived_cl26])).
% 4.10/1.14 thf(zip_derived_cl54, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl19, plain, ( (group_element @ e_5)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_5])).
% 4.10/1.14 thf(zip_derived_cl90, plain,
% 4.10/1.14 (( (product @ e_1 @ e_5 @ e_5)
% 4.10/1.14 | (product @ e_1 @ e_5 @ e_4)
% 4.10/1.14 | (product @ e_1 @ e_5 @ e_3)
% 4.10/1.14 | (product @ e_1 @ e_5 @ e_2)
% 4.10/1.14 | (product @ e_1 @ e_5 @ e_1))),
% 4.10/1.14 inference('s_sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl19])).
% 4.10/1.14 thf('36', plain,
% 4.10/1.14 (( (product @ e_1 @ e_5 @ e_2)) | ( (product @ e_1 @ e_5 @ e_3)) |
% 4.10/1.14 ( (product @ e_1 @ e_5 @ e_5)) | ( (product @ e_1 @ e_5 @ e_4)) |
% 4.10/1.14 ( (product @ e_1 @ e_5 @ e_1))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl90])).
% 4.10/1.14 thf(zip_derived_cl232, plain,
% 4.10/1.14 (( (product @ e_1 @ e_5 @ e_5)) <= (( (product @ e_1 @ e_5 @ e_5)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl90])).
% 4.10/1.14 thf(zip_derived_cl65, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl43])).
% 4.10/1.14 thf(zip_derived_cl241, plain,
% 4.10/1.14 (( (equalish @ e_5 @ e_1)) <= (( (product @ e_1 @ e_5 @ e_5)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl232, zip_derived_cl65])).
% 4.10/1.14 thf(zip_derived_cl36, plain, (~ (equalish @ e_5 @ e_1)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_5_is_not_e_1])).
% 4.10/1.14 thf('37', plain, (~ ( (product @ e_1 @ e_5 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl241, zip_derived_cl36])).
% 4.10/1.14 thf(zip_derived_cl236, plain,
% 4.10/1.14 (( (product @ e_1 @ e_5 @ e_1)) <= (( (product @ e_1 @ e_5 @ e_1)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl90])).
% 4.10/1.14 thf(zip_derived_cl60, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl42])).
% 4.10/1.14 thf(zip_derived_cl1084, plain,
% 4.10/1.14 (( (equalish @ e_1 @ e_5)) <= (( (product @ e_1 @ e_5 @ e_1)))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl236, zip_derived_cl60])).
% 4.10/1.14 thf(zip_derived_cl23, plain, (~ (equalish @ e_1 @ e_5)),
% 4.10/1.14 inference('cnf', [status(esa)], [e_1_is_not_e_5])).
% 4.10/1.14 thf('38', plain, (~ ( (product @ e_1 @ e_5 @ e_1))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl1084, zip_derived_cl23])).
% 4.10/1.14 thf('39', plain,
% 4.10/1.14 (( (product @ e_1 @ e_4 @ e_3)) | ( (product @ e_1 @ e_4 @ e_2)) |
% 4.10/1.14 ( (product @ e_1 @ e_4 @ e_4)) | ( (product @ e_1 @ e_4 @ e_1)) |
% 4.10/1.14 ( (product @ e_1 @ e_4 @ e_5))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl89])).
% 4.10/1.14 thf(zip_derived_cl18, plain, ( (group_element @ e_4)),
% 4.10/1.14 inference('cnf', [status(esa)], [element_4])).
% 4.10/1.14 thf(zip_derived_cl54, plain,
% 4.10/1.14 (![X0 : $i]:
% 4.10/1.14 (~ (group_element @ X0)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_1)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_2)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_3)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_4)
% 4.10/1.14 | (product @ e_1 @ X0 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl40])).
% 4.10/1.14 thf(zip_derived_cl94, plain,
% 4.10/1.14 (( (product @ e_1 @ e_4 @ e_1)
% 4.10/1.14 | (product @ e_1 @ e_4 @ e_2)
% 4.10/1.14 | (product @ e_1 @ e_4 @ e_3)
% 4.10/1.14 | (product @ e_1 @ e_4 @ e_4)
% 4.10/1.14 | (product @ e_1 @ e_4 @ e_5))),
% 4.10/1.14 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl54])).
% 4.10/1.14 thf(zip_derived_cl294, plain,
% 4.10/1.14 (( (product @ e_1 @ e_4 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_4)))),
% 4.10/1.14 inference('split', [status(esa)], [zip_derived_cl94])).
% 4.10/1.14 thf(zip_derived_cl65, plain,
% 4.10/1.14 (![X0 : $i, X1 : $i]:
% 4.10/1.14 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl43])).
% 4.10/1.15 thf(zip_derived_cl302, plain,
% 4.10/1.15 (( (equalish @ e_4 @ e_1)) <= (( (product @ e_1 @ e_4 @ e_4)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl294, zip_derived_cl65])).
% 4.10/1.15 thf(zip_derived_cl32, plain, (~ (equalish @ e_4 @ e_1)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 4.10/1.15 thf('40', plain, (~ ( (product @ e_1 @ e_4 @ e_4))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl302, zip_derived_cl32])).
% 4.10/1.15 thf(zip_derived_cl217, plain,
% 4.10/1.15 (( (product @ e_1 @ e_4 @ e_1)) <= (( (product @ e_1 @ e_4 @ e_1)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl89])).
% 4.10/1.15 thf(zip_derived_cl60, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl42])).
% 4.10/1.15 thf(zip_derived_cl500, plain,
% 4.10/1.15 (( (equalish @ e_1 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_1)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl217, zip_derived_cl60])).
% 4.10/1.15 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 4.10/1.15 thf(zip_derived_cl22, plain, (~ (equalish @ e_1 @ e_4)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 4.10/1.15 thf('41', plain, (~ ( (product @ e_1 @ e_4 @ e_1))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl500, zip_derived_cl22])).
% 4.10/1.15 thf(zip_derived_cl235, plain,
% 4.10/1.15 (( (product @ e_1 @ e_5 @ e_2)) <= (( (product @ e_1 @ e_5 @ e_2)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl90])).
% 4.10/1.15 thf(zip_derived_cl201, plain,
% 4.10/1.15 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl88])).
% 4.10/1.15 thf(zip_derived_cl42, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.15 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.15 | (equalish @ X1 @ X3))),
% 4.10/1.15 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.15 thf(zip_derived_cl266, plain,
% 4.10/1.15 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_3 @ X0)))
% 4.10/1.15 <= (( (product @ e_1 @ e_3 @ e_2)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl201, zip_derived_cl42])).
% 4.10/1.15 thf(zip_derived_cl1070, plain,
% 4.10/1.15 (( (equalish @ e_3 @ e_5))
% 4.10/1.15 <= (( (product @ e_1 @ e_3 @ e_2)) & ( (product @ e_1 @ e_5 @ e_2)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl235, zip_derived_cl266])).
% 4.10/1.15 thf(zip_derived_cl31, plain, (~ (equalish @ e_3 @ e_5)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_3_is_not_e_5])).
% 4.10/1.15 thf('42', plain,
% 4.10/1.15 (~ ( (product @ e_1 @ e_3 @ e_2)) | ~ ( (product @ e_1 @ e_5 @ e_2))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl1070, zip_derived_cl31])).
% 4.10/1.15 thf(zip_derived_cl216, plain,
% 4.10/1.15 (( (product @ e_1 @ e_4 @ e_2)) <= (( (product @ e_1 @ e_4 @ e_2)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl89])).
% 4.10/1.15 thf(zip_derived_cl266, plain,
% 4.10/1.15 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_3 @ X0)))
% 4.10/1.15 <= (( (product @ e_1 @ e_3 @ e_2)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl201, zip_derived_cl42])).
% 4.10/1.15 thf(zip_derived_cl456, plain,
% 4.10/1.15 (( (equalish @ e_3 @ e_4))
% 4.10/1.15 <= (( (product @ e_1 @ e_3 @ e_2)) & ( (product @ e_1 @ e_4 @ e_2)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl216, zip_derived_cl266])).
% 4.10/1.15 thf(zip_derived_cl30, plain, (~ (equalish @ e_3 @ e_4)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 4.10/1.15 thf('43', plain,
% 4.10/1.15 (~ ( (product @ e_1 @ e_4 @ e_2)) | ~ ( (product @ e_1 @ e_3 @ e_2))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl456, zip_derived_cl30])).
% 4.10/1.15 thf(zip_derived_cl234, plain,
% 4.10/1.15 (( (product @ e_1 @ e_5 @ e_3)) <= (( (product @ e_1 @ e_5 @ e_3)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl90])).
% 4.10/1.15 thf(zip_derived_cl215, plain,
% 4.10/1.15 (( (product @ e_1 @ e_4 @ e_3)) <= (( (product @ e_1 @ e_4 @ e_3)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl89])).
% 4.10/1.15 thf(zip_derived_cl42, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.15 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.15 | (equalish @ X1 @ X3))),
% 4.10/1.15 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.15 thf(zip_derived_cl395, plain,
% 4.10/1.15 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_4 @ X0)))
% 4.10/1.15 <= (( (product @ e_1 @ e_4 @ e_3)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl215, zip_derived_cl42])).
% 4.10/1.15 thf(zip_derived_cl1055, plain,
% 4.10/1.15 (( (equalish @ e_4 @ e_5))
% 4.10/1.15 <= (( (product @ e_1 @ e_4 @ e_3)) & ( (product @ e_1 @ e_5 @ e_3)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl234, zip_derived_cl395])).
% 4.10/1.15 thf(zip_derived_cl35, plain, (~ (equalish @ e_4 @ e_5)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_5])).
% 4.10/1.15 thf('44', plain,
% 4.10/1.15 (~ ( (product @ e_1 @ e_5 @ e_3)) | ~ ( (product @ e_1 @ e_4 @ e_3))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl1055, zip_derived_cl35])).
% 4.10/1.15 thf(zip_derived_cl200, plain,
% 4.10/1.15 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl88])).
% 4.10/1.15 thf(zip_derived_cl65, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i]:
% 4.10/1.15 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl43])).
% 4.10/1.15 thf(zip_derived_cl254, plain,
% 4.10/1.15 (( (equalish @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl200, zip_derived_cl65])).
% 4.10/1.15 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 4.10/1.15 thf(zip_derived_cl28, plain, (~ (equalish @ e_3 @ e_1)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 4.10/1.15 thf('45', plain, (~ ( (product @ e_1 @ e_3 @ e_3))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl254, zip_derived_cl28])).
% 4.10/1.15 thf(zip_derived_cl56, plain,
% 4.10/1.15 (![X0 : $i]:
% 4.10/1.15 (~ (group_element @ X0)
% 4.10/1.15 | (product @ e_3 @ X0 @ e_1)
% 4.10/1.15 | (product @ e_3 @ X0 @ e_2)
% 4.10/1.15 | (product @ e_3 @ X0 @ e_3)
% 4.10/1.15 | (product @ e_3 @ X0 @ e_4)
% 4.10/1.15 | (product @ e_3 @ X0 @ e_5))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl40])).
% 4.10/1.15 thf(zip_derived_cl15, plain, ( (group_element @ e_1)),
% 4.10/1.15 inference('cnf', [status(esa)], [element_1])).
% 4.10/1.15 thf(zip_derived_cl136, plain,
% 4.10/1.15 (( (product @ e_3 @ e_1 @ e_5)
% 4.10/1.15 | (product @ e_3 @ e_1 @ e_4)
% 4.10/1.15 | (product @ e_3 @ e_1 @ e_3)
% 4.10/1.15 | (product @ e_3 @ e_1 @ e_2)
% 4.10/1.15 | (product @ e_3 @ e_1 @ e_1))),
% 4.10/1.15 inference('s_sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl15])).
% 4.10/1.15 thf(zip_derived_cl483, plain,
% 4.10/1.15 (( (product @ e_3 @ e_1 @ e_1)) <= (( (product @ e_3 @ e_1 @ e_1)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl136])).
% 4.10/1.15 thf(zip_derived_cl65, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i]:
% 4.10/1.15 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl43])).
% 4.10/1.15 thf(zip_derived_cl1532, plain,
% 4.10/1.15 (( (equalish @ e_1 @ e_3)) <= (( (product @ e_3 @ e_1 @ e_1)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl483, zip_derived_cl65])).
% 4.10/1.15 thf(zip_derived_cl21, plain, (~ (equalish @ e_1 @ e_3)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 4.10/1.15 thf('46', plain, (~ ( (product @ e_3 @ e_1 @ e_1))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl1532, zip_derived_cl21])).
% 4.10/1.15 thf(zip_derived_cl481, plain,
% 4.10/1.15 (( (product @ e_3 @ e_1 @ e_3)) <= (( (product @ e_3 @ e_1 @ e_3)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl136])).
% 4.10/1.15 thf(zip_derived_cl60, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl42])).
% 4.10/1.15 thf(zip_derived_cl1500, plain,
% 4.10/1.15 (( (equalish @ e_3 @ e_1)) <= (( (product @ e_3 @ e_1 @ e_3)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl481, zip_derived_cl60])).
% 4.10/1.15 thf(zip_derived_cl28, plain, (~ (equalish @ e_3 @ e_1)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 4.10/1.15 thf('47', plain, (~ ( (product @ e_3 @ e_1 @ e_3))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl1500, zip_derived_cl28])).
% 4.10/1.15 thf(e_3_then_e_4, axiom, (next @ e_3 @ e_4)).
% 4.10/1.15 thf(zip_derived_cl2, plain, ( (next @ e_3 @ e_4)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_3_then_e_4])).
% 4.10/1.15 thf(zip_derived_cl479, plain,
% 4.10/1.15 (( (product @ e_3 @ e_1 @ e_5)) <= (( (product @ e_3 @ e_1 @ e_5)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl136])).
% 4.10/1.15 thf(zip_derived_cl14, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.10/1.15 (~ (product @ X0 @ e_1 @ X1)
% 4.10/1.15 | ~ (next @ X0 @ X2)
% 4.10/1.15 | ~ (greater @ X1 @ X2))),
% 4.10/1.15 inference('cnf', [status(esa)], [no_redundancy])).
% 4.10/1.15 thf(zip_derived_cl488, plain,
% 4.10/1.15 ((![X0 : $i]: (~ (next @ e_3 @ X0) | ~ (greater @ e_5 @ X0)))
% 4.10/1.15 <= (( (product @ e_3 @ e_1 @ e_5)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl479, zip_derived_cl14])).
% 4.10/1.15 thf(zip_derived_cl493, plain,
% 4.10/1.15 ((~ (greater @ e_5 @ e_4)) <= (( (product @ e_3 @ e_1 @ e_5)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl488])).
% 4.10/1.15 thf(e_5_greater_e_4, axiom, (greater @ e_5 @ e_4)).
% 4.10/1.15 thf(zip_derived_cl13, plain, ( (greater @ e_5 @ e_4)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_5_greater_e_4])).
% 4.10/1.15 thf('48', plain, (~ ( (product @ e_3 @ e_1 @ e_5))),
% 4.10/1.15 inference('demod', [status(thm)], [zip_derived_cl493, zip_derived_cl13])).
% 4.10/1.15 thf(zip_derived_cl1391, plain, ( (product @ e_2 @ e_1 @ e_3)),
% 4.10/1.15 inference('simpl_trail', [status(thm)], [zip_derived_cl403, '25'])).
% 4.10/1.15 thf(zip_derived_cl116, plain,
% 4.10/1.15 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl87])).
% 4.10/1.15 thf(zip_derived_cl45, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.15 ( (product @ X0 @ X1 @ X2)
% 4.10/1.15 | ~ (product @ X3 @ X2 @ X1)
% 4.10/1.15 | ~ (product @ X2 @ X3 @ X0))),
% 4.10/1.15 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.10/1.15 thf(zip_derived_cl130, plain,
% 4.10/1.15 ((![X0 : $i]:
% 4.10/1.15 ( (product @ X0 @ e_3 @ e_2) | ~ (product @ e_2 @ e_1 @ X0)))
% 4.10/1.15 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl45])).
% 4.10/1.15 thf(zip_derived_cl1399, plain,
% 4.10/1.15 (( (product @ e_3 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 4.10/1.15 inference('s_sup-', [status(thm)],
% 4.10/1.15 [zip_derived_cl1391, zip_derived_cl130])).
% 4.10/1.15 thf(zip_derived_cl49, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl41])).
% 4.10/1.15 thf(zip_derived_cl1573, plain,
% 4.10/1.15 (( (equalish @ e_3 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl1399, zip_derived_cl49])).
% 4.10/1.15 thf(zip_derived_cl29, plain, (~ (equalish @ e_3 @ e_2)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 4.10/1.15 thf('49', plain, (~ ( (product @ e_1 @ e_2 @ e_3))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl1573, zip_derived_cl29])).
% 4.10/1.15 thf(zip_derived_cl117, plain,
% 4.10/1.15 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl87])).
% 4.10/1.15 thf(zip_derived_cl65, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i]:
% 4.10/1.15 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl43])).
% 4.10/1.15 thf(zip_derived_cl135, plain,
% 4.10/1.15 (( (equalish @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl117, zip_derived_cl65])).
% 4.10/1.15 thf(zip_derived_cl24, plain, (~ (equalish @ e_2 @ e_1)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 4.10/1.15 thf('50', plain, (~ ( (product @ e_1 @ e_2 @ e_2))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl135, zip_derived_cl24])).
% 4.10/1.15 thf(zip_derived_cl118, plain,
% 4.10/1.15 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl87])).
% 4.10/1.15 thf(zip_derived_cl60, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl42])).
% 4.10/1.15 thf(zip_derived_cl177, plain,
% 4.10/1.15 (( (equalish @ e_1 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl60])).
% 4.10/1.15 thf(zip_derived_cl20, plain, (~ (equalish @ e_1 @ e_2)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 4.10/1.15 thf('51', plain, (~ ( (product @ e_1 @ e_2 @ e_1))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl177, zip_derived_cl20])).
% 4.10/1.15 thf(zip_derived_cl482, plain,
% 4.10/1.15 (( (product @ e_3 @ e_1 @ e_2)) <= (( (product @ e_3 @ e_1 @ e_2)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl136])).
% 4.10/1.15 thf(zip_derived_cl323, plain,
% 4.10/1.15 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl98])).
% 4.10/1.15 thf(zip_derived_cl114, plain,
% 4.10/1.15 (( (product @ e_1 @ e_2 @ e_5)) <= (( (product @ e_1 @ e_2 @ e_5)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl87])).
% 4.10/1.15 thf(zip_derived_cl45, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.15 ( (product @ X0 @ X1 @ X2)
% 4.10/1.15 | ~ (product @ X3 @ X2 @ X1)
% 4.10/1.15 | ~ (product @ X2 @ X3 @ X0))),
% 4.10/1.15 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.10/1.15 thf(zip_derived_cl122, plain,
% 4.10/1.15 ((![X0 : $i]:
% 4.10/1.15 ( (product @ X0 @ e_5 @ e_2) | ~ (product @ e_2 @ e_1 @ X0)))
% 4.10/1.15 <= (( (product @ e_1 @ e_2 @ e_5)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl45])).
% 4.10/1.15 thf(zip_derived_cl1159, plain,
% 4.10/1.15 (( (product @ e_3 @ e_5 @ e_2))
% 4.10/1.15 <= (( (product @ e_1 @ e_2 @ e_5)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl323, zip_derived_cl122])).
% 4.10/1.15 thf('52', plain, (( (product @ e_2 @ e_1 @ e_3))),
% 4.10/1.15 inference('sat_resolution*', [status(thm)],
% 4.10/1.15 ['20', '21', '22', '23', '24'])).
% 4.10/1.15 thf(zip_derived_cl1198, plain,
% 4.10/1.15 (( (product @ e_3 @ e_5 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_5)))),
% 4.10/1.15 inference('simpl_trail', [status(thm)], [zip_derived_cl1159, '52'])).
% 4.10/1.15 thf(zip_derived_cl42, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.15 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.15 | (equalish @ X1 @ X3))),
% 4.10/1.15 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.15 thf(zip_derived_cl1248, plain,
% 4.10/1.15 ((![X0 : $i]: (~ (product @ e_3 @ X0 @ e_2) | (equalish @ e_5 @ X0)))
% 4.10/1.15 <= (( (product @ e_1 @ e_2 @ e_5)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl1198, zip_derived_cl42])).
% 4.10/1.15 thf(zip_derived_cl1516, plain,
% 4.10/1.15 (( (equalish @ e_5 @ e_1))
% 4.10/1.15 <= (( (product @ e_1 @ e_2 @ e_5)) & ( (product @ e_3 @ e_1 @ e_2)))),
% 4.10/1.15 inference('s_sup-', [status(thm)],
% 4.10/1.15 [zip_derived_cl482, zip_derived_cl1248])).
% 4.10/1.15 thf(zip_derived_cl36, plain, (~ (equalish @ e_5 @ e_1)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_5_is_not_e_1])).
% 4.10/1.15 thf('53', plain,
% 4.10/1.15 (~ ( (product @ e_1 @ e_2 @ e_5)) | ~ ( (product @ e_3 @ e_1 @ e_2))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl1516, zip_derived_cl36])).
% 4.10/1.15 thf(zip_derived_cl482, plain,
% 4.10/1.15 (( (product @ e_3 @ e_1 @ e_2)) <= (( (product @ e_3 @ e_1 @ e_2)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl136])).
% 4.10/1.15 thf(zip_derived_cl323, plain,
% 4.10/1.15 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl98])).
% 4.10/1.15 thf(zip_derived_cl115, plain,
% 4.10/1.15 (( (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl87])).
% 4.10/1.15 thf(zip_derived_cl45, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.15 ( (product @ X0 @ X1 @ X2)
% 4.10/1.15 | ~ (product @ X3 @ X2 @ X1)
% 4.10/1.15 | ~ (product @ X2 @ X3 @ X0))),
% 4.10/1.15 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.10/1.15 thf(zip_derived_cl126, plain,
% 4.10/1.15 ((![X0 : $i]:
% 4.10/1.15 ( (product @ X0 @ e_4 @ e_2) | ~ (product @ e_2 @ e_1 @ X0)))
% 4.10/1.15 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl115, zip_derived_cl45])).
% 4.10/1.15 thf(zip_derived_cl1160, plain,
% 4.10/1.15 (( (product @ e_3 @ e_4 @ e_2))
% 4.10/1.15 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl323, zip_derived_cl126])).
% 4.10/1.15 thf('54', plain, (( (product @ e_2 @ e_1 @ e_3))),
% 4.10/1.15 inference('sat_resolution*', [status(thm)],
% 4.10/1.15 ['20', '21', '22', '23', '24'])).
% 4.10/1.15 thf(zip_derived_cl1195, plain,
% 4.10/1.15 (( (product @ e_3 @ e_4 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 4.10/1.15 inference('simpl_trail', [status(thm)], [zip_derived_cl1160, '54'])).
% 4.10/1.15 thf(zip_derived_cl42, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.15 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.15 | (equalish @ X1 @ X3))),
% 4.10/1.15 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.15 thf(zip_derived_cl1202, plain,
% 4.10/1.15 ((![X0 : $i]: (~ (product @ e_3 @ X0 @ e_2) | (equalish @ e_4 @ X0)))
% 4.10/1.15 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl1195, zip_derived_cl42])).
% 4.10/1.15 thf(zip_derived_cl1515, plain,
% 4.10/1.15 (( (equalish @ e_4 @ e_1))
% 4.10/1.15 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_3 @ e_1 @ e_2)))),
% 4.10/1.15 inference('s_sup-', [status(thm)],
% 4.10/1.15 [zip_derived_cl482, zip_derived_cl1202])).
% 4.10/1.15 thf(zip_derived_cl32, plain, (~ (equalish @ e_4 @ e_1)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 4.10/1.15 thf('55', plain,
% 4.10/1.15 (~ ( (product @ e_3 @ e_1 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_4))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl1515, zip_derived_cl32])).
% 4.10/1.15 thf('56', plain,
% 4.10/1.15 (( (product @ e_3 @ e_1 @ e_4)) | ( (product @ e_3 @ e_1 @ e_2)) |
% 4.10/1.15 ( (product @ e_3 @ e_1 @ e_5)) | ( (product @ e_3 @ e_1 @ e_3)) |
% 4.10/1.15 ( (product @ e_3 @ e_1 @ e_1))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl136])).
% 4.10/1.15 thf(zip_derived_cl568, plain,
% 4.10/1.15 (( (product @ e_3 @ e_1 @ e_4)) <= (( (product @ e_3 @ e_1 @ e_4)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl141])).
% 4.10/1.15 thf(zip_derived_cl199, plain,
% 4.10/1.15 (( (product @ e_1 @ e_3 @ e_4)) <= (( (product @ e_1 @ e_3 @ e_4)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl88])).
% 4.10/1.15 thf(zip_derived_cl45, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.15 ( (product @ X0 @ X1 @ X2)
% 4.10/1.15 | ~ (product @ X3 @ X2 @ X1)
% 4.10/1.15 | ~ (product @ X2 @ X3 @ X0))),
% 4.10/1.15 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.10/1.15 thf(zip_derived_cl247, plain,
% 4.10/1.15 ((![X0 : $i]:
% 4.10/1.15 ( (product @ X0 @ e_4 @ e_3) | ~ (product @ e_3 @ e_1 @ X0)))
% 4.10/1.15 <= (( (product @ e_1 @ e_3 @ e_4)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl199, zip_derived_cl45])).
% 4.10/1.15 thf(zip_derived_cl578, plain,
% 4.10/1.15 (( (product @ e_4 @ e_4 @ e_3))
% 4.10/1.15 <= (( (product @ e_1 @ e_3 @ e_4)) & ( (product @ e_3 @ e_1 @ e_4)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl568, zip_derived_cl247])).
% 4.10/1.15 thf(zip_derived_cl49, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl41])).
% 4.10/1.15 thf(zip_derived_cl590, plain,
% 4.10/1.15 (( (equalish @ e_4 @ e_3))
% 4.10/1.15 <= (( (product @ e_1 @ e_3 @ e_4)) & ( (product @ e_3 @ e_1 @ e_4)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl578, zip_derived_cl49])).
% 4.10/1.15 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 4.10/1.15 thf(zip_derived_cl34, plain, (~ (equalish @ e_4 @ e_3)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 4.10/1.15 thf('57', plain,
% 4.10/1.15 (~ ( (product @ e_1 @ e_3 @ e_4)) | ~ ( (product @ e_3 @ e_1 @ e_4))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl590, zip_derived_cl34])).
% 4.10/1.15 thf('58', plain,
% 4.10/1.15 (( (product @ e_1 @ e_3 @ e_5)) | ( (product @ e_1 @ e_3 @ e_4)) |
% 4.10/1.15 ( (product @ e_1 @ e_3 @ e_3)) | ( (product @ e_1 @ e_3 @ e_2)) |
% 4.10/1.15 ( (product @ e_1 @ e_3 @ e_1))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl88])).
% 4.10/1.15 thf(zip_derived_cl198, plain,
% 4.10/1.15 (( (product @ e_1 @ e_3 @ e_5)) <= (( (product @ e_1 @ e_3 @ e_5)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl88])).
% 4.10/1.15 thf(zip_derived_cl120, plain,
% 4.10/1.15 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_5) | (equalish @ e_2 @ X0)))
% 4.10/1.15 <= (( (product @ e_1 @ e_2 @ e_5)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl42])).
% 4.10/1.15 thf(zip_derived_cl207, plain,
% 4.10/1.15 (( (equalish @ e_2 @ e_3))
% 4.10/1.15 <= (( (product @ e_1 @ e_2 @ e_5)) & ( (product @ e_1 @ e_3 @ e_5)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl198, zip_derived_cl120])).
% 4.10/1.15 thf(zip_derived_cl25, plain, (~ (equalish @ e_2 @ e_3)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 4.10/1.15 thf('59', plain,
% 4.10/1.15 (~ ( (product @ e_1 @ e_2 @ e_5)) | ~ ( (product @ e_1 @ e_3 @ e_5))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl207, zip_derived_cl25])).
% 4.10/1.15 thf('60', plain,
% 4.10/1.15 (( (product @ e_1 @ e_2 @ e_4)) | ( (product @ e_1 @ e_2 @ e_5)) |
% 4.10/1.15 ( (product @ e_1 @ e_2 @ e_3)) | ( (product @ e_1 @ e_2 @ e_2)) |
% 4.10/1.15 ( (product @ e_1 @ e_2 @ e_1))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl87])).
% 4.10/1.15 thf(zip_derived_cl550, plain,
% 4.10/1.15 (( (product @ e_3 @ e_5 @ e_2)) <= (( (product @ e_3 @ e_5 @ e_2)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl140])).
% 4.10/1.15 thf(zip_derived_cl1202, plain,
% 4.10/1.15 ((![X0 : $i]: (~ (product @ e_3 @ X0 @ e_2) | (equalish @ e_4 @ X0)))
% 4.10/1.15 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl1195, zip_derived_cl42])).
% 4.10/1.15 thf(zip_derived_cl1750, plain,
% 4.10/1.15 (( (equalish @ e_4 @ e_5))
% 4.10/1.15 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_3 @ e_5 @ e_2)))),
% 4.10/1.15 inference('s_sup-', [status(thm)],
% 4.10/1.15 [zip_derived_cl550, zip_derived_cl1202])).
% 4.10/1.15 thf(zip_derived_cl35, plain, (~ (equalish @ e_4 @ e_5)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_5])).
% 4.10/1.15 thf('61', plain,
% 4.10/1.15 (~ ( (product @ e_3 @ e_5 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_4))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl1750, zip_derived_cl35])).
% 4.10/1.15 thf('62', plain,
% 4.10/1.15 (( (product @ e_3 @ e_5 @ e_1)) | ( (product @ e_3 @ e_5 @ e_2)) |
% 4.10/1.15 ( (product @ e_3 @ e_5 @ e_5)) | ( (product @ e_3 @ e_5 @ e_3)) |
% 4.10/1.15 ( (product @ e_3 @ e_5 @ e_4))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl140])).
% 4.10/1.15 thf(zip_derived_cl551, plain,
% 4.10/1.15 (( (product @ e_3 @ e_5 @ e_1)) <= (( (product @ e_3 @ e_5 @ e_1)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl140])).
% 4.10/1.15 thf(zip_derived_cl507, plain,
% 4.10/1.15 (( (product @ e_3 @ e_2 @ e_1)) <= (( (product @ e_3 @ e_2 @ e_1)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl137])).
% 4.10/1.15 thf(zip_derived_cl42, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.15 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.15 | (equalish @ X1 @ X3))),
% 4.10/1.15 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.15 thf(zip_derived_cl1607, plain,
% 4.10/1.15 ((![X0 : $i]: (~ (product @ e_3 @ X0 @ e_1) | (equalish @ e_2 @ X0)))
% 4.10/1.15 <= (( (product @ e_3 @ e_2 @ e_1)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl507, zip_derived_cl42])).
% 4.10/1.15 thf(zip_derived_cl1770, plain,
% 4.10/1.15 (( (equalish @ e_2 @ e_5))
% 4.10/1.15 <= (( (product @ e_3 @ e_2 @ e_1)) & ( (product @ e_3 @ e_5 @ e_1)))),
% 4.10/1.15 inference('s_sup-', [status(thm)],
% 4.10/1.15 [zip_derived_cl551, zip_derived_cl1607])).
% 4.10/1.15 thf(zip_derived_cl27, plain, (~ (equalish @ e_2 @ e_5)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_2_is_not_e_5])).
% 4.10/1.15 thf('63', plain,
% 4.10/1.15 (~ ( (product @ e_3 @ e_2 @ e_1)) | ~ ( (product @ e_3 @ e_5 @ e_1))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl1770, zip_derived_cl27])).
% 4.10/1.15 thf('64', plain,
% 4.10/1.15 (( (product @ e_3 @ e_2 @ e_5)) | ( (product @ e_3 @ e_2 @ e_1)) |
% 4.10/1.15 ( (product @ e_3 @ e_2 @ e_3)) | ( (product @ e_3 @ e_2 @ e_2)) |
% 4.10/1.15 ( (product @ e_3 @ e_2 @ e_4))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl137])).
% 4.10/1.15 thf(zip_derived_cl690, plain,
% 4.10/1.15 (( (product @ e_4 @ e_2 @ e_5)) <= (( (product @ e_4 @ e_2 @ e_5)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl158])).
% 4.10/1.15 thf(zip_derived_cl503, plain,
% 4.10/1.15 (( (product @ e_3 @ e_2 @ e_5)) <= (( (product @ e_3 @ e_2 @ e_5)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl137])).
% 4.10/1.15 thf(zip_derived_cl43, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.15 | ~ (product @ X3 @ X1 @ X2)
% 4.10/1.15 | (equalish @ X0 @ X3))),
% 4.10/1.15 inference('cnf', [status(esa)], [product_left_cancellation])).
% 4.10/1.15 thf(zip_derived_cl510, plain,
% 4.10/1.15 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_5) | (equalish @ e_3 @ X0)))
% 4.10/1.15 <= (( (product @ e_3 @ e_2 @ e_5)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl503, zip_derived_cl43])).
% 4.10/1.15 thf(zip_derived_cl1000, plain,
% 4.10/1.15 (( (equalish @ e_3 @ e_4))
% 4.10/1.15 <= (( (product @ e_3 @ e_2 @ e_5)) & ( (product @ e_4 @ e_2 @ e_5)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl690, zip_derived_cl510])).
% 4.10/1.15 thf(zip_derived_cl30, plain, (~ (equalish @ e_3 @ e_4)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 4.10/1.15 thf('65', plain,
% 4.10/1.15 (~ ( (product @ e_4 @ e_2 @ e_5)) | ~ ( (product @ e_3 @ e_2 @ e_5))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl1000, zip_derived_cl30])).
% 4.10/1.15 thf(zip_derived_cl16, plain, ( (group_element @ e_2)),
% 4.10/1.15 inference('cnf', [status(esa)], [element_2])).
% 4.10/1.15 thf(zip_derived_cl57, plain,
% 4.10/1.15 (![X0 : $i]:
% 4.10/1.15 (~ (group_element @ X0)
% 4.10/1.15 | (product @ e_4 @ X0 @ e_1)
% 4.10/1.15 | (product @ e_4 @ X0 @ e_2)
% 4.10/1.15 | (product @ e_4 @ X0 @ e_3)
% 4.10/1.15 | (product @ e_4 @ X0 @ e_4)
% 4.10/1.15 | (product @ e_4 @ X0 @ e_5))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl40])).
% 4.10/1.15 thf(zip_derived_cl163, plain,
% 4.10/1.15 (( (product @ e_4 @ e_2 @ e_1)
% 4.10/1.15 | (product @ e_4 @ e_2 @ e_2)
% 4.10/1.15 | (product @ e_4 @ e_2 @ e_3)
% 4.10/1.15 | (product @ e_4 @ e_2 @ e_4)
% 4.10/1.15 | (product @ e_4 @ e_2 @ e_5))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl57])).
% 4.10/1.15 thf(zip_derived_cl777, plain,
% 4.10/1.15 (( (product @ e_4 @ e_2 @ e_4)) <= (( (product @ e_4 @ e_2 @ e_4)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl163])).
% 4.10/1.15 thf(zip_derived_cl60, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl42])).
% 4.10/1.15 thf(zip_derived_cl785, plain,
% 4.10/1.15 (( (equalish @ e_4 @ e_2)) <= (( (product @ e_4 @ e_2 @ e_4)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl777, zip_derived_cl60])).
% 4.10/1.15 thf(zip_derived_cl33, plain, (~ (equalish @ e_4 @ e_2)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 4.10/1.15 thf('66', plain, (~ ( (product @ e_4 @ e_2 @ e_4))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl785, zip_derived_cl33])).
% 4.10/1.15 thf(zip_derived_cl568, plain,
% 4.10/1.15 (( (product @ e_3 @ e_1 @ e_4)) <= (( (product @ e_3 @ e_1 @ e_4)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl141])).
% 4.10/1.15 thf(zip_derived_cl198, plain,
% 4.10/1.15 (( (product @ e_1 @ e_3 @ e_5)) <= (( (product @ e_1 @ e_3 @ e_5)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl88])).
% 4.10/1.15 thf(zip_derived_cl45, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.15 ( (product @ X0 @ X1 @ X2)
% 4.10/1.15 | ~ (product @ X3 @ X2 @ X1)
% 4.10/1.15 | ~ (product @ X2 @ X3 @ X0))),
% 4.10/1.15 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.10/1.15 thf(zip_derived_cl206, plain,
% 4.10/1.15 ((![X0 : $i]:
% 4.10/1.15 ( (product @ X0 @ e_5 @ e_3) | ~ (product @ e_3 @ e_1 @ X0)))
% 4.10/1.15 <= (( (product @ e_1 @ e_3 @ e_5)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl198, zip_derived_cl45])).
% 4.10/1.15 thf(zip_derived_cl577, plain,
% 4.10/1.15 (( (product @ e_4 @ e_5 @ e_3))
% 4.10/1.15 <= (( (product @ e_1 @ e_3 @ e_5)) & ( (product @ e_3 @ e_1 @ e_4)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl568, zip_derived_cl206])).
% 4.10/1.15 thf('67', plain, (( (product @ e_1 @ e_3 @ e_5))),
% 4.10/1.15 inference('sat_resolution*', [status(thm)],
% 4.10/1.15 ['2', '59', '3', '4', '5', '6', '7', '8', '9', '63', '10',
% 4.10/1.15 '11', '12', '62', '13', '14', '15', '16', '17', '18', '19',
% 4.10/1.15 '26', '27', '28', '61', '29', '30', '31', '32', '33', '34',
% 4.10/1.15 '35', '64', '36', '37', '38', '39', '40', '41', '42', '43',
% 4.10/1.15 '44', '45', '46', '47', '48', '49', '50', '51', '53', '55',
% 4.10/1.15 '60', '56', '57', '58'])).
% 4.10/1.15 thf('68', plain, (( (product @ e_3 @ e_1 @ e_4))),
% 4.10/1.15 inference('sat_resolution*', [status(thm)],
% 4.10/1.15 ['46', '47', '48', '49', '50', '51', '53', '55', '60', '56'])).
% 4.10/1.15 thf(zip_derived_cl1928, plain, ( (product @ e_4 @ e_5 @ e_3)),
% 4.10/1.15 inference('simpl_trail', [status(thm)], [zip_derived_cl577, '67', '68'])).
% 4.10/1.15 thf(zip_derived_cl692, plain,
% 4.10/1.15 (( (product @ e_4 @ e_2 @ e_3)) <= (( (product @ e_4 @ e_2 @ e_3)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl158])).
% 4.10/1.15 thf(zip_derived_cl42, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.15 | ~ (product @ X0 @ X3 @ X2)
% 4.10/1.15 | (equalish @ X1 @ X3))),
% 4.10/1.15 inference('cnf', [status(esa)], [product_right_cancellation])).
% 4.10/1.15 thf(zip_derived_cl1999, plain,
% 4.10/1.15 ((![X0 : $i]: (~ (product @ e_4 @ X0 @ e_3) | (equalish @ e_2 @ X0)))
% 4.10/1.15 <= (( (product @ e_4 @ e_2 @ e_3)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl692, zip_derived_cl42])).
% 4.10/1.15 thf(zip_derived_cl2155, plain,
% 4.10/1.15 (( (equalish @ e_2 @ e_5)) <= (( (product @ e_4 @ e_2 @ e_3)))),
% 4.10/1.15 inference('s_sup-', [status(thm)],
% 4.10/1.15 [zip_derived_cl1928, zip_derived_cl1999])).
% 4.10/1.15 thf(zip_derived_cl27, plain, (~ (equalish @ e_2 @ e_5)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_2_is_not_e_5])).
% 4.10/1.15 thf('69', plain, (~ ( (product @ e_4 @ e_2 @ e_3))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl2155, zip_derived_cl27])).
% 4.10/1.15 thf('70', plain,
% 4.10/1.15 (( (product @ e_4 @ e_2 @ e_1)) | ( (product @ e_4 @ e_2 @ e_3)) |
% 4.10/1.15 ( (product @ e_4 @ e_2 @ e_4)) | ( (product @ e_4 @ e_2 @ e_5)) |
% 4.10/1.15 ( (product @ e_4 @ e_2 @ e_2))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl158])).
% 4.10/1.15 thf('71', plain, (( (product @ e_4 @ e_2 @ e_1))),
% 4.10/1.15 inference('sat_resolution*', [status(thm)],
% 4.10/1.15 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 4.10/1.15 '12', '13', '14', '15', '16', '17', '18', '19', '26', '27',
% 4.10/1.15 '28', '29', '30', '31', '32', '33', '34', '35', '36', '37',
% 4.10/1.15 '38', '39', '40', '41', '42', '43', '44', '45', '46', '47',
% 4.10/1.15 '48', '49', '50', '51', '53', '55', '56', '57', '58', '59',
% 4.10/1.15 '60', '61', '62', '63', '64', '65', '66', '69', '70'])).
% 4.10/1.15 thf(zip_derived_cl2166, plain, ( (product @ e_4 @ e_2 @ e_1)),
% 4.10/1.15 inference('simpl_trail', [status(thm)], [zip_derived_cl694, '71'])).
% 4.10/1.15 thf(zip_derived_cl372, plain,
% 4.10/1.15 ((![X0 : $i]:
% 4.10/1.15 ( (product @ X0 @ e_5 @ e_4) | ~ (product @ e_4 @ e_2 @ X0)))
% 4.10/1.15 <= (( (product @ e_2 @ e_4 @ e_5)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl364, zip_derived_cl45])).
% 4.10/1.15 thf(zip_derived_cl344, plain,
% 4.10/1.15 (( (product @ e_2 @ e_3 @ e_5)) <= (( (product @ e_2 @ e_3 @ e_5)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl100])).
% 4.10/1.15 thf(zip_derived_cl198, plain,
% 4.10/1.15 (( (product @ e_1 @ e_3 @ e_5)) <= (( (product @ e_1 @ e_3 @ e_5)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl88])).
% 4.10/1.15 thf(zip_derived_cl43, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.15 | ~ (product @ X3 @ X1 @ X2)
% 4.10/1.15 | (equalish @ X0 @ X3))),
% 4.10/1.15 inference('cnf', [status(esa)], [product_left_cancellation])).
% 4.10/1.15 thf(zip_derived_cl205, plain,
% 4.10/1.15 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_5) | (equalish @ e_1 @ X0)))
% 4.10/1.15 <= (( (product @ e_1 @ e_3 @ e_5)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl198, zip_derived_cl43])).
% 4.10/1.15 thf(zip_derived_cl353, plain,
% 4.10/1.15 (( (equalish @ e_1 @ e_2))
% 4.10/1.15 <= (( (product @ e_1 @ e_3 @ e_5)) & ( (product @ e_2 @ e_3 @ e_5)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl344, zip_derived_cl205])).
% 4.10/1.15 thf(zip_derived_cl20, plain, (~ (equalish @ e_1 @ e_2)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 4.10/1.15 thf('72', plain,
% 4.10/1.15 (~ ( (product @ e_2 @ e_3 @ e_5)) | ~ ( (product @ e_1 @ e_3 @ e_5))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl353, zip_derived_cl20])).
% 4.10/1.15 thf(zip_derived_cl551, plain,
% 4.10/1.15 (( (product @ e_3 @ e_5 @ e_1)) <= (( (product @ e_3 @ e_5 @ e_1)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl140])).
% 4.10/1.15 thf(zip_derived_cl384, plain,
% 4.10/1.15 (( (product @ e_2 @ e_5 @ e_1)) <= (( (product @ e_2 @ e_5 @ e_1)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl102])).
% 4.10/1.15 thf(zip_derived_cl43, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.15 | ~ (product @ X3 @ X1 @ X2)
% 4.10/1.15 | (equalish @ X0 @ X3))),
% 4.10/1.15 inference('cnf', [status(esa)], [product_left_cancellation])).
% 4.10/1.15 thf(zip_derived_cl1368, plain,
% 4.10/1.15 ((![X0 : $i]: (~ (product @ X0 @ e_5 @ e_1) | (equalish @ e_2 @ X0)))
% 4.10/1.15 <= (( (product @ e_2 @ e_5 @ e_1)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl384, zip_derived_cl43])).
% 4.10/1.15 thf(zip_derived_cl1769, plain,
% 4.10/1.15 (( (equalish @ e_2 @ e_3))
% 4.10/1.15 <= (( (product @ e_2 @ e_5 @ e_1)) & ( (product @ e_3 @ e_5 @ e_1)))),
% 4.10/1.15 inference('s_sup-', [status(thm)],
% 4.10/1.15 [zip_derived_cl551, zip_derived_cl1368])).
% 4.10/1.15 thf(zip_derived_cl25, plain, (~ (equalish @ e_2 @ e_3)),
% 4.10/1.15 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 4.10/1.15 thf('73', plain,
% 4.10/1.15 (~ ( (product @ e_2 @ e_5 @ e_1)) | ~ ( (product @ e_3 @ e_5 @ e_1))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl1769, zip_derived_cl25])).
% 4.10/1.15 thf('74', plain, (( (product @ e_2 @ e_4 @ e_5))),
% 4.10/1.15 inference('sat_resolution*', [status(thm)],
% 4.10/1.15 ['72', '2', '3', '4', '5', '6', '7', '8', '9', '63', '11',
% 4.10/1.15 '12', '13', '14', '16', '18', '19', '26', '27', '29', '31',
% 4.10/1.15 '32', '33', '34', '35', '64', '36', '37', '38', '39', '40',
% 4.10/1.15 '41', '42', '43', '44', '45', '46', '47', '48', '49', '50',
% 4.10/1.15 '51', '53', '55', '56', '57', '58', '59', '60', '61', '62',
% 4.10/1.15 '73', '17', '15', '10', '28', '30'])).
% 4.10/1.15 thf(zip_derived_cl1905, plain,
% 4.10/1.15 (![X0 : $i]: ( (product @ X0 @ e_5 @ e_4) | ~ (product @ e_4 @ e_2 @ X0))),
% 4.10/1.15 inference('simpl_trail', [status(thm)], [zip_derived_cl372, '74'])).
% 4.10/1.15 thf(zip_derived_cl2405, plain, ( (product @ e_1 @ e_5 @ e_4)),
% 4.10/1.15 inference('s_sup-', [status(thm)],
% 4.10/1.15 [zip_derived_cl2166, zip_derived_cl1905])).
% 4.10/1.15 thf(zip_derived_cl462, plain,
% 4.10/1.15 (( (product @ e_2 @ e_5 @ e_4)) <= (( (product @ e_2 @ e_5 @ e_4)))),
% 4.10/1.15 inference('split', [status(esa)], [zip_derived_cl107])).
% 4.10/1.15 thf(zip_derived_cl43, plain,
% 4.10/1.15 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.10/1.15 (~ (product @ X0 @ X1 @ X2)
% 4.10/1.15 | ~ (product @ X3 @ X1 @ X2)
% 4.10/1.15 | (equalish @ X0 @ X3))),
% 4.10/1.15 inference('cnf', [status(esa)], [product_left_cancellation])).
% 4.10/1.15 thf(zip_derived_cl468, plain,
% 4.10/1.15 ((![X0 : $i]: (~ (product @ X0 @ e_5 @ e_4) | (equalish @ e_2 @ X0)))
% 4.10/1.15 <= (( (product @ e_2 @ e_5 @ e_4)))),
% 4.10/1.15 inference('s_sup-', [status(thm)], [zip_derived_cl462, zip_derived_cl43])).
% 4.10/1.15 thf('75', plain, (( (product @ e_2 @ e_5 @ e_4))),
% 4.10/1.15 inference('sat_resolution*', [status(thm)],
% 4.10/1.15 ['2', '3', '4', '5', '6', '7', '8', '9', '63', '10', '11',
% 4.10/1.15 '12', '13', '14', '15', '16', '18', '19', '26', '27', '28',
% 4.10/1.15 '29', '30', '31', '32', '33', '34', '35', '64', '36', '37',
% 4.10/1.15 '38', '39', '40', '41', '42', '43', '44', '45', '46', '47',
% 4.10/1.15 '48', '49', '50', '51', '53', '55', '56', '57', '58', '59',
% 4.10/1.15 '60', '61', '62', '73', '17'])).
% 4.10/1.15 thf(zip_derived_cl1913, plain,
% 4.10/1.15 (![X0 : $i]: (~ (product @ X0 @ e_5 @ e_4) | (equalish @ e_2 @ X0))),
% 4.10/1.15 inference('simpl_trail', [status(thm)], [zip_derived_cl468, '75'])).
% 4.10/1.15 thf(zip_derived_cl2414, plain, ( (equalish @ e_2 @ e_1)),
% 4.10/1.15 inference('s_sup-', [status(thm)],
% 4.10/1.15 [zip_derived_cl2405, zip_derived_cl1913])).
% 4.10/1.15 thf(zip_derived_cl2416, plain, ($false),
% 4.10/1.15 inference('demod', [status(thm)], [zip_derived_cl24, zip_derived_cl2414])).
% 4.10/1.15
% 4.10/1.15 % SZS output end Refutation
% 4.10/1.15
% 4.10/1.15
% 4.10/1.15 % Terminating...
% 4.10/1.25 % Runner terminated.
% 4.10/1.27 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------