TSTP Solution File: GRP129-2.004 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP129-2.004 : 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.JKQUAcRvDH true
% Computer : n003.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 01:50:13 EDT 2023
% Result : Unsatisfiable 7.48s 1.67s
% Output : Refutation 7.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP129-2.004 : TPTP v8.1.2. Released v1.2.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.JKQUAcRvDH true
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 01:35:10 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.57/0.65 % Total configuration time : 435
% 0.57/0.65 % Estimated wc time : 1092
% 0.57/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.57/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.57/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.57/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 7.48/1.67 % Solved by fo/fo1_av.sh.
% 7.48/1.67 % done 4241 iterations in 0.880s
% 7.48/1.67 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 7.48/1.67 % SZS output start Refutation
% 7.48/1.67 thf(group_element_type, type, group_element: $i > $o).
% 7.48/1.67 thf(e_4_type, type, e_4: $i).
% 7.48/1.67 thf(greater_type, type, greater: $i > $i > $o).
% 7.48/1.67 thf(equalish_type, type, equalish: $i > $i > $o).
% 7.48/1.67 thf(e_3_type, type, e_3: $i).
% 7.48/1.67 thf(e_2_type, type, e_2: $i).
% 7.48/1.67 thf(e_1_type, type, e_1: $i).
% 7.48/1.67 thf(next_type, type, next: $i > $i > $o).
% 7.48/1.67 thf(product_type, type, product: $i > $i > $i > $o).
% 7.48/1.67 thf(element_2, axiom, (group_element @ e_2)).
% 7.48/1.67 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_2])).
% 7.48/1.67 thf(product_total_function1, axiom,
% 7.48/1.67 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 7.48/1.67 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 7.48/1.67 ( product @ X @ Y @ e_3 ) | ( product @ X @ Y @ e_4 ))).
% 7.48/1.67 thf(zip_derived_cl26, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | ~ (group_element @ X1)
% 7.48/1.67 | (product @ X0 @ X1 @ e_1)
% 7.48/1.67 | (product @ X0 @ X1 @ e_2)
% 7.48/1.67 | (product @ X0 @ X1 @ e_3)
% 7.48/1.67 | (product @ X0 @ X1 @ e_4))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_total_function1])).
% 7.48/1.67 thf(zip_derived_cl33, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl26])).
% 7.48/1.67 thf(element_1, axiom, (group_element @ e_1)).
% 7.48/1.67 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_1])).
% 7.48/1.67 thf(zip_derived_cl61, plain,
% 7.48/1.67 (( (product @ e_2 @ e_1 @ e_4)
% 7.48/1.67 | (product @ e_2 @ e_1 @ e_3)
% 7.48/1.67 | (product @ e_2 @ e_1 @ e_2)
% 7.48/1.67 | (product @ e_2 @ e_1 @ e_1))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl33, zip_derived_cl10])).
% 7.48/1.67 thf(zip_derived_cl281, plain,
% 7.48/1.67 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl61])).
% 7.48/1.67 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_1])).
% 7.48/1.67 thf(zip_derived_cl26, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | ~ (group_element @ X1)
% 7.48/1.67 | (product @ X0 @ X1 @ e_1)
% 7.48/1.67 | (product @ X0 @ X1 @ e_2)
% 7.48/1.67 | (product @ X0 @ X1 @ e_3)
% 7.48/1.67 | (product @ X0 @ X1 @ e_4))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_total_function1])).
% 7.48/1.67 thf(zip_derived_cl32, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_2])).
% 7.48/1.67 thf(zip_derived_cl42, plain,
% 7.48/1.67 (( (product @ e_1 @ e_2 @ e_4)
% 7.48/1.67 | (product @ e_1 @ e_2 @ e_3)
% 7.48/1.67 | (product @ e_1 @ e_2 @ e_2)
% 7.48/1.67 | (product @ e_1 @ e_2 @ e_1))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl11])).
% 7.48/1.67 thf(zip_derived_cl141, plain,
% 7.48/1.67 (( (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl42])).
% 7.48/1.67 thf(qg3, conjecture,
% 7.48/1.67 (~( ( product @ Z1 @ Y @ Z2 ) | ( ~( product @ X @ Z1 @ Z2 ) ) |
% 7.48/1.67 ( ~( product @ Y @ X @ Z1 ) ) ))).
% 7.48/1.67 thf(zf_stmt_0, negated_conjecture,
% 7.48/1.67 (( product @ Z1 @ Y @ Z2 ) | ( ~( product @ X @ Z1 @ Z2 ) ) |
% 7.48/1.67 ( ~( product @ Y @ X @ Z1 ) )),
% 7.48/1.67 inference('cnf.neg', [status(esa)], [qg3])).
% 7.48/1.67 thf(zip_derived_cl30, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 ( (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.67 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.67 thf(zip_derived_cl148, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_2 @ X0 @ e_4) | ~ (product @ X0 @ e_1 @ e_2)))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl141, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl1018, plain,
% 7.48/1.67 (( (product @ e_2 @ e_2 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl281, zip_derived_cl148])).
% 7.48/1.67 thf(zip_derived_cl141, plain,
% 7.48/1.67 (( (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl42])).
% 7.48/1.67 thf(product_left_cancellation, axiom,
% 7.48/1.67 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 7.48/1.67 ( equalish @ W @ Z ))).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl147, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_4) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl141, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl2885, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_2))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)],
% 7.48/1.67 [zip_derived_cl1018, zip_derived_cl147])).
% 7.48/1.67 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 7.48/1.67 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 7.48/1.67 thf('0', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_2 @ e_4)) | ~ ( (product @ e_2 @ e_1 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2885, zip_derived_cl14])).
% 7.48/1.67 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_2])).
% 7.48/1.67 thf(element_3, axiom, (group_element @ e_3)).
% 7.48/1.67 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_3])).
% 7.48/1.67 thf(zip_derived_cl26, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | ~ (group_element @ X1)
% 7.48/1.67 | (product @ X0 @ X1 @ e_1)
% 7.48/1.67 | (product @ X0 @ X1 @ e_2)
% 7.48/1.67 | (product @ X0 @ X1 @ e_3)
% 7.48/1.67 | (product @ X0 @ X1 @ e_4))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_total_function1])).
% 7.48/1.67 thf(zip_derived_cl34, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl98, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_1)
% 7.48/1.67 | (product @ e_3 @ e_2 @ e_2)
% 7.48/1.67 | (product @ e_3 @ e_2 @ e_3)
% 7.48/1.67 | (product @ e_3 @ e_2 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl34])).
% 7.48/1.67 thf(zip_derived_cl510, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_3)) <= (( (product @ e_3 @ e_2 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl98])).
% 7.48/1.67 thf(zip_derived_cl33, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_3])).
% 7.48/1.67 thf(zip_derived_cl63, plain,
% 7.48/1.67 (( (product @ e_2 @ e_3 @ e_4)
% 7.48/1.67 | (product @ e_2 @ e_3 @ e_3)
% 7.48/1.67 | (product @ e_2 @ e_3 @ e_2)
% 7.48/1.67 | (product @ e_2 @ e_3 @ e_1))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl33, zip_derived_cl12])).
% 7.48/1.67 thf(zip_derived_cl317, plain,
% 7.48/1.67 (( (product @ e_2 @ e_3 @ e_4)) <= (( (product @ e_2 @ e_3 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl63])).
% 7.48/1.67 thf(zip_derived_cl30, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 ( (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.67 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.67 thf(zip_derived_cl324, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_3 @ X0 @ e_4) | ~ (product @ X0 @ e_2 @ e_3)))
% 7.48/1.67 <= (( (product @ e_2 @ e_3 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl317, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl1166, plain,
% 7.48/1.67 (( (product @ e_3 @ e_3 @ e_4))
% 7.48/1.67 <= (( (product @ e_2 @ e_3 @ e_4)) & ( (product @ e_3 @ e_2 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl510, zip_derived_cl324])).
% 7.48/1.67 thf(zip_derived_cl317, plain,
% 7.48/1.67 (( (product @ e_2 @ e_3 @ e_4)) <= (( (product @ e_2 @ e_3 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl63])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl323, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_4) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_2 @ e_3 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl317, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl3613, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_2 @ e_3 @ e_4)) & ( (product @ e_3 @ e_2 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)],
% 7.48/1.67 [zip_derived_cl1166, zip_derived_cl323])).
% 7.48/1.67 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 7.48/1.67 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 7.48/1.67 thf('1', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_2 @ e_3)) | ~ ( (product @ e_2 @ e_3 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl3613, zip_derived_cl18])).
% 7.48/1.67 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_2])).
% 7.48/1.67 thf(zip_derived_cl26, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | ~ (group_element @ X1)
% 7.48/1.67 | (product @ X0 @ X1 @ e_1)
% 7.48/1.67 | (product @ X0 @ X1 @ e_2)
% 7.48/1.67 | (product @ X0 @ X1 @ e_3)
% 7.48/1.67 | (product @ X0 @ X1 @ e_4))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_total_function1])).
% 7.48/1.67 thf(zip_derived_cl36, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 ( (product @ X0 @ X0 @ e_4)
% 7.48/1.67 | (product @ X0 @ X0 @ e_3)
% 7.48/1.67 | (product @ X0 @ X0 @ e_2)
% 7.48/1.67 | (product @ X0 @ X0 @ e_1)
% 7.48/1.67 | ~ (group_element @ X0))),
% 7.48/1.67 inference('eq_fact', [status(thm)], [zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl130, plain,
% 7.48/1.67 (( (product @ e_2 @ e_2 @ e_4)
% 7.48/1.67 | (product @ e_2 @ e_2 @ e_3)
% 7.48/1.67 | (product @ e_2 @ e_2 @ e_2)
% 7.48/1.67 | (product @ e_2 @ e_2 @ e_1))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl36])).
% 7.48/1.67 thf(zip_derived_cl724, plain,
% 7.48/1.67 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl130])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl728, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_2) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_2 @ e_2 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl724, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl34, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_2])).
% 7.48/1.67 thf(zip_derived_cl94, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_4)
% 7.48/1.67 | (product @ e_3 @ e_2 @ e_3)
% 7.48/1.67 | (product @ e_3 @ e_2 @ e_2)
% 7.48/1.67 | (product @ e_3 @ e_2 @ e_1))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl11])).
% 7.48/1.67 thf(zip_derived_cl441, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_2)) <= (( (product @ e_3 @ e_2 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl94])).
% 7.48/1.67 thf(zip_derived_cl2144, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_2 @ e_2 @ e_2)) & ( (product @ e_3 @ e_2 @ e_2)))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl728, zip_derived_cl441])).
% 7.48/1.67 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 7.48/1.67 thf('2', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_2 @ e_2)) | ~ ( (product @ e_2 @ e_2 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2144, zip_derived_cl18])).
% 7.48/1.67 thf(zip_derived_cl320, plain,
% 7.48/1.67 (( (product @ e_2 @ e_3 @ e_1)) <= (( (product @ e_2 @ e_3 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl63])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl1148, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_1) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_2 @ e_3 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl320, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl34, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_3])).
% 7.48/1.67 thf(zip_derived_cl95, plain,
% 7.48/1.67 (( (product @ e_3 @ e_3 @ e_4)
% 7.48/1.67 | (product @ e_3 @ e_3 @ e_3)
% 7.48/1.67 | (product @ e_3 @ e_3 @ e_2)
% 7.48/1.67 | (product @ e_3 @ e_3 @ e_1))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl12])).
% 7.48/1.67 thf(zip_derived_cl458, plain,
% 7.48/1.67 (( (product @ e_3 @ e_3 @ e_1)) <= (( (product @ e_3 @ e_3 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl95])).
% 7.48/1.67 thf(zip_derived_cl2647, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_2 @ e_3 @ e_1)) & ( (product @ e_3 @ e_3 @ e_1)))),
% 7.48/1.67 inference('s_sup+', [status(thm)],
% 7.48/1.67 [zip_derived_cl1148, zip_derived_cl458])).
% 7.48/1.67 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 7.48/1.67 thf('3', plain,
% 7.48/1.67 (~ ( (product @ e_2 @ e_3 @ e_1)) | ~ ( (product @ e_3 @ e_3 @ e_1))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2647, zip_derived_cl18])).
% 7.48/1.67 thf(zip_derived_cl33, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_2])).
% 7.48/1.67 thf(zip_derived_cl62, plain,
% 7.48/1.67 (( (product @ e_2 @ e_2 @ e_4)
% 7.48/1.67 | (product @ e_2 @ e_2 @ e_3)
% 7.48/1.67 | (product @ e_2 @ e_2 @ e_2)
% 7.48/1.67 | (product @ e_2 @ e_2 @ e_1))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl33, zip_derived_cl11])).
% 7.48/1.67 thf(zip_derived_cl306, plain,
% 7.48/1.67 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl62])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl1072, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_1) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_2 @ e_2 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl306, zip_derived_cl29])).
% 7.48/1.67 thf(element_4, axiom, (group_element @ e_4)).
% 7.48/1.67 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_4])).
% 7.48/1.67 thf(zip_derived_cl26, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | ~ (group_element @ X1)
% 7.48/1.67 | (product @ X0 @ X1 @ e_1)
% 7.48/1.67 | (product @ X0 @ X1 @ e_2)
% 7.48/1.67 | (product @ X0 @ X1 @ e_3)
% 7.48/1.67 | (product @ X0 @ X1 @ e_4))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_total_function1])).
% 7.48/1.67 thf(zip_derived_cl35, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_2])).
% 7.48/1.67 thf(zip_derived_cl113, plain,
% 7.48/1.67 (( (product @ e_4 @ e_2 @ e_4)
% 7.48/1.67 | (product @ e_4 @ e_2 @ e_3)
% 7.48/1.67 | (product @ e_4 @ e_2 @ e_2)
% 7.48/1.67 | (product @ e_4 @ e_2 @ e_1))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl11])).
% 7.48/1.67 thf(zip_derived_cl593, plain,
% 7.48/1.67 (( (product @ e_4 @ e_2 @ e_1)) <= (( (product @ e_4 @ e_2 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl113])).
% 7.48/1.67 thf(zip_derived_cl2554, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_4))
% 7.48/1.67 <= (( (product @ e_2 @ e_2 @ e_1)) & ( (product @ e_4 @ e_2 @ e_1)))),
% 7.48/1.67 inference('s_sup+', [status(thm)],
% 7.48/1.67 [zip_derived_cl1072, zip_derived_cl593])).
% 7.48/1.67 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 7.48/1.67 thf(zip_derived_cl19, plain, (~ (equalish @ e_2 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 7.48/1.67 thf('4', plain,
% 7.48/1.67 (~ ( (product @ e_2 @ e_2 @ e_1)) | ~ ( (product @ e_4 @ e_2 @ e_1))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2554, zip_derived_cl19])).
% 7.48/1.67 thf('5', plain,
% 7.48/1.67 (( (product @ e_3 @ e_3 @ e_1)) | ( (product @ e_3 @ e_3 @ e_3)) |
% 7.48/1.67 ( (product @ e_3 @ e_3 @ e_2)) | ( (product @ e_3 @ e_3 @ e_4))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl95])).
% 7.48/1.67 thf('6', plain,
% 7.48/1.67 (( (product @ e_4 @ e_2 @ e_1)) | ( (product @ e_4 @ e_2 @ e_3)) |
% 7.48/1.67 ( (product @ e_4 @ e_2 @ e_4)) | ( (product @ e_4 @ e_2 @ e_2))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl113])).
% 7.48/1.67 thf(zip_derived_cl455, plain,
% 7.48/1.67 (( (product @ e_3 @ e_3 @ e_4)) <= (( (product @ e_3 @ e_3 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl95])).
% 7.48/1.67 thf(zip_derived_cl34, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_1])).
% 7.48/1.67 thf(zip_derived_cl93, plain,
% 7.48/1.67 (( (product @ e_3 @ e_1 @ e_4)
% 7.48/1.67 | (product @ e_3 @ e_1 @ e_3)
% 7.48/1.67 | (product @ e_3 @ e_1 @ e_2)
% 7.48/1.67 | (product @ e_3 @ e_1 @ e_1))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl10])).
% 7.48/1.67 thf(zip_derived_cl420, plain,
% 7.48/1.67 (( (product @ e_3 @ e_1 @ e_4)) <= (( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl93])).
% 7.48/1.67 thf(product_right_cancellation, axiom,
% 7.48/1.67 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 7.48/1.67 ( equalish @ W @ Z ))).
% 7.48/1.67 thf(zip_derived_cl28, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.67 | (equalish @ X1 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.67 thf(zip_derived_cl425, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_3 @ X0 @ e_4) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl420, zip_derived_cl28])).
% 7.48/1.67 thf(zip_derived_cl1306, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_3))
% 7.48/1.67 <= (( (product @ e_3 @ e_1 @ e_4)) & ( (product @ e_3 @ e_3 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl455, zip_derived_cl425])).
% 7.48/1.67 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 7.48/1.67 thf(zip_derived_cl15, plain, (~ (equalish @ e_1 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 7.48/1.67 thf('7', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_3 @ e_4)) | ~ ( (product @ e_3 @ e_1 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1306, zip_derived_cl15])).
% 7.48/1.67 thf(zip_derived_cl420, plain,
% 7.48/1.67 (( (product @ e_3 @ e_1 @ e_4)) <= (( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl93])).
% 7.48/1.67 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_4])).
% 7.48/1.67 thf(zip_derived_cl32, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl48, plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_1)
% 7.48/1.67 | (product @ e_1 @ e_4 @ e_2)
% 7.48/1.67 | (product @ e_1 @ e_4 @ e_3)
% 7.48/1.67 | (product @ e_1 @ e_4 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl32])).
% 7.48/1.67 thf(zip_derived_cl269, plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_3)) <= (( (product @ e_1 @ e_4 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl48])).
% 7.48/1.67 thf(zip_derived_cl30, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 ( (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.67 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.67 thf(zip_derived_cl275, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_4 @ X0 @ e_3) | ~ (product @ X0 @ e_1 @ e_4)))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl269, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl989, plain,
% 7.48/1.67 (( (product @ e_4 @ e_3 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_3)) & ( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl420, zip_derived_cl275])).
% 7.48/1.67 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_3])).
% 7.48/1.67 thf(zip_derived_cl34, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl99, plain,
% 7.48/1.67 (( (product @ e_3 @ e_3 @ e_1)
% 7.48/1.67 | (product @ e_3 @ e_3 @ e_2)
% 7.48/1.67 | (product @ e_3 @ e_3 @ e_3)
% 7.48/1.67 | (product @ e_3 @ e_3 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl34])).
% 7.48/1.67 thf(zip_derived_cl533, plain,
% 7.48/1.67 (( (product @ e_3 @ e_3 @ e_3)) <= (( (product @ e_3 @ e_3 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl99])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl538, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_3) | (equalish @ e_3 @ X0)))
% 7.48/1.67 <= (( (product @ e_3 @ e_3 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl533, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl2335, plain,
% 7.48/1.67 (( (equalish @ e_3 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_3)) &
% 7.48/1.67 ( (product @ e_3 @ e_1 @ e_4)) &
% 7.48/1.67 ( (product @ e_3 @ e_3 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl989, zip_derived_cl538])).
% 7.48/1.67 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 7.48/1.67 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 7.48/1.67 thf('8', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_3 @ e_3)) | ~ ( (product @ e_3 @ e_1 @ e_4)) |
% 7.48/1.67 ~ ( (product @ e_1 @ e_4 @ e_3))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2335, zip_derived_cl22])).
% 7.48/1.67 thf(zip_derived_cl989, plain,
% 7.48/1.67 (( (product @ e_4 @ e_3 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_3)) & ( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl420, zip_derived_cl275])).
% 7.48/1.67 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_2])).
% 7.48/1.67 thf(zip_derived_cl35, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl117, plain,
% 7.48/1.67 (( (product @ e_4 @ e_2 @ e_1)
% 7.48/1.67 | (product @ e_4 @ e_2 @ e_2)
% 7.48/1.67 | (product @ e_4 @ e_2 @ e_3)
% 7.48/1.67 | (product @ e_4 @ e_2 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl35])).
% 7.48/1.67 thf(zip_derived_cl661, plain,
% 7.48/1.67 (( (product @ e_4 @ e_2 @ e_3)) <= (( (product @ e_4 @ e_2 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl117])).
% 7.48/1.67 thf(zip_derived_cl28, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.67 | (equalish @ X1 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.67 thf(zip_derived_cl665, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_4 @ X0 @ e_3) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_4 @ e_2 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl661, zip_derived_cl28])).
% 7.48/1.67 thf(zip_derived_cl2339, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_3)) &
% 7.48/1.67 ( (product @ e_3 @ e_1 @ e_4)) &
% 7.48/1.67 ( (product @ e_4 @ e_2 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl989, zip_derived_cl665])).
% 7.48/1.67 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 7.48/1.67 thf('9', plain,
% 7.48/1.67 (~ ( (product @ e_4 @ e_2 @ e_3)) | ~ ( (product @ e_3 @ e_1 @ e_4)) |
% 7.48/1.67 ~ ( (product @ e_1 @ e_4 @ e_3))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2339, zip_derived_cl18])).
% 7.48/1.67 thf(zip_derived_cl989, plain,
% 7.48/1.67 (( (product @ e_4 @ e_3 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_3)) & ( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl420, zip_derived_cl275])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl2327, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_3) | (equalish @ e_4 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_3)) & ( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl989, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl442, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_1)) <= (( (product @ e_3 @ e_2 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl94])).
% 7.48/1.67 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_1])).
% 7.48/1.67 thf(zip_derived_cl33, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl65, plain,
% 7.48/1.67 (( (product @ e_2 @ e_1 @ e_1)
% 7.48/1.67 | (product @ e_2 @ e_1 @ e_2)
% 7.48/1.67 | (product @ e_2 @ e_1 @ e_3)
% 7.48/1.67 | (product @ e_2 @ e_1 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl33])).
% 7.48/1.67 thf(zip_derived_cl348, plain,
% 7.48/1.67 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl65])).
% 7.48/1.67 thf(zip_derived_cl30, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 ( (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.67 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.67 thf(zip_derived_cl354, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_1 @ X0 @ e_3) | ~ (product @ X0 @ e_2 @ e_1)))
% 7.48/1.67 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl1567, plain,
% 7.48/1.67 (( (product @ e_1 @ e_3 @ e_3))
% 7.48/1.67 <= (( (product @ e_2 @ e_1 @ e_3)) & ( (product @ e_3 @ e_2 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl442, zip_derived_cl354])).
% 7.48/1.67 thf(zip_derived_cl6513, plain,
% 7.48/1.67 (( (equalish @ e_4 @ e_1))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_3)) &
% 7.48/1.67 ( (product @ e_2 @ e_1 @ e_3)) &
% 7.48/1.67 ( (product @ e_3 @ e_1 @ e_4)) &
% 7.48/1.67 ( (product @ e_3 @ e_2 @ e_1)))),
% 7.48/1.67 inference('s_sup+', [status(thm)],
% 7.48/1.67 [zip_derived_cl2327, zip_derived_cl1567])).
% 7.48/1.67 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 7.48/1.67 thf(zip_derived_cl23, plain, (~ (equalish @ e_4 @ e_1)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 7.48/1.67 thf('10', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_2 @ e_1)) | ~ ( (product @ e_3 @ e_1 @ e_4)) |
% 7.48/1.67 ~ ( (product @ e_2 @ e_1 @ e_3)) | ~ ( (product @ e_1 @ e_4 @ e_3))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl6513, zip_derived_cl23])).
% 7.48/1.67 thf(zip_derived_cl35, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_1])).
% 7.48/1.67 thf(zip_derived_cl112, plain,
% 7.48/1.67 (( (product @ e_4 @ e_1 @ e_4)
% 7.48/1.67 | (product @ e_4 @ e_1 @ e_3)
% 7.48/1.67 | (product @ e_4 @ e_1 @ e_2)
% 7.48/1.67 | (product @ e_4 @ e_1 @ e_1))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl10])).
% 7.48/1.67 thf(zip_derived_cl572, plain,
% 7.48/1.67 (( (product @ e_4 @ e_1 @ e_2)) <= (( (product @ e_4 @ e_1 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl112])).
% 7.48/1.67 thf(zip_derived_cl28, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.67 | (equalish @ X1 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.67 thf(zip_derived_cl1941, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_4 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_4 @ e_1 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl572, zip_derived_cl28])).
% 7.48/1.67 thf(zip_derived_cl592, plain,
% 7.48/1.67 (( (product @ e_4 @ e_2 @ e_2)) <= (( (product @ e_4 @ e_2 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl113])).
% 7.48/1.67 thf(zip_derived_cl3291, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_2))
% 7.48/1.67 <= (( (product @ e_4 @ e_1 @ e_2)) & ( (product @ e_4 @ e_2 @ e_2)))),
% 7.48/1.67 inference('s_sup+', [status(thm)],
% 7.48/1.67 [zip_derived_cl1941, zip_derived_cl592])).
% 7.48/1.67 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 7.48/1.67 thf('11', plain,
% 7.48/1.67 (~ ( (product @ e_4 @ e_2 @ e_2)) | ~ ( (product @ e_4 @ e_1 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl3291, zip_derived_cl14])).
% 7.48/1.67 thf(zip_derived_cl590, plain,
% 7.48/1.67 (( (product @ e_4 @ e_2 @ e_4)) <= (( (product @ e_4 @ e_2 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl113])).
% 7.48/1.67 thf(zip_derived_cl147, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_4) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl141, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl601, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_4 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl590, zip_derived_cl147])).
% 7.48/1.67 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 7.48/1.67 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 7.48/1.67 thf('12', plain,
% 7.48/1.67 (~ ( (product @ e_4 @ e_2 @ e_4)) | ~ ( (product @ e_1 @ e_2 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl601, zip_derived_cl16])).
% 7.48/1.67 thf(zip_derived_cl570, plain,
% 7.48/1.67 (( (product @ e_4 @ e_1 @ e_4)) <= (( (product @ e_4 @ e_1 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl112])).
% 7.48/1.67 thf(zip_derived_cl275, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_4 @ X0 @ e_3) | ~ (product @ X0 @ e_1 @ e_4)))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl269, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl990, plain,
% 7.48/1.67 (( (product @ e_4 @ e_4 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_3)) & ( (product @ e_4 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl570, zip_derived_cl275])).
% 7.48/1.67 thf(zip_derived_cl269, plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_3)) <= (( (product @ e_1 @ e_4 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl48])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl274, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_3) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl269, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl2819, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_3)) & ( (product @ e_4 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl990, zip_derived_cl274])).
% 7.48/1.67 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 7.48/1.67 thf('13', plain,
% 7.48/1.67 (~ ( (product @ e_4 @ e_1 @ e_4)) | ~ ( (product @ e_1 @ e_4 @ e_3))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2819, zip_derived_cl16])).
% 7.48/1.67 thf(zip_derived_cl441, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_2)) <= (( (product @ e_3 @ e_2 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl94])).
% 7.48/1.67 thf(zip_derived_cl303, plain,
% 7.48/1.67 (( (product @ e_2 @ e_2 @ e_4)) <= (( (product @ e_2 @ e_2 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl62])).
% 7.48/1.67 thf(zip_derived_cl30, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 ( (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.67 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.67 thf(zip_derived_cl310, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_2 @ X0 @ e_4) | ~ (product @ X0 @ e_2 @ e_2)))
% 7.48/1.67 <= (( (product @ e_2 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl303, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl1549, plain,
% 7.48/1.67 (( (product @ e_2 @ e_3 @ e_4))
% 7.48/1.67 <= (( (product @ e_2 @ e_2 @ e_4)) & ( (product @ e_3 @ e_2 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl441, zip_derived_cl310])).
% 7.48/1.67 thf(zip_derived_cl420, plain,
% 7.48/1.67 (( (product @ e_3 @ e_1 @ e_4)) <= (( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl93])).
% 7.48/1.67 thf(zip_derived_cl32, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_4])).
% 7.48/1.67 thf(zip_derived_cl44, plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_4)
% 7.48/1.67 | (product @ e_1 @ e_4 @ e_3)
% 7.48/1.67 | (product @ e_1 @ e_4 @ e_2)
% 7.48/1.67 | (product @ e_1 @ e_4 @ e_1))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl13])).
% 7.48/1.67 thf(zip_derived_cl185, plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl44])).
% 7.48/1.67 thf(zip_derived_cl30, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 ( (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.67 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.67 thf(zip_derived_cl192, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_4 @ X0 @ e_4) | ~ (product @ X0 @ e_1 @ e_4)))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl883, plain,
% 7.48/1.67 (( (product @ e_4 @ e_3 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)) & ( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl420, zip_derived_cl192])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl898, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_4) | (equalish @ e_4 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)) & ( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl883, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl4543, plain,
% 7.48/1.67 (( (equalish @ e_4 @ e_2))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)) &
% 7.48/1.67 ( (product @ e_2 @ e_2 @ e_4)) &
% 7.48/1.67 ( (product @ e_3 @ e_1 @ e_4)) &
% 7.48/1.67 ( (product @ e_3 @ e_2 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)],
% 7.48/1.67 [zip_derived_cl1549, zip_derived_cl898])).
% 7.48/1.67 thf(e_4_is_not_e_2, axiom, (~( equalish @ e_4 @ e_2 ))).
% 7.48/1.67 thf(zip_derived_cl24, plain, (~ (equalish @ e_4 @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 7.48/1.67 thf('14', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_2 @ e_2)) | ~ ( (product @ e_2 @ e_2 @ e_4)) |
% 7.48/1.67 ~ ( (product @ e_3 @ e_1 @ e_4)) | ~ ( (product @ e_1 @ e_4 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl4543, zip_derived_cl24])).
% 7.48/1.67 thf(zip_derived_cl883, plain,
% 7.48/1.67 (( (product @ e_4 @ e_3 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)) & ( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl420, zip_derived_cl192])).
% 7.48/1.67 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_4])).
% 7.48/1.67 thf(zip_derived_cl34, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl100, plain,
% 7.48/1.67 (( (product @ e_3 @ e_4 @ e_1)
% 7.48/1.67 | (product @ e_3 @ e_4 @ e_2)
% 7.48/1.67 | (product @ e_3 @ e_4 @ e_3)
% 7.48/1.67 | (product @ e_3 @ e_4 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl34])).
% 7.48/1.67 thf(zip_derived_cl550, plain,
% 7.48/1.67 (( (product @ e_3 @ e_4 @ e_3)) <= (( (product @ e_3 @ e_4 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl100])).
% 7.48/1.67 thf(zip_derived_cl30, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 ( (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.67 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.67 thf(zip_derived_cl556, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_4 @ X0 @ e_3) | ~ (product @ X0 @ e_3 @ e_4)))
% 7.48/1.67 <= (( (product @ e_3 @ e_4 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl550, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl1898, plain,
% 7.48/1.67 (( (product @ e_4 @ e_4 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)) &
% 7.48/1.67 ( (product @ e_3 @ e_1 @ e_4)) &
% 7.48/1.67 ( (product @ e_3 @ e_4 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl883, zip_derived_cl556])).
% 7.48/1.67 thf(zip_derived_cl550, plain,
% 7.48/1.67 (( (product @ e_3 @ e_4 @ e_3)) <= (( (product @ e_3 @ e_4 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl100])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl555, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_3) | (equalish @ e_3 @ X0)))
% 7.48/1.67 <= (( (product @ e_3 @ e_4 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl550, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl1919, plain,
% 7.48/1.67 (( (equalish @ e_3 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)) &
% 7.48/1.67 ( (product @ e_3 @ e_1 @ e_4)) &
% 7.48/1.67 ( (product @ e_3 @ e_4 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)],
% 7.48/1.67 [zip_derived_cl1898, zip_derived_cl555])).
% 7.48/1.67 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 7.48/1.67 thf('15', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_4 @ e_3)) | ~ ( (product @ e_3 @ e_1 @ e_4)) |
% 7.48/1.67 ~ ( (product @ e_1 @ e_4 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1919, zip_derived_cl22])).
% 7.48/1.67 thf(zip_derived_cl34, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_3 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_4])).
% 7.48/1.67 thf(zip_derived_cl96, plain,
% 7.48/1.67 (( (product @ e_3 @ e_4 @ e_4)
% 7.48/1.67 | (product @ e_3 @ e_4 @ e_3)
% 7.48/1.67 | (product @ e_3 @ e_4 @ e_2)
% 7.48/1.67 | (product @ e_3 @ e_4 @ e_1))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl13])).
% 7.48/1.67 thf(zip_derived_cl474, plain,
% 7.48/1.67 (( (product @ e_3 @ e_4 @ e_4)) <= (( (product @ e_3 @ e_4 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl96])).
% 7.48/1.67 thf(zip_derived_cl185, plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl44])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl191, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_4) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl783, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)) & ( (product @ e_3 @ e_4 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl474, zip_derived_cl191])).
% 7.48/1.67 thf(zip_derived_cl15, plain, (~ (equalish @ e_1 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 7.48/1.67 thf('16', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_4 @ e_4)) | ~ ( (product @ e_1 @ e_4 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl783, zip_derived_cl15])).
% 7.48/1.67 thf(zip_derived_cl510, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_3)) <= (( (product @ e_3 @ e_2 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl98])).
% 7.48/1.67 thf(zip_derived_cl142, plain,
% 7.48/1.67 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl42])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl180, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl709, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_3 @ e_2 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl510, zip_derived_cl180])).
% 7.48/1.67 thf(zip_derived_cl15, plain, (~ (equalish @ e_1 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 7.48/1.67 thf('17', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_2 @ e_3)) | ~ ( (product @ e_3 @ e_2 @ e_3))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl709, zip_derived_cl15])).
% 7.48/1.67 thf(zip_derived_cl439, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_4)) <= (( (product @ e_3 @ e_2 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl94])).
% 7.48/1.67 thf(zip_derived_cl303, plain,
% 7.48/1.67 (( (product @ e_2 @ e_2 @ e_4)) <= (( (product @ e_2 @ e_2 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl62])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl309, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_4) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_2 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl303, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl981, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_2 @ e_2 @ e_4)) & ( (product @ e_3 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl439, zip_derived_cl309])).
% 7.48/1.67 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 7.48/1.67 thf('18', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_2 @ e_4)) | ~ ( (product @ e_2 @ e_2 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl981, zip_derived_cl18])).
% 7.48/1.67 thf(zip_derived_cl303, plain,
% 7.48/1.67 (( (product @ e_2 @ e_2 @ e_4)) <= (( (product @ e_2 @ e_2 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl62])).
% 7.48/1.67 thf(zip_derived_cl147, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_4) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl141, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl343, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_2))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_2 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl303, zip_derived_cl147])).
% 7.48/1.67 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 7.48/1.67 thf('19', plain,
% 7.48/1.67 (~ ( (product @ e_2 @ e_2 @ e_4)) | ~ ( (product @ e_1 @ e_2 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl343, zip_derived_cl14])).
% 7.48/1.67 thf(zip_derived_cl33, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_2 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_4])).
% 7.48/1.67 thf(zip_derived_cl64, plain,
% 7.48/1.67 (( (product @ e_2 @ e_4 @ e_4)
% 7.48/1.67 | (product @ e_2 @ e_4 @ e_3)
% 7.48/1.67 | (product @ e_2 @ e_4 @ e_2)
% 7.48/1.67 | (product @ e_2 @ e_4 @ e_1))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl33, zip_derived_cl13])).
% 7.48/1.67 thf(zip_derived_cl332, plain,
% 7.48/1.67 (( (product @ e_2 @ e_4 @ e_2)) <= (( (product @ e_2 @ e_4 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl64])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl1188, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_2) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_2 @ e_4 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl332, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl476, plain,
% 7.48/1.67 (( (product @ e_3 @ e_4 @ e_2)) <= (( (product @ e_3 @ e_4 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl96])).
% 7.48/1.67 thf(zip_derived_cl2699, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_2 @ e_4 @ e_2)) & ( (product @ e_3 @ e_4 @ e_2)))),
% 7.48/1.67 inference('s_sup+', [status(thm)],
% 7.48/1.67 [zip_derived_cl1188, zip_derived_cl476])).
% 7.48/1.67 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 7.48/1.67 thf('20', plain,
% 7.48/1.67 (~ ( (product @ e_2 @ e_4 @ e_2)) | ~ ( (product @ e_3 @ e_4 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2699, zip_derived_cl18])).
% 7.48/1.67 thf(zip_derived_cl442, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_1)) <= (( (product @ e_3 @ e_2 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl94])).
% 7.48/1.67 thf(zip_derived_cl28, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.67 | (equalish @ X1 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.67 thf(zip_derived_cl1559, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_3 @ X0 @ e_1) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_3 @ e_2 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl442, zip_derived_cl28])).
% 7.48/1.67 thf(zip_derived_cl477, plain,
% 7.48/1.67 (( (product @ e_3 @ e_4 @ e_1)) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl96])).
% 7.48/1.67 thf(zip_derived_cl3028, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_4))
% 7.48/1.67 <= (( (product @ e_3 @ e_2 @ e_1)) & ( (product @ e_3 @ e_4 @ e_1)))),
% 7.48/1.67 inference('s_sup+', [status(thm)],
% 7.48/1.67 [zip_derived_cl1559, zip_derived_cl477])).
% 7.48/1.67 thf(zip_derived_cl19, plain, (~ (equalish @ e_2 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 7.48/1.67 thf('21', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_2 @ e_1)) | ~ ( (product @ e_3 @ e_4 @ e_1))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl3028, zip_derived_cl19])).
% 7.48/1.67 thf(zip_derived_cl883, plain,
% 7.48/1.67 (( (product @ e_4 @ e_3 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)) & ( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl420, zip_derived_cl192])).
% 7.48/1.67 thf(zip_derived_cl323, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_4) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_2 @ e_3 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl317, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl1002, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)) &
% 7.48/1.67 ( (product @ e_2 @ e_3 @ e_4)) &
% 7.48/1.67 ( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl883, zip_derived_cl323])).
% 7.48/1.67 thf(zip_derived_cl19, plain, (~ (equalish @ e_2 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 7.48/1.67 thf('22', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_4 @ e_4)) | ~ ( (product @ e_2 @ e_3 @ e_4)) |
% 7.48/1.67 ~ ( (product @ e_3 @ e_1 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1002, zip_derived_cl19])).
% 7.48/1.67 thf(zip_derived_cl422, plain,
% 7.48/1.67 (( (product @ e_3 @ e_1 @ e_2)) <= (( (product @ e_3 @ e_1 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl93])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl1459, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_2) | (equalish @ e_3 @ X0)))
% 7.48/1.67 <= (( (product @ e_3 @ e_1 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl422, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl572, plain,
% 7.48/1.67 (( (product @ e_4 @ e_1 @ e_2)) <= (( (product @ e_4 @ e_1 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl112])).
% 7.48/1.67 thf(zip_derived_cl2798, plain,
% 7.48/1.67 (( (equalish @ e_3 @ e_4))
% 7.48/1.67 <= (( (product @ e_3 @ e_1 @ e_2)) & ( (product @ e_4 @ e_1 @ e_2)))),
% 7.48/1.67 inference('s_sup+', [status(thm)],
% 7.48/1.67 [zip_derived_cl1459, zip_derived_cl572])).
% 7.48/1.67 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 7.48/1.67 thf('23', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_1 @ e_2)) | ~ ( (product @ e_4 @ e_1 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2798, zip_derived_cl22])).
% 7.48/1.67 thf(zip_derived_cl330, plain,
% 7.48/1.67 (( (product @ e_2 @ e_4 @ e_4)) <= (( (product @ e_2 @ e_4 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl64])).
% 7.48/1.67 thf(zip_derived_cl191, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_4) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl782, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_2))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)) & ( (product @ e_2 @ e_4 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl330, zip_derived_cl191])).
% 7.48/1.67 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 7.48/1.67 thf('24', plain,
% 7.48/1.67 (~ ( (product @ e_2 @ e_4 @ e_4)) | ~ ( (product @ e_1 @ e_4 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl782, zip_derived_cl14])).
% 7.48/1.67 thf(zip_derived_cl32, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_3])).
% 7.48/1.67 thf(zip_derived_cl43, plain,
% 7.48/1.67 (( (product @ e_1 @ e_3 @ e_4)
% 7.48/1.67 | (product @ e_1 @ e_3 @ e_3)
% 7.48/1.67 | (product @ e_1 @ e_3 @ e_2)
% 7.48/1.67 | (product @ e_1 @ e_3 @ e_1))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl12])).
% 7.48/1.67 thf(zip_derived_cl163, plain,
% 7.48/1.67 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl43])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl815, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_2) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl163, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl319, plain,
% 7.48/1.67 (( (product @ e_2 @ e_3 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl63])).
% 7.48/1.67 thf(zip_derived_cl2268, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_2))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_2)) & ( (product @ e_2 @ e_3 @ e_2)))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl815, zip_derived_cl319])).
% 7.48/1.67 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 7.48/1.67 thf('25', plain,
% 7.48/1.67 (~ ( (product @ e_2 @ e_3 @ e_2)) | ~ ( (product @ e_1 @ e_3 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2268, zip_derived_cl14])).
% 7.48/1.67 thf(zip_derived_cl163, plain,
% 7.48/1.67 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl43])).
% 7.48/1.67 thf(zip_derived_cl28, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.67 | (equalish @ X1 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.67 thf(zip_derived_cl814, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_3 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl163, zip_derived_cl28])).
% 7.48/1.67 thf(zip_derived_cl187, plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_2)) <= (( (product @ e_1 @ e_4 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl44])).
% 7.48/1.67 thf(zip_derived_cl2258, plain,
% 7.48/1.67 (( (equalish @ e_3 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_2)) & ( (product @ e_1 @ e_4 @ e_2)))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl814, zip_derived_cl187])).
% 7.48/1.67 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 7.48/1.67 thf('26', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_4 @ e_2)) | ~ ( (product @ e_1 @ e_3 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2258, zip_derived_cl22])).
% 7.48/1.67 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_3])).
% 7.48/1.67 thf(zip_derived_cl36, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 ( (product @ X0 @ X0 @ e_4)
% 7.48/1.67 | (product @ X0 @ X0 @ e_3)
% 7.48/1.67 | (product @ X0 @ X0 @ e_2)
% 7.48/1.67 | (product @ X0 @ X0 @ e_1)
% 7.48/1.67 | ~ (group_element @ X0))),
% 7.48/1.67 inference('eq_fact', [status(thm)], [zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl131, plain,
% 7.48/1.67 (( (product @ e_3 @ e_3 @ e_4)
% 7.48/1.67 | (product @ e_3 @ e_3 @ e_3)
% 7.48/1.67 | (product @ e_3 @ e_3 @ e_2)
% 7.48/1.67 | (product @ e_3 @ e_3 @ e_1))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl36])).
% 7.48/1.67 thf(zip_derived_cl743, plain,
% 7.48/1.67 (( (product @ e_3 @ e_3 @ e_2)) <= (( (product @ e_3 @ e_3 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl131])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl747, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_2) | (equalish @ e_3 @ X0)))
% 7.48/1.67 <= (( (product @ e_3 @ e_3 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl743, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl163, plain,
% 7.48/1.67 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl43])).
% 7.48/1.67 thf(zip_derived_cl2175, plain,
% 7.48/1.67 (( (equalish @ e_3 @ e_1))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_2)) & ( (product @ e_3 @ e_3 @ e_2)))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl747, zip_derived_cl163])).
% 7.48/1.67 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 7.48/1.67 thf(zip_derived_cl20, plain, (~ (equalish @ e_3 @ e_1)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 7.48/1.67 thf('27', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_3 @ e_2)) | ~ ( (product @ e_1 @ e_3 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2175, zip_derived_cl20])).
% 7.48/1.67 thf(e_2_then_e_3, axiom, (next @ e_2 @ e_3)).
% 7.48/1.67 thf(zip_derived_cl1, plain, ( (next @ e_2 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_then_e_3])).
% 7.48/1.67 thf(zip_derived_cl163, plain,
% 7.48/1.67 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl43])).
% 7.48/1.67 thf(zip_derived_cl439, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_4)) <= (( (product @ e_3 @ e_2 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl94])).
% 7.48/1.67 thf(zip_derived_cl30, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 ( (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.67 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.67 thf(zip_derived_cl446, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_2 @ X0 @ e_4) | ~ (product @ X0 @ e_3 @ e_2)))
% 7.48/1.67 <= (( (product @ e_3 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl439, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl1576, plain,
% 7.48/1.67 (( (product @ e_2 @ e_1 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_2)) & ( (product @ e_3 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl163, zip_derived_cl446])).
% 7.48/1.67 thf(no_redundancy, axiom,
% 7.48/1.67 (( ~( product @ X @ e_1 @ Y ) ) | ( ~( next @ X @ X1 ) ) |
% 7.48/1.67 ( ~( greater @ Y @ X1 ) ))).
% 7.48/1.67 thf(zip_derived_cl9, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.48/1.67 (~ (product @ X0 @ e_1 @ X1)
% 7.48/1.67 | ~ (next @ X0 @ X2)
% 7.48/1.67 | ~ (greater @ X1 @ X2))),
% 7.48/1.67 inference('cnf', [status(esa)], [no_redundancy])).
% 7.48/1.67 thf(zip_derived_cl4618, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (next @ e_2 @ X0) | ~ (greater @ e_4 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_2)) & ( (product @ e_3 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1576, zip_derived_cl9])).
% 7.48/1.67 thf(zip_derived_cl4634, plain,
% 7.48/1.67 ((~ (greater @ e_4 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_2)) & ( (product @ e_3 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl4618])).
% 7.48/1.67 thf(e_4_greater_e_3, axiom, (greater @ e_4 @ e_3)).
% 7.48/1.67 thf(zip_derived_cl8, plain, ( (greater @ e_4 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_4_greater_e_3])).
% 7.48/1.67 thf('28', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_2 @ e_4)) | ~ ( (product @ e_1 @ e_3 @ e_2))),
% 7.48/1.67 inference('demod', [status(thm)], [zip_derived_cl4634, zip_derived_cl8])).
% 7.48/1.67 thf(zip_derived_cl35, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_4])).
% 7.48/1.67 thf(zip_derived_cl115, plain,
% 7.48/1.67 (( (product @ e_4 @ e_4 @ e_4)
% 7.48/1.67 | (product @ e_4 @ e_4 @ e_3)
% 7.48/1.67 | (product @ e_4 @ e_4 @ e_2)
% 7.48/1.67 | (product @ e_4 @ e_4 @ e_1))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl13])).
% 7.48/1.67 thf('29', plain,
% 7.48/1.67 (( (product @ e_4 @ e_4 @ e_4)) | ( (product @ e_4 @ e_4 @ e_1)) |
% 7.48/1.67 ( (product @ e_4 @ e_4 @ e_3)) | ( (product @ e_4 @ e_4 @ e_2))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl115])).
% 7.48/1.67 thf('30', plain,
% 7.48/1.67 (( (product @ e_3 @ e_4 @ e_2)) | ( (product @ e_3 @ e_4 @ e_1)) |
% 7.48/1.67 ( (product @ e_3 @ e_4 @ e_3)) | ( (product @ e_3 @ e_4 @ e_4))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl96])).
% 7.48/1.67 thf(zip_derived_cl330, plain,
% 7.48/1.67 (( (product @ e_2 @ e_4 @ e_4)) <= (( (product @ e_2 @ e_4 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl64])).
% 7.48/1.67 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_4])).
% 7.48/1.67 thf(zip_derived_cl35, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_4 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl119, plain,
% 7.48/1.67 (( (product @ e_4 @ e_4 @ e_1)
% 7.48/1.67 | (product @ e_4 @ e_4 @ e_2)
% 7.48/1.67 | (product @ e_4 @ e_4 @ e_3)
% 7.48/1.67 | (product @ e_4 @ e_4 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl35])).
% 7.48/1.67 thf(zip_derived_cl695, plain,
% 7.48/1.67 (( (product @ e_4 @ e_4 @ e_3)) <= (( (product @ e_4 @ e_4 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl119])).
% 7.48/1.67 thf(zip_derived_cl30, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 ( (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.67 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.67 thf(zip_derived_cl701, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_4 @ X0 @ e_3) | ~ (product @ X0 @ e_4 @ e_4)))
% 7.48/1.67 <= (( (product @ e_4 @ e_4 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl695, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl2510, plain,
% 7.48/1.67 (( (product @ e_4 @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_2 @ e_4 @ e_4)) & ( (product @ e_4 @ e_4 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl330, zip_derived_cl701])).
% 7.48/1.67 thf(zip_derived_cl348, plain,
% 7.48/1.67 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl65])).
% 7.48/1.67 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_3])).
% 7.48/1.67 thf(zip_derived_cl32, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl47, plain,
% 7.48/1.67 (( (product @ e_1 @ e_3 @ e_1)
% 7.48/1.67 | (product @ e_1 @ e_3 @ e_2)
% 7.48/1.67 | (product @ e_1 @ e_3 @ e_3)
% 7.48/1.67 | (product @ e_1 @ e_3 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl32])).
% 7.48/1.67 thf(zip_derived_cl245, plain,
% 7.48/1.67 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl47])).
% 7.48/1.67 thf(zip_derived_cl30, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 ( (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.67 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.67 thf(zip_derived_cl251, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_3 @ X0 @ e_3) | ~ (product @ X0 @ e_1 @ e_3)))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl245, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl961, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl251])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl1123, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_3 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl961, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl6718, plain,
% 7.48/1.67 (( (equalish @ e_3 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)) &
% 7.48/1.67 ( (product @ e_2 @ e_1 @ e_3)) &
% 7.48/1.67 ( (product @ e_2 @ e_4 @ e_4)) &
% 7.48/1.67 ( (product @ e_4 @ e_4 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)],
% 7.48/1.67 [zip_derived_cl2510, zip_derived_cl1123])).
% 7.48/1.67 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 7.48/1.67 thf('31', plain,
% 7.48/1.67 (~ ( (product @ e_4 @ e_4 @ e_3)) | ~ ( (product @ e_2 @ e_4 @ e_4)) |
% 7.48/1.67 ~ ( (product @ e_2 @ e_1 @ e_3)) | ~ ( (product @ e_1 @ e_3 @ e_3))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl6718, zip_derived_cl22])).
% 7.48/1.67 thf(zip_derived_cl628, plain,
% 7.48/1.67 (( (product @ e_4 @ e_4 @ e_4)) <= (( (product @ e_4 @ e_4 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl115])).
% 7.48/1.67 thf(zip_derived_cl330, plain,
% 7.48/1.67 (( (product @ e_2 @ e_4 @ e_4)) <= (( (product @ e_2 @ e_4 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl64])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl336, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_4) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_2 @ e_4 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl330, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl1067, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_4))
% 7.48/1.67 <= (( (product @ e_2 @ e_4 @ e_4)) & ( (product @ e_4 @ e_4 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl628, zip_derived_cl336])).
% 7.48/1.67 thf(zip_derived_cl19, plain, (~ (equalish @ e_2 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 7.48/1.67 thf('32', plain,
% 7.48/1.67 (~ ( (product @ e_2 @ e_4 @ e_4)) | ~ ( (product @ e_4 @ e_4 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1067, zip_derived_cl19])).
% 7.48/1.67 thf(zip_derived_cl474, plain,
% 7.48/1.67 (( (product @ e_3 @ e_4 @ e_4)) <= (( (product @ e_3 @ e_4 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl96])).
% 7.48/1.67 thf(zip_derived_cl336, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_4) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_2 @ e_4 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl330, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl1065, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_2 @ e_4 @ e_4)) & ( (product @ e_3 @ e_4 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl474, zip_derived_cl336])).
% 7.48/1.67 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 7.48/1.67 thf('33', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_4 @ e_4)) | ~ ( (product @ e_2 @ e_4 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1065, zip_derived_cl18])).
% 7.48/1.67 thf(zip_derived_cl187, plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_2)) <= (( (product @ e_1 @ e_4 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl44])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl862, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_2) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl187, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl332, plain,
% 7.48/1.67 (( (product @ e_2 @ e_4 @ e_2)) <= (( (product @ e_2 @ e_4 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl64])).
% 7.48/1.67 thf(zip_derived_cl2368, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_2))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_2)) & ( (product @ e_2 @ e_4 @ e_2)))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl862, zip_derived_cl332])).
% 7.48/1.67 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 7.48/1.67 thf('34', plain,
% 7.48/1.67 (~ ( (product @ e_2 @ e_4 @ e_2)) | ~ ( (product @ e_1 @ e_4 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2368, zip_derived_cl14])).
% 7.48/1.67 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_4])).
% 7.48/1.67 thf(zip_derived_cl36, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 ( (product @ X0 @ X0 @ e_4)
% 7.48/1.67 | (product @ X0 @ X0 @ e_3)
% 7.48/1.67 | (product @ X0 @ X0 @ e_2)
% 7.48/1.67 | (product @ X0 @ X0 @ e_1)
% 7.48/1.67 | ~ (group_element @ X0))),
% 7.48/1.67 inference('eq_fact', [status(thm)], [zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl132, plain,
% 7.48/1.67 (( (product @ e_4 @ e_4 @ e_4)
% 7.48/1.67 | (product @ e_4 @ e_4 @ e_3)
% 7.48/1.67 | (product @ e_4 @ e_4 @ e_2)
% 7.48/1.67 | (product @ e_4 @ e_4 @ e_1))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl36])).
% 7.48/1.67 thf(zip_derived_cl769, plain,
% 7.48/1.67 (( (product @ e_4 @ e_4 @ e_2)) <= (( (product @ e_4 @ e_4 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl132])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl773, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_2) | (equalish @ e_4 @ X0)))
% 7.48/1.67 <= (( (product @ e_4 @ e_4 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl769, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl187, plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_2)) <= (( (product @ e_1 @ e_4 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl44])).
% 7.48/1.67 thf(zip_derived_cl2231, plain,
% 7.48/1.67 (( (equalish @ e_4 @ e_1))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_2)) & ( (product @ e_4 @ e_4 @ e_2)))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl773, zip_derived_cl187])).
% 7.48/1.67 thf(zip_derived_cl23, plain, (~ (equalish @ e_4 @ e_1)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 7.48/1.67 thf('35', plain,
% 7.48/1.67 (~ ( (product @ e_4 @ e_4 @ e_2)) | ~ ( (product @ e_1 @ e_4 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2231, zip_derived_cl23])).
% 7.48/1.67 thf(zip_derived_cl862, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_2) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl187, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl476, plain,
% 7.48/1.67 (( (product @ e_3 @ e_4 @ e_2)) <= (( (product @ e_3 @ e_4 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl96])).
% 7.48/1.67 thf(zip_derived_cl2369, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_2)) & ( (product @ e_3 @ e_4 @ e_2)))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl862, zip_derived_cl476])).
% 7.48/1.67 thf(zip_derived_cl15, plain, (~ (equalish @ e_1 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 7.48/1.67 thf('36', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_4 @ e_2)) | ~ ( (product @ e_3 @ e_4 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2369, zip_derived_cl15])).
% 7.48/1.67 thf(zip_derived_cl185, plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl44])).
% 7.48/1.67 thf(zip_derived_cl141, plain,
% 7.48/1.67 (( (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl42])).
% 7.48/1.67 thf(zip_derived_cl28, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.67 | (equalish @ X1 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.67 thf(zip_derived_cl146, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_4) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl141, zip_derived_cl28])).
% 7.48/1.67 thf(zip_derived_cl298, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_1 @ e_4 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl146])).
% 7.48/1.67 thf(zip_derived_cl19, plain, (~ (equalish @ e_2 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 7.48/1.67 thf('37', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_4 @ e_4)) | ~ ( (product @ e_1 @ e_2 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl298, zip_derived_cl19])).
% 7.48/1.67 thf(zip_derived_cl442, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_1)) <= (( (product @ e_3 @ e_2 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl94])).
% 7.48/1.67 thf(product_total_function2, axiom,
% 7.48/1.67 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 7.48/1.67 ( equalish @ W @ Z ))).
% 7.48/1.67 thf(zip_derived_cl27, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X0 @ X1 @ X3)
% 7.48/1.67 | (equalish @ X2 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_total_function2])).
% 7.48/1.67 thf(zip_derived_cl1558, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_3 @ e_2 @ X0) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_3 @ e_2 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl442, zip_derived_cl27])).
% 7.48/1.67 thf(zip_derived_cl961, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl251])).
% 7.48/1.67 thf(zip_derived_cl2986, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)) &
% 7.48/1.67 ( (product @ e_2 @ e_1 @ e_3)) &
% 7.48/1.67 ( (product @ e_3 @ e_2 @ e_1)))),
% 7.48/1.67 inference('s_sup+', [status(thm)],
% 7.48/1.67 [zip_derived_cl1558, zip_derived_cl961])).
% 7.48/1.67 thf(zip_derived_cl15, plain, (~ (equalish @ e_1 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 7.48/1.67 thf('38', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_3 @ e_3)) |
% 7.48/1.67 ~ ( (product @ e_2 @ e_1 @ e_3))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2986, zip_derived_cl15])).
% 7.48/1.67 thf(zip_derived_cl441, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_2)) <= (( (product @ e_3 @ e_2 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl94])).
% 7.48/1.67 thf(zip_derived_cl27, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X0 @ X1 @ X3)
% 7.48/1.67 | (equalish @ X2 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_total_function2])).
% 7.48/1.67 thf(zip_derived_cl1541, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_3 @ e_2 @ X0) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_3 @ e_2 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl441, zip_derived_cl27])).
% 7.48/1.67 thf(zip_derived_cl961, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl251])).
% 7.48/1.67 thf(zip_derived_cl2907, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)) &
% 7.48/1.67 ( (product @ e_2 @ e_1 @ e_3)) &
% 7.48/1.67 ( (product @ e_3 @ e_2 @ e_2)))),
% 7.48/1.67 inference('s_sup+', [status(thm)],
% 7.48/1.67 [zip_derived_cl1541, zip_derived_cl961])).
% 7.48/1.67 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 7.48/1.67 thf('39', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_2 @ e_2)) | ~ ( (product @ e_1 @ e_3 @ e_3)) |
% 7.48/1.67 ~ ( (product @ e_2 @ e_1 @ e_3))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2907, zip_derived_cl18])).
% 7.48/1.67 thf(zip_derived_cl961, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl251])).
% 7.48/1.67 thf(zip_derived_cl550, plain,
% 7.48/1.67 (( (product @ e_3 @ e_4 @ e_3)) <= (( (product @ e_3 @ e_4 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl100])).
% 7.48/1.67 thf(zip_derived_cl28, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.67 | (equalish @ X1 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.67 thf(zip_derived_cl554, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_3 @ X0 @ e_3) | (equalish @ e_4 @ X0)))
% 7.48/1.67 <= (( (product @ e_3 @ e_4 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl550, zip_derived_cl28])).
% 7.48/1.67 thf(zip_derived_cl1651, plain,
% 7.48/1.67 (( (equalish @ e_4 @ e_2))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)) &
% 7.48/1.67 ( (product @ e_2 @ e_1 @ e_3)) &
% 7.48/1.67 ( (product @ e_3 @ e_4 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl961, zip_derived_cl554])).
% 7.48/1.67 thf(zip_derived_cl24, plain, (~ (equalish @ e_4 @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 7.48/1.67 thf('40', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_4 @ e_3)) | ~ ( (product @ e_1 @ e_3 @ e_3)) |
% 7.48/1.67 ~ ( (product @ e_2 @ e_1 @ e_3))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1651, zip_derived_cl24])).
% 7.48/1.67 thf(zip_derived_cl269, plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_3)) <= (( (product @ e_1 @ e_4 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl48])).
% 7.48/1.67 thf(zip_derived_cl245, plain,
% 7.48/1.67 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl47])).
% 7.48/1.67 thf(zip_derived_cl28, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.67 | (equalish @ X1 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.67 thf(zip_derived_cl249, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_3 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl245, zip_derived_cl28])).
% 7.48/1.67 thf(zip_derived_cl921, plain,
% 7.48/1.67 (( (equalish @ e_3 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)) & ( (product @ e_1 @ e_4 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl269, zip_derived_cl249])).
% 7.48/1.67 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 7.48/1.67 thf('41', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_3 @ e_3)) | ~ ( (product @ e_1 @ e_4 @ e_3))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl921, zip_derived_cl22])).
% 7.48/1.67 thf(zip_derived_cl477, plain,
% 7.48/1.67 (( (product @ e_3 @ e_4 @ e_1)) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl96])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl1699, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_1) | (equalish @ e_3 @ X0)))
% 7.48/1.67 <= (( (product @ e_3 @ e_4 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl477, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl631, plain,
% 7.48/1.67 (( (product @ e_4 @ e_4 @ e_1)) <= (( (product @ e_4 @ e_4 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl115])).
% 7.48/1.67 thf(zip_derived_cl3226, plain,
% 7.48/1.67 (( (equalish @ e_3 @ e_4))
% 7.48/1.67 <= (( (product @ e_3 @ e_4 @ e_1)) & ( (product @ e_4 @ e_4 @ e_1)))),
% 7.48/1.67 inference('s_sup+', [status(thm)],
% 7.48/1.67 [zip_derived_cl1699, zip_derived_cl631])).
% 7.48/1.67 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 7.48/1.67 thf('42', plain,
% 7.48/1.67 (~ ( (product @ e_4 @ e_4 @ e_1)) | ~ ( (product @ e_3 @ e_4 @ e_1))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl3226, zip_derived_cl22])).
% 7.48/1.67 thf(zip_derived_cl573, plain,
% 7.48/1.67 (( (product @ e_4 @ e_1 @ e_1)) <= (( (product @ e_4 @ e_1 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl112])).
% 7.48/1.67 thf(zip_derived_cl32, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_1])).
% 7.48/1.67 thf(zip_derived_cl41, plain,
% 7.48/1.67 (( (product @ e_1 @ e_1 @ e_4)
% 7.48/1.67 | (product @ e_1 @ e_1 @ e_3)
% 7.48/1.67 | (product @ e_1 @ e_1 @ e_2)
% 7.48/1.67 | (product @ e_1 @ e_1 @ e_1))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl10])).
% 7.48/1.67 thf(zip_derived_cl52, plain,
% 7.48/1.67 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl41])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl105, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_1) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl52, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl1967, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_1)) & ( (product @ e_4 @ e_1 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl573, zip_derived_cl105])).
% 7.48/1.67 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 7.48/1.67 thf('43', plain,
% 7.48/1.67 (~ ( (product @ e_4 @ e_1 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_1))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1967, zip_derived_cl16])).
% 7.48/1.67 thf(zip_derived_cl423, plain,
% 7.48/1.67 (( (product @ e_3 @ e_1 @ e_1)) <= (( (product @ e_3 @ e_1 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl93])).
% 7.48/1.67 thf(zip_derived_cl105, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_1) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl52, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl1497, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_1)) & ( (product @ e_3 @ e_1 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl423, zip_derived_cl105])).
% 7.48/1.67 thf(zip_derived_cl15, plain, (~ (equalish @ e_1 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 7.48/1.67 thf('44', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_1 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_1))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1497, zip_derived_cl15])).
% 7.48/1.67 thf(zip_derived_cl188, plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_1)) <= (( (product @ e_1 @ e_4 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl44])).
% 7.48/1.67 thf(zip_derived_cl52, plain,
% 7.48/1.67 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl41])).
% 7.48/1.67 thf(zip_derived_cl28, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.67 | (equalish @ X1 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.67 thf(zip_derived_cl104, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_1) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl52, zip_derived_cl28])).
% 7.48/1.67 thf(zip_derived_cl880, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_1)) & ( (product @ e_1 @ e_4 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl188, zip_derived_cl104])).
% 7.48/1.67 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 7.48/1.67 thf('45', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_4 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_1))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl880, zip_derived_cl16])).
% 7.48/1.67 thf(zip_derived_cl570, plain,
% 7.48/1.67 (( (product @ e_4 @ e_1 @ e_4)) <= (( (product @ e_4 @ e_1 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl112])).
% 7.48/1.67 thf(zip_derived_cl192, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_4 @ X0 @ e_4) | ~ (product @ X0 @ e_1 @ e_4)))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl884, plain,
% 7.48/1.67 (( (product @ e_4 @ e_4 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)) & ( (product @ e_4 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl570, zip_derived_cl192])).
% 7.48/1.67 thf(zip_derived_cl191, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_4) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl951, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_4 @ e_4)) & ( (product @ e_4 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl884, zip_derived_cl191])).
% 7.48/1.67 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 7.48/1.67 thf('46', plain,
% 7.48/1.67 (~ ( (product @ e_4 @ e_1 @ e_4)) | ~ ( (product @ e_1 @ e_4 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl951, zip_derived_cl16])).
% 7.48/1.67 thf(zip_derived_cl423, plain,
% 7.48/1.67 (( (product @ e_3 @ e_1 @ e_1)) <= (( (product @ e_3 @ e_1 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl93])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl1490, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_1) | (equalish @ e_3 @ X0)))
% 7.48/1.67 <= (( (product @ e_3 @ e_1 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl423, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl573, plain,
% 7.48/1.67 (( (product @ e_4 @ e_1 @ e_1)) <= (( (product @ e_4 @ e_1 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl112])).
% 7.48/1.67 thf(zip_derived_cl2871, plain,
% 7.48/1.67 (( (equalish @ e_3 @ e_4))
% 7.48/1.67 <= (( (product @ e_3 @ e_1 @ e_1)) & ( (product @ e_4 @ e_1 @ e_1)))),
% 7.48/1.67 inference('s_sup+', [status(thm)],
% 7.48/1.67 [zip_derived_cl1490, zip_derived_cl573])).
% 7.48/1.67 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 7.48/1.67 thf('47', plain,
% 7.48/1.67 (~ ( (product @ e_4 @ e_1 @ e_1)) | ~ ( (product @ e_3 @ e_1 @ e_1))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2871, zip_derived_cl22])).
% 7.48/1.67 thf('48', plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_3)) | ( (product @ e_1 @ e_4 @ e_4)) |
% 7.48/1.67 ( (product @ e_1 @ e_4 @ e_1)) | ( (product @ e_1 @ e_4 @ e_2))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl44])).
% 7.48/1.67 thf('49', plain,
% 7.48/1.67 (( (product @ e_3 @ e_1 @ e_4)) | ( (product @ e_3 @ e_1 @ e_2)) |
% 7.48/1.67 ( (product @ e_3 @ e_1 @ e_1)) | ( (product @ e_3 @ e_1 @ e_3))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl93])).
% 7.48/1.67 thf(zip_derived_cl164, plain,
% 7.48/1.67 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl43])).
% 7.48/1.67 thf(zip_derived_cl28, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.67 | (equalish @ X1 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.67 thf(zip_derived_cl837, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_1) | (equalish @ e_3 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl164, zip_derived_cl28])).
% 7.48/1.67 thf(zip_derived_cl188, plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_1)) <= (( (product @ e_1 @ e_4 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl44])).
% 7.48/1.67 thf(zip_derived_cl2299, plain,
% 7.48/1.67 (( (equalish @ e_3 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_1)) & ( (product @ e_1 @ e_4 @ e_1)))),
% 7.48/1.67 inference('s_sup+', [status(thm)], [zip_derived_cl837, zip_derived_cl188])).
% 7.48/1.67 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 7.48/1.67 thf('50', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_4 @ e_1)) | ~ ( (product @ e_1 @ e_3 @ e_1))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl2299, zip_derived_cl22])).
% 7.48/1.67 thf(e_1_then_e_2, axiom, (next @ e_1 @ e_2)).
% 7.48/1.67 thf(zip_derived_cl0, plain, ( (next @ e_1 @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_then_e_2])).
% 7.48/1.67 thf(zip_derived_cl164, plain,
% 7.48/1.67 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl43])).
% 7.48/1.67 thf(zip_derived_cl420, plain,
% 7.48/1.67 (( (product @ e_3 @ e_1 @ e_4)) <= (( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl93])).
% 7.48/1.67 thf(zip_derived_cl30, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 ( (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.67 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.67 thf(zip_derived_cl427, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_1 @ X0 @ e_4) | ~ (product @ X0 @ e_3 @ e_1)))
% 7.48/1.67 <= (( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl420, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl1507, plain,
% 7.48/1.67 (( (product @ e_1 @ e_1 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_1)) & ( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl164, zip_derived_cl427])).
% 7.48/1.67 thf(zip_derived_cl9, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.48/1.67 (~ (product @ X0 @ e_1 @ X1)
% 7.48/1.67 | ~ (next @ X0 @ X2)
% 7.48/1.67 | ~ (greater @ X1 @ X2))),
% 7.48/1.67 inference('cnf', [status(esa)], [no_redundancy])).
% 7.48/1.67 thf(zip_derived_cl4478, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (next @ e_1 @ X0) | ~ (greater @ e_4 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_1)) & ( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1507, zip_derived_cl9])).
% 7.48/1.67 thf(zip_derived_cl4491, plain,
% 7.48/1.67 ((~ (greater @ e_4 @ e_2))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_1)) & ( (product @ e_3 @ e_1 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl4478])).
% 7.48/1.67 thf(e_4_greater_e_2, axiom, (greater @ e_4 @ e_2)).
% 7.48/1.67 thf(zip_derived_cl7, plain, ( (greater @ e_4 @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_4_greater_e_2])).
% 7.48/1.67 thf('51', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_3 @ e_1)) | ~ ( (product @ e_3 @ e_1 @ e_4))),
% 7.48/1.67 inference('demod', [status(thm)], [zip_derived_cl4491, zip_derived_cl7])).
% 7.48/1.67 thf(zip_derived_cl269, plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_3)) <= (( (product @ e_1 @ e_4 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl48])).
% 7.48/1.67 thf(zip_derived_cl142, plain,
% 7.48/1.67 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl42])).
% 7.48/1.67 thf(zip_derived_cl28, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.67 | (equalish @ X1 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.67 thf(zip_derived_cl179, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl28])).
% 7.48/1.67 thf(zip_derived_cl642, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_1 @ e_4 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl269, zip_derived_cl179])).
% 7.48/1.67 thf(zip_derived_cl19, plain, (~ (equalish @ e_2 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 7.48/1.67 thf('52', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_2 @ e_3)) | ~ ( (product @ e_1 @ e_4 @ e_3))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl642, zip_derived_cl19])).
% 7.48/1.67 thf(zip_derived_cl245, plain,
% 7.48/1.67 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl47])).
% 7.48/1.67 thf(zip_derived_cl179, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl28])).
% 7.48/1.67 thf(zip_derived_cl641, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_1 @ e_3 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl245, zip_derived_cl179])).
% 7.48/1.67 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 7.48/1.67 thf('53', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_3 @ e_3)) | ~ ( (product @ e_1 @ e_2 @ e_3))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl641, zip_derived_cl18])).
% 7.48/1.67 thf(zip_derived_cl422, plain,
% 7.48/1.67 (( (product @ e_3 @ e_1 @ e_2)) <= (( (product @ e_3 @ e_1 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl93])).
% 7.48/1.67 thf(zip_derived_cl51, plain,
% 7.48/1.67 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl41])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl87, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_2) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl51, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl1465, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_3 @ e_1 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl422, zip_derived_cl87])).
% 7.48/1.67 thf(zip_derived_cl15, plain, (~ (equalish @ e_1 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 7.48/1.67 thf('54', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_3 @ e_1 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1465, zip_derived_cl15])).
% 7.48/1.67 thf(zip_derived_cl572, plain,
% 7.48/1.67 (( (product @ e_4 @ e_1 @ e_2)) <= (( (product @ e_4 @ e_1 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl112])).
% 7.48/1.67 thf(zip_derived_cl87, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_2) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl51, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl1948, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_4 @ e_1 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl572, zip_derived_cl87])).
% 7.48/1.67 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 7.48/1.67 thf('55', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_4 @ e_1 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1948, zip_derived_cl16])).
% 7.48/1.67 thf(zip_derived_cl187, plain,
% 7.48/1.67 (( (product @ e_1 @ e_4 @ e_2)) <= (( (product @ e_1 @ e_4 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl44])).
% 7.48/1.67 thf(zip_derived_cl51, plain,
% 7.48/1.67 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl41])).
% 7.48/1.67 thf(zip_derived_cl28, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.67 | (equalish @ X1 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.67 thf(zip_derived_cl86, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl51, zip_derived_cl28])).
% 7.48/1.67 thf(zip_derived_cl867, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_1 @ e_4 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl187, zip_derived_cl86])).
% 7.48/1.67 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 7.48/1.67 thf('56', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_1 @ e_4 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl867, zip_derived_cl16])).
% 7.48/1.67 thf(zip_derived_cl163, plain,
% 7.48/1.67 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl43])).
% 7.48/1.67 thf(zip_derived_cl86, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl51, zip_derived_cl28])).
% 7.48/1.67 thf(zip_derived_cl821, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_1 @ e_3 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl163, zip_derived_cl86])).
% 7.48/1.67 thf(zip_derived_cl15, plain, (~ (equalish @ e_1 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 7.48/1.67 thf('57', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_1 @ e_3 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl821, zip_derived_cl15])).
% 7.48/1.67 thf(zip_derived_cl1, plain, ( (next @ e_2 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_then_e_3])).
% 7.48/1.67 thf(zip_derived_cl51, plain,
% 7.48/1.67 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl41])).
% 7.48/1.67 thf(zip_derived_cl148, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_2 @ X0 @ e_4) | ~ (product @ X0 @ e_1 @ e_2)))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl141, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl152, plain,
% 7.48/1.67 (( (product @ e_2 @ e_1 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_1 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl51, zip_derived_cl148])).
% 7.48/1.67 thf(zip_derived_cl9, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.48/1.67 (~ (product @ X0 @ e_1 @ X1)
% 7.48/1.67 | ~ (next @ X0 @ X2)
% 7.48/1.67 | ~ (greater @ X1 @ X2))),
% 7.48/1.67 inference('cnf', [status(esa)], [no_redundancy])).
% 7.48/1.67 thf(zip_derived_cl160, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (next @ e_2 @ X0) | ~ (greater @ e_4 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_1 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl152, zip_derived_cl9])).
% 7.48/1.67 thf(zip_derived_cl173, plain,
% 7.48/1.67 ((~ (greater @ e_4 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_1 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl160])).
% 7.48/1.67 thf(zip_derived_cl8, plain, ( (greater @ e_4 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_4_greater_e_3])).
% 7.48/1.67 thf('58', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_4))),
% 7.48/1.67 inference('demod', [status(thm)], [zip_derived_cl173, zip_derived_cl8])).
% 7.48/1.67 thf('59', plain,
% 7.48/1.67 (( (product @ e_4 @ e_1 @ e_4)) | ( (product @ e_4 @ e_1 @ e_1)) |
% 7.48/1.67 ( (product @ e_4 @ e_1 @ e_2)) | ( (product @ e_4 @ e_1 @ e_3))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl112])).
% 7.48/1.67 thf(zip_derived_cl961, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl251])).
% 7.48/1.67 thf(zip_derived_cl439, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_4)) <= (( (product @ e_3 @ e_2 @ e_4)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl94])).
% 7.48/1.67 thf(zip_derived_cl27, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X0 @ X1 @ X3)
% 7.48/1.67 | (equalish @ X2 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_total_function2])).
% 7.48/1.67 thf(zip_derived_cl443, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ e_3 @ e_2 @ X0) | (equalish @ e_4 @ X0)))
% 7.48/1.67 <= (( (product @ e_3 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl439, zip_derived_cl27])).
% 7.48/1.67 thf(zip_derived_cl1325, plain,
% 7.48/1.67 (( (equalish @ e_4 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)) &
% 7.48/1.67 ( (product @ e_2 @ e_1 @ e_3)) &
% 7.48/1.67 ( (product @ e_3 @ e_2 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl961, zip_derived_cl443])).
% 7.48/1.67 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 7.48/1.67 thf(zip_derived_cl25, plain, (~ (equalish @ e_4 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 7.48/1.67 thf('60', plain,
% 7.48/1.67 (~ ( (product @ e_3 @ e_2 @ e_4)) | ~ ( (product @ e_1 @ e_3 @ e_3)) |
% 7.48/1.67 ~ ( (product @ e_2 @ e_1 @ e_3))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1325, zip_derived_cl25])).
% 7.48/1.67 thf(zip_derived_cl961, plain,
% 7.48/1.67 (( (product @ e_3 @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl251])).
% 7.48/1.67 thf(zip_derived_cl324, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_3 @ X0 @ e_4) | ~ (product @ X0 @ e_2 @ e_3)))
% 7.48/1.67 <= (( (product @ e_2 @ e_3 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl317, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl1167, plain,
% 7.48/1.67 (( (product @ e_3 @ e_3 @ e_4))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)) &
% 7.48/1.67 ( (product @ e_2 @ e_1 @ e_3)) &
% 7.48/1.67 ( (product @ e_2 @ e_3 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl961, zip_derived_cl324])).
% 7.48/1.67 thf(zip_derived_cl323, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_4) | (equalish @ e_2 @ X0)))
% 7.48/1.67 <= (( (product @ e_2 @ e_3 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl317, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl1229, plain,
% 7.48/1.67 (( (equalish @ e_2 @ e_3))
% 7.48/1.67 <= (( (product @ e_1 @ e_3 @ e_3)) &
% 7.48/1.67 ( (product @ e_2 @ e_1 @ e_3)) &
% 7.48/1.67 ( (product @ e_2 @ e_3 @ e_4)))),
% 7.48/1.67 inference('s_sup-', [status(thm)],
% 7.48/1.67 [zip_derived_cl1167, zip_derived_cl323])).
% 7.48/1.67 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 7.48/1.67 thf('61', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_3 @ e_3)) | ~ ( (product @ e_2 @ e_3 @ e_4)) |
% 7.48/1.67 ~ ( (product @ e_2 @ e_1 @ e_3))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl1229, zip_derived_cl18])).
% 7.48/1.67 thf('62', plain,
% 7.48/1.67 (( (product @ e_1 @ e_3 @ e_2)) | ( (product @ e_1 @ e_3 @ e_3)) |
% 7.48/1.67 ( (product @ e_1 @ e_3 @ e_4)) | ( (product @ e_1 @ e_3 @ e_1))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl43])).
% 7.48/1.67 thf(zip_derived_cl281, plain,
% 7.48/1.67 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl61])).
% 7.48/1.67 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [element_2])).
% 7.48/1.67 thf(zip_derived_cl32, plain,
% 7.48/1.67 (![X0 : $i]:
% 7.48/1.67 (~ (group_element @ X0)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_1)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_2)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_3)
% 7.48/1.67 | (product @ e_1 @ X0 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl26])).
% 7.48/1.67 thf(zip_derived_cl46, plain,
% 7.48/1.67 (( (product @ e_1 @ e_2 @ e_1)
% 7.48/1.67 | (product @ e_1 @ e_2 @ e_2)
% 7.48/1.67 | (product @ e_1 @ e_2 @ e_3)
% 7.48/1.67 | (product @ e_1 @ e_2 @ e_4))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl32])).
% 7.48/1.67 thf(zip_derived_cl231, plain,
% 7.48/1.67 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl46])).
% 7.48/1.67 thf(zip_derived_cl30, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 ( (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.67 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.67 thf(zip_derived_cl235, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_2 @ X0 @ e_1) | ~ (product @ X0 @ e_1 @ e_2)))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl231, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl1021, plain,
% 7.48/1.67 (( (product @ e_2 @ e_2 @ e_1))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_1)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl281, zip_derived_cl235])).
% 7.48/1.67 thf(zip_derived_cl231, plain,
% 7.48/1.67 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl46])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl234, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_1) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_1)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl231, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl3006, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_2))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_1)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)],
% 7.48/1.67 [zip_derived_cl1021, zip_derived_cl234])).
% 7.48/1.67 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 7.48/1.67 thf('63', plain,
% 7.48/1.67 (~ ( (product @ e_1 @ e_2 @ e_1)) | ~ ( (product @ e_2 @ e_1 @ e_2))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl3006, zip_derived_cl14])).
% 7.48/1.67 thf(zip_derived_cl281, plain,
% 7.48/1.67 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl61])).
% 7.48/1.67 thf(zip_derived_cl143, plain,
% 7.48/1.67 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl42])).
% 7.48/1.67 thf(zip_derived_cl30, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 ( (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.67 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.67 thf(zip_derived_cl199, plain,
% 7.48/1.67 ((![X0 : $i]:
% 7.48/1.67 ( (product @ e_2 @ X0 @ e_2) | ~ (product @ X0 @ e_1 @ e_2)))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl30])).
% 7.48/1.67 thf(zip_derived_cl1020, plain,
% 7.48/1.67 (( (product @ e_2 @ e_2 @ e_2))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_2)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl281, zip_derived_cl199])).
% 7.48/1.67 thf(zip_derived_cl143, plain,
% 7.48/1.67 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 7.48/1.67 inference('split', [status(esa)], [zip_derived_cl42])).
% 7.48/1.67 thf(zip_derived_cl29, plain,
% 7.48/1.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.67 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.67 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.67 | (equalish @ X0 @ X3))),
% 7.48/1.67 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.67 thf(zip_derived_cl198, plain,
% 7.48/1.67 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_2) | (equalish @ e_1 @ X0)))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl29])).
% 7.48/1.67 thf(zip_derived_cl2965, plain,
% 7.48/1.67 (( (equalish @ e_1 @ e_2))
% 7.48/1.67 <= (( (product @ e_1 @ e_2 @ e_2)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 7.48/1.67 inference('s_sup-', [status(thm)],
% 7.48/1.67 [zip_derived_cl1020, zip_derived_cl198])).
% 7.48/1.67 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 7.48/1.67 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 7.48/1.68 thf('64', plain,
% 7.48/1.68 (~ ( (product @ e_1 @ e_2 @ e_2)) | ~ ( (product @ e_2 @ e_1 @ e_2))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl2965, zip_derived_cl14])).
% 7.48/1.68 thf(zip_derived_cl1, plain, ( (next @ e_2 @ e_3)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_2_then_e_3])).
% 7.48/1.68 thf(zip_derived_cl279, plain,
% 7.48/1.68 (( (product @ e_2 @ e_1 @ e_4)) <= (( (product @ e_2 @ e_1 @ e_4)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl61])).
% 7.48/1.68 thf(zip_derived_cl9, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.48/1.68 (~ (product @ X0 @ e_1 @ X1)
% 7.48/1.68 | ~ (next @ X0 @ X2)
% 7.48/1.68 | ~ (greater @ X1 @ X2))),
% 7.48/1.68 inference('cnf', [status(esa)], [no_redundancy])).
% 7.48/1.68 thf(zip_derived_cl290, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (next @ e_2 @ X0) | ~ (greater @ e_4 @ X0)))
% 7.48/1.68 <= (( (product @ e_2 @ e_1 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl279, zip_derived_cl9])).
% 7.48/1.68 thf(zip_derived_cl292, plain,
% 7.48/1.68 ((~ (greater @ e_4 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl290])).
% 7.48/1.68 thf(zip_derived_cl8, plain, ( (greater @ e_4 @ e_3)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_4_greater_e_3])).
% 7.48/1.68 thf('65', plain, (~ ( (product @ e_2 @ e_1 @ e_4))),
% 7.48/1.68 inference('demod', [status(thm)], [zip_derived_cl292, zip_derived_cl8])).
% 7.48/1.68 thf(zip_derived_cl282, plain,
% 7.48/1.68 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl61])).
% 7.48/1.68 thf(zip_derived_cl51, plain,
% 7.48/1.68 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl41])).
% 7.48/1.68 thf(zip_derived_cl30, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.68 ( (product @ X0 @ X1 @ X2)
% 7.48/1.68 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.68 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.68 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.68 thf(zip_derived_cl88, plain,
% 7.48/1.68 ((![X0 : $i]:
% 7.48/1.68 ( (product @ e_1 @ X0 @ e_2) | ~ (product @ X0 @ e_1 @ e_1)))
% 7.48/1.68 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl51, zip_derived_cl30])).
% 7.48/1.68 thf(zip_derived_cl1034, plain,
% 7.48/1.68 (( (product @ e_1 @ e_2 @ e_2))
% 7.48/1.68 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_2 @ e_1 @ e_1)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl282, zip_derived_cl88])).
% 7.48/1.68 thf(zip_derived_cl86, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl51, zip_derived_cl28])).
% 7.48/1.68 thf(zip_derived_cl3086, plain,
% 7.48/1.68 (( (equalish @ e_1 @ e_2))
% 7.48/1.68 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_2 @ e_1 @ e_1)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl1034, zip_derived_cl86])).
% 7.48/1.68 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 7.48/1.68 thf('66', plain,
% 7.48/1.68 (~ ( (product @ e_2 @ e_1 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_2))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl3086, zip_derived_cl14])).
% 7.48/1.68 thf(zip_derived_cl282, plain,
% 7.48/1.68 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl61])).
% 7.48/1.68 thf(zip_derived_cl105, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_1) | (equalish @ e_1 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl52, zip_derived_cl29])).
% 7.48/1.68 thf(zip_derived_cl1035, plain,
% 7.48/1.68 (( (equalish @ e_1 @ e_2))
% 7.48/1.68 <= (( (product @ e_1 @ e_1 @ e_1)) & ( (product @ e_2 @ e_1 @ e_1)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl282, zip_derived_cl105])).
% 7.48/1.68 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 7.48/1.68 thf('67', plain,
% 7.48/1.68 (~ ( (product @ e_2 @ e_1 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_1))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl1035, zip_derived_cl14])).
% 7.48/1.68 thf('68', plain,
% 7.48/1.68 (( (product @ e_2 @ e_4 @ e_1)) | ( (product @ e_2 @ e_4 @ e_4)) |
% 7.48/1.68 ( (product @ e_2 @ e_4 @ e_2)) | ( (product @ e_2 @ e_4 @ e_3))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl64])).
% 7.48/1.68 thf(zip_derived_cl320, plain,
% 7.48/1.68 (( (product @ e_2 @ e_3 @ e_1)) <= (( (product @ e_2 @ e_3 @ e_1)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl63])).
% 7.48/1.68 thf(zip_derived_cl28, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.68 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.68 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.68 | (equalish @ X1 @ X3))),
% 7.48/1.68 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.68 thf(zip_derived_cl1147, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_1) | (equalish @ e_3 @ X0)))
% 7.48/1.68 <= (( (product @ e_2 @ e_3 @ e_1)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl320, zip_derived_cl28])).
% 7.48/1.68 thf(zip_derived_cl333, plain,
% 7.48/1.68 (( (product @ e_2 @ e_4 @ e_1)) <= (( (product @ e_2 @ e_4 @ e_1)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl64])).
% 7.48/1.68 thf(zip_derived_cl2634, plain,
% 7.48/1.68 (( (equalish @ e_3 @ e_4))
% 7.48/1.68 <= (( (product @ e_2 @ e_3 @ e_1)) & ( (product @ e_2 @ e_4 @ e_1)))),
% 7.48/1.68 inference('s_sup+', [status(thm)],
% 7.48/1.68 [zip_derived_cl1147, zip_derived_cl333])).
% 7.48/1.68 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 7.48/1.68 thf('69', plain,
% 7.48/1.68 (~ ( (product @ e_2 @ e_3 @ e_1)) | ~ ( (product @ e_2 @ e_4 @ e_1))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl2634, zip_derived_cl22])).
% 7.48/1.68 thf(zip_derived_cl348, plain,
% 7.48/1.68 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl65])).
% 7.48/1.68 thf(zip_derived_cl161, plain,
% 7.48/1.68 (( (product @ e_1 @ e_3 @ e_4)) <= (( (product @ e_1 @ e_3 @ e_4)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl43])).
% 7.48/1.68 thf(zip_derived_cl30, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.68 ( (product @ X0 @ X1 @ X2)
% 7.48/1.68 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.68 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.68 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.68 thf(zip_derived_cl168, plain,
% 7.48/1.68 ((![X0 : $i]:
% 7.48/1.68 ( (product @ e_3 @ X0 @ e_4) | ~ (product @ X0 @ e_1 @ e_3)))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl161, zip_derived_cl30])).
% 7.48/1.68 thf(zip_derived_cl359, plain,
% 7.48/1.68 (( (product @ e_3 @ e_2 @ e_4))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_4)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl168])).
% 7.48/1.68 thf(zip_derived_cl29, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.68 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.68 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.68 | (equalish @ X0 @ X3))),
% 7.48/1.68 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.68 thf(zip_derived_cl365, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_4) | (equalish @ e_3 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_4)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl359, zip_derived_cl29])).
% 7.48/1.68 thf(zip_derived_cl303, plain,
% 7.48/1.68 (( (product @ e_2 @ e_2 @ e_4)) <= (( (product @ e_2 @ e_2 @ e_4)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl62])).
% 7.48/1.68 thf(zip_derived_cl618, plain,
% 7.48/1.68 (( (equalish @ e_3 @ e_2))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_4)) &
% 7.48/1.68 ( (product @ e_2 @ e_1 @ e_3)) &
% 7.48/1.68 ( (product @ e_2 @ e_2 @ e_4)))),
% 7.48/1.68 inference('s_sup+', [status(thm)], [zip_derived_cl365, zip_derived_cl303])).
% 7.48/1.68 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 7.48/1.68 thf(zip_derived_cl21, plain, (~ (equalish @ e_3 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 7.48/1.68 thf('70', plain,
% 7.48/1.68 (~ ( (product @ e_2 @ e_2 @ e_4)) | ~ ( (product @ e_1 @ e_3 @ e_4)) |
% 7.48/1.68 ~ ( (product @ e_2 @ e_1 @ e_3))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl618, zip_derived_cl21])).
% 7.48/1.68 thf(zip_derived_cl359, plain,
% 7.48/1.68 (( (product @ e_3 @ e_2 @ e_4))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_4)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl168])).
% 7.48/1.68 thf(zip_derived_cl330, plain,
% 7.48/1.68 (( (product @ e_2 @ e_4 @ e_4)) <= (( (product @ e_2 @ e_4 @ e_4)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl64])).
% 7.48/1.68 thf(zip_derived_cl30, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.68 ( (product @ X0 @ X1 @ X2)
% 7.48/1.68 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.68 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.68 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.68 thf(zip_derived_cl337, plain,
% 7.48/1.68 ((![X0 : $i]:
% 7.48/1.68 ( (product @ e_4 @ X0 @ e_4) | ~ (product @ X0 @ e_2 @ e_4)))
% 7.48/1.68 <= (( (product @ e_2 @ e_4 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl330, zip_derived_cl30])).
% 7.48/1.68 thf(zip_derived_cl1236, plain,
% 7.48/1.68 (( (product @ e_4 @ e_3 @ e_4))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_4)) &
% 7.48/1.68 ( (product @ e_2 @ e_1 @ e_3)) &
% 7.48/1.68 ( (product @ e_2 @ e_4 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl359, zip_derived_cl337])).
% 7.48/1.68 thf(zip_derived_cl161, plain,
% 7.48/1.68 (( (product @ e_1 @ e_3 @ e_4)) <= (( (product @ e_1 @ e_3 @ e_4)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl43])).
% 7.48/1.68 thf(zip_derived_cl29, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.68 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.68 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.68 | (equalish @ X0 @ X3))),
% 7.48/1.68 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.68 thf(zip_derived_cl167, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_4) | (equalish @ e_1 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl161, zip_derived_cl29])).
% 7.48/1.68 thf(zip_derived_cl1319, plain,
% 7.48/1.68 (( (equalish @ e_1 @ e_4))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_4)) &
% 7.48/1.68 ( (product @ e_2 @ e_1 @ e_3)) &
% 7.48/1.68 ( (product @ e_2 @ e_4 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)],
% 7.48/1.68 [zip_derived_cl1236, zip_derived_cl167])).
% 7.48/1.68 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 7.48/1.68 thf('71', plain,
% 7.48/1.68 (~ ( (product @ e_1 @ e_3 @ e_4)) | ~ ( (product @ e_2 @ e_4 @ e_4)) |
% 7.48/1.68 ~ ( (product @ e_2 @ e_1 @ e_3))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl1319, zip_derived_cl16])).
% 7.48/1.68 thf(zip_derived_cl319, plain,
% 7.48/1.68 (( (product @ e_2 @ e_3 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl63])).
% 7.48/1.68 thf(zip_derived_cl359, plain,
% 7.48/1.68 (( (product @ e_3 @ e_2 @ e_4))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_4)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl168])).
% 7.48/1.68 thf(zip_derived_cl30, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.68 ( (product @ X0 @ X1 @ X2)
% 7.48/1.68 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.68 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.68 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.68 thf(zip_derived_cl366, plain,
% 7.48/1.68 ((![X0 : $i]:
% 7.48/1.68 ( (product @ e_2 @ X0 @ e_4) | ~ (product @ X0 @ e_3 @ e_2)))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_4)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl359, zip_derived_cl30])).
% 7.48/1.68 thf(zip_derived_cl1294, plain,
% 7.48/1.68 (( (product @ e_2 @ e_2 @ e_4))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_4)) &
% 7.48/1.68 ( (product @ e_2 @ e_1 @ e_3)) &
% 7.48/1.68 ( (product @ e_2 @ e_3 @ e_2)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl319, zip_derived_cl366])).
% 7.48/1.68 thf(zip_derived_cl365, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_4) | (equalish @ e_3 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_4)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl359, zip_derived_cl29])).
% 7.48/1.68 thf(zip_derived_cl1424, plain,
% 7.48/1.68 (( (equalish @ e_3 @ e_2))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_4)) &
% 7.48/1.68 ( (product @ e_2 @ e_1 @ e_3)) &
% 7.48/1.68 ( (product @ e_2 @ e_3 @ e_2)))),
% 7.48/1.68 inference('s_sup-', [status(thm)],
% 7.48/1.68 [zip_derived_cl1294, zip_derived_cl365])).
% 7.48/1.68 thf(zip_derived_cl21, plain, (~ (equalish @ e_3 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 7.48/1.68 thf('72', plain,
% 7.48/1.68 (~ ( (product @ e_1 @ e_3 @ e_4)) | ~ ( (product @ e_2 @ e_3 @ e_2)) |
% 7.48/1.68 ~ ( (product @ e_2 @ e_1 @ e_3))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl1424, zip_derived_cl21])).
% 7.48/1.68 thf(zip_derived_cl317, plain,
% 7.48/1.68 (( (product @ e_2 @ e_3 @ e_4)) <= (( (product @ e_2 @ e_3 @ e_4)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl63])).
% 7.48/1.68 thf(zip_derived_cl167, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_4) | (equalish @ e_1 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl161, zip_derived_cl29])).
% 7.48/1.68 thf(zip_derived_cl545, plain,
% 7.48/1.68 (( (equalish @ e_1 @ e_2))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_4)) & ( (product @ e_2 @ e_3 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl317, zip_derived_cl167])).
% 7.48/1.68 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 7.48/1.68 thf('73', plain,
% 7.48/1.68 (~ ( (product @ e_1 @ e_3 @ e_4)) | ~ ( (product @ e_2 @ e_3 @ e_4))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl545, zip_derived_cl14])).
% 7.48/1.68 thf('74', plain,
% 7.48/1.68 (( (product @ e_2 @ e_3 @ e_4)) | ( (product @ e_2 @ e_3 @ e_1)) |
% 7.48/1.68 ( (product @ e_2 @ e_3 @ e_3)) | ( (product @ e_2 @ e_3 @ e_2))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl63])).
% 7.48/1.68 thf(zip_derived_cl724, plain,
% 7.48/1.68 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_2)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl130])).
% 7.48/1.68 thf(zip_derived_cl28, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.68 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.68 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.68 | (equalish @ X1 @ X3))),
% 7.48/1.68 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.68 thf(zip_derived_cl727, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_2) | (equalish @ e_2 @ X0)))
% 7.48/1.68 <= (( (product @ e_2 @ e_2 @ e_2)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl724, zip_derived_cl28])).
% 7.48/1.68 thf(zip_derived_cl332, plain,
% 7.48/1.68 (( (product @ e_2 @ e_4 @ e_2)) <= (( (product @ e_2 @ e_4 @ e_2)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl64])).
% 7.48/1.68 thf(zip_derived_cl2086, plain,
% 7.48/1.68 (( (equalish @ e_2 @ e_4))
% 7.48/1.68 <= (( (product @ e_2 @ e_2 @ e_2)) & ( (product @ e_2 @ e_4 @ e_2)))),
% 7.48/1.68 inference('s_sup+', [status(thm)], [zip_derived_cl727, zip_derived_cl332])).
% 7.48/1.68 thf(zip_derived_cl19, plain, (~ (equalish @ e_2 @ e_4)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 7.48/1.68 thf('75', plain,
% 7.48/1.68 (~ ( (product @ e_2 @ e_4 @ e_2)) | ~ ( (product @ e_2 @ e_2 @ e_2))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl2086, zip_derived_cl19])).
% 7.48/1.68 thf(zip_derived_cl161, plain,
% 7.48/1.68 (( (product @ e_1 @ e_3 @ e_4)) <= (( (product @ e_1 @ e_3 @ e_4)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl43])).
% 7.48/1.68 thf(zip_derived_cl146, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_4) | (equalish @ e_2 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl141, zip_derived_cl28])).
% 7.48/1.68 thf(zip_derived_cl297, plain,
% 7.48/1.68 (( (equalish @ e_2 @ e_3))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_1 @ e_3 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl161, zip_derived_cl146])).
% 7.48/1.68 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 7.48/1.68 thf('76', plain,
% 7.48/1.68 (~ ( (product @ e_1 @ e_3 @ e_4)) | ~ ( (product @ e_1 @ e_2 @ e_4))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl297, zip_derived_cl18])).
% 7.48/1.68 thf(zip_derived_cl1072, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_1) | (equalish @ e_2 @ X0)))
% 7.48/1.68 <= (( (product @ e_2 @ e_2 @ e_1)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl306, zip_derived_cl29])).
% 7.48/1.68 thf(zip_derived_cl442, plain,
% 7.48/1.68 (( (product @ e_3 @ e_2 @ e_1)) <= (( (product @ e_3 @ e_2 @ e_1)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl94])).
% 7.48/1.68 thf(zip_derived_cl2553, plain,
% 7.48/1.68 (( (equalish @ e_2 @ e_3))
% 7.48/1.68 <= (( (product @ e_2 @ e_2 @ e_1)) & ( (product @ e_3 @ e_2 @ e_1)))),
% 7.48/1.68 inference('s_sup+', [status(thm)],
% 7.48/1.68 [zip_derived_cl1072, zip_derived_cl442])).
% 7.48/1.68 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 7.48/1.68 thf('77', plain,
% 7.48/1.68 (~ ( (product @ e_3 @ e_2 @ e_1)) | ~ ( (product @ e_2 @ e_2 @ e_1))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl2553, zip_derived_cl18])).
% 7.48/1.68 thf(zip_derived_cl306, plain,
% 7.48/1.68 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl62])).
% 7.48/1.68 thf(zip_derived_cl28, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.68 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.68 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.68 | (equalish @ X1 @ X3))),
% 7.48/1.68 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.68 thf(zip_derived_cl1071, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_1) | (equalish @ e_2 @ X0)))
% 7.48/1.68 <= (( (product @ e_2 @ e_2 @ e_1)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl306, zip_derived_cl28])).
% 7.48/1.68 thf(zip_derived_cl320, plain,
% 7.48/1.68 (( (product @ e_2 @ e_3 @ e_1)) <= (( (product @ e_2 @ e_3 @ e_1)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl63])).
% 7.48/1.68 thf(zip_derived_cl2544, plain,
% 7.48/1.68 (( (equalish @ e_2 @ e_3))
% 7.48/1.68 <= (( (product @ e_2 @ e_2 @ e_1)) & ( (product @ e_2 @ e_3 @ e_1)))),
% 7.48/1.68 inference('s_sup+', [status(thm)],
% 7.48/1.68 [zip_derived_cl1071, zip_derived_cl320])).
% 7.48/1.68 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 7.48/1.68 thf('78', plain,
% 7.48/1.68 (~ ( (product @ e_2 @ e_2 @ e_1)) | ~ ( (product @ e_2 @ e_3 @ e_1))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl2544, zip_derived_cl18])).
% 7.48/1.68 thf(zip_derived_cl164, plain,
% 7.48/1.68 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl43])).
% 7.48/1.68 thf(zip_derived_cl104, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_1) | (equalish @ e_1 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl52, zip_derived_cl28])).
% 7.48/1.68 thf(zip_derived_cl843, plain,
% 7.48/1.68 (( (equalish @ e_1 @ e_3))
% 7.48/1.68 <= (( (product @ e_1 @ e_1 @ e_1)) & ( (product @ e_1 @ e_3 @ e_1)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl164, zip_derived_cl104])).
% 7.48/1.68 thf(zip_derived_cl15, plain, (~ (equalish @ e_1 @ e_3)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 7.48/1.68 thf('79', plain,
% 7.48/1.68 (~ ( (product @ e_1 @ e_3 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_1))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl843, zip_derived_cl15])).
% 7.48/1.68 thf('80', plain,
% 7.48/1.68 (( (product @ e_2 @ e_2 @ e_2)) | ( (product @ e_2 @ e_2 @ e_1)) |
% 7.48/1.68 ( (product @ e_2 @ e_2 @ e_3)) | ( (product @ e_2 @ e_2 @ e_4))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl62])).
% 7.48/1.68 thf('81', plain,
% 7.48/1.68 (( (product @ e_1 @ e_1 @ e_1)) | ( (product @ e_1 @ e_1 @ e_2)) |
% 7.48/1.68 ( (product @ e_1 @ e_1 @ e_4)) | ( (product @ e_1 @ e_1 @ e_3))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl41])).
% 7.48/1.68 thf(zip_derived_cl0, plain, ( (next @ e_1 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_1_then_e_2])).
% 7.48/1.68 thf(zip_derived_cl49, plain,
% 7.48/1.68 (( (product @ e_1 @ e_1 @ e_4)) <= (( (product @ e_1 @ e_1 @ e_4)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl41])).
% 7.48/1.68 thf(zip_derived_cl9, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.48/1.68 (~ (product @ X0 @ e_1 @ X1)
% 7.48/1.68 | ~ (next @ X0 @ X2)
% 7.48/1.68 | ~ (greater @ X1 @ X2))),
% 7.48/1.68 inference('cnf', [status(esa)], [no_redundancy])).
% 7.48/1.68 thf(zip_derived_cl60, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (next @ e_1 @ X0) | ~ (greater @ e_4 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_1 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl9])).
% 7.48/1.68 thf(zip_derived_cl70, plain,
% 7.48/1.68 ((~ (greater @ e_4 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl60])).
% 7.48/1.68 thf(zip_derived_cl7, plain, ( (greater @ e_4 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_4_greater_e_2])).
% 7.48/1.68 thf('82', plain, (~ ( (product @ e_1 @ e_1 @ e_4))),
% 7.48/1.68 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl7])).
% 7.48/1.68 thf(zip_derived_cl0, plain, ( (next @ e_1 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_1_then_e_2])).
% 7.48/1.68 thf(zip_derived_cl50, plain,
% 7.48/1.68 (( (product @ e_1 @ e_1 @ e_3)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl41])).
% 7.48/1.68 thf(zip_derived_cl9, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.48/1.68 (~ (product @ X0 @ e_1 @ X1)
% 7.48/1.68 | ~ (next @ X0 @ X2)
% 7.48/1.68 | ~ (greater @ X1 @ X2))),
% 7.48/1.68 inference('cnf', [status(esa)], [no_redundancy])).
% 7.48/1.68 thf(zip_derived_cl80, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (next @ e_1 @ X0) | ~ (greater @ e_3 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl9])).
% 7.48/1.68 thf(zip_derived_cl82, plain,
% 7.48/1.68 ((~ (greater @ e_3 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl80])).
% 7.48/1.68 thf(e_3_greater_e_2, axiom, (greater @ e_3 @ e_2)).
% 7.48/1.68 thf(zip_derived_cl6, plain, ( (greater @ e_3 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_3_greater_e_2])).
% 7.48/1.68 thf('83', plain, (~ ( (product @ e_1 @ e_1 @ e_3))),
% 7.48/1.68 inference('demod', [status(thm)], [zip_derived_cl82, zip_derived_cl6])).
% 7.48/1.68 thf(zip_derived_cl441, plain,
% 7.48/1.68 (( (product @ e_3 @ e_2 @ e_2)) <= (( (product @ e_3 @ e_2 @ e_2)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl94])).
% 7.48/1.68 thf(zip_derived_cl198, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_2) | (equalish @ e_1 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl29])).
% 7.48/1.68 thf(zip_derived_cl1548, plain,
% 7.48/1.68 (( (equalish @ e_1 @ e_3))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_2)) & ( (product @ e_3 @ e_2 @ e_2)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl441, zip_derived_cl198])).
% 7.48/1.68 thf(zip_derived_cl15, plain, (~ (equalish @ e_1 @ e_3)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 7.48/1.68 thf('84', plain,
% 7.48/1.68 (~ ( (product @ e_3 @ e_2 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_2))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl1548, zip_derived_cl15])).
% 7.48/1.68 thf(zip_derived_cl1, plain, ( (next @ e_2 @ e_3)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_2_then_e_3])).
% 7.48/1.68 thf(zip_derived_cl143, plain,
% 7.48/1.68 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl42])).
% 7.48/1.68 thf(zip_derived_cl310, plain,
% 7.48/1.68 ((![X0 : $i]:
% 7.48/1.68 ( (product @ e_2 @ X0 @ e_4) | ~ (product @ X0 @ e_2 @ e_2)))
% 7.48/1.68 <= (( (product @ e_2 @ e_2 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl303, zip_derived_cl30])).
% 7.48/1.68 thf(zip_derived_cl1084, plain,
% 7.48/1.68 (( (product @ e_2 @ e_1 @ e_4))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_2)) & ( (product @ e_2 @ e_2 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl310])).
% 7.48/1.68 thf(zip_derived_cl9, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.48/1.68 (~ (product @ X0 @ e_1 @ X1)
% 7.48/1.68 | ~ (next @ X0 @ X2)
% 7.48/1.68 | ~ (greater @ X1 @ X2))),
% 7.48/1.68 inference('cnf', [status(esa)], [no_redundancy])).
% 7.48/1.68 thf(zip_derived_cl3313, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (next @ e_2 @ X0) | ~ (greater @ e_4 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_2)) & ( (product @ e_2 @ e_2 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl1084, zip_derived_cl9])).
% 7.48/1.68 thf(zip_derived_cl3331, plain,
% 7.48/1.68 ((~ (greater @ e_4 @ e_3))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_2)) & ( (product @ e_2 @ e_2 @ e_4)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl3313])).
% 7.48/1.68 thf(zip_derived_cl8, plain, ( (greater @ e_4 @ e_3)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_4_greater_e_3])).
% 7.48/1.68 thf('85', plain,
% 7.48/1.68 (~ ( (product @ e_2 @ e_2 @ e_4)) | ~ ( (product @ e_1 @ e_2 @ e_2))),
% 7.48/1.68 inference('demod', [status(thm)], [zip_derived_cl3331, zip_derived_cl8])).
% 7.48/1.68 thf(zip_derived_cl724, plain,
% 7.48/1.68 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_2)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl130])).
% 7.48/1.68 thf(zip_derived_cl198, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_2) | (equalish @ e_1 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl29])).
% 7.48/1.68 thf(zip_derived_cl851, plain,
% 7.48/1.68 (( (equalish @ e_1 @ e_2))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_2)) & ( (product @ e_2 @ e_2 @ e_2)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl724, zip_derived_cl198])).
% 7.48/1.68 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 7.48/1.68 thf('86', plain,
% 7.48/1.68 (~ ( (product @ e_1 @ e_2 @ e_2)) | ~ ( (product @ e_2 @ e_2 @ e_2))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl851, zip_derived_cl14])).
% 7.48/1.68 thf(zip_derived_cl163, plain,
% 7.48/1.68 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl43])).
% 7.48/1.68 thf(zip_derived_cl143, plain,
% 7.48/1.68 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl42])).
% 7.48/1.68 thf(zip_derived_cl28, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.68 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.68 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.68 | (equalish @ X1 @ X3))),
% 7.48/1.68 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.68 thf(zip_derived_cl197, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_2 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl28])).
% 7.48/1.68 thf(zip_derived_cl822, plain,
% 7.48/1.68 (( (equalish @ e_2 @ e_3))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_2)) & ( (product @ e_1 @ e_3 @ e_2)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl163, zip_derived_cl197])).
% 7.48/1.68 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 7.48/1.68 thf('87', plain,
% 7.48/1.68 (~ ( (product @ e_1 @ e_2 @ e_2)) | ~ ( (product @ e_1 @ e_3 @ e_2))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl822, zip_derived_cl18])).
% 7.48/1.68 thf(zip_derived_cl143, plain,
% 7.48/1.68 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl42])).
% 7.48/1.68 thf(zip_derived_cl86, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl51, zip_derived_cl28])).
% 7.48/1.68 thf(zip_derived_cl203, plain,
% 7.48/1.68 (( (equalish @ e_1 @ e_2))
% 7.48/1.68 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_1 @ e_2 @ e_2)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl86])).
% 7.48/1.68 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 7.48/1.68 thf('88', plain,
% 7.48/1.68 (~ ( (product @ e_1 @ e_2 @ e_2)) | ~ ( (product @ e_1 @ e_1 @ e_2))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl203, zip_derived_cl14])).
% 7.48/1.68 thf(zip_derived_cl319, plain,
% 7.48/1.68 (( (product @ e_2 @ e_3 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl63])).
% 7.48/1.68 thf(zip_derived_cl510, plain,
% 7.48/1.68 (( (product @ e_3 @ e_2 @ e_3)) <= (( (product @ e_3 @ e_2 @ e_3)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl98])).
% 7.48/1.68 thf(zip_derived_cl30, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.68 ( (product @ X0 @ X1 @ X2)
% 7.48/1.68 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.68 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.68 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.68 thf(zip_derived_cl516, plain,
% 7.48/1.68 ((![X0 : $i]:
% 7.48/1.68 ( (product @ e_2 @ X0 @ e_3) | ~ (product @ X0 @ e_3 @ e_2)))
% 7.48/1.68 <= (( (product @ e_3 @ e_2 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl510, zip_derived_cl30])).
% 7.48/1.68 thf(zip_derived_cl1812, plain,
% 7.48/1.68 (( (product @ e_2 @ e_2 @ e_3))
% 7.48/1.68 <= (( (product @ e_2 @ e_3 @ e_2)) & ( (product @ e_3 @ e_2 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl319, zip_derived_cl516])).
% 7.48/1.68 thf(zip_derived_cl1123, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_3 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl961, zip_derived_cl29])).
% 7.48/1.68 thf(zip_derived_cl5092, plain,
% 7.48/1.68 (( (equalish @ e_3 @ e_2))
% 7.48/1.68 <= (( (product @ e_1 @ e_3 @ e_3)) &
% 7.48/1.68 ( (product @ e_2 @ e_1 @ e_3)) &
% 7.48/1.68 ( (product @ e_2 @ e_3 @ e_2)) &
% 7.48/1.68 ( (product @ e_3 @ e_2 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)],
% 7.48/1.68 [zip_derived_cl1812, zip_derived_cl1123])).
% 7.48/1.68 thf(zip_derived_cl21, plain, (~ (equalish @ e_3 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 7.48/1.68 thf('89', plain,
% 7.48/1.68 (~ ( (product @ e_2 @ e_3 @ e_2)) | ~ ( (product @ e_3 @ e_2 @ e_3)) |
% 7.48/1.68 ~ ( (product @ e_2 @ e_1 @ e_3)) | ~ ( (product @ e_1 @ e_3 @ e_3))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl5092, zip_derived_cl21])).
% 7.48/1.68 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 7.48/1.68 inference('cnf', [status(esa)], [element_3])).
% 7.48/1.68 thf(zip_derived_cl33, plain,
% 7.48/1.68 (![X0 : $i]:
% 7.48/1.68 (~ (group_element @ X0)
% 7.48/1.68 | (product @ e_2 @ X0 @ e_1)
% 7.48/1.68 | (product @ e_2 @ X0 @ e_2)
% 7.48/1.68 | (product @ e_2 @ X0 @ e_3)
% 7.48/1.68 | (product @ e_2 @ X0 @ e_4))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl26])).
% 7.48/1.68 thf(zip_derived_cl67, plain,
% 7.48/1.68 (( (product @ e_2 @ e_3 @ e_1)
% 7.48/1.68 | (product @ e_2 @ e_3 @ e_2)
% 7.48/1.68 | (product @ e_2 @ e_3 @ e_3)
% 7.48/1.68 | (product @ e_2 @ e_3 @ e_4))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl33])).
% 7.48/1.68 thf(zip_derived_cl390, plain,
% 7.48/1.68 (( (product @ e_2 @ e_3 @ e_3)) <= (( (product @ e_2 @ e_3 @ e_3)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl67])).
% 7.48/1.68 thf(zip_derived_cl348, plain,
% 7.48/1.68 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl65])).
% 7.48/1.68 thf(zip_derived_cl28, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.68 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.68 | ~ (product @ X0 @ X3 @ X2)
% 7.48/1.68 | (equalish @ X1 @ X3))),
% 7.48/1.68 inference('cnf', [status(esa)], [product_right_cancellation])).
% 7.48/1.68 thf(zip_derived_cl352, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 7.48/1.68 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl28])).
% 7.48/1.68 thf(zip_derived_cl1100, plain,
% 7.48/1.68 (( (equalish @ e_1 @ e_3))
% 7.48/1.68 <= (( (product @ e_2 @ e_1 @ e_3)) & ( (product @ e_2 @ e_3 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl390, zip_derived_cl352])).
% 7.48/1.68 thf(zip_derived_cl15, plain, (~ (equalish @ e_1 @ e_3)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 7.48/1.68 thf('90', plain,
% 7.48/1.68 (~ ( (product @ e_2 @ e_3 @ e_3)) | ~ ( (product @ e_2 @ e_1 @ e_3))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl1100, zip_derived_cl15])).
% 7.48/1.68 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [element_2])).
% 7.48/1.68 thf(zip_derived_cl33, plain,
% 7.48/1.68 (![X0 : $i]:
% 7.48/1.68 (~ (group_element @ X0)
% 7.48/1.68 | (product @ e_2 @ X0 @ e_1)
% 7.48/1.68 | (product @ e_2 @ X0 @ e_2)
% 7.48/1.68 | (product @ e_2 @ X0 @ e_3)
% 7.48/1.68 | (product @ e_2 @ X0 @ e_4))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl26])).
% 7.48/1.68 thf(zip_derived_cl66, plain,
% 7.48/1.68 (( (product @ e_2 @ e_2 @ e_1)
% 7.48/1.68 | (product @ e_2 @ e_2 @ e_2)
% 7.48/1.68 | (product @ e_2 @ e_2 @ e_3)
% 7.48/1.68 | (product @ e_2 @ e_2 @ e_4))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl33])).
% 7.48/1.68 thf(zip_derived_cl375, plain,
% 7.48/1.68 (( (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl66])).
% 7.48/1.68 thf(zip_derived_cl352, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 7.48/1.68 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl28])).
% 7.48/1.68 thf(zip_derived_cl1099, plain,
% 7.48/1.68 (( (equalish @ e_1 @ e_2))
% 7.48/1.68 <= (( (product @ e_2 @ e_1 @ e_3)) & ( (product @ e_2 @ e_2 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl375, zip_derived_cl352])).
% 7.48/1.68 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 7.48/1.68 thf('91', plain,
% 7.48/1.68 (~ ( (product @ e_2 @ e_2 @ e_3)) | ~ ( (product @ e_2 @ e_1 @ e_3))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl1099, zip_derived_cl14])).
% 7.48/1.68 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 7.48/1.68 inference('cnf', [status(esa)], [element_4])).
% 7.48/1.68 thf(zip_derived_cl33, plain,
% 7.48/1.68 (![X0 : $i]:
% 7.48/1.68 (~ (group_element @ X0)
% 7.48/1.68 | (product @ e_2 @ X0 @ e_1)
% 7.48/1.68 | (product @ e_2 @ X0 @ e_2)
% 7.48/1.68 | (product @ e_2 @ X0 @ e_3)
% 7.48/1.68 | (product @ e_2 @ X0 @ e_4))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl26])).
% 7.48/1.68 thf(zip_derived_cl68, plain,
% 7.48/1.68 (( (product @ e_2 @ e_4 @ e_1)
% 7.48/1.68 | (product @ e_2 @ e_4 @ e_2)
% 7.48/1.68 | (product @ e_2 @ e_4 @ e_3)
% 7.48/1.68 | (product @ e_2 @ e_4 @ e_4))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl33])).
% 7.48/1.68 thf(zip_derived_cl407, plain,
% 7.48/1.68 (( (product @ e_2 @ e_4 @ e_3)) <= (( (product @ e_2 @ e_4 @ e_3)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl68])).
% 7.48/1.68 thf(zip_derived_cl352, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 7.48/1.68 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl28])).
% 7.48/1.68 thf(zip_derived_cl1101, plain,
% 7.48/1.68 (( (equalish @ e_1 @ e_4))
% 7.48/1.68 <= (( (product @ e_2 @ e_1 @ e_3)) & ( (product @ e_2 @ e_4 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl407, zip_derived_cl352])).
% 7.48/1.68 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 7.48/1.68 thf('92', plain,
% 7.48/1.68 (~ ( (product @ e_2 @ e_4 @ e_3)) | ~ ( (product @ e_2 @ e_1 @ e_3))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl1101, zip_derived_cl16])).
% 7.48/1.68 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 7.48/1.68 inference('cnf', [status(esa)], [element_1])).
% 7.48/1.68 thf(zip_derived_cl34, plain,
% 7.48/1.68 (![X0 : $i]:
% 7.48/1.68 (~ (group_element @ X0)
% 7.48/1.68 | (product @ e_3 @ X0 @ e_1)
% 7.48/1.68 | (product @ e_3 @ X0 @ e_2)
% 7.48/1.68 | (product @ e_3 @ X0 @ e_3)
% 7.48/1.68 | (product @ e_3 @ X0 @ e_4))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl26])).
% 7.48/1.68 thf(zip_derived_cl97, plain,
% 7.48/1.68 (( (product @ e_3 @ e_1 @ e_1)
% 7.48/1.68 | (product @ e_3 @ e_1 @ e_2)
% 7.48/1.68 | (product @ e_3 @ e_1 @ e_3)
% 7.48/1.68 | (product @ e_3 @ e_1 @ e_4))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl34])).
% 7.48/1.68 thf(zip_derived_cl493, plain,
% 7.48/1.68 (( (product @ e_3 @ e_1 @ e_3)) <= (( (product @ e_3 @ e_1 @ e_3)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl97])).
% 7.48/1.68 thf(zip_derived_cl348, plain,
% 7.48/1.68 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl65])).
% 7.48/1.68 thf(zip_derived_cl29, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.68 (~ (product @ X0 @ X1 @ X2)
% 7.48/1.68 | ~ (product @ X3 @ X1 @ X2)
% 7.48/1.68 | (equalish @ X0 @ X3))),
% 7.48/1.68 inference('cnf', [status(esa)], [product_left_cancellation])).
% 7.48/1.68 thf(zip_derived_cl353, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_3) | (equalish @ e_2 @ X0)))
% 7.48/1.68 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl29])).
% 7.48/1.68 thf(zip_derived_cl1108, plain,
% 7.48/1.68 (( (equalish @ e_2 @ e_3))
% 7.48/1.68 <= (( (product @ e_2 @ e_1 @ e_3)) & ( (product @ e_3 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl493, zip_derived_cl353])).
% 7.48/1.68 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 7.48/1.68 thf('93', plain,
% 7.48/1.68 (~ ( (product @ e_3 @ e_1 @ e_3)) | ~ ( (product @ e_2 @ e_1 @ e_3))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl1108, zip_derived_cl18])).
% 7.48/1.68 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 7.48/1.68 inference('cnf', [status(esa)], [element_1])).
% 7.48/1.68 thf(zip_derived_cl35, plain,
% 7.48/1.68 (![X0 : $i]:
% 7.48/1.68 (~ (group_element @ X0)
% 7.48/1.68 | (product @ e_4 @ X0 @ e_1)
% 7.48/1.68 | (product @ e_4 @ X0 @ e_2)
% 7.48/1.68 | (product @ e_4 @ X0 @ e_3)
% 7.48/1.68 | (product @ e_4 @ X0 @ e_4))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl26])).
% 7.48/1.68 thf(zip_derived_cl116, plain,
% 7.48/1.68 (( (product @ e_4 @ e_1 @ e_1)
% 7.48/1.68 | (product @ e_4 @ e_1 @ e_2)
% 7.48/1.68 | (product @ e_4 @ e_1 @ e_3)
% 7.48/1.68 | (product @ e_4 @ e_1 @ e_4))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl35])).
% 7.48/1.68 thf(zip_derived_cl645, plain,
% 7.48/1.68 (( (product @ e_4 @ e_1 @ e_3)) <= (( (product @ e_4 @ e_1 @ e_3)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl116])).
% 7.48/1.68 thf(zip_derived_cl353, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_3) | (equalish @ e_2 @ X0)))
% 7.48/1.68 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl29])).
% 7.48/1.68 thf(zip_derived_cl1109, plain,
% 7.48/1.68 (( (equalish @ e_2 @ e_4))
% 7.48/1.68 <= (( (product @ e_2 @ e_1 @ e_3)) & ( (product @ e_4 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl645, zip_derived_cl353])).
% 7.48/1.68 thf(zip_derived_cl19, plain, (~ (equalish @ e_2 @ e_4)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 7.48/1.68 thf('94', plain,
% 7.48/1.68 (~ ( (product @ e_4 @ e_1 @ e_3)) | ~ ( (product @ e_2 @ e_1 @ e_3))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl1109, zip_derived_cl19])).
% 7.48/1.68 thf(zip_derived_cl0, plain, ( (next @ e_1 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_1_then_e_2])).
% 7.48/1.68 thf(zip_derived_cl231, plain,
% 7.48/1.68 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl46])).
% 7.48/1.68 thf(zip_derived_cl354, plain,
% 7.48/1.68 ((![X0 : $i]:
% 7.48/1.68 ( (product @ e_1 @ X0 @ e_3) | ~ (product @ X0 @ e_2 @ e_1)))
% 7.48/1.68 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl348, zip_derived_cl30])).
% 7.48/1.68 thf(zip_derived_cl1284, plain,
% 7.48/1.68 (( (product @ e_1 @ e_1 @ e_3))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_1)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl231, zip_derived_cl354])).
% 7.48/1.68 thf(zip_derived_cl9, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i]:
% 7.48/1.68 (~ (product @ X0 @ e_1 @ X1)
% 7.48/1.68 | ~ (next @ X0 @ X2)
% 7.48/1.68 | ~ (greater @ X1 @ X2))),
% 7.48/1.68 inference('cnf', [status(esa)], [no_redundancy])).
% 7.48/1.68 thf(zip_derived_cl3946, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (next @ e_1 @ X0) | ~ (greater @ e_3 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_1)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl1284, zip_derived_cl9])).
% 7.48/1.68 thf(zip_derived_cl3961, plain,
% 7.48/1.68 ((~ (greater @ e_3 @ e_2))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_1)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl3946])).
% 7.48/1.68 thf(zip_derived_cl6, plain, ( (greater @ e_3 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_3_greater_e_2])).
% 7.48/1.68 thf('95', plain,
% 7.48/1.68 (~ ( (product @ e_1 @ e_2 @ e_1)) | ~ ( (product @ e_2 @ e_1 @ e_3))),
% 7.48/1.68 inference('demod', [status(thm)], [zip_derived_cl3961, zip_derived_cl6])).
% 7.48/1.68 thf('96', plain,
% 7.48/1.68 (( (product @ e_3 @ e_2 @ e_3)) | ( (product @ e_3 @ e_2 @ e_2)) |
% 7.48/1.68 ( (product @ e_3 @ e_2 @ e_4)) | ( (product @ e_3 @ e_2 @ e_1))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl94])).
% 7.48/1.68 thf('97', plain,
% 7.48/1.68 (( (product @ e_2 @ e_1 @ e_2)) | ( (product @ e_2 @ e_1 @ e_3)) |
% 7.48/1.68 ( (product @ e_2 @ e_1 @ e_4)) | ( (product @ e_2 @ e_1 @ e_1))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl61])).
% 7.48/1.68 thf(zip_derived_cl281, plain,
% 7.48/1.68 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl61])).
% 7.48/1.68 thf(zip_derived_cl142, plain,
% 7.48/1.68 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl42])).
% 7.48/1.68 thf(zip_derived_cl30, plain,
% 7.48/1.68 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 7.48/1.68 ( (product @ X0 @ X1 @ X2)
% 7.48/1.68 | ~ (product @ X3 @ X0 @ X2)
% 7.48/1.68 | ~ (product @ X1 @ X3 @ X0))),
% 7.48/1.68 inference('cnf', [status(esa)], [zf_stmt_0])).
% 7.48/1.68 thf(zip_derived_cl181, plain,
% 7.48/1.68 ((![X0 : $i]:
% 7.48/1.68 ( (product @ e_2 @ X0 @ e_3) | ~ (product @ X0 @ e_1 @ e_2)))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl30])).
% 7.48/1.68 thf(zip_derived_cl1019, plain,
% 7.48/1.68 (( (product @ e_2 @ e_2 @ e_3))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl281, zip_derived_cl181])).
% 7.48/1.68 thf(zip_derived_cl180, plain,
% 7.48/1.68 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_1 @ X0)))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl29])).
% 7.48/1.68 thf(zip_derived_cl2933, plain,
% 7.48/1.68 (( (equalish @ e_1 @ e_2))
% 7.48/1.68 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 7.48/1.68 inference('s_sup-', [status(thm)],
% 7.48/1.68 [zip_derived_cl1019, zip_derived_cl180])).
% 7.48/1.68 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 7.48/1.68 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 7.48/1.68 thf('98', plain,
% 7.48/1.68 (~ ( (product @ e_1 @ e_2 @ e_3)) | ~ ( (product @ e_2 @ e_1 @ e_2))),
% 7.48/1.68 inference('s_sup-', [status(thm)], [zip_derived_cl2933, zip_derived_cl14])).
% 7.48/1.68 thf('99', plain,
% 7.48/1.68 (( (product @ e_1 @ e_2 @ e_3)) | ( (product @ e_1 @ e_2 @ e_4)) |
% 7.48/1.68 ( (product @ e_1 @ e_2 @ e_1)) | ( (product @ e_1 @ e_2 @ e_2))),
% 7.48/1.68 inference('split', [status(esa)], [zip_derived_cl42])).
% 7.48/1.68 thf(zip_derived_cl7627, plain, ($false),
% 7.48/1.68 inference('sat_resolution*', [status(thm)],
% 7.48/1.68 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 7.48/1.68 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 7.48/1.68 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 7.48/1.68 '32', '33', '34', '35', '36', '37', '38', '39', '40', '41',
% 7.48/1.68 '42', '43', '44', '45', '46', '47', '48', '49', '50', '51',
% 7.48/1.68 '52', '53', '54', '55', '56', '57', '58', '59', '60', '61',
% 7.48/1.68 '62', '63', '64', '65', '66', '67', '68', '69', '70', '71',
% 7.48/1.68 '72', '73', '74', '75', '76', '77', '78', '79', '80', '81',
% 7.48/1.68 '82', '83', '84', '85', '86', '87', '88', '89', '90', '91',
% 7.48/1.68 '92', '93', '94', '95', '96', '97', '98', '99'])).
% 7.48/1.68
% 7.48/1.68 % SZS output end Refutation
% 7.48/1.68
% 7.48/1.68
% 7.48/1.68 % Terminating...
% 8.12/1.77 % Runner terminated.
% 8.12/1.78 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------