TSTP Solution File: GRP133-1.003 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP133-1.003 : 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.dzhQOhqvSs true
% Computer : n029.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 01:50:17 EDT 2023
% Result : Unsatisfiable 1.19s 0.95s
% Output : Refutation 1.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP133-1.003 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.dzhQOhqvSs true
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 02:34:56 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
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.57/0.60 % Total configuration time : 435
% 0.57/0.60 % Estimated wc time : 1092
% 0.57/0.60 % Estimated cpu time (7 cpus) : 156.0
% 0.83/0.65 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.83/0.66 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.83/0.70 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.83/0.70 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.83/0.70 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.83/0.71 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.83/0.71 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.19/0.95 % Solved by fo/fo1_av.sh.
% 1.19/0.95 % done 1320 iterations in 0.216s
% 1.19/0.95 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.19/0.95 % SZS output start Refutation
% 1.19/0.95 thf(e_1_type, type, e_1: $i).
% 1.19/0.95 thf(e_3_type, type, e_3: $i).
% 1.19/0.95 thf(group_element_type, type, group_element: $i > $o).
% 1.19/0.95 thf(e_2_type, type, e_2: $i).
% 1.19/0.95 thf(product_type, type, product: $i > $i > $i > $o).
% 1.19/0.95 thf(equalish_type, type, equalish: $i > $i > $o).
% 1.19/0.95 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 1.19/0.95 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 1.19/0.95 thf(element_2, axiom, (group_element @ e_2)).
% 1.19/0.95 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_2])).
% 1.19/0.95 thf(product_total_function1, axiom,
% 1.19/0.95 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 1.19/0.95 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 1.19/0.95 ( product @ X @ Y @ e_3 ))).
% 1.19/0.95 thf(zip_derived_cl9, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i]:
% 1.19/0.95 (~ (group_element @ X0)
% 1.19/0.95 | ~ (group_element @ X1)
% 1.19/0.95 | (product @ X0 @ X1 @ e_1)
% 1.19/0.95 | (product @ X0 @ X1 @ e_2)
% 1.19/0.95 | (product @ X0 @ X1 @ e_3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_total_function1])).
% 1.19/0.95 thf(zip_derived_cl22, plain,
% 1.19/0.95 (![X0 : $i]:
% 1.19/0.95 ( (product @ X0 @ X0 @ e_3)
% 1.19/0.95 | (product @ X0 @ X0 @ e_2)
% 1.19/0.95 | (product @ X0 @ X0 @ e_1)
% 1.19/0.95 | ~ (group_element @ X0))),
% 1.19/0.95 inference('eq_fact', [status(thm)], [zip_derived_cl9])).
% 1.19/0.95 thf(zip_derived_cl25, plain,
% 1.19/0.95 (( (product @ e_2 @ e_2 @ e_3)
% 1.19/0.95 | (product @ e_2 @ e_2 @ e_2)
% 1.19/0.95 | (product @ e_2 @ e_2 @ e_1))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl22])).
% 1.19/0.95 thf(zip_derived_cl65, plain,
% 1.19/0.95 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl25])).
% 1.19/0.95 thf(product_total_function2, axiom,
% 1.19/0.95 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 1.19/0.95 ( equalish @ W @ Z ))).
% 1.19/0.95 thf(zip_derived_cl10, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X0 @ X1 @ X3)
% 1.19/0.95 | (equalish @ X2 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_total_function2])).
% 1.19/0.95 thf(zip_derived_cl154, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_2 @ e_2 @ X0) | (equalish @ e_2 @ X0)))
% 1.19/0.95 <= (( (product @ e_2 @ e_2 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl10])).
% 1.19/0.95 thf(element_1, axiom, (group_element @ e_1)).
% 1.19/0.95 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_1])).
% 1.19/0.95 thf(zip_derived_cl9, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i]:
% 1.19/0.95 (~ (group_element @ X0)
% 1.19/0.95 | ~ (group_element @ X1)
% 1.19/0.95 | (product @ X0 @ X1 @ e_1)
% 1.19/0.95 | (product @ X0 @ X1 @ e_2)
% 1.19/0.95 | (product @ X0 @ X1 @ e_3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_total_function1])).
% 1.19/0.95 thf(zip_derived_cl19, plain,
% 1.19/0.95 (![X0 : $i]:
% 1.19/0.95 (~ (group_element @ X0)
% 1.19/0.95 | (product @ e_1 @ X0 @ e_1)
% 1.19/0.95 | (product @ e_1 @ X0 @ e_2)
% 1.19/0.95 | (product @ e_1 @ X0 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 1.19/0.95 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_1])).
% 1.19/0.95 thf(zip_derived_cl27, plain,
% 1.19/0.95 (( (product @ e_1 @ e_1 @ e_3)
% 1.19/0.95 | (product @ e_1 @ e_1 @ e_2)
% 1.19/0.95 | (product @ e_1 @ e_1 @ e_1))),
% 1.19/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl0])).
% 1.19/0.95 thf(zip_derived_cl111, plain,
% 1.19/0.95 (( (product @ e_1 @ e_1 @ e_3)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl27])).
% 1.19/0.95 thf(zip_derived_cl64, plain,
% 1.19/0.95 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl25])).
% 1.19/0.95 thf(qg3, conjecture,
% 1.19/0.95 (~( ( product @ Z1 @ Z2 @ X ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 1.19/0.95 ( ~( product @ X @ Y @ Z1 ) ) ))).
% 1.19/0.95 thf(zf_stmt_0, negated_conjecture,
% 1.19/0.95 (( product @ Z1 @ Z2 @ X ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 1.19/0.95 ( ~( product @ X @ Y @ Z1 ) )),
% 1.19/0.95 inference('cnf.neg', [status(esa)], [qg3])).
% 1.19/0.95 thf(zip_derived_cl13, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 ( (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X3 @ X2 @ X1)
% 1.19/0.95 | ~ (product @ X2 @ X3 @ X0))),
% 1.19/0.95 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.19/0.95 thf(zip_derived_cl18, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i]:
% 1.19/0.95 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 1.19/0.95 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 1.19/0.95 thf(zip_derived_cl74, plain,
% 1.19/0.95 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl18])).
% 1.19/0.95 thf(zip_derived_cl10, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X0 @ X1 @ X3)
% 1.19/0.95 | (equalish @ X2 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_total_function2])).
% 1.19/0.95 thf(zip_derived_cl98, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_1 @ e_1 @ X0) | (equalish @ e_2 @ X0)))
% 1.19/0.95 <= (( (product @ e_2 @ e_2 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl10])).
% 1.19/0.95 thf(zip_derived_cl472, plain,
% 1.19/0.95 (( (equalish @ e_2 @ e_3))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_3)) & ( (product @ e_2 @ e_2 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl98])).
% 1.19/0.95 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 1.19/0.95 thf('0', plain,
% 1.19/0.95 (~ ( (product @ e_2 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl472, zip_derived_cl6])).
% 1.19/0.95 thf(zip_derived_cl74, plain,
% 1.19/0.95 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl18])).
% 1.19/0.95 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_1])).
% 1.19/0.95 thf(zip_derived_cl22, plain,
% 1.19/0.95 (![X0 : $i]:
% 1.19/0.95 ( (product @ X0 @ X0 @ e_3)
% 1.19/0.95 | (product @ X0 @ X0 @ e_2)
% 1.19/0.95 | (product @ X0 @ X0 @ e_1)
% 1.19/0.95 | ~ (group_element @ X0))),
% 1.19/0.95 inference('eq_fact', [status(thm)], [zip_derived_cl9])).
% 1.19/0.95 thf(zip_derived_cl24, plain,
% 1.19/0.95 (( (product @ e_1 @ e_1 @ e_3)
% 1.19/0.95 | (product @ e_1 @ e_1 @ e_2)
% 1.19/0.95 | (product @ e_1 @ e_1 @ e_1))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl22])).
% 1.19/0.95 thf(zip_derived_cl45, plain,
% 1.19/0.95 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl24])).
% 1.19/0.95 thf(zip_derived_cl10, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X0 @ X1 @ X3)
% 1.19/0.95 | (equalish @ X2 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_total_function2])).
% 1.19/0.95 thf(zip_derived_cl48, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_1 @ e_1 @ X0) | (equalish @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl10])).
% 1.19/0.95 thf(zip_derived_cl106, plain,
% 1.19/0.95 (( (equalish @ e_1 @ e_2))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_1)) & ( (product @ e_2 @ e_2 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl48])).
% 1.19/0.95 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 1.19/0.95 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.19/0.95 thf('1', plain,
% 1.19/0.95 (~ ( (product @ e_2 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_1))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl3])).
% 1.19/0.95 thf(zip_derived_cl19, plain,
% 1.19/0.95 (![X0 : $i]:
% 1.19/0.95 (~ (group_element @ X0)
% 1.19/0.95 | (product @ e_1 @ X0 @ e_1)
% 1.19/0.95 | (product @ e_1 @ X0 @ e_2)
% 1.19/0.95 | (product @ e_1 @ X0 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 1.19/0.95 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_2])).
% 1.19/0.95 thf(zip_derived_cl28, plain,
% 1.19/0.95 (( (product @ e_1 @ e_2 @ e_3)
% 1.19/0.95 | (product @ e_1 @ e_2 @ e_2)
% 1.19/0.95 | (product @ e_1 @ e_2 @ e_1))),
% 1.19/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl1])).
% 1.19/0.95 thf(zip_derived_cl124, plain,
% 1.19/0.95 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl28])).
% 1.19/0.95 thf(zip_derived_cl46, plain,
% 1.19/0.95 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl24])).
% 1.19/0.95 thf(zip_derived_cl18, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i]:
% 1.19/0.95 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 1.19/0.95 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 1.19/0.95 thf(zip_derived_cl63, plain,
% 1.19/0.95 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl18])).
% 1.19/0.95 thf(product_left_cancellation, axiom,
% 1.19/0.95 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 1.19/0.95 ( equalish @ W @ Z ))).
% 1.19/0.95 thf(zip_derived_cl12, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X3 @ X1 @ X2)
% 1.19/0.95 | (equalish @ X0 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.19/0.95 thf(zip_derived_cl77, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_1) | (equalish @ e_2 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl12])).
% 1.19/0.95 thf(zip_derived_cl426, plain,
% 1.19/0.95 (( (equalish @ e_2 @ e_1))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_1 @ e_2 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl124, zip_derived_cl77])).
% 1.19/0.95 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 1.19/0.95 thf(zip_derived_cl5, plain, (~ (equalish @ e_2 @ e_1)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 1.19/0.95 thf('2', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_1))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl426, zip_derived_cl5])).
% 1.19/0.95 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_2])).
% 1.19/0.95 thf(zip_derived_cl19, plain,
% 1.19/0.95 (![X0 : $i]:
% 1.19/0.95 (~ (group_element @ X0)
% 1.19/0.95 | (product @ e_1 @ X0 @ e_1)
% 1.19/0.95 | (product @ e_1 @ X0 @ e_2)
% 1.19/0.95 | (product @ e_1 @ X0 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 1.19/0.95 thf(zip_derived_cl31, plain,
% 1.19/0.95 (( (product @ e_1 @ e_2 @ e_1)
% 1.19/0.95 | (product @ e_1 @ e_2 @ e_2)
% 1.19/0.95 | (product @ e_1 @ e_2 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl19])).
% 1.19/0.95 thf(zip_derived_cl184, plain,
% 1.19/0.95 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl31])).
% 1.19/0.95 thf(zip_derived_cl46, plain,
% 1.19/0.95 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl24])).
% 1.19/0.95 thf(product_right_cancellation, axiom,
% 1.19/0.95 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 1.19/0.95 ( equalish @ W @ Z ))).
% 1.19/0.95 thf(zip_derived_cl11, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X0 @ X3 @ X2)
% 1.19/0.95 | (equalish @ X1 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.19/0.95 thf(zip_derived_cl57, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl11])).
% 1.19/0.95 thf(zip_derived_cl244, plain,
% 1.19/0.95 (( (equalish @ e_1 @ e_2))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_1 @ e_2 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl184, zip_derived_cl57])).
% 1.19/0.95 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.19/0.95 thf('3', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_2))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl244, zip_derived_cl3])).
% 1.19/0.95 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_2])).
% 1.19/0.95 thf(zip_derived_cl9, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i]:
% 1.19/0.95 (~ (group_element @ X0)
% 1.19/0.95 | ~ (group_element @ X1)
% 1.19/0.95 | (product @ X0 @ X1 @ e_1)
% 1.19/0.95 | (product @ X0 @ X1 @ e_2)
% 1.19/0.95 | (product @ X0 @ X1 @ e_3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_total_function1])).
% 1.19/0.95 thf(zip_derived_cl20, plain,
% 1.19/0.95 (![X0 : $i]:
% 1.19/0.95 (~ (group_element @ X0)
% 1.19/0.95 | (product @ e_2 @ X0 @ e_1)
% 1.19/0.95 | (product @ e_2 @ X0 @ e_2)
% 1.19/0.95 | (product @ e_2 @ X0 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 1.19/0.95 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_1])).
% 1.19/0.95 thf(zip_derived_cl33, plain,
% 1.19/0.95 (( (product @ e_2 @ e_1 @ e_3)
% 1.19/0.95 | (product @ e_2 @ e_1 @ e_2)
% 1.19/0.95 | (product @ e_2 @ e_1 @ e_1))),
% 1.19/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 1.19/0.95 thf(zip_derived_cl219, plain,
% 1.19/0.95 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl33])).
% 1.19/0.95 thf(zip_derived_cl66, plain,
% 1.19/0.95 (( (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl25])).
% 1.19/0.95 thf(zip_derived_cl11, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X0 @ X3 @ X2)
% 1.19/0.95 | (equalish @ X1 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.19/0.95 thf(zip_derived_cl176, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_3) | (equalish @ e_2 @ X0)))
% 1.19/0.95 <= (( (product @ e_2 @ e_2 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl66, zip_derived_cl11])).
% 1.19/0.95 thf(zip_derived_cl671, plain,
% 1.19/0.95 (( (equalish @ e_2 @ e_1))
% 1.19/0.95 <= (( (product @ e_2 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl219, zip_derived_cl176])).
% 1.19/0.95 thf(zip_derived_cl5, plain, (~ (equalish @ e_2 @ e_1)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 1.19/0.95 thf('4', plain,
% 1.19/0.95 (~ ( (product @ e_2 @ e_1 @ e_3)) | ~ ( (product @ e_2 @ e_2 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl671, zip_derived_cl5])).
% 1.19/0.95 thf(zip_derived_cl219, plain,
% 1.19/0.95 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl33])).
% 1.19/0.95 thf(zip_derived_cl111, plain,
% 1.19/0.95 (( (product @ e_1 @ e_1 @ e_3)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl27])).
% 1.19/0.95 thf(zip_derived_cl12, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X3 @ X1 @ X2)
% 1.19/0.95 | (equalish @ X0 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.19/0.95 thf(zip_derived_cl114, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_3) | (equalish @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl12])).
% 1.19/0.95 thf(zip_derived_cl521, plain,
% 1.19/0.95 (( (equalish @ e_1 @ e_2))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl219, zip_derived_cl114])).
% 1.19/0.95 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.19/0.95 thf('5', plain,
% 1.19/0.95 (~ ( (product @ e_2 @ e_1 @ e_3)) | ~ ( (product @ e_1 @ e_1 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl521, zip_derived_cl3])).
% 1.19/0.95 thf(zip_derived_cl184, plain,
% 1.19/0.95 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl31])).
% 1.19/0.95 thf(zip_derived_cl65, plain,
% 1.19/0.95 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl25])).
% 1.19/0.95 thf(zip_derived_cl12, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X3 @ X1 @ X2)
% 1.19/0.95 | (equalish @ X0 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.19/0.95 thf(zip_derived_cl156, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_2) | (equalish @ e_2 @ X0)))
% 1.19/0.95 <= (( (product @ e_2 @ e_2 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl12])).
% 1.19/0.95 thf(zip_derived_cl623, plain,
% 1.19/0.95 (( (equalish @ e_2 @ e_1))
% 1.19/0.95 <= (( (product @ e_2 @ e_2 @ e_2)) & ( (product @ e_1 @ e_2 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl184, zip_derived_cl156])).
% 1.19/0.95 thf(zip_derived_cl5, plain, (~ (equalish @ e_2 @ e_1)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 1.19/0.95 thf('6', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_2 @ e_2)) | ~ ( (product @ e_2 @ e_2 @ e_2))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl623, zip_derived_cl5])).
% 1.19/0.95 thf('7', plain,
% 1.19/0.95 (( (product @ e_1 @ e_2 @ e_1)) | ( (product @ e_1 @ e_2 @ e_2)) |
% 1.19/0.95 ( (product @ e_1 @ e_2 @ e_3))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl28])).
% 1.19/0.95 thf(zip_derived_cl19, plain,
% 1.19/0.95 (![X0 : $i]:
% 1.19/0.95 (~ (group_element @ X0)
% 1.19/0.95 | (product @ e_1 @ X0 @ e_1)
% 1.19/0.95 | (product @ e_1 @ X0 @ e_2)
% 1.19/0.95 | (product @ e_1 @ X0 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 1.19/0.95 thf(element_3, axiom, (group_element @ e_3)).
% 1.19/0.95 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_3])).
% 1.19/0.95 thf(zip_derived_cl29, plain,
% 1.19/0.95 (( (product @ e_1 @ e_3 @ e_3)
% 1.19/0.95 | (product @ e_1 @ e_3 @ e_2)
% 1.19/0.95 | (product @ e_1 @ e_3 @ e_1))),
% 1.19/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl2])).
% 1.19/0.95 thf('8', plain,
% 1.19/0.95 (( (product @ e_1 @ e_3 @ e_2)) | ( (product @ e_1 @ e_3 @ e_3)) |
% 1.19/0.95 ( (product @ e_1 @ e_3 @ e_1))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl29])).
% 1.19/0.95 thf(zip_derived_cl146, plain,
% 1.19/0.95 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl29])).
% 1.19/0.95 thf(zip_derived_cl45, plain,
% 1.19/0.95 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl24])).
% 1.19/0.95 thf(zip_derived_cl11, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X0 @ X3 @ X2)
% 1.19/0.95 | (equalish @ X1 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.19/0.95 thf(zip_derived_cl49, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_1) | (equalish @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl11])).
% 1.19/0.95 thf(zip_derived_cl340, plain,
% 1.19/0.95 (( (equalish @ e_1 @ e_3))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_1)) & ( (product @ e_1 @ e_3 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl146, zip_derived_cl49])).
% 1.19/0.95 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 1.19/0.95 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 1.19/0.95 thf('9', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_3 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_1))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl340, zip_derived_cl4])).
% 1.19/0.95 thf(zip_derived_cl20, plain,
% 1.19/0.95 (![X0 : $i]:
% 1.19/0.95 (~ (group_element @ X0)
% 1.19/0.95 | (product @ e_2 @ X0 @ e_1)
% 1.19/0.95 | (product @ e_2 @ X0 @ e_2)
% 1.19/0.95 | (product @ e_2 @ X0 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 1.19/0.95 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_3])).
% 1.19/0.95 thf(zip_derived_cl35, plain,
% 1.19/0.95 (( (product @ e_2 @ e_3 @ e_3)
% 1.19/0.95 | (product @ e_2 @ e_3 @ e_2)
% 1.19/0.95 | (product @ e_2 @ e_3 @ e_1))),
% 1.19/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl2])).
% 1.19/0.95 thf('10', plain,
% 1.19/0.95 (( (product @ e_2 @ e_3 @ e_3)) | ( (product @ e_2 @ e_3 @ e_2)) |
% 1.19/0.95 ( (product @ e_2 @ e_3 @ e_1))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl35])).
% 1.19/0.95 thf('11', plain,
% 1.19/0.95 (( (product @ e_2 @ e_1 @ e_1)) | ( (product @ e_2 @ e_1 @ e_2)) |
% 1.19/0.95 ( (product @ e_2 @ e_1 @ e_3))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl33])).
% 1.19/0.95 thf(zip_derived_cl250, plain,
% 1.19/0.95 (( (product @ e_2 @ e_3 @ e_1)) <= (( (product @ e_2 @ e_3 @ e_1)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl35])).
% 1.19/0.95 thf(zip_derived_cl63, plain,
% 1.19/0.95 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl18])).
% 1.19/0.95 thf(zip_derived_cl11, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X0 @ X3 @ X2)
% 1.19/0.95 | (equalish @ X1 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.19/0.95 thf(zip_derived_cl76, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_1) | (equalish @ e_2 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl11])).
% 1.19/0.95 thf(zip_derived_cl856, plain,
% 1.19/0.95 (( (equalish @ e_2 @ e_3))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_2 @ e_3 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl250, zip_derived_cl76])).
% 1.19/0.95 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 1.19/0.95 thf('12', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_2 @ e_3 @ e_1))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl856, zip_derived_cl6])).
% 1.19/0.95 thf(zip_derived_cl221, plain,
% 1.19/0.95 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl33])).
% 1.19/0.95 thf(zip_derived_cl76, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_1) | (equalish @ e_2 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl11])).
% 1.19/0.95 thf(zip_derived_cl421, plain,
% 1.19/0.95 (( (equalish @ e_2 @ e_1))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_2)) & ( (product @ e_2 @ e_1 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl221, zip_derived_cl76])).
% 1.19/0.95 thf(zip_derived_cl5, plain, (~ (equalish @ e_2 @ e_1)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 1.19/0.95 thf('13', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_2 @ e_1 @ e_1))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl421, zip_derived_cl5])).
% 1.19/0.95 thf(zip_derived_cl219, plain,
% 1.19/0.95 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl33])).
% 1.19/0.95 thf(zip_derived_cl122, plain,
% 1.19/0.95 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl28])).
% 1.19/0.95 thf(zip_derived_cl13, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 ( (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X3 @ X2 @ X1)
% 1.19/0.95 | ~ (product @ X2 @ X3 @ X0))),
% 1.19/0.95 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.19/0.95 thf(zip_derived_cl128, plain,
% 1.19/0.95 ((![X0 : $i]:
% 1.19/0.95 ( (product @ X0 @ e_3 @ e_2) | ~ (product @ e_2 @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl13])).
% 1.19/0.95 thf(zip_derived_cl561, plain,
% 1.19/0.95 (( (product @ e_3 @ e_3 @ e_2))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl219, zip_derived_cl128])).
% 1.19/0.95 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_3])).
% 1.19/0.95 thf(zip_derived_cl20, plain,
% 1.19/0.95 (![X0 : $i]:
% 1.19/0.95 (~ (group_element @ X0)
% 1.19/0.95 | (product @ e_2 @ X0 @ e_1)
% 1.19/0.95 | (product @ e_2 @ X0 @ e_2)
% 1.19/0.95 | (product @ e_2 @ X0 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 1.19/0.95 thf(zip_derived_cl38, plain,
% 1.19/0.95 (( (product @ e_2 @ e_3 @ e_1)
% 1.19/0.95 | (product @ e_2 @ e_3 @ e_2)
% 1.19/0.95 | (product @ e_2 @ e_3 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl20])).
% 1.19/0.95 thf(zip_derived_cl304, plain,
% 1.19/0.95 (( (product @ e_2 @ e_3 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl38])).
% 1.19/0.95 thf(zip_derived_cl12, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X3 @ X1 @ X2)
% 1.19/0.95 | (equalish @ X0 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.19/0.95 thf(zip_derived_cl308, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_2) | (equalish @ e_2 @ X0)))
% 1.19/0.95 <= (( (product @ e_2 @ e_3 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl304, zip_derived_cl12])).
% 1.19/0.95 thf(zip_derived_cl1332, plain,
% 1.19/0.95 (( (equalish @ e_2 @ e_3))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_3)) &
% 1.19/0.95 ( (product @ e_2 @ e_1 @ e_3)) &
% 1.19/0.95 ( (product @ e_2 @ e_3 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl561, zip_derived_cl308])).
% 1.19/0.95 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 1.19/0.95 thf('14', plain,
% 1.19/0.95 (~ ( (product @ e_2 @ e_3 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_3)) |
% 1.19/0.95 ~ ( (product @ e_2 @ e_1 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1332, zip_derived_cl6])).
% 1.19/0.95 thf(zip_derived_cl248, plain,
% 1.19/0.95 (( (product @ e_2 @ e_3 @ e_3)) <= (( (product @ e_2 @ e_3 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl35])).
% 1.19/0.95 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_3])).
% 1.19/0.95 thf(zip_derived_cl22, plain,
% 1.19/0.95 (![X0 : $i]:
% 1.19/0.95 ( (product @ X0 @ X0 @ e_3)
% 1.19/0.95 | (product @ X0 @ X0 @ e_2)
% 1.19/0.95 | (product @ X0 @ X0 @ e_1)
% 1.19/0.95 | ~ (group_element @ X0))),
% 1.19/0.95 inference('eq_fact', [status(thm)], [zip_derived_cl9])).
% 1.19/0.95 thf(zip_derived_cl26, plain,
% 1.19/0.95 (( (product @ e_3 @ e_3 @ e_3)
% 1.19/0.95 | (product @ e_3 @ e_3 @ e_2)
% 1.19/0.95 | (product @ e_3 @ e_3 @ e_1))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl22])).
% 1.19/0.95 thf(zip_derived_cl85, plain,
% 1.19/0.95 (( (product @ e_3 @ e_3 @ e_3)) <= (( (product @ e_3 @ e_3 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl26])).
% 1.19/0.95 thf(zip_derived_cl12, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X3 @ X1 @ X2)
% 1.19/0.95 | (equalish @ X0 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.19/0.95 thf(zip_derived_cl232, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_3) | (equalish @ e_3 @ X0)))
% 1.19/0.95 <= (( (product @ e_3 @ e_3 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl12])).
% 1.19/0.95 thf(zip_derived_cl812, plain,
% 1.19/0.95 (( (equalish @ e_3 @ e_2))
% 1.19/0.95 <= (( (product @ e_3 @ e_3 @ e_3)) & ( (product @ e_2 @ e_3 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl248, zip_derived_cl232])).
% 1.19/0.95 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 1.19/0.95 thf(zip_derived_cl8, plain, (~ (equalish @ e_3 @ e_2)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 1.19/0.95 thf('15', plain,
% 1.19/0.95 (~ ( (product @ e_3 @ e_3 @ e_3)) | ~ ( (product @ e_2 @ e_3 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl812, zip_derived_cl8])).
% 1.19/0.95 thf('16', plain,
% 1.19/0.95 (( (product @ e_3 @ e_3 @ e_1)) | ( (product @ e_3 @ e_3 @ e_3)) |
% 1.19/0.95 ( (product @ e_3 @ e_3 @ e_2))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl26])).
% 1.19/0.95 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_1])).
% 1.19/0.95 thf(zip_derived_cl20, plain,
% 1.19/0.95 (![X0 : $i]:
% 1.19/0.95 (~ (group_element @ X0)
% 1.19/0.95 | (product @ e_2 @ X0 @ e_1)
% 1.19/0.95 | (product @ e_2 @ X0 @ e_2)
% 1.19/0.95 | (product @ e_2 @ X0 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 1.19/0.95 thf(zip_derived_cl36, plain,
% 1.19/0.95 (( (product @ e_2 @ e_1 @ e_1)
% 1.19/0.95 | (product @ e_2 @ e_1 @ e_2)
% 1.19/0.95 | (product @ e_2 @ e_1 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl20])).
% 1.19/0.95 thf(zip_derived_cl271, plain,
% 1.19/0.95 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl36])).
% 1.19/0.95 thf(zip_derived_cl128, plain,
% 1.19/0.95 ((![X0 : $i]:
% 1.19/0.95 ( (product @ X0 @ e_3 @ e_2) | ~ (product @ e_2 @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl13])).
% 1.19/0.95 thf(zip_derived_cl560, plain,
% 1.19/0.95 (( (product @ e_2 @ e_3 @ e_2))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl271, zip_derived_cl128])).
% 1.19/0.95 thf(zip_derived_cl271, plain,
% 1.19/0.95 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl36])).
% 1.19/0.95 thf(zip_derived_cl11, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X0 @ X3 @ X2)
% 1.19/0.95 | (equalish @ X1 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.19/0.95 thf(zip_derived_cl274, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl271, zip_derived_cl11])).
% 1.19/0.95 thf(zip_derived_cl1312, plain,
% 1.19/0.95 (( (equalish @ e_1 @ e_3))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl560, zip_derived_cl274])).
% 1.19/0.95 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 1.19/0.95 thf('17', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_2 @ e_3)) | ~ ( (product @ e_2 @ e_1 @ e_2))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1312, zip_derived_cl4])).
% 1.19/0.95 thf(zip_derived_cl144, plain,
% 1.19/0.95 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl29])).
% 1.19/0.95 thf(zip_derived_cl122, plain,
% 1.19/0.95 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl28])).
% 1.19/0.95 thf(zip_derived_cl11, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X0 @ X3 @ X2)
% 1.19/0.95 | (equalish @ X1 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.19/0.95 thf(zip_derived_cl126, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_2 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl11])).
% 1.19/0.95 thf(zip_derived_cl540, plain,
% 1.19/0.95 (( (equalish @ e_2 @ e_3))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_1 @ e_3 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl144, zip_derived_cl126])).
% 1.19/0.95 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 1.19/0.95 thf('18', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_2 @ e_3)) | ~ ( (product @ e_1 @ e_3 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl540, zip_derived_cl6])).
% 1.19/0.95 thf(zip_derived_cl84, plain,
% 1.19/0.95 (( (product @ e_3 @ e_3 @ e_2)) <= (( (product @ e_3 @ e_3 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl26])).
% 1.19/0.95 thf(zip_derived_cl18, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i]:
% 1.19/0.95 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 1.19/0.95 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 1.19/0.95 thf(zip_derived_cl200, plain,
% 1.19/0.95 (( (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_3 @ e_3 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl84, zip_derived_cl18])).
% 1.19/0.95 thf(zip_derived_cl122, plain,
% 1.19/0.95 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl28])).
% 1.19/0.95 thf(zip_derived_cl12, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X3 @ X1 @ X2)
% 1.19/0.95 | (equalish @ X0 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.19/0.95 thf(zip_derived_cl127, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl12])).
% 1.19/0.95 thf(zip_derived_cl545, plain,
% 1.19/0.95 (( (equalish @ e_1 @ e_2))
% 1.19/0.95 <= (( (product @ e_3 @ e_3 @ e_2)) & ( (product @ e_1 @ e_2 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl200, zip_derived_cl127])).
% 1.19/0.95 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.19/0.95 thf('19', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_2 @ e_3)) | ~ ( (product @ e_3 @ e_3 @ e_2))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl545, zip_derived_cl3])).
% 1.19/0.95 thf(zip_derived_cl126, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_2 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl11])).
% 1.19/0.95 thf(zip_derived_cl83, plain,
% 1.19/0.95 (( (product @ e_3 @ e_3 @ e_1)) <= (( (product @ e_3 @ e_3 @ e_1)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl26])).
% 1.19/0.95 thf(zip_derived_cl18, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i]:
% 1.19/0.95 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 1.19/0.95 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 1.19/0.95 thf(zip_derived_cl93, plain,
% 1.19/0.95 (( (product @ e_1 @ e_1 @ e_3)) <= (( (product @ e_3 @ e_3 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl83, zip_derived_cl18])).
% 1.19/0.95 thf(zip_derived_cl534, plain,
% 1.19/0.95 (( (equalish @ e_2 @ e_1))
% 1.19/0.95 <= (( (product @ e_3 @ e_3 @ e_1)) & ( (product @ e_1 @ e_2 @ e_3)))),
% 1.19/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl93])).
% 1.19/0.95 thf(zip_derived_cl5, plain, (~ (equalish @ e_2 @ e_1)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 1.19/0.95 thf('20', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_2 @ e_3)) | ~ ( (product @ e_3 @ e_3 @ e_1))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl534, zip_derived_cl5])).
% 1.19/0.95 thf(zip_derived_cl122, plain,
% 1.19/0.95 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl28])).
% 1.19/0.95 thf(zip_derived_cl111, plain,
% 1.19/0.95 (( (product @ e_1 @ e_1 @ e_3)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl27])).
% 1.19/0.95 thf(zip_derived_cl11, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X0 @ X3 @ X2)
% 1.19/0.95 | (equalish @ X1 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.19/0.95 thf(zip_derived_cl113, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl11])).
% 1.19/0.95 thf(zip_derived_cl513, plain,
% 1.19/0.95 (( (equalish @ e_1 @ e_2))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_3)) & ( (product @ e_1 @ e_2 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl113])).
% 1.19/0.95 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.19/0.95 thf('21', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_2 @ e_3)) | ~ ( (product @ e_1 @ e_1 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl513, zip_derived_cl3])).
% 1.19/0.95 thf(zip_derived_cl561, plain,
% 1.19/0.95 (( (product @ e_3 @ e_3 @ e_2))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl219, zip_derived_cl128])).
% 1.19/0.95 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_3])).
% 1.19/0.95 thf(zip_derived_cl19, plain,
% 1.19/0.95 (![X0 : $i]:
% 1.19/0.95 (~ (group_element @ X0)
% 1.19/0.95 | (product @ e_1 @ X0 @ e_1)
% 1.19/0.95 | (product @ e_1 @ X0 @ e_2)
% 1.19/0.95 | (product @ e_1 @ X0 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 1.19/0.95 thf(zip_derived_cl32, plain,
% 1.19/0.95 (( (product @ e_1 @ e_3 @ e_1)
% 1.19/0.95 | (product @ e_1 @ e_3 @ e_2)
% 1.19/0.95 | (product @ e_1 @ e_3 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl19])).
% 1.19/0.95 thf(zip_derived_cl202, plain,
% 1.19/0.95 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl32])).
% 1.19/0.95 thf(zip_derived_cl12, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X3 @ X1 @ X2)
% 1.19/0.95 | (equalish @ X0 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.19/0.95 thf(zip_derived_cl206, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_2) | (equalish @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_3 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl202, zip_derived_cl12])).
% 1.19/0.95 thf(zip_derived_cl1330, plain,
% 1.19/0.95 (( (equalish @ e_1 @ e_3))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_3)) &
% 1.19/0.95 ( (product @ e_1 @ e_3 @ e_2)) &
% 1.19/0.95 ( (product @ e_2 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl561, zip_derived_cl206])).
% 1.19/0.95 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 1.19/0.95 thf('22', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_2 @ e_3)) | ~ ( (product @ e_1 @ e_3 @ e_2)) |
% 1.19/0.95 ~ ( (product @ e_2 @ e_1 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1330, zip_derived_cl4])).
% 1.19/0.95 thf(zip_derived_cl221, plain,
% 1.19/0.95 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl33])).
% 1.19/0.95 thf(zip_derived_cl45, plain,
% 1.19/0.95 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl24])).
% 1.19/0.95 thf(zip_derived_cl12, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X3 @ X1 @ X2)
% 1.19/0.95 | (equalish @ X0 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.19/0.95 thf(zip_derived_cl50, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_1) | (equalish @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl12])).
% 1.19/0.95 thf(zip_derived_cl384, plain,
% 1.19/0.95 (( (equalish @ e_1 @ e_2))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_1)) & ( (product @ e_2 @ e_1 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl221, zip_derived_cl50])).
% 1.19/0.95 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.19/0.95 thf('23', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_1 @ e_1)) | ~ ( (product @ e_2 @ e_1 @ e_1))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl384, zip_derived_cl3])).
% 1.19/0.95 thf(zip_derived_cl124, plain,
% 1.19/0.95 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl28])).
% 1.19/0.95 thf(zip_derived_cl49, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_1) | (equalish @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl11])).
% 1.19/0.95 thf(zip_derived_cl268, plain,
% 1.19/0.95 (( (equalish @ e_1 @ e_2))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_1)) & ( (product @ e_1 @ e_2 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl124, zip_derived_cl49])).
% 1.19/0.95 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.19/0.95 thf('24', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_1 @ e_1)) | ~ ( (product @ e_1 @ e_2 @ e_1))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl268, zip_derived_cl3])).
% 1.19/0.95 thf(zip_derived_cl271, plain,
% 1.19/0.95 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl36])).
% 1.19/0.95 thf(zip_derived_cl184, plain,
% 1.19/0.95 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl31])).
% 1.19/0.95 thf(zip_derived_cl13, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 ( (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X3 @ X2 @ X1)
% 1.19/0.95 | ~ (product @ X2 @ X3 @ X0))),
% 1.19/0.95 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.19/0.95 thf(zip_derived_cl189, plain,
% 1.19/0.95 ((![X0 : $i]:
% 1.19/0.95 ( (product @ X0 @ e_2 @ e_2) | ~ (product @ e_2 @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl184, zip_derived_cl13])).
% 1.19/0.95 thf(zip_derived_cl721, plain,
% 1.19/0.95 (( (product @ e_2 @ e_2 @ e_2))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_2)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl271, zip_derived_cl189])).
% 1.19/0.95 thf(zip_derived_cl184, plain,
% 1.19/0.95 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl31])).
% 1.19/0.95 thf(zip_derived_cl12, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X3 @ X1 @ X2)
% 1.19/0.95 | (equalish @ X0 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.19/0.95 thf(zip_derived_cl188, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_2) | (equalish @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl184, zip_derived_cl12])).
% 1.19/0.95 thf(zip_derived_cl1428, plain,
% 1.19/0.95 (( (equalish @ e_1 @ e_2))
% 1.19/0.95 <= (( (product @ e_1 @ e_2 @ e_2)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl721, zip_derived_cl188])).
% 1.19/0.95 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.19/0.95 thf('25', plain,
% 1.19/0.95 (~ ( (product @ e_2 @ e_1 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_2))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1428, zip_derived_cl3])).
% 1.19/0.95 thf('26', plain,
% 1.19/0.95 (( (product @ e_1 @ e_1 @ e_3)) | ( (product @ e_1 @ e_1 @ e_1)) |
% 1.19/0.95 ( (product @ e_1 @ e_1 @ e_2))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl24])).
% 1.19/0.95 thf(zip_derived_cl66, plain,
% 1.19/0.95 (( (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl25])).
% 1.19/0.95 thf(zip_derived_cl18, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i]:
% 1.19/0.95 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 1.19/0.95 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 1.19/0.95 thf(zip_derived_cl182, plain,
% 1.19/0.95 (( (product @ e_3 @ e_3 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl66, zip_derived_cl18])).
% 1.19/0.95 thf(zip_derived_cl111, plain,
% 1.19/0.95 (( (product @ e_1 @ e_1 @ e_3)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl27])).
% 1.19/0.95 thf(zip_derived_cl18, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i]:
% 1.19/0.95 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 1.19/0.95 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 1.19/0.95 thf(zip_derived_cl119, plain,
% 1.19/0.95 (( (product @ e_3 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl18])).
% 1.19/0.95 thf(zip_derived_cl10, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X0 @ X1 @ X3)
% 1.19/0.95 | (equalish @ X2 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_total_function2])).
% 1.19/0.95 thf(zip_derived_cl167, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_3 @ e_3 @ X0) | (equalish @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl119, zip_derived_cl10])).
% 1.19/0.95 thf(zip_derived_cl633, plain,
% 1.19/0.95 (( (equalish @ e_1 @ e_2))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_3)) & ( (product @ e_2 @ e_2 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl182, zip_derived_cl167])).
% 1.19/0.95 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.19/0.95 thf('27', plain,
% 1.19/0.95 (~ ( (product @ e_2 @ e_2 @ e_3)) | ~ ( (product @ e_1 @ e_1 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl633, zip_derived_cl3])).
% 1.19/0.95 thf('28', plain,
% 1.19/0.95 (( (product @ e_2 @ e_2 @ e_2)) | ( (product @ e_2 @ e_2 @ e_3)) |
% 1.19/0.95 ( (product @ e_2 @ e_2 @ e_1))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl25])).
% 1.19/0.95 thf('29', plain, (( (product @ e_2 @ e_2 @ e_2))),
% 1.19/0.95 inference('sat_resolution*', [status(thm)],
% 1.19/0.95 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 1.19/0.95 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 1.19/0.95 '22', '23', '24', '25', '26', '27', '28'])).
% 1.19/0.95 thf(zip_derived_cl1465, plain,
% 1.19/0.95 (![X0 : $i]: (~ (product @ e_2 @ e_2 @ X0) | (equalish @ e_2 @ X0))),
% 1.19/0.95 inference('simpl_trail', [status(thm)], [zip_derived_cl154, '29'])).
% 1.19/0.95 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_1])).
% 1.19/0.95 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_3])).
% 1.19/0.95 thf(zip_derived_cl9, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i]:
% 1.19/0.95 (~ (group_element @ X0)
% 1.19/0.95 | ~ (group_element @ X1)
% 1.19/0.95 | (product @ X0 @ X1 @ e_1)
% 1.19/0.95 | (product @ X0 @ X1 @ e_2)
% 1.19/0.95 | (product @ X0 @ X1 @ e_3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_total_function1])).
% 1.19/0.95 thf(zip_derived_cl21, plain,
% 1.19/0.95 (![X0 : $i]:
% 1.19/0.95 (~ (group_element @ X0)
% 1.19/0.95 | (product @ e_3 @ X0 @ e_1)
% 1.19/0.95 | (product @ e_3 @ X0 @ e_2)
% 1.19/0.95 | (product @ e_3 @ X0 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl9])).
% 1.19/0.95 thf(zip_derived_cl42, plain,
% 1.19/0.95 (( (product @ e_3 @ e_1 @ e_1)
% 1.19/0.95 | (product @ e_3 @ e_1 @ e_2)
% 1.19/0.95 | (product @ e_3 @ e_1 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl21])).
% 1.19/0.95 thf(zip_derived_cl366, plain,
% 1.19/0.95 (( (product @ e_3 @ e_1 @ e_2)) <= (( (product @ e_3 @ e_1 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl42])).
% 1.19/0.95 thf(zip_derived_cl202, plain,
% 1.19/0.95 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl32])).
% 1.19/0.95 thf(zip_derived_cl13, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 ( (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X3 @ X2 @ X1)
% 1.19/0.95 | ~ (product @ X2 @ X3 @ X0))),
% 1.19/0.95 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.19/0.95 thf(zip_derived_cl207, plain,
% 1.19/0.95 ((![X0 : $i]:
% 1.19/0.95 ( (product @ X0 @ e_2 @ e_3) | ~ (product @ e_3 @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_3 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl202, zip_derived_cl13])).
% 1.19/0.95 thf(zip_derived_cl772, plain,
% 1.19/0.95 (( (product @ e_2 @ e_2 @ e_3))
% 1.19/0.95 <= (( (product @ e_1 @ e_3 @ e_2)) & ( (product @ e_3 @ e_1 @ e_2)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl366, zip_derived_cl207])).
% 1.19/0.95 thf(zip_derived_cl119, plain,
% 1.19/0.95 (( (product @ e_3 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl18])).
% 1.19/0.95 thf(zip_derived_cl12, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X3 @ X1 @ X2)
% 1.19/0.95 | (equalish @ X0 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.19/0.95 thf(zip_derived_cl169, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_1) | (equalish @ e_3 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl119, zip_derived_cl12])).
% 1.19/0.95 thf(zip_derived_cl146, plain,
% 1.19/0.95 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl29])).
% 1.19/0.95 thf(zip_derived_cl647, plain,
% 1.19/0.95 (( (equalish @ e_3 @ e_1))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_3)) & ( (product @ e_1 @ e_3 @ e_1)))),
% 1.19/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl169, zip_derived_cl146])).
% 1.19/0.95 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 1.19/0.95 thf(zip_derived_cl7, plain, (~ (equalish @ e_3 @ e_1)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 1.19/0.95 thf('30', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_3 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl647, zip_derived_cl7])).
% 1.19/0.95 thf(zip_derived_cl144, plain,
% 1.19/0.95 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl29])).
% 1.19/0.95 thf(zip_derived_cl113, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl11])).
% 1.19/0.95 thf(zip_derived_cl514, plain,
% 1.19/0.95 (( (equalish @ e_1 @ e_3))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_3)) & ( (product @ e_1 @ e_3 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl144, zip_derived_cl113])).
% 1.19/0.95 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 1.19/0.95 thf('31', plain,
% 1.19/0.95 (~ ( (product @ e_1 @ e_3 @ e_3)) | ~ ( (product @ e_1 @ e_1 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl514, zip_derived_cl4])).
% 1.19/0.95 thf('32', plain, (( (product @ e_1 @ e_3 @ e_2))),
% 1.19/0.95 inference('sat_resolution*', [status(thm)],
% 1.19/0.95 ['30', '28', '1', '2', '3', '4', '5', '6', '7', '9', '10',
% 1.19/0.95 '11', '12', '13', '14', '15', '16', '17', '18', '19', '20',
% 1.19/0.95 '21', '22', '23', '24', '25', '26', '31', '8'])).
% 1.19/0.95 thf(zip_derived_cl21, plain,
% 1.19/0.95 (![X0 : $i]:
% 1.19/0.95 (~ (group_element @ X0)
% 1.19/0.95 | (product @ e_3 @ X0 @ e_1)
% 1.19/0.95 | (product @ e_3 @ X0 @ e_2)
% 1.19/0.95 | (product @ e_3 @ X0 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl9])).
% 1.19/0.95 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 1.19/0.95 inference('cnf', [status(esa)], [element_1])).
% 1.19/0.95 thf(zip_derived_cl39, plain,
% 1.19/0.95 (( (product @ e_3 @ e_1 @ e_3)
% 1.19/0.95 | (product @ e_3 @ e_1 @ e_2)
% 1.19/0.95 | (product @ e_3 @ e_1 @ e_1))),
% 1.19/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl0])).
% 1.19/0.95 thf(zip_derived_cl325, plain,
% 1.19/0.95 (( (product @ e_3 @ e_1 @ e_1)) <= (( (product @ e_3 @ e_1 @ e_1)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl39])).
% 1.19/0.95 thf(zip_derived_cl119, plain,
% 1.19/0.95 (( (product @ e_3 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl18])).
% 1.19/0.95 thf(zip_derived_cl11, plain,
% 1.19/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.19/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.19/0.95 | ~ (product @ X0 @ X3 @ X2)
% 1.19/0.95 | (equalish @ X1 @ X3))),
% 1.19/0.95 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.19/0.95 thf(zip_derived_cl168, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ e_3 @ X0 @ e_1) | (equalish @ e_3 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl119, zip_derived_cl11])).
% 1.19/0.95 thf(zip_derived_cl1024, plain,
% 1.19/0.95 (( (equalish @ e_3 @ e_1))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_3)) & ( (product @ e_3 @ e_1 @ e_1)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl325, zip_derived_cl168])).
% 1.19/0.95 thf(zip_derived_cl7, plain, (~ (equalish @ e_3 @ e_1)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 1.19/0.95 thf('33', plain,
% 1.19/0.95 (~ ( (product @ e_3 @ e_1 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1024, zip_derived_cl7])).
% 1.19/0.95 thf(zip_derived_cl323, plain,
% 1.19/0.95 (( (product @ e_3 @ e_1 @ e_3)) <= (( (product @ e_3 @ e_1 @ e_3)))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl39])).
% 1.19/0.95 thf(zip_derived_cl114, plain,
% 1.19/0.95 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_3) | (equalish @ e_1 @ X0)))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl12])).
% 1.19/0.95 thf(zip_derived_cl522, plain,
% 1.19/0.95 (( (equalish @ e_1 @ e_3))
% 1.19/0.95 <= (( (product @ e_1 @ e_1 @ e_3)) & ( (product @ e_3 @ e_1 @ e_3)))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl323, zip_derived_cl114])).
% 1.19/0.95 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 1.19/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 1.19/0.95 thf('34', plain,
% 1.19/0.95 (~ ( (product @ e_3 @ e_1 @ e_3)) | ~ ( (product @ e_1 @ e_1 @ e_3))),
% 1.19/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl522, zip_derived_cl4])).
% 1.19/0.95 thf('35', plain,
% 1.19/0.95 (( (product @ e_3 @ e_1 @ e_2)) | ( (product @ e_3 @ e_1 @ e_3)) |
% 1.19/0.95 ( (product @ e_3 @ e_1 @ e_1))),
% 1.19/0.95 inference('split', [status(esa)], [zip_derived_cl39])).
% 1.19/0.95 thf('36', plain, (( (product @ e_3 @ e_1 @ e_2))),
% 1.19/0.95 inference('sat_resolution*', [status(thm)],
% 1.19/0.95 ['33', '28', '1', '2', '3', '4', '5', '6', '7', '8', '9',
% 1.19/0.95 '10', '11', '12', '13', '14', '15', '16', '17', '18', '19',
% 1.19/0.95 '20', '21', '22', '23', '24', '25', '26', '34', '35'])).
% 1.19/0.95 thf(zip_derived_cl1442, plain, ( (product @ e_2 @ e_2 @ e_3)),
% 1.19/0.95 inference('simpl_trail', [status(thm)], [zip_derived_cl772, '32', '36'])).
% 1.19/0.95 thf(zip_derived_cl1606, plain, ( (equalish @ e_2 @ e_3)),
% 1.19/0.95 inference('s_sup+', [status(thm)],
% 1.19/0.95 [zip_derived_cl1465, zip_derived_cl1442])).
% 1.19/0.95 thf(zip_derived_cl1609, plain, ($false),
% 1.19/0.95 inference('demod', [status(thm)], [zip_derived_cl6, zip_derived_cl1606])).
% 1.19/0.95
% 1.19/0.95 % SZS output end Refutation
% 1.19/0.95
% 1.19/0.95
% 1.19/0.95 % Terminating...
% 1.19/1.01 % Runner terminated.
% 1.65/1.02 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------