%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP134-2.003 : TPTP v9.2.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.d4eYEOvvNz true
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:35:48 PM UTC 2025
% Result : Unsatisfiable 0.76s 0.96s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : GRP134-2.003 : TPTP v9.2.0. Released v1.2.0.
% 0.09/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.d4eYEOvvNz true
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Oct 1 14:14:53 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % Running portfolio for 300 s
% 0.11/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.32 % Number of cores: 8
% 0.11/0.32 % Python version: Python 3.6.8
% 0.11/0.33 % Running in FO mode
% 0.54/0.63 % Total configuration time : 435
% 0.54/0.63 % Estimated wc time : 1092
% 0.54/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.58/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.75/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.75/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.75/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.75/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.75/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.75/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.76/0.96 % Solved by fo/fo1_av.sh.
% 0.76/0.96 % done 705 iterations in 0.213s
% 0.76/0.96 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.76/0.96 % SZS output start Refutation
% 0.76/0.96 thf(greater_type, type, greater: $i > $i > $o).
% 0.76/0.96 thf(product_type, type, product: $i > $i > $i > $o).
% 0.76/0.96 thf(e_3_type, type, e_3: $i).
% 0.76/0.96 thf(e_2_type, type, e_2: $i).
% 0.76/0.96 thf(e_1_type, type, e_1: $i).
% 0.76/0.96 thf(next_type, type, next: $i > $i > $o).
% 0.76/0.96 thf(group_element_type, type, group_element: $i > $o).
% 0.76/0.96 thf(equalish_type, type, equalish: $i > $i > $o).
% 0.76/0.96 thf(element_2, axiom, (group_element @ e_2)).
% 0.76/0.96 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [element_2])).
% 0.76/0.96 thf(product_total_function1, axiom,
% 0.76/0.96 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 0.76/0.96 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 0.76/0.96 ( product @ X @ Y @ e_3 ))).
% 0.76/0.96 thf(zip_derived_cl15, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i]:
% 0.76/0.96 (~ (group_element @ X0)
% 0.76/0.96 | ~ (group_element @ X1)
% 0.76/0.96 | (product @ X0 @ X1 @ e_1)
% 0.76/0.96 | (product @ X0 @ X1 @ e_2)
% 0.76/0.96 | (product @ X0 @ X1 @ e_3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_total_function1])).
% 0.76/0.96 thf(zip_derived_cl22, plain,
% 0.76/0.96 (![X0 : $i]:
% 0.76/0.96 (~ (group_element @ X0)
% 0.76/0.96 | (product @ e_2 @ X0 @ e_1)
% 0.76/0.96 | (product @ e_2 @ X0 @ e_2)
% 0.76/0.96 | (product @ e_2 @ X0 @ e_3))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl15])).
% 0.76/0.96 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [element_2])).
% 0.76/0.96 thf(zip_derived_cl49, plain,
% 0.76/0.96 (( (product @ e_2 @ e_2 @ e_3)
% 0.76/0.96 | (product @ e_2 @ e_2 @ e_2)
% 0.76/0.96 | (product @ e_2 @ e_2 @ e_1))),
% 0.76/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl7])).
% 0.76/0.96 thf(zip_derived_cl204, plain,
% 0.76/0.96 (( (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl49])).
% 0.76/0.96 thf(product_total_function2, axiom,
% 0.76/0.96 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 0.76/0.96 ( equalish @ W @ Z ))).
% 0.76/0.96 thf(zip_derived_cl16, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X0 @ X1 @ X3)
% 0.76/0.96 | (equalish @ X2 @ X3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_total_function2])).
% 0.76/0.96 thf(zip_derived_cl207, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (product @ e_2 @ e_2 @ X0) | (equalish @ e_3 @ X0)))
% 0.76/0.96 <= (( (product @ e_2 @ e_2 @ e_3)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl204, zip_derived_cl16])).
% 0.76/0.96 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 0.76/0.96 thf(zip_derived_cl13, plain, (~ (equalish @ e_3 @ e_1)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.76/0.96 thf(zip_derived_cl635, plain,
% 0.76/0.96 ((~ (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl207, zip_derived_cl13])).
% 0.76/0.96 thf(element_1, axiom, (group_element @ e_1)).
% 0.76/0.96 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.76/0.96 inference('cnf', [status(esa)], [element_1])).
% 0.76/0.96 thf(zip_derived_cl22, plain,
% 0.76/0.96 (![X0 : $i]:
% 0.76/0.96 (~ (group_element @ X0)
% 0.76/0.96 | (product @ e_2 @ X0 @ e_1)
% 0.76/0.96 | (product @ e_2 @ X0 @ e_2)
% 0.76/0.96 | (product @ e_2 @ X0 @ e_3))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl15])).
% 0.76/0.96 thf(zip_derived_cl51, plain,
% 0.76/0.96 (( (product @ e_2 @ e_1 @ e_1)
% 0.76/0.96 | (product @ e_2 @ e_1 @ e_2)
% 0.76/0.96 | (product @ e_2 @ e_1 @ e_3))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl22])).
% 0.76/0.96 thf(zip_derived_cl249, plain,
% 0.76/0.96 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl51])).
% 0.76/0.96 thf(product_right_cancellation, axiom,
% 0.76/0.96 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 0.76/0.96 ( equalish @ W @ Z ))).
% 0.76/0.96 thf(zip_derived_cl17, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.76/0.96 | (equalish @ X1 @ X3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.76/0.96 thf(zip_derived_cl252, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 0.76/0.96 <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl249, zip_derived_cl17])).
% 0.76/0.96 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 0.76/0.96 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.76/0.96 thf(zip_derived_cl700, plain,
% 0.76/0.96 ((~ (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl252, zip_derived_cl9])).
% 0.76/0.96 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [element_2])).
% 0.76/0.96 thf(zip_derived_cl22, plain,
% 0.76/0.96 (![X0 : $i]:
% 0.76/0.96 (~ (group_element @ X0)
% 0.76/0.96 | (product @ e_2 @ X0 @ e_1)
% 0.76/0.96 | (product @ e_2 @ X0 @ e_2)
% 0.76/0.96 | (product @ e_2 @ X0 @ e_3))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl15])).
% 0.76/0.96 thf(zip_derived_cl52, plain,
% 0.76/0.96 (( (product @ e_2 @ e_2 @ e_1)
% 0.76/0.96 | (product @ e_2 @ e_2 @ e_2)
% 0.76/0.96 | (product @ e_2 @ e_2 @ e_3))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl22])).
% 0.76/0.96 thf(zip_derived_cl282, plain,
% 0.76/0.96 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_2)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl52])).
% 0.76/0.96 thf('0', plain,
% 0.76/0.96 (~ ( (product @ e_2 @ e_2 @ e_2)) | ~ ( (product @ e_2 @ e_1 @ e_2))),
% 0.76/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl700, zip_derived_cl282])).
% 0.76/0.96 thf(zip_derived_cl282, plain,
% 0.76/0.96 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_2)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl52])).
% 0.76/0.96 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.76/0.96 inference('cnf', [status(esa)], [element_1])).
% 0.76/0.96 thf(zip_derived_cl15, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i]:
% 0.76/0.96 (~ (group_element @ X0)
% 0.76/0.96 | ~ (group_element @ X1)
% 0.76/0.96 | (product @ X0 @ X1 @ e_1)
% 0.76/0.96 | (product @ X0 @ X1 @ e_2)
% 0.76/0.96 | (product @ X0 @ X1 @ e_3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_total_function1])).
% 0.76/0.96 thf(zip_derived_cl21, plain,
% 0.76/0.96 (![X0 : $i]:
% 0.76/0.96 (~ (group_element @ X0)
% 0.76/0.96 | (product @ e_1 @ X0 @ e_1)
% 0.76/0.96 | (product @ e_1 @ X0 @ e_2)
% 0.76/0.96 | (product @ e_1 @ X0 @ e_3))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl15])).
% 0.76/0.96 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.76/0.96 inference('cnf', [status(esa)], [element_1])).
% 0.76/0.96 thf(zip_derived_cl30, plain,
% 0.76/0.96 (( (product @ e_1 @ e_1 @ e_3)
% 0.76/0.96 | (product @ e_1 @ e_1 @ e_2)
% 0.76/0.96 | (product @ e_1 @ e_1 @ e_1))),
% 0.76/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl6])).
% 0.76/0.96 thf(zip_derived_cl37, plain,
% 0.76/0.96 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.76/0.96 thf(qg4, conjecture,
% 0.76/0.96 (~( ( product @ Z1 @ Z2 @ Y ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 0.76/0.96 ( ~( product @ X @ Y @ Z1 ) ) ))).
% 0.76/0.96 thf(zf_stmt_0, negated_conjecture,
% 0.76/0.96 (( product @ Z1 @ Z2 @ Y ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 0.76/0.96 ( ~( product @ X @ Y @ Z1 ) )),
% 0.76/0.96 inference('cnf.neg', [status(esa)], [qg4])).
% 0.76/0.96 thf(zip_derived_cl19, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 ( (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X2 @ X3 @ X1)
% 0.76/0.96 | ~ (product @ X3 @ X2 @ X0))),
% 0.76/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.76/0.96 thf(zip_derived_cl28, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i]:
% 0.76/0.96 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 0.76/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 0.76/0.96 thf(zip_derived_cl65, plain,
% 0.76/0.96 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl28])).
% 0.76/0.96 thf(zip_derived_cl16, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X0 @ X1 @ X3)
% 0.76/0.96 | (equalish @ X2 @ X3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_total_function2])).
% 0.76/0.96 thf(zip_derived_cl69, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (product @ e_2 @ e_2 @ X0) | (equalish @ e_1 @ X0)))
% 0.76/0.96 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl16])).
% 0.76/0.96 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.76/0.96 thf(zip_derived_cl101, plain,
% 0.76/0.96 ((~ (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl69, zip_derived_cl9])).
% 0.76/0.96 thf('1', plain,
% 0.76/0.96 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_2 @ e_2 @ e_2))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl282, zip_derived_cl101])).
% 0.76/0.96 thf(zip_derived_cl22, plain,
% 0.76/0.96 (![X0 : $i]:
% 0.76/0.96 (~ (group_element @ X0)
% 0.76/0.96 | (product @ e_2 @ X0 @ e_1)
% 0.76/0.96 | (product @ e_2 @ X0 @ e_2)
% 0.76/0.96 | (product @ e_2 @ X0 @ e_3))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl15])).
% 0.76/0.96 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.76/0.96 inference('cnf', [status(esa)], [element_1])).
% 0.76/0.96 thf(zip_derived_cl48, plain,
% 0.76/0.96 (( (product @ e_2 @ e_1 @ e_3)
% 0.76/0.96 | (product @ e_2 @ e_1 @ e_2)
% 0.76/0.96 | (product @ e_2 @ e_1 @ e_1))),
% 0.76/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl6])).
% 0.76/0.96 thf(zip_derived_cl184, plain,
% 0.76/0.96 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl48])).
% 0.76/0.96 thf(zip_derived_cl65, plain,
% 0.76/0.96 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl28])).
% 0.76/0.96 thf(zip_derived_cl17, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.76/0.96 | (equalish @ X1 @ X3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.76/0.96 thf(zip_derived_cl70, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_1) | (equalish @ e_2 @ X0)))
% 0.76/0.96 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl17])).
% 0.76/0.96 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 0.76/0.96 thf(zip_derived_cl11, plain, (~ (equalish @ e_2 @ e_1)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.76/0.96 thf(zip_derived_cl115, plain,
% 0.76/0.96 ((~ (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl70, zip_derived_cl11])).
% 0.76/0.96 thf('2', plain,
% 0.76/0.96 (~ ( (product @ e_2 @ e_1 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_2))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl184, zip_derived_cl115])).
% 0.76/0.96 thf(zip_derived_cl249, plain,
% 0.76/0.96 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl51])).
% 0.76/0.96 thf(zip_derived_cl37, plain,
% 0.76/0.96 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.76/0.96 thf(product_left_cancellation, axiom,
% 0.76/0.96 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 0.76/0.96 ( equalish @ W @ Z ))).
% 0.76/0.96 thf(zip_derived_cl18, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X3 @ X1 @ X2)
% 0.76/0.96 | (equalish @ X0 @ X3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.76/0.96 thf(zip_derived_cl60, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_2) | (equalish @ e_1 @ X0)))
% 0.76/0.96 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl18])).
% 0.76/0.96 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.76/0.96 thf(zip_derived_cl141, plain,
% 0.76/0.96 ((~ (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl9])).
% 0.76/0.96 thf('3', plain,
% 0.76/0.96 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_2 @ e_1 @ e_2))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl249, zip_derived_cl141])).
% 0.76/0.96 thf(zip_derived_cl38, plain,
% 0.76/0.96 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.76/0.96 thf(zip_derived_cl17, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.76/0.96 | (equalish @ X1 @ X3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.76/0.96 thf(zip_derived_cl86, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_1) | (equalish @ e_1 @ X0)))
% 0.76/0.96 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl17])).
% 0.76/0.96 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.76/0.96 thf(zip_derived_cl244, plain,
% 0.76/0.96 ((~ (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl86, zip_derived_cl9])).
% 0.76/0.96 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [element_2])).
% 0.76/0.96 thf(zip_derived_cl21, plain,
% 0.76/0.96 (![X0 : $i]:
% 0.76/0.96 (~ (group_element @ X0)
% 0.76/0.96 | (product @ e_1 @ X0 @ e_1)
% 0.76/0.96 | (product @ e_1 @ X0 @ e_2)
% 0.76/0.96 | (product @ e_1 @ X0 @ e_3))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl15])).
% 0.76/0.96 thf(zip_derived_cl34, plain,
% 0.76/0.96 (( (product @ e_1 @ e_2 @ e_1)
% 0.76/0.96 | (product @ e_1 @ e_2 @ e_2)
% 0.76/0.96 | (product @ e_1 @ e_2 @ e_3))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl21])).
% 0.76/0.96 thf(zip_derived_cl151, plain,
% 0.76/0.96 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl34])).
% 0.76/0.96 thf('4', plain,
% 0.76/0.96 (~ ( (product @ e_1 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_1))),
% 0.76/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl244, zip_derived_cl151])).
% 0.76/0.96 thf(zip_derived_cl151, plain,
% 0.76/0.96 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl34])).
% 0.76/0.96 thf(zip_derived_cl65, plain,
% 0.76/0.96 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl28])).
% 0.76/0.96 thf(zip_derived_cl18, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X3 @ X1 @ X2)
% 0.76/0.96 | (equalish @ X0 @ X3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.76/0.96 thf(zip_derived_cl71, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_1) | (equalish @ e_2 @ X0)))
% 0.76/0.96 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl18])).
% 0.76/0.96 thf(zip_derived_cl11, plain, (~ (equalish @ e_2 @ e_1)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.76/0.96 thf(zip_derived_cl136, plain,
% 0.76/0.96 ((~ (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl11])).
% 0.76/0.96 thf('5', plain,
% 0.76/0.96 (~ ( (product @ e_1 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_2))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl136])).
% 0.76/0.96 thf('6', plain,
% 0.76/0.96 (( (product @ e_1 @ e_1 @ e_1)) | ( (product @ e_1 @ e_1 @ e_2)) |
% 0.76/0.96 ( (product @ e_1 @ e_1 @ e_3))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.76/0.96 thf(e_1_then_e_2, axiom, (next @ e_1 @ e_2)).
% 0.76/0.96 thf(zip_derived_cl0, plain, ( (next @ e_1 @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_1_then_e_2])).
% 0.76/0.96 thf(zip_derived_cl36, plain,
% 0.76/0.96 (( (product @ e_1 @ e_1 @ e_3)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.76/0.96 thf(no_redundancy, axiom,
% 0.76/0.96 (( ~( product @ X @ e_1 @ Y ) ) | ( ~( next @ X @ X1 ) ) |
% 0.76/0.96 ( ~( greater @ Y @ X1 ) ))).
% 0.76/0.96 thf(zip_derived_cl5, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.76/0.96 (~ (product @ X0 @ e_1 @ X1)
% 0.76/0.96 | ~ (next @ X0 @ X2)
% 0.76/0.96 | ~ (greater @ X1 @ X2))),
% 0.76/0.96 inference('cnf', [status(esa)], [no_redundancy])).
% 0.76/0.96 thf(zip_derived_cl47, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (next @ e_1 @ X0) | ~ (greater @ e_3 @ X0)))
% 0.76/0.96 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl5])).
% 0.76/0.96 thf(zip_derived_cl55, plain,
% 0.76/0.96 ((~ (greater @ e_3 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl47])).
% 0.76/0.96 thf(e_3_greater_e_2, axiom, (greater @ e_3 @ e_2)).
% 0.76/0.96 thf(zip_derived_cl4, plain, ( (greater @ e_3 @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_3_greater_e_2])).
% 0.76/0.96 thf('7', plain, (~ ( (product @ e_1 @ e_1 @ e_3))),
% 0.76/0.96 inference('demod', [status(thm)], [zip_derived_cl55, zip_derived_cl4])).
% 0.76/0.96 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [element_2])).
% 0.76/0.96 thf(zip_derived_cl15, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i]:
% 0.76/0.96 (~ (group_element @ X0)
% 0.76/0.96 | ~ (group_element @ X1)
% 0.76/0.96 | (product @ X0 @ X1 @ e_1)
% 0.76/0.96 | (product @ X0 @ X1 @ e_2)
% 0.76/0.96 | (product @ X0 @ X1 @ e_3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_total_function1])).
% 0.76/0.96 thf(zip_derived_cl24, plain,
% 0.76/0.96 (![X0 : $i]:
% 0.76/0.96 ( (product @ X0 @ X0 @ e_3)
% 0.76/0.96 | (product @ X0 @ X0 @ e_2)
% 0.76/0.96 | (product @ X0 @ X0 @ e_1)
% 0.76/0.96 | ~ (group_element @ X0))),
% 0.76/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl15])).
% 0.76/0.96 thf(zip_derived_cl97, plain,
% 0.76/0.96 (( (product @ e_2 @ e_2 @ e_3)
% 0.76/0.96 | (product @ e_2 @ e_2 @ e_2)
% 0.76/0.96 | (product @ e_2 @ e_2 @ e_1))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl24])).
% 0.76/0.96 thf(zip_derived_cl451, plain,
% 0.76/0.96 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl97])).
% 0.76/0.96 thf(zip_derived_cl28, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i]:
% 0.76/0.96 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 0.76/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 0.76/0.96 thf(zip_derived_cl459, plain,
% 0.76/0.96 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl451, zip_derived_cl28])).
% 0.76/0.96 thf(zip_derived_cl21, plain,
% 0.76/0.96 (![X0 : $i]:
% 0.76/0.96 (~ (group_element @ X0)
% 0.76/0.96 | (product @ e_1 @ X0 @ e_1)
% 0.76/0.96 | (product @ e_1 @ X0 @ e_2)
% 0.76/0.96 | (product @ e_1 @ X0 @ e_3))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl15])).
% 0.76/0.96 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [element_2])).
% 0.76/0.96 thf(zip_derived_cl31, plain,
% 0.76/0.96 (( (product @ e_1 @ e_2 @ e_3)
% 0.76/0.96 | (product @ e_1 @ e_2 @ e_2)
% 0.76/0.96 | (product @ e_1 @ e_2 @ e_1))),
% 0.76/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl7])).
% 0.76/0.96 thf(zip_derived_cl104, plain,
% 0.76/0.96 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.76/0.96 thf(zip_derived_cl17, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.76/0.96 | (equalish @ X1 @ X3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.76/0.96 thf(zip_derived_cl118, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_2 @ X0)))
% 0.76/0.96 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl104, zip_derived_cl17])).
% 0.76/0.96 thf(zip_derived_cl11, plain, (~ (equalish @ e_2 @ e_1)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.76/0.96 thf(zip_derived_cl497, plain,
% 0.76/0.96 ((~ (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl11])).
% 0.76/0.96 thf('8', plain,
% 0.76/0.96 (~ ( (product @ e_2 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_2 @ e_2))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl459, zip_derived_cl497])).
% 0.76/0.96 thf(zip_derived_cl459, plain,
% 0.76/0.96 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl451, zip_derived_cl28])).
% 0.76/0.96 thf(zip_derived_cl38, plain,
% 0.76/0.96 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.76/0.96 thf(zip_derived_cl16, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X0 @ X1 @ X3)
% 0.76/0.96 | (equalish @ X2 @ X3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_total_function2])).
% 0.76/0.96 thf(zip_derived_cl85, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (product @ e_1 @ e_1 @ X0) | (equalish @ e_1 @ X0)))
% 0.76/0.96 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl16])).
% 0.76/0.96 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.76/0.96 thf(zip_derived_cl143, plain,
% 0.76/0.96 ((~ (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl9])).
% 0.76/0.96 thf('9', plain,
% 0.76/0.96 (~ ( (product @ e_2 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_1))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl459, zip_derived_cl143])).
% 0.76/0.96 thf('10', plain,
% 0.76/0.96 (( (product @ e_2 @ e_1 @ e_2)) | ( (product @ e_2 @ e_1 @ e_1)) |
% 0.76/0.96 ( (product @ e_2 @ e_1 @ e_3))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl48])).
% 0.76/0.96 thf(zip_derived_cl103, plain,
% 0.76/0.96 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.76/0.96 thf(zip_derived_cl18, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X3 @ X1 @ X2)
% 0.76/0.96 | (equalish @ X0 @ X3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.76/0.96 thf(zip_derived_cl108, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_1 @ X0)))
% 0.76/0.96 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl103, zip_derived_cl18])).
% 0.76/0.96 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.76/0.96 thf(zip_derived_cl479, plain,
% 0.76/0.96 ((~ (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl108, zip_derived_cl9])).
% 0.76/0.96 thf(zip_derived_cl204, plain,
% 0.76/0.96 (( (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl49])).
% 0.76/0.96 thf('11', plain,
% 0.76/0.96 (~ ( (product @ e_1 @ e_2 @ e_3)) | ~ ( (product @ e_2 @ e_2 @ e_3))),
% 0.76/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl479, zip_derived_cl204])).
% 0.76/0.96 thf(zip_derived_cl0, plain, ( (next @ e_1 @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_1_then_e_2])).
% 0.76/0.96 thf(zip_derived_cl182, plain,
% 0.76/0.96 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl48])).
% 0.76/0.96 thf(zip_derived_cl103, plain,
% 0.76/0.96 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.76/0.96 thf(zip_derived_cl19, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 ( (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X2 @ X3 @ X1)
% 0.76/0.96 | ~ (product @ X3 @ X2 @ X0))),
% 0.76/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.76/0.96 thf(zip_derived_cl109, plain,
% 0.76/0.96 ((![X0 : $i]:
% 0.76/0.96 ( (product @ X0 @ e_3 @ e_1) | ~ (product @ e_2 @ e_1 @ X0)))
% 0.76/0.96 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl103, zip_derived_cl19])).
% 0.76/0.96 thf(zip_derived_cl195, plain,
% 0.76/0.96 (( (product @ e_3 @ e_3 @ e_1))
% 0.76/0.96 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl182, zip_derived_cl109])).
% 0.76/0.96 thf(zip_derived_cl28, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i]:
% 0.76/0.96 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 0.76/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 0.76/0.96 thf(zip_derived_cl203, plain,
% 0.76/0.96 (( (product @ e_1 @ e_1 @ e_3))
% 0.76/0.96 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl195, zip_derived_cl28])).
% 0.76/0.96 thf(zip_derived_cl5, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.76/0.96 (~ (product @ X0 @ e_1 @ X1)
% 0.76/0.96 | ~ (next @ X0 @ X2)
% 0.76/0.96 | ~ (greater @ X1 @ X2))),
% 0.76/0.96 inference('cnf', [status(esa)], [no_redundancy])).
% 0.76/0.96 thf(zip_derived_cl225, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (next @ e_1 @ X0) | ~ (greater @ e_3 @ X0)))
% 0.76/0.96 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl203, zip_derived_cl5])).
% 0.76/0.96 thf(zip_derived_cl241, plain,
% 0.76/0.96 ((~ (greater @ e_3 @ e_2))
% 0.76/0.96 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl225])).
% 0.76/0.96 thf(zip_derived_cl4, plain, ( (greater @ e_3 @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_3_greater_e_2])).
% 0.76/0.96 thf('12', plain,
% 0.76/0.96 (~ ( (product @ e_2 @ e_1 @ e_3)) | ~ ( (product @ e_1 @ e_2 @ e_3))),
% 0.76/0.96 inference('demod', [status(thm)], [zip_derived_cl241, zip_derived_cl4])).
% 0.76/0.96 thf(zip_derived_cl184, plain,
% 0.76/0.96 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl48])).
% 0.76/0.96 thf(zip_derived_cl38, plain,
% 0.76/0.96 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.76/0.96 thf(zip_derived_cl18, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X3 @ X1 @ X2)
% 0.76/0.96 | (equalish @ X0 @ X3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.76/0.96 thf(zip_derived_cl87, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_1) | (equalish @ e_1 @ X0)))
% 0.76/0.96 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl18])).
% 0.76/0.96 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.76/0.96 thf(zip_derived_cl411, plain,
% 0.76/0.96 ((~ (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl87, zip_derived_cl9])).
% 0.76/0.96 thf('13', plain,
% 0.76/0.96 (~ ( (product @ e_2 @ e_1 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_1))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl184, zip_derived_cl411])).
% 0.76/0.96 thf('14', plain,
% 0.76/0.96 (( (product @ e_1 @ e_2 @ e_2)) | ( (product @ e_1 @ e_2 @ e_3)) |
% 0.76/0.96 ( (product @ e_1 @ e_2 @ e_1))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.76/0.96 thf(zip_derived_cl104, plain,
% 0.76/0.96 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.76/0.96 thf(zip_derived_cl18, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X3 @ X1 @ X2)
% 0.76/0.96 | (equalish @ X0 @ X3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.76/0.96 thf(zip_derived_cl119, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_2) | (equalish @ e_1 @ X0)))
% 0.76/0.96 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl104, zip_derived_cl18])).
% 0.76/0.96 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.76/0.96 thf(zip_derived_cl503, plain,
% 0.76/0.96 ((~ (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl119, zip_derived_cl9])).
% 0.76/0.96 thf(zip_derived_cl282, plain,
% 0.76/0.96 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_2)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl52])).
% 0.76/0.96 thf('15', plain,
% 0.76/0.96 (~ ( (product @ e_2 @ e_2 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_2))),
% 0.76/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl503, zip_derived_cl282])).
% 0.76/0.96 thf('16', plain,
% 0.76/0.96 (( (product @ e_2 @ e_2 @ e_3)) | ( (product @ e_2 @ e_2 @ e_2)) |
% 0.76/0.96 ( (product @ e_2 @ e_2 @ e_1))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl49])).
% 0.76/0.96 thf('17', plain, (( (product @ e_2 @ e_2 @ e_3))),
% 0.76/0.96 inference('sat_resolution*', [status(thm)],
% 0.76/0.96 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 0.76/0.96 '12', '13', '14', '15', '16'])).
% 0.76/0.96 thf(zip_derived_cl808, plain, (~ (product @ e_2 @ e_2 @ e_1)),
% 0.76/0.96 inference('simpl_trail', [status(thm)], [zip_derived_cl635, '17'])).
% 0.76/0.96 thf(zip_derived_cl249, plain,
% 0.76/0.96 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl51])).
% 0.76/0.96 thf(zip_derived_cl182, plain,
% 0.76/0.96 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl48])).
% 0.76/0.96 thf(zip_derived_cl17, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.76/0.96 | (equalish @ X1 @ X3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.76/0.96 thf(zip_derived_cl186, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 0.76/0.96 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl182, zip_derived_cl17])).
% 0.76/0.96 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.76/0.96 thf(zip_derived_cl584, plain,
% 0.76/0.96 ((~ (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl186, zip_derived_cl9])).
% 0.76/0.96 thf(zip_derived_cl204, plain,
% 0.76/0.96 (( (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl49])).
% 0.76/0.96 thf('18', plain,
% 0.76/0.96 (~ ( (product @ e_2 @ e_1 @ e_3)) | ~ ( (product @ e_2 @ e_2 @ e_3))),
% 0.76/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl584, zip_derived_cl204])).
% 0.76/0.96 thf(zip_derived_cl104, plain,
% 0.76/0.96 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.76/0.96 thf(zip_derived_cl37, plain,
% 0.76/0.96 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.76/0.96 thf(zip_derived_cl17, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.76/0.96 | (equalish @ X1 @ X3))),
% 0.76/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.76/0.96 thf(zip_derived_cl59, plain,
% 0.76/0.96 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 0.76/0.96 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl17])).
% 0.76/0.96 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.76/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.76/0.96 thf(zip_derived_cl113, plain,
% 0.76/0.96 ((~ (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl9])).
% 0.76/0.96 thf('19', plain,
% 0.76/0.96 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_2))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl104, zip_derived_cl113])).
% 0.76/0.96 thf('20', plain, (( (product @ e_2 @ e_1 @ e_2))),
% 0.76/0.96 inference('sat_resolution*', [status(thm)],
% 0.76/0.96 ['15', '18', '0', '1', '16', '2', '3', '4', '5', '7', '8',
% 0.76/0.96 '9', '11', '12', '14', '19', '6', '13', '10'])).
% 0.76/0.96 thf(zip_derived_cl779, plain, ( (product @ e_2 @ e_1 @ e_2)),
% 0.76/0.96 inference('simpl_trail', [status(thm)], [zip_derived_cl249, '20'])).
% 0.76/0.96 thf(zip_derived_cl104, plain,
% 0.76/0.96 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.76/0.96 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.76/0.96 thf(zip_derived_cl19, plain,
% 0.76/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.76/0.96 ( (product @ X0 @ X1 @ X2)
% 0.76/0.96 | ~ (product @ X2 @ X3 @ X1)
% 0.76/0.96 | ~ (product @ X3 @ X2 @ X0))),
% 0.76/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.76/0.96 thf(zip_derived_cl120, plain,
% 0.76/0.96 ((![X0 : $i]:
% 0.76/0.96 ( (product @ X0 @ e_2 @ e_1) | ~ (product @ e_2 @ e_1 @ X0)))
% 0.76/0.96 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl104, zip_derived_cl19])).
% 0.76/0.96 thf('21', plain, (( (product @ e_1 @ e_2 @ e_2))),
% 0.76/0.96 inference('sat_resolution*', [status(thm)],
% 0.76/0.96 ['0', '1', '16', '2', '3', '4', '5', '6', '7', '8', '9', '10',
% 0.76/0.96 '11', '12', '13', '14'])).
% 0.76/0.96 thf(zip_derived_cl757, plain,
% 0.76/0.96 (![X0 : $i]: ( (product @ X0 @ e_2 @ e_1) | ~ (product @ e_2 @ e_1 @ X0))),
% 0.76/0.96 inference('simpl_trail', [status(thm)], [zip_derived_cl120, '21'])).
% 0.76/0.96 thf(zip_derived_cl956, plain, ( (product @ e_2 @ e_2 @ e_1)),
% 0.76/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl779, zip_derived_cl757])).
% 0.76/0.96 thf(zip_derived_cl967, plain, ($false),
% 0.76/0.96 inference('demod', [status(thm)], [zip_derived_cl808, zip_derived_cl956])).
% 0.76/0.96
% 0.76/0.96 % SZS output end Refutation
% 0.76/0.96
% 0.76/0.96
% 0.76/0.96 % Terminating...
% 1.81/1.04 % Runner terminated.
% 1.81/1.06 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------