%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP130-2.003 : 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.yDOLWUss6A true
% Computer : n016.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 04:35:46 PM UTC 2025
% Result : Unsatisfiable 0.79s 0.83s
% Output : Refutation 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GRP130-2.003 : TPTP v9.2.0. Released v1.2.0.
% 0.02/0.10 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.yDOLWUss6A true
% 0.09/0.30 % Computer : n016.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Wed Oct 1 14:06:23 EDT 2025
% 0.09/0.31 % CPUTime :
% 0.09/0.31 % Running portfolio for 300 s
% 0.09/0.31 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.31 % Number of cores: 8
% 0.09/0.31 % Python version: Python 3.6.8
% 0.15/0.31 % Running in FO mode
% 0.48/0.56 % Total configuration time : 435
% 0.48/0.56 % Estimated wc time : 1092
% 0.48/0.56 % Estimated cpu time (7 cpus) : 156.0
% 0.75/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.75/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.75/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.75/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.75/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.75/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.75/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.79/0.83 % Solved by fo/fo1_av.sh.
% 0.79/0.83 % done 402 iterations in 0.136s
% 0.79/0.83 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.79/0.83 % SZS output start Refutation
% 0.79/0.83 thf(greater_type, type, greater: $i > $i > $o).
% 0.79/0.83 thf(product_type, type, product: $i > $i > $i > $o).
% 0.79/0.83 thf(e_3_type, type, e_3: $i).
% 0.79/0.83 thf(e_2_type, type, e_2: $i).
% 0.79/0.83 thf(e_1_type, type, e_1: $i).
% 0.79/0.83 thf(next_type, type, next: $i > $i > $o).
% 0.79/0.83 thf(group_element_type, type, group_element: $i > $o).
% 0.79/0.83 thf(equalish_type, type, equalish: $i > $i > $o).
% 0.79/0.83 thf(element_2, axiom, (group_element @ e_2)).
% 0.79/0.83 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.79/0.83 inference('cnf', [status(esa)], [element_2])).
% 0.79/0.83 thf(element_3, axiom, (group_element @ e_3)).
% 0.79/0.83 thf(zip_derived_cl8, plain, ( (group_element @ e_3)),
% 0.79/0.83 inference('cnf', [status(esa)], [element_3])).
% 0.79/0.83 thf(product_total_function1, axiom,
% 0.79/0.83 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 0.79/0.83 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 0.79/0.83 ( product @ X @ Y @ e_3 ))).
% 0.79/0.83 thf(zip_derived_cl15, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i]:
% 0.79/0.83 (~ (group_element @ X0)
% 0.79/0.83 | ~ (group_element @ X1)
% 0.79/0.83 | (product @ X0 @ X1 @ e_1)
% 0.79/0.83 | (product @ X0 @ X1 @ e_2)
% 0.79/0.83 | (product @ X0 @ X1 @ e_3))),
% 0.79/0.83 inference('cnf', [status(esa)], [product_total_function1])).
% 0.79/0.83 thf(zip_derived_cl23, plain,
% 0.79/0.83 (![X0 : $i]:
% 0.79/0.83 (~ (group_element @ X0)
% 0.79/0.83 | (product @ e_3 @ X0 @ e_1)
% 0.79/0.83 | (product @ e_3 @ X0 @ e_2)
% 0.79/0.83 | (product @ e_3 @ X0 @ e_3))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl15])).
% 0.79/0.83 thf(zip_derived_cl80, plain,
% 0.79/0.83 (( (product @ e_3 @ e_2 @ e_1)
% 0.79/0.83 | (product @ e_3 @ e_2 @ e_2)
% 0.79/0.83 | (product @ e_3 @ e_2 @ e_3))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl23])).
% 0.79/0.83 thf(zip_derived_cl485, plain,
% 0.79/0.83 (( (product @ e_3 @ e_2 @ e_2)) <= (( (product @ e_3 @ e_2 @ e_2)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl80])).
% 0.79/0.83 thf(qg3, conjecture,
% 0.79/0.83 (~( ( product @ Z2 @ Y @ X ) | ( ~( product @ X @ Z1 @ Z2 ) ) |
% 0.79/0.83 ( ~( product @ X @ Y @ Z1 ) ) ))).
% 0.79/0.83 thf(zf_stmt_0, negated_conjecture,
% 0.79/0.83 (( product @ Z2 @ Y @ X ) | ( ~( product @ X @ Z1 @ Z2 ) ) |
% 0.79/0.83 ( ~( product @ X @ Y @ Z1 ) )),
% 0.79/0.83 inference('cnf.neg', [status(esa)], [qg3])).
% 0.79/0.83 thf(zip_derived_cl19, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.79/0.83 ( (product @ X0 @ X1 @ X2)
% 0.79/0.83 | ~ (product @ X2 @ X3 @ X0)
% 0.79/0.83 | ~ (product @ X2 @ X1 @ X3))),
% 0.79/0.83 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.79/0.83 thf(zip_derived_cl28, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i]:
% 0.79/0.83 (~ (product @ X1 @ X0 @ X0) | (product @ X0 @ X0 @ X1))),
% 0.79/0.83 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 0.79/0.83 thf(zip_derived_cl494, plain,
% 0.79/0.83 (( (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_3 @ e_2 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl485, zip_derived_cl28])).
% 0.79/0.83 thf(element_1, axiom, (group_element @ e_1)).
% 0.79/0.83 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.79/0.83 inference('cnf', [status(esa)], [element_1])).
% 0.79/0.83 thf(zip_derived_cl15, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i]:
% 0.79/0.83 (~ (group_element @ X0)
% 0.79/0.83 | ~ (group_element @ X1)
% 0.79/0.83 | (product @ X0 @ X1 @ e_1)
% 0.79/0.83 | (product @ X0 @ X1 @ e_2)
% 0.79/0.83 | (product @ X0 @ X1 @ e_3))),
% 0.79/0.83 inference('cnf', [status(esa)], [product_total_function1])).
% 0.79/0.83 thf(zip_derived_cl21, plain,
% 0.79/0.83 (![X0 : $i]:
% 0.79/0.83 (~ (group_element @ X0)
% 0.79/0.83 | (product @ e_1 @ X0 @ e_1)
% 0.79/0.83 | (product @ e_1 @ X0 @ e_2)
% 0.79/0.83 | (product @ e_1 @ X0 @ e_3))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl15])).
% 0.79/0.83 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.79/0.83 inference('cnf', [status(esa)], [element_2])).
% 0.79/0.83 thf(zip_derived_cl31, plain,
% 0.79/0.83 (( (product @ e_1 @ e_2 @ e_3)
% 0.79/0.83 | (product @ e_1 @ e_2 @ e_2)
% 0.79/0.83 | (product @ e_1 @ e_2 @ e_1))),
% 0.79/0.83 inference('s_sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl7])).
% 0.79/0.83 thf(zip_derived_cl109, plain,
% 0.79/0.83 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.79/0.83 thf(product_left_cancellation, axiom,
% 0.79/0.83 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 0.79/0.83 ( equalish @ W @ Z ))).
% 0.79/0.83 thf(zip_derived_cl18, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.79/0.83 (~ (product @ X0 @ X1 @ X2)
% 0.79/0.83 | ~ (product @ X3 @ X1 @ X2)
% 0.79/0.83 | (equalish @ X0 @ X3))),
% 0.79/0.83 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.79/0.83 thf(zip_derived_cl114, plain,
% 0.79/0.83 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_1 @ X0)))
% 0.79/0.83 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl18])).
% 0.79/0.83 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 0.79/0.83 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.79/0.83 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.79/0.83 thf(zip_derived_cl516, plain,
% 0.79/0.83 ((~ (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl9])).
% 0.79/0.83 thf('0', plain,
% 0.79/0.83 (~ ( (product @ e_3 @ e_2 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_3))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl494, zip_derived_cl516])).
% 0.79/0.83 thf(zip_derived_cl114, plain,
% 0.79/0.83 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_1 @ X0)))
% 0.79/0.83 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl18])).
% 0.79/0.83 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 0.79/0.83 thf(zip_derived_cl10, plain, (~ (equalish @ e_1 @ e_3)),
% 0.79/0.83 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.79/0.83 thf(zip_derived_cl517, plain,
% 0.79/0.83 ((~ (product @ e_3 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl10])).
% 0.79/0.83 thf(zip_derived_cl23, plain,
% 0.79/0.83 (![X0 : $i]:
% 0.79/0.83 (~ (group_element @ X0)
% 0.79/0.83 | (product @ e_3 @ X0 @ e_1)
% 0.79/0.83 | (product @ e_3 @ X0 @ e_2)
% 0.79/0.83 | (product @ e_3 @ X0 @ e_3))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl15])).
% 0.79/0.83 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.79/0.83 inference('cnf', [status(esa)], [element_2])).
% 0.79/0.83 thf(zip_derived_cl77, plain,
% 0.79/0.83 (( (product @ e_3 @ e_2 @ e_3)
% 0.79/0.83 | (product @ e_3 @ e_2 @ e_2)
% 0.79/0.83 | (product @ e_3 @ e_2 @ e_1))),
% 0.79/0.83 inference('s_sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl7])).
% 0.79/0.83 thf(zip_derived_cl421, plain,
% 0.79/0.83 (( (product @ e_3 @ e_2 @ e_3)) <= (( (product @ e_3 @ e_2 @ e_3)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl77])).
% 0.79/0.83 thf('1', plain,
% 0.79/0.83 (~ ( (product @ e_3 @ e_2 @ e_3)) | ~ ( (product @ e_1 @ e_2 @ e_3))),
% 0.79/0.83 inference('s_sup+', [status(thm)], [zip_derived_cl517, zip_derived_cl421])).
% 0.79/0.83 thf(zip_derived_cl21, plain,
% 0.79/0.83 (![X0 : $i]:
% 0.79/0.83 (~ (group_element @ X0)
% 0.79/0.83 | (product @ e_1 @ X0 @ e_1)
% 0.79/0.83 | (product @ e_1 @ X0 @ e_2)
% 0.79/0.83 | (product @ e_1 @ X0 @ e_3))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl15])).
% 0.79/0.83 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.79/0.83 inference('cnf', [status(esa)], [element_1])).
% 0.79/0.83 thf(zip_derived_cl30, plain,
% 0.79/0.83 (( (product @ e_1 @ e_1 @ e_3)
% 0.79/0.83 | (product @ e_1 @ e_1 @ e_2)
% 0.79/0.83 | (product @ e_1 @ e_1 @ e_1))),
% 0.79/0.83 inference('s_sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl6])).
% 0.79/0.83 thf(zip_derived_cl38, plain,
% 0.79/0.83 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.79/0.83 thf(product_right_cancellation, axiom,
% 0.79/0.83 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 0.79/0.83 ( equalish @ W @ Z ))).
% 0.79/0.83 thf(zip_derived_cl17, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.79/0.83 (~ (product @ X0 @ X1 @ X2)
% 0.79/0.83 | ~ (product @ X0 @ X3 @ X2)
% 0.79/0.83 | (equalish @ X1 @ X3))),
% 0.79/0.83 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.79/0.83 thf(zip_derived_cl87, plain,
% 0.79/0.83 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_1) | (equalish @ e_1 @ X0)))
% 0.79/0.83 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl17])).
% 0.79/0.83 thf(zip_derived_cl10, plain, (~ (equalish @ e_1 @ e_3)),
% 0.79/0.83 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.79/0.83 thf(zip_derived_cl307, plain,
% 0.79/0.83 ((~ (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl87, zip_derived_cl10])).
% 0.79/0.83 thf(zip_derived_cl21, plain,
% 0.79/0.83 (![X0 : $i]:
% 0.79/0.83 (~ (group_element @ X0)
% 0.79/0.83 | (product @ e_1 @ X0 @ e_1)
% 0.79/0.83 | (product @ e_1 @ X0 @ e_2)
% 0.79/0.83 | (product @ e_1 @ X0 @ e_3))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl15])).
% 0.79/0.83 thf(zip_derived_cl8, plain, ( (group_element @ e_3)),
% 0.79/0.83 inference('cnf', [status(esa)], [element_3])).
% 0.79/0.83 thf(zip_derived_cl32, plain,
% 0.79/0.83 (( (product @ e_1 @ e_3 @ e_3)
% 0.79/0.83 | (product @ e_1 @ e_3 @ e_2)
% 0.79/0.83 | (product @ e_1 @ e_3 @ e_1))),
% 0.79/0.83 inference('s_sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl8])).
% 0.79/0.83 thf(zip_derived_cl142, plain,
% 0.79/0.83 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl32])).
% 0.79/0.83 thf('2', plain,
% 0.79/0.83 (~ ( (product @ e_1 @ e_3 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_1))),
% 0.79/0.83 inference('s_sup+', [status(thm)], [zip_derived_cl307, zip_derived_cl142])).
% 0.79/0.83 thf(zip_derived_cl8, plain, ( (group_element @ e_3)),
% 0.79/0.83 inference('cnf', [status(esa)], [element_3])).
% 0.79/0.83 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.79/0.83 inference('cnf', [status(esa)], [element_2])).
% 0.79/0.83 thf(zip_derived_cl15, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i]:
% 0.79/0.83 (~ (group_element @ X0)
% 0.79/0.83 | ~ (group_element @ X1)
% 0.79/0.83 | (product @ X0 @ X1 @ e_1)
% 0.79/0.83 | (product @ X0 @ X1 @ e_2)
% 0.79/0.83 | (product @ X0 @ X1 @ e_3))),
% 0.79/0.83 inference('cnf', [status(esa)], [product_total_function1])).
% 0.79/0.83 thf(zip_derived_cl22, plain,
% 0.79/0.83 (![X0 : $i]:
% 0.79/0.83 (~ (group_element @ X0)
% 0.79/0.83 | (product @ e_2 @ X0 @ e_1)
% 0.79/0.83 | (product @ e_2 @ X0 @ e_2)
% 0.79/0.83 | (product @ e_2 @ X0 @ e_3))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl15])).
% 0.79/0.83 thf(zip_derived_cl52, plain,
% 0.79/0.83 (( (product @ e_2 @ e_3 @ e_1)
% 0.79/0.83 | (product @ e_2 @ e_3 @ e_2)
% 0.79/0.83 | (product @ e_2 @ e_3 @ e_3))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl22])).
% 0.79/0.83 thf(zip_derived_cl297, plain,
% 0.79/0.83 (( (product @ e_2 @ e_3 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl52])).
% 0.79/0.83 thf(zip_derived_cl110, plain,
% 0.79/0.83 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.79/0.83 thf(zip_derived_cl28, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i]:
% 0.79/0.83 (~ (product @ X1 @ X0 @ X0) | (product @ X0 @ X0 @ X1))),
% 0.79/0.83 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 0.79/0.83 thf(zip_derived_cl137, plain,
% 0.79/0.83 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl28])).
% 0.79/0.83 thf(zip_derived_cl19, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.79/0.83 ( (product @ X0 @ X1 @ X2)
% 0.79/0.83 | ~ (product @ X2 @ X3 @ X0)
% 0.79/0.83 | ~ (product @ X2 @ X1 @ X3))),
% 0.79/0.83 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.79/0.83 thf(zip_derived_cl154, plain,
% 0.79/0.83 ((![X0 : $i]:
% 0.79/0.83 ( (product @ e_1 @ X0 @ e_2) | ~ (product @ e_2 @ X0 @ e_2)))
% 0.79/0.83 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl19])).
% 0.79/0.83 thf(zip_derived_cl696, plain,
% 0.79/0.83 (( (product @ e_1 @ e_3 @ e_2))
% 0.79/0.83 <= (( (product @ e_1 @ e_2 @ e_2)) & ( (product @ e_2 @ e_3 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl297, zip_derived_cl154])).
% 0.79/0.83 thf(zip_derived_cl110, plain,
% 0.79/0.83 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.79/0.83 thf(zip_derived_cl17, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.79/0.83 (~ (product @ X0 @ X1 @ X2)
% 0.79/0.83 | ~ (product @ X0 @ X3 @ X2)
% 0.79/0.83 | (equalish @ X1 @ X3))),
% 0.79/0.83 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.79/0.83 thf(zip_derived_cl131, plain,
% 0.79/0.83 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_2 @ X0)))
% 0.79/0.83 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl17])).
% 0.79/0.83 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 0.79/0.83 thf(zip_derived_cl12, plain, (~ (equalish @ e_2 @ e_3)),
% 0.79/0.83 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.79/0.83 thf(zip_derived_cl573, plain,
% 0.79/0.83 ((~ (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl12])).
% 0.79/0.83 thf('3', plain,
% 0.79/0.83 (~ ( (product @ e_2 @ e_3 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_2))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl696, zip_derived_cl573])).
% 0.79/0.83 thf(zip_derived_cl22, plain,
% 0.79/0.83 (![X0 : $i]:
% 0.79/0.83 (~ (group_element @ X0)
% 0.79/0.83 | (product @ e_2 @ X0 @ e_1)
% 0.79/0.83 | (product @ e_2 @ X0 @ e_2)
% 0.79/0.83 | (product @ e_2 @ X0 @ e_3))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl15])).
% 0.79/0.83 thf(zip_derived_cl8, plain, ( (group_element @ e_3)),
% 0.79/0.83 inference('cnf', [status(esa)], [element_3])).
% 0.79/0.83 thf(zip_derived_cl49, plain,
% 0.79/0.83 (( (product @ e_2 @ e_3 @ e_3)
% 0.79/0.83 | (product @ e_2 @ e_3 @ e_2)
% 0.79/0.83 | (product @ e_2 @ e_3 @ e_1))),
% 0.79/0.83 inference('s_sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl8])).
% 0.79/0.83 thf(zip_derived_cl243, plain,
% 0.79/0.83 (( (product @ e_2 @ e_3 @ e_1)) <= (( (product @ e_2 @ e_3 @ e_1)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl49])).
% 0.79/0.83 thf(zip_derived_cl137, plain,
% 0.79/0.83 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl28])).
% 0.79/0.83 thf(zip_derived_cl17, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.79/0.83 (~ (product @ X0 @ X1 @ X2)
% 0.79/0.83 | ~ (product @ X0 @ X3 @ X2)
% 0.79/0.83 | (equalish @ X1 @ X3))),
% 0.79/0.83 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.79/0.83 thf(zip_derived_cl152, plain,
% 0.79/0.83 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_1) | (equalish @ e_2 @ X0)))
% 0.79/0.83 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl17])).
% 0.79/0.83 thf(zip_derived_cl12, plain, (~ (equalish @ e_2 @ e_3)),
% 0.79/0.83 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.79/0.83 thf(zip_derived_cl202, plain,
% 0.79/0.83 ((~ (product @ e_2 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl152, zip_derived_cl12])).
% 0.79/0.83 thf('4', plain,
% 0.79/0.83 (~ ( (product @ e_2 @ e_3 @ e_1)) | ~ ( (product @ e_1 @ e_2 @ e_2))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl243, zip_derived_cl202])).
% 0.79/0.83 thf(e_1_then_e_2, axiom, (next @ e_1 @ e_2)).
% 0.79/0.83 thf(zip_derived_cl0, plain, ( (next @ e_1 @ e_2)),
% 0.79/0.83 inference('cnf', [status(esa)], [e_1_then_e_2])).
% 0.79/0.83 thf(zip_derived_cl36, plain,
% 0.79/0.83 (( (product @ e_1 @ e_1 @ e_3)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.79/0.83 thf(no_redundancy, axiom,
% 0.79/0.83 (( ~( product @ X @ e_1 @ Y ) ) | ( ~( next @ X @ X1 ) ) |
% 0.79/0.83 ( ~( greater @ Y @ X1 ) ))).
% 0.79/0.83 thf(zip_derived_cl5, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.79/0.83 (~ (product @ X0 @ e_1 @ X1)
% 0.79/0.83 | ~ (next @ X0 @ X2)
% 0.79/0.83 | ~ (greater @ X1 @ X2))),
% 0.79/0.83 inference('cnf', [status(esa)], [no_redundancy])).
% 0.79/0.83 thf(zip_derived_cl46, plain,
% 0.79/0.83 ((![X0 : $i]: (~ (next @ e_1 @ X0) | ~ (greater @ e_3 @ X0)))
% 0.79/0.83 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl5])).
% 0.79/0.83 thf(zip_derived_cl54, plain,
% 0.79/0.83 ((~ (greater @ e_3 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl46])).
% 0.79/0.83 thf(e_3_greater_e_2, axiom, (greater @ e_3 @ e_2)).
% 0.79/0.83 thf(zip_derived_cl4, plain, ( (greater @ e_3 @ e_2)),
% 0.79/0.83 inference('cnf', [status(esa)], [e_3_greater_e_2])).
% 0.79/0.83 thf('5', plain, (~ ( (product @ e_1 @ e_1 @ e_3))),
% 0.79/0.83 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl4])).
% 0.79/0.83 thf(zip_derived_cl37, plain,
% 0.79/0.83 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.79/0.83 thf(zip_derived_cl19, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.79/0.83 ( (product @ X0 @ X1 @ X2)
% 0.79/0.83 | ~ (product @ X2 @ X3 @ X0)
% 0.79/0.83 | ~ (product @ X2 @ X1 @ X3))),
% 0.79/0.83 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.79/0.83 thf(zip_derived_cl60, plain,
% 0.79/0.83 ((![X0 : $i]:
% 0.79/0.83 ( (product @ e_2 @ X0 @ e_1) | ~ (product @ e_1 @ X0 @ e_1)))
% 0.79/0.83 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl19])).
% 0.79/0.83 thf(zip_derived_cl18, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.79/0.83 (~ (product @ X0 @ X1 @ X2)
% 0.79/0.83 | ~ (product @ X3 @ X1 @ X2)
% 0.79/0.83 | (equalish @ X0 @ X3))),
% 0.79/0.83 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.79/0.83 thf(zip_derived_cl69, plain,
% 0.79/0.83 ((![X0 : $i, X1 : $i]:
% 0.79/0.83 (~ (product @ e_1 @ X0 @ e_1)
% 0.79/0.83 | ~ (product @ X1 @ X0 @ e_1)
% 0.79/0.83 | (equalish @ e_2 @ X1)))
% 0.79/0.83 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl18])).
% 0.79/0.83 thf(zip_derived_cl360, plain,
% 0.79/0.83 ((![X0 : $i]: ( (equalish @ e_2 @ e_1) | ~ (product @ e_1 @ X0 @ e_1)))
% 0.79/0.83 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.79/0.83 inference('eq_fact', [status(thm)], [zip_derived_cl69])).
% 0.79/0.83 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 0.79/0.83 thf(zip_derived_cl11, plain, (~ (equalish @ e_2 @ e_1)),
% 0.79/0.83 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.79/0.83 thf(zip_derived_cl375, plain,
% 0.79/0.83 ((![X0 : $i]: ~ (product @ e_1 @ X0 @ e_1))
% 0.79/0.83 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.79/0.83 inference('clc', [status(thm)], [zip_derived_cl360, zip_derived_cl11])).
% 0.79/0.83 thf(zip_derived_cl142, plain,
% 0.79/0.83 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl32])).
% 0.79/0.83 thf('6', plain,
% 0.79/0.83 (~ ( (product @ e_1 @ e_3 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_2))),
% 0.79/0.83 inference('s_sup+', [status(thm)], [zip_derived_cl375, zip_derived_cl142])).
% 0.79/0.83 thf(zip_derived_cl375, plain,
% 0.79/0.83 ((![X0 : $i]: ~ (product @ e_1 @ X0 @ e_1))
% 0.79/0.83 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.79/0.83 inference('clc', [status(thm)], [zip_derived_cl360, zip_derived_cl11])).
% 0.79/0.83 thf(zip_derived_cl111, plain,
% 0.79/0.83 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.79/0.83 thf('7', plain,
% 0.79/0.83 (~ ( (product @ e_1 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_2))),
% 0.79/0.83 inference('s_sup+', [status(thm)], [zip_derived_cl375, zip_derived_cl111])).
% 0.79/0.83 thf(zip_derived_cl8, plain, ( (group_element @ e_3)),
% 0.79/0.83 inference('cnf', [status(esa)], [element_3])).
% 0.79/0.83 thf(zip_derived_cl21, plain,
% 0.79/0.83 (![X0 : $i]:
% 0.79/0.83 (~ (group_element @ X0)
% 0.79/0.83 | (product @ e_1 @ X0 @ e_1)
% 0.79/0.83 | (product @ e_1 @ X0 @ e_2)
% 0.79/0.83 | (product @ e_1 @ X0 @ e_3))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl15])).
% 0.79/0.83 thf(zip_derived_cl35, plain,
% 0.79/0.83 (( (product @ e_1 @ e_3 @ e_1)
% 0.79/0.83 | (product @ e_1 @ e_3 @ e_2)
% 0.79/0.83 | (product @ e_1 @ e_3 @ e_3))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl21])).
% 0.79/0.83 thf(zip_derived_cl189, plain,
% 0.79/0.83 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl35])).
% 0.79/0.83 thf(zip_derived_cl37, plain,
% 0.79/0.83 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.79/0.83 thf(zip_derived_cl17, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.79/0.83 (~ (product @ X0 @ X1 @ X2)
% 0.79/0.83 | ~ (product @ X0 @ X3 @ X2)
% 0.79/0.83 | (equalish @ X1 @ X3))),
% 0.79/0.83 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.79/0.83 thf(zip_derived_cl58, plain,
% 0.79/0.83 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 0.79/0.83 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl17])).
% 0.79/0.83 thf(zip_derived_cl10, plain, (~ (equalish @ e_1 @ e_3)),
% 0.79/0.83 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.79/0.83 thf(zip_derived_cl120, plain,
% 0.79/0.83 ((~ (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl10])).
% 0.79/0.83 thf('8', plain,
% 0.79/0.83 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_1 @ e_3 @ e_2))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl189, zip_derived_cl120])).
% 0.79/0.83 thf(zip_derived_cl110, plain,
% 0.79/0.83 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.79/0.83 thf(zip_derived_cl58, plain,
% 0.79/0.83 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 0.79/0.83 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl17])).
% 0.79/0.83 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.79/0.83 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.79/0.83 thf(zip_derived_cl119, plain,
% 0.79/0.83 ((~ (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl9])).
% 0.79/0.83 thf('9', plain,
% 0.79/0.83 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_2))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl119])).
% 0.79/0.83 thf(zip_derived_cl140, plain,
% 0.79/0.83 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl32])).
% 0.79/0.83 thf(zip_derived_cl28, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i]:
% 0.79/0.83 (~ (product @ X1 @ X0 @ X0) | (product @ X0 @ X0 @ X1))),
% 0.79/0.83 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 0.79/0.83 thf(zip_derived_cl150, plain,
% 0.79/0.83 (( (product @ e_3 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl140, zip_derived_cl28])).
% 0.79/0.83 thf(zip_derived_cl17, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.79/0.83 (~ (product @ X0 @ X1 @ X2)
% 0.79/0.83 | ~ (product @ X0 @ X3 @ X2)
% 0.79/0.83 | (equalish @ X1 @ X3))),
% 0.79/0.83 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.79/0.83 thf(zip_derived_cl167, plain,
% 0.79/0.83 ((![X0 : $i]: (~ (product @ e_3 @ X0 @ e_1) | (equalish @ e_3 @ X0)))
% 0.79/0.83 <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl150, zip_derived_cl17])).
% 0.79/0.83 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 0.79/0.83 thf(zip_derived_cl13, plain, (~ (equalish @ e_3 @ e_1)),
% 0.79/0.83 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.79/0.83 thf(zip_derived_cl308, plain,
% 0.79/0.83 ((~ (product @ e_3 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl167, zip_derived_cl13])).
% 0.79/0.83 thf(zip_derived_cl109, plain,
% 0.79/0.83 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.79/0.83 thf(zip_derived_cl19, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.79/0.83 ( (product @ X0 @ X1 @ X2)
% 0.79/0.83 | ~ (product @ X2 @ X3 @ X0)
% 0.79/0.83 | ~ (product @ X2 @ X1 @ X3))),
% 0.79/0.83 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.79/0.83 thf(zip_derived_cl115, plain,
% 0.79/0.83 ((![X0 : $i]:
% 0.79/0.83 ( (product @ e_3 @ X0 @ e_1) | ~ (product @ e_1 @ X0 @ e_2)))
% 0.79/0.83 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl19])).
% 0.79/0.83 thf(zip_derived_cl326, plain,
% 0.79/0.83 ((~ (product @ e_1 @ e_1 @ e_2))
% 0.79/0.83 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_1 @ e_3 @ e_3)))),
% 0.79/0.83 inference('s_sup+', [status(thm)], [zip_derived_cl308, zip_derived_cl115])).
% 0.79/0.83 thf(zip_derived_cl37, plain,
% 0.79/0.83 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.79/0.83 thf('10', plain,
% 0.79/0.83 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_3)) |
% 0.79/0.83 ~ ( (product @ e_1 @ e_3 @ e_3))),
% 0.79/0.83 inference('s_sup+', [status(thm)], [zip_derived_cl326, zip_derived_cl37])).
% 0.79/0.83 thf('11', plain,
% 0.79/0.83 (( (product @ e_1 @ e_1 @ e_1)) | ( (product @ e_1 @ e_1 @ e_2)) |
% 0.79/0.83 ( (product @ e_1 @ e_1 @ e_3))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl30])).
% 0.79/0.83 thf(zip_derived_cl87, plain,
% 0.79/0.83 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_1) | (equalish @ e_1 @ X0)))
% 0.79/0.83 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl17])).
% 0.79/0.83 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.79/0.83 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.79/0.83 thf(zip_derived_cl306, plain,
% 0.79/0.83 ((~ (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl87, zip_derived_cl9])).
% 0.79/0.83 thf(zip_derived_cl111, plain,
% 0.79/0.83 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.79/0.83 thf('12', plain,
% 0.79/0.83 (~ ( (product @ e_1 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_1))),
% 0.79/0.83 inference('s_sup+', [status(thm)], [zip_derived_cl306, zip_derived_cl111])).
% 0.79/0.83 thf(zip_derived_cl109, plain,
% 0.79/0.83 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.79/0.83 thf(zip_derived_cl17, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.79/0.83 (~ (product @ X0 @ X1 @ X2)
% 0.79/0.83 | ~ (product @ X0 @ X3 @ X2)
% 0.79/0.83 | (equalish @ X1 @ X3))),
% 0.79/0.83 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.79/0.83 thf(zip_derived_cl113, plain,
% 0.79/0.83 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_2 @ X0)))
% 0.79/0.83 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl17])).
% 0.79/0.83 thf(zip_derived_cl12, plain, (~ (equalish @ e_2 @ e_3)),
% 0.79/0.83 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.79/0.83 thf(zip_derived_cl513, plain,
% 0.79/0.83 ((~ (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl113, zip_derived_cl12])).
% 0.79/0.83 thf(zip_derived_cl140, plain,
% 0.79/0.83 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl32])).
% 0.79/0.83 thf('13', plain,
% 0.79/0.83 (~ ( (product @ e_1 @ e_3 @ e_3)) | ~ ( (product @ e_1 @ e_2 @ e_3))),
% 0.79/0.83 inference('s_sup+', [status(thm)], [zip_derived_cl513, zip_derived_cl140])).
% 0.79/0.83 thf(zip_derived_cl150, plain,
% 0.79/0.83 (( (product @ e_3 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl140, zip_derived_cl28])).
% 0.79/0.83 thf(product_total_function2, axiom,
% 0.79/0.83 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 0.79/0.83 ( equalish @ W @ Z ))).
% 0.79/0.83 thf(zip_derived_cl16, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.79/0.83 (~ (product @ X0 @ X1 @ X2)
% 0.79/0.83 | ~ (product @ X0 @ X1 @ X3)
% 0.79/0.83 | (equalish @ X2 @ X3))),
% 0.79/0.83 inference('cnf', [status(esa)], [product_total_function2])).
% 0.79/0.83 thf(zip_derived_cl166, plain,
% 0.79/0.83 ((![X0 : $i]: (~ (product @ e_3 @ e_3 @ X0) | (equalish @ e_1 @ X0)))
% 0.79/0.83 <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl150, zip_derived_cl16])).
% 0.79/0.83 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 0.79/0.83 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.79/0.83 thf(zip_derived_cl292, plain,
% 0.79/0.83 ((~ (product @ e_3 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl166, zip_derived_cl9])).
% 0.79/0.83 thf(zip_derived_cl241, plain,
% 0.79/0.83 (( (product @ e_2 @ e_3 @ e_3)) <= (( (product @ e_2 @ e_3 @ e_3)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl49])).
% 0.79/0.83 thf(zip_derived_cl28, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i]:
% 0.79/0.83 (~ (product @ X1 @ X0 @ X0) | (product @ X0 @ X0 @ X1))),
% 0.79/0.83 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 0.79/0.83 thf(zip_derived_cl251, plain,
% 0.79/0.83 (( (product @ e_3 @ e_3 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl241, zip_derived_cl28])).
% 0.79/0.83 thf('14', plain,
% 0.79/0.83 (~ ( (product @ e_2 @ e_3 @ e_3)) | ~ ( (product @ e_1 @ e_3 @ e_3))),
% 0.79/0.83 inference('s_sup+', [status(thm)], [zip_derived_cl292, zip_derived_cl251])).
% 0.79/0.83 thf('15', plain,
% 0.79/0.83 (( (product @ e_2 @ e_3 @ e_2)) | ( (product @ e_2 @ e_3 @ e_1)) |
% 0.79/0.83 ( (product @ e_2 @ e_3 @ e_3))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl49])).
% 0.79/0.83 thf('16', plain,
% 0.79/0.83 (( (product @ e_1 @ e_3 @ e_2)) | ( (product @ e_1 @ e_3 @ e_3)) |
% 0.79/0.83 ( (product @ e_1 @ e_3 @ e_1))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl32])).
% 0.79/0.83 thf(zip_derived_cl573, plain,
% 0.79/0.83 ((~ (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl12])).
% 0.79/0.83 thf(zip_derived_cl189, plain,
% 0.79/0.83 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl35])).
% 0.79/0.83 thf('17', plain,
% 0.79/0.83 (~ ( (product @ e_1 @ e_2 @ e_2)) | ~ ( (product @ e_1 @ e_3 @ e_2))),
% 0.79/0.83 inference('s_sup+', [status(thm)], [zip_derived_cl573, zip_derived_cl189])).
% 0.79/0.83 thf('18', plain,
% 0.79/0.83 (( (product @ e_1 @ e_2 @ e_3)) | ( (product @ e_1 @ e_2 @ e_2)) |
% 0.79/0.83 ( (product @ e_1 @ e_2 @ e_1))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.79/0.83 thf(zip_derived_cl115, plain,
% 0.79/0.83 ((![X0 : $i]:
% 0.79/0.83 ( (product @ e_3 @ X0 @ e_1) | ~ (product @ e_1 @ X0 @ e_2)))
% 0.79/0.83 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl19])).
% 0.79/0.83 thf(zip_derived_cl17, plain,
% 0.79/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.79/0.83 (~ (product @ X0 @ X1 @ X2)
% 0.79/0.83 | ~ (product @ X0 @ X3 @ X2)
% 0.79/0.83 | (equalish @ X1 @ X3))),
% 0.79/0.83 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.79/0.83 thf(zip_derived_cl122, plain,
% 0.79/0.83 ((![X0 : $i, X1 : $i]:
% 0.79/0.83 (~ (product @ e_1 @ X0 @ e_2)
% 0.79/0.83 | ~ (product @ e_3 @ X1 @ e_1)
% 0.79/0.83 | (equalish @ X0 @ X1)))
% 0.79/0.83 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl115, zip_derived_cl17])).
% 0.79/0.83 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 0.79/0.83 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_2)),
% 0.79/0.83 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 0.79/0.83 thf(zip_derived_cl583, plain,
% 0.79/0.83 (((~ (product @ e_3 @ e_2 @ e_1) | ~ (product @ e_1 @ e_3 @ e_2)))
% 0.79/0.83 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.79/0.83 inference('s_sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl14])).
% 0.79/0.83 thf('19', plain,
% 0.79/0.83 (~ ( (product @ e_3 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_2 @ e_3)) |
% 0.79/0.83 ~ ( (product @ e_1 @ e_3 @ e_2))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl583])).
% 0.79/0.83 thf('20', plain,
% 0.79/0.83 (( (product @ e_3 @ e_2 @ e_1)) | ( (product @ e_3 @ e_2 @ e_3)) |
% 0.79/0.83 ( (product @ e_3 @ e_2 @ e_2))),
% 0.79/0.83 inference('split', [status(esa)], [zip_derived_cl77])).
% 0.79/0.83 thf(zip_derived_cl726, plain, ($false),
% 0.79/0.83 inference('sat_resolution*', [status(thm)],
% 0.79/0.83 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 0.79/0.83 '12', '13', '14', '15', '16', '17', '18', '19', '20'])).
% 0.79/0.83
% 0.79/0.83 % SZS output end Refutation
% 0.79/0.83
% 0.79/0.83
% 0.79/0.83 % Terminating...
% 1.45/0.91 % Runner terminated.
% 1.45/0.92 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------