%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP128-1.003 : 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.HVSxMkjMO9 true
% Computer : n001.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 04:35:45 PM UTC 2025
% Result : Unsatisfiable 0.64s 0.96s
% Output : Refutation 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP128-1.003 : TPTP v9.2.0. Released v1.2.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HVSxMkjMO9 true
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 14:23:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.58/0.68 % Total configuration time : 435
% 0.58/0.68 % Estimated wc time : 1092
% 0.58/0.68 % Estimated cpu time (7 cpus) : 156.0
% 0.62/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.63/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.63/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.63/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.63/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.63/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.63/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.64/0.96 % Solved by fo/fo1_av.sh.
% 0.64/0.96 % done 664 iterations in 0.147s
% 0.64/0.96 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.64/0.96 % SZS output start Refutation
% 0.64/0.96 thf(e_1_type, type, e_1: $i).
% 0.64/0.96 thf(e_3_type, type, e_3: $i).
% 0.64/0.96 thf(group_element_type, type, group_element: $i > $o).
% 0.64/0.96 thf(e_2_type, type, e_2: $i).
% 0.64/0.96 thf(product_type, type, product: $i > $i > $i > $o).
% 0.64/0.96 thf(equalish_type, type, equalish: $i > $i > $o).
% 0.64/0.96 thf(element_1, axiom, (group_element @ e_1)).
% 0.64/0.96 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.64/0.96 inference('cnf', [status(esa)], [element_1])).
% 0.64/0.96 thf(element_3, axiom, (group_element @ e_3)).
% 0.64/0.96 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.64/0.96 inference('cnf', [status(esa)], [element_3])).
% 0.64/0.96 thf(product_total_function1, axiom,
% 0.64/0.96 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 0.64/0.96 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 0.64/0.96 ( product @ X @ Y @ e_3 ))).
% 0.64/0.96 thf(zip_derived_cl9, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i]:
% 0.64/0.96 (~ (group_element @ X0)
% 0.64/0.96 | ~ (group_element @ X1)
% 0.64/0.96 | (product @ X0 @ X1 @ e_1)
% 0.64/0.96 | (product @ X0 @ X1 @ e_2)
% 0.64/0.96 | (product @ X0 @ X1 @ e_3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_total_function1])).
% 0.64/0.96 thf(zip_derived_cl21, plain,
% 0.64/0.96 (![X0 : $i]:
% 0.64/0.96 (~ (group_element @ X0)
% 0.64/0.96 | (product @ e_3 @ X0 @ e_1)
% 0.64/0.96 | (product @ e_3 @ X0 @ e_2)
% 0.64/0.96 | (product @ e_3 @ X0 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl9])).
% 0.64/0.96 thf(zip_derived_cl42, plain,
% 0.64/0.96 (( (product @ e_3 @ e_1 @ e_1)
% 0.64/0.96 | (product @ e_3 @ e_1 @ e_2)
% 0.64/0.96 | (product @ e_3 @ e_1 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl21])).
% 0.64/0.96 thf(zip_derived_cl396, plain,
% 0.64/0.96 (( (product @ e_3 @ e_1 @ e_2)) <= (( (product @ e_3 @ e_1 @ e_2)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl42])).
% 0.64/0.96 thf(qg3, conjecture,
% 0.64/0.96 (~( ( product @ X @ Z1 @ Z2 ) | ( ~( product @ Z1 @ Y @ Z2 ) ) |
% 0.64/0.96 ( ~( product @ X @ Y @ Z1 ) ) ))).
% 0.64/0.96 thf(zf_stmt_0, negated_conjecture,
% 0.64/0.96 (( product @ X @ Z1 @ Z2 ) | ( ~( product @ Z1 @ Y @ Z2 ) ) |
% 0.64/0.96 ( ~( product @ X @ Y @ Z1 ) )),
% 0.64/0.96 inference('cnf.neg', [status(esa)], [qg3])).
% 0.64/0.96 thf(zip_derived_cl13, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 ( (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X1 @ X3 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X3 @ X1))),
% 0.64/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.64/0.96 thf(zip_derived_cl401, plain,
% 0.64/0.96 ((![X0 : $i]:
% 0.64/0.96 ( (product @ X0 @ e_3 @ e_2) | ~ (product @ X0 @ e_1 @ e_3)))
% 0.64/0.96 <= (( (product @ e_3 @ e_1 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl396, zip_derived_cl13])).
% 0.64/0.96 thf(zip_derived_cl396, plain,
% 0.64/0.96 (( (product @ e_3 @ e_1 @ e_2)) <= (( (product @ e_3 @ e_1 @ e_2)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl42])).
% 0.64/0.96 thf(product_right_cancellation, axiom,
% 0.64/0.96 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 0.64/0.96 ( equalish @ W @ Z ))).
% 0.64/0.96 thf(zip_derived_cl11, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.64/0.96 | (equalish @ X1 @ X3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.64/0.96 thf(zip_derived_cl399, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ e_3 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 0.64/0.96 <= (( (product @ e_3 @ e_1 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl396, zip_derived_cl11])).
% 0.64/0.96 thf(zip_derived_cl913, plain,
% 0.64/0.96 (((~ (product @ e_3 @ e_1 @ e_3) | (equalish @ e_1 @ e_3)))
% 0.64/0.96 <= (( (product @ e_3 @ e_1 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl401, zip_derived_cl399])).
% 0.64/0.96 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 0.64/0.96 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.64/0.96 thf(zip_derived_cl916, plain,
% 0.64/0.96 ((~ (product @ e_3 @ e_1 @ e_3)) <= (( (product @ e_3 @ e_1 @ e_2)))),
% 0.64/0.96 inference('demod', [status(thm)], [zip_derived_cl913, zip_derived_cl4])).
% 0.64/0.96 thf(zip_derived_cl21, plain,
% 0.64/0.96 (![X0 : $i]:
% 0.64/0.96 (~ (group_element @ X0)
% 0.64/0.96 | (product @ e_3 @ X0 @ e_1)
% 0.64/0.96 | (product @ e_3 @ X0 @ e_2)
% 0.64/0.96 | (product @ e_3 @ X0 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl9])).
% 0.64/0.96 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.64/0.96 inference('cnf', [status(esa)], [element_1])).
% 0.64/0.96 thf(zip_derived_cl39, plain,
% 0.64/0.96 (( (product @ e_3 @ e_1 @ e_3)
% 0.64/0.96 | (product @ e_3 @ e_1 @ e_2)
% 0.64/0.96 | (product @ e_3 @ e_1 @ e_1))),
% 0.64/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl0])).
% 0.64/0.96 thf(zip_derived_cl332, plain,
% 0.64/0.96 (( (product @ e_3 @ e_1 @ e_3)) <= (( (product @ e_3 @ e_1 @ e_3)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl39])).
% 0.64/0.96 thf(zip_derived_cl13, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 ( (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X1 @ X3 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X3 @ X1))),
% 0.64/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.64/0.96 thf(zip_derived_cl18, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X0) | (product @ X0 @ X0 @ X0))),
% 0.64/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 0.64/0.96 thf(zip_derived_cl342, plain,
% 0.64/0.96 (( (product @ e_3 @ e_3 @ e_3)) <= (( (product @ e_3 @ e_1 @ e_3)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl332, zip_derived_cl18])).
% 0.64/0.96 thf(zip_derived_cl332, plain,
% 0.64/0.96 (( (product @ e_3 @ e_1 @ e_3)) <= (( (product @ e_3 @ e_1 @ e_3)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl39])).
% 0.64/0.96 thf(zip_derived_cl11, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.64/0.96 | (equalish @ X1 @ X3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.64/0.96 thf(zip_derived_cl336, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ e_3 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 0.64/0.96 <= (( (product @ e_3 @ e_1 @ e_3)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl332, zip_derived_cl11])).
% 0.64/0.96 thf(zip_derived_cl876, plain,
% 0.64/0.96 (( (equalish @ e_1 @ e_3)) <= (( (product @ e_3 @ e_1 @ e_3)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl342, zip_derived_cl336])).
% 0.64/0.96 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.64/0.96 thf('0', plain, (~ ( (product @ e_3 @ e_1 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl876, zip_derived_cl4])).
% 0.64/0.96 thf(zip_derived_cl21, plain,
% 0.64/0.96 (![X0 : $i]:
% 0.64/0.96 (~ (group_element @ X0)
% 0.64/0.96 | (product @ e_3 @ X0 @ e_1)
% 0.64/0.96 | (product @ e_3 @ X0 @ e_2)
% 0.64/0.96 | (product @ e_3 @ X0 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl9])).
% 0.64/0.96 thf(element_2, axiom, (group_element @ e_2)).
% 0.64/0.96 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.64/0.96 inference('cnf', [status(esa)], [element_2])).
% 0.64/0.96 thf(zip_derived_cl40, plain,
% 0.64/0.96 (( (product @ e_3 @ e_2 @ e_3)
% 0.64/0.96 | (product @ e_3 @ e_2 @ e_2)
% 0.64/0.96 | (product @ e_3 @ e_2 @ e_1))),
% 0.64/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl1])).
% 0.64/0.96 thf(zip_derived_cl361, plain,
% 0.64/0.96 (( (product @ e_3 @ e_2 @ e_1)) <= (( (product @ e_3 @ e_2 @ e_1)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl40])).
% 0.64/0.96 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.64/0.96 inference('cnf', [status(esa)], [element_2])).
% 0.64/0.96 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.64/0.96 inference('cnf', [status(esa)], [element_1])).
% 0.64/0.96 thf(zip_derived_cl9, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i]:
% 0.64/0.96 (~ (group_element @ X0)
% 0.64/0.96 | ~ (group_element @ X1)
% 0.64/0.96 | (product @ X0 @ X1 @ e_1)
% 0.64/0.96 | (product @ X0 @ X1 @ e_2)
% 0.64/0.96 | (product @ X0 @ X1 @ e_3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_total_function1])).
% 0.64/0.96 thf(zip_derived_cl19, plain,
% 0.64/0.96 (![X0 : $i]:
% 0.64/0.96 (~ (group_element @ X0)
% 0.64/0.96 | (product @ e_1 @ X0 @ e_1)
% 0.64/0.96 | (product @ e_1 @ X0 @ e_2)
% 0.64/0.96 | (product @ e_1 @ X0 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 0.64/0.96 thf(zip_derived_cl31, plain,
% 0.64/0.96 (( (product @ e_1 @ e_2 @ e_1)
% 0.64/0.96 | (product @ e_1 @ e_2 @ e_2)
% 0.64/0.96 | (product @ e_1 @ e_2 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl19])).
% 0.64/0.96 thf(zip_derived_cl189, plain,
% 0.64/0.96 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.64/0.96 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.64/0.96 inference('cnf', [status(esa)], [element_2])).
% 0.64/0.96 thf(zip_derived_cl9, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i]:
% 0.64/0.96 (~ (group_element @ X0)
% 0.64/0.96 | ~ (group_element @ X1)
% 0.64/0.96 | (product @ X0 @ X1 @ e_1)
% 0.64/0.96 | (product @ X0 @ X1 @ e_2)
% 0.64/0.96 | (product @ X0 @ X1 @ e_3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_total_function1])).
% 0.64/0.96 thf(zip_derived_cl22, plain,
% 0.64/0.96 (![X0 : $i]:
% 0.64/0.96 ( (product @ X0 @ X0 @ e_3)
% 0.64/0.96 | (product @ X0 @ X0 @ e_2)
% 0.64/0.96 | (product @ X0 @ X0 @ e_1)
% 0.64/0.96 | ~ (group_element @ X0))),
% 0.64/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl9])).
% 0.64/0.96 thf(zip_derived_cl25, plain,
% 0.64/0.96 (( (product @ e_2 @ e_2 @ e_3)
% 0.64/0.96 | (product @ e_2 @ e_2 @ e_2)
% 0.64/0.96 | (product @ e_2 @ e_2 @ e_1))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl22])).
% 0.64/0.96 thf(zip_derived_cl64, plain,
% 0.64/0.96 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_2)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.64/0.96 thf(product_left_cancellation, axiom,
% 0.64/0.96 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 0.64/0.96 ( equalish @ W @ Z ))).
% 0.64/0.96 thf(zip_derived_cl12, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X3 @ X1 @ X2)
% 0.64/0.96 | (equalish @ X0 @ X3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.64/0.96 thf(zip_derived_cl102, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_2) | (equalish @ e_2 @ X0)))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl12])).
% 0.64/0.96 thf(zip_derived_cl519, plain,
% 0.64/0.96 (( (equalish @ e_2 @ e_1))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_2)) & ( (product @ e_1 @ e_2 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl189, zip_derived_cl102])).
% 0.64/0.96 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 0.64/0.96 thf(zip_derived_cl5, plain, (~ (equalish @ e_2 @ e_1)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.64/0.96 thf('1', plain,
% 0.64/0.96 (~ ( (product @ e_1 @ e_2 @ e_2)) | ~ ( (product @ e_2 @ e_2 @ e_2))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl519, zip_derived_cl5])).
% 0.64/0.96 thf(zip_derived_cl189, plain,
% 0.64/0.96 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.64/0.96 thf(zip_derived_cl63, plain,
% 0.64/0.96 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.64/0.96 thf(zip_derived_cl13, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 ( (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X1 @ X3 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X3 @ X1))),
% 0.64/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.64/0.96 thf(zip_derived_cl69, plain,
% 0.64/0.96 ((![X0 : $i]:
% 0.64/0.96 ( (product @ X0 @ e_2 @ e_1) | ~ (product @ X0 @ e_2 @ e_2)))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl13])).
% 0.64/0.96 thf(zip_derived_cl198, plain,
% 0.64/0.96 (( (product @ e_1 @ e_2 @ e_1))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_1)) & ( (product @ e_1 @ e_2 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl189, zip_derived_cl69])).
% 0.64/0.96 thf(zip_derived_cl63, plain,
% 0.64/0.96 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.64/0.96 thf(zip_derived_cl12, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X3 @ X1 @ X2)
% 0.64/0.96 | (equalish @ X0 @ X3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.64/0.96 thf(zip_derived_cl68, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_1) | (equalish @ e_2 @ X0)))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl12])).
% 0.64/0.96 thf(zip_derived_cl329, plain,
% 0.64/0.96 (( (equalish @ e_2 @ e_1))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_1)) & ( (product @ e_1 @ e_2 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl198, zip_derived_cl68])).
% 0.64/0.96 thf(zip_derived_cl5, plain, (~ (equalish @ e_2 @ e_1)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.64/0.96 thf('2', plain,
% 0.64/0.96 (~ ( (product @ e_1 @ e_2 @ e_2)) | ~ ( (product @ e_2 @ e_2 @ e_1))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl329, zip_derived_cl5])).
% 0.64/0.96 thf(zip_derived_cl359, plain,
% 0.64/0.96 (( (product @ e_3 @ e_2 @ e_3)) <= (( (product @ e_3 @ e_2 @ e_3)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl40])).
% 0.64/0.96 thf(zip_derived_cl19, plain,
% 0.64/0.96 (![X0 : $i]:
% 0.64/0.96 (~ (group_element @ X0)
% 0.64/0.96 | (product @ e_1 @ X0 @ e_1)
% 0.64/0.96 | (product @ e_1 @ X0 @ e_2)
% 0.64/0.96 | (product @ e_1 @ X0 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl9])).
% 0.64/0.96 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.64/0.96 inference('cnf', [status(esa)], [element_2])).
% 0.64/0.96 thf(zip_derived_cl28, plain,
% 0.64/0.96 (( (product @ e_1 @ e_2 @ e_3)
% 0.64/0.96 | (product @ e_1 @ e_2 @ e_2)
% 0.64/0.96 | (product @ e_1 @ e_2 @ e_1))),
% 0.64/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl1])).
% 0.64/0.96 thf(zip_derived_cl122, plain,
% 0.64/0.96 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl28])).
% 0.64/0.96 thf(zip_derived_cl12, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X3 @ X1 @ X2)
% 0.64/0.96 | (equalish @ X0 @ X3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.64/0.96 thf(zip_derived_cl127, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_1 @ X0)))
% 0.64/0.96 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl12])).
% 0.64/0.96 thf(zip_derived_cl556, plain,
% 0.64/0.96 (( (equalish @ e_1 @ e_3))
% 0.64/0.96 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_3 @ e_2 @ e_3)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl359, zip_derived_cl127])).
% 0.64/0.96 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.64/0.96 thf('3', plain,
% 0.64/0.96 (~ ( (product @ e_3 @ e_2 @ e_3)) | ~ ( (product @ e_1 @ e_2 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl556, zip_derived_cl4])).
% 0.64/0.96 thf(zip_derived_cl124, plain,
% 0.64/0.96 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl28])).
% 0.64/0.96 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.64/0.96 inference('cnf', [status(esa)], [element_1])).
% 0.64/0.96 thf(zip_derived_cl22, plain,
% 0.64/0.96 (![X0 : $i]:
% 0.64/0.96 ( (product @ X0 @ X0 @ e_3)
% 0.64/0.96 | (product @ X0 @ X0 @ e_2)
% 0.64/0.96 | (product @ X0 @ X0 @ e_1)
% 0.64/0.96 | ~ (group_element @ X0))),
% 0.64/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl9])).
% 0.64/0.96 thf(zip_derived_cl24, plain,
% 0.64/0.96 (( (product @ e_1 @ e_1 @ e_3)
% 0.64/0.96 | (product @ e_1 @ e_1 @ e_2)
% 0.64/0.96 | (product @ e_1 @ e_1 @ e_1))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl22])).
% 0.64/0.96 thf(zip_derived_cl45, plain,
% 0.64/0.96 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl24])).
% 0.64/0.96 thf(zip_derived_cl11, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.64/0.96 | (equalish @ X1 @ X3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.64/0.96 thf(zip_derived_cl49, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_1) | (equalish @ e_1 @ X0)))
% 0.64/0.96 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl11])).
% 0.64/0.96 thf(zip_derived_cl547, plain,
% 0.64/0.96 (( (equalish @ e_1 @ e_2))
% 0.64/0.96 <= (( (product @ e_1 @ e_1 @ e_1)) & ( (product @ e_1 @ e_2 @ e_1)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl124, zip_derived_cl49])).
% 0.64/0.96 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 0.64/0.96 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.64/0.96 thf('4', plain,
% 0.64/0.96 (~ ( (product @ e_1 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_1))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl547, zip_derived_cl3])).
% 0.64/0.96 thf(zip_derived_cl124, plain,
% 0.64/0.96 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl28])).
% 0.64/0.96 thf(zip_derived_cl18, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X0) | (product @ X0 @ X0 @ X0))),
% 0.64/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 0.64/0.96 thf(zip_derived_cl545, plain,
% 0.64/0.96 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl124, zip_derived_cl18])).
% 0.64/0.96 thf(zip_derived_cl46, plain,
% 0.64/0.96 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl24])).
% 0.64/0.96 thf(zip_derived_cl13, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 ( (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X1 @ X3 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X3 @ X1))),
% 0.64/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.64/0.96 thf(zip_derived_cl59, plain,
% 0.64/0.96 ((![X0 : $i]:
% 0.64/0.96 ( (product @ X0 @ e_1 @ e_2) | ~ (product @ X0 @ e_1 @ e_1)))
% 0.64/0.96 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl13])).
% 0.64/0.96 thf(product_total_function2, axiom,
% 0.64/0.96 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 0.64/0.96 ( equalish @ W @ Z ))).
% 0.64/0.96 thf(zip_derived_cl10, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X1 @ X3)
% 0.64/0.96 | (equalish @ X2 @ X3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_total_function2])).
% 0.64/0.96 thf(zip_derived_cl73, plain,
% 0.64/0.96 ((![X0 : $i, X1 : $i]:
% 0.64/0.96 (~ (product @ X0 @ e_1 @ e_1)
% 0.64/0.96 | ~ (product @ X0 @ e_1 @ X1)
% 0.64/0.96 | (equalish @ e_2 @ X1)))
% 0.64/0.96 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl10])).
% 0.64/0.96 thf(zip_derived_cl459, plain,
% 0.64/0.96 ((![X0 : $i]: ( (equalish @ e_2 @ e_1) | ~ (product @ X0 @ e_1 @ e_1)))
% 0.64/0.96 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.64/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl73])).
% 0.64/0.96 thf(zip_derived_cl5, plain, (~ (equalish @ e_2 @ e_1)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.64/0.96 thf(zip_derived_cl460, plain,
% 0.64/0.96 ((![X0 : $i]: ~ (product @ X0 @ e_1 @ e_1))
% 0.64/0.96 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 0.64/0.96 inference('demod', [status(thm)], [zip_derived_cl459, zip_derived_cl5])).
% 0.64/0.96 thf('5', plain,
% 0.64/0.96 (~ ( (product @ e_1 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_2))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl545, zip_derived_cl460])).
% 0.64/0.96 thf('6', plain,
% 0.64/0.96 (( (product @ e_1 @ e_1 @ e_1)) | ( (product @ e_1 @ e_1 @ e_2)) |
% 0.64/0.96 ( (product @ e_1 @ e_1 @ e_3))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl24])).
% 0.64/0.96 thf(zip_derived_cl47, plain,
% 0.64/0.96 (( (product @ e_1 @ e_1 @ e_3)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl24])).
% 0.64/0.96 thf(zip_derived_cl13, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 ( (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X1 @ X3 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X3 @ X1))),
% 0.64/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.64/0.96 thf(zip_derived_cl86, plain,
% 0.64/0.96 ((![X0 : $i]:
% 0.64/0.96 ( (product @ X0 @ e_1 @ e_3) | ~ (product @ X0 @ e_1 @ e_1)))
% 0.64/0.96 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl47, zip_derived_cl13])).
% 0.64/0.96 thf(zip_derived_cl10, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X1 @ X3)
% 0.64/0.96 | (equalish @ X2 @ X3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_total_function2])).
% 0.64/0.96 thf(zip_derived_cl153, plain,
% 0.64/0.96 ((![X0 : $i, X1 : $i]:
% 0.64/0.96 (~ (product @ X0 @ e_1 @ e_1)
% 0.64/0.96 | ~ (product @ X0 @ e_1 @ X1)
% 0.64/0.96 | (equalish @ e_3 @ X1)))
% 0.64/0.96 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl86, zip_derived_cl10])).
% 0.64/0.96 thf(zip_derived_cl683, plain,
% 0.64/0.96 ((![X0 : $i]: ( (equalish @ e_3 @ e_1) | ~ (product @ X0 @ e_1 @ e_1)))
% 0.64/0.96 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.64/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl153])).
% 0.64/0.96 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 0.64/0.96 thf(zip_derived_cl7, plain, (~ (equalish @ e_3 @ e_1)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.64/0.96 thf(zip_derived_cl684, plain,
% 0.64/0.96 ((![X0 : $i]: ~ (product @ X0 @ e_1 @ e_1))
% 0.64/0.96 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 0.64/0.96 inference('demod', [status(thm)], [zip_derived_cl683, zip_derived_cl7])).
% 0.64/0.96 thf(zip_derived_cl545, plain,
% 0.64/0.96 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl124, zip_derived_cl18])).
% 0.64/0.96 thf('7', plain,
% 0.64/0.96 (~ ( (product @ e_1 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_3))),
% 0.64/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl684, zip_derived_cl545])).
% 0.64/0.96 thf(zip_derived_cl65, plain,
% 0.64/0.96 (( (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.64/0.96 thf(zip_derived_cl13, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 ( (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X1 @ X3 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X3 @ X1))),
% 0.64/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.64/0.96 thf(zip_derived_cl139, plain,
% 0.64/0.96 ((![X0 : $i]:
% 0.64/0.96 ( (product @ X0 @ e_2 @ e_3) | ~ (product @ X0 @ e_2 @ e_2)))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_3)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl13])).
% 0.64/0.96 thf(zip_derived_cl189, plain,
% 0.64/0.96 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.64/0.96 thf(zip_derived_cl10, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X1 @ X3)
% 0.64/0.96 | (equalish @ X2 @ X3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_total_function2])).
% 0.64/0.96 thf(zip_derived_cl191, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ e_1 @ e_2 @ X0) | (equalish @ e_2 @ X0)))
% 0.64/0.96 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl189, zip_derived_cl10])).
% 0.64/0.96 thf(zip_derived_cl700, plain,
% 0.64/0.96 (((~ (product @ e_1 @ e_2 @ e_2) | (equalish @ e_2 @ e_3)))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_3)) & ( (product @ e_1 @ e_2 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl139, zip_derived_cl191])).
% 0.64/0.96 thf(zip_derived_cl189, plain,
% 0.64/0.96 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl31])).
% 0.64/0.96 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 0.64/0.96 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.64/0.96 thf('8', plain,
% 0.64/0.96 (~ ( (product @ e_2 @ e_2 @ e_3)) | ~ ( (product @ e_1 @ e_2 @ e_2))),
% 0.64/0.96 inference('demod', [status(thm)],
% 0.64/0.96 [zip_derived_cl700, zip_derived_cl189, zip_derived_cl6])).
% 0.64/0.96 thf(zip_derived_cl127, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_1 @ X0)))
% 0.64/0.96 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl12])).
% 0.64/0.96 thf(zip_derived_cl65, plain,
% 0.64/0.96 (( (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.64/0.96 thf(zip_derived_cl553, plain,
% 0.64/0.96 (( (equalish @ e_1 @ e_2))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_3)) & ( (product @ e_1 @ e_2 @ e_3)))),
% 0.64/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl127, zip_derived_cl65])).
% 0.64/0.96 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.64/0.96 thf('9', plain,
% 0.64/0.96 (~ ( (product @ e_2 @ e_2 @ e_3)) | ~ ( (product @ e_1 @ e_2 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl553, zip_derived_cl3])).
% 0.64/0.96 thf('10', plain,
% 0.64/0.96 (( (product @ e_1 @ e_2 @ e_3)) | ( (product @ e_1 @ e_2 @ e_2)) |
% 0.64/0.96 ( (product @ e_1 @ e_2 @ e_1))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl28])).
% 0.64/0.96 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.64/0.96 inference('cnf', [status(esa)], [element_2])).
% 0.64/0.96 thf(zip_derived_cl9, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i]:
% 0.64/0.96 (~ (group_element @ X0)
% 0.64/0.96 | ~ (group_element @ X1)
% 0.64/0.96 | (product @ X0 @ X1 @ e_1)
% 0.64/0.96 | (product @ X0 @ X1 @ e_2)
% 0.64/0.96 | (product @ X0 @ X1 @ e_3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_total_function1])).
% 0.64/0.96 thf(zip_derived_cl20, plain,
% 0.64/0.96 (![X0 : $i]:
% 0.64/0.96 (~ (group_element @ X0)
% 0.64/0.96 | (product @ e_2 @ X0 @ e_1)
% 0.64/0.96 | (product @ e_2 @ X0 @ e_2)
% 0.64/0.96 | (product @ e_2 @ X0 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 0.64/0.96 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.64/0.96 inference('cnf', [status(esa)], [element_3])).
% 0.64/0.96 thf(zip_derived_cl35, plain,
% 0.64/0.96 (( (product @ e_2 @ e_3 @ e_3)
% 0.64/0.96 | (product @ e_2 @ e_3 @ e_2)
% 0.64/0.96 | (product @ e_2 @ e_3 @ e_1))),
% 0.64/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl2])).
% 0.64/0.96 thf('11', plain,
% 0.64/0.96 (( (product @ e_2 @ e_3 @ e_1)) | ( (product @ e_2 @ e_3 @ e_3)) |
% 0.64/0.96 ( (product @ e_2 @ e_3 @ e_2))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl35])).
% 0.64/0.96 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.64/0.96 inference('cnf', [status(esa)], [element_3])).
% 0.64/0.96 thf(zip_derived_cl20, plain,
% 0.64/0.96 (![X0 : $i]:
% 0.64/0.96 (~ (group_element @ X0)
% 0.64/0.96 | (product @ e_2 @ X0 @ e_1)
% 0.64/0.96 | (product @ e_2 @ X0 @ e_2)
% 0.64/0.96 | (product @ e_2 @ X0 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 0.64/0.96 thf(zip_derived_cl38, plain,
% 0.64/0.96 (( (product @ e_2 @ e_3 @ e_1)
% 0.64/0.96 | (product @ e_2 @ e_3 @ e_2)
% 0.64/0.96 | (product @ e_2 @ e_3 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl20])).
% 0.64/0.96 thf(zip_derived_cl318, plain,
% 0.64/0.96 (( (product @ e_2 @ e_3 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl38])).
% 0.64/0.96 thf(zip_derived_cl18, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X0) | (product @ X0 @ X0 @ X0))),
% 0.64/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 0.64/0.96 thf(zip_derived_cl327, plain,
% 0.64/0.96 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl318, zip_derived_cl18])).
% 0.64/0.96 thf(zip_derived_cl65, plain,
% 0.64/0.96 (( (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.64/0.96 thf(zip_derived_cl10, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X1 @ X3)
% 0.64/0.96 | (equalish @ X2 @ X3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_total_function2])).
% 0.64/0.96 thf(zip_derived_cl136, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ e_2 @ e_2 @ X0) | (equalish @ e_3 @ X0)))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_3)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl10])).
% 0.64/0.96 thf(zip_derived_cl563, plain,
% 0.64/0.96 (( (equalish @ e_3 @ e_2))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_3)) & ( (product @ e_2 @ e_3 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl327, zip_derived_cl136])).
% 0.64/0.96 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 0.64/0.96 thf(zip_derived_cl8, plain, (~ (equalish @ e_3 @ e_2)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 0.64/0.96 thf('12', plain,
% 0.64/0.96 (~ ( (product @ e_2 @ e_3 @ e_2)) | ~ ( (product @ e_2 @ e_2 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl563, zip_derived_cl8])).
% 0.64/0.96 thf(zip_derived_cl318, plain,
% 0.64/0.96 (( (product @ e_2 @ e_3 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl38])).
% 0.64/0.96 thf(zip_derived_cl64, plain,
% 0.64/0.96 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_2)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.64/0.96 thf(zip_derived_cl11, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.64/0.96 | (equalish @ X1 @ X3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.64/0.96 thf(zip_derived_cl101, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_2) | (equalish @ e_2 @ X0)))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl11])).
% 0.64/0.96 thf(zip_derived_cl515, plain,
% 0.64/0.96 (( (equalish @ e_2 @ e_3))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_2)) & ( (product @ e_2 @ e_3 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl318, zip_derived_cl101])).
% 0.64/0.96 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.64/0.96 thf('13', plain,
% 0.64/0.96 (~ ( (product @ e_2 @ e_3 @ e_2)) | ~ ( (product @ e_2 @ e_2 @ e_2))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl515, zip_derived_cl6])).
% 0.64/0.96 thf(zip_derived_cl327, plain,
% 0.64/0.96 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl318, zip_derived_cl18])).
% 0.64/0.96 thf(zip_derived_cl63, plain,
% 0.64/0.96 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.64/0.96 thf(zip_derived_cl10, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X1 @ X3)
% 0.64/0.96 | (equalish @ X2 @ X3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_total_function2])).
% 0.64/0.96 thf(zip_derived_cl66, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ e_2 @ e_2 @ X0) | (equalish @ e_1 @ X0)))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl10])).
% 0.64/0.96 thf(zip_derived_cl393, plain,
% 0.64/0.96 (( (equalish @ e_1 @ e_2))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_1)) & ( (product @ e_2 @ e_3 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl327, zip_derived_cl66])).
% 0.64/0.96 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.64/0.96 thf('14', plain,
% 0.64/0.96 (~ ( (product @ e_2 @ e_3 @ e_2)) | ~ ( (product @ e_2 @ e_2 @ e_1))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl393, zip_derived_cl3])).
% 0.64/0.96 thf(zip_derived_cl20, plain,
% 0.64/0.96 (![X0 : $i]:
% 0.64/0.96 (~ (group_element @ X0)
% 0.64/0.96 | (product @ e_2 @ X0 @ e_1)
% 0.64/0.96 | (product @ e_2 @ X0 @ e_2)
% 0.64/0.96 | (product @ e_2 @ X0 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 0.64/0.96 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.64/0.96 inference('cnf', [status(esa)], [element_1])).
% 0.64/0.96 thf(zip_derived_cl33, plain,
% 0.64/0.96 (( (product @ e_2 @ e_1 @ e_3)
% 0.64/0.96 | (product @ e_2 @ e_1 @ e_2)
% 0.64/0.96 | (product @ e_2 @ e_1 @ e_1))),
% 0.64/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl0])).
% 0.64/0.96 thf('15', plain,
% 0.64/0.96 (( (product @ e_2 @ e_1 @ e_3)) | ( (product @ e_2 @ e_1 @ e_1)) |
% 0.64/0.96 ( (product @ e_2 @ e_1 @ e_2))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl33])).
% 0.64/0.96 thf(zip_derived_cl262, plain,
% 0.64/0.96 (( (product @ e_2 @ e_3 @ e_1)) <= (( (product @ e_2 @ e_3 @ e_1)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl35])).
% 0.64/0.96 thf(zip_derived_cl63, plain,
% 0.64/0.96 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.64/0.96 thf(zip_derived_cl11, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.64/0.96 | (equalish @ X1 @ X3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.64/0.96 thf(zip_derived_cl67, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_1) | (equalish @ e_2 @ X0)))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl11])).
% 0.64/0.96 thf(zip_derived_cl833, plain,
% 0.64/0.96 (( (equalish @ e_2 @ e_3))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_1)) & ( (product @ e_2 @ e_3 @ e_1)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl262, zip_derived_cl67])).
% 0.64/0.96 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.64/0.96 thf('16', plain,
% 0.64/0.96 (~ ( (product @ e_2 @ e_2 @ e_1)) | ~ ( (product @ e_2 @ e_3 @ e_1))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl833, zip_derived_cl6])).
% 0.64/0.96 thf(zip_derived_cl237, plain,
% 0.64/0.96 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl33])).
% 0.64/0.96 thf(zip_derived_cl67, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_1) | (equalish @ e_2 @ X0)))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl11])).
% 0.64/0.96 thf(zip_derived_cl778, plain,
% 0.64/0.96 (( (equalish @ e_2 @ e_1))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_1)) & ( (product @ e_2 @ e_1 @ e_1)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl237, zip_derived_cl67])).
% 0.64/0.96 thf(zip_derived_cl5, plain, (~ (equalish @ e_2 @ e_1)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.64/0.96 thf('17', plain,
% 0.64/0.96 (~ ( (product @ e_2 @ e_1 @ e_1)) | ~ ( (product @ e_2 @ e_2 @ e_1))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl778, zip_derived_cl5])).
% 0.64/0.96 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.64/0.96 inference('cnf', [status(esa)], [element_1])).
% 0.64/0.96 thf(zip_derived_cl20, plain,
% 0.64/0.96 (![X0 : $i]:
% 0.64/0.96 (~ (group_element @ X0)
% 0.64/0.96 | (product @ e_2 @ X0 @ e_1)
% 0.64/0.96 | (product @ e_2 @ X0 @ e_2)
% 0.64/0.96 | (product @ e_2 @ X0 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl9])).
% 0.64/0.96 thf(zip_derived_cl36, plain,
% 0.64/0.96 (( (product @ e_2 @ e_1 @ e_1)
% 0.64/0.96 | (product @ e_2 @ e_1 @ e_2)
% 0.64/0.96 | (product @ e_2 @ e_1 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl20])).
% 0.64/0.96 thf(zip_derived_cl283, plain,
% 0.64/0.96 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl36])).
% 0.64/0.96 thf(zip_derived_cl18, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X0) | (product @ X0 @ X0 @ X0))),
% 0.64/0.96 inference('eq_fact', [status(thm)], [zip_derived_cl13])).
% 0.64/0.96 thf(zip_derived_cl292, plain,
% 0.64/0.96 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl283, zip_derived_cl18])).
% 0.64/0.96 thf(zip_derived_cl66, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ e_2 @ e_2 @ X0) | (equalish @ e_1 @ X0)))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_1)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl10])).
% 0.64/0.96 thf(zip_derived_cl352, plain,
% 0.64/0.96 (( (equalish @ e_1 @ e_2))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_1)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl292, zip_derived_cl66])).
% 0.64/0.96 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.64/0.96 thf('18', plain,
% 0.64/0.96 (~ ( (product @ e_2 @ e_1 @ e_2)) | ~ ( (product @ e_2 @ e_2 @ e_1))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl352, zip_derived_cl3])).
% 0.64/0.96 thf(zip_derived_cl260, plain,
% 0.64/0.96 (( (product @ e_2 @ e_3 @ e_3)) <= (( (product @ e_2 @ e_3 @ e_3)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl35])).
% 0.64/0.96 thf(zip_derived_cl235, plain,
% 0.64/0.96 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl33])).
% 0.64/0.96 thf(zip_derived_cl11, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.64/0.96 | (equalish @ X1 @ X3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.64/0.96 thf(zip_derived_cl239, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 0.64/0.96 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl235, zip_derived_cl11])).
% 0.64/0.96 thf(zip_derived_cl744, plain,
% 0.64/0.96 (( (equalish @ e_1 @ e_3))
% 0.64/0.96 <= (( (product @ e_2 @ e_1 @ e_3)) & ( (product @ e_2 @ e_3 @ e_3)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl260, zip_derived_cl239])).
% 0.64/0.96 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_3)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.64/0.96 thf('19', plain,
% 0.64/0.96 (~ ( (product @ e_2 @ e_3 @ e_3)) | ~ ( (product @ e_2 @ e_1 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl744, zip_derived_cl4])).
% 0.64/0.96 thf('20', plain,
% 0.64/0.96 (( (product @ e_2 @ e_2 @ e_2)) | ( (product @ e_2 @ e_2 @ e_1)) |
% 0.64/0.96 ( (product @ e_2 @ e_2 @ e_3))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.64/0.96 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.64/0.96 inference('cnf', [status(esa)], [element_2])).
% 0.64/0.96 thf(zip_derived_cl21, plain,
% 0.64/0.96 (![X0 : $i]:
% 0.64/0.96 (~ (group_element @ X0)
% 0.64/0.96 | (product @ e_3 @ X0 @ e_1)
% 0.64/0.96 | (product @ e_3 @ X0 @ e_2)
% 0.64/0.96 | (product @ e_3 @ X0 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl9])).
% 0.64/0.96 thf(zip_derived_cl43, plain,
% 0.64/0.96 (( (product @ e_3 @ e_2 @ e_1)
% 0.64/0.96 | (product @ e_3 @ e_2 @ e_2)
% 0.64/0.96 | (product @ e_3 @ e_2 @ e_3))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl21])).
% 0.64/0.96 thf(zip_derived_cl422, plain,
% 0.64/0.96 (( (product @ e_3 @ e_2 @ e_2)) <= (( (product @ e_3 @ e_2 @ e_2)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl43])).
% 0.64/0.96 thf(zip_derived_cl102, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_2) | (equalish @ e_2 @ X0)))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl12])).
% 0.64/0.96 thf(zip_derived_cl523, plain,
% 0.64/0.96 (( (equalish @ e_2 @ e_3))
% 0.64/0.96 <= (( (product @ e_2 @ e_2 @ e_2)) & ( (product @ e_3 @ e_2 @ e_2)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl422, zip_derived_cl102])).
% 0.64/0.96 thf(zip_derived_cl6, plain, (~ (equalish @ e_2 @ e_3)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.64/0.96 thf('21', plain,
% 0.64/0.96 (~ ( (product @ e_3 @ e_2 @ e_2)) | ~ ( (product @ e_2 @ e_2 @ e_2))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl523, zip_derived_cl6])).
% 0.64/0.96 thf('22', plain,
% 0.64/0.96 (( (product @ e_3 @ e_2 @ e_1)) | ( (product @ e_3 @ e_2 @ e_2)) |
% 0.64/0.96 ( (product @ e_3 @ e_2 @ e_3))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl40])).
% 0.64/0.96 thf('23', plain, (( (product @ e_3 @ e_2 @ e_1))),
% 0.64/0.96 inference('sat_resolution*', [status(thm)],
% 0.64/0.96 ['1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 0.64/0.96 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 0.64/0.96 '22'])).
% 0.64/0.96 thf(zip_derived_cl892, plain, ( (product @ e_3 @ e_2 @ e_1)),
% 0.64/0.96 inference('simpl_trail', [status(thm)], [zip_derived_cl361, '23'])).
% 0.64/0.96 thf(zip_derived_cl334, plain,
% 0.64/0.96 (( (product @ e_3 @ e_1 @ e_1)) <= (( (product @ e_3 @ e_1 @ e_1)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl39])).
% 0.64/0.96 thf(zip_derived_cl11, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.64/0.96 | (equalish @ X1 @ X3))),
% 0.64/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.64/0.96 thf(zip_derived_cl881, plain,
% 0.64/0.96 ((![X0 : $i]: (~ (product @ e_3 @ X0 @ e_1) | (equalish @ e_1 @ X0)))
% 0.64/0.96 <= (( (product @ e_3 @ e_1 @ e_1)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl334, zip_derived_cl11])).
% 0.64/0.96 thf(zip_derived_cl946, plain,
% 0.64/0.96 (( (equalish @ e_1 @ e_2)) <= (( (product @ e_3 @ e_1 @ e_1)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl892, zip_derived_cl881])).
% 0.64/0.96 thf(zip_derived_cl3, plain, (~ (equalish @ e_1 @ e_2)),
% 0.64/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.64/0.96 thf('24', plain, (~ ( (product @ e_3 @ e_1 @ e_1))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl946, zip_derived_cl3])).
% 0.64/0.96 thf('25', plain,
% 0.64/0.96 (( (product @ e_3 @ e_1 @ e_2)) | ( (product @ e_3 @ e_1 @ e_1)) |
% 0.64/0.96 ( (product @ e_3 @ e_1 @ e_3))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl39])).
% 0.64/0.96 thf('26', plain, (( (product @ e_3 @ e_1 @ e_2))),
% 0.64/0.96 inference('sat_resolution*', [status(thm)], ['0', '24', '25'])).
% 0.64/0.96 thf(zip_derived_cl957, plain, (~ (product @ e_3 @ e_1 @ e_3)),
% 0.64/0.96 inference('simpl_trail', [status(thm)], [zip_derived_cl916, '26'])).
% 0.64/0.96 thf(zip_derived_cl892, plain, ( (product @ e_3 @ e_2 @ e_1)),
% 0.64/0.96 inference('simpl_trail', [status(thm)], [zip_derived_cl361, '23'])).
% 0.64/0.96 thf(zip_derived_cl122, plain,
% 0.64/0.96 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl28])).
% 0.64/0.96 thf(zip_derived_cl13, plain,
% 0.64/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.64/0.96 ( (product @ X0 @ X1 @ X2)
% 0.64/0.96 | ~ (product @ X1 @ X3 @ X2)
% 0.64/0.96 | ~ (product @ X0 @ X3 @ X1))),
% 0.64/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.64/0.96 thf(zip_derived_cl128, plain,
% 0.64/0.96 ((![X0 : $i]:
% 0.64/0.96 ( (product @ X0 @ e_1 @ e_3) | ~ (product @ X0 @ e_2 @ e_1)))
% 0.64/0.96 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl13])).
% 0.64/0.96 thf('27', plain,
% 0.64/0.96 (( (product @ e_1 @ e_1 @ e_2)) | ( (product @ e_1 @ e_1 @ e_1)) |
% 0.64/0.96 ( (product @ e_1 @ e_1 @ e_3))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl24])).
% 0.64/0.96 thf('28', plain,
% 0.64/0.96 (~ ( (product @ e_2 @ e_2 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_2))),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl519, zip_derived_cl5])).
% 0.64/0.96 thf('29', plain,
% 0.64/0.96 (( (product @ e_2 @ e_2 @ e_1)) | ( (product @ e_2 @ e_2 @ e_2)) |
% 0.64/0.96 ( (product @ e_2 @ e_2 @ e_3))),
% 0.64/0.96 inference('split', [status(esa)], [zip_derived_cl25])).
% 0.64/0.96 thf('30', plain, (( (product @ e_1 @ e_2 @ e_3))),
% 0.64/0.96 inference('sat_resolution*', [status(thm)],
% 0.64/0.96 ['4', '5', '27', '7', '8', '9', '28', '2', '29', '10'])).
% 0.64/0.96 thf(zip_derived_cl709, plain,
% 0.64/0.96 (![X0 : $i]: ( (product @ X0 @ e_1 @ e_3) | ~ (product @ X0 @ e_2 @ e_1))),
% 0.64/0.96 inference('simpl_trail', [status(thm)], [zip_derived_cl128, '30'])).
% 0.64/0.96 thf(zip_derived_cl975, plain, ( (product @ e_3 @ e_1 @ e_3)),
% 0.64/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl892, zip_derived_cl709])).
% 0.64/0.96 thf(zip_derived_cl1008, plain, ($false),
% 0.64/0.96 inference('demod', [status(thm)], [zip_derived_cl957, zip_derived_cl975])).
% 0.64/0.96
% 0.64/0.96 % SZS output end Refutation
% 0.64/0.96
% 0.64/0.96
% 0.64/0.96 % Terminating...
% 1.73/1.00 % Runner terminated.
% 1.73/1.03 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------