%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP126-2.004 : TPTP v9.2.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.0ypYA4dICN true
% Computer : n019.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 04:35:44 PM UTC 2025
% Result : Unsatisfiable 0.46s 0.87s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GRP126-2.004 : TPTP v9.2.0. Released v1.2.0.
% 0.02/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.0ypYA4dICN true
% 0.10/0.31 % Computer : n019.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Oct 1 14:13:38 EDT 2025
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % Running portfolio for 300 s
% 0.10/0.31 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.31 % Number of cores: 8
% 0.10/0.32 % Python version: Python 3.6.8
% 0.10/0.32 % Running in FO mode
% 0.45/0.58 % Total configuration time : 435
% 0.45/0.58 % Estimated wc time : 1092
% 0.45/0.58 % Estimated cpu time (7 cpus) : 156.0
% 0.45/0.68 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.45/0.68 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.45/0.68 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.45/0.68 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.45/0.68 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.45/0.68 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.45/0.68 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.46/0.87 % Solved by fo/fo1_av.sh.
% 0.46/0.87 % done 395 iterations in 0.161s
% 0.46/0.87 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.46/0.87 % SZS output start Refutation
% 0.46/0.87 thf(group_element_type, type, group_element: $i > $o).
% 0.46/0.87 thf(e_4_type, type, e_4: $i).
% 0.46/0.87 thf(greater_type, type, greater: $i > $i > $o).
% 0.46/0.87 thf(equalish_type, type, equalish: $i > $i > $o).
% 0.46/0.87 thf(e_3_type, type, e_3: $i).
% 0.46/0.87 thf(e_2_type, type, e_2: $i).
% 0.46/0.87 thf(e_1_type, type, e_1: $i).
% 0.46/0.87 thf(next_type, type, next: $i > $i > $o).
% 0.46/0.87 thf(product_type, type, product: $i > $i > $i > $o).
% 0.46/0.87 thf(element_1, axiom, (group_element @ e_1)).
% 0.46/0.87 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 0.46/0.87 inference('cnf', [status(esa)], [element_1])).
% 0.46/0.87 thf(product_total_function1, axiom,
% 0.46/0.87 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 0.46/0.87 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 0.46/0.87 ( product @ X @ Y @ e_3 ) | ( product @ X @ Y @ e_4 ))).
% 0.46/0.87 thf(zip_derived_cl26, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i]:
% 0.46/0.87 (~ (group_element @ X0)
% 0.46/0.87 | ~ (group_element @ X1)
% 0.46/0.87 | (product @ X0 @ X1 @ e_1)
% 0.46/0.87 | (product @ X0 @ X1 @ e_2)
% 0.46/0.87 | (product @ X0 @ X1 @ e_3)
% 0.46/0.87 | (product @ X0 @ X1 @ e_4))),
% 0.46/0.87 inference('cnf', [status(esa)], [product_total_function1])).
% 0.46/0.87 thf(zip_derived_cl33, plain,
% 0.46/0.87 (![X0 : $i]:
% 0.46/0.87 (~ (group_element @ X0)
% 0.46/0.87 | (product @ e_1 @ X0 @ e_1)
% 0.46/0.87 | (product @ e_1 @ X0 @ e_2)
% 0.46/0.87 | (product @ e_1 @ X0 @ e_3)
% 0.46/0.87 | (product @ e_1 @ X0 @ e_4))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl26])).
% 0.46/0.87 thf(element_3, axiom, (group_element @ e_3)).
% 0.46/0.87 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 0.46/0.87 inference('cnf', [status(esa)], [element_3])).
% 0.46/0.87 thf(zip_derived_cl64, plain,
% 0.46/0.87 (( (product @ e_1 @ e_3 @ e_4)
% 0.46/0.87 | (product @ e_1 @ e_3 @ e_3)
% 0.46/0.87 | (product @ e_1 @ e_3 @ e_2)
% 0.46/0.87 | (product @ e_1 @ e_3 @ e_1))),
% 0.46/0.87 inference('s_sup+', [status(thm)], [zip_derived_cl33, zip_derived_cl12])).
% 0.46/0.87 thf(zip_derived_cl153, plain,
% 0.46/0.87 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl64])).
% 0.46/0.87 thf(product_idempotence, axiom, (product @ X @ X @ X)).
% 0.46/0.87 thf(zip_derived_cl30, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.46/0.87 inference('cnf', [status(esa)], [product_idempotence])).
% 0.46/0.87 thf(product_right_cancellation, axiom,
% 0.46/0.87 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 0.46/0.87 ( equalish @ W @ Z ))).
% 0.46/0.87 thf(zip_derived_cl28, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.46/0.87 (~ (product @ X0 @ X1 @ X2)
% 0.46/0.87 | ~ (product @ X0 @ X3 @ X2)
% 0.46/0.87 | (equalish @ X1 @ X3))),
% 0.46/0.87 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.46/0.87 thf(zip_derived_cl44, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i]:
% 0.46/0.87 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 0.46/0.87 thf(zip_derived_cl203, plain,
% 0.46/0.87 (( (equalish @ e_1 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl153, zip_derived_cl44])).
% 0.46/0.87 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 0.46/0.87 thf(zip_derived_cl15, plain, (~ (equalish @ e_1 @ e_3)),
% 0.46/0.87 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.46/0.87 thf('0', plain, (~ ( (product @ e_1 @ e_3 @ e_1))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl203, zip_derived_cl15])).
% 0.46/0.87 thf(zip_derived_cl151, plain,
% 0.46/0.87 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl64])).
% 0.46/0.87 thf(zip_derived_cl30, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.46/0.87 inference('cnf', [status(esa)], [product_idempotence])).
% 0.46/0.87 thf(product_left_cancellation, axiom,
% 0.46/0.87 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 0.46/0.87 ( equalish @ W @ Z ))).
% 0.46/0.87 thf(zip_derived_cl29, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.46/0.87 (~ (product @ X0 @ X1 @ X2)
% 0.46/0.87 | ~ (product @ X3 @ X1 @ X2)
% 0.46/0.87 | (equalish @ X0 @ X3))),
% 0.46/0.87 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.46/0.87 thf(zip_derived_cl49, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i]:
% 0.46/0.87 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 0.46/0.87 thf(zip_derived_cl164, plain,
% 0.46/0.87 (( (equalish @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl49])).
% 0.46/0.87 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 0.46/0.87 thf(zip_derived_cl20, plain, (~ (equalish @ e_3 @ e_1)),
% 0.46/0.87 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.46/0.87 thf('1', plain, (~ ( (product @ e_1 @ e_3 @ e_3))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl164, zip_derived_cl20])).
% 0.46/0.87 thf(zip_derived_cl150, plain,
% 0.46/0.87 (( (product @ e_1 @ e_3 @ e_4)) <= (( (product @ e_1 @ e_3 @ e_4)))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl64])).
% 0.46/0.87 thf(zip_derived_cl33, plain,
% 0.46/0.87 (![X0 : $i]:
% 0.46/0.87 (~ (group_element @ X0)
% 0.46/0.87 | (product @ e_1 @ X0 @ e_1)
% 0.46/0.87 | (product @ e_1 @ X0 @ e_2)
% 0.46/0.87 | (product @ e_1 @ X0 @ e_3)
% 0.46/0.87 | (product @ e_1 @ X0 @ e_4))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl26])).
% 0.46/0.87 thf(element_2, axiom, (group_element @ e_2)).
% 0.46/0.87 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 0.46/0.87 inference('cnf', [status(esa)], [element_2])).
% 0.46/0.87 thf(zip_derived_cl63, plain,
% 0.46/0.87 (( (product @ e_1 @ e_2 @ e_4)
% 0.46/0.87 | (product @ e_1 @ e_2 @ e_3)
% 0.46/0.87 | (product @ e_1 @ e_2 @ e_2)
% 0.46/0.87 | (product @ e_1 @ e_2 @ e_1))),
% 0.46/0.87 inference('s_sup+', [status(thm)], [zip_derived_cl33, zip_derived_cl11])).
% 0.46/0.87 thf(zip_derived_cl72, plain,
% 0.46/0.87 (( (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl63])).
% 0.46/0.87 thf(zip_derived_cl28, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.46/0.87 (~ (product @ X0 @ X1 @ X2)
% 0.46/0.87 | ~ (product @ X0 @ X3 @ X2)
% 0.46/0.87 | (equalish @ X1 @ X3))),
% 0.46/0.87 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.46/0.87 thf(zip_derived_cl77, plain,
% 0.46/0.87 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_4) | (equalish @ e_2 @ X0)))
% 0.46/0.87 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl28])).
% 0.46/0.87 thf(zip_derived_cl158, plain,
% 0.46/0.87 (( (equalish @ e_2 @ e_3))
% 0.46/0.87 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_1 @ e_3 @ e_4)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl150, zip_derived_cl77])).
% 0.46/0.87 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 0.46/0.87 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 0.46/0.87 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.46/0.87 thf('2', plain,
% 0.46/0.87 (~ ( (product @ e_1 @ e_3 @ e_4)) | ~ ( (product @ e_1 @ e_2 @ e_4))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl158, zip_derived_cl18])).
% 0.46/0.87 thf(zip_derived_cl75, plain,
% 0.46/0.87 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl63])).
% 0.46/0.87 thf(zip_derived_cl44, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i]:
% 0.46/0.87 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 0.46/0.87 thf(zip_derived_cl144, plain,
% 0.46/0.87 (( (equalish @ e_1 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl75, zip_derived_cl44])).
% 0.46/0.87 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 0.46/0.87 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 0.46/0.87 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.46/0.87 thf('3', plain, (~ ( (product @ e_1 @ e_2 @ e_1))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl144, zip_derived_cl14])).
% 0.46/0.87 thf(zip_derived_cl74, plain,
% 0.46/0.87 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl63])).
% 0.46/0.87 thf(zip_derived_cl49, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i]:
% 0.46/0.87 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 0.46/0.87 thf(zip_derived_cl125, plain,
% 0.46/0.87 (( (equalish @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl49])).
% 0.46/0.87 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 0.46/0.87 thf(zip_derived_cl17, plain, (~ (equalish @ e_2 @ e_1)),
% 0.46/0.87 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.46/0.87 thf('4', plain, (~ ( (product @ e_1 @ e_2 @ e_2))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl125, zip_derived_cl17])).
% 0.46/0.87 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 0.46/0.87 inference('cnf', [status(esa)], [element_1])).
% 0.46/0.87 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 0.46/0.87 inference('cnf', [status(esa)], [element_2])).
% 0.46/0.87 thf(zip_derived_cl26, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i]:
% 0.46/0.87 (~ (group_element @ X0)
% 0.46/0.87 | ~ (group_element @ X1)
% 0.46/0.87 | (product @ X0 @ X1 @ e_1)
% 0.46/0.87 | (product @ X0 @ X1 @ e_2)
% 0.46/0.87 | (product @ X0 @ X1 @ e_3)
% 0.46/0.87 | (product @ X0 @ X1 @ e_4))),
% 0.46/0.87 inference('cnf', [status(esa)], [product_total_function1])).
% 0.46/0.87 thf(zip_derived_cl34, plain,
% 0.46/0.87 (![X0 : $i]:
% 0.46/0.87 (~ (group_element @ X0)
% 0.46/0.87 | (product @ e_2 @ X0 @ e_1)
% 0.46/0.87 | (product @ e_2 @ X0 @ e_2)
% 0.46/0.87 | (product @ e_2 @ X0 @ e_3)
% 0.46/0.87 | (product @ e_2 @ X0 @ e_4))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl26])).
% 0.46/0.87 thf(zip_derived_cl95, plain,
% 0.46/0.87 (( (product @ e_2 @ e_1 @ e_1)
% 0.46/0.87 | (product @ e_2 @ e_1 @ e_2)
% 0.46/0.87 | (product @ e_2 @ e_1 @ e_3)
% 0.46/0.87 | (product @ e_2 @ e_1 @ e_4))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl34])).
% 0.46/0.87 thf(zip_derived_cl320, plain,
% 0.46/0.87 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl95])).
% 0.46/0.87 thf(zip_derived_cl44, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i]:
% 0.46/0.87 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 0.46/0.87 thf(zip_derived_cl326, plain,
% 0.46/0.87 (( (equalish @ e_2 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl320, zip_derived_cl44])).
% 0.46/0.87 thf(zip_derived_cl17, plain, (~ (equalish @ e_2 @ e_1)),
% 0.46/0.87 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.46/0.87 thf('5', plain, (~ ( (product @ e_2 @ e_1 @ e_2))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl326, zip_derived_cl17])).
% 0.46/0.87 thf(e_2_then_e_3, axiom, (next @ e_2 @ e_3)).
% 0.46/0.87 thf(zip_derived_cl1, plain, ( (next @ e_2 @ e_3)),
% 0.46/0.87 inference('cnf', [status(esa)], [e_2_then_e_3])).
% 0.46/0.87 thf(zip_derived_cl34, plain,
% 0.46/0.87 (![X0 : $i]:
% 0.46/0.87 (~ (group_element @ X0)
% 0.46/0.87 | (product @ e_2 @ X0 @ e_1)
% 0.46/0.87 | (product @ e_2 @ X0 @ e_2)
% 0.46/0.87 | (product @ e_2 @ X0 @ e_3)
% 0.46/0.87 | (product @ e_2 @ X0 @ e_4))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl26])).
% 0.46/0.87 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 0.46/0.87 inference('cnf', [status(esa)], [element_1])).
% 0.46/0.87 thf(zip_derived_cl91, plain,
% 0.46/0.87 (( (product @ e_2 @ e_1 @ e_4)
% 0.46/0.87 | (product @ e_2 @ e_1 @ e_3)
% 0.46/0.87 | (product @ e_2 @ e_1 @ e_2)
% 0.46/0.87 | (product @ e_2 @ e_1 @ e_1))),
% 0.46/0.87 inference('s_sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl10])).
% 0.46/0.87 thf(zip_derived_cl252, plain,
% 0.46/0.87 (( (product @ e_2 @ e_1 @ e_4)) <= (( (product @ e_2 @ e_1 @ e_4)))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl91])).
% 0.46/0.87 thf(no_redundancy, axiom,
% 0.46/0.87 (( ~( product @ X @ e_1 @ Y ) ) | ( ~( next @ X @ X1 ) ) |
% 0.46/0.87 ( ~( greater @ Y @ X1 ) ))).
% 0.46/0.87 thf(zip_derived_cl9, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.46/0.87 (~ (product @ X0 @ e_1 @ X1)
% 0.46/0.87 | ~ (next @ X0 @ X2)
% 0.46/0.87 | ~ (greater @ X1 @ X2))),
% 0.46/0.87 inference('cnf', [status(esa)], [no_redundancy])).
% 0.46/0.87 thf(zip_derived_cl260, plain,
% 0.46/0.87 ((![X0 : $i]: (~ (next @ e_2 @ X0) | ~ (greater @ e_4 @ X0)))
% 0.46/0.87 <= (( (product @ e_2 @ e_1 @ e_4)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl252, zip_derived_cl9])).
% 0.46/0.87 thf(zip_derived_cl264, plain,
% 0.46/0.87 ((~ (greater @ e_4 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_4)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl260])).
% 0.46/0.87 thf(e_4_greater_e_3, axiom, (greater @ e_4 @ e_3)).
% 0.46/0.87 thf(zip_derived_cl8, plain, ( (greater @ e_4 @ e_3)),
% 0.46/0.87 inference('cnf', [status(esa)], [e_4_greater_e_3])).
% 0.46/0.87 thf('6', plain, (~ ( (product @ e_2 @ e_1 @ e_4))),
% 0.46/0.87 inference('demod', [status(thm)], [zip_derived_cl264, zip_derived_cl8])).
% 0.46/0.87 thf(zip_derived_cl255, plain,
% 0.46/0.87 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl91])).
% 0.46/0.87 thf(zip_derived_cl49, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i]:
% 0.46/0.87 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 0.46/0.87 thf(zip_derived_cl667, plain,
% 0.46/0.87 (( (equalish @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl255, zip_derived_cl49])).
% 0.46/0.87 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 0.46/0.87 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.46/0.87 thf('7', plain, (~ ( (product @ e_2 @ e_1 @ e_1))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl667, zip_derived_cl14])).
% 0.46/0.87 thf('8', plain,
% 0.46/0.87 (( (product @ e_2 @ e_1 @ e_3)) | ( (product @ e_2 @ e_1 @ e_1)) |
% 0.46/0.87 ( (product @ e_2 @ e_1 @ e_4)) | ( (product @ e_2 @ e_1 @ e_2))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl91])).
% 0.46/0.87 thf(zip_derived_cl253, plain,
% 0.46/0.87 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl91])).
% 0.46/0.87 thf(zip_derived_cl73, plain,
% 0.46/0.87 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl63])).
% 0.46/0.87 thf(qg4, conjecture,
% 0.46/0.87 (~( ( product @ Z1 @ Z2 @ Y ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 0.46/0.87 ( ~( product @ X @ Y @ Z1 ) ) ))).
% 0.46/0.87 thf(zf_stmt_0, negated_conjecture,
% 0.46/0.87 (( product @ Z1 @ Z2 @ Y ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 0.46/0.87 ( ~( product @ X @ Y @ Z1 ) )),
% 0.46/0.87 inference('cnf.neg', [status(esa)], [qg4])).
% 0.46/0.87 thf(zip_derived_cl31, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.46/0.87 ( (product @ X0 @ X1 @ X2)
% 0.46/0.87 | ~ (product @ X2 @ X3 @ X1)
% 0.46/0.87 | ~ (product @ X3 @ X2 @ X0))),
% 0.46/0.87 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.46/0.87 thf(zip_derived_cl87, plain,
% 0.46/0.87 ((![X0 : $i]:
% 0.46/0.87 ( (product @ X0 @ e_3 @ e_1) | ~ (product @ e_2 @ e_1 @ X0)))
% 0.46/0.87 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl73, zip_derived_cl31])).
% 0.46/0.87 thf(zip_derived_cl273, plain,
% 0.46/0.87 (( (product @ e_3 @ e_3 @ e_1))
% 0.46/0.87 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl253, zip_derived_cl87])).
% 0.46/0.87 thf(zip_derived_cl30, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.46/0.87 inference('cnf', [status(esa)], [product_idempotence])).
% 0.46/0.87 thf(product_total_function2, axiom,
% 0.46/0.87 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 0.46/0.87 ( equalish @ W @ Z ))).
% 0.46/0.87 thf(zip_derived_cl27, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.46/0.87 (~ (product @ X0 @ X1 @ X2)
% 0.46/0.87 | ~ (product @ X0 @ X1 @ X3)
% 0.46/0.87 | (equalish @ X2 @ X3))),
% 0.46/0.87 inference('cnf', [status(esa)], [product_total_function2])).
% 0.46/0.87 thf(zip_derived_cl40, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i]:
% 0.46/0.87 (~ (product @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl27])).
% 0.46/0.87 thf(zip_derived_cl282, plain,
% 0.46/0.87 (( (equalish @ e_3 @ e_1))
% 0.46/0.87 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl273, zip_derived_cl40])).
% 0.46/0.87 thf(zip_derived_cl20, plain, (~ (equalish @ e_3 @ e_1)),
% 0.46/0.87 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.46/0.87 thf('9', plain,
% 0.46/0.87 (~ ( (product @ e_1 @ e_2 @ e_3)) | ~ ( (product @ e_2 @ e_1 @ e_3))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl282, zip_derived_cl20])).
% 0.46/0.87 thf('10', plain,
% 0.46/0.87 (( (product @ e_1 @ e_2 @ e_4)) | ( (product @ e_1 @ e_2 @ e_3)) |
% 0.46/0.87 ( (product @ e_1 @ e_2 @ e_2)) | ( (product @ e_1 @ e_2 @ e_1))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl63])).
% 0.46/0.87 thf(zip_derived_cl72, plain,
% 0.46/0.87 (( (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl63])).
% 0.46/0.87 thf(zip_derived_cl253, plain,
% 0.46/0.87 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl91])).
% 0.46/0.87 thf(zip_derived_cl31, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.46/0.87 ( (product @ X0 @ X1 @ X2)
% 0.46/0.87 | ~ (product @ X2 @ X3 @ X1)
% 0.46/0.87 | ~ (product @ X3 @ X2 @ X0))),
% 0.46/0.87 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.46/0.87 thf(zip_derived_cl270, plain,
% 0.46/0.87 ((![X0 : $i]:
% 0.46/0.87 ( (product @ X0 @ e_3 @ e_2) | ~ (product @ e_1 @ e_2 @ X0)))
% 0.46/0.87 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl253, zip_derived_cl31])).
% 0.46/0.87 thf(zip_derived_cl373, plain,
% 0.46/0.87 (( (product @ e_4 @ e_3 @ e_2))
% 0.46/0.87 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl270])).
% 0.46/0.87 thf(zip_derived_cl152, plain,
% 0.46/0.87 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl64])).
% 0.46/0.87 thf(zip_derived_cl29, plain,
% 0.46/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.46/0.87 (~ (product @ X0 @ X1 @ X2)
% 0.46/0.87 | ~ (product @ X3 @ X1 @ X2)
% 0.46/0.87 | (equalish @ X0 @ X3))),
% 0.46/0.87 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.46/0.87 thf(zip_derived_cl179, plain,
% 0.46/0.87 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_2) | (equalish @ e_1 @ X0)))
% 0.46/0.87 <= (( (product @ e_1 @ e_3 @ e_2)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl152, zip_derived_cl29])).
% 0.46/0.87 thf(zip_derived_cl394, plain,
% 0.46/0.87 (( (equalish @ e_1 @ e_4))
% 0.46/0.87 <= (( (product @ e_1 @ e_2 @ e_4)) &
% 0.46/0.87 ( (product @ e_1 @ e_3 @ e_2)) &
% 0.46/0.87 ( (product @ e_2 @ e_1 @ e_3)))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl373, zip_derived_cl179])).
% 0.46/0.87 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 0.46/0.87 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 0.46/0.87 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 0.46/0.87 thf('11', plain,
% 0.46/0.87 (~ ( (product @ e_1 @ e_3 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_4)) |
% 0.46/0.87 ~ ( (product @ e_2 @ e_1 @ e_3))),
% 0.46/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl394, zip_derived_cl16])).
% 0.46/0.87 thf('12', plain,
% 0.46/0.87 (( (product @ e_1 @ e_3 @ e_2)) | ( (product @ e_1 @ e_3 @ e_4)) |
% 0.46/0.87 ( (product @ e_1 @ e_3 @ e_3)) | ( (product @ e_1 @ e_3 @ e_1))),
% 0.46/0.87 inference('split', [status(esa)], [zip_derived_cl64])).
% 0.46/0.87 thf(zip_derived_cl676, plain, ($false),
% 0.46/0.87 inference('sat_resolution*', [status(thm)],
% 0.46/0.87 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 0.46/0.87 '12'])).
% 0.46/0.87
% 0.46/0.87 % SZS output end Refutation
% 0.46/0.87
% 0.46/0.87
% 0.46/0.87 % Terminating...
% 0.52/0.99 % Runner terminated.
% 0.52/1.00 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------