%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP127-3.004 : 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.xIGsYpKX9c true
% Computer : n004.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 0.57s 1.03s
% Output : Refutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP127-3.004 : TPTP v9.2.0. Released v1.2.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.xIGsYpKX9c true
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 1 14:19:38 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running portfolio for 300 s
% 0.14/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34 % Number of cores: 8
% 0.14/0.34 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.54/0.64 % Total configuration time : 435
% 0.54/0.64 % Estimated wc time : 1092
% 0.54/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.77 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.57/1.03 % Solved by fo/fo1_av.sh.
% 0.57/1.03 % done 858 iterations in 0.252s
% 0.57/1.03 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.57/1.03 % SZS output start Refutation
% 0.57/1.03 thf(e_4_type, type, e_4: $i).
% 0.57/1.03 thf(e_3_type, type, e_3: $i).
% 0.57/1.03 thf(e_2_type, type, e_2: $i).
% 0.57/1.03 thf(e_1_type, type, e_1: $i).
% 0.57/1.03 thf(product_type, type, product: $i > $i > $i > $o).
% 0.57/1.03 thf(group_element_type, type, group_element: $i > $o).
% 0.57/1.03 thf(equalish_type, type, equalish: $i > $i > $o).
% 0.57/1.03 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 0.57/1.03 thf(zip_derived_cl25, plain, (~ (equalish @ e_1 @ e_2)),
% 0.57/1.03 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.57/1.03 thf(element_2, axiom, (group_element @ e_2)).
% 0.57/1.03 thf(zip_derived_cl22, plain, ( (group_element @ e_2)),
% 0.57/1.03 inference('cnf', [status(esa)], [element_2])).
% 0.57/1.03 thf(product_total_function1, axiom,
% 0.57/1.03 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 0.57/1.03 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 0.57/1.03 ( product @ X @ Y @ e_3 ) | ( product @ X @ Y @ e_4 ))).
% 0.57/1.03 thf(zip_derived_cl37, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i]:
% 0.57/1.03 (~ (group_element @ X0)
% 0.57/1.03 | ~ (group_element @ X1)
% 0.57/1.03 | (product @ X0 @ X1 @ e_1)
% 0.57/1.03 | (product @ X0 @ X1 @ e_2)
% 0.57/1.03 | (product @ X0 @ X1 @ e_3)
% 0.57/1.03 | (product @ X0 @ X1 @ e_4))),
% 0.57/1.03 inference('cnf', [status(esa)], [product_total_function1])).
% 0.57/1.03 thf(zip_derived_cl96, plain,
% 0.57/1.03 (![X0 : $i]:
% 0.57/1.03 (~ (group_element @ X0)
% 0.57/1.03 | (product @ e_2 @ X0 @ e_1)
% 0.57/1.03 | (product @ e_2 @ X0 @ e_2)
% 0.57/1.03 | (product @ e_2 @ X0 @ e_3)
% 0.57/1.03 | (product @ e_2 @ X0 @ e_4))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl37])).
% 0.57/1.03 thf(element_1, axiom, (group_element @ e_1)).
% 0.57/1.03 thf(zip_derived_cl21, plain, ( (group_element @ e_1)),
% 0.57/1.03 inference('cnf', [status(esa)], [element_1])).
% 0.57/1.03 thf(zip_derived_cl246, plain,
% 0.57/1.03 (( (product @ e_2 @ e_1 @ e_4)
% 0.57/1.03 | (product @ e_2 @ e_1 @ e_3)
% 0.57/1.03 | (product @ e_2 @ e_1 @ e_2)
% 0.57/1.03 | (product @ e_2 @ e_1 @ e_1))),
% 0.57/1.03 inference('s_sup+', [status(thm)], [zip_derived_cl96, zip_derived_cl21])).
% 0.57/1.03 thf(zip_derived_cl912, plain,
% 0.57/1.03 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl246])).
% 0.57/1.03 thf(element_3, axiom, (group_element @ e_3)).
% 0.57/1.03 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 0.57/1.03 inference('cnf', [status(esa)], [element_3])).
% 0.57/1.03 thf(zip_derived_cl37, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i]:
% 0.57/1.03 (~ (group_element @ X0)
% 0.57/1.03 | ~ (group_element @ X1)
% 0.57/1.03 | (product @ X0 @ X1 @ e_1)
% 0.57/1.03 | (product @ X0 @ X1 @ e_2)
% 0.57/1.03 | (product @ X0 @ X1 @ e_3)
% 0.57/1.03 | (product @ X0 @ X1 @ e_4))),
% 0.57/1.03 inference('cnf', [status(esa)], [product_total_function1])).
% 0.57/1.03 thf(zip_derived_cl97, plain,
% 0.57/1.03 (![X0 : $i]:
% 0.57/1.03 (~ (group_element @ X0)
% 0.57/1.03 | (product @ e_3 @ X0 @ e_1)
% 0.57/1.03 | (product @ e_3 @ X0 @ e_2)
% 0.57/1.03 | (product @ e_3 @ X0 @ e_3)
% 0.57/1.03 | (product @ e_3 @ X0 @ e_4))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl37])).
% 0.57/1.03 thf(element_4, axiom, (group_element @ e_4)).
% 0.57/1.03 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 0.57/1.03 inference('cnf', [status(esa)], [element_4])).
% 0.57/1.03 thf(zip_derived_cl269, plain,
% 0.57/1.03 (( (product @ e_3 @ e_4 @ e_4)
% 0.57/1.03 | (product @ e_3 @ e_4 @ e_3)
% 0.57/1.03 | (product @ e_3 @ e_4 @ e_2)
% 0.57/1.03 | (product @ e_3 @ e_4 @ e_1))),
% 0.57/1.03 inference('s_sup+', [status(thm)], [zip_derived_cl97, zip_derived_cl24])).
% 0.57/1.03 thf(zip_derived_cl1095, plain,
% 0.57/1.03 (( (product @ e_3 @ e_4 @ e_4)) <= (( (product @ e_3 @ e_4 @ e_4)))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl269])).
% 0.57/1.03 thf(product_idempotence, axiom, (product @ X @ X @ X)).
% 0.57/1.03 thf(zip_derived_cl41, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.57/1.03 inference('cnf', [status(esa)], [product_idempotence])).
% 0.57/1.03 thf(product_left_cancellation, axiom,
% 0.57/1.03 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 0.57/1.03 ( equalish @ W @ Z ))).
% 0.57/1.03 thf(zip_derived_cl40, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.03 (~ (product @ X0 @ X1 @ X2)
% 0.57/1.03 | ~ (product @ X3 @ X1 @ X2)
% 0.57/1.03 | (equalish @ X0 @ X3))),
% 0.57/1.03 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.57/1.03 thf(zip_derived_cl70, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i]:
% 0.57/1.03 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.57/1.03 thf(zip_derived_cl1103, plain,
% 0.57/1.03 (( (equalish @ e_4 @ e_3)) <= (( (product @ e_3 @ e_4 @ e_4)))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl1095, zip_derived_cl70])).
% 0.57/1.03 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 0.57/1.03 thf(zip_derived_cl36, plain, (~ (equalish @ e_4 @ e_3)),
% 0.57/1.03 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 0.57/1.03 thf('0', plain, (~ ( (product @ e_3 @ e_4 @ e_4))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl1103, zip_derived_cl36])).
% 0.57/1.03 thf(zip_derived_cl21, plain, ( (group_element @ e_1)),
% 0.57/1.03 inference('cnf', [status(esa)], [element_1])).
% 0.57/1.03 thf(zip_derived_cl37, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i]:
% 0.57/1.03 (~ (group_element @ X0)
% 0.57/1.03 | ~ (group_element @ X1)
% 0.57/1.03 | (product @ X0 @ X1 @ e_1)
% 0.57/1.03 | (product @ X0 @ X1 @ e_2)
% 0.57/1.03 | (product @ X0 @ X1 @ e_3)
% 0.57/1.03 | (product @ X0 @ X1 @ e_4))),
% 0.57/1.03 inference('cnf', [status(esa)], [product_total_function1])).
% 0.57/1.03 thf(zip_derived_cl95, plain,
% 0.57/1.03 (![X0 : $i]:
% 0.57/1.03 (~ (group_element @ X0)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_1)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_2)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_3)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_4))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.57/1.03 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 0.57/1.03 inference('cnf', [status(esa)], [element_4])).
% 0.57/1.03 thf(zip_derived_cl215, plain,
% 0.57/1.03 (( (product @ e_1 @ e_4 @ e_4)
% 0.57/1.03 | (product @ e_1 @ e_4 @ e_3)
% 0.57/1.03 | (product @ e_1 @ e_4 @ e_2)
% 0.57/1.03 | (product @ e_1 @ e_4 @ e_1))),
% 0.57/1.03 inference('s_sup+', [status(thm)], [zip_derived_cl95, zip_derived_cl24])).
% 0.57/1.03 thf(zip_derived_cl789, plain,
% 0.57/1.03 (( (product @ e_1 @ e_4 @ e_2)) <= (( (product @ e_1 @ e_4 @ e_2)))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl215])).
% 0.57/1.03 thf(zip_derived_cl96, plain,
% 0.57/1.03 (![X0 : $i]:
% 0.57/1.03 (~ (group_element @ X0)
% 0.57/1.03 | (product @ e_2 @ X0 @ e_1)
% 0.57/1.03 | (product @ e_2 @ X0 @ e_2)
% 0.57/1.03 | (product @ e_2 @ X0 @ e_3)
% 0.57/1.03 | (product @ e_2 @ X0 @ e_4))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl37])).
% 0.57/1.03 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 0.57/1.03 inference('cnf', [status(esa)], [element_4])).
% 0.57/1.03 thf(zip_derived_cl249, plain,
% 0.57/1.03 (( (product @ e_2 @ e_4 @ e_4)
% 0.57/1.03 | (product @ e_2 @ e_4 @ e_3)
% 0.57/1.03 | (product @ e_2 @ e_4 @ e_2)
% 0.57/1.03 | (product @ e_2 @ e_4 @ e_1))),
% 0.57/1.03 inference('s_sup+', [status(thm)], [zip_derived_cl96, zip_derived_cl24])).
% 0.57/1.03 thf('1', plain,
% 0.57/1.03 (( (product @ e_2 @ e_4 @ e_1)) | ( (product @ e_2 @ e_4 @ e_3)) |
% 0.57/1.03 ( (product @ e_2 @ e_4 @ e_4)) | ( (product @ e_2 @ e_4 @ e_2))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl249])).
% 0.57/1.03 thf(zip_derived_cl961, plain,
% 0.57/1.03 (( (product @ e_2 @ e_4 @ e_4)) <= (( (product @ e_2 @ e_4 @ e_4)))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl249])).
% 0.57/1.03 thf(zip_derived_cl70, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i]:
% 0.57/1.03 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.57/1.03 thf(zip_derived_cl969, plain,
% 0.57/1.03 (( (equalish @ e_4 @ e_2)) <= (( (product @ e_2 @ e_4 @ e_4)))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl961, zip_derived_cl70])).
% 0.57/1.03 thf(e_4_is_not_e_2, axiom, (~( equalish @ e_4 @ e_2 ))).
% 0.57/1.03 thf(zip_derived_cl35, plain, (~ (equalish @ e_4 @ e_2)),
% 0.57/1.03 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 0.57/1.03 thf('2', plain, (~ ( (product @ e_2 @ e_4 @ e_4))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl969, zip_derived_cl35])).
% 0.57/1.03 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 0.57/1.03 inference('cnf', [status(esa)], [element_4])).
% 0.57/1.03 thf(zip_derived_cl95, plain,
% 0.57/1.03 (![X0 : $i]:
% 0.57/1.03 (~ (group_element @ X0)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_1)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_2)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_3)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_4))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.57/1.03 thf(zip_derived_cl219, plain,
% 0.57/1.03 (( (product @ e_1 @ e_4 @ e_1)
% 0.57/1.03 | (product @ e_1 @ e_4 @ e_2)
% 0.57/1.03 | (product @ e_1 @ e_4 @ e_3)
% 0.57/1.03 | (product @ e_1 @ e_4 @ e_4))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl95])).
% 0.57/1.03 thf(zip_derived_cl865, plain,
% 0.57/1.03 (( (product @ e_1 @ e_4 @ e_3)) <= (( (product @ e_1 @ e_4 @ e_3)))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl219])).
% 0.57/1.03 thf(qg3, conjecture,
% 0.57/1.03 (~( ( product @ Z2 @ Y @ X ) | ( ~( product @ Z1 @ Y @ Z2 ) ) |
% 0.57/1.03 ( ~( product @ Y @ X @ Z1 ) ) ))).
% 0.57/1.03 thf(zf_stmt_0, negated_conjecture,
% 0.57/1.03 (( product @ Z2 @ Y @ X ) | ( ~( product @ Z1 @ Y @ Z2 ) ) |
% 0.57/1.03 ( ~( product @ Y @ X @ Z1 ) )),
% 0.57/1.03 inference('cnf.neg', [status(esa)], [qg3])).
% 0.57/1.03 thf(zip_derived_cl42, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.03 ( (product @ X0 @ X1 @ X2)
% 0.57/1.03 | ~ (product @ X3 @ X1 @ X0)
% 0.57/1.03 | ~ (product @ X1 @ X2 @ X3))),
% 0.57/1.03 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/1.03 thf(zip_derived_cl871, plain,
% 0.57/1.03 ((![X0 : $i]:
% 0.57/1.03 ( (product @ e_3 @ e_4 @ X0) | ~ (product @ e_4 @ X0 @ e_1)))
% 0.57/1.03 <= (( (product @ e_1 @ e_4 @ e_3)))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl865, zip_derived_cl42])).
% 0.57/1.03 thf(zip_derived_cl95, plain,
% 0.57/1.03 (![X0 : $i]:
% 0.57/1.03 (~ (group_element @ X0)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_1)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_2)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_3)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_4))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.57/1.03 thf(zip_derived_cl22, plain, ( (group_element @ e_2)),
% 0.57/1.03 inference('cnf', [status(esa)], [element_2])).
% 0.57/1.03 thf(zip_derived_cl213, plain,
% 0.57/1.03 (( (product @ e_1 @ e_2 @ e_4)
% 0.57/1.03 | (product @ e_1 @ e_2 @ e_3)
% 0.57/1.03 | (product @ e_1 @ e_2 @ e_2)
% 0.57/1.03 | (product @ e_1 @ e_2 @ e_1))),
% 0.57/1.03 inference('s_sup+', [status(thm)], [zip_derived_cl95, zip_derived_cl22])).
% 0.57/1.03 thf(zip_derived_cl740, plain,
% 0.57/1.03 (( (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl213])).
% 0.57/1.03 thf(zip_derived_cl42, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.03 ( (product @ X0 @ X1 @ X2)
% 0.57/1.03 | ~ (product @ X3 @ X1 @ X0)
% 0.57/1.03 | ~ (product @ X1 @ X2 @ X3))),
% 0.57/1.03 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/1.03 thf(zip_derived_cl747, plain,
% 0.57/1.03 ((![X0 : $i]:
% 0.57/1.03 ( (product @ e_4 @ e_2 @ X0) | ~ (product @ e_2 @ X0 @ e_1)))
% 0.57/1.03 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl740, zip_derived_cl42])).
% 0.57/1.03 thf(zip_derived_cl926, plain,
% 0.57/1.03 ((( (product @ e_3 @ e_4 @ e_2) | ~ (product @ e_2 @ e_1 @ e_1)))
% 0.57/1.03 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_1 @ e_4 @ e_3)))),
% 0.57/1.03 inference('s_sup+', [status(thm)], [zip_derived_cl871, zip_derived_cl747])).
% 0.57/1.03 thf(zip_derived_cl930, plain,
% 0.57/1.03 (( (product @ e_3 @ e_4 @ e_2)) <= (( (product @ e_3 @ e_4 @ e_2)))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl926])).
% 0.57/1.03 thf(zip_derived_cl42, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.03 ( (product @ X0 @ X1 @ X2)
% 0.57/1.03 | ~ (product @ X3 @ X1 @ X0)
% 0.57/1.03 | ~ (product @ X1 @ X2 @ X3))),
% 0.57/1.03 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/1.03 thf(zip_derived_cl935, plain,
% 0.57/1.03 ((![X0 : $i]:
% 0.57/1.03 ( (product @ e_2 @ e_4 @ X0) | ~ (product @ e_4 @ X0 @ e_3)))
% 0.57/1.03 <= (( (product @ e_3 @ e_4 @ e_2)))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl930, zip_derived_cl42])).
% 0.57/1.03 thf(zip_derived_cl747, plain,
% 0.57/1.03 ((![X0 : $i]:
% 0.57/1.03 ( (product @ e_4 @ e_2 @ X0) | ~ (product @ e_2 @ X0 @ e_1)))
% 0.57/1.03 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl740, zip_derived_cl42])).
% 0.57/1.03 thf(zip_derived_cl1161, plain,
% 0.57/1.03 ((( (product @ e_2 @ e_4 @ e_2) | ~ (product @ e_2 @ e_3 @ e_1)))
% 0.57/1.03 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_3 @ e_4 @ e_2)))),
% 0.57/1.03 inference('s_sup+', [status(thm)], [zip_derived_cl935, zip_derived_cl747])).
% 0.57/1.03 thf(zip_derived_cl1232, plain,
% 0.57/1.03 (( (product @ e_2 @ e_4 @ e_2)) <= (( (product @ e_2 @ e_4 @ e_2)))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl1161])).
% 0.57/1.03 thf(zip_derived_cl41, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.57/1.03 inference('cnf', [status(esa)], [product_idempotence])).
% 0.57/1.03 thf(product_right_cancellation, axiom,
% 0.57/1.03 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 0.57/1.03 ( equalish @ W @ Z ))).
% 0.57/1.03 thf(zip_derived_cl39, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.03 (~ (product @ X0 @ X1 @ X2)
% 0.57/1.03 | ~ (product @ X0 @ X3 @ X2)
% 0.57/1.03 | (equalish @ X1 @ X3))),
% 0.57/1.03 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.57/1.03 thf(zip_derived_cl66, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i]:
% 0.57/1.03 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.57/1.03 thf(zip_derived_cl1238, plain,
% 0.57/1.03 (( (equalish @ e_2 @ e_4)) <= (( (product @ e_2 @ e_4 @ e_2)))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl1232, zip_derived_cl66])).
% 0.57/1.03 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 0.57/1.03 thf(zip_derived_cl30, plain, (~ (equalish @ e_2 @ e_4)),
% 0.57/1.03 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 0.57/1.03 thf('3', plain, (~ ( (product @ e_2 @ e_4 @ e_2))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl1238, zip_derived_cl30])).
% 0.57/1.03 thf('4', plain,
% 0.57/1.03 (( (product @ e_1 @ e_2 @ e_3)) | ( (product @ e_1 @ e_2 @ e_4)) |
% 0.57/1.03 ( (product @ e_1 @ e_2 @ e_2)) | ( (product @ e_1 @ e_2 @ e_1))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl213])).
% 0.57/1.03 thf(zip_derived_cl742, plain,
% 0.57/1.03 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl213])).
% 0.57/1.03 thf(zip_derived_cl70, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i]:
% 0.57/1.03 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.57/1.03 thf(zip_derived_cl1069, plain,
% 0.57/1.03 (( (equalish @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl742, zip_derived_cl70])).
% 0.57/1.03 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 0.57/1.03 thf(zip_derived_cl28, plain, (~ (equalish @ e_2 @ e_1)),
% 0.57/1.03 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.57/1.03 thf('5', plain, (~ ( (product @ e_1 @ e_2 @ e_2))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl1069, zip_derived_cl28])).
% 0.57/1.03 thf(zip_derived_cl743, plain,
% 0.57/1.03 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl213])).
% 0.57/1.03 thf(zip_derived_cl66, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i]:
% 0.57/1.03 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.57/1.03 thf(zip_derived_cl1113, plain,
% 0.57/1.03 (( (equalish @ e_1 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl743, zip_derived_cl66])).
% 0.57/1.03 thf(zip_derived_cl25, plain, (~ (equalish @ e_1 @ e_2)),
% 0.57/1.03 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.57/1.03 thf('6', plain, (~ ( (product @ e_1 @ e_2 @ e_1))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl1113, zip_derived_cl25])).
% 0.57/1.03 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 0.57/1.03 inference('cnf', [status(esa)], [element_4])).
% 0.57/1.03 thf(zip_derived_cl96, plain,
% 0.57/1.03 (![X0 : $i]:
% 0.57/1.03 (~ (group_element @ X0)
% 0.57/1.03 | (product @ e_2 @ X0 @ e_1)
% 0.57/1.03 | (product @ e_2 @ X0 @ e_2)
% 0.57/1.03 | (product @ e_2 @ X0 @ e_3)
% 0.57/1.03 | (product @ e_2 @ X0 @ e_4))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl37])).
% 0.57/1.03 thf(zip_derived_cl253, plain,
% 0.57/1.03 (( (product @ e_2 @ e_4 @ e_1)
% 0.57/1.03 | (product @ e_2 @ e_4 @ e_2)
% 0.57/1.03 | (product @ e_2 @ e_4 @ e_3)
% 0.57/1.03 | (product @ e_2 @ e_4 @ e_4))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl96])).
% 0.57/1.03 thf(zip_derived_cl1033, plain,
% 0.57/1.03 (( (product @ e_2 @ e_4 @ e_3)) <= (( (product @ e_2 @ e_4 @ e_3)))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl253])).
% 0.57/1.03 thf(zip_derived_cl865, plain,
% 0.57/1.03 (( (product @ e_1 @ e_4 @ e_3)) <= (( (product @ e_1 @ e_4 @ e_3)))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl219])).
% 0.57/1.03 thf(zip_derived_cl40, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.03 (~ (product @ X0 @ X1 @ X2)
% 0.57/1.03 | ~ (product @ X3 @ X1 @ X2)
% 0.57/1.03 | (equalish @ X0 @ X3))),
% 0.57/1.03 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.57/1.03 thf(zip_derived_cl870, plain,
% 0.57/1.03 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_3) | (equalish @ e_1 @ X0)))
% 0.57/1.03 <= (( (product @ e_1 @ e_4 @ e_3)))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl865, zip_derived_cl40])).
% 0.57/1.03 thf(zip_derived_cl1174, plain,
% 0.57/1.03 (( (equalish @ e_1 @ e_2))
% 0.57/1.03 <= (( (product @ e_1 @ e_4 @ e_3)) & ( (product @ e_2 @ e_4 @ e_3)))),
% 0.57/1.03 inference('s_sup-', [status(thm)],
% 0.57/1.03 [zip_derived_cl1033, zip_derived_cl870])).
% 0.57/1.03 thf(zip_derived_cl25, plain, (~ (equalish @ e_1 @ e_2)),
% 0.57/1.03 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.57/1.03 thf('7', plain,
% 0.57/1.03 (~ ( (product @ e_2 @ e_4 @ e_3)) | ~ ( (product @ e_1 @ e_4 @ e_3))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl1174, zip_derived_cl25])).
% 0.57/1.03 thf(zip_derived_cl865, plain,
% 0.57/1.03 (( (product @ e_1 @ e_4 @ e_3)) <= (( (product @ e_1 @ e_4 @ e_3)))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl219])).
% 0.57/1.03 thf(zip_derived_cl22, plain, ( (group_element @ e_2)),
% 0.57/1.03 inference('cnf', [status(esa)], [element_2])).
% 0.57/1.03 thf(zip_derived_cl95, plain,
% 0.57/1.03 (![X0 : $i]:
% 0.57/1.03 (~ (group_element @ X0)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_1)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_2)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_3)
% 0.57/1.03 | (product @ e_1 @ X0 @ e_4))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.57/1.03 thf(zip_derived_cl217, plain,
% 0.57/1.03 (( (product @ e_1 @ e_2 @ e_1)
% 0.57/1.03 | (product @ e_1 @ e_2 @ e_2)
% 0.57/1.03 | (product @ e_1 @ e_2 @ e_3)
% 0.57/1.03 | (product @ e_1 @ e_2 @ e_4))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl95])).
% 0.57/1.03 thf(zip_derived_cl812, plain,
% 0.57/1.03 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl217])).
% 0.57/1.03 thf(zip_derived_cl39, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.03 (~ (product @ X0 @ X1 @ X2)
% 0.57/1.03 | ~ (product @ X0 @ X3 @ X2)
% 0.57/1.03 | (equalish @ X1 @ X3))),
% 0.57/1.03 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.57/1.03 thf(zip_derived_cl816, plain,
% 0.57/1.03 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_2 @ X0)))
% 0.57/1.03 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl812, zip_derived_cl39])).
% 0.57/1.03 thf(zip_derived_cl996, plain,
% 0.57/1.03 (( (equalish @ e_2 @ e_4))
% 0.57/1.03 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_1 @ e_4 @ e_3)))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl865, zip_derived_cl816])).
% 0.57/1.03 thf(zip_derived_cl30, plain, (~ (equalish @ e_2 @ e_4)),
% 0.57/1.03 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 0.57/1.03 thf('8', plain,
% 0.57/1.03 (~ ( (product @ e_1 @ e_4 @ e_3)) | ~ ( (product @ e_1 @ e_2 @ e_3))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl996, zip_derived_cl30])).
% 0.57/1.03 thf(zip_derived_cl935, plain,
% 0.57/1.03 ((![X0 : $i]:
% 0.57/1.03 ( (product @ e_2 @ e_4 @ X0) | ~ (product @ e_4 @ X0 @ e_3)))
% 0.57/1.03 <= (( (product @ e_3 @ e_4 @ e_2)))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl930, zip_derived_cl42])).
% 0.57/1.03 thf(zip_derived_cl909, plain,
% 0.57/1.03 (( (product @ e_2 @ e_1 @ e_4)) <= (( (product @ e_2 @ e_1 @ e_4)))),
% 0.57/1.03 inference('split', [status(esa)], [zip_derived_cl246])).
% 0.57/1.03 thf(zip_derived_cl42, plain,
% 0.57/1.03 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.03 ( (product @ X0 @ X1 @ X2)
% 0.57/1.03 | ~ (product @ X3 @ X1 @ X0)
% 0.57/1.03 | ~ (product @ X1 @ X2 @ X3))),
% 0.57/1.03 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/1.03 thf(zip_derived_cl916, plain,
% 0.57/1.03 ((![X0 : $i]:
% 0.57/1.03 ( (product @ e_4 @ e_1 @ X0) | ~ (product @ e_1 @ X0 @ e_2)))
% 0.57/1.03 <= (( (product @ e_2 @ e_1 @ e_4)))),
% 0.57/1.03 inference('s_sup-', [status(thm)], [zip_derived_cl909, zip_derived_cl42])).
% 0.57/1.03 thf(zip_derived_cl1160, plain,
% 0.57/1.03 ((( (product @ e_2 @ e_4 @ e_1) | ~ (product @ e_1 @ e_3 @ e_2)))
% 0.57/1.03 <= (( (product @ e_2 @ e_1 @ e_4)) & ( (product @ e_3 @ e_4 @ e_2)))),
% 0.57/1.03 inference('s_sup+', [status(thm)], [zip_derived_cl935, zip_derived_cl916])).
% 0.57/1.04 thf(zip_derived_cl1209, plain,
% 0.57/1.04 (( (product @ e_2 @ e_4 @ e_1)) <= (( (product @ e_2 @ e_4 @ e_1)))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl1160])).
% 0.57/1.04 thf(zip_derived_cl747, plain,
% 0.57/1.04 ((![X0 : $i]:
% 0.57/1.04 ( (product @ e_4 @ e_2 @ X0) | ~ (product @ e_2 @ X0 @ e_1)))
% 0.57/1.04 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl740, zip_derived_cl42])).
% 0.57/1.04 thf(zip_derived_cl66, plain,
% 0.57/1.04 (![X0 : $i, X1 : $i]:
% 0.57/1.04 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.57/1.04 thf(zip_derived_cl760, plain,
% 0.57/1.04 (((~ (product @ e_2 @ e_4 @ e_1) | (equalish @ e_4 @ e_2)))
% 0.57/1.04 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl747, zip_derived_cl66])).
% 0.57/1.04 thf(zip_derived_cl35, plain, (~ (equalish @ e_4 @ e_2)),
% 0.57/1.04 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 0.57/1.04 thf(zip_derived_cl763, plain,
% 0.57/1.04 ((~ (product @ e_2 @ e_4 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.57/1.04 inference('demod', [status(thm)], [zip_derived_cl760, zip_derived_cl35])).
% 0.57/1.04 thf('9', plain,
% 0.57/1.04 (~ ( (product @ e_1 @ e_2 @ e_4)) | ~ ( (product @ e_2 @ e_4 @ e_1))),
% 0.57/1.04 inference('s_sup-', [status(thm)],
% 0.57/1.04 [zip_derived_cl1209, zip_derived_cl763])).
% 0.57/1.04 thf(zip_derived_cl787, plain,
% 0.57/1.04 (( (product @ e_1 @ e_4 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_4)))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl215])).
% 0.57/1.04 thf(zip_derived_cl70, plain,
% 0.57/1.04 (![X0 : $i, X1 : $i]:
% 0.57/1.04 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.57/1.04 thf(zip_derived_cl795, plain,
% 0.57/1.04 (( (equalish @ e_4 @ e_1)) <= (( (product @ e_1 @ e_4 @ e_4)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl787, zip_derived_cl70])).
% 0.57/1.04 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 0.57/1.04 thf(zip_derived_cl34, plain, (~ (equalish @ e_4 @ e_1)),
% 0.57/1.04 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.57/1.04 thf('10', plain, (~ ( (product @ e_1 @ e_4 @ e_4))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl795, zip_derived_cl34])).
% 0.57/1.04 thf(zip_derived_cl790, plain,
% 0.57/1.04 (( (product @ e_1 @ e_4 @ e_1)) <= (( (product @ e_1 @ e_4 @ e_1)))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl215])).
% 0.57/1.04 thf(zip_derived_cl66, plain,
% 0.57/1.04 (![X0 : $i, X1 : $i]:
% 0.57/1.04 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.57/1.04 thf(zip_derived_cl1522, plain,
% 0.57/1.04 (( (equalish @ e_1 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_1)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl790, zip_derived_cl66])).
% 0.57/1.04 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 0.57/1.04 thf(zip_derived_cl27, plain, (~ (equalish @ e_1 @ e_4)),
% 0.57/1.04 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 0.57/1.04 thf('11', plain, (~ ( (product @ e_1 @ e_4 @ e_1))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl1522, zip_derived_cl27])).
% 0.57/1.04 thf('12', plain,
% 0.57/1.04 (( (product @ e_1 @ e_4 @ e_2)) | ( (product @ e_1 @ e_4 @ e_1)) |
% 0.57/1.04 ( (product @ e_1 @ e_4 @ e_4)) | ( (product @ e_1 @ e_4 @ e_3))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl215])).
% 0.57/1.04 thf('13', plain, (( (product @ e_1 @ e_4 @ e_2))),
% 0.57/1.04 inference('sat_resolution*', [status(thm)],
% 0.57/1.04 ['1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12'])).
% 0.57/1.04 thf(zip_derived_cl1530, plain, ( (product @ e_1 @ e_4 @ e_2)),
% 0.57/1.04 inference('simpl_trail', [status(thm)], [zip_derived_cl789, '13'])).
% 0.57/1.04 thf(zip_derived_cl930, plain,
% 0.57/1.04 (( (product @ e_3 @ e_4 @ e_2)) <= (( (product @ e_3 @ e_4 @ e_2)))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl926])).
% 0.57/1.04 thf(zip_derived_cl40, plain,
% 0.57/1.04 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.04 (~ (product @ X0 @ X1 @ X2)
% 0.57/1.04 | ~ (product @ X3 @ X1 @ X2)
% 0.57/1.04 | (equalish @ X0 @ X3))),
% 0.57/1.04 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.57/1.04 thf(zip_derived_cl934, plain,
% 0.57/1.04 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_2) | (equalish @ e_3 @ X0)))
% 0.57/1.04 <= (( (product @ e_3 @ e_4 @ e_2)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl930, zip_derived_cl40])).
% 0.57/1.04 thf(zip_derived_cl1554, plain,
% 0.57/1.04 (( (equalish @ e_3 @ e_1)) <= (( (product @ e_3 @ e_4 @ e_2)))),
% 0.57/1.04 inference('s_sup-', [status(thm)],
% 0.57/1.04 [zip_derived_cl1530, zip_derived_cl934])).
% 0.57/1.04 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 0.57/1.04 thf(zip_derived_cl31, plain, (~ (equalish @ e_3 @ e_1)),
% 0.57/1.04 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.57/1.04 thf('14', plain, (~ ( (product @ e_3 @ e_4 @ e_2))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl1554, zip_derived_cl31])).
% 0.57/1.04 thf(zip_derived_cl871, plain,
% 0.57/1.04 ((![X0 : $i]:
% 0.57/1.04 ( (product @ e_3 @ e_4 @ X0) | ~ (product @ e_4 @ X0 @ e_1)))
% 0.57/1.04 <= (( (product @ e_1 @ e_4 @ e_3)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl865, zip_derived_cl42])).
% 0.57/1.04 thf(zip_derived_cl95, plain,
% 0.57/1.04 (![X0 : $i]:
% 0.57/1.04 (~ (group_element @ X0)
% 0.57/1.04 | (product @ e_1 @ X0 @ e_1)
% 0.57/1.04 | (product @ e_1 @ X0 @ e_2)
% 0.57/1.04 | (product @ e_1 @ X0 @ e_3)
% 0.57/1.04 | (product @ e_1 @ X0 @ e_4))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.57/1.04 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 0.57/1.04 inference('cnf', [status(esa)], [element_3])).
% 0.57/1.04 thf(zip_derived_cl214, plain,
% 0.57/1.04 (( (product @ e_1 @ e_3 @ e_4)
% 0.57/1.04 | (product @ e_1 @ e_3 @ e_3)
% 0.57/1.04 | (product @ e_1 @ e_3 @ e_2)
% 0.57/1.04 | (product @ e_1 @ e_3 @ e_1))),
% 0.57/1.04 inference('s_sup+', [status(thm)], [zip_derived_cl95, zip_derived_cl23])).
% 0.57/1.04 thf(zip_derived_cl769, plain,
% 0.57/1.04 (( (product @ e_1 @ e_3 @ e_4)) <= (( (product @ e_1 @ e_3 @ e_4)))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl214])).
% 0.57/1.04 thf(zip_derived_cl42, plain,
% 0.57/1.04 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.04 ( (product @ X0 @ X1 @ X2)
% 0.57/1.04 | ~ (product @ X3 @ X1 @ X0)
% 0.57/1.04 | ~ (product @ X1 @ X2 @ X3))),
% 0.57/1.04 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/1.04 thf(zip_derived_cl776, plain,
% 0.57/1.04 ((![X0 : $i]:
% 0.57/1.04 ( (product @ e_4 @ e_3 @ X0) | ~ (product @ e_3 @ X0 @ e_1)))
% 0.57/1.04 <= (( (product @ e_1 @ e_3 @ e_4)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl769, zip_derived_cl42])).
% 0.57/1.04 thf(zip_derived_cl927, plain,
% 0.57/1.04 ((( (product @ e_3 @ e_4 @ e_3) | ~ (product @ e_3 @ e_1 @ e_1)))
% 0.57/1.04 <= (( (product @ e_1 @ e_3 @ e_4)) & ( (product @ e_1 @ e_4 @ e_3)))),
% 0.57/1.04 inference('s_sup+', [status(thm)], [zip_derived_cl871, zip_derived_cl776])).
% 0.57/1.04 thf(zip_derived_cl936, plain,
% 0.57/1.04 (( (product @ e_3 @ e_4 @ e_3)) <= (( (product @ e_3 @ e_4 @ e_3)))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl927])).
% 0.57/1.04 thf(zip_derived_cl66, plain,
% 0.57/1.04 (![X0 : $i, X1 : $i]:
% 0.57/1.04 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.57/1.04 thf(zip_derived_cl942, plain,
% 0.57/1.04 (( (equalish @ e_3 @ e_4)) <= (( (product @ e_3 @ e_4 @ e_3)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl936, zip_derived_cl66])).
% 0.57/1.04 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 0.57/1.04 thf(zip_derived_cl33, plain, (~ (equalish @ e_3 @ e_4)),
% 0.57/1.04 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 0.57/1.04 thf('15', plain, (~ ( (product @ e_3 @ e_4 @ e_3))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl942, zip_derived_cl33])).
% 0.57/1.04 thf('16', plain,
% 0.57/1.04 (( (product @ e_3 @ e_4 @ e_4)) | ( (product @ e_3 @ e_4 @ e_1)) |
% 0.57/1.04 ( (product @ e_3 @ e_4 @ e_3)) | ( (product @ e_3 @ e_4 @ e_2))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl269])).
% 0.57/1.04 thf(zip_derived_cl1209, plain,
% 0.57/1.04 (( (product @ e_2 @ e_4 @ e_1)) <= (( (product @ e_2 @ e_4 @ e_1)))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl1160])).
% 0.57/1.04 thf(zip_derived_cl916, plain,
% 0.57/1.04 ((![X0 : $i]:
% 0.57/1.04 ( (product @ e_4 @ e_1 @ X0) | ~ (product @ e_1 @ X0 @ e_2)))
% 0.57/1.04 <= (( (product @ e_2 @ e_1 @ e_4)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl909, zip_derived_cl42])).
% 0.57/1.04 thf(zip_derived_cl871, plain,
% 0.57/1.04 ((![X0 : $i]:
% 0.57/1.04 ( (product @ e_3 @ e_4 @ X0) | ~ (product @ e_4 @ X0 @ e_1)))
% 0.57/1.04 <= (( (product @ e_1 @ e_4 @ e_3)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl865, zip_derived_cl42])).
% 0.57/1.04 thf(zip_derived_cl1019, plain,
% 0.57/1.04 (((~ (product @ e_1 @ e_1 @ e_2) | (product @ e_3 @ e_4 @ e_1)))
% 0.57/1.04 <= (( (product @ e_1 @ e_4 @ e_3)) & ( (product @ e_2 @ e_1 @ e_4)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl916, zip_derived_cl871])).
% 0.57/1.04 thf(zip_derived_cl1023, plain,
% 0.57/1.04 (( (product @ e_3 @ e_4 @ e_1)) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl1019])).
% 0.57/1.04 thf(zip_derived_cl40, plain,
% 0.57/1.04 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.04 (~ (product @ X0 @ X1 @ X2)
% 0.57/1.04 | ~ (product @ X3 @ X1 @ X2)
% 0.57/1.04 | (equalish @ X0 @ X3))),
% 0.57/1.04 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.57/1.04 thf(zip_derived_cl1027, plain,
% 0.57/1.04 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_1) | (equalish @ e_3 @ X0)))
% 0.57/1.04 <= (( (product @ e_3 @ e_4 @ e_1)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl1023, zip_derived_cl40])).
% 0.57/1.04 thf(zip_derived_cl1215, plain,
% 0.57/1.04 (( (equalish @ e_3 @ e_2))
% 0.57/1.04 <= (( (product @ e_2 @ e_4 @ e_1)) & ( (product @ e_3 @ e_4 @ e_1)))),
% 0.57/1.04 inference('s_sup-', [status(thm)],
% 0.57/1.04 [zip_derived_cl1209, zip_derived_cl1027])).
% 0.57/1.04 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 0.57/1.04 thf(zip_derived_cl32, plain, (~ (equalish @ e_3 @ e_2)),
% 0.57/1.04 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 0.57/1.04 thf('17', plain,
% 0.57/1.04 (~ ( (product @ e_2 @ e_4 @ e_1)) | ~ ( (product @ e_3 @ e_4 @ e_1))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl1215, zip_derived_cl32])).
% 0.57/1.04 thf(zip_derived_cl1033, plain,
% 0.57/1.04 (( (product @ e_2 @ e_4 @ e_3)) <= (( (product @ e_2 @ e_4 @ e_3)))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl253])).
% 0.57/1.04 thf(zip_derived_cl21, plain, ( (group_element @ e_1)),
% 0.57/1.04 inference('cnf', [status(esa)], [element_1])).
% 0.57/1.04 thf(zip_derived_cl96, plain,
% 0.57/1.04 (![X0 : $i]:
% 0.57/1.04 (~ (group_element @ X0)
% 0.57/1.04 | (product @ e_2 @ X0 @ e_1)
% 0.57/1.04 | (product @ e_2 @ X0 @ e_2)
% 0.57/1.04 | (product @ e_2 @ X0 @ e_3)
% 0.57/1.04 | (product @ e_2 @ X0 @ e_4))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl37])).
% 0.57/1.04 thf(zip_derived_cl250, plain,
% 0.57/1.04 (( (product @ e_2 @ e_1 @ e_1)
% 0.57/1.04 | (product @ e_2 @ e_1 @ e_2)
% 0.57/1.04 | (product @ e_2 @ e_1 @ e_3)
% 0.57/1.04 | (product @ e_2 @ e_1 @ e_4))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl96])).
% 0.57/1.04 thf(zip_derived_cl982, plain,
% 0.57/1.04 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl250])).
% 0.57/1.04 thf(zip_derived_cl39, plain,
% 0.57/1.04 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/1.04 (~ (product @ X0 @ X1 @ X2)
% 0.57/1.04 | ~ (product @ X0 @ X3 @ X2)
% 0.57/1.04 | (equalish @ X1 @ X3))),
% 0.57/1.04 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.57/1.04 thf(zip_derived_cl986, plain,
% 0.57/1.04 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 0.57/1.04 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl982, zip_derived_cl39])).
% 0.57/1.04 thf(zip_derived_cl1348, plain,
% 0.57/1.04 (( (equalish @ e_1 @ e_4))
% 0.57/1.04 <= (( (product @ e_2 @ e_1 @ e_3)) & ( (product @ e_2 @ e_4 @ e_3)))),
% 0.57/1.04 inference('s_sup-', [status(thm)],
% 0.57/1.04 [zip_derived_cl1033, zip_derived_cl986])).
% 0.57/1.04 thf(zip_derived_cl27, plain, (~ (equalish @ e_1 @ e_4)),
% 0.57/1.04 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 0.57/1.04 thf('18', plain,
% 0.57/1.04 (~ ( (product @ e_2 @ e_1 @ e_3)) | ~ ( (product @ e_2 @ e_4 @ e_3))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl1348, zip_derived_cl27])).
% 0.57/1.04 thf('19', plain,
% 0.57/1.04 (( (product @ e_2 @ e_4 @ e_3)) | ( (product @ e_2 @ e_4 @ e_1)) |
% 0.57/1.04 ( (product @ e_2 @ e_4 @ e_4)) | ( (product @ e_2 @ e_4 @ e_2))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl249])).
% 0.57/1.04 thf('20', plain,
% 0.57/1.04 (( (product @ e_1 @ e_2 @ e_4)) | ( (product @ e_1 @ e_2 @ e_3)) |
% 0.57/1.04 ( (product @ e_1 @ e_2 @ e_2)) | ( (product @ e_1 @ e_2 @ e_1))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl213])).
% 0.57/1.04 thf('21', plain,
% 0.57/1.04 (~ ( (product @ e_1 @ e_4 @ e_3)) | ~ ( (product @ e_2 @ e_4 @ e_3))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl1174, zip_derived_cl25])).
% 0.57/1.04 thf('22', plain,
% 0.57/1.04 (~ ( (product @ e_2 @ e_4 @ e_1)) | ~ ( (product @ e_1 @ e_2 @ e_4))),
% 0.57/1.04 inference('s_sup-', [status(thm)],
% 0.57/1.04 [zip_derived_cl1209, zip_derived_cl763])).
% 0.57/1.04 thf(zip_derived_cl789, plain,
% 0.57/1.04 (( (product @ e_1 @ e_4 @ e_2)) <= (( (product @ e_1 @ e_4 @ e_2)))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl215])).
% 0.57/1.04 thf(zip_derived_cl916, plain,
% 0.57/1.04 ((![X0 : $i]:
% 0.57/1.04 ( (product @ e_4 @ e_1 @ X0) | ~ (product @ e_1 @ X0 @ e_2)))
% 0.57/1.04 <= (( (product @ e_2 @ e_1 @ e_4)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl909, zip_derived_cl42])).
% 0.57/1.04 thf(zip_derived_cl66, plain,
% 0.57/1.04 (![X0 : $i, X1 : $i]:
% 0.57/1.04 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.57/1.04 thf(zip_derived_cl1014, plain,
% 0.57/1.04 (((~ (product @ e_1 @ e_4 @ e_2) | (equalish @ e_4 @ e_1)))
% 0.57/1.04 <= (( (product @ e_2 @ e_1 @ e_4)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl916, zip_derived_cl66])).
% 0.57/1.04 thf(zip_derived_cl34, plain, (~ (equalish @ e_4 @ e_1)),
% 0.57/1.04 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.57/1.04 thf(zip_derived_cl1020, plain,
% 0.57/1.04 ((~ (product @ e_1 @ e_4 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_4)))),
% 0.57/1.04 inference('demod', [status(thm)], [zip_derived_cl1014, zip_derived_cl34])).
% 0.57/1.04 thf('23', plain,
% 0.57/1.04 (~ ( (product @ e_2 @ e_1 @ e_4)) | ~ ( (product @ e_1 @ e_4 @ e_2))),
% 0.57/1.04 inference('s_sup-', [status(thm)],
% 0.57/1.04 [zip_derived_cl789, zip_derived_cl1020])).
% 0.57/1.04 thf(zip_derived_cl911, plain,
% 0.57/1.04 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl246])).
% 0.57/1.04 thf(zip_derived_cl66, plain,
% 0.57/1.04 (![X0 : $i, X1 : $i]:
% 0.57/1.04 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.57/1.04 thf(zip_derived_cl1615, plain,
% 0.57/1.04 (( (equalish @ e_2 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl911, zip_derived_cl66])).
% 0.57/1.04 thf(zip_derived_cl28, plain, (~ (equalish @ e_2 @ e_1)),
% 0.57/1.04 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.57/1.04 thf('24', plain, (~ ( (product @ e_2 @ e_1 @ e_2))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl1615, zip_derived_cl28])).
% 0.57/1.04 thf('25', plain,
% 0.57/1.04 (( (product @ e_2 @ e_1 @ e_1)) | ( (product @ e_2 @ e_1 @ e_2)) |
% 0.57/1.04 ( (product @ e_2 @ e_1 @ e_4)) | ( (product @ e_2 @ e_1 @ e_3))),
% 0.57/1.04 inference('split', [status(esa)], [zip_derived_cl246])).
% 0.57/1.04 thf('26', plain, (( (product @ e_2 @ e_1 @ e_1))),
% 0.57/1.04 inference('sat_resolution*', [status(thm)],
% 0.57/1.04 ['0', '14', '15', '16', '17', '18', '19', '2', '3', '20', '5',
% 0.57/1.04 '6', '21', '8', '22', '10', '11', '12', '23', '24', '25'])).
% 0.57/1.04 thf(zip_derived_cl1626, plain, ( (product @ e_2 @ e_1 @ e_1)),
% 0.57/1.04 inference('simpl_trail', [status(thm)], [zip_derived_cl912, '26'])).
% 0.57/1.04 thf(zip_derived_cl70, plain,
% 0.57/1.04 (![X0 : $i, X1 : $i]:
% 0.57/1.04 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.57/1.04 thf(zip_derived_cl1631, plain, ( (equalish @ e_1 @ e_2)),
% 0.57/1.04 inference('s_sup-', [status(thm)], [zip_derived_cl1626, zip_derived_cl70])).
% 0.57/1.04 thf(zip_derived_cl1675, plain, ($false),
% 0.57/1.04 inference('demod', [status(thm)], [zip_derived_cl25, zip_derived_cl1631])).
% 0.57/1.04
% 0.57/1.04 % SZS output end Refutation
% 0.57/1.04
% 0.57/1.04
% 0.57/1.04 % Terminating...
% 0.58/1.09 % Runner terminated.
% 0.58/1.10 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------