TSTP Solution File: GRP124-7.004 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP124-7.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.QHZY4zvEL9 true
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:50:06 EDT 2023
% Result : Unsatisfiable 3.78s 1.21s
% Output : Refutation 3.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.15 % Problem : GRP124-7.004 : TPTP v8.1.2. Released v1.2.0.
% 0.13/0.16 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.QHZY4zvEL9 true
% 0.15/0.38 % Computer : n016.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Mon Aug 28 23:52:30 EDT 2023
% 0.15/0.38 % CPUTime :
% 0.15/0.38 % Running portfolio for 300 s
% 0.15/0.38 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.38 % Number of cores: 8
% 0.15/0.38 % Python version: Python 3.6.8
% 0.15/0.38 % Running in FO mode
% 0.56/0.67 % Total configuration time : 435
% 0.56/0.67 % Estimated wc time : 1092
% 0.56/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.57/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.57/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.57/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 3.78/1.21 % Solved by fo/fo1_av.sh.
% 3.78/1.21 % done 556 iterations in 0.459s
% 3.78/1.21 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 3.78/1.21 % SZS output start Refutation
% 3.78/1.21 thf(group_element_type, type, group_element: $i > $o).
% 3.78/1.21 thf(e_4_type, type, e_4: $i).
% 3.78/1.21 thf(equalish_type, type, equalish: $i > $i > $o).
% 3.78/1.21 thf(e_3_type, type, e_3: $i).
% 3.78/1.21 thf(e_2_type, type, e_2: $i).
% 3.78/1.21 thf(product2_type, type, product2: $i > $i > $i > $o).
% 3.78/1.21 thf(e_1_type, type, e_1: $i).
% 3.78/1.21 thf(product1_type, type, product1: $i > $i > $i > $o).
% 3.78/1.21 thf(product1_total_function1, axiom,
% 3.78/1.21 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 3.78/1.21 ( product1 @ X @ Y @ e_1 ) | ( product1 @ X @ Y @ e_2 ) |
% 3.78/1.21 ( product1 @ X @ Y @ e_3 ) | ( product1 @ X @ Y @ e_4 ))).
% 3.78/1.21 thf(zip_derived_cl26, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (group_element @ X0)
% 3.78/1.21 | ~ (group_element @ X1)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_1)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_2)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_3)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_4))),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_total_function1])).
% 3.78/1.21 thf(zip_derived_cl26, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (group_element @ X0)
% 3.78/1.21 | ~ (group_element @ X1)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_1)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_2)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_3)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_4))),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_total_function1])).
% 3.78/1.21 thf(product1_idempotence, axiom, (product1 @ X @ X @ X)).
% 3.78/1.21 thf(zip_derived_cl30, plain, (![X0 : $i]: (product1 @ X0 @ X0 @ X0)),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_idempotence])).
% 3.78/1.21 thf(product1_right_cancellation, axiom,
% 3.78/1.21 (( ~( product1 @ X @ W @ Y ) ) | ( ~( product1 @ X @ Z @ Y ) ) |
% 3.78/1.21 ( equalish @ W @ Z ))).
% 3.78/1.21 thf(zip_derived_cl28, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.78/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.78/1.21 | ~ (product1 @ X0 @ X3 @ X2)
% 3.78/1.21 | (equalish @ X1 @ X3))),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 3.78/1.21 thf(zip_derived_cl46, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (product1 @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 3.78/1.21 thf(zip_derived_cl53, plain,
% 3.78/1.21 (![X0 : $i]:
% 3.78/1.21 ( (product1 @ e_4 @ X0 @ e_3)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_2)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_1)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | ~ (group_element @ e_4)
% 3.78/1.21 | (equalish @ e_4 @ X0))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl46])).
% 3.78/1.21 thf(element_4, axiom, (group_element @ e_4)).
% 3.78/1.21 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_4])).
% 3.78/1.21 thf(zip_derived_cl54, plain,
% 3.78/1.21 (![X0 : $i]:
% 3.78/1.21 ( (product1 @ e_4 @ X0 @ e_3)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_2)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_1)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (equalish @ e_4 @ X0))),
% 3.78/1.21 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl13])).
% 3.78/1.21 thf(zip_derived_cl26, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (group_element @ X0)
% 3.78/1.21 | ~ (group_element @ X1)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_1)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_2)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_3)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_4))),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_total_function1])).
% 3.78/1.21 thf(zip_derived_cl30, plain, (![X0 : $i]: (product1 @ X0 @ X0 @ X0)),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_idempotence])).
% 3.78/1.21 thf(product1_left_cancellation, axiom,
% 3.78/1.21 (( ~( product1 @ W @ Y @ X ) ) | ( ~( product1 @ Z @ Y @ X ) ) |
% 3.78/1.21 ( equalish @ W @ Z ))).
% 3.78/1.21 thf(zip_derived_cl29, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.78/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.78/1.21 | ~ (product1 @ X3 @ X1 @ X2)
% 3.78/1.21 | (equalish @ X0 @ X3))),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 3.78/1.21 thf(zip_derived_cl56, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (product1 @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 3.78/1.21 thf(zip_derived_cl63, plain,
% 3.78/1.21 (![X0 : $i]:
% 3.78/1.21 ( (product1 @ X0 @ e_4 @ e_3)
% 3.78/1.21 | (product1 @ X0 @ e_4 @ e_2)
% 3.78/1.21 | (product1 @ X0 @ e_4 @ e_1)
% 3.78/1.21 | ~ (group_element @ e_4)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (equalish @ e_4 @ X0))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl56])).
% 3.78/1.21 thf(zip_derived_cl13, plain, ( (group_element @ e_4)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_4])).
% 3.78/1.21 thf(zip_derived_cl64, plain,
% 3.78/1.21 (![X0 : $i]:
% 3.78/1.21 ( (product1 @ X0 @ e_4 @ e_3)
% 3.78/1.21 | (product1 @ X0 @ e_4 @ e_2)
% 3.78/1.21 | (product1 @ X0 @ e_4 @ e_1)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (equalish @ e_4 @ X0))),
% 3.78/1.21 inference('demod', [status(thm)], [zip_derived_cl63, zip_derived_cl13])).
% 3.78/1.21 thf(zip_derived_cl46, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (product1 @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 3.78/1.21 thf(zip_derived_cl374, plain,
% 3.78/1.21 (( (equalish @ e_4 @ e_3)
% 3.78/1.21 | ~ (group_element @ e_3)
% 3.78/1.21 | (product1 @ e_3 @ e_4 @ e_1)
% 3.78/1.21 | (product1 @ e_3 @ e_4 @ e_2)
% 3.78/1.21 | (equalish @ e_3 @ e_4))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl46])).
% 3.78/1.21 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 3.78/1.21 thf(zip_derived_cl25, plain, (~ (equalish @ e_4 @ e_3)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 3.78/1.21 thf(element_3, axiom, (group_element @ e_3)).
% 3.78/1.21 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_3])).
% 3.78/1.21 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 3.78/1.21 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 3.78/1.21 thf(zip_derived_cl382, plain,
% 3.78/1.21 (( (product1 @ e_3 @ e_4 @ e_1) | (product1 @ e_3 @ e_4 @ e_2))),
% 3.78/1.21 inference('demod', [status(thm)],
% 3.78/1.21 [zip_derived_cl374, zip_derived_cl25, zip_derived_cl12,
% 3.78/1.21 zip_derived_cl22])).
% 3.78/1.21 thf(zip_derived_cl528, plain,
% 3.78/1.21 (( (product1 @ e_3 @ e_4 @ e_2)) <= (( (product1 @ e_3 @ e_4 @ e_2)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl382])).
% 3.78/1.21 thf(qg2a, conjecture,
% 3.78/1.21 (~( ( product2 @ Z2 @ Y @ X ) | ( ~( product1 @ Z1 @ X @ Z2 ) ) |
% 3.78/1.21 ( ~( product1 @ X @ Y @ Z1 ) ) ))).
% 3.78/1.21 thf(zf_stmt_0, negated_conjecture,
% 3.78/1.21 (( product2 @ Z2 @ Y @ X ) | ( ~( product1 @ Z1 @ X @ Z2 ) ) |
% 3.78/1.21 ( ~( product1 @ X @ Y @ Z1 ) )),
% 3.78/1.21 inference('cnf.neg', [status(esa)], [qg2a])).
% 3.78/1.21 thf(zip_derived_cl36, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.78/1.21 ( (product2 @ X0 @ X1 @ X2)
% 3.78/1.21 | ~ (product1 @ X3 @ X2 @ X0)
% 3.78/1.21 | ~ (product1 @ X2 @ X1 @ X3))),
% 3.78/1.21 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.78/1.21 thf(zip_derived_cl674, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 ( (product2 @ e_2 @ X0 @ e_4) | ~ (product1 @ e_4 @ X0 @ e_3)))
% 3.78/1.21 <= (( (product1 @ e_3 @ e_4 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl528, zip_derived_cl36])).
% 3.78/1.21 thf(product2_idempotence, axiom, (product2 @ X @ X @ X)).
% 3.78/1.21 thf(zip_derived_cl35, plain, (![X0 : $i]: (product2 @ X0 @ X0 @ X0)),
% 3.78/1.21 inference('cnf', [status(esa)], [product2_idempotence])).
% 3.78/1.21 thf(product2_total_function2, axiom,
% 3.78/1.21 (( ~( product2 @ X @ Y @ W ) ) | ( ~( product2 @ X @ Y @ Z ) ) |
% 3.78/1.21 ( equalish @ W @ Z ))).
% 3.78/1.21 thf(zip_derived_cl32, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.78/1.21 (~ (product2 @ X0 @ X1 @ X2)
% 3.78/1.21 | ~ (product2 @ X0 @ X1 @ X3)
% 3.78/1.21 | (equalish @ X2 @ X3))),
% 3.78/1.21 inference('cnf', [status(esa)], [product2_total_function2])).
% 3.78/1.21 thf(zip_derived_cl67, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (product2 @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl32])).
% 3.78/1.21 thf(zip_derived_cl1149, plain,
% 3.78/1.21 (((~ (product1 @ e_4 @ e_2 @ e_3) | (equalish @ e_2 @ e_4)))
% 3.78/1.21 <= (( (product1 @ e_3 @ e_4 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl674, zip_derived_cl67])).
% 3.78/1.21 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 3.78/1.21 thf(zip_derived_cl19, plain, (~ (equalish @ e_2 @ e_4)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 3.78/1.21 thf(zip_derived_cl1155, plain,
% 3.78/1.21 ((~ (product1 @ e_4 @ e_2 @ e_3)) <= (( (product1 @ e_3 @ e_4 @ e_2)))),
% 3.78/1.21 inference('demod', [status(thm)], [zip_derived_cl1149, zip_derived_cl19])).
% 3.78/1.21 thf(zip_derived_cl1161, plain,
% 3.78/1.21 ((( (equalish @ e_4 @ e_2)
% 3.78/1.21 | ~ (group_element @ e_2)
% 3.78/1.21 | (product1 @ e_4 @ e_2 @ e_1)
% 3.78/1.21 | (product1 @ e_4 @ e_2 @ e_2))) <= (( (product1 @ e_3 @ e_4 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl1155])).
% 3.78/1.21 thf(e_4_is_not_e_2, axiom, (~( equalish @ e_4 @ e_2 ))).
% 3.78/1.21 thf(zip_derived_cl24, plain, (~ (equalish @ e_4 @ e_2)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 3.78/1.21 thf(element_2, axiom, (group_element @ e_2)).
% 3.78/1.21 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_2])).
% 3.78/1.21 thf(zip_derived_cl1162, plain,
% 3.78/1.21 ((( (product1 @ e_4 @ e_2 @ e_1) | (product1 @ e_4 @ e_2 @ e_2)))
% 3.78/1.21 <= (( (product1 @ e_3 @ e_4 @ e_2)))),
% 3.78/1.21 inference('demod', [status(thm)],
% 3.78/1.21 [zip_derived_cl1161, zip_derived_cl24, zip_derived_cl11])).
% 3.78/1.21 thf(zip_derived_cl1629, plain,
% 3.78/1.21 (( (product1 @ e_4 @ e_2 @ e_2)) <= (( (product1 @ e_4 @ e_2 @ e_2)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl1162])).
% 3.78/1.21 thf(zip_derived_cl54, plain,
% 3.78/1.21 (![X0 : $i]:
% 3.78/1.21 ( (product1 @ e_4 @ X0 @ e_3)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_2)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_1)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (equalish @ e_4 @ X0))),
% 3.78/1.21 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl13])).
% 3.78/1.21 thf(zip_derived_cl527, plain,
% 3.78/1.21 (( (product1 @ e_3 @ e_4 @ e_1)) <= (( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl382])).
% 3.78/1.21 thf(zip_derived_cl36, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.78/1.21 ( (product2 @ X0 @ X1 @ X2)
% 3.78/1.21 | ~ (product1 @ X3 @ X2 @ X0)
% 3.78/1.21 | ~ (product1 @ X2 @ X1 @ X3))),
% 3.78/1.21 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.78/1.21 thf(zip_derived_cl532, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 ( (product2 @ e_1 @ X0 @ e_4) | ~ (product1 @ e_4 @ X0 @ e_3)))
% 3.78/1.21 <= (( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl527, zip_derived_cl36])).
% 3.78/1.21 thf(zip_derived_cl67, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (product2 @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl32])).
% 3.78/1.21 thf(zip_derived_cl556, plain,
% 3.78/1.21 (((~ (product1 @ e_4 @ e_1 @ e_3) | (equalish @ e_1 @ e_4)))
% 3.78/1.21 <= (( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl532, zip_derived_cl67])).
% 3.78/1.21 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 3.78/1.21 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 3.78/1.21 thf(zip_derived_cl560, plain,
% 3.78/1.21 ((~ (product1 @ e_4 @ e_1 @ e_3)) <= (( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('demod', [status(thm)], [zip_derived_cl556, zip_derived_cl16])).
% 3.78/1.21 thf(zip_derived_cl610, plain,
% 3.78/1.21 ((( (equalish @ e_4 @ e_1)
% 3.78/1.21 | ~ (group_element @ e_1)
% 3.78/1.21 | (product1 @ e_4 @ e_1 @ e_1)
% 3.78/1.21 | (product1 @ e_4 @ e_1 @ e_2))) <= (( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl560])).
% 3.78/1.21 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 3.78/1.21 thf(zip_derived_cl23, plain, (~ (equalish @ e_4 @ e_1)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 3.78/1.21 thf(element_1, axiom, (group_element @ e_1)).
% 3.78/1.21 thf(zip_derived_cl10, plain, ( (group_element @ e_1)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_1])).
% 3.78/1.21 thf(zip_derived_cl611, plain,
% 3.78/1.21 ((( (product1 @ e_4 @ e_1 @ e_1) | (product1 @ e_4 @ e_1 @ e_2)))
% 3.78/1.21 <= (( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('demod', [status(thm)],
% 3.78/1.21 [zip_derived_cl610, zip_derived_cl23, zip_derived_cl10])).
% 3.78/1.21 thf(zip_derived_cl805, plain,
% 3.78/1.21 (( (product1 @ e_4 @ e_1 @ e_2)) <= (( (product1 @ e_4 @ e_1 @ e_2)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl611])).
% 3.78/1.21 thf(zip_derived_cl532, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 ( (product2 @ e_1 @ X0 @ e_4) | ~ (product1 @ e_4 @ X0 @ e_3)))
% 3.78/1.21 <= (( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl527, zip_derived_cl36])).
% 3.78/1.21 thf(zip_derived_cl56, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (product1 @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 3.78/1.21 thf(zip_derived_cl54, plain,
% 3.78/1.21 (![X0 : $i]:
% 3.78/1.21 ( (product1 @ e_4 @ X0 @ e_3)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_2)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_1)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (equalish @ e_4 @ X0))),
% 3.78/1.21 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl13])).
% 3.78/1.21 thf(zip_derived_cl249, plain,
% 3.78/1.21 (( (equalish @ e_3 @ e_4)
% 3.78/1.21 | (product1 @ e_4 @ e_3 @ e_2)
% 3.78/1.21 | (product1 @ e_4 @ e_3 @ e_1)
% 3.78/1.21 | ~ (group_element @ e_3)
% 3.78/1.21 | (equalish @ e_4 @ e_3))),
% 3.78/1.21 inference('s_sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl54])).
% 3.78/1.21 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 3.78/1.21 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_3])).
% 3.78/1.21 thf(zip_derived_cl25, plain, (~ (equalish @ e_4 @ e_3)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 3.78/1.21 thf(zip_derived_cl250, plain,
% 3.78/1.21 (( (product1 @ e_4 @ e_3 @ e_2) | (product1 @ e_4 @ e_3 @ e_1))),
% 3.78/1.21 inference('demod', [status(thm)],
% 3.78/1.21 [zip_derived_cl249, zip_derived_cl22, zip_derived_cl12,
% 3.78/1.21 zip_derived_cl25])).
% 3.78/1.21 thf(zip_derived_cl255, plain,
% 3.78/1.21 (( (product1 @ e_4 @ e_3 @ e_1)) <= (( (product1 @ e_4 @ e_3 @ e_1)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl250])).
% 3.78/1.21 thf(zip_derived_cl36, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.78/1.21 ( (product2 @ X0 @ X1 @ X2)
% 3.78/1.21 | ~ (product1 @ X3 @ X2 @ X0)
% 3.78/1.21 | ~ (product1 @ X2 @ X1 @ X3))),
% 3.78/1.21 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.78/1.21 thf(zip_derived_cl260, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 ( (product2 @ e_1 @ X0 @ e_3) | ~ (product1 @ e_3 @ X0 @ e_4)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl255, zip_derived_cl36])).
% 3.78/1.21 thf(zip_derived_cl32, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.78/1.21 (~ (product2 @ X0 @ X1 @ X2)
% 3.78/1.21 | ~ (product2 @ X0 @ X1 @ X3)
% 3.78/1.21 | (equalish @ X2 @ X3))),
% 3.78/1.21 inference('cnf', [status(esa)], [product2_total_function2])).
% 3.78/1.21 thf(zip_derived_cl275, plain,
% 3.78/1.21 ((![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (product1 @ e_3 @ X0 @ e_4)
% 3.78/1.21 | ~ (product2 @ e_1 @ X0 @ X1)
% 3.78/1.21 | (equalish @ e_3 @ X1)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl260, zip_derived_cl32])).
% 3.78/1.21 thf(zip_derived_cl559, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 (~ (product1 @ e_4 @ X0 @ e_3)
% 3.78/1.21 | ~ (product1 @ e_3 @ X0 @ e_4)
% 3.78/1.21 | (equalish @ e_3 @ e_4)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) & ( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl532, zip_derived_cl275])).
% 3.78/1.21 thf(zip_derived_cl22, plain, (~ (equalish @ e_3 @ e_4)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 3.78/1.21 thf(zip_derived_cl563, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 (~ (product1 @ e_4 @ X0 @ e_3) | ~ (product1 @ e_3 @ X0 @ e_4)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) & ( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('demod', [status(thm)], [zip_derived_cl559, zip_derived_cl22])).
% 3.78/1.21 thf(zip_derived_cl54, plain,
% 3.78/1.21 (![X0 : $i]:
% 3.78/1.21 ( (product1 @ e_4 @ X0 @ e_3)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_2)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_1)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (equalish @ e_4 @ X0))),
% 3.78/1.21 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl13])).
% 3.78/1.21 thf(zip_derived_cl566, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 (~ (product1 @ e_3 @ X0 @ e_4)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_2)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_1)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (equalish @ e_4 @ X0)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) & ( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('s_sup+', [status(thm)], [zip_derived_cl563, zip_derived_cl54])).
% 3.78/1.21 thf(zip_derived_cl28, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.78/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.78/1.21 | ~ (product1 @ X0 @ X3 @ X2)
% 3.78/1.21 | (equalish @ X1 @ X3))),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 3.78/1.21 thf(zip_derived_cl575, plain,
% 3.78/1.21 ((![X0 : $i, X1 : $i]:
% 3.78/1.21 ( (equalish @ e_4 @ X0)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_1)
% 3.78/1.21 | ~ (product1 @ e_3 @ X0 @ e_4)
% 3.78/1.21 | ~ (product1 @ e_4 @ X1 @ e_2)
% 3.78/1.21 | (equalish @ X0 @ X1)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) & ( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl566, zip_derived_cl28])).
% 3.78/1.21 thf(zip_derived_cl862, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 ( (equalish @ e_4 @ X0)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_1)
% 3.78/1.21 | ~ (product1 @ e_3 @ X0 @ e_4)
% 3.78/1.21 | (equalish @ X0 @ e_1)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl805, zip_derived_cl575])).
% 3.78/1.21 thf(product1_total_function2, axiom,
% 3.78/1.21 (( ~( product1 @ X @ Y @ W ) ) | ( ~( product1 @ X @ Y @ Z ) ) |
% 3.78/1.21 ( equalish @ W @ Z ))).
% 3.78/1.21 thf(zip_derived_cl27, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.78/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.78/1.21 | ~ (product1 @ X0 @ X1 @ X3)
% 3.78/1.21 | (equalish @ X2 @ X3))),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_total_function2])).
% 3.78/1.21 thf(zip_derived_cl868, plain,
% 3.78/1.21 ((![X0 : $i, X1 : $i]:
% 3.78/1.21 ( (equalish @ X0 @ e_1)
% 3.78/1.21 | ~ (product1 @ e_3 @ X0 @ e_4)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (equalish @ e_4 @ X0)
% 3.78/1.21 | ~ (product1 @ e_4 @ X0 @ X1)
% 3.78/1.21 | (equalish @ e_1 @ X1)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl862, zip_derived_cl27])).
% 3.78/1.21 thf(zip_derived_cl1639, plain,
% 3.78/1.21 ((( (equalish @ e_2 @ e_1)
% 3.78/1.21 | ~ (product1 @ e_3 @ e_2 @ e_4)
% 3.78/1.21 | ~ (group_element @ e_2)
% 3.78/1.21 | (equalish @ e_4 @ e_2)
% 3.78/1.21 | (equalish @ e_1 @ e_2)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_2 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)],
% 3.78/1.21 [zip_derived_cl1629, zip_derived_cl868])).
% 3.78/1.21 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 3.78/1.21 thf(zip_derived_cl17, plain, (~ (equalish @ e_2 @ e_1)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 3.78/1.21 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_2])).
% 3.78/1.21 thf(zip_derived_cl24, plain, (~ (equalish @ e_4 @ e_2)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 3.78/1.21 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 3.78/1.21 thf(zip_derived_cl14, plain, (~ (equalish @ e_1 @ e_2)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 3.78/1.21 thf(zip_derived_cl1649, plain,
% 3.78/1.21 ((~ (product1 @ e_3 @ e_2 @ e_4))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_2 @ e_2)))),
% 3.78/1.21 inference('demod', [status(thm)],
% 3.78/1.21 [zip_derived_cl1639, zip_derived_cl17, zip_derived_cl11,
% 3.78/1.21 zip_derived_cl24, zip_derived_cl14])).
% 3.78/1.21 thf(zip_derived_cl1652, plain,
% 3.78/1.21 ((( (product1 @ e_3 @ e_2 @ e_3)
% 3.78/1.21 | (product1 @ e_3 @ e_2 @ e_2)
% 3.78/1.21 | (product1 @ e_3 @ e_2 @ e_1)
% 3.78/1.21 | ~ (group_element @ e_2)
% 3.78/1.21 | ~ (group_element @ e_3)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_2 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl1649])).
% 3.78/1.21 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_2])).
% 3.78/1.21 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_3])).
% 3.78/1.21 thf(zip_derived_cl1653, plain,
% 3.78/1.21 ((( (product1 @ e_3 @ e_2 @ e_3)
% 3.78/1.21 | (product1 @ e_3 @ e_2 @ e_2)
% 3.78/1.21 | (product1 @ e_3 @ e_2 @ e_1)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_2 @ e_2)))),
% 3.78/1.21 inference('demod', [status(thm)],
% 3.78/1.21 [zip_derived_cl1652, zip_derived_cl11, zip_derived_cl12])).
% 3.78/1.21 thf(zip_derived_cl1655, plain,
% 3.78/1.21 (( (product1 @ e_3 @ e_2 @ e_3)) <= (( (product1 @ e_3 @ e_2 @ e_3)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl1653])).
% 3.78/1.21 thf(zip_derived_cl46, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (product1 @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 3.78/1.21 thf(zip_derived_cl1663, plain,
% 3.78/1.21 (( (equalish @ e_3 @ e_2)) <= (( (product1 @ e_3 @ e_2 @ e_3)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1655, zip_derived_cl46])).
% 3.78/1.21 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 3.78/1.21 thf(zip_derived_cl21, plain, (~ (equalish @ e_3 @ e_2)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 3.78/1.21 thf('0', plain, (~ ( (product1 @ e_3 @ e_2 @ e_3))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1663, zip_derived_cl21])).
% 3.78/1.21 thf(zip_derived_cl1649, plain,
% 3.78/1.21 ((~ (product1 @ e_3 @ e_2 @ e_4))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_2 @ e_2)))),
% 3.78/1.21 inference('demod', [status(thm)],
% 3.78/1.21 [zip_derived_cl1639, zip_derived_cl17, zip_derived_cl11,
% 3.78/1.21 zip_derived_cl24, zip_derived_cl14])).
% 3.78/1.21 thf(zip_derived_cl26, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (group_element @ X0)
% 3.78/1.21 | ~ (group_element @ X1)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_1)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_2)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_3)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_4))),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_total_function1])).
% 3.78/1.21 thf(zip_derived_cl1651, plain,
% 3.78/1.21 (((~ (group_element @ e_3)
% 3.78/1.21 | ~ (group_element @ e_2)
% 3.78/1.21 | (product1 @ e_3 @ e_2 @ e_1)
% 3.78/1.21 | (product1 @ e_3 @ e_2 @ e_2)
% 3.78/1.21 | (product1 @ e_3 @ e_2 @ e_3)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_2 @ e_2)))),
% 3.78/1.21 inference('s_sup+', [status(thm)], [zip_derived_cl1649, zip_derived_cl26])).
% 3.78/1.21 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_3])).
% 3.78/1.21 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_2])).
% 3.78/1.21 thf(zip_derived_cl1654, plain,
% 3.78/1.21 ((( (product1 @ e_3 @ e_2 @ e_1)
% 3.78/1.21 | (product1 @ e_3 @ e_2 @ e_2)
% 3.78/1.21 | (product1 @ e_3 @ e_2 @ e_3)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_2 @ e_2)))),
% 3.78/1.21 inference('demod', [status(thm)],
% 3.78/1.21 [zip_derived_cl1651, zip_derived_cl12, zip_derived_cl11])).
% 3.78/1.21 thf(zip_derived_cl1679, plain,
% 3.78/1.21 (( (product1 @ e_3 @ e_2 @ e_2)) <= (( (product1 @ e_3 @ e_2 @ e_2)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl1654])).
% 3.78/1.21 thf(zip_derived_cl56, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (product1 @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 3.78/1.21 thf(zip_derived_cl1686, plain,
% 3.78/1.21 (( (equalish @ e_2 @ e_3)) <= (( (product1 @ e_3 @ e_2 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1679, zip_derived_cl56])).
% 3.78/1.21 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 3.78/1.21 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 3.78/1.21 thf('1', plain, (~ ( (product1 @ e_3 @ e_2 @ e_2))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1686, zip_derived_cl18])).
% 3.78/1.21 thf(zip_derived_cl804, plain,
% 3.78/1.21 (( (product1 @ e_4 @ e_1 @ e_1)) <= (( (product1 @ e_4 @ e_1 @ e_1)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl611])).
% 3.78/1.21 thf(zip_derived_cl56, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (product1 @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 3.78/1.21 thf(zip_derived_cl811, plain,
% 3.78/1.21 (( (equalish @ e_1 @ e_4)) <= (( (product1 @ e_4 @ e_1 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl804, zip_derived_cl56])).
% 3.78/1.21 thf(zip_derived_cl16, plain, (~ (equalish @ e_1 @ e_4)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 3.78/1.21 thf('2', plain, (~ ( (product1 @ e_4 @ e_1 @ e_1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl811, zip_derived_cl16])).
% 3.78/1.21 thf(zip_derived_cl1629, plain,
% 3.78/1.21 (( (product1 @ e_4 @ e_2 @ e_2)) <= (( (product1 @ e_4 @ e_2 @ e_2)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl1162])).
% 3.78/1.21 thf(zip_derived_cl56, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (product1 @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 3.78/1.21 thf(zip_derived_cl1635, plain,
% 3.78/1.21 (( (equalish @ e_2 @ e_4)) <= (( (product1 @ e_4 @ e_2 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1629, zip_derived_cl56])).
% 3.78/1.21 thf(zip_derived_cl19, plain, (~ (equalish @ e_2 @ e_4)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 3.78/1.21 thf('3', plain, (~ ( (product1 @ e_4 @ e_2 @ e_2))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1635, zip_derived_cl19])).
% 3.78/1.21 thf(zip_derived_cl566, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 (~ (product1 @ e_3 @ X0 @ e_4)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_2)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_1)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (equalish @ e_4 @ X0)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) & ( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('s_sup+', [status(thm)], [zip_derived_cl563, zip_derived_cl54])).
% 3.78/1.21 thf(zip_derived_cl56, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (product1 @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 3.78/1.21 thf(zip_derived_cl580, plain,
% 3.78/1.21 ((( (equalish @ e_4 @ e_2)
% 3.78/1.21 | ~ (group_element @ e_2)
% 3.78/1.21 | (product1 @ e_4 @ e_2 @ e_1)
% 3.78/1.21 | ~ (product1 @ e_3 @ e_2 @ e_4)
% 3.78/1.21 | (equalish @ e_2 @ e_4)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) & ( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl566, zip_derived_cl56])).
% 3.78/1.21 thf(zip_derived_cl24, plain, (~ (equalish @ e_4 @ e_2)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 3.78/1.21 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_2])).
% 3.78/1.21 thf(zip_derived_cl19, plain, (~ (equalish @ e_2 @ e_4)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 3.78/1.21 thf(zip_derived_cl588, plain,
% 3.78/1.21 ((( (product1 @ e_4 @ e_2 @ e_1) | ~ (product1 @ e_3 @ e_2 @ e_4)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) & ( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('demod', [status(thm)],
% 3.78/1.21 [zip_derived_cl580, zip_derived_cl24, zip_derived_cl11,
% 3.78/1.21 zip_derived_cl19])).
% 3.78/1.21 thf(zip_derived_cl598, plain,
% 3.78/1.21 (( (product1 @ e_4 @ e_2 @ e_1)) <= (( (product1 @ e_4 @ e_2 @ e_1)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl588])).
% 3.78/1.21 thf(zip_derived_cl255, plain,
% 3.78/1.21 (( (product1 @ e_4 @ e_3 @ e_1)) <= (( (product1 @ e_4 @ e_3 @ e_1)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl250])).
% 3.78/1.21 thf(zip_derived_cl28, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.78/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.78/1.21 | ~ (product1 @ X0 @ X3 @ X2)
% 3.78/1.21 | (equalish @ X1 @ X3))),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 3.78/1.21 thf(zip_derived_cl258, plain,
% 3.78/1.21 ((![X0 : $i]: (~ (product1 @ e_4 @ X0 @ e_1) | (equalish @ e_3 @ X0)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl255, zip_derived_cl28])).
% 3.78/1.21 thf(zip_derived_cl606, plain,
% 3.78/1.21 (( (equalish @ e_3 @ e_2))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) & ( (product1 @ e_4 @ e_2 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl598, zip_derived_cl258])).
% 3.78/1.21 thf(zip_derived_cl21, plain, (~ (equalish @ e_3 @ e_2)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 3.78/1.21 thf('4', plain,
% 3.78/1.21 (~ ( (product1 @ e_4 @ e_3 @ e_1)) | ~ ( (product1 @ e_4 @ e_2 @ e_1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl606, zip_derived_cl21])).
% 3.78/1.21 thf(zip_derived_cl26, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (group_element @ X0)
% 3.78/1.21 | ~ (group_element @ X1)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_1)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_2)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_3)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_4))),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_total_function1])).
% 3.78/1.21 thf(zip_derived_cl862, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 ( (equalish @ e_4 @ X0)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (product1 @ e_4 @ X0 @ e_1)
% 3.78/1.21 | ~ (product1 @ e_3 @ X0 @ e_4)
% 3.78/1.21 | (equalish @ X0 @ e_1)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl805, zip_derived_cl575])).
% 3.78/1.21 thf(zip_derived_cl258, plain,
% 3.78/1.21 ((![X0 : $i]: (~ (product1 @ e_4 @ X0 @ e_1) | (equalish @ e_3 @ X0)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl255, zip_derived_cl28])).
% 3.78/1.21 thf(zip_derived_cl880, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 ( (equalish @ X0 @ e_1)
% 3.78/1.21 | ~ (product1 @ e_3 @ X0 @ e_4)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (equalish @ e_4 @ X0)
% 3.78/1.21 | (equalish @ e_3 @ X0)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl862, zip_derived_cl258])).
% 3.78/1.21 thf(zip_derived_cl904, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 ( (product1 @ e_3 @ X0 @ e_3)
% 3.78/1.21 | (product1 @ e_3 @ X0 @ e_2)
% 3.78/1.21 | (product1 @ e_3 @ X0 @ e_1)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | ~ (group_element @ e_3)
% 3.78/1.21 | (equalish @ X0 @ e_1)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (equalish @ e_4 @ X0)
% 3.78/1.21 | (equalish @ e_3 @ X0)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl880])).
% 3.78/1.21 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_3])).
% 3.78/1.21 thf(zip_derived_cl905, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 ( (product1 @ e_3 @ X0 @ e_3)
% 3.78/1.21 | (product1 @ e_3 @ X0 @ e_2)
% 3.78/1.21 | (product1 @ e_3 @ X0 @ e_1)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (equalish @ X0 @ e_1)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (equalish @ e_4 @ X0)
% 3.78/1.21 | (equalish @ e_3 @ X0)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)))),
% 3.78/1.21 inference('demod', [status(thm)], [zip_derived_cl904, zip_derived_cl12])).
% 3.78/1.21 thf(zip_derived_cl906, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 ( (equalish @ e_3 @ X0)
% 3.78/1.21 | (equalish @ e_4 @ X0)
% 3.78/1.21 | (equalish @ X0 @ e_1)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (product1 @ e_3 @ X0 @ e_1)
% 3.78/1.21 | (product1 @ e_3 @ X0 @ e_2)
% 3.78/1.21 | (product1 @ e_3 @ X0 @ e_3)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)))),
% 3.78/1.21 inference('simplify', [status(thm)], [zip_derived_cl905])).
% 3.78/1.21 thf(zip_derived_cl527, plain,
% 3.78/1.21 (( (product1 @ e_3 @ e_4 @ e_1)) <= (( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl382])).
% 3.78/1.21 thf(zip_derived_cl28, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.78/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.78/1.21 | ~ (product1 @ X0 @ X3 @ X2)
% 3.78/1.21 | (equalish @ X1 @ X3))),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 3.78/1.21 thf(zip_derived_cl530, plain,
% 3.78/1.21 ((![X0 : $i]: (~ (product1 @ e_3 @ X0 @ e_1) | (equalish @ e_4 @ X0)))
% 3.78/1.21 <= (( (product1 @ e_3 @ e_4 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl527, zip_derived_cl28])).
% 3.78/1.21 thf(zip_derived_cl2475, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 ( (product1 @ e_3 @ X0 @ e_3)
% 3.78/1.21 | (product1 @ e_3 @ X0 @ e_2)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (equalish @ X0 @ e_1)
% 3.78/1.21 | (equalish @ e_4 @ X0)
% 3.78/1.21 | (equalish @ e_3 @ X0)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)))),
% 3.78/1.21 inference('clc', [status(thm)], [zip_derived_cl906, zip_derived_cl530])).
% 3.78/1.21 thf(zip_derived_cl46, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (product1 @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl28])).
% 3.78/1.21 thf(zip_derived_cl2476, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 ( (equalish @ e_3 @ X0)
% 3.78/1.21 | (equalish @ e_4 @ X0)
% 3.78/1.21 | (equalish @ X0 @ e_1)
% 3.78/1.21 | ~ (group_element @ X0)
% 3.78/1.21 | (product1 @ e_3 @ X0 @ e_2)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)))),
% 3.78/1.21 inference('clc', [status(thm)], [zip_derived_cl2475, zip_derived_cl46])).
% 3.78/1.21 thf(zip_derived_cl56, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (product1 @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl29])).
% 3.78/1.21 thf(zip_derived_cl2486, plain,
% 3.78/1.21 (((~ (group_element @ e_2)
% 3.78/1.21 | (equalish @ e_2 @ e_1)
% 3.78/1.21 | (equalish @ e_4 @ e_2)
% 3.78/1.21 | (equalish @ e_3 @ e_2)
% 3.78/1.21 | (equalish @ e_2 @ e_3)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_3 @ e_4 @ e_1)) &
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl2476, zip_derived_cl56])).
% 3.78/1.21 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_2])).
% 3.78/1.21 thf(zip_derived_cl17, plain, (~ (equalish @ e_2 @ e_1)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 3.78/1.21 thf(zip_derived_cl24, plain, (~ (equalish @ e_4 @ e_2)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 3.78/1.21 thf(zip_derived_cl21, plain, (~ (equalish @ e_3 @ e_2)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 3.78/1.21 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 3.78/1.21 thf('5', plain,
% 3.78/1.21 (~ ( (product1 @ e_4 @ e_1 @ e_2)) | ~ ( (product1 @ e_3 @ e_4 @ e_1)) |
% 3.78/1.21 ~ ( (product1 @ e_4 @ e_3 @ e_1))),
% 3.78/1.21 inference('demod', [status(thm)],
% 3.78/1.21 [zip_derived_cl2486, zip_derived_cl11, zip_derived_cl17,
% 3.78/1.21 zip_derived_cl24, zip_derived_cl21, zip_derived_cl18])).
% 3.78/1.21 thf('6', plain,
% 3.78/1.21 (( (product1 @ e_4 @ e_3 @ e_2)) | ( (product1 @ e_4 @ e_3 @ e_1))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl250])).
% 3.78/1.21 thf(zip_derived_cl805, plain,
% 3.78/1.21 (( (product1 @ e_4 @ e_1 @ e_2)) <= (( (product1 @ e_4 @ e_1 @ e_2)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl611])).
% 3.78/1.21 thf(zip_derived_cl256, plain,
% 3.78/1.21 (( (product1 @ e_4 @ e_3 @ e_2)) <= (( (product1 @ e_4 @ e_3 @ e_2)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl250])).
% 3.78/1.21 thf(zip_derived_cl28, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.78/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.78/1.21 | ~ (product1 @ X0 @ X3 @ X2)
% 3.78/1.21 | (equalish @ X1 @ X3))),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_right_cancellation])).
% 3.78/1.21 thf(zip_derived_cl291, plain,
% 3.78/1.21 ((![X0 : $i]: (~ (product1 @ e_4 @ X0 @ e_2) | (equalish @ e_3 @ X0)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl256, zip_derived_cl28])).
% 3.78/1.21 thf(zip_derived_cl861, plain,
% 3.78/1.21 (( (equalish @ e_3 @ e_1))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_2)) & ( (product1 @ e_4 @ e_1 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl805, zip_derived_cl291])).
% 3.78/1.21 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 3.78/1.21 thf(zip_derived_cl20, plain, (~ (equalish @ e_3 @ e_1)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 3.78/1.21 thf('7', plain,
% 3.78/1.21 (~ ( (product1 @ e_4 @ e_1 @ e_2)) | ~ ( (product1 @ e_4 @ e_3 @ e_2))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl861, zip_derived_cl20])).
% 3.78/1.21 thf('8', plain,
% 3.78/1.21 (~ ( (product1 @ e_3 @ e_4 @ e_1)) | ( (product1 @ e_4 @ e_1 @ e_2)) |
% 3.78/1.21 ( (product1 @ e_4 @ e_1 @ e_1))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl611])).
% 3.78/1.21 thf('9', plain,
% 3.78/1.21 (( (product1 @ e_3 @ e_4 @ e_2)) | ( (product1 @ e_3 @ e_4 @ e_1))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl382])).
% 3.78/1.21 thf('10', plain,
% 3.78/1.21 (( (product1 @ e_4 @ e_2 @ e_1)) | ~ ( (product1 @ e_3 @ e_4 @ e_2)) |
% 3.78/1.21 ( (product1 @ e_4 @ e_2 @ e_2))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl1162])).
% 3.78/1.21 thf(zip_derived_cl1657, plain,
% 3.78/1.21 (( (product1 @ e_3 @ e_2 @ e_1)) <= (( (product1 @ e_3 @ e_2 @ e_1)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl1653])).
% 3.78/1.21 thf(zip_derived_cl598, plain,
% 3.78/1.21 (( (product1 @ e_4 @ e_2 @ e_1)) <= (( (product1 @ e_4 @ e_2 @ e_1)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl588])).
% 3.78/1.21 thf(zip_derived_cl29, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.78/1.21 (~ (product1 @ X0 @ X1 @ X2)
% 3.78/1.21 | ~ (product1 @ X3 @ X1 @ X2)
% 3.78/1.21 | (equalish @ X0 @ X3))),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_left_cancellation])).
% 3.78/1.21 thf(zip_derived_cl602, plain,
% 3.78/1.21 ((![X0 : $i]: (~ (product1 @ X0 @ e_2 @ e_1) | (equalish @ e_4 @ X0)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_2 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl598, zip_derived_cl29])).
% 3.78/1.21 thf(zip_derived_cl1826, plain,
% 3.78/1.21 (( (equalish @ e_4 @ e_3))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_2 @ e_1)) & ( (product1 @ e_3 @ e_2 @ e_1)))),
% 3.78/1.21 inference('s_sup-', [status(thm)],
% 3.78/1.21 [zip_derived_cl1657, zip_derived_cl602])).
% 3.78/1.21 thf(zip_derived_cl25, plain, (~ (equalish @ e_4 @ e_3)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 3.78/1.21 thf('11', plain,
% 3.78/1.21 (~ ( (product1 @ e_3 @ e_2 @ e_1)) | ~ ( (product1 @ e_4 @ e_2 @ e_1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1826, zip_derived_cl25])).
% 3.78/1.21 thf(zip_derived_cl26, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (group_element @ X0)
% 3.78/1.21 | ~ (group_element @ X1)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_1)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_2)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_3)
% 3.78/1.21 | (product1 @ X0 @ X1 @ e_4))),
% 3.78/1.21 inference('cnf', [status(esa)], [product1_total_function1])).
% 3.78/1.21 thf(zip_derived_cl256, plain,
% 3.78/1.21 (( (product1 @ e_4 @ e_3 @ e_2)) <= (( (product1 @ e_4 @ e_3 @ e_2)))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl250])).
% 3.78/1.21 thf(zip_derived_cl36, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.78/1.21 ( (product2 @ X0 @ X1 @ X2)
% 3.78/1.21 | ~ (product1 @ X3 @ X2 @ X0)
% 3.78/1.21 | ~ (product1 @ X2 @ X1 @ X3))),
% 3.78/1.21 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.78/1.21 thf(zip_derived_cl293, plain,
% 3.78/1.21 ((![X0 : $i]:
% 3.78/1.21 ( (product2 @ e_2 @ X0 @ e_3) | ~ (product1 @ e_3 @ X0 @ e_4)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl256, zip_derived_cl36])).
% 3.78/1.21 thf(zip_derived_cl67, plain,
% 3.78/1.21 (![X0 : $i, X1 : $i]:
% 3.78/1.21 (~ (product2 @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl32])).
% 3.78/1.21 thf(zip_derived_cl314, plain,
% 3.78/1.21 (((~ (product1 @ e_3 @ e_2 @ e_4) | (equalish @ e_2 @ e_3)))
% 3.78/1.21 <= (( (product1 @ e_4 @ e_3 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl293, zip_derived_cl67])).
% 3.78/1.21 thf(zip_derived_cl18, plain, (~ (equalish @ e_2 @ e_3)),
% 3.78/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 3.78/1.21 thf(zip_derived_cl316, plain,
% 3.78/1.21 ((~ (product1 @ e_3 @ e_2 @ e_4)) <= (( (product1 @ e_4 @ e_3 @ e_2)))),
% 3.78/1.21 inference('demod', [status(thm)], [zip_derived_cl314, zip_derived_cl18])).
% 3.78/1.21 thf(zip_derived_cl319, plain,
% 3.78/1.21 ((( (product1 @ e_3 @ e_2 @ e_3)
% 3.78/1.21 | (product1 @ e_3 @ e_2 @ e_2)
% 3.78/1.21 | (product1 @ e_3 @ e_2 @ e_1)
% 3.78/1.21 | ~ (group_element @ e_2)
% 3.78/1.21 | ~ (group_element @ e_3))) <= (( (product1 @ e_4 @ e_3 @ e_2)))),
% 3.78/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl316])).
% 3.78/1.21 thf(zip_derived_cl11, plain, ( (group_element @ e_2)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_2])).
% 3.78/1.21 thf(zip_derived_cl12, plain, ( (group_element @ e_3)),
% 3.78/1.21 inference('cnf', [status(esa)], [element_3])).
% 3.78/1.21 thf(zip_derived_cl320, plain,
% 3.78/1.21 ((( (product1 @ e_3 @ e_2 @ e_3)
% 3.78/1.21 | (product1 @ e_3 @ e_2 @ e_2)
% 3.78/1.21 | (product1 @ e_3 @ e_2 @ e_1))) <= (( (product1 @ e_4 @ e_3 @ e_2)))),
% 3.78/1.21 inference('demod', [status(thm)],
% 3.78/1.21 [zip_derived_cl319, zip_derived_cl11, zip_derived_cl12])).
% 3.78/1.21 thf('12', plain, (( (product1 @ e_4 @ e_3 @ e_2))),
% 3.78/1.21 inference('sat_resolution*', [status(thm)],
% 3.78/1.21 ['8', '2', '9', '10', '3', '4', '5', '6'])).
% 3.78/1.21 thf(zip_derived_cl3206, plain,
% 3.78/1.21 (( (product1 @ e_3 @ e_2 @ e_3)
% 3.78/1.21 | (product1 @ e_3 @ e_2 @ e_2)
% 3.78/1.21 | (product1 @ e_3 @ e_2 @ e_1))),
% 3.78/1.21 inference('simpl_trail', [status(thm)], [zip_derived_cl320, '12'])).
% 3.78/1.21 thf('13', plain,
% 3.78/1.21 (( (product1 @ e_3 @ e_2 @ e_1)) | ( (product1 @ e_3 @ e_2 @ e_2)) |
% 3.78/1.21 ( (product1 @ e_3 @ e_2 @ e_3))),
% 3.78/1.21 inference('split', [status(esa)], [zip_derived_cl3206])).
% 3.78/1.21 thf(zip_derived_cl3212, plain, ($false),
% 3.78/1.21 inference('sat_resolution*', [status(thm)],
% 3.78/1.21 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 3.78/1.21 '13'])).
% 3.78/1.21
% 3.78/1.21 % SZS output end Refutation
% 3.78/1.21
% 3.78/1.21
% 3.78/1.21 % Terminating...
% 4.14/1.32 % Runner terminated.
% 4.14/1.33 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------