TSTP Solution File: GRP129-4.004 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP129-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.APblosHabp true
% Computer : n025.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 01:50:14 EDT 2023
% Result : Unsatisfiable 1.31s 1.21s
% Output : Refutation 1.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP129-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.APblosHabp true
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 20:28:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.22/0.65 % Total configuration time : 435
% 0.22/0.65 % Estimated wc time : 1092
% 0.22/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 1.01/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.01/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.01/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 1.01/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 1.31/1.21 % Solved by fo/fo1_av.sh.
% 1.31/1.21 % done 724 iterations in 0.444s
% 1.31/1.21 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.31/1.21 % SZS output start Refutation
% 1.31/1.21 thf(e_1_type, type, e_1: $i).
% 1.31/1.21 thf(product_type, type, product: $i > $i > $i > $o).
% 1.31/1.21 thf(e_2_type, type, e_2: $i).
% 1.31/1.21 thf(group_element_type, type, group_element: $i > $o).
% 1.31/1.21 thf(e_4_type, type, e_4: $i).
% 1.31/1.21 thf(equalish_type, type, equalish: $i > $i > $o).
% 1.31/1.21 thf(e_3_type, type, e_3: $i).
% 1.31/1.21 thf(row_surjectivity, axiom,
% 1.31/1.21 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 1.31/1.21 ( product @ e_1 @ X @ Y ) | ( product @ e_2 @ X @ Y ) |
% 1.31/1.21 ( product @ e_3 @ X @ Y ) | ( product @ e_4 @ X @ Y ))).
% 1.31/1.21 thf(zip_derived_cl0, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | ~ (group_element @ X1)
% 1.31/1.21 | (product @ e_1 @ X0 @ X1)
% 1.31/1.21 | (product @ e_2 @ X0 @ X1)
% 1.31/1.21 | (product @ e_3 @ X0 @ X1)
% 1.31/1.21 | (product @ e_4 @ X0 @ X1))),
% 1.31/1.21 inference('cnf', [status(esa)], [row_surjectivity])).
% 1.31/1.21 thf(column_surjectivity, axiom,
% 1.31/1.21 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 1.31/1.21 ( product @ X @ e_1 @ Y ) | ( product @ X @ e_2 @ Y ) |
% 1.31/1.21 ( product @ X @ e_3 @ Y ) | ( product @ X @ e_4 @ Y ))).
% 1.31/1.21 thf(zip_derived_cl1, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | ~ (group_element @ X1)
% 1.31/1.21 | (product @ X0 @ e_1 @ X1)
% 1.31/1.21 | (product @ X0 @ e_2 @ X1)
% 1.31/1.21 | (product @ X0 @ e_3 @ X1)
% 1.31/1.21 | (product @ X0 @ e_4 @ X1))),
% 1.31/1.21 inference('cnf', [status(esa)], [column_surjectivity])).
% 1.31/1.21 thf(qg3_1, conjecture,
% 1.31/1.21 (~( ( ~( product @ X @ Z1 @ Z2 ) ) | ( ~( product @ Z1 @ Y @ Z2 ) ) |
% 1.31/1.21 ( product @ Y @ X @ Z1 ) ))).
% 1.31/1.21 thf(zf_stmt_0, negated_conjecture,
% 1.31/1.21 (( ~( product @ X @ Z1 @ Z2 ) ) | ( ~( product @ Z1 @ Y @ Z2 ) ) |
% 1.31/1.21 ( product @ Y @ X @ Z1 )),
% 1.31/1.21 inference('cnf.neg', [status(esa)], [qg3_1])).
% 1.31/1.21 thf(zip_derived_cl2, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X1 @ X3 @ X2)
% 1.31/1.21 | (product @ X3 @ X0 @ X1))),
% 1.31/1.21 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.31/1.21 thf(zip_derived_cl42, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 ( (product @ X1 @ X1 @ X1) | ~ (product @ X1 @ X1 @ X0))),
% 1.31/1.21 inference('eq_fact', [status(thm)], [zip_derived_cl2])).
% 1.31/1.21 thf(zip_derived_cl44, plain,
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 ( (product @ e_4 @ e_3 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.21 | ~ (group_element @ X0)
% 1.31/1.21 | ~ (group_element @ e_4)
% 1.31/1.21 | (product @ e_4 @ e_4 @ e_4))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl42])).
% 1.31/1.21 thf(element_4, axiom, (group_element @ e_4)).
% 1.31/1.21 thf(zip_derived_cl7, plain, ( (group_element @ e_4)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_4])).
% 1.31/1.21 thf(zip_derived_cl47, plain,
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 ( (product @ e_4 @ e_3 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.21 | ~ (group_element @ X0)
% 1.31/1.21 | (product @ e_4 @ e_4 @ e_4))),
% 1.31/1.21 inference('demod', [status(thm)], [zip_derived_cl44, zip_derived_cl7])).
% 1.31/1.21 thf(zip_derived_cl511, plain,
% 1.31/1.21 (( (product @ e_4 @ e_4 @ e_4)) <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.21 inference('split', [status(esa)], [zip_derived_cl47])).
% 1.31/1.21 thf(product_total_function2, axiom,
% 1.31/1.21 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 1.31/1.21 ( equalish @ W @ Z ))).
% 1.31/1.21 thf(zip_derived_cl21, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X0 @ X1 @ X3)
% 1.31/1.21 | (equalish @ X2 @ X3))),
% 1.31/1.21 inference('cnf', [status(esa)], [product_total_function2])).
% 1.31/1.21 thf(zip_derived_cl545, plain,
% 1.31/1.21 ((![X0 : $i]: (~ (product @ e_4 @ e_4 @ X0) | (equalish @ e_4 @ X0)))
% 1.31/1.21 <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl511, zip_derived_cl21])).
% 1.31/1.21 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 1.31/1.21 thf(zip_derived_cl17, plain, (~ (equalish @ e_4 @ e_1)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 1.31/1.21 thf(zip_derived_cl633, plain,
% 1.31/1.21 ((~ (product @ e_4 @ e_4 @ e_1)) <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl545, zip_derived_cl17])).
% 1.31/1.21 thf(zip_derived_cl639, plain,
% 1.31/1.21 ((( (product @ e_3 @ e_4 @ e_1)
% 1.31/1.21 | (product @ e_2 @ e_4 @ e_1)
% 1.31/1.21 | (product @ e_1 @ e_4 @ e_1)
% 1.31/1.21 | ~ (group_element @ e_1)
% 1.31/1.21 | ~ (group_element @ e_4))) <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl633])).
% 1.31/1.21 thf(element_1, axiom, (group_element @ e_1)).
% 1.31/1.21 thf(zip_derived_cl4, plain, ( (group_element @ e_1)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_1])).
% 1.31/1.21 thf(product_total_function1, axiom,
% 1.31/1.21 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 1.31/1.21 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 1.31/1.21 ( product @ X @ Y @ e_3 ) | ( product @ X @ Y @ e_4 ))).
% 1.31/1.21 thf(zip_derived_cl20, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | ~ (group_element @ X1)
% 1.31/1.21 | (product @ X0 @ X1 @ e_1)
% 1.31/1.21 | (product @ X0 @ X1 @ e_2)
% 1.31/1.21 | (product @ X0 @ X1 @ e_3)
% 1.31/1.21 | (product @ X0 @ X1 @ e_4))),
% 1.31/1.21 inference('cnf', [status(esa)], [product_total_function1])).
% 1.31/1.21 thf(zip_derived_cl20, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | ~ (group_element @ X1)
% 1.31/1.21 | (product @ X0 @ X1 @ e_1)
% 1.31/1.21 | (product @ X0 @ X1 @ e_2)
% 1.31/1.21 | (product @ X0 @ X1 @ e_3)
% 1.31/1.21 | (product @ X0 @ X1 @ e_4))),
% 1.31/1.21 inference('cnf', [status(esa)], [product_total_function1])).
% 1.31/1.21 thf(zip_derived_cl42, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 ( (product @ X1 @ X1 @ X1) | ~ (product @ X1 @ X1 @ X0))),
% 1.31/1.21 inference('eq_fact', [status(thm)], [zip_derived_cl2])).
% 1.31/1.21 thf(zip_derived_cl61, plain,
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 ( (product @ X0 @ X0 @ e_3)
% 1.31/1.21 | (product @ X0 @ X0 @ e_2)
% 1.31/1.21 | (product @ X0 @ X0 @ e_1)
% 1.31/1.21 | ~ (group_element @ X0)
% 1.31/1.21 | ~ (group_element @ X0)
% 1.31/1.21 | (product @ X0 @ X0 @ X0))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl42])).
% 1.31/1.21 thf(zip_derived_cl62, plain,
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 ( (product @ X0 @ X0 @ X0)
% 1.31/1.21 | ~ (group_element @ X0)
% 1.31/1.21 | (product @ X0 @ X0 @ e_1)
% 1.31/1.21 | (product @ X0 @ X0 @ e_2)
% 1.31/1.21 | (product @ X0 @ X0 @ e_3))),
% 1.31/1.21 inference('simplify', [status(thm)], [zip_derived_cl61])).
% 1.31/1.21 thf(zip_derived_cl42, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 ( (product @ X1 @ X1 @ X1) | ~ (product @ X1 @ X1 @ X0))),
% 1.31/1.21 inference('eq_fact', [status(thm)], [zip_derived_cl2])).
% 1.31/1.21 thf(zip_derived_cl68, plain,
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 ( (product @ X0 @ X0 @ e_3)
% 1.31/1.21 | (product @ X0 @ X0 @ e_2)
% 1.31/1.21 | ~ (group_element @ X0)
% 1.31/1.21 | (product @ X0 @ X0 @ X0))),
% 1.31/1.21 inference('clc', [status(thm)], [zip_derived_cl62, zip_derived_cl42])).
% 1.31/1.21 thf(zip_derived_cl42, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 ( (product @ X1 @ X1 @ X1) | ~ (product @ X1 @ X1 @ X0))),
% 1.31/1.21 inference('eq_fact', [status(thm)], [zip_derived_cl2])).
% 1.31/1.21 thf(zip_derived_cl69, plain,
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 ( (product @ X0 @ X0 @ X0)
% 1.31/1.21 | ~ (group_element @ X0)
% 1.31/1.21 | (product @ X0 @ X0 @ e_2))),
% 1.31/1.21 inference('clc', [status(thm)], [zip_derived_cl68, zip_derived_cl42])).
% 1.31/1.21 thf(zip_derived_cl42, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 ( (product @ X1 @ X1 @ X1) | ~ (product @ X1 @ X1 @ X0))),
% 1.31/1.21 inference('eq_fact', [status(thm)], [zip_derived_cl2])).
% 1.31/1.21 thf(zip_derived_cl70, plain,
% 1.31/1.21 (![X0 : $i]: (~ (group_element @ X0) | (product @ X0 @ X0 @ X0))),
% 1.31/1.21 inference('clc', [status(thm)], [zip_derived_cl69, zip_derived_cl42])).
% 1.31/1.21 thf(zip_derived_cl21, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X0 @ X1 @ X3)
% 1.31/1.21 | (equalish @ X2 @ X3))),
% 1.31/1.21 inference('cnf', [status(esa)], [product_total_function2])).
% 1.31/1.21 thf(zip_derived_cl73, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | ~ (product @ X0 @ X0 @ X1)
% 1.31/1.21 | (equalish @ X0 @ X1))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl70, zip_derived_cl21])).
% 1.31/1.21 thf(zip_derived_cl82, plain,
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 ( (product @ X0 @ X0 @ e_3)
% 1.31/1.21 | (product @ X0 @ X0 @ e_2)
% 1.31/1.21 | (product @ X0 @ X0 @ e_1)
% 1.31/1.21 | ~ (group_element @ X0)
% 1.31/1.21 | ~ (group_element @ X0)
% 1.31/1.21 | ~ (group_element @ X0)
% 1.31/1.21 | (equalish @ X0 @ e_4))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl73])).
% 1.31/1.21 thf(zip_derived_cl86, plain,
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 ( (equalish @ X0 @ e_4)
% 1.31/1.21 | ~ (group_element @ X0)
% 1.31/1.21 | (product @ X0 @ X0 @ e_1)
% 1.31/1.21 | (product @ X0 @ X0 @ e_2)
% 1.31/1.21 | (product @ X0 @ X0 @ e_3))),
% 1.31/1.21 inference('simplify', [status(thm)], [zip_derived_cl82])).
% 1.31/1.21 thf(zip_derived_cl132, plain,
% 1.31/1.21 (( (equalish @ e_1 @ e_4)
% 1.31/1.21 | (product @ e_1 @ e_1 @ e_1)
% 1.31/1.21 | (product @ e_1 @ e_1 @ e_2)
% 1.31/1.21 | (product @ e_1 @ e_1 @ e_3))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl86])).
% 1.31/1.21 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 1.31/1.21 thf(zip_derived_cl10, plain, (~ (equalish @ e_1 @ e_4)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 1.31/1.21 thf(zip_derived_cl140, plain,
% 1.31/1.21 (( (product @ e_1 @ e_1 @ e_3)
% 1.31/1.21 | (product @ e_1 @ e_1 @ e_2)
% 1.31/1.21 | (product @ e_1 @ e_1 @ e_1))),
% 1.31/1.21 inference('clc', [status(thm)], [zip_derived_cl132, zip_derived_cl10])).
% 1.31/1.21 thf(zip_derived_cl42, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 ( (product @ X1 @ X1 @ X1) | ~ (product @ X1 @ X1 @ X0))),
% 1.31/1.21 inference('eq_fact', [status(thm)], [zip_derived_cl2])).
% 1.31/1.21 thf(zip_derived_cl141, plain,
% 1.31/1.21 (( (product @ e_1 @ e_1 @ e_1) | (product @ e_1 @ e_1 @ e_2))),
% 1.31/1.21 inference('clc', [status(thm)], [zip_derived_cl140, zip_derived_cl42])).
% 1.31/1.21 thf(zip_derived_cl42, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 ( (product @ X1 @ X1 @ X1) | ~ (product @ X1 @ X1 @ X0))),
% 1.31/1.21 inference('eq_fact', [status(thm)], [zip_derived_cl2])).
% 1.31/1.21 thf(zip_derived_cl142, plain, ( (product @ e_1 @ e_1 @ e_1)),
% 1.31/1.21 inference('clc', [status(thm)], [zip_derived_cl141, zip_derived_cl42])).
% 1.31/1.21 thf(product_right_cancellation, axiom,
% 1.31/1.21 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 1.31/1.21 ( equalish @ W @ Z ))).
% 1.31/1.21 thf(zip_derived_cl22, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X0 @ X3 @ X2)
% 1.31/1.21 | (equalish @ X1 @ X3))),
% 1.31/1.21 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.31/1.21 thf(zip_derived_cl146, plain,
% 1.31/1.21 (![X0 : $i]: (~ (product @ e_1 @ X0 @ e_1) | (equalish @ e_1 @ X0))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl22])).
% 1.31/1.21 thf(zip_derived_cl10, plain, (~ (equalish @ e_1 @ e_4)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 1.31/1.21 thf(zip_derived_cl193, plain, (~ (product @ e_1 @ e_4 @ e_1)),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl146, zip_derived_cl10])).
% 1.31/1.21 thf(zip_derived_cl4, plain, ( (group_element @ e_1)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_1])).
% 1.31/1.21 thf(zip_derived_cl7, plain, ( (group_element @ e_4)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_4])).
% 1.31/1.21 thf(zip_derived_cl641, plain,
% 1.31/1.21 ((( (product @ e_3 @ e_4 @ e_1) | (product @ e_2 @ e_4 @ e_1)))
% 1.31/1.21 <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.21 inference('demod', [status(thm)],
% 1.31/1.21 [zip_derived_cl639, zip_derived_cl193, zip_derived_cl4,
% 1.31/1.21 zip_derived_cl7])).
% 1.31/1.21 thf(zip_derived_cl1, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | ~ (group_element @ X1)
% 1.31/1.21 | (product @ X0 @ e_1 @ X1)
% 1.31/1.21 | (product @ X0 @ e_2 @ X1)
% 1.31/1.21 | (product @ X0 @ e_3 @ X1)
% 1.31/1.21 | (product @ X0 @ e_4 @ X1))),
% 1.31/1.21 inference('cnf', [status(esa)], [column_surjectivity])).
% 1.31/1.21 thf(zip_derived_cl0, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | ~ (group_element @ X1)
% 1.31/1.21 | (product @ e_1 @ X0 @ X1)
% 1.31/1.21 | (product @ e_2 @ X0 @ X1)
% 1.31/1.21 | (product @ e_3 @ X0 @ X1)
% 1.31/1.21 | (product @ e_4 @ X0 @ X1))),
% 1.31/1.21 inference('cnf', [status(esa)], [row_surjectivity])).
% 1.31/1.21 thf(zip_derived_cl42, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 ( (product @ X1 @ X1 @ X1) | ~ (product @ X1 @ X1 @ X0))),
% 1.31/1.21 inference('eq_fact', [status(thm)], [zip_derived_cl2])).
% 1.31/1.21 thf(zip_derived_cl45, plain,
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 ( (product @ e_3 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | ~ (group_element @ X0)
% 1.31/1.21 | ~ (group_element @ e_4)
% 1.31/1.21 | (product @ e_4 @ e_4 @ e_4))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl42])).
% 1.31/1.21 thf(zip_derived_cl7, plain, ( (group_element @ e_4)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_4])).
% 1.31/1.21 thf(zip_derived_cl48, plain,
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 ( (product @ e_3 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | ~ (group_element @ X0)
% 1.31/1.21 | (product @ e_4 @ e_4 @ e_4))),
% 1.31/1.21 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl7])).
% 1.31/1.21 thf(zip_derived_cl750, plain,
% 1.31/1.21 ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0)))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0))))),
% 1.31/1.21 inference('split', [status(esa)], [zip_derived_cl48])).
% 1.31/1.21 thf(zip_derived_cl510, plain,
% 1.31/1.21 ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_3 @ X0)))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_3 @ X0))))),
% 1.31/1.21 inference('split', [status(esa)], [zip_derived_cl47])).
% 1.31/1.21 thf(zip_derived_cl70, plain,
% 1.31/1.21 (![X0 : $i]: (~ (group_element @ X0) | (product @ X0 @ X0 @ X0))),
% 1.31/1.21 inference('clc', [status(thm)], [zip_derived_cl69, zip_derived_cl42])).
% 1.31/1.21 thf(qg3, conjecture,
% 1.31/1.21 (~( ( product @ Z1 @ Y @ Z2 ) | ( ~( product @ X @ Z1 @ Z2 ) ) |
% 1.31/1.21 ( ~( product @ Y @ X @ Z1 ) ) ))).
% 1.31/1.21 thf(zf_stmt_1, negated_conjecture,
% 1.31/1.21 (( product @ Z1 @ Y @ Z2 ) | ( ~( product @ X @ Z1 @ Z2 ) ) |
% 1.31/1.21 ( ~( product @ Y @ X @ Z1 ) )),
% 1.31/1.21 inference('cnf.neg', [status(esa)], [qg3])).
% 1.31/1.21 thf(zip_derived_cl24, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 ( (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X3 @ X0 @ X2)
% 1.31/1.21 | ~ (product @ X1 @ X3 @ X0))),
% 1.31/1.21 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.31/1.21 thf(zip_derived_cl76, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ X0 @ X1 @ X0)
% 1.31/1.21 | ~ (product @ X1 @ X0 @ X0))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl70, zip_derived_cl24])).
% 1.31/1.21 thf(zip_derived_cl526, plain,
% 1.31/1.21 ((( (product @ e_4 @ e_2 @ e_3)
% 1.31/1.21 | (product @ e_4 @ e_1 @ e_3)
% 1.31/1.21 | ~ (group_element @ e_3)
% 1.31/1.21 | ~ (group_element @ e_3)
% 1.31/1.21 | (product @ e_3 @ e_4 @ e_3)))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_3 @ X0))))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl510, zip_derived_cl76])).
% 1.31/1.21 thf(element_3, axiom, (group_element @ e_3)).
% 1.31/1.21 thf(zip_derived_cl6, plain, ( (group_element @ e_3)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_3])).
% 1.31/1.21 thf(zip_derived_cl6, plain, ( (group_element @ e_3)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_3])).
% 1.31/1.21 thf(zip_derived_cl6, plain, ( (group_element @ e_3)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_3])).
% 1.31/1.21 thf(zip_derived_cl86, plain,
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 ( (equalish @ X0 @ e_4)
% 1.31/1.21 | ~ (group_element @ X0)
% 1.31/1.21 | (product @ X0 @ X0 @ e_1)
% 1.31/1.21 | (product @ X0 @ X0 @ e_2)
% 1.31/1.21 | (product @ X0 @ X0 @ e_3))),
% 1.31/1.21 inference('simplify', [status(thm)], [zip_derived_cl82])).
% 1.31/1.21 thf(zip_derived_cl134, plain,
% 1.31/1.21 (( (equalish @ e_3 @ e_4)
% 1.31/1.21 | (product @ e_3 @ e_3 @ e_1)
% 1.31/1.21 | (product @ e_3 @ e_3 @ e_2)
% 1.31/1.21 | (product @ e_3 @ e_3 @ e_3))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl86])).
% 1.31/1.21 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 1.31/1.21 thf(zip_derived_cl16, plain, (~ (equalish @ e_3 @ e_4)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 1.31/1.21 thf(zip_derived_cl284, plain,
% 1.31/1.21 (( (product @ e_3 @ e_3 @ e_3)
% 1.31/1.21 | (product @ e_3 @ e_3 @ e_2)
% 1.31/1.21 | (product @ e_3 @ e_3 @ e_1))),
% 1.31/1.21 inference('clc', [status(thm)], [zip_derived_cl134, zip_derived_cl16])).
% 1.31/1.21 thf(zip_derived_cl42, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 ( (product @ X1 @ X1 @ X1) | ~ (product @ X1 @ X1 @ X0))),
% 1.31/1.21 inference('eq_fact', [status(thm)], [zip_derived_cl2])).
% 1.31/1.21 thf(zip_derived_cl285, plain,
% 1.31/1.21 (( (product @ e_3 @ e_3 @ e_1) | (product @ e_3 @ e_3 @ e_3))),
% 1.31/1.21 inference('clc', [status(thm)], [zip_derived_cl284, zip_derived_cl42])).
% 1.31/1.21 thf(zip_derived_cl42, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 ( (product @ X1 @ X1 @ X1) | ~ (product @ X1 @ X1 @ X0))),
% 1.31/1.21 inference('eq_fact', [status(thm)], [zip_derived_cl2])).
% 1.31/1.21 thf(zip_derived_cl286, plain, ( (product @ e_3 @ e_3 @ e_3)),
% 1.31/1.21 inference('clc', [status(thm)], [zip_derived_cl285, zip_derived_cl42])).
% 1.31/1.21 thf(zip_derived_cl22, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X0 @ X3 @ X2)
% 1.31/1.21 | (equalish @ X1 @ X3))),
% 1.31/1.21 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.31/1.21 thf(zip_derived_cl290, plain,
% 1.31/1.21 (![X0 : $i]: (~ (product @ e_3 @ X0 @ e_3) | (equalish @ e_3 @ X0))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl286, zip_derived_cl22])).
% 1.31/1.21 thf(zip_derived_cl16, plain, (~ (equalish @ e_3 @ e_4)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 1.31/1.21 thf(zip_derived_cl406, plain, (~ (product @ e_3 @ e_4 @ e_3)),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl290, zip_derived_cl16])).
% 1.31/1.21 thf(zip_derived_cl538, plain,
% 1.31/1.21 ((( (product @ e_4 @ e_2 @ e_3) | (product @ e_4 @ e_1 @ e_3)))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_3 @ X0))))),
% 1.31/1.21 inference('demod', [status(thm)],
% 1.31/1.21 [zip_derived_cl526, zip_derived_cl6, zip_derived_cl6,
% 1.31/1.21 zip_derived_cl406])).
% 1.31/1.21 thf(zip_derived_cl1009, plain,
% 1.31/1.21 (( (product @ e_4 @ e_1 @ e_3)) <= (( (product @ e_4 @ e_1 @ e_3)))),
% 1.31/1.21 inference('split', [status(esa)], [zip_derived_cl538])).
% 1.31/1.21 thf(zip_derived_cl24, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 ( (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X3 @ X0 @ X2)
% 1.31/1.21 | ~ (product @ X1 @ X3 @ X0))),
% 1.31/1.21 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.31/1.21 thf(zip_derived_cl1061, plain,
% 1.31/1.21 ((![X0 : $i]:
% 1.31/1.21 ( (product @ e_1 @ X0 @ e_3) | ~ (product @ X0 @ e_4 @ e_1)))
% 1.31/1.21 <= (( (product @ e_4 @ e_1 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1009, zip_derived_cl24])).
% 1.31/1.21 thf(zip_derived_cl1667, plain,
% 1.31/1.21 ((( (product @ e_2 @ e_4 @ e_1)
% 1.31/1.21 | (product @ e_1 @ e_4 @ e_1)
% 1.31/1.21 | ~ (group_element @ e_1)
% 1.31/1.21 | (product @ e_1 @ e_3 @ e_3)))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0))) &
% 1.31/1.21 ( (product @ e_4 @ e_1 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)],
% 1.31/1.21 [zip_derived_cl750, zip_derived_cl1061])).
% 1.31/1.21 thf(zip_derived_cl193, plain, (~ (product @ e_1 @ e_4 @ e_1)),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl146, zip_derived_cl10])).
% 1.31/1.21 thf(zip_derived_cl4, plain, ( (group_element @ e_1)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_1])).
% 1.31/1.21 thf(zip_derived_cl286, plain, ( (product @ e_3 @ e_3 @ e_3)),
% 1.31/1.21 inference('clc', [status(thm)], [zip_derived_cl285, zip_derived_cl42])).
% 1.31/1.21 thf(product_left_cancellation, axiom,
% 1.31/1.21 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 1.31/1.21 ( equalish @ W @ Z ))).
% 1.31/1.21 thf(zip_derived_cl23, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X3 @ X1 @ X2)
% 1.31/1.21 | (equalish @ X0 @ X3))),
% 1.31/1.21 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.31/1.21 thf(zip_derived_cl291, plain,
% 1.31/1.21 (![X0 : $i]: (~ (product @ X0 @ e_3 @ e_3) | (equalish @ e_3 @ X0))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl286, zip_derived_cl23])).
% 1.31/1.21 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 1.31/1.21 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_1)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 1.31/1.21 thf(zip_derived_cl453, plain, (~ (product @ e_1 @ e_3 @ e_3)),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl291, zip_derived_cl14])).
% 1.31/1.21 thf(zip_derived_cl1670, plain,
% 1.31/1.21 (( (product @ e_2 @ e_4 @ e_1))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0))) &
% 1.31/1.21 ( (product @ e_4 @ e_1 @ e_3)))),
% 1.31/1.21 inference('demod', [status(thm)],
% 1.31/1.21 [zip_derived_cl1667, zip_derived_cl193, zip_derived_cl4,
% 1.31/1.21 zip_derived_cl453])).
% 1.31/1.21 thf(zip_derived_cl21, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X0 @ X1 @ X3)
% 1.31/1.21 | (equalish @ X2 @ X3))),
% 1.31/1.21 inference('cnf', [status(esa)], [product_total_function2])).
% 1.31/1.21 thf(zip_derived_cl1676, plain,
% 1.31/1.21 ((![X0 : $i]: (~ (product @ e_2 @ e_4 @ X0) | (equalish @ e_1 @ X0)))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0))) &
% 1.31/1.21 ( (product @ e_4 @ e_1 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1670, zip_derived_cl21])).
% 1.31/1.21 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 1.31/1.21 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_3)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 1.31/1.21 thf(zip_derived_cl1755, plain,
% 1.31/1.21 ((~ (product @ e_2 @ e_4 @ e_3))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0))) &
% 1.31/1.21 ( (product @ e_4 @ e_1 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1676, zip_derived_cl9])).
% 1.31/1.21 thf(zip_derived_cl1807, plain,
% 1.31/1.21 ((( (product @ e_2 @ e_3 @ e_3)
% 1.31/1.21 | (product @ e_2 @ e_2 @ e_3)
% 1.31/1.21 | (product @ e_2 @ e_1 @ e_3)
% 1.31/1.21 | ~ (group_element @ e_3)
% 1.31/1.21 | ~ (group_element @ e_2)))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0))) &
% 1.31/1.21 ( (product @ e_4 @ e_1 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl1755])).
% 1.31/1.21 thf(element_2, axiom, (group_element @ e_2)).
% 1.31/1.21 thf(zip_derived_cl5, plain, ( (group_element @ e_2)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_2])).
% 1.31/1.21 thf(zip_derived_cl86, plain,
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 ( (equalish @ X0 @ e_4)
% 1.31/1.21 | ~ (group_element @ X0)
% 1.31/1.21 | (product @ X0 @ X0 @ e_1)
% 1.31/1.21 | (product @ X0 @ X0 @ e_2)
% 1.31/1.21 | (product @ X0 @ X0 @ e_3))),
% 1.31/1.21 inference('simplify', [status(thm)], [zip_derived_cl82])).
% 1.31/1.21 thf(zip_derived_cl133, plain,
% 1.31/1.21 (( (equalish @ e_2 @ e_4)
% 1.31/1.21 | (product @ e_2 @ e_2 @ e_1)
% 1.31/1.21 | (product @ e_2 @ e_2 @ e_2)
% 1.31/1.21 | (product @ e_2 @ e_2 @ e_3))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl86])).
% 1.31/1.21 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 1.31/1.21 thf(zip_derived_cl13, plain, (~ (equalish @ e_2 @ e_4)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 1.31/1.21 thf(zip_derived_cl209, plain,
% 1.31/1.21 (( (product @ e_2 @ e_2 @ e_3)
% 1.31/1.21 | (product @ e_2 @ e_2 @ e_2)
% 1.31/1.21 | (product @ e_2 @ e_2 @ e_1))),
% 1.31/1.21 inference('clc', [status(thm)], [zip_derived_cl133, zip_derived_cl13])).
% 1.31/1.21 thf(zip_derived_cl42, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 ( (product @ X1 @ X1 @ X1) | ~ (product @ X1 @ X1 @ X0))),
% 1.31/1.21 inference('eq_fact', [status(thm)], [zip_derived_cl2])).
% 1.31/1.21 thf(zip_derived_cl210, plain,
% 1.31/1.21 (( (product @ e_2 @ e_2 @ e_1) | (product @ e_2 @ e_2 @ e_2))),
% 1.31/1.21 inference('clc', [status(thm)], [zip_derived_cl209, zip_derived_cl42])).
% 1.31/1.21 thf(zip_derived_cl42, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 ( (product @ X1 @ X1 @ X1) | ~ (product @ X1 @ X1 @ X0))),
% 1.31/1.21 inference('eq_fact', [status(thm)], [zip_derived_cl2])).
% 1.31/1.21 thf(zip_derived_cl211, plain, ( (product @ e_2 @ e_2 @ e_2)),
% 1.31/1.21 inference('clc', [status(thm)], [zip_derived_cl210, zip_derived_cl42])).
% 1.31/1.21 thf(zip_derived_cl21, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X0 @ X1 @ X3)
% 1.31/1.21 | (equalish @ X2 @ X3))),
% 1.31/1.21 inference('cnf', [status(esa)], [product_total_function2])).
% 1.31/1.21 thf(zip_derived_cl214, plain,
% 1.31/1.21 (![X0 : $i]: (~ (product @ e_2 @ e_2 @ X0) | (equalish @ e_2 @ X0))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl211, zip_derived_cl21])).
% 1.31/1.21 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 1.31/1.21 thf(zip_derived_cl12, plain, (~ (equalish @ e_2 @ e_3)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 1.31/1.21 thf(zip_derived_cl237, plain, (~ (product @ e_2 @ e_2 @ e_3)),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl214, zip_derived_cl12])).
% 1.31/1.21 thf(zip_derived_cl1009, plain,
% 1.31/1.21 (( (product @ e_4 @ e_1 @ e_3)) <= (( (product @ e_4 @ e_1 @ e_3)))),
% 1.31/1.21 inference('split', [status(esa)], [zip_derived_cl538])).
% 1.31/1.21 thf(zip_derived_cl23, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X3 @ X1 @ X2)
% 1.31/1.21 | (equalish @ X0 @ X3))),
% 1.31/1.21 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.31/1.21 thf(zip_derived_cl1059, plain,
% 1.31/1.21 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_3) | (equalish @ e_4 @ X0)))
% 1.31/1.21 <= (( (product @ e_4 @ e_1 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1009, zip_derived_cl23])).
% 1.31/1.21 thf(e_4_is_not_e_2, axiom, (~( equalish @ e_4 @ e_2 ))).
% 1.31/1.21 thf(zip_derived_cl18, plain, (~ (equalish @ e_4 @ e_2)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 1.31/1.21 thf(zip_derived_cl1265, plain,
% 1.31/1.21 ((~ (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_4 @ e_1 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1059, zip_derived_cl18])).
% 1.31/1.21 thf(zip_derived_cl6, plain, ( (group_element @ e_3)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_3])).
% 1.31/1.21 thf(zip_derived_cl5, plain, ( (group_element @ e_2)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_2])).
% 1.31/1.21 thf(zip_derived_cl1808, plain,
% 1.31/1.21 (( (product @ e_2 @ e_3 @ e_3))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0))) &
% 1.31/1.21 ( (product @ e_4 @ e_1 @ e_3)))),
% 1.31/1.21 inference('demod', [status(thm)],
% 1.31/1.21 [zip_derived_cl1807, zip_derived_cl237, zip_derived_cl1265,
% 1.31/1.21 zip_derived_cl6, zip_derived_cl5])).
% 1.31/1.21 thf(zip_derived_cl291, plain,
% 1.31/1.21 (![X0 : $i]: (~ (product @ X0 @ e_3 @ e_3) | (equalish @ e_3 @ X0))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl286, zip_derived_cl23])).
% 1.31/1.21 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 1.31/1.21 thf(zip_derived_cl15, plain, (~ (equalish @ e_3 @ e_2)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 1.31/1.21 thf(zip_derived_cl454, plain, (~ (product @ e_2 @ e_3 @ e_3)),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl291, zip_derived_cl15])).
% 1.31/1.21 thf('0', plain,
% 1.31/1.21 (~
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0))) |
% 1.31/1.21 ~ ( (product @ e_4 @ e_1 @ e_3))),
% 1.31/1.21 inference('s_sup-', [status(thm)],
% 1.31/1.21 [zip_derived_cl1808, zip_derived_cl454])).
% 1.31/1.21 thf(zip_derived_cl510, plain,
% 1.31/1.21 ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_3 @ X0)))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_3 @ X0))))),
% 1.31/1.21 inference('split', [status(esa)], [zip_derived_cl47])).
% 1.31/1.21 thf(zip_derived_cl750, plain,
% 1.31/1.21 ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0)))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0))))),
% 1.31/1.21 inference('split', [status(esa)], [zip_derived_cl48])).
% 1.31/1.21 thf(zip_derived_cl0, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | ~ (group_element @ X1)
% 1.31/1.21 | (product @ e_1 @ X0 @ X1)
% 1.31/1.21 | (product @ e_2 @ X0 @ X1)
% 1.31/1.21 | (product @ e_3 @ X0 @ X1)
% 1.31/1.21 | (product @ e_4 @ X0 @ X1))),
% 1.31/1.21 inference('cnf', [status(esa)], [row_surjectivity])).
% 1.31/1.21 thf(zip_derived_cl1008, plain,
% 1.31/1.21 (( (product @ e_4 @ e_2 @ e_3)) <= (( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('split', [status(esa)], [zip_derived_cl538])).
% 1.31/1.21 thf(zip_derived_cl21, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X0 @ X1 @ X3)
% 1.31/1.21 | (equalish @ X2 @ X3))),
% 1.31/1.21 inference('cnf', [status(esa)], [product_total_function2])).
% 1.31/1.21 thf(zip_derived_cl1012, plain,
% 1.31/1.21 ((![X0 : $i]: (~ (product @ e_4 @ e_2 @ X0) | (equalish @ e_3 @ X0)))
% 1.31/1.21 <= (( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1008, zip_derived_cl21])).
% 1.31/1.21 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_1)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 1.31/1.21 thf(zip_derived_cl1080, plain,
% 1.31/1.21 ((~ (product @ e_4 @ e_2 @ e_1)) <= (( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1012, zip_derived_cl14])).
% 1.31/1.21 thf(zip_derived_cl1084, plain,
% 1.31/1.21 ((( (product @ e_3 @ e_2 @ e_1)
% 1.31/1.21 | (product @ e_2 @ e_2 @ e_1)
% 1.31/1.21 | (product @ e_1 @ e_2 @ e_1)
% 1.31/1.21 | ~ (group_element @ e_1)
% 1.31/1.21 | ~ (group_element @ e_2))) <= (( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl1080])).
% 1.31/1.21 thf(zip_derived_cl214, plain,
% 1.31/1.21 (![X0 : $i]: (~ (product @ e_2 @ e_2 @ X0) | (equalish @ e_2 @ X0))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl211, zip_derived_cl21])).
% 1.31/1.21 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 1.31/1.21 thf(zip_derived_cl11, plain, (~ (equalish @ e_2 @ e_1)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 1.31/1.21 thf(zip_derived_cl236, plain, (~ (product @ e_2 @ e_2 @ e_1)),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl214, zip_derived_cl11])).
% 1.31/1.21 thf(zip_derived_cl146, plain,
% 1.31/1.21 (![X0 : $i]: (~ (product @ e_1 @ X0 @ e_1) | (equalish @ e_1 @ X0))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl22])).
% 1.31/1.21 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 1.31/1.21 thf(zip_derived_cl8, plain, (~ (equalish @ e_1 @ e_2)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.31/1.21 thf(zip_derived_cl191, plain, (~ (product @ e_1 @ e_2 @ e_1)),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl146, zip_derived_cl8])).
% 1.31/1.21 thf(zip_derived_cl4, plain, ( (group_element @ e_1)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_1])).
% 1.31/1.21 thf(zip_derived_cl5, plain, ( (group_element @ e_2)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_2])).
% 1.31/1.21 thf(zip_derived_cl1085, plain,
% 1.31/1.21 (( (product @ e_3 @ e_2 @ e_1)) <= (( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('demod', [status(thm)],
% 1.31/1.21 [zip_derived_cl1084, zip_derived_cl236, zip_derived_cl191,
% 1.31/1.21 zip_derived_cl4, zip_derived_cl5])).
% 1.31/1.21 thf(zip_derived_cl22, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X0 @ X3 @ X2)
% 1.31/1.21 | (equalish @ X1 @ X3))),
% 1.31/1.21 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.31/1.21 thf(zip_derived_cl1168, plain,
% 1.31/1.21 ((![X0 : $i]: (~ (product @ e_3 @ X0 @ e_1) | (equalish @ e_2 @ X0)))
% 1.31/1.21 <= (( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1085, zip_derived_cl22])).
% 1.31/1.21 thf(zip_derived_cl13, plain, (~ (equalish @ e_2 @ e_4)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 1.31/1.21 thf(zip_derived_cl1418, plain,
% 1.31/1.21 ((~ (product @ e_3 @ e_4 @ e_1)) <= (( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1168, zip_derived_cl13])).
% 1.31/1.21 thf(zip_derived_cl1422, plain,
% 1.31/1.21 ((( (product @ e_2 @ e_4 @ e_1)
% 1.31/1.21 | (product @ e_1 @ e_4 @ e_1)
% 1.31/1.21 | ~ (group_element @ e_1)))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0))) &
% 1.31/1.21 ( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)],
% 1.31/1.21 [zip_derived_cl750, zip_derived_cl1418])).
% 1.31/1.21 thf(zip_derived_cl193, plain, (~ (product @ e_1 @ e_4 @ e_1)),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl146, zip_derived_cl10])).
% 1.31/1.21 thf(zip_derived_cl4, plain, ( (group_element @ e_1)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_1])).
% 1.31/1.21 thf(zip_derived_cl1424, plain,
% 1.31/1.21 (( (product @ e_2 @ e_4 @ e_1))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0))) &
% 1.31/1.21 ( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('demod', [status(thm)],
% 1.31/1.21 [zip_derived_cl1422, zip_derived_cl193, zip_derived_cl4])).
% 1.31/1.21 thf(zip_derived_cl2, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X1 @ X3 @ X2)
% 1.31/1.21 | (product @ X3 @ X0 @ X1))),
% 1.31/1.21 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.31/1.21 thf(zip_derived_cl1427, plain,
% 1.31/1.21 ((![X0 : $i]:
% 1.31/1.21 (~ (product @ e_4 @ X0 @ e_1) | (product @ X0 @ e_2 @ e_4)))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0))) &
% 1.31/1.21 ( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1424, zip_derived_cl2])).
% 1.31/1.21 thf(zip_derived_cl1480, plain,
% 1.31/1.21 ((( (product @ e_4 @ e_2 @ e_1)
% 1.31/1.21 | (product @ e_4 @ e_1 @ e_1)
% 1.31/1.21 | ~ (group_element @ e_1)
% 1.31/1.21 | (product @ e_3 @ e_2 @ e_4)))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_3 @ X0))) &
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0))) &
% 1.31/1.21 ( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)],
% 1.31/1.21 [zip_derived_cl510, zip_derived_cl1427])).
% 1.31/1.21 thf(zip_derived_cl142, plain, ( (product @ e_1 @ e_1 @ e_1)),
% 1.31/1.21 inference('clc', [status(thm)], [zip_derived_cl141, zip_derived_cl42])).
% 1.31/1.21 thf(zip_derived_cl23, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X3 @ X1 @ X2)
% 1.31/1.21 | (equalish @ X0 @ X3))),
% 1.31/1.21 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.31/1.21 thf(zip_derived_cl147, plain,
% 1.31/1.21 (![X0 : $i]: (~ (product @ X0 @ e_1 @ e_1) | (equalish @ e_1 @ X0))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl23])).
% 1.31/1.21 thf(zip_derived_cl10, plain, (~ (equalish @ e_1 @ e_4)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 1.31/1.21 thf(zip_derived_cl204, plain, (~ (product @ e_4 @ e_1 @ e_1)),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl147, zip_derived_cl10])).
% 1.31/1.21 thf(zip_derived_cl4, plain, ( (group_element @ e_1)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_1])).
% 1.31/1.21 thf(zip_derived_cl1085, plain,
% 1.31/1.21 (( (product @ e_3 @ e_2 @ e_1)) <= (( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('demod', [status(thm)],
% 1.31/1.21 [zip_derived_cl1084, zip_derived_cl236, zip_derived_cl191,
% 1.31/1.21 zip_derived_cl4, zip_derived_cl5])).
% 1.31/1.21 thf(zip_derived_cl21, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X0 @ X1 @ X3)
% 1.31/1.21 | (equalish @ X2 @ X3))),
% 1.31/1.21 inference('cnf', [status(esa)], [product_total_function2])).
% 1.31/1.21 thf(zip_derived_cl1167, plain,
% 1.31/1.21 ((![X0 : $i]: (~ (product @ e_3 @ e_2 @ X0) | (equalish @ e_1 @ X0)))
% 1.31/1.21 <= (( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1085, zip_derived_cl21])).
% 1.31/1.21 thf(zip_derived_cl10, plain, (~ (equalish @ e_1 @ e_4)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 1.31/1.21 thf(zip_derived_cl1322, plain,
% 1.31/1.21 ((~ (product @ e_3 @ e_2 @ e_4)) <= (( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1167, zip_derived_cl10])).
% 1.31/1.21 thf(zip_derived_cl1483, plain,
% 1.31/1.21 (( (product @ e_4 @ e_2 @ e_1))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_3 @ X0))) &
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0))) &
% 1.31/1.21 ( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('demod', [status(thm)],
% 1.31/1.21 [zip_derived_cl1480, zip_derived_cl204, zip_derived_cl4,
% 1.31/1.21 zip_derived_cl1322])).
% 1.31/1.21 thf(zip_derived_cl1080, plain,
% 1.31/1.21 ((~ (product @ e_4 @ e_2 @ e_1)) <= (( (product @ e_4 @ e_2 @ e_3)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl1012, zip_derived_cl14])).
% 1.31/1.21 thf('1', plain,
% 1.31/1.21 (~
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0))) |
% 1.31/1.21 ~ ( (product @ e_4 @ e_2 @ e_3)) |
% 1.31/1.21 ~
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_3 @ X0)))),
% 1.31/1.21 inference('s_sup-', [status(thm)],
% 1.31/1.21 [zip_derived_cl1483, zip_derived_cl1080])).
% 1.31/1.21 thf('2', plain,
% 1.31/1.21 (( (product @ e_4 @ e_4 @ e_4)) |
% 1.31/1.21 (![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.21 | (product @ e_3 @ e_4 @ X0)))),
% 1.31/1.21 inference('split', [status(esa)], [zip_derived_cl48])).
% 1.31/1.21 thf(zip_derived_cl510, plain,
% 1.31/1.21 ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_3 @ X0)))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_3 @ X0))))),
% 1.31/1.21 inference('split', [status(esa)], [zip_derived_cl47])).
% 1.31/1.21 thf(zip_derived_cl511, plain,
% 1.31/1.21 (( (product @ e_4 @ e_4 @ e_4)) <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.21 inference('split', [status(esa)], [zip_derived_cl47])).
% 1.31/1.21 thf(zip_derived_cl22, plain,
% 1.31/1.21 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.21 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.21 | ~ (product @ X0 @ X3 @ X2)
% 1.31/1.21 | (equalish @ X1 @ X3))),
% 1.31/1.21 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.31/1.21 thf(zip_derived_cl546, plain,
% 1.31/1.21 ((![X0 : $i]: (~ (product @ e_4 @ X0 @ e_4) | (equalish @ e_4 @ X0)))
% 1.31/1.21 <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl511, zip_derived_cl22])).
% 1.31/1.21 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 1.31/1.21 thf(zip_derived_cl19, plain, (~ (equalish @ e_4 @ e_3)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 1.31/1.21 thf(zip_derived_cl788, plain,
% 1.31/1.21 ((~ (product @ e_4 @ e_3 @ e_4)) <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl546, zip_derived_cl19])).
% 1.31/1.21 thf(zip_derived_cl810, plain,
% 1.31/1.21 ((( (product @ e_4 @ e_2 @ e_4)
% 1.31/1.21 | (product @ e_4 @ e_1 @ e_4)
% 1.31/1.21 | ~ (group_element @ e_4)))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_3 @ X0))) &
% 1.31/1.21 ( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl510, zip_derived_cl788])).
% 1.31/1.21 thf(zip_derived_cl546, plain,
% 1.31/1.21 ((![X0 : $i]: (~ (product @ e_4 @ X0 @ e_4) | (equalish @ e_4 @ X0)))
% 1.31/1.21 <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl511, zip_derived_cl22])).
% 1.31/1.21 thf(zip_derived_cl17, plain, (~ (equalish @ e_4 @ e_1)),
% 1.31/1.21 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 1.31/1.21 thf(zip_derived_cl786, plain,
% 1.31/1.21 ((~ (product @ e_4 @ e_1 @ e_4)) <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.21 inference('s_sup-', [status(thm)], [zip_derived_cl546, zip_derived_cl17])).
% 1.31/1.21 thf(zip_derived_cl7, plain, ( (group_element @ e_4)),
% 1.31/1.21 inference('cnf', [status(esa)], [element_4])).
% 1.31/1.21 thf(zip_derived_cl813, plain,
% 1.31/1.21 (( (product @ e_4 @ e_2 @ e_4))
% 1.31/1.21 <= ((![X0 : $i]:
% 1.31/1.21 (~ (group_element @ X0)
% 1.31/1.21 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.21 | (product @ e_4 @ e_3 @ X0))) &
% 1.31/1.21 ( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.21 inference('demod', [status(thm)],
% 1.31/1.22 [zip_derived_cl810, zip_derived_cl786, zip_derived_cl7])).
% 1.31/1.22 thf(zip_derived_cl546, plain,
% 1.31/1.22 ((![X0 : $i]: (~ (product @ e_4 @ X0 @ e_4) | (equalish @ e_4 @ X0)))
% 1.31/1.22 <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl511, zip_derived_cl22])).
% 1.31/1.22 thf(zip_derived_cl18, plain, (~ (equalish @ e_4 @ e_2)),
% 1.31/1.22 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 1.31/1.22 thf(zip_derived_cl787, plain,
% 1.31/1.22 ((~ (product @ e_4 @ e_2 @ e_4)) <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl546, zip_derived_cl18])).
% 1.31/1.22 thf('3', plain,
% 1.31/1.22 (~
% 1.31/1.22 (![X0 : $i]:
% 1.31/1.22 (~ (group_element @ X0)
% 1.31/1.22 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.22 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.22 | (product @ e_4 @ e_3 @ X0))) |
% 1.31/1.22 ~ ( (product @ e_4 @ e_4 @ e_4))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl813, zip_derived_cl787])).
% 1.31/1.22 thf('4', plain,
% 1.31/1.22 (( (product @ e_4 @ e_1 @ e_3)) |
% 1.31/1.22 ~
% 1.31/1.22 (![X0 : $i]:
% 1.31/1.22 (~ (group_element @ X0)
% 1.31/1.22 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.22 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.22 | (product @ e_4 @ e_3 @ X0))) |
% 1.31/1.22 ( (product @ e_4 @ e_2 @ e_3))),
% 1.31/1.22 inference('split', [status(esa)], [zip_derived_cl538])).
% 1.31/1.22 thf('5', plain,
% 1.31/1.22 (( (product @ e_4 @ e_4 @ e_4)) |
% 1.31/1.22 (![X0 : $i]:
% 1.31/1.22 (~ (group_element @ X0)
% 1.31/1.22 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.22 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.22 | (product @ e_4 @ e_3 @ X0)))),
% 1.31/1.22 inference('split', [status(esa)], [zip_derived_cl47])).
% 1.31/1.22 thf('6', plain, (( (product @ e_4 @ e_4 @ e_4))),
% 1.31/1.22 inference('sat_resolution*', [status(thm)],
% 1.31/1.22 ['0', '1', '2', '3', '4', '5'])).
% 1.31/1.22 thf(zip_derived_cl2616, plain,
% 1.31/1.22 (( (product @ e_3 @ e_4 @ e_1) | (product @ e_2 @ e_4 @ e_1))),
% 1.31/1.22 inference('simpl_trail', [status(thm)], [zip_derived_cl641, '6'])).
% 1.31/1.22 thf(zip_derived_cl2617, plain,
% 1.31/1.22 (( (product @ e_3 @ e_4 @ e_1)) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 1.31/1.22 inference('split', [status(esa)], [zip_derived_cl2616])).
% 1.31/1.22 thf(zip_derived_cl21, plain,
% 1.31/1.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.22 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.22 | ~ (product @ X0 @ X1 @ X3)
% 1.31/1.22 | (equalish @ X2 @ X3))),
% 1.31/1.22 inference('cnf', [status(esa)], [product_total_function2])).
% 1.31/1.22 thf(zip_derived_cl2621, plain,
% 1.31/1.22 ((![X0 : $i]: (~ (product @ e_3 @ e_4 @ X0) | (equalish @ e_1 @ X0)))
% 1.31/1.22 <= (( (product @ e_3 @ e_4 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl2617, zip_derived_cl21])).
% 1.31/1.22 thf(zip_derived_cl8, plain, (~ (equalish @ e_1 @ e_2)),
% 1.31/1.22 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.31/1.22 thf(zip_derived_cl2687, plain,
% 1.31/1.22 ((~ (product @ e_3 @ e_4 @ e_2)) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl2621, zip_derived_cl8])).
% 1.31/1.22 thf(zip_derived_cl1, plain,
% 1.31/1.22 (![X0 : $i, X1 : $i]:
% 1.31/1.22 (~ (group_element @ X0)
% 1.31/1.22 | ~ (group_element @ X1)
% 1.31/1.22 | (product @ X0 @ e_1 @ X1)
% 1.31/1.22 | (product @ X0 @ e_2 @ X1)
% 1.31/1.22 | (product @ X0 @ e_3 @ X1)
% 1.31/1.22 | (product @ X0 @ e_4 @ X1))),
% 1.31/1.22 inference('cnf', [status(esa)], [column_surjectivity])).
% 1.31/1.22 thf(zip_derived_cl2617, plain,
% 1.31/1.22 (( (product @ e_3 @ e_4 @ e_1)) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 1.31/1.22 inference('split', [status(esa)], [zip_derived_cl2616])).
% 1.31/1.22 thf(zip_derived_cl23, plain,
% 1.31/1.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.22 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.22 | ~ (product @ X3 @ X1 @ X2)
% 1.31/1.22 | (equalish @ X0 @ X3))),
% 1.31/1.22 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.31/1.22 thf(zip_derived_cl2623, plain,
% 1.31/1.22 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_1) | (equalish @ e_3 @ X0)))
% 1.31/1.22 <= (( (product @ e_3 @ e_4 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl2617, zip_derived_cl23])).
% 1.31/1.22 thf(zip_derived_cl15, plain, (~ (equalish @ e_3 @ e_2)),
% 1.31/1.22 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 1.31/1.22 thf(zip_derived_cl2709, plain,
% 1.31/1.22 ((~ (product @ e_2 @ e_4 @ e_1)) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl2623, zip_derived_cl15])).
% 1.31/1.22 thf(zip_derived_cl2712, plain,
% 1.31/1.22 ((( (product @ e_2 @ e_3 @ e_1)
% 1.31/1.22 | (product @ e_2 @ e_2 @ e_1)
% 1.31/1.22 | (product @ e_2 @ e_1 @ e_1)
% 1.31/1.22 | ~ (group_element @ e_1)
% 1.31/1.22 | ~ (group_element @ e_2))) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl2709])).
% 1.31/1.22 thf(zip_derived_cl236, plain, (~ (product @ e_2 @ e_2 @ e_1)),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl214, zip_derived_cl11])).
% 1.31/1.22 thf(zip_derived_cl147, plain,
% 1.31/1.22 (![X0 : $i]: (~ (product @ X0 @ e_1 @ e_1) | (equalish @ e_1 @ X0))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl142, zip_derived_cl23])).
% 1.31/1.22 thf(zip_derived_cl8, plain, (~ (equalish @ e_1 @ e_2)),
% 1.31/1.22 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.31/1.22 thf(zip_derived_cl202, plain, (~ (product @ e_2 @ e_1 @ e_1)),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl147, zip_derived_cl8])).
% 1.31/1.22 thf(zip_derived_cl4, plain, ( (group_element @ e_1)),
% 1.31/1.22 inference('cnf', [status(esa)], [element_1])).
% 1.31/1.22 thf(zip_derived_cl5, plain, ( (group_element @ e_2)),
% 1.31/1.22 inference('cnf', [status(esa)], [element_2])).
% 1.31/1.22 thf(zip_derived_cl2713, plain,
% 1.31/1.22 (( (product @ e_2 @ e_3 @ e_1)) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 1.31/1.22 inference('demod', [status(thm)],
% 1.31/1.22 [zip_derived_cl2712, zip_derived_cl236, zip_derived_cl202,
% 1.31/1.22 zip_derived_cl4, zip_derived_cl5])).
% 1.31/1.22 thf(zip_derived_cl1, plain,
% 1.31/1.22 (![X0 : $i, X1 : $i]:
% 1.31/1.22 (~ (group_element @ X0)
% 1.31/1.22 | ~ (group_element @ X1)
% 1.31/1.22 | (product @ X0 @ e_1 @ X1)
% 1.31/1.22 | (product @ X0 @ e_2 @ X1)
% 1.31/1.22 | (product @ X0 @ e_3 @ X1)
% 1.31/1.22 | (product @ X0 @ e_4 @ X1))),
% 1.31/1.22 inference('cnf', [status(esa)], [column_surjectivity])).
% 1.31/1.22 thf(zip_derived_cl633, plain,
% 1.31/1.22 ((~ (product @ e_4 @ e_4 @ e_1)) <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl545, zip_derived_cl17])).
% 1.31/1.22 thf(zip_derived_cl638, plain,
% 1.31/1.22 ((( (product @ e_4 @ e_3 @ e_1)
% 1.31/1.22 | (product @ e_4 @ e_2 @ e_1)
% 1.31/1.22 | (product @ e_4 @ e_1 @ e_1)
% 1.31/1.22 | ~ (group_element @ e_1)
% 1.31/1.22 | ~ (group_element @ e_4))) <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl633])).
% 1.31/1.22 thf(zip_derived_cl204, plain, (~ (product @ e_4 @ e_1 @ e_1)),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl147, zip_derived_cl10])).
% 1.31/1.22 thf(zip_derived_cl4, plain, ( (group_element @ e_1)),
% 1.31/1.22 inference('cnf', [status(esa)], [element_1])).
% 1.31/1.22 thf(zip_derived_cl7, plain, ( (group_element @ e_4)),
% 1.31/1.22 inference('cnf', [status(esa)], [element_4])).
% 1.31/1.22 thf(zip_derived_cl640, plain,
% 1.31/1.22 ((( (product @ e_4 @ e_3 @ e_1) | (product @ e_4 @ e_2 @ e_1)))
% 1.31/1.22 <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.22 inference('demod', [status(thm)],
% 1.31/1.22 [zip_derived_cl638, zip_derived_cl204, zip_derived_cl4,
% 1.31/1.22 zip_derived_cl7])).
% 1.31/1.22 thf(zip_derived_cl1930, plain,
% 1.31/1.22 (( (product @ e_4 @ e_2 @ e_1)) <= (( (product @ e_4 @ e_2 @ e_1)))),
% 1.31/1.22 inference('split', [status(esa)], [zip_derived_cl640])).
% 1.31/1.22 thf(zip_derived_cl2, plain,
% 1.31/1.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.22 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.22 | ~ (product @ X1 @ X3 @ X2)
% 1.31/1.22 | (product @ X3 @ X0 @ X1))),
% 1.31/1.22 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.31/1.22 thf(zip_derived_cl1979, plain,
% 1.31/1.22 ((![X0 : $i]:
% 1.31/1.22 (~ (product @ e_2 @ X0 @ e_1) | (product @ X0 @ e_4 @ e_2)))
% 1.31/1.22 <= (( (product @ e_4 @ e_2 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl1930, zip_derived_cl2])).
% 1.31/1.22 thf(zip_derived_cl1929, plain,
% 1.31/1.22 (( (product @ e_4 @ e_3 @ e_1)) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 1.31/1.22 inference('split', [status(esa)], [zip_derived_cl640])).
% 1.31/1.22 thf(zip_derived_cl23, plain,
% 1.31/1.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.22 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.22 | ~ (product @ X3 @ X1 @ X2)
% 1.31/1.22 | (equalish @ X0 @ X3))),
% 1.31/1.22 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.31/1.22 thf(zip_derived_cl1935, plain,
% 1.31/1.22 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_1) | (equalish @ e_4 @ X0)))
% 1.31/1.22 <= (( (product @ e_4 @ e_3 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl1929, zip_derived_cl23])).
% 1.31/1.22 thf(zip_derived_cl18, plain, (~ (equalish @ e_4 @ e_2)),
% 1.31/1.22 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 1.31/1.22 thf(zip_derived_cl2143, plain,
% 1.31/1.22 ((~ (product @ e_2 @ e_3 @ e_1)) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl1935, zip_derived_cl18])).
% 1.31/1.22 thf(zip_derived_cl1, plain,
% 1.31/1.22 (![X0 : $i, X1 : $i]:
% 1.31/1.22 (~ (group_element @ X0)
% 1.31/1.22 | ~ (group_element @ X1)
% 1.31/1.22 | (product @ X0 @ e_1 @ X1)
% 1.31/1.22 | (product @ X0 @ e_2 @ X1)
% 1.31/1.22 | (product @ X0 @ e_3 @ X1)
% 1.31/1.22 | (product @ X0 @ e_4 @ X1))),
% 1.31/1.22 inference('cnf', [status(esa)], [column_surjectivity])).
% 1.31/1.22 thf(zip_derived_cl0, plain,
% 1.31/1.22 (![X0 : $i, X1 : $i]:
% 1.31/1.22 (~ (group_element @ X0)
% 1.31/1.22 | ~ (group_element @ X1)
% 1.31/1.22 | (product @ e_1 @ X0 @ X1)
% 1.31/1.22 | (product @ e_2 @ X0 @ X1)
% 1.31/1.22 | (product @ e_3 @ X0 @ X1)
% 1.31/1.22 | (product @ e_4 @ X0 @ X1))),
% 1.31/1.22 inference('cnf', [status(esa)], [row_surjectivity])).
% 1.31/1.22 thf(zip_derived_cl1929, plain,
% 1.31/1.22 (( (product @ e_4 @ e_3 @ e_1)) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 1.31/1.22 inference('split', [status(esa)], [zip_derived_cl640])).
% 1.31/1.22 thf(zip_derived_cl22, plain,
% 1.31/1.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.22 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.22 | ~ (product @ X0 @ X3 @ X2)
% 1.31/1.22 | (equalish @ X1 @ X3))),
% 1.31/1.22 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.31/1.22 thf(zip_derived_cl1934, plain,
% 1.31/1.22 ((![X0 : $i]: (~ (product @ e_4 @ X0 @ e_1) | (equalish @ e_3 @ X0)))
% 1.31/1.22 <= (( (product @ e_4 @ e_3 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl1929, zip_derived_cl22])).
% 1.31/1.22 thf(zip_derived_cl15, plain, (~ (equalish @ e_3 @ e_2)),
% 1.31/1.22 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 1.31/1.22 thf(zip_derived_cl2086, plain,
% 1.31/1.22 ((~ (product @ e_4 @ e_2 @ e_1)) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl1934, zip_derived_cl15])).
% 1.31/1.22 thf(zip_derived_cl2090, plain,
% 1.31/1.22 ((( (product @ e_3 @ e_2 @ e_1)
% 1.31/1.22 | (product @ e_2 @ e_2 @ e_1)
% 1.31/1.22 | (product @ e_1 @ e_2 @ e_1)
% 1.31/1.22 | ~ (group_element @ e_1)
% 1.31/1.22 | ~ (group_element @ e_2))) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2086])).
% 1.31/1.22 thf(zip_derived_cl236, plain, (~ (product @ e_2 @ e_2 @ e_1)),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl214, zip_derived_cl11])).
% 1.31/1.22 thf(zip_derived_cl191, plain, (~ (product @ e_1 @ e_2 @ e_1)),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl146, zip_derived_cl8])).
% 1.31/1.22 thf(zip_derived_cl4, plain, ( (group_element @ e_1)),
% 1.31/1.22 inference('cnf', [status(esa)], [element_1])).
% 1.31/1.22 thf(zip_derived_cl5, plain, ( (group_element @ e_2)),
% 1.31/1.22 inference('cnf', [status(esa)], [element_2])).
% 1.31/1.22 thf(zip_derived_cl2092, plain,
% 1.31/1.22 (( (product @ e_3 @ e_2 @ e_1)) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 1.31/1.22 inference('demod', [status(thm)],
% 1.31/1.22 [zip_derived_cl2090, zip_derived_cl236, zip_derived_cl191,
% 1.31/1.22 zip_derived_cl4, zip_derived_cl5])).
% 1.31/1.22 thf(zip_derived_cl1929, plain,
% 1.31/1.22 (( (product @ e_4 @ e_3 @ e_1)) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 1.31/1.22 inference('split', [status(esa)], [zip_derived_cl640])).
% 1.31/1.22 thf(zip_derived_cl2, plain,
% 1.31/1.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.22 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.22 | ~ (product @ X1 @ X3 @ X2)
% 1.31/1.22 | (product @ X3 @ X0 @ X1))),
% 1.31/1.22 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.31/1.22 thf(zip_derived_cl1931, plain,
% 1.31/1.22 ((![X0 : $i]:
% 1.31/1.22 (~ (product @ e_3 @ X0 @ e_1) | (product @ X0 @ e_4 @ e_3)))
% 1.31/1.22 <= (( (product @ e_4 @ e_3 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl1929, zip_derived_cl2])).
% 1.31/1.22 thf(zip_derived_cl2407, plain,
% 1.31/1.22 (( (product @ e_2 @ e_4 @ e_3)) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)],
% 1.31/1.22 [zip_derived_cl2092, zip_derived_cl1931])).
% 1.31/1.22 thf(zip_derived_cl21, plain,
% 1.31/1.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.31/1.22 (~ (product @ X0 @ X1 @ X2)
% 1.31/1.22 | ~ (product @ X0 @ X1 @ X3)
% 1.31/1.22 | (equalish @ X2 @ X3))),
% 1.31/1.22 inference('cnf', [status(esa)], [product_total_function2])).
% 1.31/1.22 thf(zip_derived_cl2411, plain,
% 1.31/1.22 ((![X0 : $i]: (~ (product @ e_2 @ e_4 @ X0) | (equalish @ e_3 @ X0)))
% 1.31/1.22 <= (( (product @ e_4 @ e_3 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl2407, zip_derived_cl21])).
% 1.31/1.22 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_1)),
% 1.31/1.22 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 1.31/1.22 thf(zip_derived_cl2488, plain,
% 1.31/1.22 ((~ (product @ e_2 @ e_4 @ e_1)) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl2411, zip_derived_cl14])).
% 1.31/1.22 thf(zip_derived_cl2492, plain,
% 1.31/1.22 ((( (product @ e_2 @ e_3 @ e_1)
% 1.31/1.22 | (product @ e_2 @ e_2 @ e_1)
% 1.31/1.22 | (product @ e_2 @ e_1 @ e_1)
% 1.31/1.22 | ~ (group_element @ e_1)
% 1.31/1.22 | ~ (group_element @ e_2))) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl2488])).
% 1.31/1.22 thf(zip_derived_cl236, plain, (~ (product @ e_2 @ e_2 @ e_1)),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl214, zip_derived_cl11])).
% 1.31/1.22 thf(zip_derived_cl202, plain, (~ (product @ e_2 @ e_1 @ e_1)),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl147, zip_derived_cl8])).
% 1.31/1.22 thf(zip_derived_cl4, plain, ( (group_element @ e_1)),
% 1.31/1.22 inference('cnf', [status(esa)], [element_1])).
% 1.31/1.22 thf(zip_derived_cl5, plain, ( (group_element @ e_2)),
% 1.31/1.22 inference('cnf', [status(esa)], [element_2])).
% 1.31/1.22 thf(zip_derived_cl2493, plain,
% 1.31/1.22 (( (product @ e_2 @ e_3 @ e_1)) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 1.31/1.22 inference('demod', [status(thm)],
% 1.31/1.22 [zip_derived_cl2492, zip_derived_cl236, zip_derived_cl202,
% 1.31/1.22 zip_derived_cl4, zip_derived_cl5])).
% 1.31/1.22 thf('7', plain, (~ ( (product @ e_4 @ e_3 @ e_1))),
% 1.31/1.22 inference('demod', [status(thm)],
% 1.31/1.22 [zip_derived_cl2143, zip_derived_cl2493])).
% 1.31/1.22 thf('8', plain,
% 1.31/1.22 (( (product @ e_4 @ e_2 @ e_1)) | ( (product @ e_4 @ e_3 @ e_1)) |
% 1.31/1.22 ~ ( (product @ e_4 @ e_4 @ e_4))),
% 1.31/1.22 inference('split', [status(esa)], [zip_derived_cl640])).
% 1.31/1.22 thf('9', plain, (( (product @ e_4 @ e_2 @ e_1))),
% 1.31/1.22 inference('sat_resolution*', [status(thm)],
% 1.31/1.22 ['0', '1', '2', '3', '4', '5', '7', '8'])).
% 1.31/1.22 thf(zip_derived_cl2545, plain,
% 1.31/1.22 (![X0 : $i]: (~ (product @ e_2 @ X0 @ e_1) | (product @ X0 @ e_4 @ e_2))),
% 1.31/1.22 inference('simpl_trail', [status(thm)], [zip_derived_cl1979, '9'])).
% 1.31/1.22 thf(zip_derived_cl2830, plain,
% 1.31/1.22 (( (product @ e_3 @ e_4 @ e_2)) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)],
% 1.31/1.22 [zip_derived_cl2713, zip_derived_cl2545])).
% 1.31/1.22 thf(zip_derived_cl2618, plain,
% 1.31/1.22 (( (product @ e_2 @ e_4 @ e_1)) <= (( (product @ e_2 @ e_4 @ e_1)))),
% 1.31/1.22 inference('split', [status(esa)], [zip_derived_cl2616])).
% 1.31/1.22 thf(zip_derived_cl2545, plain,
% 1.31/1.22 (![X0 : $i]: (~ (product @ e_2 @ X0 @ e_1) | (product @ X0 @ e_4 @ e_2))),
% 1.31/1.22 inference('simpl_trail', [status(thm)], [zip_derived_cl1979, '9'])).
% 1.31/1.22 thf(zip_derived_cl2780, plain,
% 1.31/1.22 (( (product @ e_4 @ e_4 @ e_2)) <= (( (product @ e_2 @ e_4 @ e_1)))),
% 1.31/1.22 inference('s_sup-', [status(thm)],
% 1.31/1.22 [zip_derived_cl2618, zip_derived_cl2545])).
% 1.31/1.22 thf(zip_derived_cl545, plain,
% 1.31/1.22 ((![X0 : $i]: (~ (product @ e_4 @ e_4 @ X0) | (equalish @ e_4 @ X0)))
% 1.31/1.22 <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl511, zip_derived_cl21])).
% 1.31/1.22 thf(zip_derived_cl18, plain, (~ (equalish @ e_4 @ e_2)),
% 1.31/1.22 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 1.31/1.22 thf(zip_derived_cl634, plain,
% 1.31/1.22 ((~ (product @ e_4 @ e_4 @ e_2)) <= (( (product @ e_4 @ e_4 @ e_4)))),
% 1.31/1.22 inference('s_sup-', [status(thm)], [zip_derived_cl545, zip_derived_cl18])).
% 1.31/1.22 thf('10', plain,
% 1.31/1.22 (~ ( (product @ e_4 @ e_1 @ e_3)) |
% 1.31/1.22 ~
% 1.31/1.22 (![X0 : $i]:
% 1.31/1.22 (~ (group_element @ X0)
% 1.31/1.22 | (product @ e_1 @ e_4 @ X0)
% 1.31/1.22 | (product @ e_2 @ e_4 @ X0)
% 1.31/1.22 | (product @ e_3 @ e_4 @ X0)))),
% 1.31/1.22 inference('s_sup-', [status(thm)],
% 1.31/1.22 [zip_derived_cl1808, zip_derived_cl454])).
% 1.31/1.22 thf('11', plain,
% 1.31/1.22 (( (product @ e_4 @ e_2 @ e_3)) | ( (product @ e_4 @ e_1 @ e_3)) |
% 1.31/1.22 ~
% 1.31/1.22 (![X0 : $i]:
% 1.31/1.22 (~ (group_element @ X0)
% 1.31/1.22 | (product @ e_4 @ e_1 @ X0)
% 1.31/1.22 | (product @ e_4 @ e_2 @ X0)
% 1.31/1.22 | (product @ e_4 @ e_3 @ X0)))),
% 1.31/1.22 inference('split', [status(esa)], [zip_derived_cl538])).
% 1.31/1.22 thf('12', plain, (( (product @ e_4 @ e_4 @ e_4))),
% 1.31/1.22 inference('sat_resolution*', [status(thm)],
% 1.31/1.22 ['10', '1', '2', '3', '11', '5'])).
% 1.31/1.22 thf(zip_derived_cl1968, plain, (~ (product @ e_4 @ e_4 @ e_2)),
% 1.31/1.22 inference('simpl_trail', [status(thm)], [zip_derived_cl634, '12'])).
% 1.31/1.22 thf('13', plain, (~ ( (product @ e_2 @ e_4 @ e_1))),
% 1.31/1.22 inference('s_sup-', [status(thm)],
% 1.31/1.22 [zip_derived_cl2780, zip_derived_cl1968])).
% 1.31/1.22 thf('14', plain,
% 1.31/1.22 (( (product @ e_3 @ e_4 @ e_1)) | ( (product @ e_2 @ e_4 @ e_1))),
% 1.31/1.22 inference('split', [status(esa)], [zip_derived_cl2616])).
% 1.31/1.22 thf('15', plain, (( (product @ e_3 @ e_4 @ e_1))),
% 1.31/1.22 inference('sat_resolution*', [status(thm)], ['13', '14'])).
% 1.31/1.22 thf(zip_derived_cl2928, plain, ( (product @ e_3 @ e_4 @ e_2)),
% 1.31/1.22 inference('simpl_trail', [status(thm)], [zip_derived_cl2830, '15'])).
% 1.31/1.22 thf(zip_derived_cl2933, plain,
% 1.31/1.22 (($false) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 1.31/1.22 inference('demod', [status(thm)],
% 1.31/1.22 [zip_derived_cl2687, zip_derived_cl2928])).
% 1.31/1.22 thf('16', plain, (( (product @ e_3 @ e_4 @ e_1))),
% 1.31/1.22 inference('sat_resolution*', [status(thm)], ['13', '14'])).
% 1.31/1.22 thf(zip_derived_cl2934, plain, ($false),
% 1.31/1.22 inference('simpl_trail', [status(thm)], [zip_derived_cl2933, '16'])).
% 1.31/1.22
% 1.31/1.22 % SZS output end Refutation
% 1.31/1.22
% 1.31/1.22
% 1.31/1.22 % Terminating...
% 1.88/1.32 % Runner terminated.
% 1.88/1.33 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------