TSTP Solution File: GRP133-2.003 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP133-2.003 : 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.K4LyoWhXFD 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 01:50:17 EDT 2023
% Result : Unsatisfiable 1.26s 0.87s
% Output : Refutation 1.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP133-2.003 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.K4LyoWhXFD true
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 20:22:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % 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
% 0.20/0.64 % Total configuration time : 435
% 0.20/0.64 % Estimated wc time : 1092
% 0.20/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.20/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.26/0.87 % Solved by fo/fo1_av.sh.
% 1.26/0.87 % done 618 iterations in 0.126s
% 1.26/0.87 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.26/0.87 % SZS output start Refutation
% 1.26/0.87 thf(greater_type, type, greater: $i > $i > $o).
% 1.26/0.87 thf(product_type, type, product: $i > $i > $i > $o).
% 1.26/0.87 thf(e_3_type, type, e_3: $i).
% 1.26/0.87 thf(e_2_type, type, e_2: $i).
% 1.26/0.87 thf(e_1_type, type, e_1: $i).
% 1.26/0.87 thf(next_type, type, next: $i > $i > $o).
% 1.26/0.87 thf(group_element_type, type, group_element: $i > $o).
% 1.26/0.87 thf(equalish_type, type, equalish: $i > $i > $o).
% 1.26/0.87 thf(element_2, axiom, (group_element @ e_2)).
% 1.26/0.87 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 1.26/0.87 inference('cnf', [status(esa)], [element_2])).
% 1.26/0.87 thf(product_total_function1, axiom,
% 1.26/0.87 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 1.26/0.87 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 1.26/0.87 ( product @ X @ Y @ e_3 ))).
% 1.26/0.87 thf(zip_derived_cl15, plain,
% 1.26/0.87 (![X0 : $i, X1 : $i]:
% 1.26/0.87 (~ (group_element @ X0)
% 1.26/0.87 | ~ (group_element @ X1)
% 1.26/0.87 | (product @ X0 @ X1 @ e_1)
% 1.26/0.87 | (product @ X0 @ X1 @ e_2)
% 1.26/0.87 | (product @ X0 @ X1 @ e_3))),
% 1.26/0.87 inference('cnf', [status(esa)], [product_total_function1])).
% 1.26/0.87 thf(zip_derived_cl22, plain,
% 1.26/0.87 (![X0 : $i]:
% 1.26/0.87 (~ (group_element @ X0)
% 1.26/0.87 | (product @ e_2 @ X0 @ e_1)
% 1.26/0.87 | (product @ e_2 @ X0 @ e_2)
% 1.26/0.87 | (product @ e_2 @ X0 @ e_3))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl15])).
% 1.26/0.87 thf(element_1, axiom, (group_element @ e_1)).
% 1.26/0.87 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 1.26/0.87 inference('cnf', [status(esa)], [element_1])).
% 1.26/0.87 thf(zip_derived_cl48, plain,
% 1.26/0.87 (( (product @ e_2 @ e_1 @ e_3)
% 1.26/0.87 | (product @ e_2 @ e_1 @ e_2)
% 1.26/0.87 | (product @ e_2 @ e_1 @ e_1))),
% 1.26/0.87 inference('s_sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl6])).
% 1.26/0.87 thf(zip_derived_cl182, plain,
% 1.26/0.87 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 1.26/0.87 inference('split', [status(esa)], [zip_derived_cl48])).
% 1.26/0.87 thf(product_right_cancellation, axiom,
% 1.26/0.87 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 1.26/0.87 ( equalish @ W @ Z ))).
% 1.26/0.87 thf(zip_derived_cl17, plain,
% 1.26/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.26/0.87 (~ (product @ X0 @ X1 @ X2)
% 1.26/0.87 | ~ (product @ X0 @ X3 @ X2)
% 1.26/0.87 | (equalish @ X1 @ X3))),
% 1.26/0.87 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.26/0.87 thf(zip_derived_cl186, plain,
% 1.26/0.87 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 1.26/0.87 <= (( (product @ e_2 @ e_1 @ e_3)))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl182, zip_derived_cl17])).
% 1.26/0.87 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 1.26/0.87 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 1.26/0.87 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.26/0.87 thf(zip_derived_cl595, plain,
% 1.26/0.87 ((~ (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl186, zip_derived_cl9])).
% 1.26/0.87 thf(zip_derived_cl22, plain,
% 1.26/0.87 (![X0 : $i]:
% 1.26/0.87 (~ (group_element @ X0)
% 1.26/0.87 | (product @ e_2 @ X0 @ e_1)
% 1.26/0.87 | (product @ e_2 @ X0 @ e_2)
% 1.26/0.87 | (product @ e_2 @ X0 @ e_3))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl15])).
% 1.26/0.87 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 1.26/0.87 inference('cnf', [status(esa)], [element_2])).
% 1.26/0.87 thf(zip_derived_cl49, plain,
% 1.26/0.87 (( (product @ e_2 @ e_2 @ e_3)
% 1.26/0.87 | (product @ e_2 @ e_2 @ e_2)
% 1.26/0.87 | (product @ e_2 @ e_2 @ e_1))),
% 1.26/0.87 inference('s_sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl7])).
% 1.26/0.87 thf(zip_derived_cl204, plain,
% 1.26/0.87 (( (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 1.26/0.87 inference('split', [status(esa)], [zip_derived_cl49])).
% 1.26/0.87 thf('0', plain,
% 1.26/0.87 (~ ( (product @ e_2 @ e_2 @ e_3)) | ~ ( (product @ e_2 @ e_1 @ e_3))),
% 1.26/0.87 inference('s_sup+', [status(thm)], [zip_derived_cl595, zip_derived_cl204])).
% 1.26/0.87 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 1.26/0.87 inference('cnf', [status(esa)], [element_1])).
% 1.26/0.87 thf(zip_derived_cl15, plain,
% 1.26/0.87 (![X0 : $i, X1 : $i]:
% 1.26/0.87 (~ (group_element @ X0)
% 1.26/0.87 | ~ (group_element @ X1)
% 1.26/0.87 | (product @ X0 @ X1 @ e_1)
% 1.26/0.87 | (product @ X0 @ X1 @ e_2)
% 1.26/0.87 | (product @ X0 @ X1 @ e_3))),
% 1.26/0.87 inference('cnf', [status(esa)], [product_total_function1])).
% 1.26/0.87 thf(zip_derived_cl21, plain,
% 1.26/0.87 (![X0 : $i]:
% 1.26/0.87 (~ (group_element @ X0)
% 1.26/0.87 | (product @ e_1 @ X0 @ e_1)
% 1.26/0.87 | (product @ e_1 @ X0 @ e_2)
% 1.26/0.87 | (product @ e_1 @ X0 @ e_3))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl15])).
% 1.26/0.87 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 1.26/0.87 inference('cnf', [status(esa)], [element_2])).
% 1.26/0.87 thf(zip_derived_cl31, plain,
% 1.26/0.87 (( (product @ e_1 @ e_2 @ e_3)
% 1.26/0.87 | (product @ e_1 @ e_2 @ e_2)
% 1.26/0.87 | (product @ e_1 @ e_2 @ e_1))),
% 1.26/0.87 inference('s_sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl7])).
% 1.26/0.87 thf(zip_derived_cl104, plain,
% 1.26/0.87 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.26/0.87 inference('split', [status(esa)], [zip_derived_cl31])).
% 1.26/0.87 thf(product_left_cancellation, axiom,
% 1.26/0.87 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 1.26/0.87 ( equalish @ W @ Z ))).
% 1.26/0.87 thf(zip_derived_cl18, plain,
% 1.26/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.26/0.87 (~ (product @ X0 @ X1 @ X2)
% 1.26/0.87 | ~ (product @ X3 @ X1 @ X2)
% 1.26/0.87 | (equalish @ X0 @ X3))),
% 1.26/0.87 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.26/0.87 thf(zip_derived_cl119, plain,
% 1.26/0.87 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_2) | (equalish @ e_1 @ X0)))
% 1.26/0.87 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl104, zip_derived_cl18])).
% 1.26/0.87 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 1.26/0.87 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.26/0.87 thf(zip_derived_cl502, plain,
% 1.26/0.87 ((~ (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl119, zip_derived_cl9])).
% 1.26/0.87 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 1.26/0.87 inference('cnf', [status(esa)], [element_2])).
% 1.26/0.87 thf(zip_derived_cl22, plain,
% 1.26/0.87 (![X0 : $i]:
% 1.26/0.87 (~ (group_element @ X0)
% 1.26/0.87 | (product @ e_2 @ X0 @ e_1)
% 1.26/0.87 | (product @ e_2 @ X0 @ e_2)
% 1.26/0.87 | (product @ e_2 @ X0 @ e_3))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl15])).
% 1.26/0.87 thf(zip_derived_cl52, plain,
% 1.26/0.87 (( (product @ e_2 @ e_2 @ e_1)
% 1.26/0.87 | (product @ e_2 @ e_2 @ e_2)
% 1.26/0.87 | (product @ e_2 @ e_2 @ e_3))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl22])).
% 1.26/0.87 thf(zip_derived_cl269, plain,
% 1.26/0.87 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_2)))),
% 1.26/0.87 inference('split', [status(esa)], [zip_derived_cl52])).
% 1.26/0.87 thf('1', plain,
% 1.26/0.87 (~ ( (product @ e_2 @ e_2 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_2))),
% 1.26/0.87 inference('s_sup+', [status(thm)], [zip_derived_cl502, zip_derived_cl269])).
% 1.26/0.87 thf(zip_derived_cl21, plain,
% 1.26/0.87 (![X0 : $i]:
% 1.26/0.87 (~ (group_element @ X0)
% 1.26/0.87 | (product @ e_1 @ X0 @ e_1)
% 1.26/0.87 | (product @ e_1 @ X0 @ e_2)
% 1.26/0.87 | (product @ e_1 @ X0 @ e_3))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl15])).
% 1.26/0.87 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 1.26/0.87 inference('cnf', [status(esa)], [element_1])).
% 1.26/0.87 thf(zip_derived_cl30, plain,
% 1.26/0.87 (( (product @ e_1 @ e_1 @ e_3)
% 1.26/0.87 | (product @ e_1 @ e_1 @ e_2)
% 1.26/0.87 | (product @ e_1 @ e_1 @ e_1))),
% 1.26/0.87 inference('s_sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl6])).
% 1.26/0.87 thf(zip_derived_cl38, plain,
% 1.26/0.87 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 1.26/0.87 inference('split', [status(esa)], [zip_derived_cl30])).
% 1.26/0.87 thf(zip_derived_cl17, plain,
% 1.26/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.26/0.87 (~ (product @ X0 @ X1 @ X2)
% 1.26/0.87 | ~ (product @ X0 @ X3 @ X2)
% 1.26/0.87 | (equalish @ X1 @ X3))),
% 1.26/0.87 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.26/0.87 thf(zip_derived_cl86, plain,
% 1.26/0.87 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_1) | (equalish @ e_1 @ X0)))
% 1.26/0.87 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl17])).
% 1.26/0.87 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 1.26/0.87 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.26/0.87 thf(zip_derived_cl237, plain,
% 1.26/0.87 ((~ (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl86, zip_derived_cl9])).
% 1.26/0.87 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 1.26/0.87 inference('cnf', [status(esa)], [element_2])).
% 1.26/0.87 thf(zip_derived_cl21, plain,
% 1.26/0.87 (![X0 : $i]:
% 1.26/0.87 (~ (group_element @ X0)
% 1.26/0.87 | (product @ e_1 @ X0 @ e_1)
% 1.26/0.87 | (product @ e_1 @ X0 @ e_2)
% 1.26/0.87 | (product @ e_1 @ X0 @ e_3))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl15])).
% 1.26/0.87 thf(zip_derived_cl34, plain,
% 1.26/0.87 (( (product @ e_1 @ e_2 @ e_1)
% 1.26/0.87 | (product @ e_1 @ e_2 @ e_2)
% 1.26/0.87 | (product @ e_1 @ e_2 @ e_3))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl21])).
% 1.26/0.87 thf(zip_derived_cl151, plain,
% 1.26/0.87 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 1.26/0.87 inference('split', [status(esa)], [zip_derived_cl34])).
% 1.26/0.87 thf('2', plain,
% 1.26/0.87 (~ ( (product @ e_1 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_1 @ e_1))),
% 1.26/0.87 inference('s_sup+', [status(thm)], [zip_derived_cl237, zip_derived_cl151])).
% 1.26/0.87 thf(zip_derived_cl151, plain,
% 1.26/0.87 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 1.26/0.87 inference('split', [status(esa)], [zip_derived_cl34])).
% 1.26/0.87 thf(zip_derived_cl37, plain,
% 1.26/0.87 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 1.26/0.87 inference('split', [status(esa)], [zip_derived_cl30])).
% 1.26/0.87 thf(qg3, conjecture,
% 1.26/0.87 (~( ( product @ Z1 @ Z2 @ X ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 1.26/0.87 ( ~( product @ X @ Y @ Z1 ) ) ))).
% 1.26/0.87 thf(zf_stmt_0, negated_conjecture,
% 1.26/0.87 (( product @ Z1 @ Z2 @ X ) | ( ~( product @ Y @ X @ Z2 ) ) |
% 1.26/0.87 ( ~( product @ X @ Y @ Z1 ) )),
% 1.26/0.87 inference('cnf.neg', [status(esa)], [qg3])).
% 1.26/0.87 thf(zip_derived_cl19, plain,
% 1.26/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.26/0.87 ( (product @ X0 @ X1 @ X2)
% 1.26/0.87 | ~ (product @ X3 @ X2 @ X1)
% 1.26/0.87 | ~ (product @ X2 @ X3 @ X0))),
% 1.26/0.87 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.26/0.87 thf(zip_derived_cl28, plain,
% 1.26/0.87 (![X0 : $i, X1 : $i]:
% 1.26/0.87 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 1.26/0.87 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 1.26/0.87 thf(zip_derived_cl65, plain,
% 1.26/0.87 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl28])).
% 1.26/0.87 thf(zip_derived_cl18, plain,
% 1.26/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.26/0.87 (~ (product @ X0 @ X1 @ X2)
% 1.26/0.87 | ~ (product @ X3 @ X1 @ X2)
% 1.26/0.87 | (equalish @ X0 @ X3))),
% 1.26/0.87 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.26/0.87 thf(zip_derived_cl71, plain,
% 1.26/0.87 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_1) | (equalish @ e_2 @ X0)))
% 1.26/0.87 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl18])).
% 1.26/0.87 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 1.26/0.87 thf(zip_derived_cl11, plain, (~ (equalish @ e_2 @ e_1)),
% 1.26/0.87 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 1.26/0.87 thf(zip_derived_cl136, plain,
% 1.26/0.87 ((~ (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl11])).
% 1.26/0.87 thf('3', plain,
% 1.26/0.87 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_1))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl136])).
% 1.26/0.87 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 1.26/0.87 inference('cnf', [status(esa)], [element_1])).
% 1.26/0.87 thf(zip_derived_cl22, plain,
% 1.26/0.87 (![X0 : $i]:
% 1.26/0.87 (~ (group_element @ X0)
% 1.26/0.87 | (product @ e_2 @ X0 @ e_1)
% 1.26/0.87 | (product @ e_2 @ X0 @ e_2)
% 1.26/0.87 | (product @ e_2 @ X0 @ e_3))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl15])).
% 1.26/0.87 thf(zip_derived_cl51, plain,
% 1.26/0.87 (( (product @ e_2 @ e_1 @ e_1)
% 1.26/0.87 | (product @ e_2 @ e_1 @ e_2)
% 1.26/0.87 | (product @ e_2 @ e_1 @ e_3))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl22])).
% 1.26/0.87 thf(zip_derived_cl250, plain,
% 1.26/0.87 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.26/0.87 inference('split', [status(esa)], [zip_derived_cl51])).
% 1.26/0.87 thf(zip_derived_cl18, plain,
% 1.26/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.26/0.87 (~ (product @ X0 @ X1 @ X2)
% 1.26/0.87 | ~ (product @ X3 @ X1 @ X2)
% 1.26/0.87 | (equalish @ X0 @ X3))),
% 1.26/0.87 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.26/0.87 thf(zip_derived_cl254, plain,
% 1.26/0.87 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_2) | (equalish @ e_2 @ X0)))
% 1.26/0.87 <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl250, zip_derived_cl18])).
% 1.26/0.87 thf(zip_derived_cl11, plain, (~ (equalish @ e_2 @ e_1)),
% 1.26/0.87 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 1.26/0.87 thf(zip_derived_cl742, plain,
% 1.26/0.87 ((~ (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl254, zip_derived_cl11])).
% 1.26/0.87 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 1.26/0.87 inference('cnf', [status(esa)], [element_2])).
% 1.26/0.87 thf(zip_derived_cl15, plain,
% 1.26/0.87 (![X0 : $i, X1 : $i]:
% 1.26/0.87 (~ (group_element @ X0)
% 1.26/0.87 | ~ (group_element @ X1)
% 1.26/0.87 | (product @ X0 @ X1 @ e_1)
% 1.26/0.87 | (product @ X0 @ X1 @ e_2)
% 1.26/0.87 | (product @ X0 @ X1 @ e_3))),
% 1.26/0.87 inference('cnf', [status(esa)], [product_total_function1])).
% 1.26/0.87 thf(zip_derived_cl24, plain,
% 1.26/0.87 (![X0 : $i]:
% 1.26/0.87 ( (product @ X0 @ X0 @ e_3)
% 1.26/0.87 | (product @ X0 @ X0 @ e_2)
% 1.26/0.87 | (product @ X0 @ X0 @ e_1)
% 1.26/0.87 | ~ (group_element @ X0))),
% 1.26/0.87 inference('eq_fact', [status(thm)], [zip_derived_cl15])).
% 1.26/0.87 thf(zip_derived_cl97, plain,
% 1.26/0.87 (( (product @ e_2 @ e_2 @ e_3)
% 1.26/0.87 | (product @ e_2 @ e_2 @ e_2)
% 1.26/0.87 | (product @ e_2 @ e_2 @ e_1))),
% 1.26/0.87 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl24])).
% 1.26/0.87 thf(zip_derived_cl440, plain,
% 1.26/0.87 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 1.26/0.87 inference('split', [status(esa)], [zip_derived_cl97])).
% 1.26/0.87 thf(zip_derived_cl28, plain,
% 1.26/0.87 (![X0 : $i, X1 : $i]:
% 1.26/0.87 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 1.26/0.87 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 1.26/0.87 thf(zip_derived_cl448, plain,
% 1.26/0.87 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl440, zip_derived_cl28])).
% 1.26/0.88 thf('4', plain,
% 1.26/0.88 (~ ( (product @ e_2 @ e_2 @ e_1)) | ~ ( (product @ e_2 @ e_1 @ e_2))),
% 1.26/0.88 inference('s_sup+', [status(thm)], [zip_derived_cl742, zip_derived_cl448])).
% 1.26/0.88 thf(zip_derived_cl250, plain,
% 1.26/0.88 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl51])).
% 1.26/0.88 thf(zip_derived_cl17, plain,
% 1.26/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.26/0.88 (~ (product @ X0 @ X1 @ X2)
% 1.26/0.88 | ~ (product @ X0 @ X3 @ X2)
% 1.26/0.88 | (equalish @ X1 @ X3))),
% 1.26/0.88 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.26/0.88 thf(zip_derived_cl253, plain,
% 1.26/0.88 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 1.26/0.88 <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl250, zip_derived_cl17])).
% 1.26/0.88 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 1.26/0.88 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.26/0.88 thf(zip_derived_cl734, plain,
% 1.26/0.88 ((~ (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl253, zip_derived_cl9])).
% 1.26/0.88 thf(zip_derived_cl269, plain,
% 1.26/0.88 (( (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_2)))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl52])).
% 1.26/0.88 thf('5', plain,
% 1.26/0.88 (~ ( (product @ e_2 @ e_2 @ e_2)) | ~ ( (product @ e_2 @ e_1 @ e_2))),
% 1.26/0.88 inference('s_sup+', [status(thm)], [zip_derived_cl734, zip_derived_cl269])).
% 1.26/0.88 thf(zip_derived_cl253, plain,
% 1.26/0.88 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 1.26/0.88 <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl250, zip_derived_cl17])).
% 1.26/0.88 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 1.26/0.88 thf(zip_derived_cl10, plain, (~ (equalish @ e_1 @ e_3)),
% 1.26/0.88 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 1.26/0.88 thf(zip_derived_cl735, plain,
% 1.26/0.88 ((~ (product @ e_2 @ e_3 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl253, zip_derived_cl10])).
% 1.26/0.88 thf(zip_derived_cl250, plain,
% 1.26/0.88 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl51])).
% 1.26/0.88 thf(zip_derived_cl103, plain,
% 1.26/0.88 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl31])).
% 1.26/0.88 thf(zip_derived_cl19, plain,
% 1.26/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.26/0.88 ( (product @ X0 @ X1 @ X2)
% 1.26/0.88 | ~ (product @ X3 @ X2 @ X1)
% 1.26/0.88 | ~ (product @ X2 @ X3 @ X0))),
% 1.26/0.88 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.26/0.88 thf(zip_derived_cl109, plain,
% 1.26/0.88 ((![X0 : $i]:
% 1.26/0.88 ( (product @ X0 @ e_3 @ e_2) | ~ (product @ e_2 @ e_1 @ X0)))
% 1.26/0.88 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl103, zip_derived_cl19])).
% 1.26/0.88 thf(zip_derived_cl260, plain,
% 1.26/0.88 (( (product @ e_2 @ e_3 @ e_2))
% 1.26/0.88 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl250, zip_derived_cl109])).
% 1.26/0.88 thf('6', plain,
% 1.26/0.88 (~ ( (product @ e_2 @ e_1 @ e_2)) | ~ ( (product @ e_1 @ e_2 @ e_3))),
% 1.26/0.88 inference('s_sup+', [status(thm)], [zip_derived_cl735, zip_derived_cl260])).
% 1.26/0.88 thf(zip_derived_cl250, plain,
% 1.26/0.88 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl51])).
% 1.26/0.88 thf(zip_derived_cl104, plain,
% 1.26/0.88 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl31])).
% 1.26/0.88 thf(zip_derived_cl19, plain,
% 1.26/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.26/0.88 ( (product @ X0 @ X1 @ X2)
% 1.26/0.88 | ~ (product @ X3 @ X2 @ X1)
% 1.26/0.88 | ~ (product @ X2 @ X3 @ X0))),
% 1.26/0.88 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.26/0.88 thf(zip_derived_cl120, plain,
% 1.26/0.88 ((![X0 : $i]:
% 1.26/0.88 ( (product @ X0 @ e_2 @ e_2) | ~ (product @ e_2 @ e_1 @ X0)))
% 1.26/0.88 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl104, zip_derived_cl19])).
% 1.26/0.88 thf(zip_derived_cl528, plain,
% 1.26/0.88 (( (product @ e_2 @ e_2 @ e_2))
% 1.26/0.88 <= (( (product @ e_1 @ e_2 @ e_2)) & ( (product @ e_2 @ e_1 @ e_2)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl250, zip_derived_cl120])).
% 1.26/0.88 thf(zip_derived_cl204, plain,
% 1.26/0.88 (( (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl49])).
% 1.26/0.88 thf(product_total_function2, axiom,
% 1.26/0.88 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 1.26/0.88 ( equalish @ W @ Z ))).
% 1.26/0.88 thf(zip_derived_cl16, plain,
% 1.26/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.26/0.88 (~ (product @ X0 @ X1 @ X2)
% 1.26/0.88 | ~ (product @ X0 @ X1 @ X3)
% 1.26/0.88 | (equalish @ X2 @ X3))),
% 1.26/0.88 inference('cnf', [status(esa)], [product_total_function2])).
% 1.26/0.88 thf(zip_derived_cl207, plain,
% 1.26/0.88 ((![X0 : $i]: (~ (product @ e_2 @ e_2 @ X0) | (equalish @ e_3 @ X0)))
% 1.26/0.88 <= (( (product @ e_2 @ e_2 @ e_3)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl204, zip_derived_cl16])).
% 1.26/0.88 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 1.26/0.88 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_2)),
% 1.26/0.88 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 1.26/0.88 thf(zip_derived_cl627, plain,
% 1.26/0.88 ((~ (product @ e_2 @ e_2 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_3)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl207, zip_derived_cl14])).
% 1.26/0.88 thf('7', plain,
% 1.26/0.88 (~ ( (product @ e_2 @ e_2 @ e_3)) | ~ ( (product @ e_1 @ e_2 @ e_2)) |
% 1.26/0.88 ~ ( (product @ e_2 @ e_1 @ e_2))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl528, zip_derived_cl627])).
% 1.26/0.88 thf(e_1_then_e_2, axiom, (next @ e_1 @ e_2)).
% 1.26/0.88 thf(zip_derived_cl0, plain, ( (next @ e_1 @ e_2)),
% 1.26/0.88 inference('cnf', [status(esa)], [e_1_then_e_2])).
% 1.26/0.88 thf(zip_derived_cl36, plain,
% 1.26/0.88 (( (product @ e_1 @ e_1 @ e_3)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl30])).
% 1.26/0.88 thf(no_redundancy, axiom,
% 1.26/0.88 (( ~( product @ X @ e_1 @ Y ) ) | ( ~( next @ X @ X1 ) ) |
% 1.26/0.88 ( ~( greater @ Y @ X1 ) ))).
% 1.26/0.88 thf(zip_derived_cl5, plain,
% 1.26/0.88 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.26/0.88 (~ (product @ X0 @ e_1 @ X1)
% 1.26/0.88 | ~ (next @ X0 @ X2)
% 1.26/0.88 | ~ (greater @ X1 @ X2))),
% 1.26/0.88 inference('cnf', [status(esa)], [no_redundancy])).
% 1.26/0.88 thf(zip_derived_cl47, plain,
% 1.26/0.88 ((![X0 : $i]: (~ (next @ e_1 @ X0) | ~ (greater @ e_3 @ X0)))
% 1.26/0.88 <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl5])).
% 1.26/0.88 thf(zip_derived_cl55, plain,
% 1.26/0.88 ((~ (greater @ e_3 @ e_2)) <= (( (product @ e_1 @ e_1 @ e_3)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl47])).
% 1.26/0.88 thf(e_3_greater_e_2, axiom, (greater @ e_3 @ e_2)).
% 1.26/0.88 thf(zip_derived_cl4, plain, ( (greater @ e_3 @ e_2)),
% 1.26/0.88 inference('cnf', [status(esa)], [e_3_greater_e_2])).
% 1.26/0.88 thf('8', plain, (~ ( (product @ e_1 @ e_1 @ e_3))),
% 1.26/0.88 inference('demod', [status(thm)], [zip_derived_cl55, zip_derived_cl4])).
% 1.26/0.88 thf(zip_derived_cl184, plain,
% 1.26/0.88 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl48])).
% 1.26/0.88 thf(zip_derived_cl38, plain,
% 1.26/0.88 (( (product @ e_1 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl30])).
% 1.26/0.88 thf(zip_derived_cl18, plain,
% 1.26/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.26/0.88 (~ (product @ X0 @ X1 @ X2)
% 1.26/0.88 | ~ (product @ X3 @ X1 @ X2)
% 1.26/0.88 | (equalish @ X0 @ X3))),
% 1.26/0.88 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.26/0.88 thf(zip_derived_cl87, plain,
% 1.26/0.88 ((![X0 : $i]: (~ (product @ X0 @ e_1 @ e_1) | (equalish @ e_1 @ X0)))
% 1.26/0.88 <= (( (product @ e_1 @ e_1 @ e_1)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl38, zip_derived_cl18])).
% 1.26/0.88 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 1.26/0.88 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.26/0.88 thf(zip_derived_cl348, plain,
% 1.26/0.88 ((~ (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_1)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl87, zip_derived_cl9])).
% 1.26/0.88 thf('9', plain,
% 1.26/0.88 (~ ( (product @ e_1 @ e_1 @ e_1)) | ~ ( (product @ e_2 @ e_1 @ e_1))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl184, zip_derived_cl348])).
% 1.26/0.88 thf(zip_derived_cl184, plain,
% 1.26/0.88 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl48])).
% 1.26/0.88 thf(zip_derived_cl65, plain,
% 1.26/0.88 (( (product @ e_2 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl37, zip_derived_cl28])).
% 1.26/0.88 thf(zip_derived_cl17, plain,
% 1.26/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.26/0.88 (~ (product @ X0 @ X1 @ X2)
% 1.26/0.88 | ~ (product @ X0 @ X3 @ X2)
% 1.26/0.88 | (equalish @ X1 @ X3))),
% 1.26/0.88 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.26/0.88 thf(zip_derived_cl70, plain,
% 1.26/0.88 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_1) | (equalish @ e_2 @ X0)))
% 1.26/0.88 <= (( (product @ e_1 @ e_1 @ e_2)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl17])).
% 1.26/0.88 thf(zip_derived_cl11, plain, (~ (equalish @ e_2 @ e_1)),
% 1.26/0.88 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 1.26/0.88 thf(zip_derived_cl115, plain,
% 1.26/0.88 ((~ (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_1 @ e_1 @ e_2)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl70, zip_derived_cl11])).
% 1.26/0.88 thf('10', plain,
% 1.26/0.88 (~ ( (product @ e_1 @ e_1 @ e_2)) | ~ ( (product @ e_2 @ e_1 @ e_1))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl184, zip_derived_cl115])).
% 1.26/0.88 thf('11', plain,
% 1.26/0.88 (( (product @ e_1 @ e_1 @ e_1)) | ( (product @ e_1 @ e_1 @ e_2)) |
% 1.26/0.88 ( (product @ e_1 @ e_1 @ e_3))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl30])).
% 1.26/0.88 thf('12', plain,
% 1.26/0.88 (( (product @ e_2 @ e_1 @ e_3)) | ( (product @ e_2 @ e_1 @ e_1)) |
% 1.26/0.88 ( (product @ e_2 @ e_1 @ e_2))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl48])).
% 1.26/0.88 thf(zip_derived_cl103, plain,
% 1.26/0.88 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl31])).
% 1.26/0.88 thf(zip_derived_cl18, plain,
% 1.26/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.26/0.88 (~ (product @ X0 @ X1 @ X2)
% 1.26/0.88 | ~ (product @ X3 @ X1 @ X2)
% 1.26/0.88 | (equalish @ X0 @ X3))),
% 1.26/0.88 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.26/0.88 thf(zip_derived_cl108, plain,
% 1.26/0.88 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_1 @ X0)))
% 1.26/0.88 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl103, zip_derived_cl18])).
% 1.26/0.88 thf(zip_derived_cl9, plain, (~ (equalish @ e_1 @ e_2)),
% 1.26/0.88 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.26/0.88 thf(zip_derived_cl484, plain,
% 1.26/0.88 ((~ (product @ e_2 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl108, zip_derived_cl9])).
% 1.26/0.88 thf(zip_derived_cl182, plain,
% 1.26/0.88 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl48])).
% 1.26/0.88 thf(zip_derived_cl109, plain,
% 1.26/0.88 ((![X0 : $i]:
% 1.26/0.88 ( (product @ X0 @ e_3 @ e_2) | ~ (product @ e_2 @ e_1 @ X0)))
% 1.26/0.88 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl103, zip_derived_cl19])).
% 1.26/0.88 thf(zip_derived_cl195, plain,
% 1.26/0.88 (( (product @ e_3 @ e_3 @ e_2))
% 1.26/0.88 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl182, zip_derived_cl109])).
% 1.26/0.88 thf(zip_derived_cl28, plain,
% 1.26/0.88 (![X0 : $i, X1 : $i]:
% 1.26/0.88 (~ (product @ X1 @ X1 @ X0) | (product @ X0 @ X0 @ X1))),
% 1.26/0.88 inference('eq_fact', [status(thm)], [zip_derived_cl19])).
% 1.26/0.88 thf(zip_derived_cl203, plain,
% 1.26/0.88 (( (product @ e_2 @ e_2 @ e_3))
% 1.26/0.88 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_1 @ e_3)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl195, zip_derived_cl28])).
% 1.26/0.88 thf('13', plain,
% 1.26/0.88 (~ ( (product @ e_1 @ e_2 @ e_3)) | ~ ( (product @ e_2 @ e_1 @ e_3))),
% 1.26/0.88 inference('s_sup+', [status(thm)], [zip_derived_cl484, zip_derived_cl203])).
% 1.26/0.88 thf('14', plain,
% 1.26/0.88 (( (product @ e_1 @ e_2 @ e_2)) | ( (product @ e_1 @ e_2 @ e_3)) |
% 1.26/0.88 ( (product @ e_1 @ e_2 @ e_1))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl31])).
% 1.26/0.88 thf(zip_derived_cl448, plain,
% 1.26/0.88 (( (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_2 @ e_1)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl440, zip_derived_cl28])).
% 1.26/0.88 thf(zip_derived_cl104, plain,
% 1.26/0.88 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl31])).
% 1.26/0.88 thf(zip_derived_cl17, plain,
% 1.26/0.88 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.26/0.88 (~ (product @ X0 @ X1 @ X2)
% 1.26/0.88 | ~ (product @ X0 @ X3 @ X2)
% 1.26/0.88 | (equalish @ X1 @ X3))),
% 1.26/0.88 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.26/0.88 thf(zip_derived_cl118, plain,
% 1.26/0.88 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_2) | (equalish @ e_2 @ X0)))
% 1.26/0.88 <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl104, zip_derived_cl17])).
% 1.26/0.88 thf(zip_derived_cl11, plain, (~ (equalish @ e_2 @ e_1)),
% 1.26/0.88 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 1.26/0.88 thf(zip_derived_cl500, plain,
% 1.26/0.88 ((~ (product @ e_1 @ e_1 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl11])).
% 1.26/0.88 thf('15', plain,
% 1.26/0.88 (~ ( (product @ e_2 @ e_2 @ e_1)) | ~ ( (product @ e_1 @ e_2 @ e_2))),
% 1.26/0.88 inference('s_sup-', [status(thm)], [zip_derived_cl448, zip_derived_cl500])).
% 1.26/0.88 thf('16', plain,
% 1.26/0.88 (( (product @ e_2 @ e_2 @ e_1)) | ( (product @ e_2 @ e_2 @ e_2)) |
% 1.26/0.88 ( (product @ e_2 @ e_2 @ e_3))),
% 1.26/0.88 inference('split', [status(esa)], [zip_derived_cl49])).
% 1.26/0.88 thf(zip_derived_cl854, plain, ($false),
% 1.26/0.88 inference('sat_resolution*', [status(thm)],
% 1.26/0.88 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 1.26/0.88 '12', '13', '14', '15', '16'])).
% 1.26/0.88
% 1.26/0.88 % SZS output end Refutation
% 1.26/0.88
% 1.26/0.88
% 1.26/0.88 % Terminating...
% 1.66/0.95 % Runner terminated.
% 1.66/0.96 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------