TSTP Solution File: GRP124-3.004 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP124-3.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ti8ppq3Oia true
% Computer : n003.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 01:50:05 EDT 2023
% Result : Unsatisfiable 0.55s 1.08s
% Output : Refutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP124-3.004 : TPTP v8.1.2. Released v1.2.0.
% 0.03/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ti8ppq3Oia true
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 20:48:40 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in FO mode
% 0.50/0.65 % Total configuration time : 435
% 0.50/0.65 % Estimated wc time : 1092
% 0.50/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.53/0.71 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.72 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.54/0.73 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.54/0.73 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.55/0.80 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 0.55/1.08 % Solved by fo/fo1_av.sh.
% 0.55/1.08 % done 990 iterations in 0.331s
% 0.55/1.08 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.55/1.08 % SZS output start Refutation
% 0.55/1.08 thf(e_4_type, type, e_4: $i).
% 0.55/1.08 thf(e_3_type, type, e_3: $i).
% 0.55/1.08 thf(e_2_type, type, e_2: $i).
% 0.55/1.08 thf(e_1_type, type, e_1: $i).
% 0.55/1.08 thf(product_type, type, product: $i > $i > $i > $o).
% 0.55/1.08 thf(group_element_type, type, group_element: $i > $o).
% 0.55/1.08 thf(equalish_type, type, equalish: $i > $i > $o).
% 0.55/1.08 thf(element_1, axiom, (group_element @ e_1)).
% 0.55/1.08 thf(zip_derived_cl21, plain, ( (group_element @ e_1)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_1])).
% 0.55/1.08 thf(product_total_function1, axiom,
% 0.55/1.08 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 0.55/1.08 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 0.55/1.08 ( product @ X @ Y @ e_3 ) | ( product @ X @ Y @ e_4 ))).
% 0.55/1.08 thf(zip_derived_cl37, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | ~ (group_element @ X1)
% 0.55/1.08 | (product @ X0 @ X1 @ e_1)
% 0.55/1.08 | (product @ X0 @ X1 @ e_2)
% 0.55/1.08 | (product @ X0 @ X1 @ e_3)
% 0.55/1.08 | (product @ X0 @ X1 @ e_4))),
% 0.55/1.08 inference('cnf', [status(esa)], [product_total_function1])).
% 0.55/1.08 thf(zip_derived_cl99, plain,
% 0.55/1.08 (![X0 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_1)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_2)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_3)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.55/1.08 thf(element_3, axiom, (group_element @ e_3)).
% 0.55/1.08 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_3])).
% 0.55/1.08 thf(zip_derived_cl284, plain,
% 0.55/1.08 (( (product @ e_1 @ e_3 @ e_4)
% 0.55/1.08 | (product @ e_1 @ e_3 @ e_3)
% 0.55/1.08 | (product @ e_1 @ e_3 @ e_2)
% 0.55/1.08 | (product @ e_1 @ e_3 @ e_1))),
% 0.55/1.08 inference('s_sup+', [status(thm)], [zip_derived_cl99, zip_derived_cl23])).
% 0.55/1.08 thf(zip_derived_cl834, plain,
% 0.55/1.08 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl284])).
% 0.55/1.08 thf(product_idempotence, axiom, (product @ X @ X @ X)).
% 0.55/1.08 thf(zip_derived_cl41, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.55/1.08 inference('cnf', [status(esa)], [product_idempotence])).
% 0.55/1.08 thf(product_right_cancellation, axiom,
% 0.55/1.08 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 0.55/1.08 ( equalish @ W @ Z ))).
% 0.55/1.08 thf(zip_derived_cl39, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.08 (~ (product @ X0 @ X1 @ X2)
% 0.55/1.08 | ~ (product @ X0 @ X3 @ X2)
% 0.55/1.08 | (equalish @ X1 @ X3))),
% 0.55/1.08 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.55/1.08 thf(zip_derived_cl59, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i]:
% 0.55/1.08 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.55/1.08 thf(zip_derived_cl1545, plain,
% 0.55/1.08 (( (equalish @ e_1 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl834, zip_derived_cl59])).
% 0.55/1.08 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 0.55/1.08 thf(zip_derived_cl26, plain, (~ (equalish @ e_1 @ e_3)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.55/1.08 thf('0', plain, (~ ( (product @ e_1 @ e_3 @ e_1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1545, zip_derived_cl26])).
% 0.55/1.08 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_3])).
% 0.55/1.08 thf(zip_derived_cl99, plain,
% 0.55/1.08 (![X0 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_1)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_2)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_3)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.55/1.08 thf(zip_derived_cl288, plain,
% 0.55/1.08 (( (product @ e_1 @ e_3 @ e_1)
% 0.55/1.08 | (product @ e_1 @ e_3 @ e_2)
% 0.55/1.08 | (product @ e_1 @ e_3 @ e_3)
% 0.55/1.08 | (product @ e_1 @ e_3 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl99])).
% 0.55/1.08 thf(zip_derived_cl923, plain,
% 0.55/1.08 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl288])).
% 0.55/1.08 thf(zip_derived_cl41, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.55/1.08 inference('cnf', [status(esa)], [product_idempotence])).
% 0.55/1.08 thf(product_left_cancellation, axiom,
% 0.55/1.08 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 0.55/1.08 ( equalish @ W @ Z ))).
% 0.55/1.08 thf(zip_derived_cl40, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.08 (~ (product @ X0 @ X1 @ X2)
% 0.55/1.08 | ~ (product @ X3 @ X1 @ X2)
% 0.55/1.08 | (equalish @ X0 @ X3))),
% 0.55/1.08 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.55/1.08 thf(zip_derived_cl70, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i]:
% 0.55/1.08 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.55/1.08 thf(zip_derived_cl935, plain,
% 0.55/1.08 (( (equalish @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl923, zip_derived_cl70])).
% 0.55/1.08 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 0.55/1.08 thf(zip_derived_cl31, plain, (~ (equalish @ e_3 @ e_1)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.55/1.08 thf('1', plain, (~ ( (product @ e_1 @ e_3 @ e_3))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl935, zip_derived_cl31])).
% 0.55/1.08 thf(zip_derived_cl21, plain, ( (group_element @ e_1)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_1])).
% 0.55/1.08 thf(element_2, axiom, (group_element @ e_2)).
% 0.55/1.08 thf(zip_derived_cl22, plain, ( (group_element @ e_2)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_2])).
% 0.55/1.08 thf(zip_derived_cl37, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | ~ (group_element @ X1)
% 0.55/1.08 | (product @ X0 @ X1 @ e_1)
% 0.55/1.08 | (product @ X0 @ X1 @ e_2)
% 0.55/1.08 | (product @ X0 @ X1 @ e_3)
% 0.55/1.08 | (product @ X0 @ X1 @ e_4))),
% 0.55/1.08 inference('cnf', [status(esa)], [product_total_function1])).
% 0.55/1.08 thf(zip_derived_cl100, plain,
% 0.55/1.08 (![X0 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_1)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_2)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_3)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl37])).
% 0.55/1.08 thf(zip_derived_cl305, plain,
% 0.55/1.08 (( (product @ e_2 @ e_1 @ e_1)
% 0.55/1.08 | (product @ e_2 @ e_1 @ e_2)
% 0.55/1.08 | (product @ e_2 @ e_1 @ e_3)
% 0.55/1.08 | (product @ e_2 @ e_1 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl100])).
% 0.55/1.08 thf(zip_derived_cl1104, plain,
% 0.55/1.08 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl305])).
% 0.55/1.08 thf(zip_derived_cl70, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i]:
% 0.55/1.08 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.55/1.08 thf(zip_derived_cl1116, plain,
% 0.55/1.08 (( (equalish @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1104, zip_derived_cl70])).
% 0.55/1.08 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 0.55/1.08 thf(zip_derived_cl25, plain, (~ (equalish @ e_1 @ e_2)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.55/1.08 thf('2', plain, (~ ( (product @ e_2 @ e_1 @ e_1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1116, zip_derived_cl25])).
% 0.55/1.08 thf(zip_derived_cl100, plain,
% 0.55/1.08 (![X0 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_1)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_2)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_3)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl37])).
% 0.55/1.08 thf(zip_derived_cl21, plain, ( (group_element @ e_1)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_1])).
% 0.55/1.08 thf(zip_derived_cl301, plain,
% 0.55/1.08 (( (product @ e_2 @ e_1 @ e_4)
% 0.55/1.08 | (product @ e_2 @ e_1 @ e_3)
% 0.55/1.08 | (product @ e_2 @ e_1 @ e_2)
% 0.55/1.08 | (product @ e_2 @ e_1 @ e_1))),
% 0.55/1.08 inference('s_sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl21])).
% 0.55/1.08 thf(zip_derived_cl978, plain,
% 0.55/1.08 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl301])).
% 0.55/1.08 thf(zip_derived_cl59, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i]:
% 0.55/1.08 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.55/1.08 thf(zip_derived_cl991, plain,
% 0.55/1.08 (( (equalish @ e_2 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl978, zip_derived_cl59])).
% 0.55/1.08 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 0.55/1.08 thf(zip_derived_cl28, plain, (~ (equalish @ e_2 @ e_1)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.55/1.08 thf('3', plain, (~ ( (product @ e_2 @ e_1 @ e_2))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl991, zip_derived_cl28])).
% 0.55/1.08 thf(zip_derived_cl980, plain,
% 0.55/1.08 (( (product @ e_2 @ e_1 @ e_4)) <= (( (product @ e_2 @ e_1 @ e_4)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl301])).
% 0.55/1.08 thf(zip_derived_cl99, plain,
% 0.55/1.08 (![X0 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_1)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_2)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_3)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.55/1.08 thf(element_4, axiom, (group_element @ e_4)).
% 0.55/1.08 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_4])).
% 0.55/1.08 thf(zip_derived_cl285, plain,
% 0.55/1.08 (( (product @ e_1 @ e_4 @ e_4)
% 0.55/1.08 | (product @ e_1 @ e_4 @ e_3)
% 0.55/1.08 | (product @ e_1 @ e_4 @ e_2)
% 0.55/1.08 | (product @ e_1 @ e_4 @ e_1))),
% 0.55/1.08 inference('s_sup+', [status(thm)], [zip_derived_cl99, zip_derived_cl24])).
% 0.55/1.08 thf(zip_derived_cl860, plain,
% 0.55/1.08 (( (product @ e_1 @ e_4 @ e_2)) <= (( (product @ e_1 @ e_4 @ e_2)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl285])).
% 0.55/1.08 thf(qg2_1, conjecture,
% 0.55/1.08 (~( ( equalish @ X1 @ X2 ) | ( ~( product @ Z2 @ X2 @ Y2 ) ) |
% 0.55/1.08 ( ~( product @ Z2 @ X1 @ Y1 ) ) | ( ~( product @ X2 @ Y2 @ Z1 ) ) |
% 0.55/1.08 ( ~( product @ X1 @ Y1 @ Z1 ) ) ))).
% 0.55/1.08 thf(zf_stmt_0, negated_conjecture,
% 0.55/1.08 (( equalish @ X1 @ X2 ) | ( ~( product @ Z2 @ X2 @ Y2 ) ) |
% 0.55/1.08 ( ~( product @ Z2 @ X1 @ Y1 ) ) | ( ~( product @ X2 @ Y2 @ Z1 ) ) |
% 0.55/1.08 ( ~( product @ X1 @ Y1 @ Z1 ) )),
% 0.55/1.08 inference('cnf.neg', [status(esa)], [qg2_1])).
% 0.55/1.08 thf(zip_derived_cl42, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.55/1.08 ( (equalish @ X0 @ X1)
% 0.55/1.08 | ~ (product @ X2 @ X1 @ X3)
% 0.55/1.08 | ~ (product @ X2 @ X0 @ X4)
% 0.55/1.08 | ~ (product @ X1 @ X3 @ X5)
% 0.55/1.08 | ~ (product @ X0 @ X4 @ X5))),
% 0.55/1.08 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.55/1.08 thf(zip_derived_cl86, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.08 (~ (product @ X2 @ X1 @ X0)
% 0.55/1.08 | ~ (product @ X0 @ X0 @ X0)
% 0.55/1.08 | ~ (product @ X0 @ X2 @ X1)
% 0.55/1.08 | (equalish @ X2 @ X0))),
% 0.55/1.08 inference('eq_fact', [status(thm)], [zip_derived_cl42])).
% 0.55/1.08 thf(zip_derived_cl41, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.55/1.08 inference('cnf', [status(esa)], [product_idempotence])).
% 0.55/1.08 thf(zip_derived_cl89, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.08 (~ (product @ X2 @ X1 @ X0)
% 0.55/1.08 | ~ (product @ X0 @ X2 @ X1)
% 0.55/1.08 | (equalish @ X2 @ X0))),
% 0.55/1.08 inference('demod', [status(thm)], [zip_derived_cl86, zip_derived_cl41])).
% 0.55/1.08 thf(zip_derived_cl1617, plain,
% 0.55/1.08 (((~ (product @ e_2 @ e_1 @ e_4) | (equalish @ e_1 @ e_2)))
% 0.55/1.08 <= (( (product @ e_1 @ e_4 @ e_2)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl860, zip_derived_cl89])).
% 0.55/1.08 thf(zip_derived_cl25, plain, (~ (equalish @ e_1 @ e_2)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.55/1.08 thf(zip_derived_cl1624, plain,
% 0.55/1.08 ((~ (product @ e_2 @ e_1 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_2)))),
% 0.55/1.08 inference('demod', [status(thm)], [zip_derived_cl1617, zip_derived_cl25])).
% 0.55/1.08 thf('4', plain,
% 0.55/1.08 (~ ( (product @ e_2 @ e_1 @ e_4)) | ~ ( (product @ e_1 @ e_4 @ e_2))),
% 0.55/1.08 inference('s_sup-', [status(thm)],
% 0.55/1.08 [zip_derived_cl980, zip_derived_cl1624])).
% 0.55/1.08 thf('5', plain,
% 0.55/1.08 (( (product @ e_2 @ e_1 @ e_3)) | ( (product @ e_2 @ e_1 @ e_4)) |
% 0.55/1.08 ( (product @ e_2 @ e_1 @ e_2)) | ( (product @ e_2 @ e_1 @ e_1))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl301])).
% 0.55/1.08 thf(zip_derived_cl981, plain,
% 0.55/1.08 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl301])).
% 0.55/1.08 thf(zip_derived_cl833, plain,
% 0.55/1.08 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl284])).
% 0.55/1.08 thf(zip_derived_cl89, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.08 (~ (product @ X2 @ X1 @ X0)
% 0.55/1.08 | ~ (product @ X0 @ X2 @ X1)
% 0.55/1.08 | (equalish @ X2 @ X0))),
% 0.55/1.08 inference('demod', [status(thm)], [zip_derived_cl86, zip_derived_cl41])).
% 0.55/1.08 thf(zip_derived_cl1301, plain,
% 0.55/1.08 (((~ (product @ e_2 @ e_1 @ e_3) | (equalish @ e_1 @ e_2)))
% 0.55/1.08 <= (( (product @ e_1 @ e_3 @ e_2)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl833, zip_derived_cl89])).
% 0.55/1.08 thf(zip_derived_cl25, plain, (~ (equalish @ e_1 @ e_2)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.55/1.08 thf(zip_derived_cl1308, plain,
% 0.55/1.08 ((~ (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 0.55/1.08 inference('demod', [status(thm)], [zip_derived_cl1301, zip_derived_cl25])).
% 0.55/1.08 thf('6', plain,
% 0.55/1.08 (~ ( (product @ e_1 @ e_3 @ e_2)) | ~ ( (product @ e_2 @ e_1 @ e_3))),
% 0.55/1.08 inference('s_sup-', [status(thm)],
% 0.55/1.08 [zip_derived_cl981, zip_derived_cl1308])).
% 0.55/1.08 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_4])).
% 0.55/1.08 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_3])).
% 0.55/1.08 thf(zip_derived_cl37, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | ~ (group_element @ X1)
% 0.55/1.08 | (product @ X0 @ X1 @ e_1)
% 0.55/1.08 | (product @ X0 @ X1 @ e_2)
% 0.55/1.08 | (product @ X0 @ X1 @ e_3)
% 0.55/1.08 | (product @ X0 @ X1 @ e_4))),
% 0.55/1.08 inference('cnf', [status(esa)], [product_total_function1])).
% 0.55/1.08 thf(zip_derived_cl101, plain,
% 0.55/1.08 (![X0 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | (product @ e_3 @ X0 @ e_1)
% 0.55/1.08 | (product @ e_3 @ X0 @ e_2)
% 0.55/1.08 | (product @ e_3 @ X0 @ e_3)
% 0.55/1.08 | (product @ e_3 @ X0 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl37])).
% 0.55/1.08 thf(zip_derived_cl334, plain,
% 0.55/1.08 (( (product @ e_3 @ e_4 @ e_1)
% 0.55/1.08 | (product @ e_3 @ e_4 @ e_2)
% 0.55/1.08 | (product @ e_3 @ e_4 @ e_3)
% 0.55/1.08 | (product @ e_3 @ e_4 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl101])).
% 0.55/1.08 thf(zip_derived_cl100, plain,
% 0.55/1.08 (![X0 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_1)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_2)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_3)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl37])).
% 0.55/1.08 thf(zip_derived_cl23, plain, ( (group_element @ e_3)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_3])).
% 0.55/1.08 thf(zip_derived_cl303, plain,
% 0.55/1.08 (( (product @ e_2 @ e_3 @ e_4)
% 0.55/1.08 | (product @ e_2 @ e_3 @ e_3)
% 0.55/1.08 | (product @ e_2 @ e_3 @ e_2)
% 0.55/1.08 | (product @ e_2 @ e_3 @ e_1))),
% 0.55/1.08 inference('s_sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl23])).
% 0.55/1.08 thf(zip_derived_cl1024, plain,
% 0.55/1.08 (( (product @ e_2 @ e_3 @ e_4)) <= (( (product @ e_2 @ e_3 @ e_4)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl303])).
% 0.55/1.08 thf(qg2_2, conjecture,
% 0.55/1.08 (~( ( equalish @ Y1 @ Y2 ) | ( ~( product @ Z2 @ X2 @ Y2 ) ) |
% 0.55/1.08 ( ~( product @ Z2 @ X1 @ Y1 ) ) | ( ~( product @ X2 @ Y2 @ Z1 ) ) |
% 0.55/1.08 ( ~( product @ X1 @ Y1 @ Z1 ) ) ))).
% 0.55/1.08 thf(zf_stmt_1, negated_conjecture,
% 0.55/1.08 (( equalish @ Y1 @ Y2 ) | ( ~( product @ Z2 @ X2 @ Y2 ) ) |
% 0.55/1.08 ( ~( product @ Z2 @ X1 @ Y1 ) ) | ( ~( product @ X2 @ Y2 @ Z1 ) ) |
% 0.55/1.08 ( ~( product @ X1 @ Y1 @ Z1 ) )),
% 0.55/1.08 inference('cnf.neg', [status(esa)], [qg2_2])).
% 0.55/1.08 thf(zip_derived_cl43, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.55/1.08 ( (equalish @ X0 @ X1)
% 0.55/1.08 | ~ (product @ X2 @ X3 @ X1)
% 0.55/1.08 | ~ (product @ X2 @ X4 @ X0)
% 0.55/1.08 | ~ (product @ X3 @ X1 @ X5)
% 0.55/1.08 | ~ (product @ X4 @ X0 @ X5))),
% 0.55/1.08 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.55/1.08 thf(zip_derived_cl130, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.55/1.08 (~ (product @ X2 @ X1 @ X0)
% 0.55/1.08 | ~ (product @ X1 @ X0 @ X0)
% 0.55/1.08 | ~ (product @ X2 @ X2 @ X1)
% 0.55/1.08 | (equalish @ X1 @ X0))),
% 0.55/1.08 inference('eq_fact', [status(thm)], [zip_derived_cl43])).
% 0.55/1.08 thf(zip_derived_cl1035, plain,
% 0.55/1.08 (((~ (product @ e_3 @ e_4 @ e_4)
% 0.55/1.08 | ~ (product @ e_2 @ e_2 @ e_3)
% 0.55/1.08 | (equalish @ e_3 @ e_4))) <= (( (product @ e_2 @ e_3 @ e_4)))),
% 0.55/1.08 inference('s_sup-', [status(thm)],
% 0.55/1.08 [zip_derived_cl1024, zip_derived_cl130])).
% 0.55/1.08 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 0.55/1.08 thf(zip_derived_cl33, plain, (~ (equalish @ e_3 @ e_4)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 0.55/1.08 thf(zip_derived_cl1041, plain,
% 0.55/1.08 (((~ (product @ e_3 @ e_4 @ e_4) | ~ (product @ e_2 @ e_2 @ e_3)))
% 0.55/1.08 <= (( (product @ e_2 @ e_3 @ e_4)))),
% 0.55/1.08 inference('demod', [status(thm)], [zip_derived_cl1035, zip_derived_cl33])).
% 0.55/1.08 thf(zip_derived_cl1125, plain,
% 0.55/1.08 ((~ (product @ e_3 @ e_4 @ e_4)) <= (~ ( (product @ e_3 @ e_4 @ e_4)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl1041])).
% 0.55/1.08 thf(zip_derived_cl101, plain,
% 0.55/1.08 (![X0 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | (product @ e_3 @ X0 @ e_1)
% 0.55/1.08 | (product @ e_3 @ X0 @ e_2)
% 0.55/1.08 | (product @ e_3 @ X0 @ e_3)
% 0.55/1.08 | (product @ e_3 @ X0 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl37])).
% 0.55/1.08 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_4])).
% 0.55/1.08 thf(zip_derived_cl330, plain,
% 0.55/1.08 (( (product @ e_3 @ e_4 @ e_4)
% 0.55/1.08 | (product @ e_3 @ e_4 @ e_3)
% 0.55/1.08 | (product @ e_3 @ e_4 @ e_2)
% 0.55/1.08 | (product @ e_3 @ e_4 @ e_1))),
% 0.55/1.08 inference('s_sup+', [status(thm)], [zip_derived_cl101, zip_derived_cl24])).
% 0.55/1.08 thf(zip_derived_cl1244, plain,
% 0.55/1.08 (( (product @ e_3 @ e_4 @ e_4)) <= (( (product @ e_3 @ e_4 @ e_4)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl330])).
% 0.55/1.08 thf(zip_derived_cl70, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i]:
% 0.55/1.08 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.55/1.08 thf(zip_derived_cl1257, plain,
% 0.55/1.08 (( (equalish @ e_4 @ e_3)) <= (( (product @ e_3 @ e_4 @ e_4)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1244, zip_derived_cl70])).
% 0.55/1.08 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 0.55/1.08 thf(zip_derived_cl36, plain, (~ (equalish @ e_4 @ e_3)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 0.55/1.08 thf('7', plain, (~ ( (product @ e_3 @ e_4 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1257, zip_derived_cl36])).
% 0.55/1.08 thf('8', plain, (~ ( (product @ e_3 @ e_4 @ e_4))),
% 0.55/1.08 inference('sat_resolution*', [status(thm)], ['7'])).
% 0.55/1.08 thf(zip_derived_cl1294, plain, (~ (product @ e_3 @ e_4 @ e_4)),
% 0.55/1.08 inference('simpl_trail', [status(thm)], [zip_derived_cl1125, '8'])).
% 0.55/1.08 thf(zip_derived_cl1339, plain,
% 0.55/1.08 (( (product @ e_3 @ e_4 @ e_3)
% 0.55/1.08 | (product @ e_3 @ e_4 @ e_2)
% 0.55/1.08 | (product @ e_3 @ e_4 @ e_1))),
% 0.55/1.08 inference('clc', [status(thm)], [zip_derived_cl334, zip_derived_cl1294])).
% 0.55/1.08 thf(zip_derived_cl1340, plain,
% 0.55/1.08 (( (product @ e_3 @ e_4 @ e_3)) <= (( (product @ e_3 @ e_4 @ e_3)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl1339])).
% 0.55/1.08 thf(zip_derived_cl59, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i]:
% 0.55/1.08 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.55/1.08 thf(zip_derived_cl1352, plain,
% 0.55/1.08 (( (equalish @ e_3 @ e_4)) <= (( (product @ e_3 @ e_4 @ e_3)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1340, zip_derived_cl59])).
% 0.55/1.08 thf(zip_derived_cl33, plain, (~ (equalish @ e_3 @ e_4)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 0.55/1.08 thf('9', plain, (~ ( (product @ e_3 @ e_4 @ e_3))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1352, zip_derived_cl33])).
% 0.55/1.08 thf(zip_derived_cl861, plain,
% 0.55/1.08 (( (product @ e_1 @ e_4 @ e_1)) <= (( (product @ e_1 @ e_4 @ e_1)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl285])).
% 0.55/1.08 thf(zip_derived_cl59, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i]:
% 0.55/1.08 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.55/1.08 thf(zip_derived_cl1658, plain,
% 0.55/1.08 (( (equalish @ e_1 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_1)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl861, zip_derived_cl59])).
% 0.55/1.08 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 0.55/1.08 thf(zip_derived_cl27, plain, (~ (equalish @ e_1 @ e_4)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 0.55/1.08 thf('10', plain, (~ ( (product @ e_1 @ e_4 @ e_1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1658, zip_derived_cl27])).
% 0.55/1.08 thf(zip_derived_cl858, plain,
% 0.55/1.08 (( (product @ e_1 @ e_4 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_4)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl285])).
% 0.55/1.08 thf(zip_derived_cl70, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i]:
% 0.55/1.08 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.55/1.08 thf(zip_derived_cl871, plain,
% 0.55/1.08 (( (equalish @ e_4 @ e_1)) <= (( (product @ e_1 @ e_4 @ e_4)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl858, zip_derived_cl70])).
% 0.55/1.08 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 0.55/1.08 thf(zip_derived_cl34, plain, (~ (equalish @ e_4 @ e_1)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.55/1.08 thf('11', plain, (~ ( (product @ e_1 @ e_4 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl871, zip_derived_cl34])).
% 0.55/1.08 thf(zip_derived_cl100, plain,
% 0.55/1.08 (![X0 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_1)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_2)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_3)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl37])).
% 0.55/1.08 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_4])).
% 0.55/1.08 thf(zip_derived_cl304, plain,
% 0.55/1.08 (( (product @ e_2 @ e_4 @ e_4)
% 0.55/1.08 | (product @ e_2 @ e_4 @ e_3)
% 0.55/1.08 | (product @ e_2 @ e_4 @ e_2)
% 0.55/1.08 | (product @ e_2 @ e_4 @ e_1))),
% 0.55/1.08 inference('s_sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl24])).
% 0.55/1.08 thf('12', plain,
% 0.55/1.08 (( (product @ e_2 @ e_4 @ e_1)) | ( (product @ e_2 @ e_4 @ e_3)) |
% 0.55/1.08 ( (product @ e_2 @ e_4 @ e_4)) | ( (product @ e_2 @ e_4 @ e_2))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl304])).
% 0.55/1.08 thf(zip_derived_cl1054, plain,
% 0.55/1.08 (( (product @ e_2 @ e_4 @ e_4)) <= (( (product @ e_2 @ e_4 @ e_4)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl304])).
% 0.55/1.08 thf(zip_derived_cl70, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i]:
% 0.55/1.08 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.55/1.08 thf(zip_derived_cl1067, plain,
% 0.55/1.08 (( (equalish @ e_4 @ e_2)) <= (( (product @ e_2 @ e_4 @ e_4)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1054, zip_derived_cl70])).
% 0.55/1.08 thf(e_4_is_not_e_2, axiom, (~( equalish @ e_4 @ e_2 ))).
% 0.55/1.08 thf(zip_derived_cl35, plain, (~ (equalish @ e_4 @ e_2)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 0.55/1.08 thf('13', plain, (~ ( (product @ e_2 @ e_4 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1067, zip_derived_cl35])).
% 0.55/1.08 thf(zip_derived_cl1056, plain,
% 0.55/1.08 (( (product @ e_2 @ e_4 @ e_2)) <= (( (product @ e_2 @ e_4 @ e_2)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl304])).
% 0.55/1.08 thf(zip_derived_cl59, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i]:
% 0.55/1.08 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.55/1.08 thf(zip_derived_cl2054, plain,
% 0.55/1.08 (( (equalish @ e_2 @ e_4)) <= (( (product @ e_2 @ e_4 @ e_2)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1056, zip_derived_cl59])).
% 0.55/1.08 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 0.55/1.08 thf(zip_derived_cl30, plain, (~ (equalish @ e_2 @ e_4)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 0.55/1.08 thf('14', plain, (~ ( (product @ e_2 @ e_4 @ e_2))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl2054, zip_derived_cl30])).
% 0.55/1.08 thf(zip_derived_cl99, plain,
% 0.55/1.08 (![X0 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_1)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_2)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_3)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.55/1.08 thf(zip_derived_cl22, plain, ( (group_element @ e_2)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_2])).
% 0.55/1.08 thf(zip_derived_cl283, plain,
% 0.55/1.08 (( (product @ e_1 @ e_2 @ e_4)
% 0.55/1.08 | (product @ e_1 @ e_2 @ e_3)
% 0.55/1.08 | (product @ e_1 @ e_2 @ e_2)
% 0.55/1.08 | (product @ e_1 @ e_2 @ e_1))),
% 0.55/1.08 inference('s_sup+', [status(thm)], [zip_derived_cl99, zip_derived_cl22])).
% 0.55/1.08 thf('15', plain,
% 0.55/1.08 (( (product @ e_1 @ e_2 @ e_4)) | ( (product @ e_1 @ e_2 @ e_3)) |
% 0.55/1.08 ( (product @ e_1 @ e_2 @ e_2)) | ( (product @ e_1 @ e_2 @ e_1))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl283])).
% 0.55/1.08 thf(zip_derived_cl801, plain,
% 0.55/1.08 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl283])).
% 0.55/1.08 thf(zip_derived_cl70, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i]:
% 0.55/1.08 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 0.55/1.08 thf(zip_derived_cl1089, plain,
% 0.55/1.08 (( (equalish @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl801, zip_derived_cl70])).
% 0.55/1.08 thf(zip_derived_cl28, plain, (~ (equalish @ e_2 @ e_1)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.55/1.08 thf('16', plain, (~ ( (product @ e_1 @ e_2 @ e_2))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1089, zip_derived_cl28])).
% 0.55/1.08 thf(zip_derived_cl802, plain,
% 0.55/1.08 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl283])).
% 0.55/1.08 thf(zip_derived_cl59, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i]:
% 0.55/1.08 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.55/1.08 thf(zip_derived_cl1182, plain,
% 0.55/1.08 (( (equalish @ e_1 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl802, zip_derived_cl59])).
% 0.55/1.08 thf(zip_derived_cl25, plain, (~ (equalish @ e_1 @ e_2)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.55/1.08 thf('17', plain, (~ ( (product @ e_1 @ e_2 @ e_1))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1182, zip_derived_cl25])).
% 0.55/1.08 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_4])).
% 0.55/1.08 thf(zip_derived_cl100, plain,
% 0.55/1.08 (![X0 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_1)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_2)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_3)
% 0.55/1.08 | (product @ e_2 @ X0 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl37])).
% 0.55/1.08 thf(zip_derived_cl308, plain,
% 0.55/1.08 (( (product @ e_2 @ e_4 @ e_1)
% 0.55/1.08 | (product @ e_2 @ e_4 @ e_2)
% 0.55/1.08 | (product @ e_2 @ e_4 @ e_3)
% 0.55/1.08 | (product @ e_2 @ e_4 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl100])).
% 0.55/1.08 thf(zip_derived_cl1154, plain,
% 0.55/1.08 (( (product @ e_2 @ e_4 @ e_3)) <= (( (product @ e_2 @ e_4 @ e_3)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl308])).
% 0.55/1.08 thf(zip_derived_cl24, plain, ( (group_element @ e_4)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_4])).
% 0.55/1.08 thf(zip_derived_cl99, plain,
% 0.55/1.08 (![X0 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_1)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_2)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_3)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.55/1.08 thf(zip_derived_cl289, plain,
% 0.55/1.08 (( (product @ e_1 @ e_4 @ e_1)
% 0.55/1.08 | (product @ e_1 @ e_4 @ e_2)
% 0.55/1.08 | (product @ e_1 @ e_4 @ e_3)
% 0.55/1.08 | (product @ e_1 @ e_4 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl99])).
% 0.55/1.08 thf(zip_derived_cl953, plain,
% 0.55/1.08 (( (product @ e_1 @ e_4 @ e_3)) <= (( (product @ e_1 @ e_4 @ e_3)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl289])).
% 0.55/1.08 thf(zip_derived_cl40, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.08 (~ (product @ X0 @ X1 @ X2)
% 0.55/1.08 | ~ (product @ X3 @ X1 @ X2)
% 0.55/1.08 | (equalish @ X0 @ X3))),
% 0.55/1.08 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.55/1.08 thf(zip_derived_cl958, plain,
% 0.55/1.08 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_3) | (equalish @ e_1 @ X0)))
% 0.55/1.08 <= (( (product @ e_1 @ e_4 @ e_3)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl953, zip_derived_cl40])).
% 0.55/1.08 thf(zip_derived_cl1844, plain,
% 0.55/1.08 (( (equalish @ e_1 @ e_2))
% 0.55/1.08 <= (( (product @ e_1 @ e_4 @ e_3)) & ( (product @ e_2 @ e_4 @ e_3)))),
% 0.55/1.08 inference('s_sup-', [status(thm)],
% 0.55/1.08 [zip_derived_cl1154, zip_derived_cl958])).
% 0.55/1.08 thf(zip_derived_cl25, plain, (~ (equalish @ e_1 @ e_2)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.55/1.08 thf('18', plain,
% 0.55/1.08 (~ ( (product @ e_2 @ e_4 @ e_3)) | ~ ( (product @ e_1 @ e_4 @ e_3))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1844, zip_derived_cl25])).
% 0.55/1.08 thf(zip_derived_cl953, plain,
% 0.55/1.08 (( (product @ e_1 @ e_4 @ e_3)) <= (( (product @ e_1 @ e_4 @ e_3)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl289])).
% 0.55/1.08 thf(zip_derived_cl22, plain, ( (group_element @ e_2)),
% 0.55/1.08 inference('cnf', [status(esa)], [element_2])).
% 0.55/1.08 thf(zip_derived_cl99, plain,
% 0.55/1.08 (![X0 : $i]:
% 0.55/1.08 (~ (group_element @ X0)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_1)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_2)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_3)
% 0.55/1.08 | (product @ e_1 @ X0 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl37])).
% 0.55/1.08 thf(zip_derived_cl287, plain,
% 0.55/1.08 (( (product @ e_1 @ e_2 @ e_1)
% 0.55/1.08 | (product @ e_1 @ e_2 @ e_2)
% 0.55/1.08 | (product @ e_1 @ e_2 @ e_3)
% 0.55/1.08 | (product @ e_1 @ e_2 @ e_4))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl99])).
% 0.55/1.08 thf(zip_derived_cl893, plain,
% 0.55/1.08 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl287])).
% 0.55/1.08 thf(zip_derived_cl39, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.08 (~ (product @ X0 @ X1 @ X2)
% 0.55/1.08 | ~ (product @ X0 @ X3 @ X2)
% 0.55/1.08 | (equalish @ X1 @ X3))),
% 0.55/1.08 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.55/1.08 thf(zip_derived_cl897, plain,
% 0.55/1.08 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_3) | (equalish @ e_2 @ X0)))
% 0.55/1.08 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl893, zip_derived_cl39])).
% 0.55/1.08 thf(zip_derived_cl1784, plain,
% 0.55/1.08 (( (equalish @ e_2 @ e_4))
% 0.55/1.08 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_1 @ e_4 @ e_3)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl953, zip_derived_cl897])).
% 0.55/1.08 thf(zip_derived_cl30, plain, (~ (equalish @ e_2 @ e_4)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 0.55/1.08 thf('19', plain,
% 0.55/1.08 (~ ( (product @ e_1 @ e_2 @ e_3)) | ~ ( (product @ e_1 @ e_4 @ e_3))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1784, zip_derived_cl30])).
% 0.55/1.08 thf(zip_derived_cl1057, plain,
% 0.55/1.08 (( (product @ e_2 @ e_4 @ e_1)) <= (( (product @ e_2 @ e_4 @ e_1)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl304])).
% 0.55/1.08 thf(zip_derived_cl799, plain,
% 0.55/1.08 (( (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl283])).
% 0.55/1.08 thf(zip_derived_cl41, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.55/1.08 inference('cnf', [status(esa)], [product_idempotence])).
% 0.55/1.08 thf(zip_derived_cl42, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.55/1.08 ( (equalish @ X0 @ X1)
% 0.55/1.08 | ~ (product @ X2 @ X1 @ X3)
% 0.55/1.08 | ~ (product @ X2 @ X0 @ X4)
% 0.55/1.08 | ~ (product @ X1 @ X3 @ X5)
% 0.55/1.08 | ~ (product @ X0 @ X4 @ X5))),
% 0.55/1.08 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.55/1.08 thf(zip_derived_cl84, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.08 ( (equalish @ X1 @ X0)
% 0.55/1.08 | ~ (product @ X0 @ X1 @ X2)
% 0.55/1.08 | ~ (product @ X0 @ X0 @ X3)
% 0.55/1.08 | ~ (product @ X1 @ X2 @ X3))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl42])).
% 0.55/1.08 thf(zip_derived_cl806, plain,
% 0.55/1.08 ((![X0 : $i]:
% 0.55/1.08 ( (equalish @ e_2 @ e_1)
% 0.55/1.08 | ~ (product @ e_1 @ e_1 @ X0)
% 0.55/1.08 | ~ (product @ e_2 @ e_4 @ X0)))
% 0.55/1.08 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl799, zip_derived_cl84])).
% 0.55/1.08 thf(zip_derived_cl28, plain, (~ (equalish @ e_2 @ e_1)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.55/1.08 thf(zip_derived_cl813, plain,
% 0.55/1.08 ((![X0 : $i]:
% 0.55/1.08 (~ (product @ e_1 @ e_1 @ X0) | ~ (product @ e_2 @ e_4 @ X0)))
% 0.55/1.08 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 0.55/1.08 inference('demod', [status(thm)], [zip_derived_cl806, zip_derived_cl28])).
% 0.55/1.08 thf(zip_derived_cl2086, plain,
% 0.55/1.08 ((~ (product @ e_1 @ e_1 @ e_1))
% 0.55/1.08 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_2 @ e_4 @ e_1)))),
% 0.55/1.08 inference('s_sup-', [status(thm)],
% 0.55/1.08 [zip_derived_cl1057, zip_derived_cl813])).
% 0.55/1.08 thf(zip_derived_cl41, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.55/1.08 inference('cnf', [status(esa)], [product_idempotence])).
% 0.55/1.08 thf('20', plain,
% 0.55/1.08 (~ ( (product @ e_2 @ e_4 @ e_1)) | ~ ( (product @ e_1 @ e_2 @ e_4))),
% 0.55/1.08 inference('demod', [status(thm)], [zip_derived_cl2086, zip_derived_cl41])).
% 0.55/1.08 thf('21', plain,
% 0.55/1.08 (( (product @ e_1 @ e_4 @ e_2)) | ( (product @ e_1 @ e_4 @ e_3)) |
% 0.55/1.08 ( (product @ e_1 @ e_4 @ e_4)) | ( (product @ e_1 @ e_4 @ e_1))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl285])).
% 0.55/1.08 thf(zip_derived_cl1341, plain,
% 0.55/1.08 (( (product @ e_3 @ e_4 @ e_2)) <= (( (product @ e_3 @ e_4 @ e_2)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl1339])).
% 0.55/1.08 thf(zip_derived_cl40, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.08 (~ (product @ X0 @ X1 @ X2)
% 0.55/1.08 | ~ (product @ X3 @ X1 @ X2)
% 0.55/1.08 | (equalish @ X0 @ X3))),
% 0.55/1.08 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.55/1.08 thf(zip_derived_cl1417, plain,
% 0.55/1.08 ((![X0 : $i]: (~ (product @ X0 @ e_4 @ e_2) | (equalish @ e_3 @ X0)))
% 0.55/1.08 <= (( (product @ e_3 @ e_4 @ e_2)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1341, zip_derived_cl40])).
% 0.55/1.08 thf(zip_derived_cl860, plain,
% 0.55/1.08 (( (product @ e_1 @ e_4 @ e_2)) <= (( (product @ e_1 @ e_4 @ e_2)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl285])).
% 0.55/1.08 thf(zip_derived_cl1789, plain,
% 0.55/1.08 (( (equalish @ e_3 @ e_1))
% 0.55/1.08 <= (( (product @ e_1 @ e_4 @ e_2)) & ( (product @ e_3 @ e_4 @ e_2)))),
% 0.55/1.08 inference('s_sup+', [status(thm)],
% 0.55/1.08 [zip_derived_cl1417, zip_derived_cl860])).
% 0.55/1.08 thf(zip_derived_cl31, plain, (~ (equalish @ e_3 @ e_1)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.55/1.08 thf('22', plain,
% 0.55/1.08 (~ ( (product @ e_3 @ e_4 @ e_2)) | ~ ( (product @ e_1 @ e_4 @ e_2))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl1789, zip_derived_cl31])).
% 0.55/1.08 thf('23', plain,
% 0.55/1.08 (( (product @ e_3 @ e_4 @ e_1)) | ( (product @ e_3 @ e_4 @ e_2)) |
% 0.55/1.08 ( (product @ e_3 @ e_4 @ e_4)) | ( (product @ e_3 @ e_4 @ e_3))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl330])).
% 0.55/1.08 thf(zip_derived_cl1342, plain,
% 0.55/1.08 (( (product @ e_3 @ e_4 @ e_1)) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl1339])).
% 0.55/1.08 thf(zip_derived_cl831, plain,
% 0.55/1.08 (( (product @ e_1 @ e_3 @ e_4)) <= (( (product @ e_1 @ e_3 @ e_4)))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl284])).
% 0.55/1.08 thf(zip_derived_cl84, plain,
% 0.55/1.08 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.55/1.08 ( (equalish @ X1 @ X0)
% 0.55/1.08 | ~ (product @ X0 @ X1 @ X2)
% 0.55/1.08 | ~ (product @ X0 @ X0 @ X3)
% 0.55/1.08 | ~ (product @ X1 @ X2 @ X3))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl42])).
% 0.55/1.08 thf(zip_derived_cl838, plain,
% 0.55/1.08 ((![X0 : $i]:
% 0.55/1.08 ( (equalish @ e_3 @ e_1)
% 0.55/1.08 | ~ (product @ e_1 @ e_1 @ X0)
% 0.55/1.08 | ~ (product @ e_3 @ e_4 @ X0)))
% 0.55/1.08 <= (( (product @ e_1 @ e_3 @ e_4)))),
% 0.55/1.08 inference('s_sup-', [status(thm)], [zip_derived_cl831, zip_derived_cl84])).
% 0.55/1.08 thf(zip_derived_cl31, plain, (~ (equalish @ e_3 @ e_1)),
% 0.55/1.08 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.55/1.08 thf(zip_derived_cl846, plain,
% 0.55/1.08 ((![X0 : $i]:
% 0.55/1.08 (~ (product @ e_1 @ e_1 @ X0) | ~ (product @ e_3 @ e_4 @ X0)))
% 0.55/1.08 <= (( (product @ e_1 @ e_3 @ e_4)))),
% 0.55/1.08 inference('demod', [status(thm)], [zip_derived_cl838, zip_derived_cl31])).
% 0.55/1.08 thf(zip_derived_cl1475, plain,
% 0.55/1.08 ((~ (product @ e_1 @ e_1 @ e_1))
% 0.55/1.08 <= (( (product @ e_1 @ e_3 @ e_4)) & ( (product @ e_3 @ e_4 @ e_1)))),
% 0.55/1.08 inference('s_sup-', [status(thm)],
% 0.55/1.08 [zip_derived_cl1342, zip_derived_cl846])).
% 0.55/1.08 thf(zip_derived_cl41, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.55/1.08 inference('cnf', [status(esa)], [product_idempotence])).
% 0.55/1.08 thf('24', plain,
% 0.55/1.08 (~ ( (product @ e_1 @ e_3 @ e_4)) | ~ ( (product @ e_3 @ e_4 @ e_1))),
% 0.55/1.08 inference('demod', [status(thm)], [zip_derived_cl1475, zip_derived_cl41])).
% 0.55/1.08 thf('25', plain,
% 0.55/1.08 (( (product @ e_1 @ e_3 @ e_4)) | ( (product @ e_1 @ e_3 @ e_2)) |
% 0.55/1.08 ( (product @ e_1 @ e_3 @ e_3)) | ( (product @ e_1 @ e_3 @ e_1))),
% 0.55/1.08 inference('split', [status(esa)], [zip_derived_cl284])).
% 0.55/1.08 thf(zip_derived_cl2102, plain, ($false),
% 0.55/1.08 inference('sat_resolution*', [status(thm)],
% 0.55/1.08 ['0', '1', '2', '3', '4', '5', '6', '9', '7', '10', '11',
% 0.55/1.08 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 0.55/1.08 '22', '23', '24', '25'])).
% 0.55/1.08
% 0.55/1.08 % SZS output end Refutation
% 0.55/1.08
% 0.55/1.08
% 0.55/1.08 % Terminating...
% 2.51/1.14 % Runner terminated.
% 2.51/1.15 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------