TSTP Solution File: GRP127-1.004 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP127-1.004 : 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.wlvUasrCZx true
% Computer : n020.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 01:50:10 EDT 2023
% Result : Unsatisfiable 0.62s 0.96s
% Output : Refutation 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP127-1.004 : TPTP v8.1.2. Released v1.2.0.
% 0.14/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.wlvUasrCZx true
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 19:47:28 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.35 % Number of cores: 8
% 0.21/0.35 % Python version: Python 3.6.8
% 0.21/0.35 % Running in FO mode
% 0.59/0.66 % Total configuration time : 435
% 0.59/0.66 % Estimated wc time : 1092
% 0.59/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.59/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.59/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.61/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.61/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.61/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.61/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.61/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.62/0.96 % Solved by fo/fo1_av.sh.
% 0.62/0.96 % done 371 iterations in 0.197s
% 0.62/0.96 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.62/0.96 % SZS output start Refutation
% 0.62/0.96 thf(product_type, type, product: $i > $i > $i > $o).
% 0.62/0.96 thf(e_1_type, type, e_1: $i).
% 0.62/0.96 thf(e_3_type, type, e_3: $i).
% 0.62/0.96 thf(group_element_type, type, group_element: $i > $o).
% 0.62/0.96 thf(e_2_type, type, e_2: $i).
% 0.62/0.96 thf(e_4_type, type, e_4: $i).
% 0.62/0.96 thf(equalish_type, type, equalish: $i > $i > $o).
% 0.62/0.96 thf(element_1, axiom, (group_element @ e_1)).
% 0.62/0.96 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.62/0.96 inference('cnf', [status(esa)], [element_1])).
% 0.62/0.96 thf(product_total_function1, axiom,
% 0.62/0.96 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 0.62/0.96 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 0.62/0.96 ( product @ X @ Y @ e_3 ) | ( product @ X @ Y @ e_4 ))).
% 0.62/0.96 thf(zip_derived_cl16, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (group_element @ X0)
% 0.62/0.96 | ~ (group_element @ X1)
% 0.62/0.96 | (product @ X0 @ X1 @ e_1)
% 0.62/0.96 | (product @ X0 @ X1 @ e_2)
% 0.62/0.96 | (product @ X0 @ X1 @ e_3)
% 0.62/0.96 | (product @ X0 @ X1 @ e_4))),
% 0.62/0.96 inference('cnf', [status(esa)], [product_total_function1])).
% 0.62/0.96 thf(product_idempotence, axiom, (product @ X @ X @ X)).
% 0.62/0.96 thf(zip_derived_cl20, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.62/0.96 inference('cnf', [status(esa)], [product_idempotence])).
% 0.62/0.96 thf(qg3, conjecture,
% 0.62/0.96 (~( ( product @ Z2 @ Y @ X ) | ( ~( product @ Z1 @ Y @ Z2 ) ) |
% 0.62/0.96 ( ~( product @ Y @ X @ Z1 ) ) ))).
% 0.62/0.96 thf(zf_stmt_0, negated_conjecture,
% 0.62/0.96 (( product @ Z2 @ Y @ X ) | ( ~( product @ Z1 @ Y @ Z2 ) ) |
% 0.62/0.96 ( ~( product @ Y @ X @ Z1 ) )),
% 0.62/0.96 inference('cnf.neg', [status(esa)], [qg3])).
% 0.62/0.96 thf(zip_derived_cl21, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.62/0.96 ( (product @ X0 @ X1 @ X2)
% 0.62/0.96 | ~ (product @ X3 @ X1 @ X0)
% 0.62/0.96 | ~ (product @ X1 @ X2 @ X3))),
% 0.62/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.62/0.96 thf(zip_derived_cl52, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 ( (product @ X0 @ X0 @ X1) | ~ (product @ X0 @ X1 @ X0))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl21])).
% 0.62/0.96 thf(zip_derived_cl57, plain,
% 0.62/0.96 (![X0 : $i]:
% 0.62/0.96 ( (product @ e_4 @ X0 @ e_3)
% 0.62/0.96 | (product @ e_4 @ X0 @ e_2)
% 0.62/0.96 | (product @ e_4 @ X0 @ e_1)
% 0.62/0.96 | ~ (group_element @ X0)
% 0.62/0.96 | ~ (group_element @ e_4)
% 0.62/0.96 | (product @ e_4 @ e_4 @ X0))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl52])).
% 0.62/0.96 thf(element_4, axiom, (group_element @ e_4)).
% 0.62/0.96 thf(zip_derived_cl3, plain, ( (group_element @ e_4)),
% 0.62/0.96 inference('cnf', [status(esa)], [element_4])).
% 0.62/0.96 thf(zip_derived_cl59, plain,
% 0.62/0.96 (![X0 : $i]:
% 0.62/0.96 ( (product @ e_4 @ X0 @ e_3)
% 0.62/0.96 | (product @ e_4 @ X0 @ e_2)
% 0.62/0.96 | (product @ e_4 @ X0 @ e_1)
% 0.62/0.96 | ~ (group_element @ X0)
% 0.62/0.96 | (product @ e_4 @ e_4 @ X0))),
% 0.62/0.96 inference('demod', [status(thm)], [zip_derived_cl57, zip_derived_cl3])).
% 0.62/0.96 thf(zip_derived_cl60, plain,
% 0.62/0.96 (( (product @ e_4 @ e_1 @ e_3)
% 0.62/0.96 | (product @ e_4 @ e_1 @ e_2)
% 0.62/0.96 | (product @ e_4 @ e_1 @ e_1)
% 0.62/0.96 | (product @ e_4 @ e_4 @ e_1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl59])).
% 0.62/0.96 thf(zip_derived_cl66, plain,
% 0.62/0.96 (( (product @ e_4 @ e_1 @ e_2)) <= (( (product @ e_4 @ e_1 @ e_2)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl60])).
% 0.62/0.96 thf(zip_derived_cl21, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.62/0.96 ( (product @ X0 @ X1 @ X2)
% 0.62/0.96 | ~ (product @ X3 @ X1 @ X0)
% 0.62/0.96 | ~ (product @ X1 @ X2 @ X3))),
% 0.62/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.62/0.96 thf(zip_derived_cl94, plain,
% 0.62/0.96 ((![X0 : $i]:
% 0.62/0.96 ( (product @ e_2 @ e_1 @ X0) | ~ (product @ e_1 @ X0 @ e_4)))
% 0.62/0.96 <= (( (product @ e_4 @ e_1 @ e_2)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl66, zip_derived_cl21])).
% 0.62/0.96 thf(zip_derived_cl20, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.62/0.96 inference('cnf', [status(esa)], [product_idempotence])).
% 0.62/0.96 thf(product_right_cancellation, axiom,
% 0.62/0.96 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 0.62/0.96 ( equalish @ W @ Z ))).
% 0.62/0.96 thf(zip_derived_cl18, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.62/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.62/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.62/0.96 | (equalish @ X1 @ X3))),
% 0.62/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.62/0.96 thf(zip_derived_cl31, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 0.62/0.96 thf(zip_derived_cl159, plain,
% 0.62/0.96 (((~ (product @ e_1 @ e_2 @ e_4) | (equalish @ e_2 @ e_1)))
% 0.62/0.96 <= (( (product @ e_4 @ e_1 @ e_2)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl94, zip_derived_cl31])).
% 0.62/0.96 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 0.62/0.96 thf(zip_derived_cl7, plain, (~ (equalish @ e_2 @ e_1)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.62/0.96 thf(zip_derived_cl167, plain,
% 0.62/0.96 ((~ (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_4 @ e_1 @ e_2)))),
% 0.62/0.96 inference('demod', [status(thm)], [zip_derived_cl159, zip_derived_cl7])).
% 0.62/0.96 thf(zip_derived_cl16, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (group_element @ X0)
% 0.62/0.96 | ~ (group_element @ X1)
% 0.62/0.96 | (product @ X0 @ X1 @ e_1)
% 0.62/0.96 | (product @ X0 @ X1 @ e_2)
% 0.62/0.96 | (product @ X0 @ X1 @ e_3)
% 0.62/0.96 | (product @ X0 @ X1 @ e_4))),
% 0.62/0.96 inference('cnf', [status(esa)], [product_total_function1])).
% 0.62/0.96 thf(zip_derived_cl177, plain,
% 0.62/0.96 (((~ (group_element @ e_1)
% 0.62/0.96 | ~ (group_element @ e_2)
% 0.62/0.96 | (product @ e_1 @ e_2 @ e_1)
% 0.62/0.96 | (product @ e_1 @ e_2 @ e_2)
% 0.62/0.96 | (product @ e_1 @ e_2 @ e_3))) <= (( (product @ e_4 @ e_1 @ e_2)))),
% 0.62/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl167, zip_derived_cl16])).
% 0.62/0.96 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.62/0.96 inference('cnf', [status(esa)], [element_1])).
% 0.62/0.96 thf(element_2, axiom, (group_element @ e_2)).
% 0.62/0.96 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.62/0.96 inference('cnf', [status(esa)], [element_2])).
% 0.62/0.96 thf(zip_derived_cl180, plain,
% 0.62/0.96 ((( (product @ e_1 @ e_2 @ e_1)
% 0.62/0.96 | (product @ e_1 @ e_2 @ e_2)
% 0.62/0.96 | (product @ e_1 @ e_2 @ e_3))) <= (( (product @ e_4 @ e_1 @ e_2)))),
% 0.62/0.96 inference('demod', [status(thm)],
% 0.62/0.96 [zip_derived_cl177, zip_derived_cl0, zip_derived_cl1])).
% 0.62/0.96 thf(zip_derived_cl1326, plain,
% 0.62/0.96 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl180])).
% 0.62/0.96 thf(zip_derived_cl20, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.62/0.96 inference('cnf', [status(esa)], [product_idempotence])).
% 0.62/0.96 thf(product_left_cancellation, axiom,
% 0.62/0.96 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 0.62/0.96 ( equalish @ W @ Z ))).
% 0.62/0.96 thf(zip_derived_cl19, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.62/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.62/0.96 | ~ (product @ X3 @ X1 @ X2)
% 0.62/0.96 | (equalish @ X0 @ X3))),
% 0.62/0.96 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.62/0.96 thf(zip_derived_cl41, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 0.62/0.96 thf(zip_derived_cl1333, plain,
% 0.62/0.96 (( (equalish @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1326, zip_derived_cl41])).
% 0.62/0.96 thf(zip_derived_cl7, plain, (~ (equalish @ e_2 @ e_1)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.62/0.96 thf('0', plain, (~ ( (product @ e_1 @ e_2 @ e_2))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1333, zip_derived_cl7])).
% 0.62/0.96 thf(zip_derived_cl16, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (group_element @ X0)
% 0.62/0.96 | ~ (group_element @ X1)
% 0.62/0.96 | (product @ X0 @ X1 @ e_1)
% 0.62/0.96 | (product @ X0 @ X1 @ e_2)
% 0.62/0.96 | (product @ X0 @ X1 @ e_3)
% 0.62/0.96 | (product @ X0 @ X1 @ e_4))),
% 0.62/0.96 inference('cnf', [status(esa)], [product_total_function1])).
% 0.62/0.96 thf(zip_derived_cl167, plain,
% 0.62/0.96 ((~ (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_4 @ e_1 @ e_2)))),
% 0.62/0.96 inference('demod', [status(thm)], [zip_derived_cl159, zip_derived_cl7])).
% 0.62/0.96 thf(zip_derived_cl178, plain,
% 0.62/0.96 ((( (product @ e_1 @ e_2 @ e_3)
% 0.62/0.96 | (product @ e_1 @ e_2 @ e_2)
% 0.62/0.96 | (product @ e_1 @ e_2 @ e_1)
% 0.62/0.96 | ~ (group_element @ e_2)
% 0.62/0.96 | ~ (group_element @ e_1))) <= (( (product @ e_4 @ e_1 @ e_2)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl167])).
% 0.62/0.96 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.62/0.96 inference('cnf', [status(esa)], [element_2])).
% 0.62/0.96 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.62/0.96 inference('cnf', [status(esa)], [element_1])).
% 0.62/0.96 thf(zip_derived_cl179, plain,
% 0.62/0.96 ((( (product @ e_1 @ e_2 @ e_3)
% 0.62/0.96 | (product @ e_1 @ e_2 @ e_2)
% 0.62/0.96 | (product @ e_1 @ e_2 @ e_1))) <= (( (product @ e_4 @ e_1 @ e_2)))),
% 0.62/0.96 inference('demod', [status(thm)],
% 0.62/0.96 [zip_derived_cl178, zip_derived_cl1, zip_derived_cl0])).
% 0.62/0.96 thf(zip_derived_cl1272, plain,
% 0.62/0.96 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl179])).
% 0.62/0.96 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 0.62/0.96 inference('cnf', [status(esa)], [element_2])).
% 0.62/0.96 thf(zip_derived_cl59, plain,
% 0.62/0.96 (![X0 : $i]:
% 0.62/0.96 ( (product @ e_4 @ X0 @ e_3)
% 0.62/0.96 | (product @ e_4 @ X0 @ e_2)
% 0.62/0.96 | (product @ e_4 @ X0 @ e_1)
% 0.62/0.96 | ~ (group_element @ X0)
% 0.62/0.96 | (product @ e_4 @ e_4 @ X0))),
% 0.62/0.96 inference('demod', [status(thm)], [zip_derived_cl57, zip_derived_cl3])).
% 0.62/0.96 thf(zip_derived_cl61, plain,
% 0.62/0.96 (( (product @ e_4 @ e_2 @ e_3)
% 0.62/0.96 | (product @ e_4 @ e_2 @ e_2)
% 0.62/0.96 | (product @ e_4 @ e_2 @ e_1)
% 0.62/0.96 | (product @ e_4 @ e_4 @ e_2))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl59])).
% 0.62/0.96 thf(zip_derived_cl454, plain,
% 0.62/0.96 (( (product @ e_4 @ e_2 @ e_3)) <= (( (product @ e_4 @ e_2 @ e_3)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl61])).
% 0.62/0.96 thf(zip_derived_cl19, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.62/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.62/0.96 | ~ (product @ X3 @ X1 @ X2)
% 0.62/0.96 | (equalish @ X0 @ X3))),
% 0.62/0.96 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.62/0.96 thf(zip_derived_cl530, plain,
% 0.62/0.96 ((![X0 : $i]: (~ (product @ X0 @ e_2 @ e_3) | (equalish @ e_4 @ X0)))
% 0.62/0.96 <= (( (product @ e_4 @ e_2 @ e_3)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl454, zip_derived_cl19])).
% 0.62/0.96 thf(zip_derived_cl1283, plain,
% 0.62/0.96 (( (equalish @ e_4 @ e_1))
% 0.62/0.96 <= (( (product @ e_4 @ e_2 @ e_3)) & ( (product @ e_1 @ e_2 @ e_3)))),
% 0.62/0.96 inference('s_sup-', [status(thm)],
% 0.62/0.96 [zip_derived_cl1272, zip_derived_cl530])).
% 0.62/0.96 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 0.62/0.96 thf(zip_derived_cl13, plain, (~ (equalish @ e_4 @ e_1)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.62/0.96 thf('1', plain,
% 0.62/0.96 (~ ( (product @ e_1 @ e_2 @ e_3)) | ~ ( (product @ e_4 @ e_2 @ e_3))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1283, zip_derived_cl13])).
% 0.62/0.96 thf(zip_derived_cl453, plain,
% 0.62/0.96 (( (product @ e_4 @ e_2 @ e_2)) <= (( (product @ e_4 @ e_2 @ e_2)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl61])).
% 0.62/0.96 thf(zip_derived_cl41, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 0.62/0.96 thf(zip_derived_cl511, plain,
% 0.62/0.96 (( (equalish @ e_2 @ e_4)) <= (( (product @ e_4 @ e_2 @ e_2)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl453, zip_derived_cl41])).
% 0.62/0.96 thf(e_2_is_not_e_4, axiom, (~( equalish @ e_2 @ e_4 ))).
% 0.62/0.96 thf(zip_derived_cl9, plain, (~ (equalish @ e_2 @ e_4)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_4])).
% 0.62/0.96 thf('2', plain, (~ ( (product @ e_4 @ e_2 @ e_2))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl511, zip_derived_cl9])).
% 0.62/0.96 thf(zip_derived_cl451, plain,
% 0.62/0.96 (( (product @ e_4 @ e_4 @ e_2)) <= (( (product @ e_4 @ e_4 @ e_2)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl61])).
% 0.62/0.96 thf(zip_derived_cl20, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 0.62/0.96 inference('cnf', [status(esa)], [product_idempotence])).
% 0.62/0.96 thf(product_total_function2, axiom,
% 0.62/0.96 (( ~( product @ X @ Y @ W ) ) | ( ~( product @ X @ Y @ Z ) ) |
% 0.62/0.96 ( equalish @ W @ Z ))).
% 0.62/0.96 thf(zip_derived_cl17, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.62/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.62/0.96 | ~ (product @ X0 @ X1 @ X3)
% 0.62/0.96 | (equalish @ X2 @ X3))),
% 0.62/0.96 inference('cnf', [status(esa)], [product_total_function2])).
% 0.62/0.96 thf(zip_derived_cl22, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (product @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl17])).
% 0.62/0.96 thf(zip_derived_cl459, plain,
% 0.62/0.96 (( (equalish @ e_4 @ e_2)) <= (( (product @ e_4 @ e_4 @ e_2)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl451, zip_derived_cl22])).
% 0.62/0.96 thf(e_4_is_not_e_2, axiom, (~( equalish @ e_4 @ e_2 ))).
% 0.62/0.96 thf(zip_derived_cl14, plain, (~ (equalish @ e_4 @ e_2)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_4_is_not_e_2])).
% 0.62/0.96 thf('3', plain, (~ ( (product @ e_4 @ e_4 @ e_2))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl459, zip_derived_cl14])).
% 0.62/0.96 thf(zip_derived_cl16, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (group_element @ X0)
% 0.62/0.96 | ~ (group_element @ X1)
% 0.62/0.96 | (product @ X0 @ X1 @ e_1)
% 0.62/0.96 | (product @ X0 @ X1 @ e_2)
% 0.62/0.96 | (product @ X0 @ X1 @ e_3)
% 0.62/0.96 | (product @ X0 @ X1 @ e_4))),
% 0.62/0.96 inference('cnf', [status(esa)], [product_total_function1])).
% 0.62/0.96 thf(zip_derived_cl67, plain,
% 0.62/0.96 (( (product @ e_4 @ e_1 @ e_3)) <= (( (product @ e_4 @ e_1 @ e_3)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl60])).
% 0.62/0.96 thf(zip_derived_cl21, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.62/0.96 ( (product @ X0 @ X1 @ X2)
% 0.62/0.96 | ~ (product @ X3 @ X1 @ X0)
% 0.62/0.96 | ~ (product @ X1 @ X2 @ X3))),
% 0.62/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.62/0.96 thf(zip_derived_cl100, plain,
% 0.62/0.96 ((![X0 : $i]:
% 0.62/0.96 ( (product @ e_3 @ e_1 @ X0) | ~ (product @ e_1 @ X0 @ e_4)))
% 0.62/0.96 <= (( (product @ e_4 @ e_1 @ e_3)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl67, zip_derived_cl21])).
% 0.62/0.96 thf(zip_derived_cl31, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 0.62/0.96 thf(zip_derived_cl192, plain,
% 0.62/0.96 (((~ (product @ e_1 @ e_3 @ e_4) | (equalish @ e_3 @ e_1)))
% 0.62/0.96 <= (( (product @ e_4 @ e_1 @ e_3)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl100, zip_derived_cl31])).
% 0.62/0.96 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 0.62/0.96 thf(zip_derived_cl10, plain, (~ (equalish @ e_3 @ e_1)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.62/0.96 thf(zip_derived_cl199, plain,
% 0.62/0.96 ((~ (product @ e_1 @ e_3 @ e_4)) <= (( (product @ e_4 @ e_1 @ e_3)))),
% 0.62/0.96 inference('demod', [status(thm)], [zip_derived_cl192, zip_derived_cl10])).
% 0.62/0.96 thf(zip_derived_cl205, plain,
% 0.62/0.96 ((( (product @ e_1 @ e_3 @ e_3)
% 0.62/0.96 | (product @ e_1 @ e_3 @ e_2)
% 0.62/0.96 | (product @ e_1 @ e_3 @ e_1)
% 0.62/0.96 | ~ (group_element @ e_3)
% 0.62/0.96 | ~ (group_element @ e_1))) <= (( (product @ e_4 @ e_1 @ e_3)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl199])).
% 0.62/0.96 thf(element_3, axiom, (group_element @ e_3)).
% 0.62/0.96 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.62/0.96 inference('cnf', [status(esa)], [element_3])).
% 0.62/0.96 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 0.62/0.96 inference('cnf', [status(esa)], [element_1])).
% 0.62/0.96 thf(zip_derived_cl206, plain,
% 0.62/0.96 ((( (product @ e_1 @ e_3 @ e_3)
% 0.62/0.96 | (product @ e_1 @ e_3 @ e_2)
% 0.62/0.96 | (product @ e_1 @ e_3 @ e_1))) <= (( (product @ e_4 @ e_1 @ e_3)))),
% 0.62/0.96 inference('demod', [status(thm)],
% 0.62/0.96 [zip_derived_cl205, zip_derived_cl2, zip_derived_cl0])).
% 0.62/0.96 thf(zip_derived_cl1512, plain,
% 0.62/0.96 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl206])).
% 0.62/0.96 thf(zip_derived_cl41, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 0.62/0.96 thf(zip_derived_cl1520, plain,
% 0.62/0.96 (( (equalish @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1512, zip_derived_cl41])).
% 0.62/0.96 thf(zip_derived_cl10, plain, (~ (equalish @ e_3 @ e_1)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.62/0.96 thf('4', plain, (~ ( (product @ e_1 @ e_3 @ e_3))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1520, zip_derived_cl10])).
% 0.62/0.96 thf(zip_derived_cl64, plain,
% 0.62/0.96 (( (product @ e_4 @ e_4 @ e_1)) <= (( (product @ e_4 @ e_4 @ e_1)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl60])).
% 0.62/0.96 thf(zip_derived_cl22, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (product @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl17])).
% 0.62/0.96 thf(zip_derived_cl72, plain,
% 0.62/0.96 (( (equalish @ e_4 @ e_1)) <= (( (product @ e_4 @ e_4 @ e_1)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl22])).
% 0.62/0.96 thf(zip_derived_cl13, plain, (~ (equalish @ e_4 @ e_1)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.62/0.96 thf('5', plain, (~ ( (product @ e_4 @ e_4 @ e_1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl13])).
% 0.62/0.96 thf(zip_derived_cl65, plain,
% 0.62/0.96 (( (product @ e_4 @ e_1 @ e_1)) <= (( (product @ e_4 @ e_1 @ e_1)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl60])).
% 0.62/0.96 thf(zip_derived_cl41, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 0.62/0.96 thf(zip_derived_cl88, plain,
% 0.62/0.96 (( (equalish @ e_1 @ e_4)) <= (( (product @ e_4 @ e_1 @ e_1)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl65, zip_derived_cl41])).
% 0.62/0.96 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 0.62/0.96 thf(zip_derived_cl6, plain, (~ (equalish @ e_1 @ e_4)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 0.62/0.96 thf('6', plain, (~ ( (product @ e_4 @ e_1 @ e_1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl6])).
% 0.62/0.96 thf(zip_derived_cl454, plain,
% 0.62/0.96 (( (product @ e_4 @ e_2 @ e_3)) <= (( (product @ e_4 @ e_2 @ e_3)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl61])).
% 0.62/0.96 thf(zip_derived_cl21, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.62/0.96 ( (product @ X0 @ X1 @ X2)
% 0.62/0.96 | ~ (product @ X3 @ X1 @ X0)
% 0.62/0.96 | ~ (product @ X1 @ X2 @ X3))),
% 0.62/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.62/0.96 thf(zip_derived_cl531, plain,
% 0.62/0.96 ((![X0 : $i]:
% 0.62/0.96 ( (product @ e_3 @ e_2 @ X0) | ~ (product @ e_2 @ X0 @ e_4)))
% 0.62/0.96 <= (( (product @ e_4 @ e_2 @ e_3)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl454, zip_derived_cl21])).
% 0.62/0.96 thf(zip_derived_cl41, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 0.62/0.96 thf(zip_derived_cl16, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (group_element @ X0)
% 0.62/0.96 | ~ (group_element @ X1)
% 0.62/0.96 | (product @ X0 @ X1 @ e_1)
% 0.62/0.96 | (product @ X0 @ X1 @ e_2)
% 0.62/0.96 | (product @ X0 @ X1 @ e_3)
% 0.62/0.96 | (product @ X0 @ X1 @ e_4))),
% 0.62/0.96 inference('cnf', [status(esa)], [product_total_function1])).
% 0.62/0.96 thf(zip_derived_cl31, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 0.62/0.96 thf(zip_derived_cl38, plain,
% 0.62/0.96 (![X0 : $i]:
% 0.62/0.96 ( (product @ e_4 @ X0 @ e_3)
% 0.62/0.96 | (product @ e_4 @ X0 @ e_2)
% 0.62/0.96 | (product @ e_4 @ X0 @ e_1)
% 0.62/0.96 | ~ (group_element @ X0)
% 0.62/0.96 | ~ (group_element @ e_4)
% 0.62/0.96 | (equalish @ e_4 @ X0))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl31])).
% 0.62/0.96 thf(zip_derived_cl3, plain, ( (group_element @ e_4)),
% 0.62/0.96 inference('cnf', [status(esa)], [element_4])).
% 0.62/0.96 thf(zip_derived_cl39, plain,
% 0.62/0.96 (![X0 : $i]:
% 0.62/0.96 ( (product @ e_4 @ X0 @ e_3)
% 0.62/0.96 | (product @ e_4 @ X0 @ e_2)
% 0.62/0.96 | (product @ e_4 @ X0 @ e_1)
% 0.62/0.96 | ~ (group_element @ X0)
% 0.62/0.96 | (equalish @ e_4 @ X0))),
% 0.62/0.96 inference('demod', [status(thm)], [zip_derived_cl38, zip_derived_cl3])).
% 0.62/0.96 thf(zip_derived_cl223, plain,
% 0.62/0.96 (( (equalish @ e_3 @ e_4)
% 0.62/0.96 | (product @ e_4 @ e_3 @ e_2)
% 0.62/0.96 | (product @ e_4 @ e_3 @ e_1)
% 0.62/0.96 | ~ (group_element @ e_3)
% 0.62/0.96 | (equalish @ e_4 @ e_3))),
% 0.62/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl39])).
% 0.62/0.96 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 0.62/0.96 thf(zip_derived_cl12, plain, (~ (equalish @ e_3 @ e_4)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 0.62/0.96 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 0.62/0.96 inference('cnf', [status(esa)], [element_3])).
% 0.62/0.96 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 0.62/0.96 thf(zip_derived_cl15, plain, (~ (equalish @ e_4 @ e_3)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 0.62/0.96 thf(zip_derived_cl228, plain,
% 0.62/0.96 (( (product @ e_4 @ e_3 @ e_2) | (product @ e_4 @ e_3 @ e_1))),
% 0.62/0.96 inference('demod', [status(thm)],
% 0.62/0.96 [zip_derived_cl223, zip_derived_cl12, zip_derived_cl2,
% 0.62/0.96 zip_derived_cl15])).
% 0.62/0.96 thf(zip_derived_cl265, plain,
% 0.62/0.96 (( (product @ e_4 @ e_3 @ e_1)) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl228])).
% 0.62/0.96 thf(zip_derived_cl21, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.62/0.96 ( (product @ X0 @ X1 @ X2)
% 0.62/0.96 | ~ (product @ X3 @ X1 @ X0)
% 0.62/0.96 | ~ (product @ X1 @ X2 @ X3))),
% 0.62/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.62/0.96 thf(zip_derived_cl270, plain,
% 0.62/0.96 ((![X0 : $i]:
% 0.62/0.96 ( (product @ e_1 @ e_3 @ X0) | ~ (product @ e_3 @ X0 @ e_4)))
% 0.62/0.96 <= (( (product @ e_4 @ e_3 @ e_1)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl265, zip_derived_cl21])).
% 0.62/0.96 thf(zip_derived_cl701, plain,
% 0.62/0.96 (((~ (product @ e_2 @ e_4 @ e_4) | (product @ e_1 @ e_3 @ e_2)))
% 0.62/0.96 <= (( (product @ e_4 @ e_3 @ e_1)) & ( (product @ e_4 @ e_2 @ e_3)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl531, zip_derived_cl270])).
% 0.62/0.96 thf(zip_derived_cl764, plain,
% 0.62/0.96 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl701])).
% 0.62/0.96 thf(zip_derived_cl266, plain,
% 0.62/0.96 (( (product @ e_4 @ e_3 @ e_2)) <= (( (product @ e_4 @ e_3 @ e_2)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl228])).
% 0.62/0.96 thf(zip_derived_cl19, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.62/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.62/0.96 | ~ (product @ X3 @ X1 @ X2)
% 0.62/0.96 | (equalish @ X0 @ X3))),
% 0.62/0.96 inference('cnf', [status(esa)], [product_left_cancellation])).
% 0.62/0.96 thf(zip_derived_cl338, plain,
% 0.62/0.96 ((![X0 : $i]: (~ (product @ X0 @ e_3 @ e_2) | (equalish @ e_4 @ X0)))
% 0.62/0.96 <= (( (product @ e_4 @ e_3 @ e_2)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl266, zip_derived_cl19])).
% 0.62/0.96 thf(zip_derived_cl815, plain,
% 0.62/0.96 (( (equalish @ e_4 @ e_1))
% 0.62/0.96 <= (( (product @ e_4 @ e_3 @ e_2)) & ( (product @ e_1 @ e_3 @ e_2)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl764, zip_derived_cl338])).
% 0.62/0.96 thf(zip_derived_cl13, plain, (~ (equalish @ e_4 @ e_1)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 0.62/0.96 thf('7', plain,
% 0.62/0.96 (~ ( (product @ e_1 @ e_3 @ e_2)) | ~ ( (product @ e_4 @ e_3 @ e_2))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl815, zip_derived_cl13])).
% 0.62/0.96 thf(zip_derived_cl266, plain,
% 0.62/0.96 (( (product @ e_4 @ e_3 @ e_2)) <= (( (product @ e_4 @ e_3 @ e_2)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl228])).
% 0.62/0.96 thf(zip_derived_cl66, plain,
% 0.62/0.96 (( (product @ e_4 @ e_1 @ e_2)) <= (( (product @ e_4 @ e_1 @ e_2)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl60])).
% 0.62/0.96 thf(zip_derived_cl18, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.62/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.62/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.62/0.96 | (equalish @ X1 @ X3))),
% 0.62/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.62/0.96 thf(zip_derived_cl92, plain,
% 0.62/0.96 ((![X0 : $i]: (~ (product @ e_4 @ X0 @ e_2) | (equalish @ e_1 @ X0)))
% 0.62/0.96 <= (( (product @ e_4 @ e_1 @ e_2)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl66, zip_derived_cl18])).
% 0.62/0.96 thf(zip_derived_cl341, plain,
% 0.62/0.96 (( (equalish @ e_1 @ e_3))
% 0.62/0.96 <= (( (product @ e_4 @ e_1 @ e_2)) & ( (product @ e_4 @ e_3 @ e_2)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl266, zip_derived_cl92])).
% 0.62/0.96 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 0.62/0.96 thf(zip_derived_cl5, plain, (~ (equalish @ e_1 @ e_3)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.62/0.96 thf('8', plain,
% 0.62/0.96 (~ ( (product @ e_4 @ e_1 @ e_2)) | ~ ( (product @ e_4 @ e_3 @ e_2))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl341, zip_derived_cl5])).
% 0.62/0.96 thf(zip_derived_cl270, plain,
% 0.62/0.96 ((![X0 : $i]:
% 0.62/0.96 ( (product @ e_1 @ e_3 @ X0) | ~ (product @ e_3 @ X0 @ e_4)))
% 0.62/0.96 <= (( (product @ e_4 @ e_3 @ e_1)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl265, zip_derived_cl21])).
% 0.62/0.96 thf(zip_derived_cl100, plain,
% 0.62/0.96 ((![X0 : $i]:
% 0.62/0.96 ( (product @ e_3 @ e_1 @ X0) | ~ (product @ e_1 @ X0 @ e_4)))
% 0.62/0.96 <= (( (product @ e_4 @ e_1 @ e_3)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl67, zip_derived_cl21])).
% 0.62/0.96 thf(zip_derived_cl286, plain,
% 0.62/0.96 ((( (product @ e_1 @ e_3 @ e_1) | ~ (product @ e_1 @ e_4 @ e_4)))
% 0.62/0.96 <= (( (product @ e_4 @ e_1 @ e_3)) & ( (product @ e_4 @ e_3 @ e_1)))),
% 0.62/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl270, zip_derived_cl100])).
% 0.62/0.96 thf(zip_derived_cl291, plain,
% 0.62/0.96 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl286])).
% 0.62/0.96 thf(zip_derived_cl31, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 0.62/0.96 thf(zip_derived_cl298, plain,
% 0.62/0.96 (( (equalish @ e_1 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl291, zip_derived_cl31])).
% 0.62/0.96 thf(zip_derived_cl5, plain, (~ (equalish @ e_1 @ e_3)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 0.62/0.96 thf('9', plain, (~ ( (product @ e_1 @ e_3 @ e_1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl298, zip_derived_cl5])).
% 0.62/0.96 thf('10', plain,
% 0.62/0.96 (( (product @ e_1 @ e_3 @ e_3)) | ( (product @ e_1 @ e_3 @ e_2)) |
% 0.62/0.96 ( (product @ e_1 @ e_3 @ e_1)) | ~ ( (product @ e_4 @ e_1 @ e_3))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl206])).
% 0.62/0.96 thf('11', plain,
% 0.62/0.96 (( (product @ e_4 @ e_3 @ e_1)) | ( (product @ e_4 @ e_3 @ e_2))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl228])).
% 0.62/0.96 thf(zip_derived_cl452, plain,
% 0.62/0.96 (( (product @ e_4 @ e_2 @ e_1)) <= (( (product @ e_4 @ e_2 @ e_1)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl61])).
% 0.62/0.96 thf(zip_derived_cl265, plain,
% 0.62/0.96 (( (product @ e_4 @ e_3 @ e_1)) <= (( (product @ e_4 @ e_3 @ e_1)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl228])).
% 0.62/0.96 thf(zip_derived_cl18, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.62/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.62/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.62/0.96 | (equalish @ X1 @ X3))),
% 0.62/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.62/0.96 thf(zip_derived_cl268, plain,
% 0.62/0.96 ((![X0 : $i]: (~ (product @ e_4 @ X0 @ e_1) | (equalish @ e_3 @ X0)))
% 0.62/0.96 <= (( (product @ e_4 @ e_3 @ e_1)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl265, zip_derived_cl18])).
% 0.62/0.96 thf(zip_derived_cl477, plain,
% 0.62/0.96 (( (equalish @ e_3 @ e_2))
% 0.62/0.96 <= (( (product @ e_4 @ e_3 @ e_1)) & ( (product @ e_4 @ e_2 @ e_1)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl452, zip_derived_cl268])).
% 0.62/0.96 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 0.62/0.96 thf(zip_derived_cl11, plain, (~ (equalish @ e_3 @ e_2)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 0.62/0.96 thf('12', plain,
% 0.62/0.96 (~ ( (product @ e_4 @ e_2 @ e_1)) | ~ ( (product @ e_4 @ e_3 @ e_1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl477, zip_derived_cl11])).
% 0.62/0.96 thf('13', plain,
% 0.62/0.96 (( (product @ e_4 @ e_2 @ e_3)) | ( (product @ e_4 @ e_2 @ e_1)) |
% 0.62/0.96 ( (product @ e_4 @ e_4 @ e_2)) | ( (product @ e_4 @ e_2 @ e_2))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl61])).
% 0.62/0.96 thf(zip_derived_cl454, plain,
% 0.62/0.96 (( (product @ e_4 @ e_2 @ e_3)) <= (( (product @ e_4 @ e_2 @ e_3)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl61])).
% 0.62/0.96 thf(zip_derived_cl67, plain,
% 0.62/0.96 (( (product @ e_4 @ e_1 @ e_3)) <= (( (product @ e_4 @ e_1 @ e_3)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl60])).
% 0.62/0.96 thf(zip_derived_cl18, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.62/0.96 (~ (product @ X0 @ X1 @ X2)
% 0.62/0.96 | ~ (product @ X0 @ X3 @ X2)
% 0.62/0.96 | (equalish @ X1 @ X3))),
% 0.62/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.62/0.96 thf(zip_derived_cl98, plain,
% 0.62/0.96 ((![X0 : $i]: (~ (product @ e_4 @ X0 @ e_3) | (equalish @ e_1 @ X0)))
% 0.62/0.96 <= (( (product @ e_4 @ e_1 @ e_3)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl67, zip_derived_cl18])).
% 0.62/0.96 thf(zip_derived_cl534, plain,
% 0.62/0.96 (( (equalish @ e_1 @ e_2))
% 0.62/0.96 <= (( (product @ e_4 @ e_1 @ e_3)) & ( (product @ e_4 @ e_2 @ e_3)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl454, zip_derived_cl98])).
% 0.62/0.96 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 0.62/0.96 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_2)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.62/0.96 thf('14', plain,
% 0.62/0.96 (~ ( (product @ e_4 @ e_1 @ e_3)) | ~ ( (product @ e_4 @ e_2 @ e_3))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl534, zip_derived_cl4])).
% 0.62/0.96 thf('15', plain,
% 0.62/0.96 (( (product @ e_4 @ e_1 @ e_2)) | ( (product @ e_4 @ e_1 @ e_3)) |
% 0.62/0.96 ( (product @ e_4 @ e_4 @ e_1)) | ( (product @ e_4 @ e_1 @ e_1))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl60])).
% 0.62/0.96 thf(zip_derived_cl452, plain,
% 0.62/0.96 (( (product @ e_4 @ e_2 @ e_1)) <= (( (product @ e_4 @ e_2 @ e_1)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl61])).
% 0.62/0.96 thf(zip_derived_cl21, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.62/0.96 ( (product @ X0 @ X1 @ X2)
% 0.62/0.96 | ~ (product @ X3 @ X1 @ X0)
% 0.62/0.96 | ~ (product @ X1 @ X2 @ X3))),
% 0.62/0.96 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.62/0.96 thf(zip_derived_cl474, plain,
% 0.62/0.96 ((![X0 : $i]:
% 0.62/0.96 ( (product @ e_1 @ e_2 @ X0) | ~ (product @ e_2 @ X0 @ e_4)))
% 0.62/0.96 <= (( (product @ e_4 @ e_2 @ e_1)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl452, zip_derived_cl21])).
% 0.62/0.96 thf(zip_derived_cl94, plain,
% 0.62/0.96 ((![X0 : $i]:
% 0.62/0.96 ( (product @ e_2 @ e_1 @ X0) | ~ (product @ e_1 @ X0 @ e_4)))
% 0.62/0.96 <= (( (product @ e_4 @ e_1 @ e_2)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl66, zip_derived_cl21])).
% 0.62/0.96 thf(zip_derived_cl678, plain,
% 0.62/0.96 ((( (product @ e_1 @ e_2 @ e_1) | ~ (product @ e_1 @ e_4 @ e_4)))
% 0.62/0.96 <= (( (product @ e_4 @ e_1 @ e_2)) & ( (product @ e_4 @ e_2 @ e_1)))),
% 0.62/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl474, zip_derived_cl94])).
% 0.62/0.96 thf(zip_derived_cl714, plain,
% 0.62/0.96 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl678])).
% 0.62/0.96 thf(zip_derived_cl31, plain,
% 0.62/0.96 (![X0 : $i, X1 : $i]:
% 0.62/0.96 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 0.62/0.96 thf(zip_derived_cl721, plain,
% 0.62/0.96 (( (equalish @ e_1 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl714, zip_derived_cl31])).
% 0.62/0.96 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_2)),
% 0.62/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 0.62/0.96 thf('16', plain, (~ ( (product @ e_1 @ e_2 @ e_1))),
% 0.62/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl721, zip_derived_cl4])).
% 0.62/0.96 thf('17', plain,
% 0.62/0.96 (( (product @ e_1 @ e_2 @ e_2)) | ( (product @ e_1 @ e_2 @ e_3)) |
% 0.62/0.96 ( (product @ e_1 @ e_2 @ e_1)) | ~ ( (product @ e_4 @ e_1 @ e_2))),
% 0.62/0.96 inference('split', [status(esa)], [zip_derived_cl179])).
% 0.62/0.96 thf(zip_derived_cl1531, plain, ($false),
% 0.62/0.96 inference('sat_resolution*', [status(thm)],
% 0.62/0.96 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 0.62/0.96 '12', '13', '14', '15', '16', '17'])).
% 0.62/0.96
% 0.62/0.96 % SZS output end Refutation
% 0.62/0.96
% 0.62/0.96
% 0.62/0.96 % Terminating...
% 0.65/1.07 % Runner terminated.
% 1.96/1.08 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------