TSTP Solution File: GRP124-1.004 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP124-1.004 : 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.OCrXZDgoZ2 true
% Computer : n008.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 01:50:04 EDT 2023
% Result : Unsatisfiable 1.44s 0.95s
% Output : Refutation 1.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP124-1.004 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.OCrXZDgoZ2 true
% 0.17/0.35 % Computer : n008.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Mon Aug 28 23:16:32 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.17/0.35 % Running portfolio for 300 s
% 0.17/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.35 % Number of cores: 8
% 0.17/0.35 % Python version: Python 3.6.8
% 0.17/0.36 % Running in FO mode
% 0.22/0.65 % Total configuration time : 435
% 0.22/0.65 % Estimated wc time : 1092
% 0.22/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.42/0.77 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.42/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.42/0.77 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.44/0.95 % Solved by fo/fo1_av.sh.
% 1.44/0.95 % done 480 iterations in 0.170s
% 1.44/0.95 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.44/0.95 % SZS output start Refutation
% 1.44/0.95 thf(product_type, type, product: $i > $i > $i > $o).
% 1.44/0.95 thf(e_1_type, type, e_1: $i).
% 1.44/0.95 thf(e_3_type, type, e_3: $i).
% 1.44/0.95 thf(group_element_type, type, group_element: $i > $o).
% 1.44/0.95 thf(e_2_type, type, e_2: $i).
% 1.44/0.95 thf(e_4_type, type, e_4: $i).
% 1.44/0.95 thf(equalish_type, type, equalish: $i > $i > $o).
% 1.44/0.95 thf(element_3, axiom, (group_element @ e_3)).
% 1.44/0.95 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 1.44/0.95 inference('cnf', [status(esa)], [element_3])).
% 1.44/0.95 thf(product_total_function1, axiom,
% 1.44/0.95 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 1.44/0.95 ( product @ X @ Y @ e_1 ) | ( product @ X @ Y @ e_2 ) |
% 1.44/0.95 ( product @ X @ Y @ e_3 ) | ( product @ X @ Y @ e_4 ))).
% 1.44/0.95 thf(zip_derived_cl16, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i]:
% 1.44/0.95 (~ (group_element @ X0)
% 1.44/0.95 | ~ (group_element @ X1)
% 1.44/0.95 | (product @ X0 @ X1 @ e_1)
% 1.44/0.95 | (product @ X0 @ X1 @ e_2)
% 1.44/0.95 | (product @ X0 @ X1 @ e_3)
% 1.44/0.95 | (product @ X0 @ X1 @ e_4))),
% 1.44/0.95 inference('cnf', [status(esa)], [product_total_function1])).
% 1.44/0.95 thf(zip_derived_cl25, plain,
% 1.44/0.95 (![X0 : $i]:
% 1.44/0.95 (~ (group_element @ X0)
% 1.44/0.95 | (product @ e_3 @ X0 @ e_1)
% 1.44/0.95 | (product @ e_3 @ X0 @ e_2)
% 1.44/0.95 | (product @ e_3 @ X0 @ e_3)
% 1.44/0.95 | (product @ e_3 @ X0 @ e_4))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl16])).
% 1.44/0.95 thf(element_1, axiom, (group_element @ e_1)).
% 1.44/0.95 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 1.44/0.95 inference('cnf', [status(esa)], [element_1])).
% 1.44/0.95 thf(zip_derived_cl162, plain,
% 1.44/0.95 (( (product @ e_3 @ e_1 @ e_4)
% 1.44/0.95 | (product @ e_3 @ e_1 @ e_3)
% 1.44/0.95 | (product @ e_3 @ e_1 @ e_2)
% 1.44/0.95 | (product @ e_3 @ e_1 @ e_1))),
% 1.44/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl0])).
% 1.44/0.95 thf(zip_derived_cl678, plain,
% 1.44/0.95 (( (product @ e_3 @ e_1 @ e_2)) <= (( (product @ e_3 @ e_1 @ e_2)))),
% 1.44/0.95 inference('split', [status(esa)], [zip_derived_cl162])).
% 1.44/0.95 thf(qg2_1, conjecture,
% 1.44/0.95 (~( ( equalish @ X1 @ X2 ) | ( ~( product @ Z2 @ X2 @ Y2 ) ) |
% 1.44/0.95 ( ~( product @ Z2 @ X1 @ Y1 ) ) | ( ~( product @ X2 @ Y2 @ Z1 ) ) |
% 1.44/0.95 ( ~( product @ X1 @ Y1 @ Z1 ) ) ))).
% 1.44/0.95 thf(zf_stmt_0, negated_conjecture,
% 1.44/0.95 (( equalish @ X1 @ X2 ) | ( ~( product @ Z2 @ X2 @ Y2 ) ) |
% 1.44/0.95 ( ~( product @ Z2 @ X1 @ Y1 ) ) | ( ~( product @ X2 @ Y2 @ Z1 ) ) |
% 1.44/0.95 ( ~( product @ X1 @ Y1 @ Z1 ) )),
% 1.44/0.95 inference('cnf.neg', [status(esa)], [qg2_1])).
% 1.44/0.95 thf(zip_derived_cl21, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.44/0.95 ( (equalish @ X0 @ X1)
% 1.44/0.95 | ~ (product @ X2 @ X1 @ X3)
% 1.44/0.95 | ~ (product @ X2 @ X0 @ X4)
% 1.44/0.95 | ~ (product @ X1 @ X3 @ X5)
% 1.44/0.95 | ~ (product @ X0 @ X4 @ X5))),
% 1.44/0.95 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.44/0.95 thf(zip_derived_cl45, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.44/0.95 (~ (product @ X2 @ X1 @ X0)
% 1.44/0.95 | ~ (product @ X0 @ X0 @ X0)
% 1.44/0.95 | ~ (product @ X0 @ X2 @ X1)
% 1.44/0.95 | (equalish @ X2 @ X0))),
% 1.44/0.95 inference('eq_fact', [status(thm)], [zip_derived_cl21])).
% 1.44/0.95 thf(product_idempotence, axiom, (product @ X @ X @ X)).
% 1.44/0.95 thf(zip_derived_cl20, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 1.44/0.95 inference('cnf', [status(esa)], [product_idempotence])).
% 1.44/0.95 thf(zip_derived_cl48, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.44/0.95 (~ (product @ X2 @ X1 @ X0)
% 1.44/0.95 | ~ (product @ X0 @ X2 @ X1)
% 1.44/0.95 | (equalish @ X2 @ X0))),
% 1.44/0.95 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl20])).
% 1.44/0.95 thf(zip_derived_cl1240, plain,
% 1.44/0.95 (((~ (product @ e_2 @ e_3 @ e_1) | (equalish @ e_3 @ e_2)))
% 1.44/0.95 <= (( (product @ e_3 @ e_1 @ e_2)))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl678, zip_derived_cl48])).
% 1.44/0.95 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 1.44/0.95 inference('cnf', [status(esa)], [element_3])).
% 1.44/0.95 thf(element_2, axiom, (group_element @ e_2)).
% 1.44/0.95 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 1.44/0.95 inference('cnf', [status(esa)], [element_2])).
% 1.44/0.95 thf(zip_derived_cl16, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i]:
% 1.44/0.95 (~ (group_element @ X0)
% 1.44/0.95 | ~ (group_element @ X1)
% 1.44/0.95 | (product @ X0 @ X1 @ e_1)
% 1.44/0.95 | (product @ X0 @ X1 @ e_2)
% 1.44/0.95 | (product @ X0 @ X1 @ e_3)
% 1.44/0.95 | (product @ X0 @ X1 @ e_4))),
% 1.44/0.95 inference('cnf', [status(esa)], [product_total_function1])).
% 1.44/0.95 thf(zip_derived_cl24, plain,
% 1.44/0.95 (![X0 : $i]:
% 1.44/0.95 (~ (group_element @ X0)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_1)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_2)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_3)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_4))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl16])).
% 1.44/0.95 thf(zip_derived_cl125, plain,
% 1.44/0.95 (( (product @ e_2 @ e_3 @ e_1)
% 1.44/0.95 | (product @ e_2 @ e_3 @ e_2)
% 1.44/0.95 | (product @ e_2 @ e_3 @ e_3)
% 1.44/0.95 | (product @ e_2 @ e_3 @ e_4))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl24])).
% 1.44/0.95 thf(zip_derived_cl533, plain,
% 1.44/0.95 (( (product @ e_2 @ e_3 @ e_1)) <= (( (product @ e_2 @ e_3 @ e_1)))),
% 1.44/0.95 inference('split', [status(esa)], [zip_derived_cl125])).
% 1.44/0.95 thf(zip_derived_cl24, plain,
% 1.44/0.95 (![X0 : $i]:
% 1.44/0.95 (~ (group_element @ X0)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_1)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_2)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_3)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_4))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl16])).
% 1.44/0.95 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 1.44/0.95 inference('cnf', [status(esa)], [element_3])).
% 1.44/0.95 thf(zip_derived_cl121, plain,
% 1.44/0.95 (( (product @ e_2 @ e_3 @ e_4)
% 1.44/0.95 | (product @ e_2 @ e_3 @ e_3)
% 1.44/0.95 | (product @ e_2 @ e_3 @ e_2)
% 1.44/0.95 | (product @ e_2 @ e_3 @ e_1))),
% 1.44/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl2])).
% 1.44/0.95 thf(zip_derived_cl448, plain,
% 1.44/0.95 (( (product @ e_2 @ e_3 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 1.44/0.95 inference('split', [status(esa)], [zip_derived_cl121])).
% 1.44/0.95 thf(zip_derived_cl20, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 1.44/0.95 inference('cnf', [status(esa)], [product_idempotence])).
% 1.44/0.95 thf(product_right_cancellation, axiom,
% 1.44/0.95 (( ~( product @ X @ W @ Y ) ) | ( ~( product @ X @ Z @ Y ) ) |
% 1.44/0.95 ( equalish @ W @ Z ))).
% 1.44/0.95 thf(zip_derived_cl18, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.44/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.44/0.95 | ~ (product @ X0 @ X3 @ X2)
% 1.44/0.95 | (equalish @ X1 @ X3))),
% 1.44/0.95 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.44/0.95 thf(zip_derived_cl32, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i]:
% 1.44/0.95 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 1.44/0.95 thf(zip_derived_cl628, plain,
% 1.44/0.95 (( (equalish @ e_2 @ e_3)) <= (( (product @ e_2 @ e_3 @ e_2)))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl448, zip_derived_cl32])).
% 1.44/0.95 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 1.44/0.95 thf(zip_derived_cl8, plain, (~ (equalish @ e_2 @ e_3)),
% 1.44/0.95 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 1.44/0.95 thf('0', plain, (~ ( (product @ e_2 @ e_3 @ e_2))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl628, zip_derived_cl8])).
% 1.44/0.95 thf(zip_derived_cl531, plain,
% 1.44/0.95 (( (product @ e_2 @ e_3 @ e_3)) <= (( (product @ e_2 @ e_3 @ e_3)))),
% 1.44/0.95 inference('split', [status(esa)], [zip_derived_cl125])).
% 1.44/0.95 thf(zip_derived_cl20, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 1.44/0.95 inference('cnf', [status(esa)], [product_idempotence])).
% 1.44/0.95 thf(product_left_cancellation, axiom,
% 1.44/0.95 (( ~( product @ W @ Y @ X ) ) | ( ~( product @ Z @ Y @ X ) ) |
% 1.44/0.95 ( equalish @ W @ Z ))).
% 1.44/0.95 thf(zip_derived_cl19, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.44/0.95 (~ (product @ X0 @ X1 @ X2)
% 1.44/0.95 | ~ (product @ X3 @ X1 @ X2)
% 1.44/0.95 | (equalish @ X0 @ X3))),
% 1.44/0.95 inference('cnf', [status(esa)], [product_left_cancellation])).
% 1.44/0.95 thf(zip_derived_cl37, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i]:
% 1.44/0.95 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 1.44/0.95 thf(zip_derived_cl543, plain,
% 1.44/0.95 (( (equalish @ e_3 @ e_2)) <= (( (product @ e_2 @ e_3 @ e_3)))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl531, zip_derived_cl37])).
% 1.44/0.95 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 1.44/0.95 thf(zip_derived_cl11, plain, (~ (equalish @ e_3 @ e_2)),
% 1.44/0.95 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 1.44/0.95 thf('1', plain, (~ ( (product @ e_2 @ e_3 @ e_3))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl543, zip_derived_cl11])).
% 1.44/0.95 thf(zip_derived_cl24, plain,
% 1.44/0.95 (![X0 : $i]:
% 1.44/0.95 (~ (group_element @ X0)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_1)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_2)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_3)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_4))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl16])).
% 1.44/0.95 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 1.44/0.95 inference('cnf', [status(esa)], [element_1])).
% 1.44/0.95 thf(zip_derived_cl119, plain,
% 1.44/0.95 (( (product @ e_2 @ e_1 @ e_4)
% 1.44/0.95 | (product @ e_2 @ e_1 @ e_3)
% 1.44/0.95 | (product @ e_2 @ e_1 @ e_2)
% 1.44/0.95 | (product @ e_2 @ e_1 @ e_1))),
% 1.44/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl0])).
% 1.44/0.95 thf(zip_derived_cl406, plain,
% 1.44/0.95 (( (product @ e_2 @ e_1 @ e_4)) <= (( (product @ e_2 @ e_1 @ e_4)))),
% 1.44/0.95 inference('split', [status(esa)], [zip_derived_cl119])).
% 1.44/0.95 thf(zip_derived_cl409, plain,
% 1.44/0.95 (( (product @ e_2 @ e_1 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 1.44/0.95 inference('split', [status(esa)], [zip_derived_cl119])).
% 1.44/0.95 thf(zip_derived_cl37, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i]:
% 1.44/0.95 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 1.44/0.95 thf(zip_derived_cl565, plain,
% 1.44/0.95 (( (equalish @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_1)))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl409, zip_derived_cl37])).
% 1.44/0.95 thf(e_1_is_not_e_2, axiom, (~( equalish @ e_1 @ e_2 ))).
% 1.44/0.95 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_2)),
% 1.44/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.44/0.95 thf('2', plain, (~ ( (product @ e_2 @ e_1 @ e_1))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl565, zip_derived_cl4])).
% 1.44/0.95 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 1.44/0.95 inference('cnf', [status(esa)], [element_1])).
% 1.44/0.95 thf(zip_derived_cl24, plain,
% 1.44/0.95 (![X0 : $i]:
% 1.44/0.95 (~ (group_element @ X0)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_1)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_2)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_3)
% 1.44/0.95 | (product @ e_2 @ X0 @ e_4))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl16])).
% 1.44/0.95 thf(zip_derived_cl123, plain,
% 1.44/0.95 (( (product @ e_2 @ e_1 @ e_1)
% 1.44/0.95 | (product @ e_2 @ e_1 @ e_2)
% 1.44/0.95 | (product @ e_2 @ e_1 @ e_3)
% 1.44/0.95 | (product @ e_2 @ e_1 @ e_4))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl24])).
% 1.44/0.95 thf(zip_derived_cl509, plain,
% 1.44/0.95 (( (product @ e_2 @ e_1 @ e_2)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.44/0.95 inference('split', [status(esa)], [zip_derived_cl123])).
% 1.44/0.95 thf(zip_derived_cl32, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i]:
% 1.44/0.95 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 1.44/0.95 thf(zip_derived_cl520, plain,
% 1.44/0.95 (( (equalish @ e_2 @ e_1)) <= (( (product @ e_2 @ e_1 @ e_2)))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl509, zip_derived_cl32])).
% 1.44/0.95 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 1.44/0.95 thf(zip_derived_cl7, plain, (~ (equalish @ e_2 @ e_1)),
% 1.44/0.95 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 1.44/0.95 thf('3', plain, (~ ( (product @ e_2 @ e_1 @ e_2))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl520, zip_derived_cl7])).
% 1.44/0.95 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 1.44/0.95 inference('cnf', [status(esa)], [element_3])).
% 1.44/0.95 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 1.44/0.95 inference('cnf', [status(esa)], [element_1])).
% 1.44/0.95 thf(zip_derived_cl16, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i]:
% 1.44/0.95 (~ (group_element @ X0)
% 1.44/0.95 | ~ (group_element @ X1)
% 1.44/0.95 | (product @ X0 @ X1 @ e_1)
% 1.44/0.95 | (product @ X0 @ X1 @ e_2)
% 1.44/0.95 | (product @ X0 @ X1 @ e_3)
% 1.44/0.95 | (product @ X0 @ X1 @ e_4))),
% 1.44/0.95 inference('cnf', [status(esa)], [product_total_function1])).
% 1.44/0.95 thf(zip_derived_cl23, plain,
% 1.44/0.95 (![X0 : $i]:
% 1.44/0.95 (~ (group_element @ X0)
% 1.44/0.95 | (product @ e_1 @ X0 @ e_1)
% 1.44/0.95 | (product @ e_1 @ X0 @ e_2)
% 1.44/0.95 | (product @ e_1 @ X0 @ e_3)
% 1.44/0.95 | (product @ e_1 @ X0 @ e_4))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl16])).
% 1.44/0.95 thf(zip_derived_cl96, plain,
% 1.44/0.95 (( (product @ e_1 @ e_3 @ e_1)
% 1.44/0.95 | (product @ e_1 @ e_3 @ e_2)
% 1.44/0.95 | (product @ e_1 @ e_3 @ e_3)
% 1.44/0.95 | (product @ e_1 @ e_3 @ e_4))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl23])).
% 1.44/0.95 thf(zip_derived_cl340, plain,
% 1.44/0.95 (( (product @ e_1 @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 1.44/0.95 inference('split', [status(esa)], [zip_derived_cl96])).
% 1.44/0.95 thf(zip_derived_cl32, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i]:
% 1.44/0.95 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 1.44/0.95 thf(zip_derived_cl350, plain,
% 1.44/0.95 (( (equalish @ e_1 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_1)))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl340, zip_derived_cl32])).
% 1.44/0.95 thf(e_1_is_not_e_3, axiom, (~( equalish @ e_1 @ e_3 ))).
% 1.44/0.95 thf(zip_derived_cl5, plain, (~ (equalish @ e_1 @ e_3)),
% 1.44/0.95 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 1.44/0.95 thf('4', plain, (~ ( (product @ e_1 @ e_3 @ e_1))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl350, zip_derived_cl5])).
% 1.44/0.95 thf(zip_derived_cl23, plain,
% 1.44/0.95 (![X0 : $i]:
% 1.44/0.95 (~ (group_element @ X0)
% 1.44/0.95 | (product @ e_1 @ X0 @ e_1)
% 1.44/0.95 | (product @ e_1 @ X0 @ e_2)
% 1.44/0.95 | (product @ e_1 @ X0 @ e_3)
% 1.44/0.95 | (product @ e_1 @ X0 @ e_4))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl16])).
% 1.44/0.95 thf(zip_derived_cl2, plain, ( (group_element @ e_3)),
% 1.44/0.95 inference('cnf', [status(esa)], [element_3])).
% 1.44/0.95 thf(zip_derived_cl92, plain,
% 1.44/0.95 (( (product @ e_1 @ e_3 @ e_4)
% 1.44/0.95 | (product @ e_1 @ e_3 @ e_3)
% 1.44/0.95 | (product @ e_1 @ e_3 @ e_2)
% 1.44/0.95 | (product @ e_1 @ e_3 @ e_1))),
% 1.44/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl2])).
% 1.44/0.95 thf(zip_derived_cl232, plain,
% 1.44/0.95 (( (product @ e_1 @ e_3 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 1.44/0.95 inference('split', [status(esa)], [zip_derived_cl92])).
% 1.44/0.95 thf(zip_derived_cl37, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i]:
% 1.44/0.95 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 1.44/0.95 thf(zip_derived_cl297, plain,
% 1.44/0.95 (( (equalish @ e_3 @ e_1)) <= (( (product @ e_1 @ e_3 @ e_3)))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl232, zip_derived_cl37])).
% 1.44/0.95 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 1.44/0.95 thf(zip_derived_cl10, plain, (~ (equalish @ e_3 @ e_1)),
% 1.44/0.95 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 1.44/0.95 thf('5', plain, (~ ( (product @ e_1 @ e_3 @ e_3))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl297, zip_derived_cl10])).
% 1.44/0.95 thf(element_4, axiom, (group_element @ e_4)).
% 1.44/0.95 thf(zip_derived_cl3, plain, ( (group_element @ e_4)),
% 1.44/0.95 inference('cnf', [status(esa)], [element_4])).
% 1.44/0.95 thf(zip_derived_cl25, plain,
% 1.44/0.95 (![X0 : $i]:
% 1.44/0.95 (~ (group_element @ X0)
% 1.44/0.95 | (product @ e_3 @ X0 @ e_1)
% 1.44/0.95 | (product @ e_3 @ X0 @ e_2)
% 1.44/0.95 | (product @ e_3 @ X0 @ e_3)
% 1.44/0.95 | (product @ e_3 @ X0 @ e_4))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl16])).
% 1.44/0.95 thf(zip_derived_cl169, plain,
% 1.44/0.95 (( (product @ e_3 @ e_4 @ e_1)
% 1.44/0.95 | (product @ e_3 @ e_4 @ e_2)
% 1.44/0.95 | (product @ e_3 @ e_4 @ e_3)
% 1.44/0.95 | (product @ e_3 @ e_4 @ e_4))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl25])).
% 1.44/0.95 thf(zip_derived_cl231, plain,
% 1.44/0.95 (( (product @ e_1 @ e_3 @ e_4)) <= (( (product @ e_1 @ e_3 @ e_4)))),
% 1.44/0.95 inference('split', [status(esa)], [zip_derived_cl92])).
% 1.44/0.95 thf(qg2_2, conjecture,
% 1.44/0.95 (~( ( equalish @ Y1 @ Y2 ) | ( ~( product @ Z2 @ X2 @ Y2 ) ) |
% 1.44/0.95 ( ~( product @ Z2 @ X1 @ Y1 ) ) | ( ~( product @ X2 @ Y2 @ Z1 ) ) |
% 1.44/0.95 ( ~( product @ X1 @ Y1 @ Z1 ) ) ))).
% 1.44/0.95 thf(zf_stmt_1, negated_conjecture,
% 1.44/0.95 (( equalish @ Y1 @ Y2 ) | ( ~( product @ Z2 @ X2 @ Y2 ) ) |
% 1.44/0.95 ( ~( product @ Z2 @ X1 @ Y1 ) ) | ( ~( product @ X2 @ Y2 @ Z1 ) ) |
% 1.44/0.95 ( ~( product @ X1 @ Y1 @ Z1 ) )),
% 1.44/0.95 inference('cnf.neg', [status(esa)], [qg2_2])).
% 1.44/0.95 thf(zip_derived_cl22, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.44/0.95 ( (equalish @ X0 @ X1)
% 1.44/0.95 | ~ (product @ X2 @ X3 @ X1)
% 1.44/0.95 | ~ (product @ X2 @ X4 @ X0)
% 1.44/0.95 | ~ (product @ X3 @ X1 @ X5)
% 1.44/0.95 | ~ (product @ X4 @ X0 @ X5))),
% 1.44/0.95 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.44/0.95 thf(zip_derived_cl65, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.44/0.95 (~ (product @ X2 @ X1 @ X0)
% 1.44/0.95 | ~ (product @ X1 @ X0 @ X0)
% 1.44/0.95 | ~ (product @ X2 @ X2 @ X1)
% 1.44/0.95 | (equalish @ X1 @ X0))),
% 1.44/0.95 inference('eq_fact', [status(thm)], [zip_derived_cl22])).
% 1.44/0.95 thf(zip_derived_cl242, plain,
% 1.44/0.95 (((~ (product @ e_3 @ e_4 @ e_4)
% 1.44/0.95 | ~ (product @ e_1 @ e_1 @ e_3)
% 1.44/0.95 | (equalish @ e_3 @ e_4))) <= (( (product @ e_1 @ e_3 @ e_4)))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl231, zip_derived_cl65])).
% 1.44/0.95 thf(e_3_is_not_e_4, axiom, (~( equalish @ e_3 @ e_4 ))).
% 1.44/0.95 thf(zip_derived_cl12, plain, (~ (equalish @ e_3 @ e_4)),
% 1.44/0.95 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 1.44/0.95 thf(zip_derived_cl250, plain,
% 1.44/0.95 (((~ (product @ e_3 @ e_4 @ e_4) | ~ (product @ e_1 @ e_1 @ e_3)))
% 1.44/0.95 <= (( (product @ e_1 @ e_3 @ e_4)))),
% 1.44/0.95 inference('demod', [status(thm)], [zip_derived_cl242, zip_derived_cl12])).
% 1.44/0.95 thf(zip_derived_cl255, plain,
% 1.44/0.95 ((~ (product @ e_3 @ e_4 @ e_4)) <= (~ ( (product @ e_3 @ e_4 @ e_4)))),
% 1.44/0.95 inference('split', [status(esa)], [zip_derived_cl250])).
% 1.44/0.95 thf(zip_derived_cl25, plain,
% 1.44/0.95 (![X0 : $i]:
% 1.44/0.95 (~ (group_element @ X0)
% 1.44/0.95 | (product @ e_3 @ X0 @ e_1)
% 1.44/0.95 | (product @ e_3 @ X0 @ e_2)
% 1.44/0.95 | (product @ e_3 @ X0 @ e_3)
% 1.44/0.95 | (product @ e_3 @ X0 @ e_4))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl16])).
% 1.44/0.95 thf(zip_derived_cl3, plain, ( (group_element @ e_4)),
% 1.44/0.95 inference('cnf', [status(esa)], [element_4])).
% 1.44/0.95 thf(zip_derived_cl165, plain,
% 1.44/0.95 (( (product @ e_3 @ e_4 @ e_4)
% 1.44/0.95 | (product @ e_3 @ e_4 @ e_3)
% 1.44/0.95 | (product @ e_3 @ e_4 @ e_2)
% 1.44/0.95 | (product @ e_3 @ e_4 @ e_1))),
% 1.44/0.95 inference('s_sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl3])).
% 1.44/0.95 thf(zip_derived_cl727, plain,
% 1.44/0.95 (( (product @ e_3 @ e_4 @ e_4)) <= (( (product @ e_3 @ e_4 @ e_4)))),
% 1.44/0.95 inference('split', [status(esa)], [zip_derived_cl165])).
% 1.44/0.95 thf(zip_derived_cl37, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i]:
% 1.44/0.95 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 1.44/0.95 thf(zip_derived_cl740, plain,
% 1.44/0.95 (( (equalish @ e_4 @ e_3)) <= (( (product @ e_3 @ e_4 @ e_4)))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl727, zip_derived_cl37])).
% 1.44/0.95 thf(e_4_is_not_e_3, axiom, (~( equalish @ e_4 @ e_3 ))).
% 1.44/0.95 thf(zip_derived_cl15, plain, (~ (equalish @ e_4 @ e_3)),
% 1.44/0.95 inference('cnf', [status(esa)], [e_4_is_not_e_3])).
% 1.44/0.95 thf('6', plain, (~ ( (product @ e_3 @ e_4 @ e_4))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl740, zip_derived_cl15])).
% 1.44/0.95 thf('7', plain, (~ ( (product @ e_3 @ e_4 @ e_4))),
% 1.44/0.95 inference('sat_resolution*', [status(thm)], ['6'])).
% 1.44/0.95 thf(zip_derived_cl776, plain, (~ (product @ e_3 @ e_4 @ e_4)),
% 1.44/0.95 inference('simpl_trail', [status(thm)], [zip_derived_cl255, '7'])).
% 1.44/0.95 thf(zip_derived_cl824, plain,
% 1.44/0.95 (( (product @ e_3 @ e_4 @ e_3)
% 1.44/0.95 | (product @ e_3 @ e_4 @ e_2)
% 1.44/0.95 | (product @ e_3 @ e_4 @ e_1))),
% 1.44/0.95 inference('clc', [status(thm)], [zip_derived_cl169, zip_derived_cl776])).
% 1.44/0.95 thf(zip_derived_cl826, plain,
% 1.44/0.95 (( (product @ e_3 @ e_4 @ e_2)) <= (( (product @ e_3 @ e_4 @ e_2)))),
% 1.44/0.95 inference('split', [status(esa)], [zip_derived_cl824])).
% 1.44/0.95 thf(zip_derived_cl446, plain,
% 1.44/0.95 (( (product @ e_2 @ e_3 @ e_4)) <= (( (product @ e_2 @ e_3 @ e_4)))),
% 1.44/0.95 inference('split', [status(esa)], [zip_derived_cl121])).
% 1.44/0.95 thf(zip_derived_cl20, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 1.44/0.95 inference('cnf', [status(esa)], [product_idempotence])).
% 1.44/0.95 thf(zip_derived_cl21, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.44/0.95 ( (equalish @ X0 @ X1)
% 1.44/0.95 | ~ (product @ X2 @ X1 @ X3)
% 1.44/0.95 | ~ (product @ X2 @ X0 @ X4)
% 1.44/0.95 | ~ (product @ X1 @ X3 @ X5)
% 1.44/0.95 | ~ (product @ X0 @ X4 @ X5))),
% 1.44/0.95 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.44/0.95 thf(zip_derived_cl43, plain,
% 1.44/0.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.44/0.95 ( (equalish @ X1 @ X0)
% 1.44/0.95 | ~ (product @ X0 @ X1 @ X2)
% 1.44/0.95 | ~ (product @ X0 @ X0 @ X3)
% 1.44/0.95 | ~ (product @ X1 @ X2 @ X3))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl21])).
% 1.44/0.95 thf(zip_derived_cl453, plain,
% 1.44/0.95 ((![X0 : $i]:
% 1.44/0.95 ( (equalish @ e_3 @ e_2)
% 1.44/0.95 | ~ (product @ e_2 @ e_2 @ X0)
% 1.44/0.95 | ~ (product @ e_3 @ e_4 @ X0)))
% 1.44/0.95 <= (( (product @ e_2 @ e_3 @ e_4)))),
% 1.44/0.95 inference('s_sup-', [status(thm)], [zip_derived_cl446, zip_derived_cl43])).
% 1.44/0.95 thf(zip_derived_cl11, plain, (~ (equalish @ e_3 @ e_2)),
% 1.44/0.95 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 1.44/0.95 thf(zip_derived_cl461, plain,
% 1.44/0.95 ((![X0 : $i]:
% 1.44/0.95 (~ (product @ e_2 @ e_2 @ X0) | ~ (product @ e_3 @ e_4 @ X0)))
% 1.44/0.95 <= (( (product @ e_2 @ e_3 @ e_4)))),
% 1.44/0.95 inference('demod', [status(thm)], [zip_derived_cl453, zip_derived_cl11])).
% 1.44/0.96 thf(zip_derived_cl882, plain,
% 1.44/0.96 ((~ (product @ e_2 @ e_2 @ e_2))
% 1.44/0.96 <= (( (product @ e_2 @ e_3 @ e_4)) & ( (product @ e_3 @ e_4 @ e_2)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl826, zip_derived_cl461])).
% 1.44/0.96 thf(zip_derived_cl20, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 1.44/0.96 inference('cnf', [status(esa)], [product_idempotence])).
% 1.44/0.96 thf('8', plain,
% 1.44/0.96 (~ ( (product @ e_3 @ e_4 @ e_2)) | ~ ( (product @ e_2 @ e_3 @ e_4))),
% 1.44/0.96 inference('demod', [status(thm)], [zip_derived_cl882, zip_derived_cl20])).
% 1.44/0.96 thf(zip_derived_cl449, plain,
% 1.44/0.96 (( (product @ e_2 @ e_3 @ e_1)) <= (( (product @ e_2 @ e_3 @ e_1)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl121])).
% 1.44/0.96 thf(zip_derived_cl23, plain,
% 1.44/0.96 (![X0 : $i]:
% 1.44/0.96 (~ (group_element @ X0)
% 1.44/0.96 | (product @ e_1 @ X0 @ e_1)
% 1.44/0.96 | (product @ e_1 @ X0 @ e_2)
% 1.44/0.96 | (product @ e_1 @ X0 @ e_3)
% 1.44/0.96 | (product @ e_1 @ X0 @ e_4))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl16])).
% 1.44/0.96 thf(zip_derived_cl1, plain, ( (group_element @ e_2)),
% 1.44/0.96 inference('cnf', [status(esa)], [element_2])).
% 1.44/0.96 thf(zip_derived_cl91, plain,
% 1.44/0.96 (( (product @ e_1 @ e_2 @ e_4)
% 1.44/0.96 | (product @ e_1 @ e_2 @ e_3)
% 1.44/0.96 | (product @ e_1 @ e_2 @ e_2)
% 1.44/0.96 | (product @ e_1 @ e_2 @ e_1))),
% 1.44/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl1])).
% 1.44/0.96 thf(zip_derived_cl101, plain,
% 1.44/0.96 (( (product @ e_1 @ e_2 @ e_3)) <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl91])).
% 1.44/0.96 thf(zip_derived_cl43, plain,
% 1.44/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.44/0.96 ( (equalish @ X1 @ X0)
% 1.44/0.96 | ~ (product @ X0 @ X1 @ X2)
% 1.44/0.96 | ~ (product @ X0 @ X0 @ X3)
% 1.44/0.96 | ~ (product @ X1 @ X2 @ X3))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl21])).
% 1.44/0.96 thf(zip_derived_cl134, plain,
% 1.44/0.96 ((![X0 : $i]:
% 1.44/0.96 ( (equalish @ e_2 @ e_1)
% 1.44/0.96 | ~ (product @ e_1 @ e_1 @ X0)
% 1.44/0.96 | ~ (product @ e_2 @ e_3 @ X0)))
% 1.44/0.96 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl101, zip_derived_cl43])).
% 1.44/0.96 thf(zip_derived_cl7, plain, (~ (equalish @ e_2 @ e_1)),
% 1.44/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 1.44/0.96 thf(zip_derived_cl141, plain,
% 1.44/0.96 ((![X0 : $i]:
% 1.44/0.96 (~ (product @ e_1 @ e_1 @ X0) | ~ (product @ e_2 @ e_3 @ X0)))
% 1.44/0.96 <= (( (product @ e_1 @ e_2 @ e_3)))),
% 1.44/0.96 inference('demod', [status(thm)], [zip_derived_cl134, zip_derived_cl7])).
% 1.44/0.96 thf(zip_derived_cl789, plain,
% 1.44/0.96 ((~ (product @ e_1 @ e_1 @ e_1))
% 1.44/0.96 <= (( (product @ e_1 @ e_2 @ e_3)) & ( (product @ e_2 @ e_3 @ e_1)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl449, zip_derived_cl141])).
% 1.44/0.96 thf(zip_derived_cl20, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 1.44/0.96 inference('cnf', [status(esa)], [product_idempotence])).
% 1.44/0.96 thf('9', plain,
% 1.44/0.96 (~ ( (product @ e_1 @ e_2 @ e_3)) | ~ ( (product @ e_2 @ e_3 @ e_1))),
% 1.44/0.96 inference('demod', [status(thm)], [zip_derived_cl789, zip_derived_cl20])).
% 1.44/0.96 thf('10', plain,
% 1.44/0.96 (( (product @ e_3 @ e_4 @ e_1)) | ( (product @ e_3 @ e_4 @ e_2)) |
% 1.44/0.96 ( (product @ e_3 @ e_4 @ e_4)) | ( (product @ e_3 @ e_4 @ e_3))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl165])).
% 1.44/0.96 thf(zip_derived_cl825, plain,
% 1.44/0.96 (( (product @ e_3 @ e_4 @ e_3)) <= (( (product @ e_3 @ e_4 @ e_3)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl824])).
% 1.44/0.96 thf(zip_derived_cl32, plain,
% 1.44/0.96 (![X0 : $i, X1 : $i]:
% 1.44/0.96 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 1.44/0.96 thf(zip_derived_cl837, plain,
% 1.44/0.96 (( (equalish @ e_3 @ e_4)) <= (( (product @ e_3 @ e_4 @ e_3)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl825, zip_derived_cl32])).
% 1.44/0.96 thf(zip_derived_cl12, plain, (~ (equalish @ e_3 @ e_4)),
% 1.44/0.96 inference('cnf', [status(esa)], [e_3_is_not_e_4])).
% 1.44/0.96 thf('11', plain, (~ ( (product @ e_3 @ e_4 @ e_3))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl837, zip_derived_cl12])).
% 1.44/0.96 thf('12', plain,
% 1.44/0.96 (( (product @ e_1 @ e_2 @ e_4)) | ( (product @ e_1 @ e_2 @ e_3)) |
% 1.44/0.96 ( (product @ e_1 @ e_2 @ e_2)) | ( (product @ e_1 @ e_2 @ e_1))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl91])).
% 1.44/0.96 thf(zip_derived_cl102, plain,
% 1.44/0.96 (( (product @ e_1 @ e_2 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl91])).
% 1.44/0.96 thf(zip_derived_cl37, plain,
% 1.44/0.96 (![X0 : $i, X1 : $i]:
% 1.44/0.96 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 1.44/0.96 thf(zip_derived_cl155, plain,
% 1.44/0.96 (( (equalish @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_2)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl102, zip_derived_cl37])).
% 1.44/0.96 thf(zip_derived_cl7, plain, (~ (equalish @ e_2 @ e_1)),
% 1.44/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 1.44/0.96 thf('13', plain, (~ ( (product @ e_1 @ e_2 @ e_2))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl155, zip_derived_cl7])).
% 1.44/0.96 thf(zip_derived_cl103, plain,
% 1.44/0.96 (( (product @ e_1 @ e_2 @ e_1)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl91])).
% 1.44/0.96 thf(zip_derived_cl32, plain,
% 1.44/0.96 (![X0 : $i, X1 : $i]:
% 1.44/0.96 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 1.44/0.96 thf(zip_derived_cl184, plain,
% 1.44/0.96 (( (equalish @ e_1 @ e_2)) <= (( (product @ e_1 @ e_2 @ e_1)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl103, zip_derived_cl32])).
% 1.44/0.96 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_2)),
% 1.44/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.44/0.96 thf('14', plain, (~ ( (product @ e_1 @ e_2 @ e_1))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl184, zip_derived_cl4])).
% 1.44/0.96 thf(zip_derived_cl827, plain,
% 1.44/0.96 (( (product @ e_3 @ e_4 @ e_1)) <= (( (product @ e_3 @ e_4 @ e_1)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl824])).
% 1.44/0.96 thf(zip_derived_cl231, plain,
% 1.44/0.96 (( (product @ e_1 @ e_3 @ e_4)) <= (( (product @ e_1 @ e_3 @ e_4)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl92])).
% 1.44/0.96 thf(zip_derived_cl43, plain,
% 1.44/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.44/0.96 ( (equalish @ X1 @ X0)
% 1.44/0.96 | ~ (product @ X0 @ X1 @ X2)
% 1.44/0.96 | ~ (product @ X0 @ X0 @ X3)
% 1.44/0.96 | ~ (product @ X1 @ X2 @ X3))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl21])).
% 1.44/0.96 thf(zip_derived_cl238, plain,
% 1.44/0.96 ((![X0 : $i]:
% 1.44/0.96 ( (equalish @ e_3 @ e_1)
% 1.44/0.96 | ~ (product @ e_1 @ e_1 @ X0)
% 1.44/0.96 | ~ (product @ e_3 @ e_4 @ X0)))
% 1.44/0.96 <= (( (product @ e_1 @ e_3 @ e_4)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl231, zip_derived_cl43])).
% 1.44/0.96 thf(zip_derived_cl10, plain, (~ (equalish @ e_3 @ e_1)),
% 1.44/0.96 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 1.44/0.96 thf(zip_derived_cl248, plain,
% 1.44/0.96 ((![X0 : $i]:
% 1.44/0.96 (~ (product @ e_1 @ e_1 @ X0) | ~ (product @ e_3 @ e_4 @ X0)))
% 1.44/0.96 <= (( (product @ e_1 @ e_3 @ e_4)))),
% 1.44/0.96 inference('demod', [status(thm)], [zip_derived_cl238, zip_derived_cl10])).
% 1.44/0.96 thf(zip_derived_cl953, plain,
% 1.44/0.96 ((~ (product @ e_1 @ e_1 @ e_1))
% 1.44/0.96 <= (( (product @ e_1 @ e_3 @ e_4)) & ( (product @ e_3 @ e_4 @ e_1)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl827, zip_derived_cl248])).
% 1.44/0.96 thf(zip_derived_cl20, plain, (![X0 : $i]: (product @ X0 @ X0 @ X0)),
% 1.44/0.96 inference('cnf', [status(esa)], [product_idempotence])).
% 1.44/0.96 thf('15', plain,
% 1.44/0.96 (~ ( (product @ e_1 @ e_3 @ e_4)) | ~ ( (product @ e_3 @ e_4 @ e_1))),
% 1.44/0.96 inference('demod', [status(thm)], [zip_derived_cl953, zip_derived_cl20])).
% 1.44/0.96 thf(zip_derived_cl231, plain,
% 1.44/0.96 (( (product @ e_1 @ e_3 @ e_4)) <= (( (product @ e_1 @ e_3 @ e_4)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl92])).
% 1.44/0.96 thf(zip_derived_cl100, plain,
% 1.44/0.96 (( (product @ e_1 @ e_2 @ e_4)) <= (( (product @ e_1 @ e_2 @ e_4)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl91])).
% 1.44/0.96 thf(zip_derived_cl18, plain,
% 1.44/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.44/0.96 (~ (product @ X0 @ X1 @ X2)
% 1.44/0.96 | ~ (product @ X0 @ X3 @ X2)
% 1.44/0.96 | (equalish @ X1 @ X3))),
% 1.44/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.44/0.96 thf(zip_derived_cl105, plain,
% 1.44/0.96 ((![X0 : $i]: (~ (product @ e_1 @ X0 @ e_4) | (equalish @ e_2 @ X0)))
% 1.44/0.96 <= (( (product @ e_1 @ e_2 @ e_4)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl100, zip_derived_cl18])).
% 1.44/0.96 thf(zip_derived_cl247, plain,
% 1.44/0.96 (( (equalish @ e_2 @ e_3))
% 1.44/0.96 <= (( (product @ e_1 @ e_2 @ e_4)) & ( (product @ e_1 @ e_3 @ e_4)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl231, zip_derived_cl105])).
% 1.44/0.96 thf(zip_derived_cl8, plain, (~ (equalish @ e_2 @ e_3)),
% 1.44/0.96 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 1.44/0.96 thf('16', plain,
% 1.44/0.96 (~ ( (product @ e_1 @ e_3 @ e_4)) | ~ ( (product @ e_1 @ e_2 @ e_4))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl247, zip_derived_cl8])).
% 1.44/0.96 thf('17', plain,
% 1.44/0.96 (( (product @ e_2 @ e_3 @ e_4)) | ( (product @ e_2 @ e_3 @ e_1)) |
% 1.44/0.96 ( (product @ e_2 @ e_3 @ e_3)) | ( (product @ e_2 @ e_3 @ e_2))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl121])).
% 1.44/0.96 thf('18', plain,
% 1.44/0.96 (( (product @ e_1 @ e_3 @ e_2)) | ( (product @ e_1 @ e_3 @ e_4)) |
% 1.44/0.96 ( (product @ e_1 @ e_3 @ e_3)) | ( (product @ e_1 @ e_3 @ e_1))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl92])).
% 1.44/0.96 thf(zip_derived_cl407, plain,
% 1.44/0.96 (( (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_2 @ e_1 @ e_3)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl119])).
% 1.44/0.96 thf(zip_derived_cl233, plain,
% 1.44/0.96 (( (product @ e_1 @ e_3 @ e_2)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl92])).
% 1.44/0.96 thf(zip_derived_cl48, plain,
% 1.44/0.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.44/0.96 (~ (product @ X2 @ X1 @ X0)
% 1.44/0.96 | ~ (product @ X0 @ X2 @ X1)
% 1.44/0.96 | (equalish @ X2 @ X0))),
% 1.44/0.96 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl20])).
% 1.44/0.96 thf(zip_derived_cl324, plain,
% 1.44/0.96 (((~ (product @ e_2 @ e_1 @ e_3) | (equalish @ e_1 @ e_2)))
% 1.44/0.96 <= (( (product @ e_1 @ e_3 @ e_2)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl233, zip_derived_cl48])).
% 1.44/0.96 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_2)),
% 1.44/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.44/0.96 thf(zip_derived_cl331, plain,
% 1.44/0.96 ((~ (product @ e_2 @ e_1 @ e_3)) <= (( (product @ e_1 @ e_3 @ e_2)))),
% 1.44/0.96 inference('demod', [status(thm)], [zip_derived_cl324, zip_derived_cl4])).
% 1.44/0.96 thf('19', plain,
% 1.44/0.96 (~ ( (product @ e_2 @ e_1 @ e_3)) | ~ ( (product @ e_1 @ e_3 @ e_2))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl407, zip_derived_cl331])).
% 1.44/0.96 thf('20', plain,
% 1.44/0.96 (( (product @ e_2 @ e_1 @ e_4)) | ( (product @ e_2 @ e_1 @ e_3)) |
% 1.44/0.96 ( (product @ e_2 @ e_1 @ e_2)) | ( (product @ e_2 @ e_1 @ e_1))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl119])).
% 1.44/0.96 thf('21', plain, (( (product @ e_2 @ e_1 @ e_4))),
% 1.44/0.96 inference('sat_resolution*', [status(thm)],
% 1.44/0.96 ['2', '3', '4', '5', '1', '0', '8', '9', '10', '6', '11',
% 1.44/0.96 '12', '13', '14', '15', '16', '17', '18', '19', '20'])).
% 1.44/0.96 thf(zip_derived_cl1045, plain, ( (product @ e_2 @ e_1 @ e_4)),
% 1.44/0.96 inference('simpl_trail', [status(thm)], [zip_derived_cl406, '21'])).
% 1.44/0.96 thf(zip_derived_cl446, plain,
% 1.44/0.96 (( (product @ e_2 @ e_3 @ e_4)) <= (( (product @ e_2 @ e_3 @ e_4)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl121])).
% 1.44/0.96 thf(zip_derived_cl18, plain,
% 1.44/0.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.44/0.96 (~ (product @ X0 @ X1 @ X2)
% 1.44/0.96 | ~ (product @ X0 @ X3 @ X2)
% 1.44/0.96 | (equalish @ X1 @ X3))),
% 1.44/0.96 inference('cnf', [status(esa)], [product_right_cancellation])).
% 1.44/0.96 thf(zip_derived_cl451, plain,
% 1.44/0.96 ((![X0 : $i]: (~ (product @ e_2 @ X0 @ e_4) | (equalish @ e_3 @ X0)))
% 1.44/0.96 <= (( (product @ e_2 @ e_3 @ e_4)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl446, zip_derived_cl18])).
% 1.44/0.96 thf(zip_derived_cl1186, plain,
% 1.44/0.96 (( (equalish @ e_3 @ e_1)) <= (( (product @ e_2 @ e_3 @ e_4)))),
% 1.44/0.96 inference('s_sup-', [status(thm)],
% 1.44/0.96 [zip_derived_cl1045, zip_derived_cl451])).
% 1.44/0.96 thf(zip_derived_cl10, plain, (~ (equalish @ e_3 @ e_1)),
% 1.44/0.96 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 1.44/0.96 thf('22', plain, (~ ( (product @ e_2 @ e_3 @ e_4))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1186, zip_derived_cl10])).
% 1.44/0.96 thf('23', plain,
% 1.44/0.96 (( (product @ e_2 @ e_3 @ e_1)) | ( (product @ e_2 @ e_3 @ e_4)) |
% 1.44/0.96 ( (product @ e_2 @ e_3 @ e_3)) | ( (product @ e_2 @ e_3 @ e_2))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl121])).
% 1.44/0.96 thf('24', plain, (( (product @ e_2 @ e_3 @ e_1))),
% 1.44/0.96 inference('sat_resolution*', [status(thm)], ['0', '1', '22', '23'])).
% 1.44/0.96 thf(zip_derived_cl1193, plain, ( (product @ e_2 @ e_3 @ e_1)),
% 1.44/0.96 inference('simpl_trail', [status(thm)], [zip_derived_cl533, '24'])).
% 1.44/0.96 thf(zip_derived_cl11, plain, (~ (equalish @ e_3 @ e_2)),
% 1.44/0.96 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 1.44/0.96 thf(zip_derived_cl1245, plain,
% 1.44/0.96 (($false) <= (( (product @ e_3 @ e_1 @ e_2)))),
% 1.44/0.96 inference('demod', [status(thm)],
% 1.44/0.96 [zip_derived_cl1240, zip_derived_cl1193, zip_derived_cl11])).
% 1.44/0.96 thf(zip_derived_cl23, plain,
% 1.44/0.96 (![X0 : $i]:
% 1.44/0.96 (~ (group_element @ X0)
% 1.44/0.96 | (product @ e_1 @ X0 @ e_1)
% 1.44/0.96 | (product @ e_1 @ X0 @ e_2)
% 1.44/0.96 | (product @ e_1 @ X0 @ e_3)
% 1.44/0.96 | (product @ e_1 @ X0 @ e_4))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl16])).
% 1.44/0.96 thf(zip_derived_cl3, plain, ( (group_element @ e_4)),
% 1.44/0.96 inference('cnf', [status(esa)], [element_4])).
% 1.44/0.96 thf(zip_derived_cl93, plain,
% 1.44/0.96 (( (product @ e_1 @ e_4 @ e_4)
% 1.44/0.96 | (product @ e_1 @ e_4 @ e_3)
% 1.44/0.96 | (product @ e_1 @ e_4 @ e_2)
% 1.44/0.96 | (product @ e_1 @ e_4 @ e_1))),
% 1.44/0.96 inference('s_sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl3])).
% 1.44/0.96 thf(zip_derived_cl262, plain,
% 1.44/0.96 (( (product @ e_1 @ e_4 @ e_1)) <= (( (product @ e_1 @ e_4 @ e_1)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl93])).
% 1.44/0.96 thf(zip_derived_cl32, plain,
% 1.44/0.96 (![X0 : $i, X1 : $i]:
% 1.44/0.96 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 1.44/0.96 thf(zip_derived_cl435, plain,
% 1.44/0.96 (( (equalish @ e_1 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_1)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl262, zip_derived_cl32])).
% 1.44/0.96 thf(e_1_is_not_e_4, axiom, (~( equalish @ e_1 @ e_4 ))).
% 1.44/0.96 thf(zip_derived_cl6, plain, (~ (equalish @ e_1 @ e_4)),
% 1.44/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_4])).
% 1.44/0.96 thf('25', plain, (~ ( (product @ e_1 @ e_4 @ e_1))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl435, zip_derived_cl6])).
% 1.44/0.96 thf(zip_derived_cl259, plain,
% 1.44/0.96 (( (product @ e_1 @ e_4 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_4)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl93])).
% 1.44/0.96 thf(zip_derived_cl37, plain,
% 1.44/0.96 (![X0 : $i, X1 : $i]:
% 1.44/0.96 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 1.44/0.96 thf(zip_derived_cl272, plain,
% 1.44/0.96 (( (equalish @ e_4 @ e_1)) <= (( (product @ e_1 @ e_4 @ e_4)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl259, zip_derived_cl37])).
% 1.44/0.96 thf(e_4_is_not_e_1, axiom, (~( equalish @ e_4 @ e_1 ))).
% 1.44/0.96 thf(zip_derived_cl13, plain, (~ (equalish @ e_4 @ e_1)),
% 1.44/0.96 inference('cnf', [status(esa)], [e_4_is_not_e_1])).
% 1.44/0.96 thf('26', plain, (~ ( (product @ e_1 @ e_4 @ e_4))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl272, zip_derived_cl13])).
% 1.44/0.96 thf('27', plain,
% 1.44/0.96 (~ ( (product @ e_2 @ e_3 @ e_4)) | ~ ( (product @ e_3 @ e_4 @ e_2))),
% 1.44/0.96 inference('demod', [status(thm)], [zip_derived_cl882, zip_derived_cl20])).
% 1.44/0.96 thf(zip_derived_cl406, plain,
% 1.44/0.96 (( (product @ e_2 @ e_1 @ e_4)) <= (( (product @ e_2 @ e_1 @ e_4)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl119])).
% 1.44/0.96 thf(zip_derived_cl261, plain,
% 1.44/0.96 (( (product @ e_1 @ e_4 @ e_2)) <= (( (product @ e_1 @ e_4 @ e_2)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl93])).
% 1.44/0.96 thf(zip_derived_cl48, plain,
% 1.44/0.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.44/0.96 (~ (product @ X2 @ X1 @ X0)
% 1.44/0.96 | ~ (product @ X0 @ X2 @ X1)
% 1.44/0.96 | (equalish @ X2 @ X0))),
% 1.44/0.96 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl20])).
% 1.44/0.96 thf(zip_derived_cl393, plain,
% 1.44/0.96 (((~ (product @ e_2 @ e_1 @ e_4) | (equalish @ e_1 @ e_2)))
% 1.44/0.96 <= (( (product @ e_1 @ e_4 @ e_2)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl261, zip_derived_cl48])).
% 1.44/0.96 thf(zip_derived_cl4, plain, (~ (equalish @ e_1 @ e_2)),
% 1.44/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_2])).
% 1.44/0.96 thf(zip_derived_cl400, plain,
% 1.44/0.96 ((~ (product @ e_2 @ e_1 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_2)))),
% 1.44/0.96 inference('demod', [status(thm)], [zip_derived_cl393, zip_derived_cl4])).
% 1.44/0.96 thf('28', plain,
% 1.44/0.96 (~ ( (product @ e_1 @ e_4 @ e_2)) | ~ ( (product @ e_2 @ e_1 @ e_4))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl406, zip_derived_cl400])).
% 1.44/0.96 thf('29', plain,
% 1.44/0.96 (( (product @ e_1 @ e_4 @ e_3)) | ( (product @ e_1 @ e_4 @ e_2)) |
% 1.44/0.96 ( (product @ e_1 @ e_4 @ e_4)) | ( (product @ e_1 @ e_4 @ e_1))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl93])).
% 1.44/0.96 thf(zip_derived_cl675, plain,
% 1.44/0.96 (( (product @ e_3 @ e_1 @ e_4)) <= (( (product @ e_3 @ e_1 @ e_4)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl162])).
% 1.44/0.96 thf(zip_derived_cl3, plain, ( (group_element @ e_4)),
% 1.44/0.96 inference('cnf', [status(esa)], [element_4])).
% 1.44/0.96 thf(zip_derived_cl23, plain,
% 1.44/0.96 (![X0 : $i]:
% 1.44/0.96 (~ (group_element @ X0)
% 1.44/0.96 | (product @ e_1 @ X0 @ e_1)
% 1.44/0.96 | (product @ e_1 @ X0 @ e_2)
% 1.44/0.96 | (product @ e_1 @ X0 @ e_3)
% 1.44/0.96 | (product @ e_1 @ X0 @ e_4))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl16])).
% 1.44/0.96 thf(zip_derived_cl97, plain,
% 1.44/0.96 (( (product @ e_1 @ e_4 @ e_1)
% 1.44/0.96 | (product @ e_1 @ e_4 @ e_2)
% 1.44/0.96 | (product @ e_1 @ e_4 @ e_3)
% 1.44/0.96 | (product @ e_1 @ e_4 @ e_4))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl23])).
% 1.44/0.96 thf(zip_derived_cl365, plain,
% 1.44/0.96 (( (product @ e_1 @ e_4 @ e_3)) <= (( (product @ e_1 @ e_4 @ e_3)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl97])).
% 1.44/0.96 thf(zip_derived_cl48, plain,
% 1.44/0.96 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.44/0.96 (~ (product @ X2 @ X1 @ X0)
% 1.44/0.96 | ~ (product @ X0 @ X2 @ X1)
% 1.44/0.96 | (equalish @ X2 @ X0))),
% 1.44/0.96 inference('demod', [status(thm)], [zip_derived_cl45, zip_derived_cl20])).
% 1.44/0.96 thf(zip_derived_cl374, plain,
% 1.44/0.96 (((~ (product @ e_3 @ e_1 @ e_4) | (equalish @ e_1 @ e_3)))
% 1.44/0.96 <= (( (product @ e_1 @ e_4 @ e_3)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl365, zip_derived_cl48])).
% 1.44/0.96 thf(zip_derived_cl5, plain, (~ (equalish @ e_1 @ e_3)),
% 1.44/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 1.44/0.96 thf(zip_derived_cl381, plain,
% 1.44/0.96 ((~ (product @ e_3 @ e_1 @ e_4)) <= (( (product @ e_1 @ e_4 @ e_3)))),
% 1.44/0.96 inference('demod', [status(thm)], [zip_derived_cl374, zip_derived_cl5])).
% 1.44/0.96 thf('30', plain,
% 1.44/0.96 (~ ( (product @ e_3 @ e_1 @ e_4)) | ~ ( (product @ e_1 @ e_4 @ e_3))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl675, zip_derived_cl381])).
% 1.44/0.96 thf(zip_derived_cl0, plain, ( (group_element @ e_1)),
% 1.44/0.96 inference('cnf', [status(esa)], [element_1])).
% 1.44/0.96 thf(zip_derived_cl25, plain,
% 1.44/0.96 (![X0 : $i]:
% 1.44/0.96 (~ (group_element @ X0)
% 1.44/0.96 | (product @ e_3 @ X0 @ e_1)
% 1.44/0.96 | (product @ e_3 @ X0 @ e_2)
% 1.44/0.96 | (product @ e_3 @ X0 @ e_3)
% 1.44/0.96 | (product @ e_3 @ X0 @ e_4))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl16])).
% 1.44/0.96 thf(zip_derived_cl166, plain,
% 1.44/0.96 (( (product @ e_3 @ e_1 @ e_1)
% 1.44/0.96 | (product @ e_3 @ e_1 @ e_2)
% 1.44/0.96 | (product @ e_3 @ e_1 @ e_3)
% 1.44/0.96 | (product @ e_3 @ e_1 @ e_4))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl25])).
% 1.44/0.96 thf(zip_derived_cl757, plain,
% 1.44/0.96 (( (product @ e_3 @ e_1 @ e_3)) <= (( (product @ e_3 @ e_1 @ e_3)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl166])).
% 1.44/0.96 thf(zip_derived_cl32, plain,
% 1.44/0.96 (![X0 : $i, X1 : $i]:
% 1.44/0.96 (~ (product @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl18])).
% 1.44/0.96 thf(zip_derived_cl769, plain,
% 1.44/0.96 (( (equalish @ e_3 @ e_1)) <= (( (product @ e_3 @ e_1 @ e_3)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl757, zip_derived_cl32])).
% 1.44/0.96 thf(zip_derived_cl10, plain, (~ (equalish @ e_3 @ e_1)),
% 1.44/0.96 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 1.44/0.96 thf('31', plain, (~ ( (product @ e_3 @ e_1 @ e_3))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl769, zip_derived_cl10])).
% 1.44/0.96 thf(zip_derived_cl677, plain,
% 1.44/0.96 (( (product @ e_3 @ e_1 @ e_1)) <= (( (product @ e_3 @ e_1 @ e_1)))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl162])).
% 1.44/0.96 thf(zip_derived_cl37, plain,
% 1.44/0.96 (![X0 : $i, X1 : $i]:
% 1.44/0.96 (~ (product @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl19])).
% 1.44/0.96 thf(zip_derived_cl1224, plain,
% 1.44/0.96 (( (equalish @ e_1 @ e_3)) <= (( (product @ e_3 @ e_1 @ e_1)))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl677, zip_derived_cl37])).
% 1.44/0.96 thf(zip_derived_cl5, plain, (~ (equalish @ e_1 @ e_3)),
% 1.44/0.96 inference('cnf', [status(esa)], [e_1_is_not_e_3])).
% 1.44/0.96 thf('32', plain, (~ ( (product @ e_3 @ e_1 @ e_1))),
% 1.44/0.96 inference('s_sup-', [status(thm)], [zip_derived_cl1224, zip_derived_cl5])).
% 1.44/0.96 thf('33', plain,
% 1.44/0.96 (( (product @ e_3 @ e_1 @ e_2)) | ( (product @ e_3 @ e_1 @ e_1)) |
% 1.44/0.96 ( (product @ e_3 @ e_1 @ e_3)) | ( (product @ e_3 @ e_1 @ e_4))),
% 1.44/0.96 inference('split', [status(esa)], [zip_derived_cl162])).
% 1.44/0.96 thf('34', plain, (( (product @ e_3 @ e_1 @ e_2))),
% 1.44/0.96 inference('sat_resolution*', [status(thm)],
% 1.44/0.96 ['25', '26', '2', '3', '4', '5', '1', '0', '27', '9', '10',
% 1.44/0.96 '6', '11', '12', '13', '14', '15', '16', '23', '18', '19',
% 1.44/0.96 '20', '28', '29', '30', '31', '32', '33'])).
% 1.44/0.96 thf(zip_derived_cl1249, plain, ($false),
% 1.44/0.96 inference('simpl_trail', [status(thm)], [zip_derived_cl1245, '34'])).
% 1.44/0.96
% 1.44/0.96 % SZS output end Refutation
% 1.44/0.96
% 1.44/0.96
% 1.44/0.96 % Terminating...
% 1.82/1.05 % Runner terminated.
% 1.93/1.07 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------