TSTP Solution File: GRP123-7.003 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP123-7.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.JJdORhTGWf true
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:50:03 EDT 2023
% Result : Unsatisfiable 0.19s 0.75s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP123-7.003 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.JJdORhTGWf true
% 0.12/0.32 % Computer : n025.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Aug 28 21:39:10 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.12/0.32 % Running portfolio for 300 s
% 0.12/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.32 % Number of cores: 8
% 0.12/0.33 % Python version: Python 3.6.8
% 0.12/0.33 % Running in FO mode
% 0.19/0.63 % Total configuration time : 435
% 0.19/0.63 % Estimated wc time : 1092
% 0.19/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.19/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.19/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.19/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.19/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.19/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.19/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.19/0.75 % Solved by fo/fo6_bce.sh.
% 0.19/0.75 % BCE start: 26
% 0.19/0.75 % BCE eliminated: 6
% 0.19/0.75 % PE start: 20
% 0.19/0.75 logic: neq
% 0.19/0.75 % PE eliminated: 0
% 0.19/0.75 % done 90 iterations in 0.059s
% 0.19/0.75 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.19/0.75 % SZS output start Refutation
% 0.19/0.75 thf(e_3_type, type, e_3: $i).
% 0.19/0.75 thf(e_2_type, type, e_2: $i).
% 0.19/0.75 thf(e_1_type, type, e_1: $i).
% 0.19/0.75 thf(product1_type, type, product1: $i > $i > $i > $o).
% 0.19/0.75 thf(group_element_type, type, group_element: $i > $o).
% 0.19/0.75 thf(product2_type, type, product2: $i > $i > $i > $o).
% 0.19/0.75 thf(equalish_type, type, equalish: $i > $i > $o).
% 0.19/0.75 thf(product1_total_function1, axiom,
% 0.19/0.75 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 0.19/0.75 ( product1 @ X @ Y @ e_1 ) | ( product1 @ X @ Y @ e_2 ) |
% 0.19/0.75 ( product1 @ X @ Y @ e_3 ))).
% 0.19/0.75 thf(zip_derived_cl15, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i]:
% 0.19/0.75 (~ (group_element @ X0)
% 0.19/0.75 | ~ (group_element @ X1)
% 0.19/0.75 | (product1 @ X0 @ X1 @ e_1)
% 0.19/0.75 | (product1 @ X0 @ X1 @ e_2)
% 0.19/0.75 | (product1 @ X0 @ X1 @ e_3))),
% 0.19/0.75 inference('cnf', [status(esa)], [product1_total_function1])).
% 0.19/0.75 thf(zip_derived_cl15, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i]:
% 0.19/0.75 (~ (group_element @ X0)
% 0.19/0.75 | ~ (group_element @ X1)
% 0.19/0.75 | (product1 @ X0 @ X1 @ e_1)
% 0.19/0.75 | (product1 @ X0 @ X1 @ e_2)
% 0.19/0.75 | (product1 @ X0 @ X1 @ e_3))),
% 0.19/0.75 inference('cnf', [status(esa)], [product1_total_function1])).
% 0.19/0.75 thf(qg1a, conjecture,
% 0.19/0.75 (~( ( product2 @ Z2 @ X @ Y ) | ( ~( product1 @ Z1 @ Y @ Z2 ) ) |
% 0.19/0.75 ( ~( product1 @ X @ Y @ Z1 ) ) ))).
% 0.19/0.75 thf(zf_stmt_0, negated_conjecture,
% 0.19/0.75 (( product2 @ Z2 @ X @ Y ) | ( ~( product1 @ Z1 @ Y @ Z2 ) ) |
% 0.19/0.75 ( ~( product1 @ X @ Y @ Z1 ) )),
% 0.19/0.75 inference('cnf.neg', [status(esa)], [qg1a])).
% 0.19/0.75 thf(zip_derived_cl25, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.19/0.75 ( (product2 @ X0 @ X1 @ X2)
% 0.19/0.75 | ~ (product1 @ X3 @ X2 @ X0)
% 0.19/0.75 | ~ (product1 @ X1 @ X2 @ X3))),
% 0.19/0.75 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.19/0.75 thf(zip_derived_cl87, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.19/0.75 ( (product1 @ X1 @ X0 @ e_2)
% 0.19/0.75 | (product1 @ X1 @ X0 @ e_1)
% 0.19/0.75 | ~ (group_element @ X0)
% 0.19/0.75 | ~ (group_element @ X1)
% 0.19/0.75 | (product2 @ e_3 @ X2 @ X0)
% 0.19/0.75 | ~ (product1 @ X2 @ X0 @ X1))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl25])).
% 0.19/0.75 thf(zip_derived_cl131, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i]:
% 0.19/0.75 ( (product1 @ X1 @ X0 @ e_2)
% 0.19/0.75 | (product1 @ X1 @ X0 @ e_1)
% 0.19/0.75 | ~ (group_element @ X0)
% 0.19/0.75 | ~ (group_element @ X1)
% 0.19/0.75 | (product1 @ e_3 @ X0 @ e_2)
% 0.19/0.75 | (product1 @ e_3 @ X0 @ e_1)
% 0.19/0.75 | ~ (group_element @ X0)
% 0.19/0.75 | ~ (group_element @ e_3)
% 0.19/0.75 | (product2 @ e_3 @ X1 @ X0))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl87])).
% 0.19/0.75 thf(element_3, axiom, (group_element @ e_3)).
% 0.19/0.75 thf(zip_derived_cl8, plain, ( (group_element @ e_3)),
% 0.19/0.75 inference('cnf', [status(esa)], [element_3])).
% 0.19/0.75 thf(zip_derived_cl133, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i]:
% 0.19/0.75 ( (product1 @ X1 @ X0 @ e_2)
% 0.19/0.75 | (product1 @ X1 @ X0 @ e_1)
% 0.19/0.75 | ~ (group_element @ X0)
% 0.19/0.75 | ~ (group_element @ X1)
% 0.19/0.75 | (product1 @ e_3 @ X0 @ e_2)
% 0.19/0.75 | (product1 @ e_3 @ X0 @ e_1)
% 0.19/0.75 | ~ (group_element @ X0)
% 0.19/0.75 | (product2 @ e_3 @ X1 @ X0))),
% 0.19/0.75 inference('demod', [status(thm)], [zip_derived_cl131, zip_derived_cl8])).
% 0.19/0.75 thf(zip_derived_cl134, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i]:
% 0.19/0.75 ( (product2 @ e_3 @ X1 @ X0)
% 0.19/0.75 | (product1 @ e_3 @ X0 @ e_1)
% 0.19/0.75 | (product1 @ e_3 @ X0 @ e_2)
% 0.19/0.75 | ~ (group_element @ X1)
% 0.19/0.75 | ~ (group_element @ X0)
% 0.19/0.75 | (product1 @ X1 @ X0 @ e_1)
% 0.19/0.75 | (product1 @ X1 @ X0 @ e_2))),
% 0.19/0.75 inference('simplify', [status(thm)], [zip_derived_cl133])).
% 0.19/0.75 thf(product2_total_function1, axiom,
% 0.19/0.75 (( ~( group_element @ X ) ) | ( ~( group_element @ Y ) ) |
% 0.19/0.75 ( product2 @ X @ Y @ e_1 ) | ( product2 @ X @ Y @ e_2 ) |
% 0.19/0.75 ( product2 @ X @ Y @ e_3 ))).
% 0.19/0.75 thf(zip_derived_cl20, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i]:
% 0.19/0.75 (~ (group_element @ X0)
% 0.19/0.75 | ~ (group_element @ X1)
% 0.19/0.75 | (product2 @ X0 @ X1 @ e_1)
% 0.19/0.75 | (product2 @ X0 @ X1 @ e_2)
% 0.19/0.75 | (product2 @ X0 @ X1 @ e_3))),
% 0.19/0.75 inference('cnf', [status(esa)], [product2_total_function1])).
% 0.19/0.75 thf(product2_idempotence, axiom, (product2 @ X @ X @ X)).
% 0.19/0.75 thf(zip_derived_cl24, plain, (![X0 : $i]: (product2 @ X0 @ X0 @ X0)),
% 0.19/0.75 inference('cnf', [status(esa)], [product2_idempotence])).
% 0.19/0.75 thf(product2_left_cancellation, axiom,
% 0.19/0.75 (( ~( product2 @ W @ Y @ X ) ) | ( ~( product2 @ Z @ Y @ X ) ) |
% 0.19/0.75 ( equalish @ W @ Z ))).
% 0.19/0.75 thf(zip_derived_cl23, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.19/0.75 (~ (product2 @ X0 @ X1 @ X2)
% 0.19/0.75 | ~ (product2 @ X3 @ X1 @ X2)
% 0.19/0.75 | (equalish @ X0 @ X3))),
% 0.19/0.75 inference('cnf', [status(esa)], [product2_left_cancellation])).
% 0.19/0.75 thf(zip_derived_cl114, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i]:
% 0.19/0.75 (~ (product2 @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl23])).
% 0.19/0.75 thf(zip_derived_cl120, plain,
% 0.19/0.75 (![X0 : $i]:
% 0.19/0.75 ( (product2 @ X0 @ e_3 @ e_2)
% 0.19/0.75 | (product2 @ X0 @ e_3 @ e_1)
% 0.19/0.75 | ~ (group_element @ e_3)
% 0.19/0.75 | ~ (group_element @ X0)
% 0.19/0.75 | (equalish @ e_3 @ X0))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl114])).
% 0.19/0.75 thf(zip_derived_cl8, plain, ( (group_element @ e_3)),
% 0.19/0.75 inference('cnf', [status(esa)], [element_3])).
% 0.19/0.75 thf(zip_derived_cl122, plain,
% 0.19/0.75 (![X0 : $i]:
% 0.19/0.75 ( (product2 @ X0 @ e_3 @ e_2)
% 0.19/0.75 | (product2 @ X0 @ e_3 @ e_1)
% 0.19/0.75 | ~ (group_element @ X0)
% 0.19/0.75 | (equalish @ e_3 @ X0))),
% 0.19/0.75 inference('demod', [status(thm)], [zip_derived_cl120, zip_derived_cl8])).
% 0.19/0.75 thf(zip_derived_cl24, plain, (![X0 : $i]: (product2 @ X0 @ X0 @ X0)),
% 0.19/0.75 inference('cnf', [status(esa)], [product2_idempotence])).
% 0.19/0.75 thf(product2_right_cancellation, axiom,
% 0.19/0.75 (( ~( product2 @ X @ W @ Y ) ) | ( ~( product2 @ X @ Z @ Y ) ) |
% 0.19/0.75 ( equalish @ W @ Z ))).
% 0.19/0.75 thf(zip_derived_cl22, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.19/0.75 (~ (product2 @ X0 @ X1 @ X2)
% 0.19/0.75 | ~ (product2 @ X0 @ X3 @ X2)
% 0.19/0.75 | (equalish @ X1 @ X3))),
% 0.19/0.75 inference('cnf', [status(esa)], [product2_right_cancellation])).
% 0.19/0.75 thf(zip_derived_cl104, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i]:
% 0.19/0.75 (~ (product2 @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 0.19/0.75 thf(zip_derived_cl156, plain,
% 0.19/0.75 (( (equalish @ e_3 @ e_2)
% 0.19/0.75 | ~ (group_element @ e_2)
% 0.19/0.75 | (product2 @ e_2 @ e_3 @ e_1)
% 0.19/0.75 | (equalish @ e_2 @ e_3))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl104])).
% 0.19/0.75 thf(e_3_is_not_e_2, axiom, (~( equalish @ e_3 @ e_2 ))).
% 0.19/0.75 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_2)),
% 0.19/0.75 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 0.19/0.75 thf(element_2, axiom, (group_element @ e_2)).
% 0.19/0.75 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.19/0.75 inference('cnf', [status(esa)], [element_2])).
% 0.19/0.75 thf(e_2_is_not_e_3, axiom, (~( equalish @ e_2 @ e_3 ))).
% 0.19/0.75 thf(zip_derived_cl12, plain, (~ (equalish @ e_2 @ e_3)),
% 0.19/0.75 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.19/0.75 thf(zip_derived_cl158, plain, ( (product2 @ e_2 @ e_3 @ e_1)),
% 0.19/0.75 inference('demod', [status(thm)],
% 0.19/0.75 [zip_derived_cl156, zip_derived_cl14, zip_derived_cl7,
% 0.19/0.75 zip_derived_cl12])).
% 0.19/0.75 thf(zip_derived_cl23, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.19/0.75 (~ (product2 @ X0 @ X1 @ X2)
% 0.19/0.75 | ~ (product2 @ X3 @ X1 @ X2)
% 0.19/0.75 | (equalish @ X0 @ X3))),
% 0.19/0.75 inference('cnf', [status(esa)], [product2_left_cancellation])).
% 0.19/0.75 thf(zip_derived_cl174, plain,
% 0.19/0.75 (![X0 : $i]: (~ (product2 @ X0 @ e_3 @ e_1) | (equalish @ e_2 @ X0))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl158, zip_derived_cl23])).
% 0.19/0.75 thf(zip_derived_cl218, plain,
% 0.19/0.75 (( (product1 @ e_3 @ e_1 @ e_2)
% 0.19/0.75 | (product1 @ e_3 @ e_1 @ e_1)
% 0.19/0.75 | ~ (group_element @ e_1)
% 0.19/0.75 | ~ (group_element @ e_3)
% 0.19/0.75 | (product1 @ e_3 @ e_1 @ e_2)
% 0.19/0.75 | (product1 @ e_3 @ e_1 @ e_1)
% 0.19/0.75 | (equalish @ e_2 @ e_3))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl174])).
% 0.19/0.75 thf(element_1, axiom, (group_element @ e_1)).
% 0.19/0.75 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.19/0.75 inference('cnf', [status(esa)], [element_1])).
% 0.19/0.75 thf(zip_derived_cl8, plain, ( (group_element @ e_3)),
% 0.19/0.75 inference('cnf', [status(esa)], [element_3])).
% 0.19/0.75 thf(zip_derived_cl12, plain, (~ (equalish @ e_2 @ e_3)),
% 0.19/0.75 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.19/0.75 thf(zip_derived_cl220, plain,
% 0.19/0.75 (( (product1 @ e_3 @ e_1 @ e_2)
% 0.19/0.75 | (product1 @ e_3 @ e_1 @ e_1)
% 0.19/0.75 | (product1 @ e_3 @ e_1 @ e_2)
% 0.19/0.75 | (product1 @ e_3 @ e_1 @ e_1))),
% 0.19/0.75 inference('demod', [status(thm)],
% 0.19/0.75 [zip_derived_cl218, zip_derived_cl6, zip_derived_cl8,
% 0.19/0.75 zip_derived_cl12])).
% 0.19/0.75 thf(zip_derived_cl221, plain,
% 0.19/0.75 (( (product1 @ e_3 @ e_1 @ e_1) | (product1 @ e_3 @ e_1 @ e_2))),
% 0.19/0.75 inference('simplify', [status(thm)], [zip_derived_cl220])).
% 0.19/0.75 thf(product1_idempotence, axiom, (product1 @ X @ X @ X)).
% 0.19/0.75 thf(zip_derived_cl19, plain, (![X0 : $i]: (product1 @ X0 @ X0 @ X0)),
% 0.19/0.75 inference('cnf', [status(esa)], [product1_idempotence])).
% 0.19/0.75 thf(zip_derived_cl25, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.19/0.75 ( (product2 @ X0 @ X1 @ X2)
% 0.19/0.75 | ~ (product1 @ X3 @ X2 @ X0)
% 0.19/0.75 | ~ (product1 @ X1 @ X2 @ X3))),
% 0.19/0.75 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.19/0.75 thf(zip_derived_cl86, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i]:
% 0.19/0.75 ( (product2 @ X0 @ X1 @ X0) | ~ (product1 @ X1 @ X0 @ X0))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl25])).
% 0.19/0.75 thf(zip_derived_cl174, plain,
% 0.19/0.75 (![X0 : $i]: (~ (product2 @ X0 @ e_3 @ e_1) | (equalish @ e_2 @ X0))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl158, zip_derived_cl23])).
% 0.19/0.75 thf(zip_derived_cl216, plain,
% 0.19/0.75 ((~ (product1 @ e_3 @ e_1 @ e_1) | (equalish @ e_2 @ e_1))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl86, zip_derived_cl174])).
% 0.19/0.75 thf(e_2_is_not_e_1, axiom, (~( equalish @ e_2 @ e_1 ))).
% 0.19/0.75 thf(zip_derived_cl11, plain, (~ (equalish @ e_2 @ e_1)),
% 0.19/0.75 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.19/0.75 thf(zip_derived_cl219, plain, (~ (product1 @ e_3 @ e_1 @ e_1)),
% 0.19/0.75 inference('demod', [status(thm)], [zip_derived_cl216, zip_derived_cl11])).
% 0.19/0.75 thf(zip_derived_cl258, plain, ( (product1 @ e_3 @ e_1 @ e_2)),
% 0.19/0.75 inference('demod', [status(thm)], [zip_derived_cl221, zip_derived_cl219])).
% 0.19/0.75 thf(zip_derived_cl87, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.19/0.75 ( (product1 @ X1 @ X0 @ e_2)
% 0.19/0.75 | (product1 @ X1 @ X0 @ e_1)
% 0.19/0.75 | ~ (group_element @ X0)
% 0.19/0.75 | ~ (group_element @ X1)
% 0.19/0.75 | (product2 @ e_3 @ X2 @ X0)
% 0.19/0.75 | ~ (product1 @ X2 @ X0 @ X1))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl25])).
% 0.19/0.75 thf(zip_derived_cl263, plain,
% 0.19/0.75 (( (product1 @ e_2 @ e_1 @ e_2)
% 0.19/0.75 | (product1 @ e_2 @ e_1 @ e_1)
% 0.19/0.75 | ~ (group_element @ e_1)
% 0.19/0.75 | ~ (group_element @ e_2)
% 0.19/0.75 | (product2 @ e_3 @ e_3 @ e_1))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl258, zip_derived_cl87])).
% 0.19/0.75 thf(zip_derived_cl86, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i]:
% 0.19/0.75 ( (product2 @ X0 @ X1 @ X0) | ~ (product1 @ X1 @ X0 @ X0))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl25])).
% 0.19/0.75 thf(zip_derived_cl20, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i]:
% 0.19/0.75 (~ (group_element @ X0)
% 0.19/0.75 | ~ (group_element @ X1)
% 0.19/0.75 | (product2 @ X0 @ X1 @ e_1)
% 0.19/0.75 | (product2 @ X0 @ X1 @ e_2)
% 0.19/0.75 | (product2 @ X0 @ X1 @ e_3))),
% 0.19/0.75 inference('cnf', [status(esa)], [product2_total_function1])).
% 0.19/0.75 thf(zip_derived_cl104, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i]:
% 0.19/0.75 (~ (product2 @ X0 @ X1 @ X0) | (equalish @ X0 @ X1))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl22])).
% 0.19/0.75 thf(zip_derived_cl111, plain,
% 0.19/0.75 (![X0 : $i]:
% 0.19/0.75 ( (product2 @ e_3 @ X0 @ e_2)
% 0.19/0.75 | (product2 @ e_3 @ X0 @ e_1)
% 0.19/0.75 | ~ (group_element @ X0)
% 0.19/0.75 | ~ (group_element @ e_3)
% 0.19/0.75 | (equalish @ e_3 @ X0))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl20, zip_derived_cl104])).
% 0.19/0.75 thf(zip_derived_cl8, plain, ( (group_element @ e_3)),
% 0.19/0.75 inference('cnf', [status(esa)], [element_3])).
% 0.19/0.75 thf(zip_derived_cl112, plain,
% 0.19/0.75 (![X0 : $i]:
% 0.19/0.75 ( (product2 @ e_3 @ X0 @ e_2)
% 0.19/0.75 | (product2 @ e_3 @ X0 @ e_1)
% 0.19/0.75 | ~ (group_element @ X0)
% 0.19/0.75 | (equalish @ e_3 @ X0))),
% 0.19/0.75 inference('demod', [status(thm)], [zip_derived_cl111, zip_derived_cl8])).
% 0.19/0.75 thf(zip_derived_cl114, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i]:
% 0.19/0.75 (~ (product2 @ X1 @ X0 @ X0) | (equalish @ X0 @ X1))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl23])).
% 0.19/0.75 thf(zip_derived_cl127, plain,
% 0.19/0.75 (( (equalish @ e_3 @ e_2)
% 0.19/0.75 | ~ (group_element @ e_2)
% 0.19/0.75 | (product2 @ e_3 @ e_2 @ e_1)
% 0.19/0.75 | (equalish @ e_2 @ e_3))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl112, zip_derived_cl114])).
% 0.19/0.75 thf(zip_derived_cl14, plain, (~ (equalish @ e_3 @ e_2)),
% 0.19/0.75 inference('cnf', [status(esa)], [e_3_is_not_e_2])).
% 0.19/0.75 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.19/0.75 inference('cnf', [status(esa)], [element_2])).
% 0.19/0.75 thf(zip_derived_cl12, plain, (~ (equalish @ e_2 @ e_3)),
% 0.19/0.75 inference('cnf', [status(esa)], [e_2_is_not_e_3])).
% 0.19/0.75 thf(zip_derived_cl129, plain, ( (product2 @ e_3 @ e_2 @ e_1)),
% 0.19/0.75 inference('demod', [status(thm)],
% 0.19/0.75 [zip_derived_cl127, zip_derived_cl14, zip_derived_cl7,
% 0.19/0.75 zip_derived_cl12])).
% 0.19/0.75 thf(zip_derived_cl23, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.19/0.75 (~ (product2 @ X0 @ X1 @ X2)
% 0.19/0.75 | ~ (product2 @ X3 @ X1 @ X2)
% 0.19/0.75 | (equalish @ X0 @ X3))),
% 0.19/0.75 inference('cnf', [status(esa)], [product2_left_cancellation])).
% 0.19/0.75 thf(zip_derived_cl137, plain,
% 0.19/0.75 (![X0 : $i]: (~ (product2 @ X0 @ e_2 @ e_1) | (equalish @ e_3 @ X0))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl129, zip_derived_cl23])).
% 0.19/0.75 thf(zip_derived_cl149, plain,
% 0.19/0.75 ((~ (product1 @ e_2 @ e_1 @ e_1) | (equalish @ e_3 @ e_1))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl86, zip_derived_cl137])).
% 0.19/0.75 thf(e_3_is_not_e_1, axiom, (~( equalish @ e_3 @ e_1 ))).
% 0.19/0.75 thf(zip_derived_cl13, plain, (~ (equalish @ e_3 @ e_1)),
% 0.19/0.75 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.19/0.75 thf(zip_derived_cl151, plain, (~ (product1 @ e_2 @ e_1 @ e_1)),
% 0.19/0.75 inference('demod', [status(thm)], [zip_derived_cl149, zip_derived_cl13])).
% 0.19/0.75 thf(zip_derived_cl6, plain, ( (group_element @ e_1)),
% 0.19/0.75 inference('cnf', [status(esa)], [element_1])).
% 0.19/0.75 thf(zip_derived_cl7, plain, ( (group_element @ e_2)),
% 0.19/0.75 inference('cnf', [status(esa)], [element_2])).
% 0.19/0.75 thf(zip_derived_cl264, plain,
% 0.19/0.75 (( (product1 @ e_2 @ e_1 @ e_2) | (product2 @ e_3 @ e_3 @ e_1))),
% 0.19/0.75 inference('demod', [status(thm)],
% 0.19/0.75 [zip_derived_cl263, zip_derived_cl151, zip_derived_cl6,
% 0.19/0.75 zip_derived_cl7])).
% 0.19/0.75 thf(zip_derived_cl24, plain, (![X0 : $i]: (product2 @ X0 @ X0 @ X0)),
% 0.19/0.75 inference('cnf', [status(esa)], [product2_idempotence])).
% 0.19/0.75 thf(product2_total_function2, axiom,
% 0.19/0.75 (( ~( product2 @ X @ Y @ W ) ) | ( ~( product2 @ X @ Y @ Z ) ) |
% 0.19/0.75 ( equalish @ W @ Z ))).
% 0.19/0.75 thf(zip_derived_cl21, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.19/0.75 (~ (product2 @ X0 @ X1 @ X2)
% 0.19/0.75 | ~ (product2 @ X0 @ X1 @ X3)
% 0.19/0.75 | (equalish @ X2 @ X3))),
% 0.19/0.75 inference('cnf', [status(esa)], [product2_total_function2])).
% 0.19/0.75 thf(zip_derived_cl95, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i]:
% 0.19/0.75 (~ (product2 @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl21])).
% 0.19/0.75 thf(zip_derived_cl320, plain,
% 0.19/0.75 (( (product1 @ e_2 @ e_1 @ e_2) | (equalish @ e_3 @ e_1))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl264, zip_derived_cl95])).
% 0.19/0.75 thf(zip_derived_cl13, plain, (~ (equalish @ e_3 @ e_1)),
% 0.19/0.75 inference('cnf', [status(esa)], [e_3_is_not_e_1])).
% 0.19/0.75 thf(zip_derived_cl325, plain, ( (product1 @ e_2 @ e_1 @ e_2)),
% 0.19/0.75 inference('demod', [status(thm)], [zip_derived_cl320, zip_derived_cl13])).
% 0.19/0.75 thf(zip_derived_cl25, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.19/0.75 ( (product2 @ X0 @ X1 @ X2)
% 0.19/0.75 | ~ (product1 @ X3 @ X2 @ X0)
% 0.19/0.75 | ~ (product1 @ X1 @ X2 @ X3))),
% 0.19/0.75 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.19/0.75 thf(zip_derived_cl354, plain,
% 0.19/0.75 (![X0 : $i]:
% 0.19/0.75 ( (product2 @ e_2 @ X0 @ e_1) | ~ (product1 @ X0 @ e_1 @ e_2))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl325, zip_derived_cl25])).
% 0.19/0.75 thf(zip_derived_cl95, plain,
% 0.19/0.75 (![X0 : $i, X1 : $i]:
% 0.19/0.75 (~ (product2 @ X0 @ X0 @ X1) | (equalish @ X0 @ X1))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl24, zip_derived_cl21])).
% 0.19/0.75 thf(zip_derived_cl377, plain,
% 0.19/0.75 ((~ (product1 @ e_2 @ e_1 @ e_2) | (equalish @ e_2 @ e_1))),
% 0.19/0.75 inference('s_sup-', [status(thm)], [zip_derived_cl354, zip_derived_cl95])).
% 0.19/0.75 thf(zip_derived_cl325, plain, ( (product1 @ e_2 @ e_1 @ e_2)),
% 0.19/0.75 inference('demod', [status(thm)], [zip_derived_cl320, zip_derived_cl13])).
% 0.19/0.75 thf(zip_derived_cl11, plain, (~ (equalish @ e_2 @ e_1)),
% 0.19/0.75 inference('cnf', [status(esa)], [e_2_is_not_e_1])).
% 0.19/0.75 thf(zip_derived_cl384, plain, ($false),
% 0.19/0.75 inference('demod', [status(thm)],
% 0.19/0.75 [zip_derived_cl377, zip_derived_cl325, zip_derived_cl11])).
% 0.19/0.75
% 0.19/0.75 % SZS output end Refutation
% 0.19/0.75
% 0.19/0.75
% 0.19/0.75 % Terminating...
% 1.57/0.82 % Runner terminated.
% 1.57/0.83 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------