TSTP Solution File: GRP039-3 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP039-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.pLPYYdOfn6 true
% Computer : n012.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 01:49:40 EDT 2023
% Result : Unsatisfiable 0.58s 0.85s
% Output : Refutation 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP039-3 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.pLPYYdOfn6 true
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 22:29:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.21/0.66 % Total configuration time : 435
% 0.21/0.66 % Estimated wc time : 1092
% 0.21/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.58/0.85 % Solved by fo/fo5.sh.
% 0.58/0.85 % done 203 iterations in 0.057s
% 0.58/0.85 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.58/0.85 % SZS output start Refutation
% 0.58/0.85 thf(inverse_type, type, inverse: $i > $i).
% 0.58/0.85 thf(a_type, type, a: $i).
% 0.58/0.85 thf(product_type, type, product: $i > $i > $i > $o).
% 0.58/0.85 thf(b_type, type, b: $i).
% 0.58/0.85 thf(d_type, type, d: $i).
% 0.58/0.85 thf(identity_type, type, identity: $i).
% 0.58/0.85 thf(subgroup_member_type, type, subgroup_member: $i > $o).
% 0.58/0.85 thf(element_in_O2_type, type, element_in_O2: $i > $i > $i).
% 0.58/0.85 thf(multiply_type, type, multiply: $i > $i > $i).
% 0.58/0.85 thf(c_type, type, c: $i).
% 0.58/0.85 thf(a_times_c_is_d, conjecture, (~( product @ a @ c @ d ))).
% 0.58/0.85 thf(zf_stmt_0, negated_conjecture, (product @ a @ c @ d),
% 0.58/0.85 inference('cnf.neg', [status(esa)], [a_times_c_is_d])).
% 0.58/0.85 thf(zip_derived_cl18, plain, ( (product @ a @ c @ d)),
% 0.58/0.85 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.58/0.85 thf(subgroup_member_inverse_are_in_subgroup, axiom,
% 0.58/0.85 (( ~( subgroup_member @ A ) ) | ( subgroup_member @ ( inverse @ A ) ))).
% 0.58/0.85 thf(zip_derived_cl13, plain,
% 0.58/0.85 (![X0 : $i]:
% 0.58/0.85 (~ (subgroup_member @ X0) | (subgroup_member @ (inverse @ X0)))),
% 0.58/0.85 inference('cnf', [status(esa)], [subgroup_member_inverse_are_in_subgroup])).
% 0.58/0.85 thf(inverse_is_self_cancelling, axiom,
% 0.58/0.85 (( inverse @ ( inverse @ A ) ) = ( A ))).
% 0.58/0.85 thf(zip_derived_cl11, plain,
% 0.58/0.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.58/0.85 inference('cnf', [status(esa)], [inverse_is_self_cancelling])).
% 0.58/0.85 thf(closure_of_product_and_inverse, axiom,
% 0.58/0.85 (( ~( subgroup_member @ A ) ) | ( ~( subgroup_member @ B ) ) |
% 0.58/0.85 ( ~( product @ A @ ( inverse @ B ) @ C ) ) | ( subgroup_member @ C ))).
% 0.58/0.85 thf(zip_derived_cl8, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.85 (~ (subgroup_member @ X0)
% 0.58/0.85 | ~ (subgroup_member @ X1)
% 0.58/0.85 | ~ (product @ X0 @ (inverse @ X1) @ X2)
% 0.58/0.85 | (subgroup_member @ X2))),
% 0.58/0.85 inference('cnf', [status(esa)], [closure_of_product_and_inverse])).
% 0.58/0.85 thf(zip_derived_cl31, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.85 (~ (product @ X2 @ X0 @ X1)
% 0.58/0.85 | (subgroup_member @ X1)
% 0.58/0.85 | ~ (subgroup_member @ (inverse @ X0))
% 0.58/0.85 | ~ (subgroup_member @ X2))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl8])).
% 0.58/0.85 thf(zip_derived_cl161, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.85 (~ (subgroup_member @ X0)
% 0.58/0.85 | ~ (subgroup_member @ X1)
% 0.58/0.85 | (subgroup_member @ X2)
% 0.58/0.85 | ~ (product @ X1 @ X0 @ X2))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl31])).
% 0.58/0.85 thf(zip_derived_cl360, plain,
% 0.58/0.85 (( (subgroup_member @ d)
% 0.58/0.85 | ~ (subgroup_member @ a)
% 0.58/0.85 | ~ (subgroup_member @ c))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl161])).
% 0.58/0.85 thf(property_of_O2, axiom,
% 0.58/0.85 (( product @ A @ ( element_in_O2 @ A @ B ) @ B ) |
% 0.58/0.85 ( subgroup_member @ B ) | ( subgroup_member @ A ))).
% 0.58/0.85 thf(zip_derived_cl15, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i]:
% 0.58/0.85 ( (product @ X0 @ (element_in_O2 @ X0 @ X1) @ X1)
% 0.58/0.85 | (subgroup_member @ X1)
% 0.58/0.85 | (subgroup_member @ X0))),
% 0.58/0.85 inference('cnf', [status(esa)], [property_of_O2])).
% 0.58/0.85 thf(zip_derived_cl18, plain, ( (product @ a @ c @ d)),
% 0.58/0.85 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.58/0.85 thf(product_right_cancellation, axiom,
% 0.58/0.85 (( ~( product @ A @ B @ C ) ) | ( ~( product @ A @ D @ C ) ) |
% 0.58/0.85 ( ( D ) = ( B ) ))).
% 0.58/0.85 thf(zip_derived_cl9, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.85 (~ (product @ X0 @ X1 @ X2)
% 0.58/0.85 | ~ (product @ X0 @ X3 @ X2)
% 0.58/0.85 | ((X3) = (X1)))),
% 0.58/0.85 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.58/0.85 thf(zip_derived_cl52, plain,
% 0.58/0.85 (![X0 : $i]: (((X0) = (c)) | ~ (product @ a @ X0 @ d))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl9])).
% 0.58/0.85 thf(zip_derived_cl182, plain,
% 0.58/0.85 (( (subgroup_member @ a)
% 0.58/0.85 | (subgroup_member @ d)
% 0.58/0.85 | ((element_in_O2 @ a @ d) = (c)))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl52])).
% 0.58/0.85 thf(prove_d_is_in_subgroup, conjecture, (subgroup_member @ d)).
% 0.58/0.85 thf(zf_stmt_1, negated_conjecture, (~( subgroup_member @ d )),
% 0.58/0.85 inference('cnf.neg', [status(esa)], [prove_d_is_in_subgroup])).
% 0.58/0.85 thf(zip_derived_cl19, plain, (~ (subgroup_member @ d)),
% 0.58/0.85 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.58/0.85 thf(zip_derived_cl190, plain,
% 0.58/0.85 (( (subgroup_member @ a) | ((element_in_O2 @ a @ d) = (c)))),
% 0.58/0.85 inference('demod', [status(thm)], [zip_derived_cl182, zip_derived_cl19])).
% 0.58/0.85 thf(an_element_in_O2, axiom,
% 0.58/0.85 (( subgroup_member @ ( element_in_O2 @ A @ B ) ) |
% 0.58/0.85 ( subgroup_member @ B ) | ( subgroup_member @ A ))).
% 0.58/0.85 thf(zip_derived_cl14, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i]:
% 0.58/0.85 ( (subgroup_member @ (element_in_O2 @ X0 @ X1))
% 0.58/0.85 | (subgroup_member @ X1)
% 0.58/0.85 | (subgroup_member @ X0))),
% 0.58/0.85 inference('cnf', [status(esa)], [an_element_in_O2])).
% 0.58/0.85 thf(zip_derived_cl192, plain,
% 0.58/0.85 (( (subgroup_member @ c)
% 0.58/0.85 | (subgroup_member @ a)
% 0.58/0.85 | (subgroup_member @ a)
% 0.58/0.85 | (subgroup_member @ d))),
% 0.58/0.85 inference('sup+', [status(thm)], [zip_derived_cl190, zip_derived_cl14])).
% 0.58/0.85 thf(zip_derived_cl194, plain,
% 0.58/0.85 (( (subgroup_member @ d)
% 0.58/0.85 | (subgroup_member @ a)
% 0.58/0.85 | (subgroup_member @ c))),
% 0.58/0.85 inference('simplify', [status(thm)], [zip_derived_cl192])).
% 0.58/0.85 thf(zip_derived_cl19, plain, (~ (subgroup_member @ d)),
% 0.58/0.85 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.58/0.85 thf(zip_derived_cl197, plain,
% 0.58/0.85 (( (subgroup_member @ c) | (subgroup_member @ a))),
% 0.58/0.85 inference('clc', [status(thm)], [zip_derived_cl194, zip_derived_cl19])).
% 0.58/0.85 thf(b_times_a_inverse_is_c, conjecture,
% 0.58/0.85 (~( product @ b @ ( inverse @ a ) @ c ))).
% 0.58/0.85 thf(zf_stmt_2, negated_conjecture, (product @ b @ ( inverse @ a ) @ c),
% 0.58/0.85 inference('cnf.neg', [status(esa)], [b_times_a_inverse_is_c])).
% 0.58/0.85 thf(zip_derived_cl17, plain, ( (product @ b @ (inverse @ a) @ c)),
% 0.58/0.85 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.58/0.85 thf(zip_derived_cl8, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.85 (~ (subgroup_member @ X0)
% 0.58/0.85 | ~ (subgroup_member @ X1)
% 0.58/0.85 | ~ (product @ X0 @ (inverse @ X1) @ X2)
% 0.58/0.85 | (subgroup_member @ X2))),
% 0.58/0.85 inference('cnf', [status(esa)], [closure_of_product_and_inverse])).
% 0.58/0.85 thf(zip_derived_cl30, plain,
% 0.58/0.85 (( (subgroup_member @ c)
% 0.58/0.85 | ~ (subgroup_member @ a)
% 0.58/0.85 | ~ (subgroup_member @ b))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl8])).
% 0.58/0.85 thf(b_is_in_subgroup, conjecture, (~( subgroup_member @ b ))).
% 0.58/0.85 thf(zf_stmt_3, negated_conjecture, (subgroup_member @ b),
% 0.58/0.85 inference('cnf.neg', [status(esa)], [b_is_in_subgroup])).
% 0.58/0.85 thf(zip_derived_cl16, plain, ( (subgroup_member @ b)),
% 0.58/0.85 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.58/0.85 thf(zip_derived_cl36, plain,
% 0.58/0.85 (( (subgroup_member @ c) | ~ (subgroup_member @ a))),
% 0.58/0.85 inference('demod', [status(thm)], [zip_derived_cl30, zip_derived_cl16])).
% 0.58/0.85 thf(zip_derived_cl198, plain, ( (subgroup_member @ c)),
% 0.58/0.85 inference('clc', [status(thm)], [zip_derived_cl197, zip_derived_cl36])).
% 0.58/0.85 thf(zip_derived_cl367, plain,
% 0.58/0.85 (( (subgroup_member @ d) | ~ (subgroup_member @ a))),
% 0.58/0.85 inference('demod', [status(thm)], [zip_derived_cl360, zip_derived_cl198])).
% 0.58/0.85 thf(zip_derived_cl19, plain, (~ (subgroup_member @ d)),
% 0.58/0.85 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.58/0.85 thf(zip_derived_cl379, plain, (~ (subgroup_member @ a)),
% 0.58/0.85 inference('clc', [status(thm)], [zip_derived_cl367, zip_derived_cl19])).
% 0.58/0.85 thf(zip_derived_cl13, plain,
% 0.58/0.85 (![X0 : $i]:
% 0.58/0.85 (~ (subgroup_member @ X0) | (subgroup_member @ (inverse @ X0)))),
% 0.58/0.85 inference('cnf', [status(esa)], [subgroup_member_inverse_are_in_subgroup])).
% 0.58/0.85 thf(zip_derived_cl17, plain, ( (product @ b @ (inverse @ a) @ c)),
% 0.58/0.85 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.58/0.85 thf(zip_derived_cl11, plain,
% 0.58/0.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.58/0.85 inference('cnf', [status(esa)], [inverse_is_self_cancelling])).
% 0.58/0.85 thf(left_identity, axiom, (product @ identity @ X @ X)).
% 0.58/0.85 thf(zip_derived_cl0, plain, (![X0 : $i]: (product @ identity @ X0 @ X0)),
% 0.58/0.85 inference('cnf', [status(esa)], [left_identity])).
% 0.58/0.85 thf(right_inverse, axiom, (product @ X @ ( inverse @ X ) @ identity)).
% 0.58/0.85 thf(zip_derived_cl3, plain,
% 0.58/0.85 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ identity)),
% 0.58/0.85 inference('cnf', [status(esa)], [right_inverse])).
% 0.58/0.85 thf(associativity1, axiom,
% 0.58/0.85 (( ~( product @ X @ Y @ U ) ) | ( ~( product @ Y @ Z @ V ) ) |
% 0.58/0.85 ( ~( product @ U @ Z @ W ) ) | ( product @ X @ V @ W ))).
% 0.58/0.85 thf(zip_derived_cl6, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.58/0.85 (~ (product @ X0 @ X1 @ X2)
% 0.58/0.85 | ~ (product @ X1 @ X3 @ X4)
% 0.58/0.85 | ~ (product @ X2 @ X3 @ X5)
% 0.58/0.85 | (product @ X0 @ X4 @ X5))),
% 0.58/0.85 inference('cnf', [status(esa)], [associativity1])).
% 0.58/0.85 thf(zip_derived_cl64, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.85 ( (product @ X0 @ X2 @ X1)
% 0.58/0.85 | ~ (product @ identity @ X3 @ X1)
% 0.58/0.85 | ~ (product @ (inverse @ X0) @ X3 @ X2))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 0.58/0.85 thf(zip_derived_cl438, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.85 (~ (product @ (inverse @ X2) @ X0 @ X1) | (product @ X2 @ X1 @ X0))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl64])).
% 0.58/0.85 thf(zip_derived_cl450, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.85 (~ (product @ X0 @ X2 @ X1) | (product @ (inverse @ X0) @ X1 @ X2))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl438])).
% 0.58/0.85 thf(zip_derived_cl458, plain,
% 0.58/0.85 ( (product @ (inverse @ b) @ c @ (inverse @ a))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl450])).
% 0.58/0.85 thf(zip_derived_cl15, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i]:
% 0.58/0.85 ( (product @ X0 @ (element_in_O2 @ X0 @ X1) @ X1)
% 0.58/0.85 | (subgroup_member @ X1)
% 0.58/0.85 | (subgroup_member @ X0))),
% 0.58/0.85 inference('cnf', [status(esa)], [property_of_O2])).
% 0.58/0.85 thf(zip_derived_cl3, plain,
% 0.58/0.85 (![X0 : $i]: (product @ X0 @ (inverse @ X0) @ identity)),
% 0.58/0.85 inference('cnf', [status(esa)], [right_inverse])).
% 0.58/0.85 thf(total_function1, axiom, (product @ X @ Y @ ( multiply @ X @ Y ))).
% 0.58/0.85 thf(zip_derived_cl4, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 0.58/0.85 inference('cnf', [status(esa)], [total_function1])).
% 0.58/0.85 thf(zip_derived_cl18, plain, ( (product @ a @ c @ d)),
% 0.58/0.85 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.58/0.85 thf(zip_derived_cl6, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.58/0.85 (~ (product @ X0 @ X1 @ X2)
% 0.58/0.85 | ~ (product @ X1 @ X3 @ X4)
% 0.58/0.85 | ~ (product @ X2 @ X3 @ X5)
% 0.58/0.85 | (product @ X0 @ X4 @ X5))),
% 0.58/0.85 inference('cnf', [status(esa)], [associativity1])).
% 0.58/0.85 thf(zip_derived_cl68, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.85 ( (product @ a @ X1 @ X0)
% 0.58/0.85 | ~ (product @ d @ X2 @ X0)
% 0.58/0.85 | ~ (product @ c @ X2 @ X1))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl6])).
% 0.58/0.85 thf(zip_derived_cl101, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i]:
% 0.58/0.85 (~ (product @ c @ X0 @ X1) | (product @ a @ X1 @ (multiply @ d @ X0)))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl68])).
% 0.58/0.85 thf(zip_derived_cl219, plain,
% 0.58/0.85 ( (product @ a @ identity @ (multiply @ d @ (inverse @ c)))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl101])).
% 0.58/0.85 thf(right_identity, axiom, (product @ X @ identity @ X)).
% 0.58/0.85 thf(zip_derived_cl1, plain, (![X0 : $i]: (product @ X0 @ identity @ X0)),
% 0.58/0.85 inference('cnf', [status(esa)], [right_identity])).
% 0.58/0.85 thf(total_function2, axiom,
% 0.58/0.85 (( ~( product @ X @ Y @ Z ) ) | ( ~( product @ X @ Y @ W ) ) |
% 0.58/0.85 ( ( Z ) = ( W ) ))).
% 0.58/0.85 thf(zip_derived_cl5, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.85 (~ (product @ X0 @ X1 @ X2)
% 0.58/0.85 | ~ (product @ X0 @ X1 @ X3)
% 0.58/0.85 | ((X2) = (X3)))),
% 0.58/0.85 inference('cnf', [status(esa)], [total_function2])).
% 0.58/0.85 thf(zip_derived_cl38, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i]: (((X0) = (X1)) | ~ (product @ X0 @ identity @ X1))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 0.58/0.85 thf(zip_derived_cl229, plain, (((a) = (multiply @ d @ (inverse @ c)))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl219, zip_derived_cl38])).
% 0.58/0.85 thf(zip_derived_cl4, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i]: (product @ X0 @ X1 @ (multiply @ X0 @ X1))),
% 0.58/0.85 inference('cnf', [status(esa)], [total_function1])).
% 0.58/0.85 thf(zip_derived_cl233, plain, ( (product @ d @ (inverse @ c) @ a)),
% 0.58/0.85 inference('sup+', [status(thm)], [zip_derived_cl229, zip_derived_cl4])).
% 0.58/0.85 thf(zip_derived_cl9, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/0.85 (~ (product @ X0 @ X1 @ X2)
% 0.58/0.85 | ~ (product @ X0 @ X3 @ X2)
% 0.58/0.85 | ((X3) = (X1)))),
% 0.58/0.85 inference('cnf', [status(esa)], [product_right_cancellation])).
% 0.58/0.85 thf(zip_derived_cl256, plain,
% 0.58/0.85 (![X0 : $i]: (((X0) = (inverse @ c)) | ~ (product @ d @ X0 @ a))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl233, zip_derived_cl9])).
% 0.58/0.85 thf(zip_derived_cl280, plain,
% 0.58/0.85 (( (subgroup_member @ d)
% 0.58/0.85 | (subgroup_member @ a)
% 0.58/0.85 | ((element_in_O2 @ d @ a) = (inverse @ c)))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl256])).
% 0.58/0.85 thf(zip_derived_cl19, plain, (~ (subgroup_member @ d)),
% 0.58/0.85 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.58/0.85 thf(zip_derived_cl282, plain,
% 0.58/0.85 (( (subgroup_member @ a) | ((element_in_O2 @ d @ a) = (inverse @ c)))),
% 0.58/0.85 inference('demod', [status(thm)], [zip_derived_cl280, zip_derived_cl19])).
% 0.58/0.85 thf(zip_derived_cl14, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i]:
% 0.58/0.85 ( (subgroup_member @ (element_in_O2 @ X0 @ X1))
% 0.58/0.85 | (subgroup_member @ X1)
% 0.58/0.85 | (subgroup_member @ X0))),
% 0.58/0.85 inference('cnf', [status(esa)], [an_element_in_O2])).
% 0.58/0.85 thf(zip_derived_cl304, plain,
% 0.58/0.85 (( (subgroup_member @ (inverse @ c))
% 0.58/0.85 | (subgroup_member @ a)
% 0.58/0.85 | (subgroup_member @ d)
% 0.58/0.85 | (subgroup_member @ a))),
% 0.58/0.85 inference('sup+', [status(thm)], [zip_derived_cl282, zip_derived_cl14])).
% 0.58/0.85 thf(zip_derived_cl19, plain, (~ (subgroup_member @ d)),
% 0.58/0.85 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.58/0.85 thf(zip_derived_cl306, plain,
% 0.58/0.85 (( (subgroup_member @ (inverse @ c))
% 0.58/0.85 | (subgroup_member @ a)
% 0.58/0.85 | (subgroup_member @ a))),
% 0.58/0.85 inference('demod', [status(thm)], [zip_derived_cl304, zip_derived_cl19])).
% 0.58/0.85 thf(zip_derived_cl307, plain,
% 0.58/0.85 (( (subgroup_member @ a) | (subgroup_member @ (inverse @ c)))),
% 0.58/0.85 inference('simplify', [status(thm)], [zip_derived_cl306])).
% 0.58/0.85 thf(zip_derived_cl379, plain, (~ (subgroup_member @ a)),
% 0.58/0.85 inference('clc', [status(thm)], [zip_derived_cl367, zip_derived_cl19])).
% 0.58/0.85 thf(zip_derived_cl382, plain, ( (subgroup_member @ (inverse @ c))),
% 0.58/0.85 inference('demod', [status(thm)], [zip_derived_cl307, zip_derived_cl379])).
% 0.58/0.85 thf(zip_derived_cl31, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/0.85 (~ (product @ X2 @ X0 @ X1)
% 0.58/0.85 | (subgroup_member @ X1)
% 0.58/0.85 | ~ (subgroup_member @ (inverse @ X0))
% 0.58/0.85 | ~ (subgroup_member @ X2))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl8])).
% 0.58/0.85 thf(zip_derived_cl384, plain,
% 0.58/0.85 (![X0 : $i, X1 : $i]:
% 0.58/0.85 (~ (subgroup_member @ X0)
% 0.58/0.85 | (subgroup_member @ X1)
% 0.58/0.85 | ~ (product @ X0 @ c @ X1))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl382, zip_derived_cl31])).
% 0.58/0.85 thf(zip_derived_cl484, plain,
% 0.58/0.85 (( (subgroup_member @ (inverse @ a))
% 0.58/0.85 | ~ (subgroup_member @ (inverse @ b)))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl458, zip_derived_cl384])).
% 0.58/0.85 thf(zip_derived_cl488, plain,
% 0.58/0.85 ((~ (subgroup_member @ b) | (subgroup_member @ (inverse @ a)))),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl484])).
% 0.58/0.85 thf(zip_derived_cl16, plain, ( (subgroup_member @ b)),
% 0.58/0.85 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.58/0.85 thf(zip_derived_cl489, plain, ( (subgroup_member @ (inverse @ a))),
% 0.58/0.85 inference('demod', [status(thm)], [zip_derived_cl488, zip_derived_cl16])).
% 0.58/0.85 thf(zip_derived_cl11, plain,
% 0.58/0.85 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.58/0.85 inference('cnf', [status(esa)], [inverse_is_self_cancelling])).
% 0.58/0.85 thf(zip_derived_cl13, plain,
% 0.58/0.85 (![X0 : $i]:
% 0.58/0.85 (~ (subgroup_member @ X0) | (subgroup_member @ (inverse @ X0)))),
% 0.58/0.85 inference('cnf', [status(esa)], [subgroup_member_inverse_are_in_subgroup])).
% 0.58/0.85 thf(zip_derived_cl21, plain,
% 0.58/0.85 (![X0 : $i]:
% 0.58/0.85 ( (subgroup_member @ X0) | ~ (subgroup_member @ (inverse @ X0)))),
% 0.58/0.85 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl13])).
% 0.58/0.85 thf(zip_derived_cl490, plain, ( (subgroup_member @ a)),
% 0.58/0.85 inference('sup-', [status(thm)], [zip_derived_cl489, zip_derived_cl21])).
% 0.58/0.85 thf(zip_derived_cl493, plain, ($false),
% 0.58/0.85 inference('demod', [status(thm)], [zip_derived_cl379, zip_derived_cl490])).
% 0.58/0.85
% 0.58/0.85 % SZS output end Refutation
% 0.58/0.85
% 0.58/0.85
% 0.58/0.85 % Terminating...
% 0.59/0.97 % Runner terminated.
% 0.59/0.98 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------