TSTP Solution File: GRP039-7 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP039-7 : TPTP v8.1.2. Bugfixed v1.0.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.fe34f6qMSj 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 01:49:40 EDT 2023
% Result : Unsatisfiable 1.81s 0.90s
% Output : Refutation 1.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP039-7 : TPTP v8.1.2. Bugfixed v1.0.1.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.fe34f6qMSj true
% 0.16/0.34 % Computer : n025.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon Aug 28 21:07:10 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.16/0.34 % Running portfolio for 300 s
% 0.16/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.34 % Number of cores: 8
% 0.16/0.35 % Python version: Python 3.6.8
% 0.16/0.35 % Running in FO mode
% 0.20/0.64 % Total configuration time : 435
% 0.20/0.64 % Estimated wc time : 1092
% 0.20/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.20/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.81/0.90 % Solved by fo/fo1_av.sh.
% 1.81/0.90 % done 249 iterations in 0.156s
% 1.81/0.90 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.81/0.90 % SZS output start Refutation
% 1.81/0.90 thf(d_type, type, d: $i).
% 1.81/0.90 thf(subgroup_member_type, type, subgroup_member: $i > $o).
% 1.81/0.90 thf(a_type, type, a: $i).
% 1.81/0.90 thf(c_type, type, c: $i).
% 1.81/0.90 thf(identity_type, type, identity: $i).
% 1.81/0.90 thf(multiply_type, type, multiply: $i > $i > $i).
% 1.81/0.90 thf(b_type, type, b: $i).
% 1.81/0.90 thf(element_in_O2_type, type, element_in_O2: $i > $i > $i).
% 1.81/0.90 thf(inverse_type, type, inverse: $i > $i).
% 1.81/0.90 thf(prove_d_in_O2, conjecture, (subgroup_member @ d)).
% 1.81/0.90 thf(zf_stmt_0, negated_conjecture, (~( subgroup_member @ d )),
% 1.81/0.90 inference('cnf.neg', [status(esa)], [prove_d_in_O2])).
% 1.81/0.90 thf(zip_derived_cl15, plain, (~ (subgroup_member @ d)),
% 1.81/0.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.81/0.90 thf(a_times_c_is_d, conjecture, (( multiply @ a @ c ) != ( d ))).
% 1.81/0.90 thf(zf_stmt_1, negated_conjecture, (( multiply @ a @ c ) = ( d )),
% 1.81/0.90 inference('cnf.neg', [status(esa)], [a_times_c_is_d])).
% 1.81/0.90 thf(zip_derived_cl14, plain, (((multiply @ a @ c) = (d))),
% 1.81/0.90 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.81/0.90 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 1.81/0.90 thf(zip_derived_cl1, plain,
% 1.81/0.90 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.81/0.90 inference('cnf', [status(esa)], [left_inverse])).
% 1.81/0.90 thf(associativity, axiom,
% 1.81/0.90 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 1.81/0.90 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 1.81/0.90 thf(zip_derived_cl2, plain,
% 1.81/0.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.81/0.90 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.81/0.90 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.81/0.90 inference('cnf', [status(esa)], [associativity])).
% 1.81/0.90 thf(zip_derived_cl35, plain,
% 1.81/0.90 (![X0 : $i, X1 : $i]:
% 1.81/0.90 ((multiply @ identity @ X0)
% 1.81/0.90 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.81/0.90 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 1.81/0.90 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 1.81/0.90 thf(zip_derived_cl0, plain,
% 1.81/0.90 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.81/0.90 inference('cnf', [status(esa)], [left_identity])).
% 1.81/0.90 thf(zip_derived_cl41, plain,
% 1.81/0.90 (![X0 : $i, X1 : $i]:
% 1.81/0.90 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.81/0.90 inference('demod', [status(thm)], [zip_derived_cl35, zip_derived_cl0])).
% 1.81/0.90 thf(zip_derived_cl152, plain, (((c) = (multiply @ (inverse @ a) @ d))),
% 1.81/0.90 inference('s_sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl41])).
% 1.81/0.90 thf(property_of_O2, axiom,
% 1.81/0.90 (( subgroup_member @ X ) | ( subgroup_member @ Y ) |
% 1.81/0.90 ( ( multiply @ X @ ( element_in_O2 @ X @ Y ) ) = ( Y ) ))).
% 1.81/0.90 thf(zip_derived_cl11, plain,
% 1.81/0.90 (![X0 : $i, X1 : $i]:
% 1.81/0.90 ( (subgroup_member @ X0)
% 1.81/0.90 | (subgroup_member @ X1)
% 1.81/0.90 | ((multiply @ X0 @ (element_in_O2 @ X0 @ X1)) = (X1)))),
% 1.81/0.90 inference('cnf', [status(esa)], [property_of_O2])).
% 1.81/0.90 thf(zip_derived_cl41, plain,
% 1.81/0.90 (![X0 : $i, X1 : $i]:
% 1.81/0.90 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.81/0.90 inference('demod', [status(thm)], [zip_derived_cl35, zip_derived_cl0])).
% 1.81/0.90 thf(zip_derived_cl144, plain,
% 1.81/0.90 (![X0 : $i, X1 : $i]:
% 1.81/0.90 ( (subgroup_member @ X0)
% 1.81/0.90 | (subgroup_member @ X1)
% 1.81/0.90 | ((element_in_O2 @ X1 @ X0) = (multiply @ (inverse @ X1) @ X0)))),
% 1.81/0.90 inference('s_sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl41])).
% 1.81/0.90 thf(zip_derived_cl1304, plain,
% 1.81/0.90 (( (subgroup_member @ d)
% 1.81/0.90 | (subgroup_member @ a)
% 1.81/0.90 | ((element_in_O2 @ a @ d) = (c)))),
% 1.81/0.90 inference('s_sup+', [status(thm)], [zip_derived_cl152, zip_derived_cl144])).
% 1.81/0.90 thf(zip_derived_cl15, plain, (~ (subgroup_member @ d)),
% 1.81/0.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.81/0.90 thf(b_times_a_inverse_is_c, conjecture,
% 1.81/0.90 (( multiply @ b @ ( inverse @ a ) ) != ( c ))).
% 1.81/0.90 thf(zf_stmt_2, negated_conjecture,
% 1.81/0.90 (( multiply @ b @ ( inverse @ a ) ) = ( c )),
% 1.81/0.90 inference('cnf.neg', [status(esa)], [b_times_a_inverse_is_c])).
% 1.81/0.90 thf(zip_derived_cl13, plain, (((multiply @ b @ (inverse @ a)) = (c))),
% 1.81/0.90 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.81/0.90 thf(closure_of_multiply, axiom,
% 1.81/0.90 (( ~( subgroup_member @ X ) ) | ( ~( subgroup_member @ Y ) ) |
% 1.81/0.90 ( ( multiply @ X @ Y ) != ( Z ) ) | ( subgroup_member @ Z ))).
% 1.81/0.90 thf(zip_derived_cl4, plain,
% 1.81/0.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.81/0.90 (~ (subgroup_member @ X0)
% 1.81/0.90 | ~ (subgroup_member @ X1)
% 1.81/0.90 | ((multiply @ X0 @ X1) != (X2))
% 1.81/0.90 | (subgroup_member @ X2))),
% 1.81/0.90 inference('cnf', [status(esa)], [closure_of_multiply])).
% 1.81/0.90 thf(zip_derived_cl54, plain,
% 1.81/0.90 (![X0 : $i]:
% 1.81/0.90 (~ (subgroup_member @ b)
% 1.81/0.90 | ~ (subgroup_member @ (inverse @ a))
% 1.81/0.90 | ((c) != (X0))
% 1.81/0.90 | (subgroup_member @ X0))),
% 1.81/0.90 inference('s_sup-', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 1.81/0.90 thf(b_in_O2, conjecture, (~( subgroup_member @ b ))).
% 1.81/0.90 thf(zf_stmt_3, negated_conjecture, (subgroup_member @ b),
% 1.81/0.90 inference('cnf.neg', [status(esa)], [b_in_O2])).
% 1.81/0.90 thf(zip_derived_cl12, plain, ( (subgroup_member @ b)),
% 1.81/0.90 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.81/0.90 thf(zip_derived_cl59, plain,
% 1.81/0.90 (![X0 : $i]:
% 1.81/0.90 (~ (subgroup_member @ (inverse @ a))
% 1.81/0.90 | ((c) != (X0))
% 1.81/0.90 | (subgroup_member @ X0))),
% 1.81/0.90 inference('demod', [status(thm)], [zip_derived_cl54, zip_derived_cl12])).
% 1.81/0.90 thf(zip_derived_cl61, plain,
% 1.81/0.90 ((~ (subgroup_member @ (inverse @ a)))
% 1.81/0.90 <= (~ ( (subgroup_member @ (inverse @ a))))),
% 1.81/0.90 inference('split', [status(esa)], [zip_derived_cl59])).
% 1.81/0.90 thf(closure_of_inverse, axiom,
% 1.81/0.90 (( ~( subgroup_member @ X ) ) | ( subgroup_member @ ( inverse @ X ) ))).
% 1.81/0.90 thf(zip_derived_cl3, plain,
% 1.81/0.90 (![X0 : $i]:
% 1.81/0.90 (~ (subgroup_member @ X0) | (subgroup_member @ (inverse @ X0)))),
% 1.81/0.90 inference('cnf', [status(esa)], [closure_of_inverse])).
% 1.81/0.90 thf(zip_derived_cl65, plain,
% 1.81/0.90 ((~ (subgroup_member @ a)) <= (~ ( (subgroup_member @ (inverse @ a))))),
% 1.81/0.90 inference('s_sup+', [status(thm)], [zip_derived_cl61, zip_derived_cl3])).
% 1.81/0.90 thf(inverse_inverse, axiom, (( inverse @ ( inverse @ X ) ) = ( X ))).
% 1.81/0.90 thf(zip_derived_cl7, plain,
% 1.81/0.90 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 1.81/0.90 inference('cnf', [status(esa)], [inverse_inverse])).
% 1.81/0.90 thf(zip_derived_cl60, plain,
% 1.81/0.90 ((![X0 : $i]: ( (subgroup_member @ X0) | ((c) != (X0))))
% 1.81/0.90 <= ((![X0 : $i]: ( (subgroup_member @ X0) | ((c) != (X0)))))),
% 1.81/0.90 inference('split', [status(esa)], [zip_derived_cl59])).
% 1.81/0.90 thf(zip_derived_cl7, plain,
% 1.81/0.90 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 1.81/0.90 inference('cnf', [status(esa)], [inverse_inverse])).
% 1.81/0.90 thf(zip_derived_cl3, plain,
% 1.81/0.90 (![X0 : $i]:
% 1.81/0.90 (~ (subgroup_member @ X0) | (subgroup_member @ (inverse @ X0)))),
% 1.81/0.90 inference('cnf', [status(esa)], [closure_of_inverse])).
% 1.81/0.90 thf(zip_derived_cl18, plain,
% 1.81/0.90 (![X0 : $i]:
% 1.81/0.90 (~ (subgroup_member @ (inverse @ X0)) | (subgroup_member @ X0))),
% 1.81/0.90 inference('s_sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl3])).
% 1.81/0.90 thf(zip_derived_cl62, plain,
% 1.81/0.90 ((![X0 : $i]: (((c) != (inverse @ X0)) | (subgroup_member @ X0)))
% 1.81/0.90 <= ((![X0 : $i]: ( (subgroup_member @ X0) | ((c) != (X0)))))),
% 1.81/0.90 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl18])).
% 1.81/0.90 thf(zip_derived_cl71, plain,
% 1.81/0.90 ((![X0 : $i]: (((c) != (X0)) | (subgroup_member @ (inverse @ X0))))
% 1.81/0.90 <= ((![X0 : $i]: ( (subgroup_member @ X0) | ((c) != (X0)))))),
% 1.81/0.90 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl62])).
% 1.81/0.90 thf(right_inverse, axiom,
% 1.81/0.90 (( multiply @ X @ ( inverse @ X ) ) = ( identity ))).
% 1.81/0.90 thf(zip_derived_cl6, plain,
% 1.81/0.90 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.81/0.90 inference('cnf', [status(esa)], [right_inverse])).
% 1.81/0.90 thf(zip_derived_cl13, plain, (((multiply @ b @ (inverse @ a)) = (c))),
% 1.81/0.90 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.81/0.90 thf(zip_derived_cl2, plain,
% 1.81/0.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.81/0.90 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.81/0.90 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.81/0.90 inference('cnf', [status(esa)], [associativity])).
% 1.81/0.90 thf(zip_derived_cl36, plain,
% 1.81/0.90 (![X0 : $i]:
% 1.81/0.90 ((multiply @ c @ X0)
% 1.81/0.90 = (multiply @ b @ (multiply @ (inverse @ a) @ X0)))),
% 1.81/0.90 inference('s_sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl2])).
% 1.81/0.90 thf(zip_derived_cl130, plain,
% 1.81/0.90 (((multiply @ c @ (inverse @ (inverse @ a))) = (multiply @ b @ identity))),
% 1.81/0.90 inference('s_sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl36])).
% 1.81/0.90 thf(zip_derived_cl7, plain,
% 1.81/0.90 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 1.81/0.90 inference('cnf', [status(esa)], [inverse_inverse])).
% 1.81/0.90 thf(right_identity, axiom, (( multiply @ X @ identity ) = ( X ))).
% 1.81/0.90 thf(zip_derived_cl5, plain,
% 1.81/0.90 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.81/0.90 inference('cnf', [status(esa)], [right_identity])).
% 1.81/0.90 thf(zip_derived_cl134, plain, (((multiply @ c @ a) = (b))),
% 1.81/0.90 inference('demod', [status(thm)],
% 1.81/0.90 [zip_derived_cl130, zip_derived_cl7, zip_derived_cl5])).
% 1.81/0.90 thf(zip_derived_cl41, plain,
% 1.81/0.90 (![X0 : $i, X1 : $i]:
% 1.81/0.90 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.81/0.90 inference('demod', [status(thm)], [zip_derived_cl35, zip_derived_cl0])).
% 1.81/0.90 thf(zip_derived_cl164, plain, (((a) = (multiply @ (inverse @ c) @ b))),
% 1.81/0.90 inference('s_sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl41])).
% 1.81/0.90 thf(zip_derived_cl4, plain,
% 1.81/0.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.81/0.90 (~ (subgroup_member @ X0)
% 1.81/0.90 | ~ (subgroup_member @ X1)
% 1.81/0.90 | ((multiply @ X0 @ X1) != (X2))
% 1.81/0.90 | (subgroup_member @ X2))),
% 1.81/0.90 inference('cnf', [status(esa)], [closure_of_multiply])).
% 1.81/0.90 thf(zip_derived_cl181, plain,
% 1.81/0.90 (![X0 : $i]:
% 1.81/0.90 (~ (subgroup_member @ (inverse @ c))
% 1.81/0.90 | ~ (subgroup_member @ b)
% 1.81/0.90 | ((a) != (X0))
% 1.81/0.90 | (subgroup_member @ X0))),
% 1.81/0.90 inference('s_sup-', [status(thm)], [zip_derived_cl164, zip_derived_cl4])).
% 1.81/0.90 thf(zip_derived_cl12, plain, ( (subgroup_member @ b)),
% 1.81/0.90 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.81/0.90 thf(zip_derived_cl183, plain,
% 1.81/0.90 (![X0 : $i]:
% 1.81/0.90 (~ (subgroup_member @ (inverse @ c))
% 1.81/0.90 | ((a) != (X0))
% 1.81/0.90 | (subgroup_member @ X0))),
% 1.81/0.90 inference('demod', [status(thm)], [zip_derived_cl181, zip_derived_cl12])).
% 1.81/0.90 thf(zip_derived_cl249, plain,
% 1.81/0.90 ((~ (subgroup_member @ (inverse @ c)))
% 1.81/0.90 <= (~ ( (subgroup_member @ (inverse @ c))))),
% 1.81/0.90 inference('split', [status(esa)], [zip_derived_cl183])).
% 1.81/0.90 thf(zip_derived_cl14, plain, (((multiply @ a @ c) = (d))),
% 1.81/0.90 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.81/0.90 thf(zip_derived_cl4, plain,
% 1.81/0.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.81/0.90 (~ (subgroup_member @ X0)
% 1.81/0.90 | ~ (subgroup_member @ X1)
% 1.81/0.90 | ((multiply @ X0 @ X1) != (X2))
% 1.81/0.90 | (subgroup_member @ X2))),
% 1.81/0.90 inference('cnf', [status(esa)], [closure_of_multiply])).
% 1.81/0.90 thf(zip_derived_cl55, plain,
% 1.81/0.90 (![X0 : $i]:
% 1.81/0.90 (~ (subgroup_member @ a)
% 1.81/0.90 | ~ (subgroup_member @ c)
% 1.81/0.90 | ((d) != (X0))
% 1.81/0.90 | (subgroup_member @ X0))),
% 1.81/0.90 inference('s_sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl4])).
% 1.81/0.90 thf('0', plain,
% 1.81/0.90 (~ ( (subgroup_member @ a)) | ~ ( (subgroup_member @ c)) |
% 1.81/0.90 (![X0 : $i]: ( (subgroup_member @ X0) | ((d) != (X0))))),
% 1.81/0.90 inference('split', [status(esa)], [zip_derived_cl55])).
% 1.81/0.90 thf(zip_derived_cl83, plain,
% 1.81/0.90 ((![X0 : $i]: ( (subgroup_member @ X0) | ((d) != (X0))))
% 1.81/0.90 <= ((![X0 : $i]: ( (subgroup_member @ X0) | ((d) != (X0)))))),
% 1.81/0.90 inference('split', [status(esa)], [zip_derived_cl55])).
% 1.81/0.90 thf(zip_derived_cl15, plain, (~ (subgroup_member @ d)),
% 1.81/0.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.81/0.90 thf(zip_derived_cl89, plain,
% 1.81/0.90 ((((d) != (d)))
% 1.81/0.90 <= ((![X0 : $i]: ( (subgroup_member @ X0) | ((d) != (X0)))))),
% 1.81/0.90 inference('s_sup-', [status(thm)], [zip_derived_cl83, zip_derived_cl15])).
% 1.81/0.90 thf('1', plain, (~ (![X0 : $i]: ( (subgroup_member @ X0) | ((d) != (X0))))),
% 1.81/0.90 inference('simplify', [status(thm)], [zip_derived_cl89])).
% 1.81/0.90 thf('2', plain,
% 1.81/0.90 ((![X0 : $i]: ( (subgroup_member @ X0) | ((c) != (X0)))) |
% 1.81/0.90 ~ ( (subgroup_member @ (inverse @ a)))),
% 1.81/0.90 inference('split', [status(esa)], [zip_derived_cl59])).
% 1.81/0.90 thf(zip_derived_cl248, plain,
% 1.81/0.90 ((![X0 : $i]: ( (subgroup_member @ X0) | ((a) != (X0))))
% 1.81/0.90 <= ((![X0 : $i]: ( (subgroup_member @ X0) | ((a) != (X0)))))),
% 1.81/0.90 inference('split', [status(esa)], [zip_derived_cl183])).
% 1.81/0.90 thf(zip_derived_cl85, plain,
% 1.81/0.90 ((~ (subgroup_member @ a)) <= (~ ( (subgroup_member @ a)))),
% 1.81/0.90 inference('split', [status(esa)], [zip_derived_cl55])).
% 1.81/0.90 thf(zip_derived_cl253, plain,
% 1.81/0.90 ((((a) != (a)))
% 1.81/0.90 <= (~ ( (subgroup_member @ a)) &
% 1.81/0.90 (![X0 : $i]: ( (subgroup_member @ X0) | ((a) != (X0)))))),
% 1.81/0.90 inference('s_sup-', [status(thm)], [zip_derived_cl248, zip_derived_cl85])).
% 1.81/0.90 thf('3', plain,
% 1.81/0.90 (~ (![X0 : $i]: ( (subgroup_member @ X0) | ((a) != (X0)))) |
% 1.81/0.90 ( (subgroup_member @ a))),
% 1.81/0.90 inference('simplify', [status(thm)], [zip_derived_cl253])).
% 1.81/0.90 thf(zip_derived_cl248, plain,
% 1.81/0.90 ((![X0 : $i]: ( (subgroup_member @ X0) | ((a) != (X0))))
% 1.81/0.90 <= ((![X0 : $i]: ( (subgroup_member @ X0) | ((a) != (X0)))))),
% 1.81/0.90 inference('split', [status(esa)], [zip_derived_cl183])).
% 1.81/0.90 thf(zip_derived_cl65, plain,
% 1.81/0.90 ((~ (subgroup_member @ a)) <= (~ ( (subgroup_member @ (inverse @ a))))),
% 1.81/0.90 inference('s_sup+', [status(thm)], [zip_derived_cl61, zip_derived_cl3])).
% 1.81/0.90 thf(zip_derived_cl252, plain,
% 1.81/0.90 ((((a) != (a)))
% 1.81/0.90 <= (~ ( (subgroup_member @ (inverse @ a))) &
% 1.81/0.90 (![X0 : $i]: ( (subgroup_member @ X0) | ((a) != (X0)))))),
% 1.81/0.90 inference('s_sup-', [status(thm)], [zip_derived_cl248, zip_derived_cl65])).
% 1.81/0.90 thf('4', plain,
% 1.81/0.90 (( (subgroup_member @ (inverse @ a))) |
% 1.81/0.90 ~ (![X0 : $i]: ( (subgroup_member @ X0) | ((a) != (X0))))),
% 1.81/0.90 inference('simplify', [status(thm)], [zip_derived_cl252])).
% 1.81/0.90 thf(zip_derived_cl60, plain,
% 1.81/0.90 ((![X0 : $i]: ( (subgroup_member @ X0) | ((c) != (X0))))
% 1.81/0.90 <= ((![X0 : $i]: ( (subgroup_member @ X0) | ((c) != (X0)))))),
% 1.81/0.90 inference('split', [status(esa)], [zip_derived_cl59])).
% 1.81/0.90 thf(zip_derived_cl84, plain,
% 1.81/0.90 ((~ (subgroup_member @ c)) <= (~ ( (subgroup_member @ c)))),
% 1.81/0.90 inference('split', [status(esa)], [zip_derived_cl55])).
% 1.81/0.90 thf(zip_derived_cl92, plain,
% 1.81/0.90 ((((c) != (c)))
% 1.81/0.90 <= (~ ( (subgroup_member @ c)) &
% 1.81/0.90 (![X0 : $i]: ( (subgroup_member @ X0) | ((c) != (X0)))))),
% 1.81/0.90 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl84])).
% 1.81/0.90 thf('5', plain,
% 1.81/0.90 (( (subgroup_member @ c)) |
% 1.81/0.90 ~ (![X0 : $i]: ( (subgroup_member @ X0) | ((c) != (X0))))),
% 1.81/0.90 inference('simplify', [status(thm)], [zip_derived_cl92])).
% 1.81/0.90 thf('6', plain,
% 1.81/0.90 (~ ( (subgroup_member @ (inverse @ c))) |
% 1.81/0.90 (![X0 : $i]: ( (subgroup_member @ X0) | ((a) != (X0))))),
% 1.81/0.90 inference('split', [status(esa)], [zip_derived_cl183])).
% 1.81/0.90 thf('7', plain, (~ ( (subgroup_member @ (inverse @ c)))),
% 1.81/0.90 inference('sat_resolution*', [status(thm)],
% 1.81/0.90 ['0', '1', '2', '3', '4', '5', '6'])).
% 1.81/0.90 thf(zip_derived_cl258, plain, (~ (subgroup_member @ (inverse @ c))),
% 1.81/0.90 inference('simpl_trail', [status(thm)], [zip_derived_cl249, '7'])).
% 1.81/0.90 thf(zip_derived_cl267, plain,
% 1.81/0.90 ((((c) != (c)))
% 1.81/0.90 <= ((![X0 : $i]: ( (subgroup_member @ X0) | ((c) != (X0)))))),
% 1.81/0.90 inference('s_sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl258])).
% 1.81/0.90 thf('8', plain, (~ (![X0 : $i]: ( (subgroup_member @ X0) | ((c) != (X0))))),
% 1.81/0.90 inference('simplify', [status(thm)], [zip_derived_cl267])).
% 1.81/0.90 thf('9', plain,
% 1.81/0.90 (~ ( (subgroup_member @ (inverse @ a))) |
% 1.81/0.90 (![X0 : $i]: ( (subgroup_member @ X0) | ((c) != (X0))))),
% 1.81/0.90 inference('split', [status(esa)], [zip_derived_cl59])).
% 1.81/0.90 thf('10', plain, (~ ( (subgroup_member @ (inverse @ a)))),
% 1.81/0.90 inference('sat_resolution*', [status(thm)], ['8', '9'])).
% 1.81/0.90 thf(zip_derived_cl272, plain, (~ (subgroup_member @ a)),
% 1.81/0.90 inference('simpl_trail', [status(thm)], [zip_derived_cl65, '10'])).
% 1.81/0.90 thf(zip_derived_cl1318, plain, (((element_in_O2 @ a @ d) = (c))),
% 1.81/0.90 inference('demod', [status(thm)],
% 1.81/0.90 [zip_derived_cl1304, zip_derived_cl15, zip_derived_cl272])).
% 1.81/0.90 thf(an_element_in_O2, axiom,
% 1.81/0.90 (( subgroup_member @ X ) | ( subgroup_member @ Y ) |
% 1.81/0.90 ( subgroup_member @ ( element_in_O2 @ X @ Y ) ))).
% 1.81/0.90 thf(zip_derived_cl10, plain,
% 1.81/0.90 (![X0 : $i, X1 : $i]:
% 1.81/0.90 ( (subgroup_member @ X0)
% 1.81/0.90 | (subgroup_member @ X1)
% 1.81/0.90 | (subgroup_member @ (element_in_O2 @ X0 @ X1)))),
% 1.81/0.90 inference('cnf', [status(esa)], [an_element_in_O2])).
% 1.81/0.90 thf(zip_derived_cl1334, plain,
% 1.81/0.90 (( (subgroup_member @ a)
% 1.81/0.90 | (subgroup_member @ d)
% 1.81/0.90 | (subgroup_member @ c))),
% 1.81/0.90 inference('s_sup+', [status(thm)], [zip_derived_cl1318, zip_derived_cl10])).
% 1.81/0.90 thf(zip_derived_cl272, plain, (~ (subgroup_member @ a)),
% 1.81/0.90 inference('simpl_trail', [status(thm)], [zip_derived_cl65, '10'])).
% 1.81/0.90 thf(zip_derived_cl258, plain, (~ (subgroup_member @ (inverse @ c))),
% 1.81/0.90 inference('simpl_trail', [status(thm)], [zip_derived_cl249, '7'])).
% 1.81/0.90 thf(zip_derived_cl3, plain,
% 1.81/0.90 (![X0 : $i]:
% 1.81/0.90 (~ (subgroup_member @ X0) | (subgroup_member @ (inverse @ X0)))),
% 1.81/0.90 inference('cnf', [status(esa)], [closure_of_inverse])).
% 1.81/0.90 thf(zip_derived_cl261, plain, (~ (subgroup_member @ c)),
% 1.81/0.90 inference('s_sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl3])).
% 1.81/0.90 thf(zip_derived_cl1337, plain, ( (subgroup_member @ d)),
% 1.81/0.90 inference('demod', [status(thm)],
% 1.81/0.90 [zip_derived_cl1334, zip_derived_cl272, zip_derived_cl261])).
% 1.81/0.90 thf(zip_derived_cl1340, plain, ($false),
% 1.81/0.90 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl1337])).
% 1.81/0.90
% 1.81/0.90 % SZS output end Refutation
% 1.81/0.90
% 1.81/0.90
% 1.81/0.90 % Terminating...
% 2.34/0.95 % Runner terminated.
% 2.34/0.96 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------