%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP402-1 : TPTP v9.2.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.8S3TdHRGkv 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 Oct 2 04:36:23 PM UTC 2025
% Result : Unsatisfiable 11.40s 5.95s
% Output : Refutation 11.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/1.06 % Problem : GRP402-1 : TPTP v9.2.0. Released v2.5.0.
% 0.14/1.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.8S3TdHRGkv true
% 0.14/1.56 % Computer : n012.cluster.edu
% 0.14/1.56 % Model : x86_64 x86_64
% 0.14/1.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/1.56 % Memory : 8042.1875MB
% 0.14/1.56 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/1.56 % CPULimit : 300
% 0.14/1.56 % WCLimit : 300
% 0.14/1.56 % DateTime : Wed Oct 1 14:07:24 EDT 2025
% 0.20/1.57 % CPUTime :
% 0.20/1.57 % Running portfolio for 300 s
% 0.20/1.57 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/1.59 % Number of cores: 8
% 0.20/1.60 % Python version: Python 3.6.8
% 0.20/1.62 % Running in FO mode
% 0.57/2.33 % Total configuration time : 435
% 0.57/2.33 % Estimated wc time : 1092
% 0.57/2.33 % Estimated cpu time (7 cpus) : 156.0
% 1.26/2.63 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 1.28/2.69 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 1.29/2.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 1.31/2.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.31/2.78 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.31/2.83 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.54/2.85 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 11.40/5.95 % Solved by fo/fo7.sh.
% 11.40/5.95 % done 834 iterations in 3.044s
% 11.40/5.95 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 11.40/5.95 % SZS output start Refutation
% 11.40/5.95 thf(commutator_type, type, commutator: $i > $i > $i).
% 11.40/5.95 thf(c_type, type, c: $i).
% 11.40/5.95 thf(multiply_type, type, multiply: $i > $i > $i).
% 11.40/5.95 thf(a_type, type, a: $i).
% 11.40/5.95 thf(b_type, type, b: $i).
% 11.40/5.95 thf(commutator, axiom,
% 11.40/5.95 (( multiply @ A @ B ) =
% 11.40/5.95 ( multiply @ B @ ( multiply @ A @ ( commutator @ A @ B ) ) ))).
% 11.40/5.95 thf(zip_derived_cl3, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]:
% 11.40/5.95 ((multiply @ X1 @ X0)
% 11.40/5.95 = (multiply @ X0 @ (multiply @ X1 @ (commutator @ X1 @ X0))))),
% 11.40/5.95 inference('cnf', [status(esa)], [commutator])).
% 11.40/5.95 thf(zip_derived_cl3, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]:
% 11.40/5.95 ((multiply @ X1 @ X0)
% 11.40/5.95 = (multiply @ X0 @ (multiply @ X1 @ (commutator @ X1 @ X0))))),
% 11.40/5.95 inference('cnf', [status(esa)], [commutator])).
% 11.40/5.95 thf(zip_derived_cl3, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]:
% 11.40/5.95 ((multiply @ X1 @ X0)
% 11.40/5.95 = (multiply @ X0 @ (multiply @ X1 @ (commutator @ X1 @ X0))))),
% 11.40/5.95 inference('cnf', [status(esa)], [commutator])).
% 11.40/5.95 thf(left_cancellation, axiom,
% 11.40/5.95 (( ( multiply @ A @ B ) != ( multiply @ A @ C ) ) | ( ( B ) = ( C ) ))).
% 11.40/5.95 thf(zip_derived_cl2, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.40/5.95 (((multiply @ X0 @ X2) != (multiply @ X0 @ X1)) | ((X2) = (X1)))),
% 11.40/5.95 inference('cnf', [status(esa)], [left_cancellation])).
% 11.40/5.95 thf(zip_derived_cl57, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.40/5.95 (((multiply @ X1 @ X0) != (multiply @ X0 @ X2))
% 11.40/5.95 | ((multiply @ X1 @ (commutator @ X1 @ X0)) = (X2)))),
% 11.40/5.95 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl2])).
% 11.40/5.95 thf(zip_derived_cl540, plain,
% 11.40/5.95 (![X0 : $i]: ((multiply @ X0 @ (commutator @ X0 @ X0)) = (X0))),
% 11.40/5.95 inference('eq_res', [status(thm)], [zip_derived_cl57])).
% 11.40/5.95 thf(nilpotency, axiom,
% 11.40/5.95 (( multiply @ ( commutator @ A @ B ) @ C ) =
% 11.40/5.95 ( multiply @ C @ ( commutator @ A @ B ) ))).
% 11.40/5.95 thf(zip_derived_cl4, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.40/5.95 ((multiply @ (commutator @ X1 @ X2) @ X0)
% 11.40/5.95 = (multiply @ X0 @ (commutator @ X1 @ X2)))),
% 11.40/5.95 inference('cnf', [status(esa)], [nilpotency])).
% 11.40/5.95 thf(associativity_of_multiply, axiom,
% 11.40/5.95 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 11.40/5.95 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 11.40/5.95 thf(zip_derived_cl0, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.40/5.95 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 11.40/5.95 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 11.40/5.95 inference('cnf', [status(esa)], [associativity_of_multiply])).
% 11.40/5.95 thf(zip_derived_cl17, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.40/5.95 ((multiply @ (multiply @ X2 @ (commutator @ X1 @ X0)) @ X3)
% 11.40/5.95 = (multiply @ (commutator @ X1 @ X0) @ (multiply @ X2 @ X3)))),
% 11.40/5.95 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 11.40/5.95 thf(zip_derived_cl557, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]:
% 11.40/5.95 ((multiply @ X0 @ X1)
% 11.40/5.95 = (multiply @ (commutator @ X0 @ X0) @ (multiply @ X0 @ X1)))),
% 11.40/5.95 inference('sup+', [status(thm)], [zip_derived_cl540, zip_derived_cl17])).
% 11.40/5.95 thf(zip_derived_cl4, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.40/5.95 ((multiply @ (commutator @ X1 @ X2) @ X0)
% 11.40/5.95 = (multiply @ X0 @ (commutator @ X1 @ X2)))),
% 11.40/5.95 inference('cnf', [status(esa)], [nilpotency])).
% 11.40/5.95 thf(zip_derived_cl784, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]:
% 11.40/5.95 ((multiply @ X1 @ X0)
% 11.40/5.95 = (multiply @ (multiply @ X1 @ X0) @ (commutator @ X1 @ X1)))),
% 11.40/5.95 inference('sup+', [status(thm)], [zip_derived_cl557, zip_derived_cl4])).
% 11.40/5.95 thf(zip_derived_cl540, plain,
% 11.40/5.95 (![X0 : $i]: ((multiply @ X0 @ (commutator @ X0 @ X0)) = (X0))),
% 11.40/5.95 inference('eq_res', [status(thm)], [zip_derived_cl57])).
% 11.40/5.95 thf(zip_derived_cl2, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.40/5.95 (((multiply @ X0 @ X2) != (multiply @ X0 @ X1)) | ((X2) = (X1)))),
% 11.40/5.95 inference('cnf', [status(esa)], [left_cancellation])).
% 11.40/5.95 thf(zip_derived_cl543, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]:
% 11.40/5.95 (((multiply @ X0 @ X1) != (X0)) | ((X1) = (commutator @ X0 @ X0)))),
% 11.40/5.95 inference('sup-', [status(thm)], [zip_derived_cl540, zip_derived_cl2])).
% 11.40/5.95 thf(zip_derived_cl1055, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]:
% 11.40/5.95 (((multiply @ X1 @ X0) != (multiply @ X1 @ X0))
% 11.40/5.95 | ((commutator @ X1 @ X1)
% 11.40/5.95 = (commutator @ (multiply @ X1 @ X0) @ (multiply @ X1 @ X0))))),
% 11.40/5.95 inference('sup-', [status(thm)], [zip_derived_cl784, zip_derived_cl543])).
% 11.40/5.95 thf(zip_derived_cl1116, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]:
% 11.40/5.95 ((commutator @ X1 @ X1)
% 11.40/5.95 = (commutator @ (multiply @ X1 @ X0) @ (multiply @ X1 @ X0)))),
% 11.40/5.95 inference('simplify', [status(thm)], [zip_derived_cl1055])).
% 11.40/5.95 thf(zip_derived_cl1599, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]:
% 11.40/5.95 ((commutator @ X0 @ X0)
% 11.40/5.95 = (commutator @
% 11.40/5.95 (multiply @ X0 @ (multiply @ X1 @ (commutator @ X1 @ X0))) @
% 11.40/5.95 (multiply @ X1 @ X0)))),
% 11.40/5.95 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1116])).
% 11.40/5.95 thf(zip_derived_cl3, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]:
% 11.40/5.95 ((multiply @ X1 @ X0)
% 11.40/5.95 = (multiply @ X0 @ (multiply @ X1 @ (commutator @ X1 @ X0))))),
% 11.40/5.95 inference('cnf', [status(esa)], [commutator])).
% 11.40/5.95 thf(zip_derived_cl1116, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]:
% 11.40/5.95 ((commutator @ X1 @ X1)
% 11.40/5.95 = (commutator @ (multiply @ X1 @ X0) @ (multiply @ X1 @ X0)))),
% 11.40/5.95 inference('simplify', [status(thm)], [zip_derived_cl1055])).
% 11.40/5.95 thf(zip_derived_cl1639, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]: ((commutator @ X0 @ X0) = (commutator @ X1 @ X1))),
% 11.40/5.95 inference('demod', [status(thm)],
% 11.40/5.95 [zip_derived_cl1599, zip_derived_cl3, zip_derived_cl1116])).
% 11.40/5.95 thf(zip_derived_cl540, plain,
% 11.40/5.95 (![X0 : $i]: ((multiply @ X0 @ (commutator @ X0 @ X0)) = (X0))),
% 11.40/5.95 inference('eq_res', [status(thm)], [zip_derived_cl57])).
% 11.40/5.95 thf(zip_derived_cl1723, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ (commutator @ X0 @ X0)) = (X1))),
% 11.40/5.95 inference('sup+', [status(thm)], [zip_derived_cl1639, zip_derived_cl540])).
% 11.40/5.95 thf(zip_derived_cl0, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.40/5.95 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 11.40/5.95 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 11.40/5.95 inference('cnf', [status(esa)], [associativity_of_multiply])).
% 11.40/5.95 thf(zip_derived_cl2, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.40/5.95 (((multiply @ X0 @ X2) != (multiply @ X0 @ X1)) | ((X2) = (X1)))),
% 11.40/5.95 inference('cnf', [status(esa)], [left_cancellation])).
% 11.40/5.95 thf(zip_derived_cl59, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.40/5.95 (((multiply @ X2 @ (multiply @ X1 @ X0))
% 11.40/5.95 != (multiply @ (multiply @ X2 @ X1) @ X3))
% 11.40/5.95 | ((X0) = (X3)))),
% 11.40/5.95 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 11.40/5.95 thf(zip_derived_cl0, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.40/5.95 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 11.40/5.95 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 11.40/5.95 inference('cnf', [status(esa)], [associativity_of_multiply])).
% 11.40/5.95 thf(zip_derived_cl68, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.40/5.95 (((multiply @ X2 @ (multiply @ X1 @ X0))
% 11.40/5.95 != (multiply @ X2 @ (multiply @ X1 @ X3)))
% 11.40/5.95 | ((X0) = (X3)))),
% 11.40/5.95 inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl0])).
% 11.40/5.95 thf(zip_derived_cl1805, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.40/5.95 (((multiply @ X2 @ X0) != (multiply @ X2 @ (multiply @ X0 @ X1)))
% 11.40/5.95 | ((commutator @ X3 @ X3) = (X1)))),
% 11.40/5.95 inference('sup-', [status(thm)], [zip_derived_cl1723, zip_derived_cl68])).
% 11.40/5.95 thf(zip_derived_cl3822, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.40/5.95 (((multiply @ X0 @ X1) != (multiply @ X1 @ X0))
% 11.40/5.95 | ((commutator @ X2 @ X2) = (commutator @ X1 @ X0)))),
% 11.40/5.95 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl1805])).
% 11.40/5.95 thf(zip_derived_cl3822, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.40/5.95 (((multiply @ X0 @ X1) != (multiply @ X1 @ X0))
% 11.40/5.95 | ((commutator @ X2 @ X2) = (commutator @ X1 @ X0)))),
% 11.40/5.95 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl1805])).
% 11.40/5.95 thf(prove_commutator_is_associative, conjecture,
% 11.40/5.95 (( commutator @ ( commutator @ a @ b ) @ c ) =
% 11.40/5.95 ( commutator @ a @ ( commutator @ b @ c ) ))).
% 11.40/5.95 thf(zf_stmt_0, negated_conjecture,
% 11.40/5.95 (( commutator @ ( commutator @ a @ b ) @ c ) !=
% 11.40/5.95 ( commutator @ a @ ( commutator @ b @ c ) )),
% 11.40/5.95 inference('cnf.neg', [status(esa)], [prove_commutator_is_associative])).
% 11.40/5.95 thf(zip_derived_cl5, plain,
% 11.40/5.95 (((commutator @ (commutator @ a @ b) @ c)
% 11.40/5.95 != (commutator @ a @ (commutator @ b @ c)))),
% 11.40/5.95 inference('cnf', [status(esa)], [zf_stmt_0])).
% 11.40/5.95 thf(zip_derived_cl4413, plain,
% 11.40/5.95 (![X0 : $i]:
% 11.40/5.95 (((commutator @ X0 @ X0) != (commutator @ a @ (commutator @ b @ c)))
% 11.40/5.95 | ((multiply @ c @ (commutator @ a @ b))
% 11.40/5.95 != (multiply @ (commutator @ a @ b) @ c)))),
% 11.40/5.95 inference('sup-', [status(thm)], [zip_derived_cl3822, zip_derived_cl5])).
% 11.40/5.95 thf(zip_derived_cl4, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.40/5.95 ((multiply @ (commutator @ X1 @ X2) @ X0)
% 11.40/5.95 = (multiply @ X0 @ (commutator @ X1 @ X2)))),
% 11.40/5.95 inference('cnf', [status(esa)], [nilpotency])).
% 11.40/5.95 thf(zip_derived_cl4544, plain,
% 11.40/5.95 (![X0 : $i]:
% 11.40/5.95 (((commutator @ X0 @ X0) != (commutator @ a @ (commutator @ b @ c)))
% 11.40/5.95 | ((multiply @ (commutator @ a @ b) @ c)
% 11.40/5.95 != (multiply @ (commutator @ a @ b) @ c)))),
% 11.40/5.95 inference('demod', [status(thm)], [zip_derived_cl4413, zip_derived_cl4])).
% 11.40/5.95 thf(zip_derived_cl4545, plain,
% 11.40/5.95 (![X0 : $i]:
% 11.40/5.95 ((commutator @ X0 @ X0) != (commutator @ a @ (commutator @ b @ c)))),
% 11.40/5.95 inference('simplify', [status(thm)], [zip_derived_cl4544])).
% 11.40/5.95 thf(zip_derived_cl4572, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]:
% 11.40/5.95 (((commutator @ X1 @ X1) != (commutator @ X0 @ X0))
% 11.40/5.95 | ((multiply @ (commutator @ b @ c) @ a)
% 11.40/5.95 != (multiply @ a @ (commutator @ b @ c))))),
% 11.40/5.95 inference('sup-', [status(thm)], [zip_derived_cl3822, zip_derived_cl4545])).
% 11.40/5.95 thf(zip_derived_cl4, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.40/5.95 ((multiply @ (commutator @ X1 @ X2) @ X0)
% 11.40/5.95 = (multiply @ X0 @ (commutator @ X1 @ X2)))),
% 11.40/5.95 inference('cnf', [status(esa)], [nilpotency])).
% 11.40/5.95 thf(zip_derived_cl4577, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]:
% 11.40/5.95 (((commutator @ X1 @ X1) != (commutator @ X0 @ X0))
% 11.40/5.95 | ((multiply @ a @ (commutator @ b @ c))
% 11.40/5.95 != (multiply @ a @ (commutator @ b @ c))))),
% 11.40/5.95 inference('demod', [status(thm)], [zip_derived_cl4572, zip_derived_cl4])).
% 11.40/5.95 thf(zip_derived_cl4578, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]: ((commutator @ X1 @ X1) != (commutator @ X0 @ X0))),
% 11.40/5.95 inference('simplify', [status(thm)], [zip_derived_cl4577])).
% 11.40/5.95 thf(zip_derived_cl1639, plain,
% 11.40/5.95 (![X0 : $i, X1 : $i]: ((commutator @ X0 @ X0) = (commutator @ X1 @ X1))),
% 11.40/5.95 inference('demod', [status(thm)],
% 11.40/5.95 [zip_derived_cl1599, zip_derived_cl3, zip_derived_cl1116])).
% 11.40/5.95 thf(zip_derived_cl4579, plain, ($false),
% 11.40/5.95 inference('simplify_reflect+', [status(thm)],
% 11.40/5.95 [zip_derived_cl4578, zip_derived_cl1639])).
% 11.40/5.95
% 11.40/5.95 % SZS output end Refutation
% 11.40/5.95
% 11.40/5.95
% 11.40/5.95 % Terminating...
% 11.65/6.16 % Runner terminated.
% 11.65/6.19 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------