%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP075-1 : TPTP v9.2.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.SCclqFYanE true
% Computer : n009.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 04:35:34 PM UTC 2025
% Result : Unsatisfiable 0.58s 1.13s
% Output : Refutation 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP075-1 : TPTP v9.2.0. Bugfixed v2.3.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.SCclqFYanE true
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 14:15:08 EDT 2025
% 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
% 0.13/0.35 % Running in FO mode
% 0.56/0.65 % Total configuration time : 435
% 0.56/0.65 % Estimated wc time : 1092
% 0.56/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.58/1.13 % Solved by fo/fo5.sh.
% 0.58/1.13 % done 479 iterations in 0.362s
% 0.58/1.13 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.58/1.13 % SZS output start Refutation
% 0.58/1.13 thf(a2_type, type, a2: $i).
% 0.58/1.13 thf(inverse_type, type, inverse: $i > $i).
% 0.58/1.13 thf(identity_type, type, identity: $i).
% 0.58/1.13 thf(b3_type, type, b3: $i).
% 0.58/1.13 thf(a1_type, type, a1: $i).
% 0.58/1.13 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 0.58/1.13 thf(c3_type, type, c3: $i).
% 0.58/1.13 thf(a3_type, type, a3: $i).
% 0.58/1.13 thf(multiply_type, type, multiply: $i > $i > $i).
% 0.58/1.13 thf(prove_these_axioms, conjecture,
% 0.58/1.13 (~( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 0.58/1.13 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 0.58/1.13 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 0.58/1.13 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) ) ))).
% 0.58/1.13 thf(zf_stmt_0, negated_conjecture,
% 0.58/1.13 (( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 0.58/1.13 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 0.58/1.13 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 0.58/1.13 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) )),
% 0.58/1.13 inference('cnf.neg', [status(esa)], [prove_these_axioms])).
% 0.58/1.13 thf(zip_derived_cl4, plain,
% 0.58/1.13 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.58/1.13 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 0.58/1.13 | ((multiply @ identity @ a2) != (a2))
% 0.58/1.13 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 0.58/1.13 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.58/1.13 thf(inverse, axiom, (( inverse @ X ) = ( double_divide @ X @ identity ))).
% 0.58/1.13 thf(zip_derived_cl2, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [inverse])).
% 0.58/1.13 thf(multiply, axiom,
% 0.58/1.13 (( multiply @ X @ Y ) =
% 0.58/1.13 ( double_divide @ ( double_divide @ Y @ X ) @ identity ))).
% 0.58/1.13 thf(zip_derived_cl1, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X1 @ X0)
% 0.58/1.13 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [multiply])).
% 0.58/1.13 thf(zip_derived_cl7, plain,
% 0.58/1.13 (![X0 : $i]:
% 0.58/1.13 ((multiply @ identity @ X0)
% 0.58/1.13 = (double_divide @ (inverse @ X0) @ identity))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.58/1.13 thf(zip_derived_cl2, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [inverse])).
% 0.58/1.13 thf(zip_derived_cl10, plain,
% 0.58/1.13 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.58/1.13 thf(zip_derived_cl23, plain,
% 0.58/1.13 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.58/1.13 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 0.58/1.13 | ((inverse @ (inverse @ a2)) != (a2))
% 0.58/1.13 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl10])).
% 0.58/1.13 thf(identity, axiom,
% 0.58/1.13 (( identity ) = ( double_divide @ X @ ( inverse @ X ) ))).
% 0.58/1.13 thf(zip_derived_cl3, plain,
% 0.58/1.13 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.58/1.13 inference('cnf', [status(esa)], [identity])).
% 0.58/1.13 thf(zip_derived_cl2, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [inverse])).
% 0.58/1.13 thf(zip_derived_cl1, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X1 @ X0)
% 0.58/1.13 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [multiply])).
% 0.58/1.13 thf(zip_derived_cl6, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.58/1.13 thf(zip_derived_cl29, plain,
% 0.58/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 0.58/1.13 thf(zip_derived_cl66, plain,
% 0.58/1.13 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.58/1.13 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 0.58/1.13 | ((inverse @ (inverse @ a2)) != (a2))
% 0.58/1.13 | ((inverse @ identity) != (identity)))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl23, zip_derived_cl29])).
% 0.58/1.13 thf(zip_derived_cl29, plain,
% 0.58/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 0.58/1.13 thf(zip_derived_cl3, plain,
% 0.58/1.13 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.58/1.13 inference('cnf', [status(esa)], [identity])).
% 0.58/1.13 thf(single_axiom, axiom,
% 0.58/1.13 (( double_divide @
% 0.58/1.13 ( double_divide @
% 0.58/1.13 ( double_divide @ X @ ( double_divide @ Y @ identity ) ) @
% 0.58/1.13 ( double_divide @
% 0.58/1.13 ( double_divide @
% 0.58/1.13 Z @ ( double_divide @ U @ ( double_divide @ U @ identity ) ) ) @
% 0.58/1.13 ( double_divide @ X @ identity ) ) ) @
% 0.58/1.13 Y ) =
% 0.58/1.13 ( Z ))).
% 0.58/1.13 thf(zip_derived_cl0, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.58/1.13 ((double_divide @
% 0.58/1.13 (double_divide @
% 0.58/1.13 (double_divide @ X1 @ (double_divide @ X2 @ identity)) @
% 0.58/1.13 (double_divide @
% 0.58/1.13 (double_divide @ X0 @
% 0.58/1.13 (double_divide @ X3 @ (double_divide @ X3 @ identity))) @
% 0.58/1.13 (double_divide @ X1 @ identity))) @
% 0.58/1.13 X2) = (X0))),
% 0.58/1.13 inference('cnf', [status(esa)], [single_axiom])).
% 0.58/1.13 thf(zip_derived_cl2, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [inverse])).
% 0.58/1.13 thf(zip_derived_cl2, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [inverse])).
% 0.58/1.13 thf(zip_derived_cl3, plain,
% 0.58/1.13 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.58/1.13 inference('cnf', [status(esa)], [identity])).
% 0.58/1.13 thf(zip_derived_cl2, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [inverse])).
% 0.58/1.13 thf(zip_derived_cl2, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [inverse])).
% 0.58/1.13 thf(zip_derived_cl13, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/1.13 ((double_divide @
% 0.58/1.13 (double_divide @ (double_divide @ X1 @ (inverse @ X2)) @
% 0.58/1.13 (double_divide @ (inverse @ X0) @ (inverse @ X1))) @
% 0.58/1.13 X2) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2,
% 0.58/1.13 zip_derived_cl3, zip_derived_cl2, zip_derived_cl2])).
% 0.58/1.13 thf(zip_derived_cl18, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((double_divide @
% 0.58/1.13 (double_divide @
% 0.58/1.13 (double_divide @ (inverse @ X0) @ (inverse @ X1)) @ identity) @
% 0.58/1.13 X1) = (X0))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 0.58/1.13 thf(zip_derived_cl1, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X1 @ X0)
% 0.58/1.13 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [multiply])).
% 0.58/1.13 thf(zip_derived_cl21, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((double_divide @ (multiply @ (inverse @ X1) @ (inverse @ X0)) @ X1)
% 0.58/1.13 = (X0))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl1])).
% 0.58/1.13 thf(zip_derived_cl116, plain,
% 0.58/1.13 (![X0 : $i]:
% 0.58/1.13 ((double_divide @ (inverse @ identity) @ (inverse @ X0)) = (X0))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl21])).
% 0.58/1.13 thf(zip_derived_cl3, plain,
% 0.58/1.13 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.58/1.13 inference('cnf', [status(esa)], [identity])).
% 0.58/1.13 thf(zip_derived_cl188, plain, (((identity) = (inverse @ identity))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl116, zip_derived_cl3])).
% 0.58/1.13 thf(zip_derived_cl205, plain,
% 0.58/1.13 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.58/1.13 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 0.58/1.13 | ((inverse @ (inverse @ a2)) != (a2))
% 0.58/1.13 | ((identity) != (identity)))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl66, zip_derived_cl188])).
% 0.58/1.13 thf(zip_derived_cl206, plain,
% 0.58/1.13 ((((inverse @ (inverse @ a2)) != (a2))
% 0.58/1.13 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.58/1.13 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 0.58/1.13 inference('simplify', [status(thm)], [zip_derived_cl205])).
% 0.58/1.13 thf(zip_derived_cl188, plain, (((identity) = (inverse @ identity))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl116, zip_derived_cl3])).
% 0.58/1.13 thf(zip_derived_cl13, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/1.13 ((double_divide @
% 0.58/1.13 (double_divide @ (double_divide @ X1 @ (inverse @ X2)) @
% 0.58/1.13 (double_divide @ (inverse @ X0) @ (inverse @ X1))) @
% 0.58/1.13 X2) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2,
% 0.58/1.13 zip_derived_cl3, zip_derived_cl2, zip_derived_cl2])).
% 0.58/1.13 thf(zip_derived_cl1, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X1 @ X0)
% 0.58/1.13 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [multiply])).
% 0.58/1.13 thf(zip_derived_cl17, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ (double_divide @ (inverse @ X0) @ (inverse @ X1)) @
% 0.58/1.13 (double_divide @ X1 @ (inverse @ identity))) = (X0))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 0.58/1.13 thf(zip_derived_cl188, plain, (((identity) = (inverse @ identity))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl116, zip_derived_cl3])).
% 0.58/1.13 thf(zip_derived_cl2, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [inverse])).
% 0.58/1.13 thf(zip_derived_cl339, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ (double_divide @ (inverse @ X0) @ (inverse @ X1)) @
% 0.58/1.13 (inverse @ X1)) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl17, zip_derived_cl188, zip_derived_cl2])).
% 0.58/1.13 thf(zip_derived_cl341, plain,
% 0.58/1.13 (![X0 : $i]:
% 0.58/1.13 ((multiply @
% 0.58/1.13 (double_divide @ (inverse @ X0) @ (inverse @ identity)) @ identity)
% 0.58/1.13 = (X0))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl188, zip_derived_cl339])).
% 0.58/1.13 thf(zip_derived_cl188, plain, (((identity) = (inverse @ identity))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl116, zip_derived_cl3])).
% 0.58/1.13 thf(zip_derived_cl2, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [inverse])).
% 0.58/1.13 thf(zip_derived_cl21, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((double_divide @ (multiply @ (inverse @ X1) @ (inverse @ X0)) @ X1)
% 0.58/1.13 = (X0))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl1])).
% 0.58/1.13 thf(zip_derived_cl2, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [inverse])).
% 0.58/1.13 thf(zip_derived_cl113, plain,
% 0.58/1.13 (![X0 : $i]:
% 0.58/1.13 ((inverse @ (multiply @ (inverse @ identity) @ (inverse @ X0))) = (X0))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl2])).
% 0.58/1.13 thf(zip_derived_cl188, plain, (((identity) = (inverse @ identity))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl116, zip_derived_cl3])).
% 0.58/1.13 thf(zip_derived_cl10, plain,
% 0.58/1.13 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.58/1.13 thf(zip_derived_cl207, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X0)))) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl113, zip_derived_cl188, zip_derived_cl10])).
% 0.58/1.13 thf(zip_derived_cl116, plain,
% 0.58/1.13 (![X0 : $i]:
% 0.58/1.13 ((double_divide @ (inverse @ identity) @ (inverse @ X0)) = (X0))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl21])).
% 0.58/1.13 thf(zip_derived_cl188, plain, (((identity) = (inverse @ identity))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl116, zip_derived_cl3])).
% 0.58/1.13 thf(zip_derived_cl208, plain,
% 0.58/1.13 (![X0 : $i]: ((double_divide @ identity @ (inverse @ X0)) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl116, zip_derived_cl188])).
% 0.58/1.13 thf(zip_derived_cl6, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.58/1.13 thf(zip_derived_cl241, plain,
% 0.58/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ identity) = (inverse @ X0))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl208, zip_derived_cl6])).
% 0.58/1.13 thf(zip_derived_cl310, plain,
% 0.58/1.13 (![X0 : $i]:
% 0.58/1.13 ((multiply @ X0 @ identity)
% 0.58/1.13 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl207, zip_derived_cl241])).
% 0.58/1.13 thf(zip_derived_cl207, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X0)))) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl113, zip_derived_cl188, zip_derived_cl10])).
% 0.58/1.13 thf(zip_derived_cl313, plain,
% 0.58/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl310, zip_derived_cl207])).
% 0.58/1.13 thf(zip_derived_cl351, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl341, zip_derived_cl188, zip_derived_cl2,
% 0.58/1.13 zip_derived_cl313])).
% 0.58/1.13 thf(zip_derived_cl358, plain,
% 0.58/1.13 ((((a2) != (a2))
% 0.58/1.13 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.58/1.13 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl206, zip_derived_cl351])).
% 0.58/1.13 thf(zip_derived_cl359, plain,
% 0.58/1.13 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.58/1.13 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 0.58/1.13 inference('simplify', [status(thm)], [zip_derived_cl358])).
% 0.58/1.13 thf(zip_derived_cl351, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl341, zip_derived_cl188, zip_derived_cl2,
% 0.58/1.13 zip_derived_cl313])).
% 0.58/1.13 thf(zip_derived_cl207, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X0)))) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl113, zip_derived_cl188, zip_derived_cl10])).
% 0.58/1.13 thf(zip_derived_cl339, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ (double_divide @ (inverse @ X0) @ (inverse @ X1)) @
% 0.58/1.13 (inverse @ X1)) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl17, zip_derived_cl188, zip_derived_cl2])).
% 0.58/1.13 thf(zip_derived_cl342, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @
% 0.58/1.13 (double_divide @ (inverse @ X1) @
% 0.58/1.13 (inverse @ (inverse @ (inverse @ (inverse @ X0))))) @
% 0.58/1.13 X0) = (X1))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl207, zip_derived_cl339])).
% 0.58/1.13 thf(zip_derived_cl207, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X0)))) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl113, zip_derived_cl188, zip_derived_cl10])).
% 0.58/1.13 thf(zip_derived_cl352, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ (double_divide @ (inverse @ X1) @ X0) @ X0) = (X1))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl342, zip_derived_cl207])).
% 0.58/1.13 thf(zip_derived_cl351, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl341, zip_derived_cl188, zip_derived_cl2,
% 0.58/1.13 zip_derived_cl313])).
% 0.58/1.13 thf(zip_derived_cl351, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl341, zip_derived_cl188, zip_derived_cl2,
% 0.58/1.13 zip_derived_cl313])).
% 0.58/1.13 thf(zip_derived_cl21, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((double_divide @ (multiply @ (inverse @ X1) @ (inverse @ X0)) @ X1)
% 0.58/1.13 = (X0))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl1])).
% 0.58/1.13 thf(zip_derived_cl6, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.58/1.13 thf(zip_derived_cl112, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ (inverse @ X0)))
% 0.58/1.13 = (inverse @ X0))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl6])).
% 0.58/1.13 thf(zip_derived_cl509, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0))
% 0.58/1.13 = (inverse @ (inverse @ X0)))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl112])).
% 0.58/1.13 thf(zip_derived_cl351, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl341, zip_derived_cl188, zip_derived_cl2,
% 0.58/1.13 zip_derived_cl313])).
% 0.58/1.13 thf(zip_derived_cl519, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl509, zip_derived_cl351])).
% 0.58/1.13 thf(zip_derived_cl532, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl519])).
% 0.58/1.13 thf(zip_derived_cl638, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ (inverse @ (double_divide @ (inverse @ X0) @ X1)) @ X0)
% 0.58/1.13 = (X1))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl352, zip_derived_cl532])).
% 0.58/1.13 thf(zip_derived_cl6, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.58/1.13 thf(zip_derived_cl651, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl638, zip_derived_cl6])).
% 0.58/1.13 thf(zip_derived_cl734, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl651])).
% 0.58/1.13 thf(zip_derived_cl13, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/1.13 ((double_divide @
% 0.58/1.13 (double_divide @ (double_divide @ X1 @ (inverse @ X2)) @
% 0.58/1.13 (double_divide @ (inverse @ X0) @ (inverse @ X1))) @
% 0.58/1.13 X2) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2,
% 0.58/1.13 zip_derived_cl3, zip_derived_cl2, zip_derived_cl2])).
% 0.58/1.13 thf(zip_derived_cl1, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X1 @ X0)
% 0.58/1.13 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [multiply])).
% 0.58/1.13 thf(zip_derived_cl1, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X1 @ X0)
% 0.58/1.13 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [multiply])).
% 0.58/1.13 thf(zip_derived_cl9, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 0.58/1.13 = (double_divide @ (multiply @ X1 @ X0) @ identity))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl1])).
% 0.58/1.13 thf(zip_derived_cl2, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.58/1.13 inference('cnf', [status(esa)], [inverse])).
% 0.58/1.13 thf(zip_derived_cl11, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 0.58/1.13 = (inverse @ (multiply @ X1 @ X0)))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 0.58/1.13 thf(zip_derived_cl100, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/1.13 ((multiply @ identity @ X0)
% 0.58/1.13 = (inverse @
% 0.58/1.13 (multiply @ X2 @
% 0.58/1.13 (double_divide @ (double_divide @ X1 @ (inverse @ X2)) @
% 0.58/1.13 (double_divide @ (inverse @ X0) @ (inverse @ X1))))))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl11])).
% 0.58/1.13 thf(zip_derived_cl10, plain,
% 0.58/1.13 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 0.58/1.13 thf(zip_derived_cl105, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/1.13 ((inverse @ (inverse @ X0))
% 0.58/1.13 = (inverse @
% 0.58/1.13 (multiply @ X2 @
% 0.58/1.13 (double_divide @ (double_divide @ X1 @ (inverse @ X2)) @
% 0.58/1.13 (double_divide @ (inverse @ X0) @ (inverse @ X1))))))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl100, zip_derived_cl10])).
% 0.58/1.13 thf(zip_derived_cl351, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl341, zip_derived_cl188, zip_derived_cl2,
% 0.58/1.13 zip_derived_cl313])).
% 0.58/1.13 thf(zip_derived_cl351, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl341, zip_derived_cl188, zip_derived_cl2,
% 0.58/1.13 zip_derived_cl313])).
% 0.58/1.13 thf(zip_derived_cl352, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ (double_divide @ (inverse @ X1) @ X0) @ X0) = (X1))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl342, zip_derived_cl207])).
% 0.58/1.13 thf(zip_derived_cl647, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ (double_divide @ X0 @ X1) @ X1) = (inverse @ X0))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl352])).
% 0.58/1.13 thf(zip_derived_cl651, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl638, zip_derived_cl6])).
% 0.58/1.13 thf(zip_derived_cl875, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ (inverse @ X0) @ X1)
% 0.58/1.13 = (double_divide @ X0 @ (inverse @ X1)))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl647, zip_derived_cl651])).
% 0.58/1.13 thf(zip_derived_cl352, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ (double_divide @ (inverse @ X1) @ X0) @ X0) = (X1))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl342, zip_derived_cl207])).
% 0.58/1.13 thf(zip_derived_cl734, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl651])).
% 0.58/1.13 thf(zip_derived_cl754, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X0 @ (inverse @ X1))
% 0.58/1.13 = (double_divide @ (inverse @ X0) @ X1))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl352, zip_derived_cl734])).
% 0.58/1.13 thf(zip_derived_cl351, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl341, zip_derived_cl188, zip_derived_cl2,
% 0.58/1.13 zip_derived_cl313])).
% 0.58/1.13 thf(zip_derived_cl6, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.58/1.13 thf(zip_derived_cl351, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl341, zip_derived_cl188, zip_derived_cl2,
% 0.58/1.13 zip_derived_cl313])).
% 0.58/1.13 thf(zip_derived_cl375, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl351])).
% 0.58/1.13 thf(zip_derived_cl1920, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/1.13 ((X0)
% 0.58/1.13 = (double_divide @
% 0.58/1.13 (double_divide @ (multiply @ (inverse @ X1) @ X2) @
% 0.58/1.13 (multiply @ X0 @ X1)) @
% 0.58/1.13 X2))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl105, zip_derived_cl351, zip_derived_cl875,
% 0.58/1.13 zip_derived_cl754, zip_derived_cl351, zip_derived_cl375])).
% 0.58/1.13 thf(zip_derived_cl1944, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/1.13 ((multiply @ X0 @ X2)
% 0.58/1.13 = (double_divide @
% 0.58/1.13 (double_divide @ (multiply @ (inverse @ (inverse @ X2)) @ X1) @
% 0.58/1.13 X0) @
% 0.58/1.13 X1))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl734, zip_derived_cl1920])).
% 0.58/1.13 thf(zip_derived_cl351, plain,
% 0.58/1.13 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.58/1.13 inference('demod', [status(thm)],
% 0.58/1.13 [zip_derived_cl341, zip_derived_cl188, zip_derived_cl2,
% 0.58/1.13 zip_derived_cl313])).
% 0.58/1.13 thf(zip_derived_cl1970, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/1.13 ((multiply @ X0 @ X2)
% 0.58/1.13 = (double_divide @ (double_divide @ (multiply @ X2 @ X1) @ X0) @ X1))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl1944, zip_derived_cl351])).
% 0.58/1.13 thf(zip_derived_cl647, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ (double_divide @ X0 @ X1) @ X1) = (inverse @ X0))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl352])).
% 0.58/1.13 thf(zip_derived_cl4081, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/1.13 ((multiply @ (multiply @ X1 @ X0) @ X2)
% 0.58/1.13 = (inverse @ (double_divide @ (multiply @ X0 @ X2) @ X1)))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl1970, zip_derived_cl647])).
% 0.58/1.13 thf(zip_derived_cl6, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i]:
% 0.58/1.13 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.58/1.13 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.58/1.13 thf(zip_derived_cl4171, plain,
% 0.58/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.58/1.13 ((multiply @ (multiply @ X1 @ X0) @ X2)
% 0.58/1.13 = (multiply @ X1 @ (multiply @ X0 @ X2)))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl4081, zip_derived_cl6])).
% 0.58/1.13 thf(zip_derived_cl4321, plain,
% 0.58/1.13 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 0.58/1.13 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 0.58/1.13 inference('demod', [status(thm)], [zip_derived_cl359, zip_derived_cl4171])).
% 0.58/1.13 thf(zip_derived_cl4322, plain, ($false),
% 0.58/1.13 inference('simplify', [status(thm)], [zip_derived_cl4321])).
% 0.58/1.13
% 0.58/1.13 % SZS output end Refutation
% 0.58/1.13
% 0.58/1.13
% 0.58/1.13 % Terminating...
% 4.41/1.25 % Runner terminated.
% 4.41/1.26 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------