TSTP Solution File: GRP495-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP495-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.M71kpTZNps true
% Computer : n021.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 01:51:52 EDT 2023
% Result : Unsatisfiable 0.57s 1.05s
% Output : Refutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP495-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.M71kpTZNps true
% 0.13/0.35 % Computer : n021.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 : Tue Aug 29 02:40:44 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.49/0.65 % Total configuration time : 435
% 0.49/0.65 % Estimated wc time : 1092
% 0.49/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.49/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.57/1.05 % Solved by fo/fo5.sh.
% 0.57/1.05 % done 449 iterations in 0.262s
% 0.57/1.05 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.57/1.05 % SZS output start Refutation
% 0.57/1.05 thf(c3_type, type, c3: $i).
% 0.57/1.05 thf(multiply_type, type, multiply: $i > $i > $i).
% 0.57/1.05 thf(b3_type, type, b3: $i).
% 0.57/1.05 thf(a3_type, type, a3: $i).
% 0.57/1.05 thf(identity_type, type, identity: $i).
% 0.57/1.05 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 0.57/1.05 thf(inverse_type, type, inverse: $i > $i).
% 0.57/1.05 thf(prove_these_axioms_3, conjecture,
% 0.57/1.05 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 0.57/1.05 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 0.57/1.05 thf(zf_stmt_0, negated_conjecture,
% 0.57/1.05 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 0.57/1.05 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 0.57/1.05 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 0.57/1.05 thf(zip_derived_cl4, plain,
% 0.57/1.05 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 0.57/1.05 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 0.57/1.05 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/1.05 thf(inverse, axiom, (( inverse @ A ) = ( double_divide @ A @ identity ))).
% 0.57/1.05 thf(zip_derived_cl2, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [inverse])).
% 0.57/1.05 thf(multiply, axiom,
% 0.57/1.05 (( multiply @ A @ B ) =
% 0.57/1.05 ( double_divide @ ( double_divide @ B @ A ) @ identity ))).
% 0.57/1.05 thf(zip_derived_cl1, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X1 @ X0)
% 0.57/1.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [multiply])).
% 0.57/1.05 thf(zip_derived_cl6, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.57/1.05 thf(identity, axiom,
% 0.57/1.05 (( identity ) = ( double_divide @ A @ ( inverse @ A ) ))).
% 0.57/1.05 thf(zip_derived_cl3, plain,
% 0.57/1.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.57/1.05 inference('cnf', [status(esa)], [identity])).
% 0.57/1.05 thf(single_axiom, axiom,
% 0.57/1.05 (( double_divide @
% 0.57/1.05 ( double_divide @ identity @ A ) @
% 0.57/1.05 ( double_divide @
% 0.57/1.05 ( double_divide @
% 0.57/1.05 ( double_divide @ B @ C ) @ ( double_divide @ identity @ identity ) ) @
% 0.57/1.05 ( double_divide @ A @ C ) ) ) =
% 0.57/1.05 ( B ))).
% 0.57/1.05 thf(zip_derived_cl0, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X1) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (double_divide @ X0 @ X2) @
% 0.57/1.05 (double_divide @ identity @ identity)) @
% 0.57/1.05 (double_divide @ X1 @ X2)))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('cnf', [status(esa)], [single_axiom])).
% 0.57/1.05 thf(zip_derived_cl2, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [inverse])).
% 0.57/1.05 thf(zip_derived_cl13, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X1) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (double_divide @ X0 @ X2) @ (inverse @ identity)) @
% 0.57/1.05 (double_divide @ X1 @ X2)))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 0.57/1.05 thf(zip_derived_cl22, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X1) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ identity @ (inverse @ identity)) @
% 0.57/1.05 (double_divide @ X1 @ (inverse @ X0))))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 0.57/1.05 thf(zip_derived_cl3, plain,
% 0.57/1.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.57/1.05 inference('cnf', [status(esa)], [identity])).
% 0.57/1.05 thf(zip_derived_cl31, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X1) @
% 0.57/1.05 (double_divide @ identity @ (double_divide @ X1 @ (inverse @ X0))))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl22, zip_derived_cl3])).
% 0.57/1.05 thf(zip_derived_cl3, plain,
% 0.57/1.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.57/1.05 inference('cnf', [status(esa)], [identity])).
% 0.57/1.05 thf(zip_derived_cl6, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl36, plain,
% 0.57/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 0.57/1.05 thf(zip_derived_cl36, plain,
% 0.57/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 0.57/1.05 thf(zip_derived_cl3, plain,
% 0.57/1.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.57/1.05 inference('cnf', [status(esa)], [identity])).
% 0.57/1.05 thf(zip_derived_cl39, plain,
% 0.57/1.05 (![X0 : $i]:
% 0.57/1.05 ((identity)
% 0.57/1.05 = (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0)))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl3])).
% 0.57/1.05 thf(zip_derived_cl2, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [inverse])).
% 0.57/1.05 thf(zip_derived_cl13, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X1) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (double_divide @ X0 @ X2) @ (inverse @ identity)) @
% 0.57/1.05 (double_divide @ X1 @ X2)))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 0.57/1.05 thf(zip_derived_cl25, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ (inverse @ identity) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (double_divide @ X0 @ X1) @ (inverse @ identity)) @
% 0.57/1.05 (double_divide @ identity @ X1)))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 0.57/1.05 thf(zip_derived_cl536, plain,
% 0.57/1.05 (![X0 : $i]:
% 0.57/1.05 ((double_divide @ (inverse @ identity) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ identity @ (inverse @ identity)) @
% 0.57/1.05 (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0))))
% 0.57/1.05 = (identity))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl25])).
% 0.57/1.05 thf(zip_derived_cl3, plain,
% 0.57/1.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.57/1.05 inference('cnf', [status(esa)], [identity])).
% 0.57/1.05 thf(zip_derived_cl39, plain,
% 0.57/1.05 (![X0 : $i]:
% 0.57/1.05 ((identity)
% 0.57/1.05 = (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0)))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl3])).
% 0.57/1.05 thf(zip_derived_cl2, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [inverse])).
% 0.57/1.05 thf(zip_derived_cl549, plain,
% 0.57/1.05 (((double_divide @ (inverse @ identity) @ (inverse @ identity))
% 0.57/1.05 = (identity))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl536, zip_derived_cl3, zip_derived_cl39,
% 0.57/1.05 zip_derived_cl2])).
% 0.57/1.05 thf(zip_derived_cl25, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ (inverse @ identity) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (double_divide @ X0 @ X1) @ (inverse @ identity)) @
% 0.57/1.05 (double_divide @ identity @ X1)))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 0.57/1.05 thf(zip_derived_cl565, plain,
% 0.57/1.05 (((double_divide @ (inverse @ identity) @
% 0.57/1.05 (double_divide @ (double_divide @ identity @ (inverse @ identity)) @
% 0.57/1.05 (double_divide @ identity @ (inverse @ identity))))
% 0.57/1.05 = (inverse @ identity))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl549, zip_derived_cl25])).
% 0.57/1.05 thf(zip_derived_cl3, plain,
% 0.57/1.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.57/1.05 inference('cnf', [status(esa)], [identity])).
% 0.57/1.05 thf(zip_derived_cl3, plain,
% 0.57/1.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.57/1.05 inference('cnf', [status(esa)], [identity])).
% 0.57/1.05 thf(zip_derived_cl2, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [inverse])).
% 0.57/1.05 thf(zip_derived_cl549, plain,
% 0.57/1.05 (((double_divide @ (inverse @ identity) @ (inverse @ identity))
% 0.57/1.05 = (identity))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl536, zip_derived_cl3, zip_derived_cl39,
% 0.57/1.05 zip_derived_cl2])).
% 0.57/1.05 thf(zip_derived_cl581, plain, (((identity) = (inverse @ identity))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl565, zip_derived_cl3, zip_derived_cl3,
% 0.57/1.05 zip_derived_cl2, zip_derived_cl549])).
% 0.57/1.05 thf(zip_derived_cl587, plain,
% 0.57/1.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl581])).
% 0.57/1.05 thf(zip_derived_cl3, plain,
% 0.57/1.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.57/1.05 inference('cnf', [status(esa)], [identity])).
% 0.57/1.05 thf(zip_derived_cl13, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X1) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (double_divide @ X0 @ X2) @ (inverse @ identity)) @
% 0.57/1.05 (double_divide @ X1 @ X2)))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 0.57/1.05 thf(zip_derived_cl18, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X1) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (double_divide @ X0 @ (inverse @ X1)) @
% 0.57/1.05 (inverse @ identity)) @
% 0.57/1.05 identity))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 0.57/1.05 thf(zip_derived_cl1, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X1 @ X0)
% 0.57/1.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [multiply])).
% 0.57/1.05 thf(zip_derived_cl28, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X1) @
% 0.57/1.05 (multiply @ (inverse @ identity) @
% 0.57/1.05 (double_divide @ X0 @ (inverse @ X1))))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl581, plain, (((identity) = (inverse @ identity))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl565, zip_derived_cl3, zip_derived_cl3,
% 0.57/1.05 zip_derived_cl2, zip_derived_cl549])).
% 0.57/1.05 thf(zip_derived_cl1, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X1 @ X0)
% 0.57/1.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [multiply])).
% 0.57/1.05 thf(zip_derived_cl1, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X1 @ X0)
% 0.57/1.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [multiply])).
% 0.57/1.05 thf(zip_derived_cl9, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 0.57/1.05 = (double_divide @ (multiply @ X1 @ X0) @ identity))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl2, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [inverse])).
% 0.57/1.05 thf(zip_derived_cl11, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 0.57/1.05 = (inverse @ (multiply @ X1 @ X0)))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 0.57/1.05 thf(zip_derived_cl677, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X1) @
% 0.57/1.05 (inverse @ (multiply @ (inverse @ X1) @ X0))) = (X0))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl28, zip_derived_cl581, zip_derived_cl11])).
% 0.57/1.05 thf(zip_derived_cl682, plain,
% 0.57/1.05 (![X0 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X0) @
% 0.57/1.05 (inverse @ identity)) = (X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl587, zip_derived_cl677])).
% 0.57/1.05 thf(zip_derived_cl581, plain, (((identity) = (inverse @ identity))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl565, zip_derived_cl3, zip_derived_cl3,
% 0.57/1.05 zip_derived_cl2, zip_derived_cl549])).
% 0.57/1.05 thf(zip_derived_cl1, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X1 @ X0)
% 0.57/1.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [multiply])).
% 0.57/1.05 thf(zip_derived_cl690, plain,
% 0.57/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl682, zip_derived_cl581, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl6, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl3, plain,
% 0.57/1.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.57/1.05 inference('cnf', [status(esa)], [identity])).
% 0.57/1.05 thf(zip_derived_cl34, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((identity)
% 0.57/1.05 = (double_divide @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ X0)))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 0.57/1.05 thf(zip_derived_cl697, plain,
% 0.57/1.05 (![X0 : $i]:
% 0.57/1.05 ((identity) = (double_divide @ (double_divide @ identity @ X0) @ X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl690, zip_derived_cl34])).
% 0.57/1.05 thf(zip_derived_cl1, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X1 @ X0)
% 0.57/1.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [multiply])).
% 0.57/1.05 thf(zip_derived_cl703, plain,
% 0.57/1.05 (![X0 : $i]:
% 0.57/1.05 ((multiply @ X0 @ (double_divide @ identity @ X0))
% 0.57/1.05 = (double_divide @ identity @ identity))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl697, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl581, plain, (((identity) = (inverse @ identity))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl565, zip_derived_cl3, zip_derived_cl3,
% 0.57/1.05 zip_derived_cl2, zip_derived_cl549])).
% 0.57/1.05 thf(zip_derived_cl3, plain,
% 0.57/1.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 0.57/1.05 inference('cnf', [status(esa)], [identity])).
% 0.57/1.05 thf(zip_derived_cl593, plain,
% 0.57/1.05 (((identity) = (double_divide @ identity @ identity))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl581, zip_derived_cl3])).
% 0.57/1.05 thf(zip_derived_cl715, plain,
% 0.57/1.05 (![X0 : $i]:
% 0.57/1.05 ((multiply @ X0 @ (double_divide @ identity @ X0)) = (identity))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl703, zip_derived_cl593])).
% 0.57/1.05 thf(zip_derived_cl677, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X1) @
% 0.57/1.05 (inverse @ (multiply @ (inverse @ X1) @ X0))) = (X0))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl28, zip_derived_cl581, zip_derived_cl11])).
% 0.57/1.05 thf(zip_derived_cl722, plain,
% 0.57/1.05 (![X0 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X0) @
% 0.57/1.05 (inverse @ identity)) = (double_divide @ identity @ (inverse @ X0)))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl715, zip_derived_cl677])).
% 0.57/1.05 thf(zip_derived_cl581, plain, (((identity) = (inverse @ identity))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl565, zip_derived_cl3, zip_derived_cl3,
% 0.57/1.05 zip_derived_cl2, zip_derived_cl549])).
% 0.57/1.05 thf(zip_derived_cl1, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X1 @ X0)
% 0.57/1.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [multiply])).
% 0.57/1.05 thf(zip_derived_cl690, plain,
% 0.57/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl682, zip_derived_cl581, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl732, plain,
% 0.57/1.05 (![X0 : $i]: ((X0) = (double_divide @ identity @ (inverse @ X0)))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl722, zip_derived_cl581, zip_derived_cl1,
% 0.57/1.05 zip_derived_cl690])).
% 0.57/1.05 thf(zip_derived_cl581, plain, (((identity) = (inverse @ identity))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl565, zip_derived_cl3, zip_derived_cl3,
% 0.57/1.05 zip_derived_cl2, zip_derived_cl549])).
% 0.57/1.05 thf(zip_derived_cl2, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [inverse])).
% 0.57/1.05 thf(zip_derived_cl13, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X1) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (double_divide @ X0 @ X2) @ (inverse @ identity)) @
% 0.57/1.05 (double_divide @ X1 @ X2)))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 0.57/1.05 thf(zip_derived_cl17, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X0) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (double_divide @ X1 @ identity) @
% 0.57/1.05 (inverse @ identity)) @
% 0.57/1.05 (inverse @ X0)))
% 0.57/1.05 = (X1))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 0.57/1.05 thf(zip_derived_cl2, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [inverse])).
% 0.57/1.05 thf(zip_derived_cl27, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X0) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (inverse @ X1) @ (inverse @ identity)) @
% 0.57/1.05 (inverse @ X0)))
% 0.57/1.05 = (X1))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl2])).
% 0.57/1.05 thf(zip_derived_cl581, plain, (((identity) = (inverse @ identity))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl565, zip_derived_cl3, zip_derived_cl3,
% 0.57/1.05 zip_derived_cl2, zip_derived_cl549])).
% 0.57/1.05 thf(zip_derived_cl2, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [inverse])).
% 0.57/1.05 thf(zip_derived_cl635, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X0) @
% 0.57/1.05 (double_divide @ (inverse @ (inverse @ X1)) @ (inverse @ X0)))
% 0.57/1.05 = (X1))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl27, zip_derived_cl581, zip_derived_cl2])).
% 0.57/1.05 thf(zip_derived_cl642, plain,
% 0.57/1.05 (![X0 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ identity) @
% 0.57/1.05 (double_divide @ (inverse @ (inverse @ X0)) @ identity)) = (
% 0.57/1.05 X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl581, zip_derived_cl635])).
% 0.57/1.05 thf(zip_derived_cl593, plain,
% 0.57/1.05 (((identity) = (double_divide @ identity @ identity))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl581, zip_derived_cl3])).
% 0.57/1.05 thf(zip_derived_cl2, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [inverse])).
% 0.57/1.05 thf(zip_derived_cl648, plain,
% 0.57/1.05 (![X0 : $i]:
% 0.57/1.05 ((double_divide @ identity @ (inverse @ (inverse @ (inverse @ X0))))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl642, zip_derived_cl593, zip_derived_cl2])).
% 0.57/1.05 thf(zip_derived_cl741, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl732, zip_derived_cl648])).
% 0.57/1.05 thf(zip_derived_cl732, plain,
% 0.57/1.05 (![X0 : $i]: ((X0) = (double_divide @ identity @ (inverse @ X0)))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl722, zip_derived_cl581, zip_derived_cl1,
% 0.57/1.05 zip_derived_cl690])).
% 0.57/1.05 thf(zip_derived_cl753, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl732])).
% 0.57/1.05 thf(zip_derived_cl753, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl732])).
% 0.57/1.05 thf(zip_derived_cl6, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl884, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X1))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl31, zip_derived_cl753, zip_derived_cl753,
% 0.57/1.05 zip_derived_cl6])).
% 0.57/1.05 thf(zip_derived_cl690, plain,
% 0.57/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl682, zip_derived_cl581, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl1, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X1 @ X0)
% 0.57/1.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [multiply])).
% 0.57/1.05 thf(zip_derived_cl13, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X1) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (double_divide @ X0 @ X2) @ (inverse @ identity)) @
% 0.57/1.05 (double_divide @ X1 @ X2)))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 0.57/1.05 thf(zip_derived_cl20, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((double_divide @
% 0.57/1.05 (double_divide @ identity @ (double_divide @ X0 @ X1)) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (double_divide @ X2 @ identity) @
% 0.57/1.05 (inverse @ identity)) @
% 0.57/1.05 (multiply @ X1 @ X0)))
% 0.57/1.05 = (X2))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl13])).
% 0.57/1.05 thf(zip_derived_cl2, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [inverse])).
% 0.57/1.05 thf(zip_derived_cl29, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((double_divide @
% 0.57/1.05 (double_divide @ identity @ (double_divide @ X0 @ X1)) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (inverse @ X2) @ (inverse @ identity)) @
% 0.57/1.05 (multiply @ X1 @ X0)))
% 0.57/1.05 = (X2))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl2])).
% 0.57/1.05 thf(zip_derived_cl753, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl732])).
% 0.57/1.05 thf(zip_derived_cl6, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl581, plain, (((identity) = (inverse @ identity))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl565, zip_derived_cl3, zip_derived_cl3,
% 0.57/1.05 zip_derived_cl2, zip_derived_cl549])).
% 0.57/1.05 thf(zip_derived_cl2, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [inverse])).
% 0.57/1.05 thf(zip_derived_cl741, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl732, zip_derived_cl648])).
% 0.57/1.05 thf(zip_derived_cl777, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((double_divide @ (multiply @ X1 @ X0) @
% 0.57/1.05 (double_divide @ X2 @ (multiply @ X1 @ X0))) = (X2))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl29, zip_derived_cl753, zip_derived_cl6,
% 0.57/1.05 zip_derived_cl581, zip_derived_cl2, zip_derived_cl741])).
% 0.57/1.05 thf(zip_derived_cl783, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ (multiply @ X0 @ identity) @
% 0.57/1.05 (double_divide @ X1 @ X0)) = (X1))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl690, zip_derived_cl777])).
% 0.57/1.05 thf(zip_derived_cl690, plain,
% 0.57/1.05 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl682, zip_derived_cl581, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl789, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ X0 @ (double_divide @ X1 @ X0)) = (X1))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl783, zip_derived_cl690])).
% 0.57/1.05 thf(zip_derived_cl6, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl869, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ (double_divide @ X0 @ X1) @ X1) = (inverse @ X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl789, zip_derived_cl6])).
% 0.57/1.05 thf(zip_derived_cl942, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1))
% 0.57/1.05 = (inverse @ (inverse @ X1)))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl884, zip_derived_cl869])).
% 0.57/1.05 thf(zip_derived_cl741, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl732, zip_derived_cl648])).
% 0.57/1.05 thf(zip_derived_cl950, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)) = (X1))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl942, zip_derived_cl741])).
% 0.57/1.05 thf(zip_derived_cl962, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((multiply @ (double_divide @ X0 @ X1) @
% 0.57/1.05 (multiply @ (multiply @ X1 @ X0) @ X2)) = (X2))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl950])).
% 0.57/1.05 thf(zip_derived_cl789, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ X0 @ (double_divide @ X1 @ X0)) = (X1))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl783, zip_derived_cl690])).
% 0.57/1.05 thf(zip_derived_cl13, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ identity @ X1) @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (double_divide @ X0 @ X2) @ (inverse @ identity)) @
% 0.57/1.05 (double_divide @ X1 @ X2)))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 0.57/1.05 thf(zip_derived_cl1, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X1 @ X0)
% 0.57/1.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [multiply])).
% 0.57/1.05 thf(zip_derived_cl16, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((multiply @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (double_divide @ X0 @ X1) @ (inverse @ identity)) @
% 0.57/1.05 (double_divide @ X2 @ X1)) @
% 0.57/1.05 (double_divide @ identity @ X2)) = (double_divide @ X0 @ identity))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl2, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [inverse])).
% 0.57/1.05 thf(zip_derived_cl33, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((multiply @
% 0.57/1.05 (double_divide @
% 0.57/1.05 (double_divide @ (double_divide @ X0 @ X1) @ (inverse @ identity)) @
% 0.57/1.05 (double_divide @ X2 @ X1)) @
% 0.57/1.05 (double_divide @ identity @ X2)) = (inverse @ X0))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl2])).
% 0.57/1.05 thf(zip_derived_cl581, plain, (((identity) = (inverse @ identity))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl565, zip_derived_cl3, zip_derived_cl3,
% 0.57/1.05 zip_derived_cl2, zip_derived_cl549])).
% 0.57/1.05 thf(zip_derived_cl1, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X1 @ X0)
% 0.57/1.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 0.57/1.05 inference('cnf', [status(esa)], [multiply])).
% 0.57/1.05 thf(zip_derived_cl753, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl732])).
% 0.57/1.05 thf(zip_derived_cl1023, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((multiply @
% 0.57/1.05 (double_divide @ (multiply @ X1 @ X0) @ (double_divide @ X2 @ X1)) @
% 0.57/1.05 (inverse @ X2)) = (inverse @ X0))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl33, zip_derived_cl581, zip_derived_cl1,
% 0.57/1.05 zip_derived_cl753])).
% 0.57/1.05 thf(zip_derived_cl789, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ X0 @ (double_divide @ X1 @ X0)) = (X1))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl783, zip_derived_cl690])).
% 0.57/1.05 thf(zip_derived_cl789, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ X0 @ (double_divide @ X1 @ X0)) = (X1))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl783, zip_derived_cl690])).
% 0.57/1.05 thf(zip_derived_cl870, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((double_divide @ (double_divide @ X0 @ X1) @ X0) = (X1))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl789, zip_derived_cl789])).
% 0.57/1.05 thf(zip_derived_cl6, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl908, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X1 @ (double_divide @ X1 @ X0)) = (inverse @ X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl870, zip_derived_cl6])).
% 0.57/1.05 thf(zip_derived_cl950, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)) = (X1))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl942, zip_derived_cl741])).
% 0.57/1.05 thf(zip_derived_cl1000, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X1 @ (inverse @ X0))
% 0.57/1.05 = (double_divide @ (inverse @ X1) @ X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl908, zip_derived_cl950])).
% 0.57/1.05 thf(zip_derived_cl6, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl1158, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X0 @ (inverse @ X1))
% 0.57/1.05 = (inverse @ (multiply @ X1 @ (inverse @ X0))))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl1000, zip_derived_cl6])).
% 0.57/1.05 thf(zip_derived_cl2029, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((multiply @ X1 @
% 0.57/1.05 (inverse @
% 0.57/1.05 (double_divide @ (multiply @ X2 @ X0) @ (double_divide @ X1 @ X2))))
% 0.57/1.05 = (inverse @ (inverse @ X0)))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl1023, zip_derived_cl1158])).
% 0.57/1.05 thf(zip_derived_cl6, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i]:
% 0.57/1.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 0.57/1.05 thf(zip_derived_cl741, plain,
% 0.57/1.05 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl732, zip_derived_cl648])).
% 0.57/1.05 thf(zip_derived_cl2043, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((multiply @ X1 @
% 0.57/1.05 (multiply @ (double_divide @ X1 @ X2) @ (multiply @ X2 @ X0)))
% 0.57/1.05 = (X0))),
% 0.57/1.05 inference('demod', [status(thm)],
% 0.57/1.05 [zip_derived_cl2029, zip_derived_cl6, zip_derived_cl741])).
% 0.57/1.05 thf(zip_derived_cl2903, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((multiply @ X2 @
% 0.57/1.05 (multiply @ X0 @ (multiply @ (double_divide @ X0 @ X2) @ X1)))
% 0.57/1.05 = (X1))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl789, zip_derived_cl2043])).
% 0.57/1.05 thf(zip_derived_cl3354, plain,
% 0.57/1.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/1.05 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 0.57/1.05 = (multiply @ (multiply @ X2 @ X1) @ X0))),
% 0.57/1.05 inference('sup+', [status(thm)], [zip_derived_cl962, zip_derived_cl2903])).
% 0.57/1.05 thf(zip_derived_cl3432, plain,
% 0.57/1.05 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 0.57/1.05 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 0.57/1.05 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl3354])).
% 0.57/1.05 thf(zip_derived_cl3433, plain, ($false),
% 0.57/1.05 inference('simplify', [status(thm)], [zip_derived_cl3432])).
% 0.57/1.05
% 0.57/1.05 % SZS output end Refutation
% 0.57/1.05
% 0.57/1.05
% 0.57/1.05 % Terminating...
% 0.57/1.07 % Runner terminated.
% 1.97/1.08 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------