%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP486-1 : TPTP v9.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.b1odo7ulHP true
% Computer : n008.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 04:36:32 PM UTC 2025
% Result : Unsatisfiable 3.22s 1.48s
% Output : Refutation 3.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.19 % Problem : GRP486-1 : TPTP v9.2.0. Released v2.6.0.
% 0.11/0.20 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.b1odo7ulHP true
% 0.12/0.40 % Computer : n008.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8042.1875MB
% 0.12/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Wed Oct 1 14:20:23 EDT 2025
% 0.12/0.40 % CPUTime :
% 0.12/0.40 % Running portfolio for 300 s
% 0.12/0.40 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40 % Number of cores: 8
% 0.12/0.41 % Python version: Python 3.6.8
% 0.12/0.41 % Running in FO mode
% 0.45/0.68 % Total configuration time : 435
% 0.45/0.68 % Estimated wc time : 1092
% 0.45/0.68 % Estimated cpu time (7 cpus) : 156.0
% 0.45/0.76 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.46/0.82 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.46/0.83 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.46/0.87 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.46/0.88 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.46/0.88 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.46/0.89 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 3.22/1.48 % Solved by fo/fo5.sh.
% 3.22/1.48 % done 466 iterations in 0.427s
% 3.22/1.48 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 3.22/1.48 % SZS output start Refutation
% 3.22/1.48 thf(c3_type, type, c3: $i).
% 3.22/1.48 thf(identity_type, type, identity: $i).
% 3.22/1.48 thf(multiply_type, type, multiply: $i > $i > $i).
% 3.22/1.48 thf(b3_type, type, b3: $i).
% 3.22/1.48 thf(a3_type, type, a3: $i).
% 3.22/1.48 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 3.22/1.48 thf(inverse_type, type, inverse: $i > $i).
% 3.22/1.48 thf(prove_these_axioms_3, conjecture,
% 3.22/1.48 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 3.22/1.48 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 3.22/1.48 thf(zf_stmt_0, negated_conjecture,
% 3.22/1.48 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 3.22/1.48 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 3.22/1.48 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 3.22/1.48 thf(zip_derived_cl4, plain,
% 3.22/1.48 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.22/1.48 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 3.22/1.48 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.22/1.48 thf(single_axiom, axiom,
% 3.22/1.48 (( double_divide @
% 3.22/1.48 ( double_divide @
% 3.22/1.48 A @
% 3.22/1.48 ( double_divide @
% 3.22/1.48 ( double_divide @ ( double_divide @ A @ B ) @ C ) @
% 3.22/1.48 ( double_divide @ B @ identity ) ) ) @
% 3.22/1.48 ( double_divide @ identity @ identity ) ) =
% 3.22/1.48 ( C ))).
% 3.22/1.48 thf(zip_derived_cl0, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X1 @ X2) @ X0) @
% 3.22/1.48 (double_divide @ X2 @ identity))) @
% 3.22/1.48 (double_divide @ identity @ identity)) = (X0))),
% 3.22/1.48 inference('cnf', [status(esa)], [single_axiom])).
% 3.22/1.48 thf(inverse, axiom, (( inverse @ A ) = ( double_divide @ A @ identity ))).
% 3.22/1.48 thf(zip_derived_cl2, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [inverse])).
% 3.22/1.48 thf(zip_derived_cl2, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [inverse])).
% 3.22/1.48 thf(zip_derived_cl13, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X1 @ X2) @ X0) @ (inverse @ X2))) @
% 3.22/1.48 (inverse @ identity)) = (X0))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl13, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X1 @ X2) @ X0) @ (inverse @ X2))) @
% 3.22/1.48 (inverse @ identity)) = (X0))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl13, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X1 @ X2) @ X0) @ (inverse @ X2))) @
% 3.22/1.48 (inverse @ identity)) = (X0))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl14, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ X3 @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X3 @ X2) @ X0) @ (inverse @ X2))) @
% 3.22/1.48 (double_divide @ (double_divide @ X0 @ X1) @
% 3.22/1.48 (inverse @ (inverse @ identity)))) @
% 3.22/1.48 (inverse @ identity)) = (X1))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 3.22/1.48 thf(zip_derived_cl122, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X3 @ X0) @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X3 @ identity) @ X2) @ X0) @
% 3.22/1.48 (inverse @ X2)) @
% 3.22/1.48 X1) @
% 3.22/1.48 (inverse @ (inverse @ identity)))) @
% 3.22/1.48 (inverse @ identity)) = (X1))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl14])).
% 3.22/1.48 thf(zip_derived_cl2, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [inverse])).
% 3.22/1.48 thf(zip_derived_cl139, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X3 @ X0) @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ (inverse @ X3) @ X2) @ X0) @
% 3.22/1.48 (inverse @ X2)) @
% 3.22/1.48 X1) @
% 3.22/1.48 (inverse @ (inverse @ identity)))) @
% 3.22/1.48 (inverse @ identity)) = (X1))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl122, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl13, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X1 @ X2) @ X0) @ (inverse @ X2))) @
% 3.22/1.48 (inverse @ identity)) = (X0))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl13, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X1 @ X2) @ X0) @ (inverse @ X2))) @
% 3.22/1.48 (inverse @ identity)) = (X0))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl18, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((double_divide @ (double_divide @ X2 @ X0) @ (inverse @ identity))
% 3.22/1.48 = (double_divide @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X2 @ identity) @ X1) @ X0) @
% 3.22/1.48 (inverse @ X1)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 3.22/1.48 thf(zip_derived_cl2, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [inverse])).
% 3.22/1.48 thf(zip_derived_cl27, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((double_divide @ (double_divide @ X2 @ X0) @ (inverse @ identity))
% 3.22/1.48 = (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ (inverse @ X2) @ X1) @ X0) @
% 3.22/1.48 (inverse @ X1)))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl2])).
% 3.22/1.48 thf(identity, axiom,
% 3.22/1.48 (( identity ) = ( double_divide @ A @ ( inverse @ A ) ))).
% 3.22/1.48 thf(zip_derived_cl3, plain,
% 3.22/1.48 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.22/1.48 inference('cnf', [status(esa)], [identity])).
% 3.22/1.48 thf(multiply, axiom,
% 3.22/1.48 (( multiply @ A @ B ) =
% 3.22/1.48 ( double_divide @ ( double_divide @ B @ A ) @ identity ))).
% 3.22/1.48 thf(zip_derived_cl1, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X1 @ X0)
% 3.22/1.48 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [multiply])).
% 3.22/1.48 thf(zip_derived_cl8, plain,
% 3.22/1.48 (![X0 : $i]:
% 3.22/1.48 ((multiply @ (inverse @ X0) @ X0)
% 3.22/1.48 = (double_divide @ identity @ identity))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl2, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [inverse])).
% 3.22/1.48 thf(zip_derived_cl1, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X1 @ X0)
% 3.22/1.48 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [multiply])).
% 3.22/1.48 thf(zip_derived_cl6, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl54, plain,
% 3.22/1.48 (![X0 : $i]:
% 3.22/1.48 ((multiply @ identity @ identity)
% 3.22/1.48 = (inverse @ (multiply @ (inverse @ X0) @ X0)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl6])).
% 3.22/1.48 thf(zip_derived_cl3, plain,
% 3.22/1.48 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.22/1.48 inference('cnf', [status(esa)], [identity])).
% 3.22/1.48 thf(zip_derived_cl149, plain,
% 3.22/1.48 (![X0 : $i]:
% 3.22/1.48 ((identity)
% 3.22/1.48 = (double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 3.22/1.48 (multiply @ identity @ identity)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl3])).
% 3.22/1.48 thf(zip_derived_cl2, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [inverse])).
% 3.22/1.48 thf(zip_derived_cl1, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X1 @ X0)
% 3.22/1.48 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [multiply])).
% 3.22/1.48 thf(zip_derived_cl7, plain,
% 3.22/1.48 (![X0 : $i]:
% 3.22/1.48 ((multiply @ identity @ X0)
% 3.22/1.48 = (double_divide @ (inverse @ X0) @ identity))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl2, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [inverse])).
% 3.22/1.48 thf(zip_derived_cl10, plain,
% 3.22/1.48 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl173, plain,
% 3.22/1.48 (![X0 : $i]:
% 3.22/1.48 ((identity)
% 3.22/1.48 = (double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 3.22/1.48 (inverse @ (inverse @ identity))))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl149, zip_derived_cl10])).
% 3.22/1.48 thf(zip_derived_cl2, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [inverse])).
% 3.22/1.48 thf(zip_derived_cl13, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X1 @ X2) @ X0) @ (inverse @ X2))) @
% 3.22/1.48 (inverse @ identity)) = (X0))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl19, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @
% 3.22/1.48 (double_divide @ (inverse @ (double_divide @ X1 @ X0)) @
% 3.22/1.48 (inverse @ X0))) @
% 3.22/1.48 (inverse @ identity)) = (identity))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 3.22/1.48 thf(zip_derived_cl6, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl332, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @
% 3.22/1.48 (double_divide @ (multiply @ X0 @ X1) @ (inverse @ X0))) @
% 3.22/1.48 (inverse @ identity)) = (identity))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl6])).
% 3.22/1.48 thf(zip_derived_cl497, plain,
% 3.22/1.48 (((double_divide @ (double_divide @ identity @ identity) @
% 3.22/1.48 (inverse @ identity)) = (identity))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl173, zip_derived_cl332])).
% 3.22/1.48 thf(zip_derived_cl2, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [inverse])).
% 3.22/1.48 thf(zip_derived_cl3, plain,
% 3.22/1.48 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.22/1.48 inference('cnf', [status(esa)], [identity])).
% 3.22/1.48 thf(zip_derived_cl3, plain,
% 3.22/1.48 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.22/1.48 inference('cnf', [status(esa)], [identity])).
% 3.22/1.48 thf(zip_derived_cl13, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X1 @ X2) @ X0) @ (inverse @ X2))) @
% 3.22/1.48 (inverse @ identity)) = (X0))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl20, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @ (double_divide @ identity @ (inverse @ X0))) @
% 3.22/1.48 (inverse @ identity)) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 3.22/1.48 thf(zip_derived_cl6, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl441, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @ (double_divide @ identity @ (inverse @ X0))) @
% 3.22/1.48 (inverse @ identity)) = (multiply @ X0 @ X1))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl6])).
% 3.22/1.48 thf(zip_derived_cl457, plain,
% 3.22/1.48 (![X0 : $i]:
% 3.22/1.48 ((double_divide @ (double_divide @ X0 @ identity) @
% 3.22/1.48 (inverse @ identity)) = (multiply @ identity @ X0))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl441])).
% 3.22/1.48 thf(zip_derived_cl2, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [inverse])).
% 3.22/1.48 thf(zip_derived_cl10, plain,
% 3.22/1.48 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl461, plain,
% 3.22/1.48 (![X0 : $i]:
% 3.22/1.48 ((double_divide @ (inverse @ X0) @ (inverse @ identity))
% 3.22/1.48 = (inverse @ (inverse @ X0)))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl457, zip_derived_cl2, zip_derived_cl10])).
% 3.22/1.48 thf(zip_derived_cl514, plain,
% 3.22/1.48 (((inverse @ (inverse @ identity)) = (identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl497, zip_derived_cl2, zip_derived_cl461])).
% 3.22/1.48 thf(zip_derived_cl461, plain,
% 3.22/1.48 (![X0 : $i]:
% 3.22/1.48 ((double_divide @ (inverse @ X0) @ (inverse @ identity))
% 3.22/1.48 = (inverse @ (inverse @ X0)))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl457, zip_derived_cl2, zip_derived_cl10])).
% 3.22/1.48 thf(zip_derived_cl529, plain,
% 3.22/1.48 (((double_divide @ identity @ (inverse @ identity))
% 3.22/1.48 = (inverse @ (inverse @ (inverse @ identity))))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl514, zip_derived_cl461])).
% 3.22/1.48 thf(zip_derived_cl3, plain,
% 3.22/1.48 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.22/1.48 inference('cnf', [status(esa)], [identity])).
% 3.22/1.48 thf(zip_derived_cl514, plain,
% 3.22/1.48 (((inverse @ (inverse @ identity)) = (identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl497, zip_derived_cl2, zip_derived_cl461])).
% 3.22/1.48 thf(zip_derived_cl542, plain, (((identity) = (inverse @ identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl529, zip_derived_cl3, zip_derived_cl514])).
% 3.22/1.48 thf(zip_derived_cl1, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X1 @ X0)
% 3.22/1.48 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [multiply])).
% 3.22/1.48 thf(zip_derived_cl583, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((multiply @ X0 @ X2)
% 3.22/1.48 = (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ (inverse @ X2) @ X1) @ X0) @
% 3.22/1.48 (inverse @ X1)))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl27, zip_derived_cl542, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl542, plain, (((identity) = (inverse @ identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl529, zip_derived_cl3, zip_derived_cl514])).
% 3.22/1.48 thf(zip_derived_cl542, plain, (((identity) = (inverse @ identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl529, zip_derived_cl3, zip_derived_cl514])).
% 3.22/1.48 thf(zip_derived_cl1, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X1 @ X0)
% 3.22/1.48 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [multiply])).
% 3.22/1.48 thf(zip_derived_cl542, plain, (((identity) = (inverse @ identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl529, zip_derived_cl3, zip_derived_cl514])).
% 3.22/1.48 thf(zip_derived_cl1, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X1 @ X0)
% 3.22/1.48 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [multiply])).
% 3.22/1.48 thf(zip_derived_cl1596, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X3 : $i]:
% 3.22/1.48 ((multiply @ (multiply @ X1 @ (multiply @ X0 @ X3)) @
% 3.22/1.48 (double_divide @ X3 @ X0)) = (X1))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl139, zip_derived_cl583, zip_derived_cl542,
% 3.22/1.48 zip_derived_cl542, zip_derived_cl1, zip_derived_cl542,
% 3.22/1.48 zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl14, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ X3 @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X3 @ X2) @ X0) @ (inverse @ X2))) @
% 3.22/1.48 (double_divide @ (double_divide @ X0 @ X1) @
% 3.22/1.48 (inverse @ (inverse @ identity)))) @
% 3.22/1.48 (inverse @ identity)) = (X1))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 3.22/1.48 thf(zip_derived_cl13, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X1 @ X2) @ X0) @ (inverse @ X2))) @
% 3.22/1.48 (inverse @ identity)) = (X0))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl111, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ X3 @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X3 @ X2) @ X1) @ (inverse @ X2))) @
% 3.22/1.48 (double_divide @ X0 @
% 3.22/1.48 (inverse @
% 3.22/1.48 (double_divide @ (double_divide @ X1 @ X0) @
% 3.22/1.48 (inverse @ (inverse @ identity)))))) @
% 3.22/1.48 (inverse @ identity)) = (inverse @ identity))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl13])).
% 3.22/1.48 thf(zip_derived_cl6, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl147, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ X3 @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X3 @ X2) @ X1) @ (inverse @ X2))) @
% 3.22/1.48 (double_divide @ X0 @
% 3.22/1.48 (multiply @ (inverse @ (inverse @ identity)) @
% 3.22/1.48 (double_divide @ X1 @ X0)))) @
% 3.22/1.48 (inverse @ identity)) = (inverse @ identity))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl111, zip_derived_cl6])).
% 3.22/1.48 thf(zip_derived_cl542, plain, (((identity) = (inverse @ identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl529, zip_derived_cl3, zip_derived_cl514])).
% 3.22/1.48 thf(zip_derived_cl583, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((multiply @ X0 @ X2)
% 3.22/1.48 = (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ (inverse @ X2) @ X1) @ X0) @
% 3.22/1.48 (inverse @ X1)))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl27, zip_derived_cl542, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl589, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X0 @ X1)
% 3.22/1.48 = (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ (inverse @ X1) @ identity) @ X0) @
% 3.22/1.48 identity))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl542, zip_derived_cl583])).
% 3.22/1.48 thf(zip_derived_cl2, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [inverse])).
% 3.22/1.48 thf(zip_derived_cl1, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X1 @ X0)
% 3.22/1.48 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [multiply])).
% 3.22/1.48 thf(zip_derived_cl598, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X0 @ X1) = (multiply @ X0 @ (inverse @ (inverse @ X1))))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl589, zip_derived_cl2, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl10, plain,
% 3.22/1.48 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl619, plain,
% 3.22/1.48 (![X0 : $i]:
% 3.22/1.48 ((multiply @ identity @ X0)
% 3.22/1.48 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl598, zip_derived_cl10])).
% 3.22/1.48 thf(zip_derived_cl10, plain,
% 3.22/1.48 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl624, plain,
% 3.22/1.48 (![X0 : $i]:
% 3.22/1.48 ((inverse @ (inverse @ X0))
% 3.22/1.48 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl619, zip_derived_cl10])).
% 3.22/1.48 thf(zip_derived_cl3, plain,
% 3.22/1.48 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.22/1.48 inference('cnf', [status(esa)], [identity])).
% 3.22/1.48 thf(zip_derived_cl6, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl33, plain,
% 3.22/1.48 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 3.22/1.48 thf(zip_derived_cl13, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X1 @ X2) @ X0) @ (inverse @ X2))) @
% 3.22/1.48 (inverse @ identity)) = (X0))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl38, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X2 @
% 3.22/1.48 (double_divide @
% 3.22/1.48 (double_divide @ (double_divide @ X2 @ identity) @ X1) @
% 3.22/1.48 (multiply @ (inverse @ X0) @ X0))) @
% 3.22/1.48 (inverse @ identity)) = (X1))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl33, zip_derived_cl13])).
% 3.22/1.48 thf(zip_derived_cl2, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [inverse])).
% 3.22/1.48 thf(zip_derived_cl44, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X2 @
% 3.22/1.48 (double_divide @ (double_divide @ (inverse @ X2) @ X1) @
% 3.22/1.48 (multiply @ (inverse @ X0) @ X0))) @
% 3.22/1.48 (inverse @ identity)) = (X1))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl38, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl33, plain,
% 3.22/1.48 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 3.22/1.48 thf(zip_derived_cl542, plain, (((identity) = (inverse @ identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl529, zip_derived_cl3, zip_derived_cl514])).
% 3.22/1.48 thf(zip_derived_cl547, plain,
% 3.22/1.48 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl542])).
% 3.22/1.48 thf(zip_derived_cl1, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X1 @ X0)
% 3.22/1.48 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [multiply])).
% 3.22/1.48 thf(zip_derived_cl542, plain, (((identity) = (inverse @ identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl529, zip_derived_cl3, zip_derived_cl514])).
% 3.22/1.48 thf(zip_derived_cl1, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X1 @ X0)
% 3.22/1.48 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [multiply])).
% 3.22/1.48 thf(zip_derived_cl1156, plain,
% 3.22/1.48 (![X1 : $i, X2 : $i]:
% 3.22/1.48 ((multiply @ (multiply @ X1 @ (inverse @ X2)) @ X2) = (X1))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl44, zip_derived_cl547, zip_derived_cl1,
% 3.22/1.48 zip_derived_cl542, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl1179, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ (multiply @ X1 @ (inverse @ (inverse @ X0))) @
% 3.22/1.48 (inverse @ (inverse @ (inverse @ X0)))) = (X1))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl624, zip_derived_cl1156])).
% 3.22/1.48 thf(zip_derived_cl598, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X0 @ X1) = (multiply @ X0 @ (inverse @ (inverse @ X1))))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl589, zip_derived_cl2, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl598, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X0 @ X1) = (multiply @ X0 @ (inverse @ (inverse @ X1))))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl589, zip_derived_cl2, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl1184, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl1179, zip_derived_cl598, zip_derived_cl598])).
% 3.22/1.48 thf(zip_derived_cl332, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @
% 3.22/1.48 (double_divide @ (multiply @ X0 @ X1) @ (inverse @ X0))) @
% 3.22/1.48 (inverse @ identity)) = (identity))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl6])).
% 3.22/1.48 thf(zip_derived_cl542, plain, (((identity) = (inverse @ identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl529, zip_derived_cl3, zip_derived_cl514])).
% 3.22/1.48 thf(zip_derived_cl1, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X1 @ X0)
% 3.22/1.48 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [multiply])).
% 3.22/1.48 thf(zip_derived_cl551, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @
% 3.22/1.48 (double_divide @ (multiply @ X0 @ X1) @ (inverse @ X0)) @ X1)
% 3.22/1.48 = (identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl332, zip_derived_cl542, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl1184, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl1179, zip_derived_cl598, zip_derived_cl598])).
% 3.22/1.48 thf(zip_derived_cl1348, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ identity @ (inverse @ X1))
% 3.22/1.48 = (double_divide @ (multiply @ X0 @ X1) @ (inverse @ X0)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl551, zip_derived_cl1184])).
% 3.22/1.48 thf(zip_derived_cl10, plain,
% 3.22/1.48 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 3.22/1.48 thf(zip_derived_cl624, plain,
% 3.22/1.48 (![X0 : $i]:
% 3.22/1.48 ((inverse @ (inverse @ X0))
% 3.22/1.48 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl619, zip_derived_cl10])).
% 3.22/1.48 thf(zip_derived_cl441, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((double_divide @
% 3.22/1.48 (double_divide @ X1 @ (double_divide @ identity @ (inverse @ X0))) @
% 3.22/1.48 (inverse @ identity)) = (multiply @ X0 @ X1))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl6])).
% 3.22/1.48 thf(zip_derived_cl542, plain, (((identity) = (inverse @ identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl529, zip_derived_cl3, zip_derived_cl514])).
% 3.22/1.48 thf(zip_derived_cl1, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X1 @ X0)
% 3.22/1.48 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [multiply])).
% 3.22/1.48 thf(zip_derived_cl552, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ (double_divide @ identity @ (inverse @ X0)) @ X1)
% 3.22/1.48 = (multiply @ X0 @ X1))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl441, zip_derived_cl542, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl1156, plain,
% 3.22/1.48 (![X1 : $i, X2 : $i]:
% 3.22/1.48 ((multiply @ (multiply @ X1 @ (inverse @ X2)) @ X2) = (X1))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl44, zip_derived_cl547, zip_derived_cl1,
% 3.22/1.48 zip_derived_cl542, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl1168, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0)
% 3.22/1.48 = (double_divide @ identity @ (inverse @ X1)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl552, zip_derived_cl1156])).
% 3.22/1.48 thf(zip_derived_cl1156, plain,
% 3.22/1.48 (![X1 : $i, X2 : $i]:
% 3.22/1.48 ((multiply @ (multiply @ X1 @ (inverse @ X2)) @ X2) = (X1))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl44, zip_derived_cl547, zip_derived_cl1,
% 3.22/1.48 zip_derived_cl542, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl1180, plain,
% 3.22/1.48 (![X1 : $i]: ((X1) = (double_divide @ identity @ (inverse @ X1)))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl1168, zip_derived_cl1156])).
% 3.22/1.48 thf(zip_derived_cl1222, plain,
% 3.22/1.48 (![X0 : $i]:
% 3.22/1.48 ((inverse @ (inverse @ (inverse @ X0)))
% 3.22/1.48 = (double_divide @ identity @ (inverse @ (inverse @ X0))))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl624, zip_derived_cl1180])).
% 3.22/1.48 thf(zip_derived_cl1180, plain,
% 3.22/1.48 (![X1 : $i]: ((X1) = (double_divide @ identity @ (inverse @ X1)))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl1168, zip_derived_cl1156])).
% 3.22/1.48 thf(zip_derived_cl1224, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl1222, zip_derived_cl1180])).
% 3.22/1.48 thf(zip_derived_cl1180, plain,
% 3.22/1.48 (![X1 : $i]: ((X1) = (double_divide @ identity @ (inverse @ X1)))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl1168, zip_derived_cl1156])).
% 3.22/1.48 thf(zip_derived_cl1254, plain,
% 3.22/1.48 (![X0 : $i]:
% 3.22/1.48 ((inverse @ (inverse @ X0))
% 3.22/1.48 = (double_divide @ identity @ (inverse @ X0)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl1224, zip_derived_cl1180])).
% 3.22/1.48 thf(zip_derived_cl1180, plain,
% 3.22/1.48 (![X1 : $i]: ((X1) = (double_divide @ identity @ (inverse @ X1)))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl1168, zip_derived_cl1156])).
% 3.22/1.48 thf(zip_derived_cl1269, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl1254, zip_derived_cl1180])).
% 3.22/1.48 thf(zip_derived_cl1271, plain,
% 3.22/1.48 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1269])).
% 3.22/1.48 thf(zip_derived_cl1357, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((inverse @ X1)
% 3.22/1.48 = (double_divide @ (multiply @ X0 @ X1) @ (inverse @ X0)))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl1348, zip_derived_cl1271])).
% 3.22/1.48 thf(zip_derived_cl1581, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((inverse @ (inverse @ X1))
% 3.22/1.48 = (double_divide @ X0 @ (inverse @ (multiply @ X0 @ X1))))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl1184, zip_derived_cl1357])).
% 3.22/1.48 thf(zip_derived_cl1269, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl1254, zip_derived_cl1180])).
% 3.22/1.48 thf(zip_derived_cl6, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl1269, plain,
% 3.22/1.48 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl1254, zip_derived_cl1180])).
% 3.22/1.48 thf(zip_derived_cl1281, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1269])).
% 3.22/1.48 thf(zip_derived_cl1590, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((X1) = (double_divide @ X0 @ (double_divide @ X1 @ X0)))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl1581, zip_derived_cl1269, zip_derived_cl1281])).
% 3.22/1.48 thf(zip_derived_cl6, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl1659, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ (double_divide @ X0 @ X1) @ X1) = (inverse @ X0))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl1590, zip_derived_cl6])).
% 3.22/1.48 thf(zip_derived_cl1156, plain,
% 3.22/1.48 (![X1 : $i, X2 : $i]:
% 3.22/1.48 ((multiply @ (multiply @ X1 @ (inverse @ X2)) @ X2) = (X1))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl44, zip_derived_cl547, zip_derived_cl1,
% 3.22/1.48 zip_derived_cl542, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl1857, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ (inverse @ X0) @ X1)
% 3.22/1.48 = (double_divide @ X0 @ (inverse @ X1)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl1659, zip_derived_cl1156])).
% 3.22/1.48 thf(zip_derived_cl6, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl542, plain, (((identity) = (inverse @ identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl529, zip_derived_cl3, zip_derived_cl514])).
% 3.22/1.48 thf(zip_derived_cl542, plain, (((identity) = (inverse @ identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl529, zip_derived_cl3, zip_derived_cl514])).
% 3.22/1.48 thf(zip_derived_cl1271, plain,
% 3.22/1.48 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1269])).
% 3.22/1.48 thf(zip_derived_cl1590, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((X1) = (double_divide @ X0 @ (double_divide @ X1 @ X0)))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl1581, zip_derived_cl1269, zip_derived_cl1281])).
% 3.22/1.48 thf(zip_derived_cl542, plain, (((identity) = (inverse @ identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl529, zip_derived_cl3, zip_derived_cl514])).
% 3.22/1.48 thf(zip_derived_cl1, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X1 @ X0)
% 3.22/1.48 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.22/1.48 inference('cnf', [status(esa)], [multiply])).
% 3.22/1.48 thf(zip_derived_cl542, plain, (((identity) = (inverse @ identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl529, zip_derived_cl3, zip_derived_cl514])).
% 3.22/1.48 thf(zip_derived_cl2754, plain,
% 3.22/1.48 (![X1 : $i, X2 : $i, X3 : $i]:
% 3.22/1.48 ((multiply @ X1 @
% 3.22/1.48 (double_divide @ X3 @
% 3.22/1.48 (multiply @ (multiply @ X1 @ (double_divide @ X3 @ X2)) @ X2)))
% 3.22/1.48 = (identity))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl147, zip_derived_cl1857, zip_derived_cl6,
% 3.22/1.48 zip_derived_cl542, zip_derived_cl542, zip_derived_cl1271,
% 3.22/1.48 zip_derived_cl1590, zip_derived_cl542, zip_derived_cl1,
% 3.22/1.48 zip_derived_cl542])).
% 3.22/1.48 thf(zip_derived_cl1184, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl1179, zip_derived_cl598, zip_derived_cl598])).
% 3.22/1.48 thf(zip_derived_cl2757, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((multiply @ identity @
% 3.22/1.48 (inverse @
% 3.22/1.48 (double_divide @ X2 @
% 3.22/1.48 (multiply @ (multiply @ X0 @ (double_divide @ X2 @ X1)) @ X1))))
% 3.22/1.48 = (X0))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl2754, zip_derived_cl1184])).
% 3.22/1.48 thf(zip_derived_cl6, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i]:
% 3.22/1.48 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.22/1.48 thf(zip_derived_cl1271, plain,
% 3.22/1.48 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl1269])).
% 3.22/1.48 thf(zip_derived_cl2848, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((multiply @
% 3.22/1.48 (multiply @ (multiply @ X0 @ (double_divide @ X2 @ X1)) @ X1) @ X2)
% 3.22/1.48 = (X0))),
% 3.22/1.48 inference('demod', [status(thm)],
% 3.22/1.48 [zip_derived_cl2757, zip_derived_cl6, zip_derived_cl1271])).
% 3.22/1.48 thf(zip_derived_cl3524, plain,
% 3.22/1.48 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.22/1.48 ((multiply @ (multiply @ X0 @ X2) @ X1)
% 3.22/1.48 = (multiply @ X0 @ (multiply @ X2 @ X1)))),
% 3.22/1.48 inference('sup+', [status(thm)], [zip_derived_cl1596, zip_derived_cl2848])).
% 3.22/1.48 thf(zip_derived_cl3590, plain,
% 3.22/1.48 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 3.22/1.48 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 3.22/1.48 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl3524])).
% 3.22/1.48 thf(zip_derived_cl3591, plain, ($false),
% 3.22/1.48 inference('simplify', [status(thm)], [zip_derived_cl3590])).
% 3.22/1.48
% 3.22/1.48 % SZS output end Refutation
% 3.22/1.48
% 3.22/1.48
% 3.22/1.48 % Terminating...
% 3.67/1.70 % Runner terminated.
% 3.67/1.74 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------