TSTP Solution File: GRP102-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP102-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Ly2S8KuopJ true
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:49:56 EDT 2023
% Result : Unsatisfiable 24.00s 4.05s
% Output : Refutation 24.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP102-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.10/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Ly2S8KuopJ true
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 01:14:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.54/0.62 % Total configuration time : 435
% 0.54/0.62 % Estimated wc time : 1092
% 0.54/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.57/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.57/0.70 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.57/0.71 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.57/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.57/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.57/0.74 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 24.00/4.05 % Solved by fo/fo5.sh.
% 24.00/4.05 % done 1308 iterations in 3.271s
% 24.00/4.05 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 24.00/4.05 % SZS output start Refutation
% 24.00/4.05 thf(a3_type, type, a3: $i).
% 24.00/4.05 thf(identity_type, type, identity: $i).
% 24.00/4.05 thf(multiply_type, type, multiply: $i > $i > $i).
% 24.00/4.05 thf(c3_type, type, c3: $i).
% 24.00/4.05 thf(a2_type, type, a2: $i).
% 24.00/4.05 thf(a1_type, type, a1: $i).
% 24.00/4.05 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 24.00/4.05 thf(inverse_type, type, inverse: $i > $i).
% 24.00/4.05 thf(b4_type, type, b4: $i).
% 24.00/4.05 thf(a4_type, type, a4: $i).
% 24.00/4.05 thf(b3_type, type, b3: $i).
% 24.00/4.05 thf(prove_these_axioms, conjecture,
% 24.00/4.05 (~( ( ( multiply @ a4 @ b4 ) != ( multiply @ b4 @ a4 ) ) |
% 24.00/4.05 ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 24.00/4.05 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 24.00/4.05 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 24.00/4.05 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) ) ))).
% 24.00/4.05 thf(zf_stmt_0, negated_conjecture,
% 24.00/4.05 (( ( multiply @ a4 @ b4 ) != ( multiply @ b4 @ a4 ) ) |
% 24.00/4.05 ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 24.00/4.05 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 24.00/4.05 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 24.00/4.05 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) )),
% 24.00/4.05 inference('cnf.neg', [status(esa)], [prove_these_axioms])).
% 24.00/4.05 thf(zip_derived_cl4, plain,
% 24.00/4.05 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 24.00/4.05 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 24.00/4.05 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 24.00/4.05 | ((multiply @ identity @ a2) != (a2))
% 24.00/4.05 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 24.00/4.05 inference('cnf', [status(esa)], [zf_stmt_0])).
% 24.00/4.05 thf(inverse, axiom, (( inverse @ X ) = ( double_divide @ X @ identity ))).
% 24.00/4.05 thf(zip_derived_cl2, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [inverse])).
% 24.00/4.05 thf(multiply, axiom,
% 24.00/4.05 (( multiply @ X @ Y ) =
% 24.00/4.05 ( double_divide @ ( double_divide @ Y @ X ) @ identity ))).
% 24.00/4.05 thf(zip_derived_cl1, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ X0)
% 24.00/4.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [multiply])).
% 24.00/4.05 thf(zip_derived_cl7, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((multiply @ identity @ X0)
% 24.00/4.05 = (double_divide @ (inverse @ X0) @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl2, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [inverse])).
% 24.00/4.05 thf(zip_derived_cl10, plain,
% 24.00/4.05 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl28, plain,
% 24.00/4.05 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 24.00/4.05 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 24.00/4.05 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 24.00/4.05 | ((inverse @ (inverse @ a2)) != (a2))
% 24.00/4.05 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl10])).
% 24.00/4.05 thf(identity, axiom,
% 24.00/4.05 (( identity ) = ( double_divide @ X @ ( inverse @ X ) ))).
% 24.00/4.05 thf(zip_derived_cl3, plain,
% 24.00/4.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 24.00/4.05 inference('cnf', [status(esa)], [identity])).
% 24.00/4.05 thf(zip_derived_cl2, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [inverse])).
% 24.00/4.05 thf(zip_derived_cl1, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ X0)
% 24.00/4.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [multiply])).
% 24.00/4.05 thf(zip_derived_cl6, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl32, plain,
% 24.00/4.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 24.00/4.05 thf(zip_derived_cl68, plain,
% 24.00/4.05 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 24.00/4.05 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 24.00/4.05 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 24.00/4.05 | ((inverse @ (inverse @ a2)) != (a2))
% 24.00/4.05 | ((inverse @ identity) != (identity)))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl28, zip_derived_cl32])).
% 24.00/4.05 thf(zip_derived_cl3, plain,
% 24.00/4.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 24.00/4.05 inference('cnf', [status(esa)], [identity])).
% 24.00/4.05 thf(zip_derived_cl3, plain,
% 24.00/4.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 24.00/4.05 inference('cnf', [status(esa)], [identity])).
% 24.00/4.05 thf(single_axiom, axiom,
% 24.00/4.05 (( double_divide @
% 24.00/4.05 ( double_divide @
% 24.00/4.05 X @
% 24.00/4.05 ( double_divide @
% 24.00/4.05 ( double_divide @ ( double_divide @ Y @ X ) @ Z ) @
% 24.00/4.05 ( double_divide @ Y @ identity ) ) ) @
% 24.00/4.05 ( double_divide @ identity @ identity ) ) =
% 24.00/4.05 ( Z ))).
% 24.00/4.05 thf(zip_derived_cl0, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X1 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X2 @ X1) @ X0) @
% 24.00/4.05 (double_divide @ X2 @ identity))) @
% 24.00/4.05 (double_divide @ identity @ identity)) = (X0))),
% 24.00/4.05 inference('cnf', [status(esa)], [single_axiom])).
% 24.00/4.05 thf(zip_derived_cl2, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [inverse])).
% 24.00/4.05 thf(zip_derived_cl2, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [inverse])).
% 24.00/4.05 thf(zip_derived_cl13, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X1 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl20, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X0 @ (double_divide @ identity @ (inverse @ X1))) @
% 24.00/4.05 (inverse @ identity)) = (inverse @ (double_divide @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 24.00/4.05 thf(zip_derived_cl6, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl651, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X0 @ (double_divide @ identity @ (inverse @ X1))) @
% 24.00/4.05 (inverse @ identity)) = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl6])).
% 24.00/4.05 thf(zip_derived_cl672, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((double_divide @ (double_divide @ X0 @ identity) @
% 24.00/4.05 (inverse @ identity)) = (multiply @ X0 @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl651])).
% 24.00/4.05 thf(zip_derived_cl2, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [inverse])).
% 24.00/4.05 thf(zip_derived_cl676, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((double_divide @ (inverse @ X0) @ (inverse @ identity))
% 24.00/4.05 = (multiply @ X0 @ identity))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl672, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl3, plain,
% 24.00/4.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 24.00/4.05 inference('cnf', [status(esa)], [identity])).
% 24.00/4.05 thf(zip_derived_cl1, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ X0)
% 24.00/4.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [multiply])).
% 24.00/4.05 thf(zip_derived_cl8, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((multiply @ (inverse @ X0) @ X0)
% 24.00/4.05 = (double_divide @ identity @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl6, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl52, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((multiply @ identity @ identity)
% 24.00/4.05 = (inverse @ (multiply @ (inverse @ X0) @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl6])).
% 24.00/4.05 thf(zip_derived_cl3, plain,
% 24.00/4.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 24.00/4.05 inference('cnf', [status(esa)], [identity])).
% 24.00/4.05 thf(zip_derived_cl69, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((identity)
% 24.00/4.05 = (double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 24.00/4.05 (multiply @ identity @ identity)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl3])).
% 24.00/4.05 thf(zip_derived_cl10, plain,
% 24.00/4.05 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl88, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((identity)
% 24.00/4.05 = (double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 24.00/4.05 (inverse @ (inverse @ identity))))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl10])).
% 24.00/4.05 thf(zip_derived_cl2, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [inverse])).
% 24.00/4.05 thf(zip_derived_cl13, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X1 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl19, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X0 @
% 24.00/4.05 (double_divide @ (inverse @ (double_divide @ X1 @ X0)) @
% 24.00/4.05 (inverse @ X1))) @
% 24.00/4.05 (inverse @ identity)) = (identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 24.00/4.05 thf(zip_derived_cl6, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl503, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X0 @
% 24.00/4.05 (double_divide @ (multiply @ X0 @ X1) @ (inverse @ X1))) @
% 24.00/4.05 (inverse @ identity)) = (identity))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl6])).
% 24.00/4.05 thf(zip_derived_cl522, plain,
% 24.00/4.05 (((double_divide @
% 24.00/4.05 (double_divide @ (inverse @ (inverse @ identity)) @ identity) @
% 24.00/4.05 (inverse @ identity)) = (identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl88, zip_derived_cl503])).
% 24.00/4.05 thf(zip_derived_cl2, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [inverse])).
% 24.00/4.05 thf(zip_derived_cl538, plain,
% 24.00/4.05 (((double_divide @ (inverse @ (inverse @ (inverse @ identity))) @
% 24.00/4.05 (inverse @ identity)) = (identity))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl522, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl698, plain,
% 24.00/4.05 (((multiply @ (inverse @ (inverse @ identity)) @ identity) = (identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl676, zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl6, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl32, plain,
% 24.00/4.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 24.00/4.05 thf(zip_derived_cl40, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X1 @ X0) @ (double_divide @ X0 @ X1))
% 24.00/4.05 = (inverse @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl32])).
% 24.00/4.05 thf(zip_derived_cl710, plain,
% 24.00/4.05 (((multiply @ identity @
% 24.00/4.05 (double_divide @ identity @ (inverse @ (inverse @ identity))))
% 24.00/4.05 = (inverse @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl698, zip_derived_cl40])).
% 24.00/4.05 thf(zip_derived_cl503, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X0 @
% 24.00/4.05 (double_divide @ (multiply @ X0 @ X1) @ (inverse @ X1))) @
% 24.00/4.05 (inverse @ identity)) = (identity))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl6])).
% 24.00/4.05 thf(zip_derived_cl879, plain,
% 24.00/4.05 (((double_divide @
% 24.00/4.05 (double_divide @ identity @
% 24.00/4.05 (double_divide @ (inverse @ identity) @
% 24.00/4.05 (inverse @
% 24.00/4.05 (double_divide @ identity @ (inverse @ (inverse @ identity)))))) @
% 24.00/4.05 (inverse @ identity)) = (identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl710, zip_derived_cl503])).
% 24.00/4.05 thf(zip_derived_cl698, plain,
% 24.00/4.05 (((multiply @ (inverse @ (inverse @ identity)) @ identity) = (identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl676, zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl6, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl3, plain,
% 24.00/4.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 24.00/4.05 inference('cnf', [status(esa)], [identity])).
% 24.00/4.05 thf(zip_derived_cl29, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((identity)
% 24.00/4.05 = (double_divide @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 24.00/4.05 thf(zip_derived_cl709, plain,
% 24.00/4.05 (((identity)
% 24.00/4.05 = (double_divide @
% 24.00/4.05 (double_divide @ identity @ (inverse @ (inverse @ identity))) @
% 24.00/4.05 identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl698, zip_derived_cl29])).
% 24.00/4.05 thf(zip_derived_cl2, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [inverse])).
% 24.00/4.05 thf(zip_derived_cl740, plain,
% 24.00/4.05 (((inverse @
% 24.00/4.05 (double_divide @ identity @ (inverse @ (inverse @ identity))))
% 24.00/4.05 = (identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl709, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl2, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [inverse])).
% 24.00/4.05 thf(zip_derived_cl885, plain,
% 24.00/4.05 (((double_divide @
% 24.00/4.05 (double_divide @ identity @ (inverse @ (inverse @ identity))) @
% 24.00/4.05 (inverse @ identity)) = (identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl879, zip_derived_cl740, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl13, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X1 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl900, plain,
% 24.00/4.05 (((double_divide @
% 24.00/4.05 (double_divide @ (inverse @ (inverse @ identity)) @
% 24.00/4.05 (double_divide @ identity @ (inverse @ identity))) @
% 24.00/4.05 (inverse @ identity)) = (inverse @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl885, zip_derived_cl13])).
% 24.00/4.05 thf(zip_derived_cl3, plain,
% 24.00/4.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 24.00/4.05 inference('cnf', [status(esa)], [identity])).
% 24.00/4.05 thf(zip_derived_cl2, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [inverse])).
% 24.00/4.05 thf(zip_derived_cl538, plain,
% 24.00/4.05 (((double_divide @ (inverse @ (inverse @ (inverse @ identity))) @
% 24.00/4.05 (inverse @ identity)) = (identity))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl522, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl911, plain, (((identity) = (inverse @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl900, zip_derived_cl3, zip_derived_cl2,
% 24.00/4.05 zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl921, plain,
% 24.00/4.05 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 24.00/4.05 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 24.00/4.05 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 24.00/4.05 | ((inverse @ (inverse @ a2)) != (a2))
% 24.00/4.05 | ((identity) != (identity)))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl911])).
% 24.00/4.05 thf(zip_derived_cl922, plain,
% 24.00/4.05 ((((inverse @ (inverse @ a2)) != (a2))
% 24.00/4.05 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 24.00/4.05 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 24.00/4.05 | ((multiply @ a4 @ b4) != (multiply @ b4 @ a4)))),
% 24.00/4.05 inference('simplify', [status(thm)], [zip_derived_cl921])).
% 24.00/4.05 thf(zip_derived_cl911, plain, (((identity) = (inverse @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl900, zip_derived_cl3, zip_derived_cl2,
% 24.00/4.05 zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl3, plain,
% 24.00/4.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 24.00/4.05 inference('cnf', [status(esa)], [identity])).
% 24.00/4.05 thf(zip_derived_cl946, plain,
% 24.00/4.05 (((identity) = (double_divide @ identity @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl911, zip_derived_cl3])).
% 24.00/4.05 thf(zip_derived_cl13, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X1 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl1, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ X0)
% 24.00/4.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [multiply])).
% 24.00/4.05 thf(zip_derived_cl15, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ (inverse @ identity) @
% 24.00/4.05 (double_divide @ X2 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X1 @ X2) @ X0) @ (inverse @ X1))))
% 24.00/4.05 = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl2, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [inverse])).
% 24.00/4.05 thf(zip_derived_cl27, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ (inverse @ identity) @
% 24.00/4.05 (double_divide @ X2 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X1 @ X2) @ X0) @ (inverse @ X1))))
% 24.00/4.05 = (inverse @ X0))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl911, plain, (((identity) = (inverse @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl900, zip_derived_cl3, zip_derived_cl2,
% 24.00/4.05 zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl1, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ X0)
% 24.00/4.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [multiply])).
% 24.00/4.05 thf(zip_derived_cl1, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ X0)
% 24.00/4.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [multiply])).
% 24.00/4.05 thf(zip_derived_cl9, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 24.00/4.05 = (double_divide @ (multiply @ X1 @ X0) @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl2, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [inverse])).
% 24.00/4.05 thf(zip_derived_cl11, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 24.00/4.05 = (inverse @ (multiply @ X1 @ X0)))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl955, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((inverse @
% 24.00/4.05 (multiply @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X1 @ X2) @ X0) @ (inverse @ X1)) @
% 24.00/4.05 X2))
% 24.00/4.05 = (inverse @ X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl27, zip_derived_cl911, zip_derived_cl11])).
% 24.00/4.05 thf(zip_derived_cl994, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((inverse @
% 24.00/4.05 (multiply @
% 24.00/4.05 (double_divide @ (double_divide @ identity @ X0) @
% 24.00/4.05 (inverse @ identity)) @
% 24.00/4.05 identity))
% 24.00/4.05 = (inverse @ X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl946, zip_derived_cl955])).
% 24.00/4.05 thf(zip_derived_cl911, plain, (((identity) = (inverse @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl900, zip_derived_cl3, zip_derived_cl2,
% 24.00/4.05 zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl1, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ X0)
% 24.00/4.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [multiply])).
% 24.00/4.05 thf(zip_derived_cl1000, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((inverse @ (multiply @ (multiply @ X0 @ identity) @ identity))
% 24.00/4.05 = (inverse @ X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl994, zip_derived_cl911, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl676, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((double_divide @ (inverse @ X0) @ (inverse @ identity))
% 24.00/4.05 = (multiply @ X0 @ identity))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl672, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl911, plain, (((identity) = (inverse @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl900, zip_derived_cl3, zip_derived_cl2,
% 24.00/4.05 zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl2, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [inverse])).
% 24.00/4.05 thf(zip_derived_cl936, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl676, zip_derived_cl911, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl936, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl676, zip_derived_cl911, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl1028, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((inverse @ (inverse @ (inverse @ (inverse @ (inverse @ X0)))))
% 24.00/4.05 = (inverse @ X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1000, zip_derived_cl936, zip_derived_cl936])).
% 24.00/4.05 thf(zip_derived_cl936, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl676, zip_derived_cl911, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl651, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X0 @ (double_divide @ identity @ (inverse @ X1))) @
% 24.00/4.05 (inverse @ identity)) = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl6])).
% 24.00/4.05 thf(zip_derived_cl911, plain, (((identity) = (inverse @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl900, zip_derived_cl3, zip_derived_cl2,
% 24.00/4.05 zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl1, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ X0)
% 24.00/4.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [multiply])).
% 24.00/4.05 thf(zip_derived_cl935, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (double_divide @ identity @ (inverse @ X1)) @ X0)
% 24.00/4.05 = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl651, zip_derived_cl911, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl1078, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((inverse @ (inverse @ (double_divide @ identity @ (inverse @ X0))))
% 24.00/4.05 = (multiply @ identity @ X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl936, zip_derived_cl935])).
% 24.00/4.05 thf(zip_derived_cl6, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl936, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl676, zip_derived_cl911, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl10, plain,
% 24.00/4.05 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl1084, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((inverse @ (inverse @ (inverse @ (inverse @ X0))))
% 24.00/4.05 = (inverse @ (inverse @ X0)))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1078, zip_derived_cl6, zip_derived_cl936,
% 24.00/4.05 zip_derived_cl10])).
% 24.00/4.05 thf(zip_derived_cl1089, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1028, zip_derived_cl1084])).
% 24.00/4.05 thf(zip_derived_cl935, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (double_divide @ identity @ (inverse @ X1)) @ X0)
% 24.00/4.05 = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl651, zip_derived_cl911, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl1114, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (double_divide @ identity @ (inverse @ X0)) @ X1)
% 24.00/4.05 = (multiply @ X1 @ (inverse @ (inverse @ X0))))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1089, zip_derived_cl935])).
% 24.00/4.05 thf(zip_derived_cl935, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (double_divide @ identity @ (inverse @ X1)) @ X0)
% 24.00/4.05 = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl651, zip_derived_cl911, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl1127, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ X0) = (multiply @ X1 @ (inverse @ (inverse @ X0))))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl1114, zip_derived_cl935])).
% 24.00/4.05 thf(zip_derived_cl935, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (double_divide @ identity @ (inverse @ X1)) @ X0)
% 24.00/4.05 = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl651, zip_derived_cl911, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl1325, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (double_divide @ identity @ (inverse @ X1)) @ X0)
% 24.00/4.05 = (multiply @ (inverse @ (inverse @ X0)) @ X1))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1127, zip_derived_cl935])).
% 24.00/4.05 thf(zip_derived_cl935, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (double_divide @ identity @ (inverse @ X1)) @ X0)
% 24.00/4.05 = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl651, zip_derived_cl911, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl1340, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ X1) = (multiply @ (inverse @ (inverse @ X0)) @ X1))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl1325, zip_derived_cl935])).
% 24.00/4.05 thf(zip_derived_cl52, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((multiply @ identity @ identity)
% 24.00/4.05 = (inverse @ (multiply @ (inverse @ X0) @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl6])).
% 24.00/4.05 thf(zip_derived_cl13, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X1 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl75, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X2 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (multiply @ (inverse @ X1) @ X1) @ X2) @ X0) @
% 24.00/4.05 (multiply @ identity @ identity))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl13])).
% 24.00/4.05 thf(zip_derived_cl10, plain,
% 24.00/4.05 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl94, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X2 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (multiply @ (inverse @ X1) @ X1) @ X2) @ X0) @
% 24.00/4.05 (inverse @ (inverse @ identity)))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl75, zip_derived_cl10])).
% 24.00/4.05 thf(zip_derived_cl32, plain,
% 24.00/4.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 24.00/4.05 thf(zip_derived_cl911, plain, (((identity) = (inverse @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl900, zip_derived_cl3, zip_derived_cl2,
% 24.00/4.05 zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl917, plain,
% 24.00/4.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl911])).
% 24.00/4.05 thf(zip_derived_cl911, plain, (((identity) = (inverse @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl900, zip_derived_cl3, zip_derived_cl2,
% 24.00/4.05 zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl911, plain, (((identity) = (inverse @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl900, zip_derived_cl3, zip_derived_cl2,
% 24.00/4.05 zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl1, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ X0)
% 24.00/4.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [multiply])).
% 24.00/4.05 thf(zip_derived_cl911, plain, (((identity) = (inverse @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl900, zip_derived_cl3, zip_derived_cl2,
% 24.00/4.05 zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl1, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ X0)
% 24.00/4.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [multiply])).
% 24.00/4.05 thf(zip_derived_cl1527, plain,
% 24.00/4.05 (![X0 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X0 @ (double_divide @ identity @ X2)) @ X2)
% 24.00/4.05 = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl94, zip_derived_cl917, zip_derived_cl911,
% 24.00/4.05 zip_derived_cl911, zip_derived_cl1, zip_derived_cl911,
% 24.00/4.05 zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl1542, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X1 @ (double_divide @ identity @ X0)) @ X0)
% 24.00/4.05 = (inverse @ (inverse @ X1)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1340, zip_derived_cl1527])).
% 24.00/4.05 thf(zip_derived_cl1527, plain,
% 24.00/4.05 (![X0 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X0 @ (double_divide @ identity @ X2)) @ X2)
% 24.00/4.05 = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl94, zip_derived_cl917, zip_derived_cl911,
% 24.00/4.05 zip_derived_cl911, zip_derived_cl1, zip_derived_cl911,
% 24.00/4.05 zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl1551, plain,
% 24.00/4.05 (![X1 : $i]: ((X1) = (inverse @ (inverse @ X1)))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1542, zip_derived_cl1527])).
% 24.00/4.05 thf(zip_derived_cl1575, plain,
% 24.00/4.05 ((((a2) != (a2))
% 24.00/4.05 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 24.00/4.05 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 24.00/4.05 | ((multiply @ a4 @ b4) != (multiply @ b4 @ a4)))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl922, zip_derived_cl1551])).
% 24.00/4.05 thf(zip_derived_cl1576, plain,
% 24.00/4.05 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 24.00/4.05 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 24.00/4.05 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 24.00/4.05 inference('simplify', [status(thm)], [zip_derived_cl1575])).
% 24.00/4.05 thf(zip_derived_cl935, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (double_divide @ identity @ (inverse @ X1)) @ X0)
% 24.00/4.05 = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl651, zip_derived_cl911, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl936, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl676, zip_derived_cl911, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl1551, plain,
% 24.00/4.05 (![X1 : $i]: ((X1) = (inverse @ (inverse @ X1)))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1542, zip_derived_cl1527])).
% 24.00/4.05 thf(zip_derived_cl1577, plain,
% 24.00/4.05 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl936, zip_derived_cl1551])).
% 24.00/4.05 thf(zip_derived_cl935, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (double_divide @ identity @ (inverse @ X1)) @ X0)
% 24.00/4.05 = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl651, zip_derived_cl911, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl1611, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((double_divide @ identity @ (inverse @ X0))
% 24.00/4.05 = (multiply @ identity @ X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1577, zip_derived_cl935])).
% 24.00/4.05 thf(zip_derived_cl1340, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ X1) = (multiply @ (inverse @ (inverse @ X0)) @ X1))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl1325, zip_derived_cl935])).
% 24.00/4.05 thf(zip_derived_cl936, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (multiply @ X0 @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl676, zip_derived_cl911, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl40, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X1 @ X0) @ (double_divide @ X0 @ X1))
% 24.00/4.05 = (inverse @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl32])).
% 24.00/4.05 thf(zip_derived_cl911, plain, (((identity) = (inverse @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl900, zip_derived_cl3, zip_derived_cl2,
% 24.00/4.05 zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl919, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X1 @ X0) @ (double_divide @ X0 @ X1))
% 24.00/4.05 = (identity))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl40, zip_derived_cl911])).
% 24.00/4.05 thf(zip_derived_cl1058, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((multiply @ (inverse @ (inverse @ X0)) @
% 24.00/4.05 (double_divide @ identity @ X0)) = (identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl936, zip_derived_cl919])).
% 24.00/4.05 thf(zip_derived_cl1350, plain,
% 24.00/4.05 (![X0 : $i]:
% 24.00/4.05 ((multiply @ X0 @ (double_divide @ identity @ X0)) = (identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1340, zip_derived_cl1058])).
% 24.00/4.05 thf(zip_derived_cl1527, plain,
% 24.00/4.05 (![X0 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X0 @ (double_divide @ identity @ X2)) @ X2)
% 24.00/4.05 = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl94, zip_derived_cl917, zip_derived_cl911,
% 24.00/4.05 zip_derived_cl911, zip_derived_cl1, zip_derived_cl911,
% 24.00/4.05 zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl1534, plain,
% 24.00/4.05 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1350, zip_derived_cl1527])).
% 24.00/4.05 thf(zip_derived_cl1616, plain,
% 24.00/4.05 (![X0 : $i]: ((double_divide @ identity @ (inverse @ X0)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1611, zip_derived_cl1534])).
% 24.00/4.05 thf(zip_derived_cl1640, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl935, zip_derived_cl1616])).
% 24.00/4.05 thf(zip_derived_cl1640, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl935, zip_derived_cl1616])).
% 24.00/4.05 thf(zip_derived_cl1640, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl935, zip_derived_cl1616])).
% 24.00/4.05 thf(zip_derived_cl1722, plain,
% 24.00/4.05 ((((multiply @ a4 @ b4) != (multiply @ a4 @ b4))
% 24.00/4.05 | ((multiply @ c3 @ (multiply @ a3 @ b3))
% 24.00/4.05 != (multiply @ a3 @ (multiply @ c3 @ b3))))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1576, zip_derived_cl1640, zip_derived_cl1640,
% 24.00/4.05 zip_derived_cl1640])).
% 24.00/4.05 thf(zip_derived_cl1723, plain,
% 24.00/4.05 (((multiply @ c3 @ (multiply @ a3 @ b3))
% 24.00/4.05 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 24.00/4.05 inference('simplify', [status(thm)], [zip_derived_cl1722])).
% 24.00/4.05 thf(zip_derived_cl3, plain,
% 24.00/4.05 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 24.00/4.05 inference('cnf', [status(esa)], [identity])).
% 24.00/4.05 thf(zip_derived_cl13, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X1 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl13, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X1 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl14, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ (inverse @ identity) @
% 24.00/4.05 (double_divide @ (double_divide @ X0 @ X1) @
% 24.00/4.05 (inverse @
% 24.00/4.05 (double_divide @ X3 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X2 @ X3) @ X0) @
% 24.00/4.05 (inverse @ X2)))))) @
% 24.00/4.05 (inverse @ identity)) = (X1))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 24.00/4.05 thf(zip_derived_cl6, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl141, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ (inverse @ identity) @
% 24.00/4.05 (double_divide @ (double_divide @ X0 @ X1) @
% 24.00/4.05 (multiply @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X2 @ X3) @ X0) @
% 24.00/4.05 (inverse @ X2)) @
% 24.00/4.05 X3))) @
% 24.00/4.05 (inverse @ identity)) = (X1))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl6])).
% 24.00/4.05 thf(zip_derived_cl158, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ (inverse @ identity) @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (inverse @ (double_divide @ X2 @ X1)) @ X0) @
% 24.00/4.05 (multiply @ (double_divide @ identity @ (inverse @ X2)) @ X1))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl141])).
% 24.00/4.05 thf(zip_derived_cl6, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl183, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ (inverse @ identity) @
% 24.00/4.05 (double_divide @ (double_divide @ (multiply @ X1 @ X2) @ X0) @
% 24.00/4.05 (multiply @ (double_divide @ identity @ (inverse @ X2)) @ X1))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl158, zip_derived_cl6])).
% 24.00/4.05 thf(zip_derived_cl911, plain, (((identity) = (inverse @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl900, zip_derived_cl3, zip_derived_cl2,
% 24.00/4.05 zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl1534, plain,
% 24.00/4.05 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1350, zip_derived_cl1527])).
% 24.00/4.05 thf(zip_derived_cl11, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 24.00/4.05 = (inverse @ (multiply @ X1 @ X0)))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl1567, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((double_divide @ X1 @ X0) = (inverse @ (multiply @ X0 @ X1)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1534, zip_derived_cl11])).
% 24.00/4.05 thf(zip_derived_cl1616, plain,
% 24.00/4.05 (![X0 : $i]: ((double_divide @ identity @ (inverse @ X0)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1611, zip_derived_cl1534])).
% 24.00/4.05 thf(zip_derived_cl1567, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((double_divide @ X1 @ X0) = (inverse @ (multiply @ X0 @ X1)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1534, zip_derived_cl11])).
% 24.00/4.05 thf(zip_derived_cl1616, plain,
% 24.00/4.05 (![X0 : $i]: ((double_divide @ identity @ (inverse @ X0)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1611, zip_derived_cl1534])).
% 24.00/4.05 thf(zip_derived_cl911, plain, (((identity) = (inverse @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl900, zip_derived_cl3, zip_derived_cl2,
% 24.00/4.05 zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl2, plain,
% 24.00/4.05 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [inverse])).
% 24.00/4.05 thf(zip_derived_cl2132, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((inverse @
% 24.00/4.05 (multiply @ (multiply @ X2 @ X1) @
% 24.00/4.05 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))
% 24.00/4.05 = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl183, zip_derived_cl911, zip_derived_cl1567,
% 24.00/4.05 zip_derived_cl1616, zip_derived_cl1567, zip_derived_cl1616,
% 24.00/4.05 zip_derived_cl911, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl1551, plain,
% 24.00/4.05 (![X1 : $i]: ((X1) = (inverse @ (inverse @ X1)))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1542, zip_derived_cl1527])).
% 24.00/4.05 thf(zip_derived_cl1577, plain,
% 24.00/4.05 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl936, zip_derived_cl1551])).
% 24.00/4.05 thf(zip_derived_cl29, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((identity)
% 24.00/4.05 = (double_divide @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 24.00/4.05 thf(zip_derived_cl13, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X1 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl109, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ (multiply @ X1 @ X2) @
% 24.00/4.05 (double_divide @ (double_divide @ identity @ X0) @
% 24.00/4.05 (inverse @ (double_divide @ X2 @ X1)))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl13])).
% 24.00/4.05 thf(zip_derived_cl6, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl138, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ (multiply @ X1 @ X2) @
% 24.00/4.05 (double_divide @ (double_divide @ identity @ X0) @
% 24.00/4.05 (multiply @ X1 @ X2))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl6])).
% 24.00/4.05 thf(zip_derived_cl1551, plain,
% 24.00/4.05 (![X1 : $i]: ((X1) = (inverse @ (inverse @ X1)))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1542, zip_derived_cl1527])).
% 24.00/4.05 thf(zip_derived_cl1616, plain,
% 24.00/4.05 (![X0 : $i]: ((double_divide @ identity @ (inverse @ X0)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1611, zip_derived_cl1534])).
% 24.00/4.05 thf(zip_derived_cl1653, plain,
% 24.00/4.05 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1551, zip_derived_cl1616])).
% 24.00/4.05 thf(zip_derived_cl911, plain, (((identity) = (inverse @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl900, zip_derived_cl3, zip_derived_cl2,
% 24.00/4.05 zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl1, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ X0)
% 24.00/4.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [multiply])).
% 24.00/4.05 thf(zip_derived_cl1678, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @
% 24.00/4.05 (double_divide @ (inverse @ X0) @ (multiply @ X1 @ X2)) @
% 24.00/4.05 (multiply @ X1 @ X2)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl138, zip_derived_cl1653, zip_derived_cl911,
% 24.00/4.05 zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl1683, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @
% 24.00/4.05 (double_divide @ (inverse @ X1) @ (multiply @ X0 @ identity)) @ X0)
% 24.00/4.05 = (X1))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1577, zip_derived_cl1678])).
% 24.00/4.05 thf(zip_derived_cl1577, plain,
% 24.00/4.05 (![X0 : $i]: ((X0) = (multiply @ X0 @ identity))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl936, zip_derived_cl1551])).
% 24.00/4.05 thf(zip_derived_cl1702, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (double_divide @ (inverse @ X1) @ X0) @ X0) = (X1))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1683, zip_derived_cl1577])).
% 24.00/4.05 thf(zip_derived_cl1567, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((double_divide @ X1 @ X0) = (inverse @ (multiply @ X0 @ X1)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1534, zip_derived_cl11])).
% 24.00/4.05 thf(zip_derived_cl1640, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl935, zip_derived_cl1616])).
% 24.00/4.05 thf(zip_derived_cl1835, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ (inverse @ (multiply @ X0 @ (inverse @ X1)))) = (X1))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1702, zip_derived_cl1567, zip_derived_cl1640])).
% 24.00/4.05 thf(zip_derived_cl1853, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1551, zip_derived_cl1835])).
% 24.00/4.05 thf(zip_derived_cl2345, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X1 @ X2) @ X0)
% 24.00/4.05 = (inverse @ (inverse @ (multiply @ X0 @ (multiply @ X2 @ X1)))))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2132, zip_derived_cl1853])).
% 24.00/4.05 thf(zip_derived_cl1551, plain,
% 24.00/4.05 (![X1 : $i]: ((X1) = (inverse @ (inverse @ X1)))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1542, zip_derived_cl1527])).
% 24.00/4.05 thf(zip_derived_cl7486, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ X0 @ (multiply @ X1 @ X2))
% 24.00/4.05 = (multiply @ (multiply @ X2 @ X1) @ X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2345, zip_derived_cl1551])).
% 24.00/4.05 thf(zip_derived_cl1853, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1551, zip_derived_cl1835])).
% 24.00/4.05 thf(zip_derived_cl2132, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((inverse @
% 24.00/4.05 (multiply @ (multiply @ X2 @ X1) @
% 24.00/4.05 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))
% 24.00/4.05 = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl183, zip_derived_cl911, zip_derived_cl1567,
% 24.00/4.05 zip_derived_cl1616, zip_derived_cl1567, zip_derived_cl1616,
% 24.00/4.05 zip_derived_cl911, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl2340, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((inverse @ (inverse @ (multiply @ X1 @ X0))) = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1853, zip_derived_cl2132])).
% 24.00/4.05 thf(zip_derived_cl917, plain,
% 24.00/4.05 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl911])).
% 24.00/4.05 thf(zip_derived_cl2633, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ (multiply @ X0 @ X1)))
% 24.00/4.05 = (identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2340, zip_derived_cl917])).
% 24.00/4.05 thf(zip_derived_cl1527, plain,
% 24.00/4.05 (![X0 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X0 @ (double_divide @ identity @ X2)) @ X2)
% 24.00/4.05 = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl94, zip_derived_cl917, zip_derived_cl911,
% 24.00/4.05 zip_derived_cl911, zip_derived_cl1, zip_derived_cl911,
% 24.00/4.05 zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl1653, plain,
% 24.00/4.05 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1551, zip_derived_cl1616])).
% 24.00/4.05 thf(zip_derived_cl1661, plain,
% 24.00/4.05 (![X0 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X0 @ (inverse @ X2)) @ X2) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1527, zip_derived_cl1653])).
% 24.00/4.05 thf(zip_derived_cl1640, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl935, zip_derived_cl1616])).
% 24.00/4.05 thf(zip_derived_cl1795, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((X0) = (multiply @ X1 @ (multiply @ X0 @ (inverse @ X1))))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1661, zip_derived_cl1640])).
% 24.00/4.05 thf(zip_derived_cl4018, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ X1) = (multiply @ (multiply @ X1 @ X0) @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2633, zip_derived_cl1795])).
% 24.00/4.05 thf(zip_derived_cl8542, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ X2 @ (multiply @ X0 @ X1))
% 24.00/4.05 = (multiply @ (multiply @ X2 @ (multiply @ X1 @ X0)) @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl7486, zip_derived_cl4018])).
% 24.00/4.05 thf(zip_derived_cl4018, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ X1) = (multiply @ (multiply @ X1 @ X0) @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2633, zip_derived_cl1795])).
% 24.00/4.05 thf(zip_derived_cl10316, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ identity @ (multiply @ X2 @ (multiply @ X0 @ X1)))
% 24.00/4.05 = (multiply @ (multiply @ X2 @ (multiply @ X1 @ X0)) @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl8542, zip_derived_cl4018])).
% 24.00/4.05 thf(zip_derived_cl2633, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ (multiply @ X0 @ X1)))
% 24.00/4.05 = (identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2340, zip_derived_cl917])).
% 24.00/4.05 thf(zip_derived_cl1661, plain,
% 24.00/4.05 (![X0 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X0 @ (inverse @ X2)) @ X2) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1527, zip_derived_cl1653])).
% 24.00/4.05 thf(zip_derived_cl4017, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ identity @ (multiply @ X0 @ X1)) = (multiply @ X1 @ X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2633, zip_derived_cl1661])).
% 24.00/4.05 thf(zip_derived_cl4018, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ X1) = (multiply @ (multiply @ X1 @ X0) @ identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2633, zip_derived_cl1795])).
% 24.00/4.05 thf(zip_derived_cl10506, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 24.00/4.05 = (multiply @ (multiply @ X1 @ X0) @ X2))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl10316, zip_derived_cl4017, zip_derived_cl4018])).
% 24.00/4.05 thf(zip_derived_cl1551, plain,
% 24.00/4.05 (![X1 : $i]: ((X1) = (inverse @ (inverse @ X1)))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1542, zip_derived_cl1527])).
% 24.00/4.05 thf(zip_derived_cl1795, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((X0) = (multiply @ X1 @ (multiply @ X0 @ (inverse @ X1))))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1661, zip_derived_cl1640])).
% 24.00/4.05 thf(zip_derived_cl1826, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((X1) = (multiply @ (inverse @ X0) @ (multiply @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1551, zip_derived_cl1795])).
% 24.00/4.05 thf(zip_derived_cl13, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X1 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl13, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @
% 24.00/4.05 (double_divide @ X1 @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X2 @ X1) @ X0) @ (inverse @ X2))) @
% 24.00/4.05 (inverse @ identity)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 24.00/4.05 thf(zip_derived_cl17, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @ (double_divide @ X2 @ X0) @ (inverse @ identity))
% 24.00/4.05 = (double_divide @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ X1 @ (double_divide @ identity @ X2)) @ X0) @
% 24.00/4.05 (inverse @ X1)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 24.00/4.05 thf(zip_derived_cl1, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ X0)
% 24.00/4.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [multiply])).
% 24.00/4.05 thf(zip_derived_cl433, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ (inverse @ X2) @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ X2 @ (double_divide @ identity @ X1)) @ X0))
% 24.00/4.05 = (double_divide @
% 24.00/4.05 (double_divide @ (double_divide @ X1 @ X0) @ (inverse @ identity)) @
% 24.00/4.05 identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl1, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ X0)
% 24.00/4.05 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 24.00/4.05 inference('cnf', [status(esa)], [multiply])).
% 24.00/4.05 thf(zip_derived_cl472, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ (inverse @ X2) @
% 24.00/4.05 (double_divide @
% 24.00/4.05 (double_divide @ X2 @ (double_divide @ identity @ X1)) @ X0))
% 24.00/4.05 = (multiply @ (inverse @ identity) @ (double_divide @ X1 @ X0)))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl433, zip_derived_cl1])).
% 24.00/4.05 thf(zip_derived_cl1653, plain,
% 24.00/4.05 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1551, zip_derived_cl1616])).
% 24.00/4.05 thf(zip_derived_cl1567, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((double_divide @ X1 @ X0) = (inverse @ (multiply @ X0 @ X1)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1534, zip_derived_cl11])).
% 24.00/4.05 thf(zip_derived_cl1640, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl935, zip_derived_cl1616])).
% 24.00/4.05 thf(zip_derived_cl1835, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ (inverse @ (multiply @ X0 @ (inverse @ X1)))) = (X1))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1702, zip_derived_cl1567, zip_derived_cl1640])).
% 24.00/4.05 thf(zip_derived_cl1844, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ (inverse @ (multiply @ (inverse @ X1) @ X0))) = (X1))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1640, zip_derived_cl1835])).
% 24.00/4.05 thf(zip_derived_cl1661, plain,
% 24.00/4.05 (![X0 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X0 @ (inverse @ X2)) @ X2) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1527, zip_derived_cl1653])).
% 24.00/4.05 thf(zip_derived_cl1835, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X0 @ (inverse @ (multiply @ X0 @ (inverse @ X1)))) = (X1))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1702, zip_derived_cl1567, zip_derived_cl1640])).
% 24.00/4.05 thf(zip_derived_cl1849, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X0 @ (inverse @ (inverse @ X1))) @
% 24.00/4.05 (inverse @ X0)) = (X1))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1661, zip_derived_cl1835])).
% 24.00/4.05 thf(zip_derived_cl1551, plain,
% 24.00/4.05 (![X1 : $i]: ((X1) = (inverse @ (inverse @ X1)))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1542, zip_derived_cl1527])).
% 24.00/4.05 thf(zip_derived_cl1640, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl935, zip_derived_cl1616])).
% 24.00/4.05 thf(zip_derived_cl1857, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1849, zip_derived_cl1551, zip_derived_cl1640])).
% 24.00/4.05 thf(zip_derived_cl2276, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (inverse @ X1) @ X0)
% 24.00/4.05 = (inverse @ (multiply @ (inverse @ X0) @ X1)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1844, zip_derived_cl1857])).
% 24.00/4.05 thf(zip_derived_cl1567, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((double_divide @ X1 @ X0) = (inverse @ (multiply @ X0 @ X1)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1534, zip_derived_cl11])).
% 24.00/4.05 thf(zip_derived_cl1853, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ X1 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1551, zip_derived_cl1835])).
% 24.00/4.05 thf(zip_derived_cl1551, plain,
% 24.00/4.05 (![X1 : $i]: ((X1) = (inverse @ (inverse @ X1)))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1542, zip_derived_cl1527])).
% 24.00/4.05 thf(zip_derived_cl1640, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]: ((multiply @ X1 @ X0) = (multiply @ X0 @ X1))),
% 24.00/4.05 inference('demod', [status(thm)], [zip_derived_cl935, zip_derived_cl1616])).
% 24.00/4.05 thf(zip_derived_cl1661, plain,
% 24.00/4.05 (![X0 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X0 @ (inverse @ X2)) @ X2) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1527, zip_derived_cl1653])).
% 24.00/4.05 thf(zip_derived_cl1800, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ (inverse @ X1) @ X0) @ X1) = (X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1640, zip_derived_cl1661])).
% 24.00/4.05 thf(zip_derived_cl1926, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X0)) = (X1))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1551, zip_derived_cl1800])).
% 24.00/4.05 thf(zip_derived_cl2329, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (inverse @ X0) @ (inverse @ X1))
% 24.00/4.05 = (inverse @ (multiply @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1853, zip_derived_cl1926])).
% 24.00/4.05 thf(zip_derived_cl7486, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ X0 @ (multiply @ X1 @ X2))
% 24.00/4.05 = (multiply @ (multiply @ X2 @ X1) @ X0))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2345, zip_derived_cl1551])).
% 24.00/4.05 thf(zip_derived_cl911, plain, (((identity) = (inverse @ identity))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl900, zip_derived_cl3, zip_derived_cl2,
% 24.00/4.05 zip_derived_cl538])).
% 24.00/4.05 thf(zip_derived_cl1567, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((double_divide @ X1 @ X0) = (inverse @ (multiply @ X0 @ X1)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1534, zip_derived_cl11])).
% 24.00/4.05 thf(zip_derived_cl2633, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ (multiply @ X0 @ X1)))
% 24.00/4.05 = (identity))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2340, zip_derived_cl917])).
% 24.00/4.05 thf(zip_derived_cl1926, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X0)) = (X1))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl1551, zip_derived_cl1800])).
% 24.00/4.05 thf(zip_derived_cl4003, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i]:
% 24.00/4.05 ((multiply @ identity @ (inverse @ (multiply @ X0 @ X1)))
% 24.00/4.05 = (inverse @ (multiply @ X1 @ X0)))),
% 24.00/4.05 inference('sup+', [status(thm)], [zip_derived_cl2633, zip_derived_cl1926])).
% 24.00/4.05 thf(zip_derived_cl13852, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((inverse @
% 24.00/4.05 (multiply @ X2 @ (multiply @ (multiply @ (inverse @ X2) @ X1) @ X0)))
% 24.00/4.05 = (inverse @ (multiply @ X1 @ X0)))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl472, zip_derived_cl1653, zip_derived_cl1567,
% 24.00/4.05 zip_derived_cl2276, zip_derived_cl1567, zip_derived_cl2329,
% 24.00/4.05 zip_derived_cl7486, zip_derived_cl911, zip_derived_cl1567,
% 24.00/4.05 zip_derived_cl4003])).
% 24.00/4.05 thf(zip_derived_cl14009, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((inverse @ (multiply @ X2 @ (multiply @ X0 @ X1)))
% 24.00/4.05 = (inverse @ (multiply @ (multiply @ X0 @ X2) @ X1)))),
% 24.00/4.05 inference('sup+', [status(thm)],
% 24.00/4.05 [zip_derived_cl1826, zip_derived_cl13852])).
% 24.00/4.05 thf(zip_derived_cl1616, plain,
% 24.00/4.05 (![X0 : $i]: ((double_divide @ identity @ (inverse @ X0)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1611, zip_derived_cl1534])).
% 24.00/4.05 thf(zip_derived_cl14134, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((double_divide @ identity @
% 24.00/4.05 (inverse @ (multiply @ X2 @ (multiply @ X1 @ X0))))
% 24.00/4.05 = (multiply @ (multiply @ X1 @ X2) @ X0))),
% 24.00/4.05 inference('sup+', [status(thm)],
% 24.00/4.05 [zip_derived_cl14009, zip_derived_cl1616])).
% 24.00/4.05 thf(zip_derived_cl1616, plain,
% 24.00/4.05 (![X0 : $i]: ((double_divide @ identity @ (inverse @ X0)) = (X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1611, zip_derived_cl1534])).
% 24.00/4.05 thf(zip_derived_cl14362, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 24.00/4.05 = (multiply @ (multiply @ X1 @ X2) @ X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl14134, zip_derived_cl1616])).
% 24.00/4.05 thf(zip_derived_cl14362, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 24.00/4.05 = (multiply @ (multiply @ X1 @ X2) @ X0))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl14134, zip_derived_cl1616])).
% 24.00/4.05 thf(zip_derived_cl14798, plain,
% 24.00/4.05 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.00/4.05 ((multiply @ X1 @ (multiply @ X0 @ X2))
% 24.00/4.05 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl10506, zip_derived_cl14362, zip_derived_cl14362])).
% 24.00/4.05 thf(zip_derived_cl14799, plain,
% 24.00/4.05 (((multiply @ a3 @ (multiply @ c3 @ b3))
% 24.00/4.05 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 24.00/4.05 inference('demod', [status(thm)],
% 24.00/4.05 [zip_derived_cl1723, zip_derived_cl14798])).
% 24.00/4.05 thf(zip_derived_cl14800, plain, ($false),
% 24.00/4.05 inference('simplify', [status(thm)], [zip_derived_cl14799])).
% 24.00/4.05
% 24.00/4.05 % SZS output end Refutation
% 24.00/4.05
% 24.00/4.05
% 24.00/4.05 % Terminating...
% 24.46/4.15 % Runner terminated.
% 24.46/4.16 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------