TSTP Solution File: GRP101-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP101-1 : 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.2lo84iseYG true
% Computer : n018.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 01:49:55 EDT 2023
% Result : Unsatisfiable 5.87s 1.42s
% Output : Refutation 6.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP101-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.2lo84iseYG true
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 23:45:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.50/0.64 % Total configuration time : 435
% 0.50/0.64 % Estimated wc time : 1092
% 0.50/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.50/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.50/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.56/0.77 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 5.87/1.42 % Solved by fo/fo5.sh.
% 5.87/1.42 % done 716 iterations in 0.635s
% 5.87/1.42 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 5.87/1.42 % SZS output start Refutation
% 5.87/1.42 thf(a3_type, type, a3: $i).
% 5.87/1.42 thf(identity_type, type, identity: $i).
% 5.87/1.42 thf(multiply_type, type, multiply: $i > $i > $i).
% 5.87/1.42 thf(c3_type, type, c3: $i).
% 5.87/1.42 thf(a2_type, type, a2: $i).
% 5.87/1.42 thf(a1_type, type, a1: $i).
% 5.87/1.42 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 5.87/1.42 thf(inverse_type, type, inverse: $i > $i).
% 5.87/1.42 thf(b4_type, type, b4: $i).
% 5.87/1.42 thf(a4_type, type, a4: $i).
% 5.87/1.42 thf(b3_type, type, b3: $i).
% 5.87/1.42 thf(prove_these_axioms, conjecture,
% 5.87/1.42 (~( ( ( multiply @ a4 @ b4 ) != ( multiply @ b4 @ a4 ) ) |
% 5.87/1.42 ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 5.87/1.42 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 5.87/1.42 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 5.87/1.42 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) ) ))).
% 5.87/1.42 thf(zf_stmt_0, negated_conjecture,
% 5.87/1.42 (( ( multiply @ a4 @ b4 ) != ( multiply @ b4 @ a4 ) ) |
% 5.87/1.42 ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 5.87/1.42 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 5.87/1.42 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 5.87/1.42 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) )),
% 5.87/1.42 inference('cnf.neg', [status(esa)], [prove_these_axioms])).
% 5.87/1.42 thf(zip_derived_cl4, plain,
% 5.87/1.42 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 5.87/1.42 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 5.87/1.42 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 5.87/1.42 | ((multiply @ identity @ a2) != (a2))
% 5.87/1.42 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 5.87/1.42 inference('cnf', [status(esa)], [zf_stmt_0])).
% 5.87/1.42 thf(inverse, axiom, (( inverse @ X ) = ( double_divide @ X @ identity ))).
% 5.87/1.42 thf(zip_derived_cl2, plain,
% 5.87/1.42 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 5.87/1.42 inference('cnf', [status(esa)], [inverse])).
% 5.87/1.42 thf(multiply, axiom,
% 5.87/1.42 (( multiply @ X @ Y ) =
% 5.87/1.42 ( double_divide @ ( double_divide @ Y @ X ) @ identity ))).
% 5.87/1.42 thf(zip_derived_cl1, plain,
% 5.87/1.42 (![X0 : $i, X1 : $i]:
% 5.87/1.42 ((multiply @ X1 @ X0)
% 5.87/1.42 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 5.87/1.42 inference('cnf', [status(esa)], [multiply])).
% 5.87/1.42 thf(zip_derived_cl7, plain,
% 5.87/1.42 (![X0 : $i]:
% 5.87/1.42 ((multiply @ identity @ X0)
% 5.87/1.42 = (double_divide @ (inverse @ X0) @ identity))),
% 5.87/1.42 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 5.87/1.42 thf(zip_derived_cl2, plain,
% 5.87/1.42 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 5.87/1.42 inference('cnf', [status(esa)], [inverse])).
% 5.87/1.42 thf(zip_derived_cl10, plain,
% 5.87/1.42 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 5.87/1.42 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 5.87/1.42 thf(zip_derived_cl22, plain,
% 5.87/1.42 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 5.87/1.42 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 5.87/1.42 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 5.87/1.42 | ((inverse @ (inverse @ a2)) != (a2))
% 5.87/1.42 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 5.87/1.42 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl10])).
% 5.87/1.42 thf(identity, axiom,
% 5.87/1.42 (( identity ) = ( double_divide @ X @ ( inverse @ X ) ))).
% 5.87/1.42 thf(zip_derived_cl3, plain,
% 5.87/1.42 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 5.87/1.42 inference('cnf', [status(esa)], [identity])).
% 5.87/1.42 thf(zip_derived_cl2, plain,
% 5.87/1.42 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 5.87/1.42 inference('cnf', [status(esa)], [inverse])).
% 5.87/1.42 thf(zip_derived_cl1, plain,
% 5.87/1.42 (![X0 : $i, X1 : $i]:
% 5.87/1.42 ((multiply @ X1 @ X0)
% 5.87/1.42 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 5.87/1.42 inference('cnf', [status(esa)], [multiply])).
% 5.87/1.42 thf(zip_derived_cl6, plain,
% 5.87/1.42 (![X0 : $i, X1 : $i]:
% 5.87/1.42 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 5.87/1.42 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 5.87/1.42 thf(zip_derived_cl26, plain,
% 5.87/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 5.87/1.42 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 5.87/1.42 thf(zip_derived_cl63, plain,
% 5.87/1.42 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 5.87/1.42 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 5.87/1.42 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 5.87/1.42 | ((inverse @ (inverse @ a2)) != (a2))
% 5.87/1.42 | ((inverse @ identity) != (identity)))),
% 5.87/1.42 inference('demod', [status(thm)], [zip_derived_cl22, zip_derived_cl26])).
% 5.87/1.42 thf(zip_derived_cl26, plain,
% 5.87/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 5.87/1.42 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 5.87/1.42 thf(zip_derived_cl3, plain,
% 5.87/1.42 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 5.87/1.42 inference('cnf', [status(esa)], [identity])).
% 5.87/1.42 thf(zip_derived_cl29, plain,
% 5.87/1.42 (![X0 : $i]:
% 5.87/1.42 ((identity)
% 5.87/1.42 = (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0)))),
% 5.87/1.42 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl3])).
% 5.87/1.42 thf(zip_derived_cl1, plain,
% 5.87/1.42 (![X0 : $i, X1 : $i]:
% 5.87/1.42 ((multiply @ X1 @ X0)
% 5.87/1.42 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 5.87/1.42 inference('cnf', [status(esa)], [multiply])).
% 5.87/1.42 thf(single_axiom, axiom,
% 5.87/1.42 (( double_divide @
% 5.87/1.42 ( double_divide @
% 5.87/1.42 X @
% 5.87/1.42 ( double_divide @
% 5.87/1.42 ( double_divide @ Y @ ( double_divide @ Z @ X ) ) @
% 5.87/1.42 ( double_divide @ Z @ identity ) ) ) @
% 5.87/1.42 ( double_divide @ identity @ identity ) ) =
% 5.87/1.42 ( Y ))).
% 5.87/1.42 thf(zip_derived_cl0, plain,
% 5.87/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.42 ((double_divide @
% 5.87/1.42 (double_divide @ X1 @
% 5.87/1.42 (double_divide @
% 5.87/1.42 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @
% 5.87/1.42 (double_divide @ X2 @ identity))) @
% 5.87/1.42 (double_divide @ identity @ identity)) = (X0))),
% 5.87/1.42 inference('cnf', [status(esa)], [single_axiom])).
% 5.87/1.42 thf(zip_derived_cl2, plain,
% 5.87/1.42 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 5.87/1.42 inference('cnf', [status(esa)], [inverse])).
% 5.87/1.42 thf(zip_derived_cl2, plain,
% 5.87/1.42 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 5.87/1.42 inference('cnf', [status(esa)], [inverse])).
% 5.87/1.42 thf(zip_derived_cl13, plain,
% 5.87/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.42 ((double_divide @
% 5.87/1.42 (double_divide @ X1 @
% 5.87/1.42 (double_divide @
% 5.87/1.42 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @ (inverse @ X2))) @
% 5.87/1.42 (inverse @ identity)) = (X0))),
% 5.87/1.42 inference('demod', [status(thm)],
% 5.87/1.42 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 5.87/1.42 thf(zip_derived_cl18, plain,
% 5.87/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.42 ((double_divide @
% 5.87/1.42 (double_divide @ identity @
% 5.87/1.42 (double_divide @ (double_divide @ X2 @ (multiply @ X1 @ X0)) @
% 5.87/1.42 (inverse @ (double_divide @ X0 @ X1)))) @
% 5.87/1.42 (inverse @ identity)) = (X2))),
% 5.87/1.42 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl13])).
% 5.87/1.42 thf(zip_derived_cl6, plain,
% 5.87/1.42 (![X0 : $i, X1 : $i]:
% 5.87/1.42 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 5.87/1.42 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 5.87/1.42 thf(zip_derived_cl372, plain,
% 5.87/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.42 ((double_divide @
% 5.87/1.42 (double_divide @ identity @
% 5.87/1.42 (double_divide @ (double_divide @ X2 @ (multiply @ X1 @ X0)) @
% 5.87/1.42 (multiply @ X1 @ X0))) @
% 5.87/1.42 (inverse @ identity)) = (X2))),
% 5.87/1.42 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl6])).
% 5.87/1.42 thf(zip_derived_cl395, plain,
% 5.87/1.42 (![X0 : $i]:
% 5.87/1.42 ((double_divide @
% 5.87/1.42 (double_divide @ identity @
% 5.87/1.42 (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0))) @
% 5.87/1.42 (inverse @ identity)) = (identity))),
% 5.87/1.42 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl372])).
% 5.87/1.42 thf(zip_derived_cl29, plain,
% 5.87/1.42 (![X0 : $i]:
% 5.87/1.42 ((identity)
% 5.87/1.42 = (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0)))),
% 5.87/1.42 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl3])).
% 5.87/1.42 thf(zip_derived_cl2, plain,
% 5.87/1.42 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 5.87/1.42 inference('cnf', [status(esa)], [inverse])).
% 5.87/1.42 thf(zip_derived_cl415, plain,
% 5.87/1.42 (((double_divide @ (inverse @ identity) @ (inverse @ identity))
% 5.87/1.42 = (identity))),
% 5.87/1.42 inference('demod', [status(thm)],
% 5.87/1.42 [zip_derived_cl395, zip_derived_cl29, zip_derived_cl2])).
% 5.87/1.42 thf(zip_derived_cl2, plain,
% 5.87/1.42 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 5.87/1.42 inference('cnf', [status(esa)], [inverse])).
% 5.87/1.42 thf(zip_derived_cl13, plain,
% 5.87/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.42 ((double_divide @
% 5.87/1.42 (double_divide @ X1 @
% 5.87/1.42 (double_divide @
% 5.87/1.42 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @ (inverse @ X2))) @
% 5.87/1.42 (inverse @ identity)) = (X0))),
% 5.87/1.42 inference('demod', [status(thm)],
% 5.87/1.42 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 5.87/1.42 thf(zip_derived_cl16, plain,
% 5.87/1.42 (![X0 : $i, X1 : $i]:
% 5.87/1.42 ((double_divide @
% 5.87/1.42 (double_divide @ identity @
% 5.87/1.42 (double_divide @ (double_divide @ X1 @ (inverse @ X0)) @
% 5.87/1.42 (inverse @ X0))) @
% 5.87/1.42 (inverse @ identity)) = (X1))),
% 5.87/1.42 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 5.87/1.42 thf(zip_derived_cl436, plain,
% 5.87/1.42 (((double_divide @
% 5.87/1.42 (double_divide @ identity @
% 5.87/1.42 (double_divide @ identity @ (inverse @ identity))) @
% 5.87/1.42 (inverse @ identity)) = (inverse @ identity))),
% 5.87/1.42 inference('sup+', [status(thm)], [zip_derived_cl415, zip_derived_cl16])).
% 5.87/1.42 thf(zip_derived_cl3, plain,
% 5.87/1.42 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 5.87/1.42 inference('cnf', [status(esa)], [identity])).
% 5.87/1.42 thf(zip_derived_cl2, plain,
% 5.87/1.42 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 5.87/1.42 inference('cnf', [status(esa)], [inverse])).
% 5.87/1.42 thf(zip_derived_cl415, plain,
% 5.87/1.42 (((double_divide @ (inverse @ identity) @ (inverse @ identity))
% 5.87/1.42 = (identity))),
% 5.87/1.42 inference('demod', [status(thm)],
% 5.87/1.42 [zip_derived_cl395, zip_derived_cl29, zip_derived_cl2])).
% 5.87/1.42 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.42 inference('demod', [status(thm)],
% 5.87/1.42 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.42 zip_derived_cl415])).
% 5.87/1.42 thf(zip_derived_cl450, plain,
% 5.87/1.42 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 5.87/1.42 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 5.87/1.42 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 5.87/1.42 | ((inverse @ (inverse @ a2)) != (a2))
% 5.87/1.42 | ((identity) != (identity)))),
% 5.87/1.42 inference('demod', [status(thm)], [zip_derived_cl63, zip_derived_cl443])).
% 5.87/1.42 thf(zip_derived_cl451, plain,
% 5.87/1.42 ((((inverse @ (inverse @ a2)) != (a2))
% 5.87/1.42 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 5.87/1.42 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 5.87/1.42 | ((multiply @ a4 @ b4) != (multiply @ b4 @ a4)))),
% 5.87/1.42 inference('simplify', [status(thm)], [zip_derived_cl450])).
% 5.87/1.42 thf(zip_derived_cl3, plain,
% 5.87/1.42 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 5.87/1.42 inference('cnf', [status(esa)], [identity])).
% 5.87/1.42 thf(zip_derived_cl3, plain,
% 5.87/1.42 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 5.87/1.42 inference('cnf', [status(esa)], [identity])).
% 5.87/1.42 thf(zip_derived_cl13, plain,
% 5.87/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.42 ((double_divide @
% 5.87/1.42 (double_divide @ X1 @
% 5.87/1.42 (double_divide @
% 5.87/1.42 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @ (inverse @ X2))) @
% 5.87/1.43 (inverse @ identity)) = (X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 5.87/1.43 thf(zip_derived_cl17, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((double_divide @
% 5.87/1.43 (double_divide @ (inverse @ X1) @
% 5.87/1.43 (double_divide @ (double_divide @ X0 @ identity) @ (inverse @ X1))) @
% 5.87/1.43 (inverse @ identity)) = (X0))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 5.87/1.43 thf(zip_derived_cl2, plain,
% 5.87/1.43 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 5.87/1.43 inference('cnf', [status(esa)], [inverse])).
% 5.87/1.43 thf(zip_derived_cl20, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((double_divide @
% 5.87/1.43 (double_divide @ (inverse @ X1) @
% 5.87/1.43 (double_divide @ (inverse @ X0) @ (inverse @ X1))) @
% 5.87/1.43 (inverse @ identity)) = (X0))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl2])).
% 5.87/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.43 zip_derived_cl415])).
% 5.87/1.43 thf(zip_derived_cl1, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ X1 @ X0)
% 5.87/1.43 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 5.87/1.43 inference('cnf', [status(esa)], [multiply])).
% 5.87/1.43 thf(zip_derived_cl490, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ (double_divide @ (inverse @ X0) @ (inverse @ X1)) @
% 5.87/1.43 (inverse @ X1)) = (X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl20, zip_derived_cl443, zip_derived_cl1])).
% 5.87/1.43 thf(zip_derived_cl494, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ identity @ (inverse @ (inverse @ X0))) = (X0))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl490])).
% 5.87/1.43 thf(zip_derived_cl10, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 5.87/1.43 thf(zip_derived_cl504, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl10])).
% 5.87/1.43 thf(zip_derived_cl504, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl10])).
% 5.87/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.43 zip_derived_cl415])).
% 5.87/1.43 thf(zip_derived_cl490, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ (double_divide @ (inverse @ X0) @ (inverse @ X1)) @
% 5.87/1.43 (inverse @ X1)) = (X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl20, zip_derived_cl443, zip_derived_cl1])).
% 5.87/1.43 thf(zip_derived_cl498, plain,
% 5.87/1.43 (![X0 : $i]:
% 5.87/1.43 ((multiply @ (double_divide @ identity @ (inverse @ X0)) @
% 5.87/1.43 (inverse @ X0)) = (identity))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl443, zip_derived_cl490])).
% 5.87/1.43 thf(zip_derived_cl615, plain,
% 5.87/1.43 (![X0 : $i]:
% 5.87/1.43 ((multiply @
% 5.87/1.43 (double_divide @ identity @
% 5.87/1.43 (inverse @ (inverse @ (inverse @ (inverse @ X0))))) @
% 5.87/1.43 X0) = (identity))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl498])).
% 5.87/1.43 thf(zip_derived_cl504, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl10])).
% 5.87/1.43 thf(zip_derived_cl624, plain,
% 5.87/1.43 (![X0 : $i]:
% 5.87/1.43 ((multiply @ (double_divide @ identity @ X0) @ X0) = (identity))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl615, zip_derived_cl504])).
% 5.87/1.43 thf(zip_derived_cl6, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 5.87/1.43 thf(zip_derived_cl3, plain,
% 5.87/1.43 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 5.87/1.43 inference('cnf', [status(esa)], [identity])).
% 5.87/1.43 thf(zip_derived_cl23, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((identity)
% 5.87/1.43 = (double_divide @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl3])).
% 5.87/1.43 thf(zip_derived_cl630, plain,
% 5.87/1.43 (![X0 : $i]:
% 5.87/1.43 ((identity)
% 5.87/1.43 = (double_divide @
% 5.87/1.43 (double_divide @ X0 @ (double_divide @ identity @ X0)) @ identity))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl624, zip_derived_cl23])).
% 5.87/1.43 thf(zip_derived_cl2, plain,
% 5.87/1.43 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 5.87/1.43 inference('cnf', [status(esa)], [inverse])).
% 5.87/1.43 thf(zip_derived_cl812, plain,
% 5.87/1.43 (![X0 : $i]:
% 5.87/1.43 ((inverse @ (double_divide @ X0 @ (double_divide @ identity @ X0)))
% 5.87/1.43 = (identity))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl630, zip_derived_cl2])).
% 5.87/1.43 thf(zip_derived_cl494, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ identity @ (inverse @ (inverse @ X0))) = (X0))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl490])).
% 5.87/1.43 thf(zip_derived_cl829, plain,
% 5.87/1.43 (![X0 : $i]:
% 5.87/1.43 ((multiply @ identity @ (inverse @ identity))
% 5.87/1.43 = (double_divide @ X0 @ (double_divide @ identity @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl812, zip_derived_cl494])).
% 5.87/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.43 zip_derived_cl415])).
% 5.87/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.43 zip_derived_cl415])).
% 5.87/1.43 thf(zip_derived_cl3, plain,
% 5.87/1.43 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 5.87/1.43 inference('cnf', [status(esa)], [identity])).
% 5.87/1.43 thf(zip_derived_cl459, plain,
% 5.87/1.43 (((identity) = (double_divide @ identity @ identity))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl443, zip_derived_cl3])).
% 5.87/1.43 thf(zip_derived_cl6, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 5.87/1.43 thf(zip_derived_cl470, plain,
% 5.87/1.43 (((multiply @ identity @ identity) = (inverse @ identity))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl459, zip_derived_cl6])).
% 5.87/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.43 zip_derived_cl415])).
% 5.87/1.43 thf(zip_derived_cl475, plain,
% 5.87/1.43 (((multiply @ identity @ identity) = (identity))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl470, zip_derived_cl443])).
% 5.87/1.43 thf(zip_derived_cl847, plain,
% 5.87/1.43 (![X0 : $i]:
% 5.87/1.43 ((identity) = (double_divide @ X0 @ (double_divide @ identity @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl829, zip_derived_cl443, zip_derived_cl475])).
% 5.87/1.43 thf(zip_derived_cl13, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.43 ((double_divide @
% 5.87/1.43 (double_divide @ X1 @
% 5.87/1.43 (double_divide @
% 5.87/1.43 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @ (inverse @ X2))) @
% 5.87/1.43 (inverse @ identity)) = (X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 5.87/1.43 thf(zip_derived_cl1, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ X1 @ X0)
% 5.87/1.43 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 5.87/1.43 inference('cnf', [status(esa)], [multiply])).
% 5.87/1.43 thf(zip_derived_cl15, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.43 ((multiply @ (inverse @ identity) @
% 5.87/1.43 (double_divide @ X2 @
% 5.87/1.43 (double_divide @
% 5.87/1.43 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @ (inverse @ X1))))
% 5.87/1.43 = (double_divide @ X0 @ identity))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 5.87/1.43 thf(zip_derived_cl2, plain,
% 5.87/1.43 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 5.87/1.43 inference('cnf', [status(esa)], [inverse])).
% 5.87/1.43 thf(zip_derived_cl21, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.43 ((multiply @ (inverse @ identity) @
% 5.87/1.43 (double_divide @ X2 @
% 5.87/1.43 (double_divide @
% 5.87/1.43 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @ (inverse @ X1))))
% 5.87/1.43 = (inverse @ X0))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl2])).
% 5.87/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.43 zip_derived_cl415])).
% 5.87/1.43 thf(zip_derived_cl1, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ X1 @ X0)
% 5.87/1.43 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 5.87/1.43 inference('cnf', [status(esa)], [multiply])).
% 5.87/1.43 thf(zip_derived_cl1, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ X1 @ X0)
% 5.87/1.43 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 5.87/1.43 inference('cnf', [status(esa)], [multiply])).
% 5.87/1.43 thf(zip_derived_cl9, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 5.87/1.43 = (double_divide @ (multiply @ X1 @ X0) @ identity))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl1])).
% 5.87/1.43 thf(zip_derived_cl2, plain,
% 5.87/1.43 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 5.87/1.43 inference('cnf', [status(esa)], [inverse])).
% 5.87/1.43 thf(zip_derived_cl11, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 5.87/1.43 = (inverse @ (multiply @ X1 @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 5.87/1.43 thf(zip_derived_cl570, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.43 ((inverse @
% 5.87/1.43 (multiply @
% 5.87/1.43 (double_divide @
% 5.87/1.43 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @ (inverse @ X1)) @
% 5.87/1.43 X2))
% 5.87/1.43 = (inverse @ X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl21, zip_derived_cl443, zip_derived_cl11])).
% 5.87/1.43 thf(zip_derived_cl868, plain,
% 5.87/1.43 (![X0 : $i]:
% 5.87/1.43 ((inverse @
% 5.87/1.43 (multiply @ (double_divide @ identity @ (inverse @ identity)) @ X0))
% 5.87/1.43 = (inverse @ X0))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl847, zip_derived_cl570])).
% 5.87/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.43 zip_derived_cl415])).
% 5.87/1.43 thf(zip_derived_cl459, plain,
% 5.87/1.43 (((identity) = (double_divide @ identity @ identity))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl443, zip_derived_cl3])).
% 5.87/1.43 thf(zip_derived_cl10, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 5.87/1.43 thf(zip_derived_cl887, plain,
% 5.87/1.43 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl868, zip_derived_cl443, zip_derived_cl459,
% 5.87/1.43 zip_derived_cl10])).
% 5.87/1.43 thf(zip_derived_cl893, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl504, zip_derived_cl887])).
% 5.87/1.43 thf(zip_derived_cl929, plain,
% 5.87/1.43 ((((a2) != (a2))
% 5.87/1.43 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 5.87/1.43 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 5.87/1.43 | ((multiply @ a4 @ b4) != (multiply @ b4 @ a4)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl451, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl930, plain,
% 5.87/1.43 ((((multiply @ a4 @ b4) != (multiply @ b4 @ a4))
% 5.87/1.43 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 5.87/1.43 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 5.87/1.43 inference('simplify', [status(thm)], [zip_derived_cl929])).
% 5.87/1.43 thf(zip_derived_cl504, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl10])).
% 5.87/1.43 thf(zip_derived_cl26, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 5.87/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.43 zip_derived_cl415])).
% 5.87/1.43 thf(zip_derived_cl446, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl443])).
% 5.87/1.43 thf(zip_derived_cl514, plain,
% 5.87/1.43 (![X0 : $i]:
% 5.87/1.43 ((multiply @ X0 @ (inverse @ (inverse @ (inverse @ X0)))) = (identity))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl446])).
% 5.87/1.43 thf(zip_derived_cl887, plain,
% 5.87/1.43 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl868, zip_derived_cl443, zip_derived_cl459,
% 5.87/1.43 zip_derived_cl10])).
% 5.87/1.43 thf(zip_derived_cl895, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl514, zip_derived_cl887])).
% 5.87/1.43 thf(zip_derived_cl13, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.43 ((double_divide @
% 5.87/1.43 (double_divide @ X1 @
% 5.87/1.43 (double_divide @
% 5.87/1.43 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @ (inverse @ X2))) @
% 5.87/1.43 (inverse @ identity)) = (X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 5.87/1.43 thf(zip_derived_cl11, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 5.87/1.43 = (inverse @ (multiply @ X1 @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 5.87/1.43 thf(zip_derived_cl95, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.43 ((multiply @ identity @ X0)
% 5.87/1.43 = (inverse @
% 5.87/1.43 (multiply @ (inverse @ identity) @
% 5.87/1.43 (double_divide @ X2 @
% 5.87/1.43 (double_divide @
% 5.87/1.43 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @
% 5.87/1.43 (inverse @ X1))))))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl11])).
% 5.87/1.43 thf(zip_derived_cl10, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 5.87/1.43 thf(zip_derived_cl100, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.43 ((inverse @ (inverse @ X0))
% 5.87/1.43 = (inverse @
% 5.87/1.43 (multiply @ (inverse @ identity) @
% 5.87/1.43 (double_divide @ X2 @
% 5.87/1.43 (double_divide @
% 5.87/1.43 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @
% 5.87/1.43 (inverse @ X1))))))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl95, zip_derived_cl10])).
% 5.87/1.43 thf(zip_derived_cl893, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl504, zip_derived_cl887])).
% 5.87/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.43 zip_derived_cl415])).
% 5.87/1.43 thf(zip_derived_cl6, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 5.87/1.43 thf(zip_derived_cl893, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl504, zip_derived_cl887])).
% 5.87/1.43 thf(zip_derived_cl943, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((double_divide @ X0 @ X1) = (inverse @ (multiply @ X1 @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl943, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((double_divide @ X0 @ X1) = (inverse @ (multiply @ X1 @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl943, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((double_divide @ X0 @ X1) = (inverse @ (multiply @ X1 @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl943, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((double_divide @ X0 @ X1) = (inverse @ (multiply @ X1 @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl10, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 5.87/1.43 thf(zip_derived_cl893, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl504, zip_derived_cl887])).
% 5.87/1.43 thf(zip_derived_cl928, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl893, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl504, zip_derived_cl887])).
% 5.87/1.43 thf(zip_derived_cl1044, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.43 ((X0)
% 5.87/1.43 = (multiply @
% 5.87/1.43 (inverse @
% 5.87/1.43 (multiply @ (inverse @ X1) @
% 5.87/1.43 (inverse @ (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X0)))) @
% 5.87/1.43 X2))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl100, zip_derived_cl893, zip_derived_cl443,
% 5.87/1.43 zip_derived_cl943, zip_derived_cl943, zip_derived_cl943,
% 5.87/1.43 zip_derived_cl943, zip_derived_cl928, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl1050, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((inverse @ (inverse @ (multiply @ X0 @ X1)))
% 5.87/1.43 = (multiply @
% 5.87/1.43 (inverse @ (multiply @ (inverse @ X1) @ (inverse @ identity))) @
% 5.87/1.43 X0))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl895, zip_derived_cl1044])).
% 5.87/1.43 thf(zip_derived_cl893, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl504, zip_derived_cl887])).
% 5.87/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.43 zip_derived_cl415])).
% 5.87/1.43 thf(zip_derived_cl504, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl10])).
% 5.87/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.43 zip_derived_cl415])).
% 5.87/1.43 thf(zip_derived_cl490, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ (double_divide @ (inverse @ X0) @ (inverse @ X1)) @
% 5.87/1.43 (inverse @ X1)) = (X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl20, zip_derived_cl443, zip_derived_cl1])).
% 5.87/1.43 thf(zip_derived_cl493, plain,
% 5.87/1.43 (![X0 : $i]:
% 5.87/1.43 ((multiply @
% 5.87/1.43 (double_divide @ (inverse @ X0) @ (inverse @ identity)) @ identity)
% 5.87/1.43 = (X0))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl443, zip_derived_cl490])).
% 5.87/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.43 zip_derived_cl415])).
% 5.87/1.43 thf(zip_derived_cl2, plain,
% 5.87/1.43 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 5.87/1.43 inference('cnf', [status(esa)], [inverse])).
% 5.87/1.43 thf(zip_derived_cl500, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ (inverse @ (inverse @ X0)) @ identity) = (X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl493, zip_derived_cl443, zip_derived_cl2])).
% 5.87/1.43 thf(zip_derived_cl522, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl500])).
% 5.87/1.43 thf(zip_derived_cl893, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl504, zip_derived_cl887])).
% 5.87/1.43 thf(zip_derived_cl934, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl522, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl893, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl504, zip_derived_cl887])).
% 5.87/1.43 thf(zip_derived_cl1062, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl1050, zip_derived_cl893, zip_derived_cl443,
% 5.87/1.43 zip_derived_cl934, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl1062, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl1050, zip_derived_cl893, zip_derived_cl443,
% 5.87/1.43 zip_derived_cl934, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl1062, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl1050, zip_derived_cl893, zip_derived_cl443,
% 5.87/1.43 zip_derived_cl934, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl1072, plain,
% 5.87/1.43 ((((multiply @ a4 @ b4) != (multiply @ a4 @ b4))
% 5.87/1.43 | ((multiply @ c3 @ (multiply @ a3 @ b3))
% 5.87/1.43 != (multiply @ a3 @ (multiply @ c3 @ b3))))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl930, zip_derived_cl1062, zip_derived_cl1062,
% 5.87/1.43 zip_derived_cl1062])).
% 5.87/1.43 thf(zip_derived_cl1073, plain,
% 5.87/1.43 (((multiply @ c3 @ (multiply @ a3 @ b3))
% 5.87/1.43 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 5.87/1.43 inference('simplify', [status(thm)], [zip_derived_cl1072])).
% 5.87/1.43 thf(zip_derived_cl504, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl10])).
% 5.87/1.43 thf(zip_derived_cl504, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl10])).
% 5.87/1.43 thf(zip_derived_cl490, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ (double_divide @ (inverse @ X0) @ (inverse @ X1)) @
% 5.87/1.43 (inverse @ X1)) = (X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl20, zip_derived_cl443, zip_derived_cl1])).
% 5.87/1.43 thf(zip_derived_cl519, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @
% 5.87/1.43 (double_divide @ (inverse @ X1) @
% 5.87/1.43 (inverse @ (inverse @ (inverse @ (inverse @ X0))))) @
% 5.87/1.43 X0) = (X1))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl490])).
% 5.87/1.43 thf(zip_derived_cl504, plain,
% 5.87/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl10])).
% 5.87/1.43 thf(zip_derived_cl531, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ (double_divide @ (inverse @ X1) @ X0) @ X0) = (X1))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl519, zip_derived_cl504])).
% 5.87/1.43 thf(zip_derived_cl647, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ (double_divide @ X0 @ X1) @ X1)
% 5.87/1.43 = (inverse @ (inverse @ (inverse @ X0))))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl531])).
% 5.87/1.43 thf(zip_derived_cl887, plain,
% 5.87/1.43 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ X0))) = (inverse @ X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl868, zip_derived_cl443, zip_derived_cl459,
% 5.87/1.43 zip_derived_cl10])).
% 5.87/1.43 thf(zip_derived_cl896, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ (double_divide @ X0 @ X1) @ X1) = (inverse @ X0))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl647, zip_derived_cl887])).
% 5.87/1.43 thf(zip_derived_cl943, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((double_divide @ X0 @ X1) = (inverse @ (multiply @ X1 @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl1062, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl1050, zip_derived_cl893, zip_derived_cl443,
% 5.87/1.43 zip_derived_cl934, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl1110, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ X1 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl896, zip_derived_cl943, zip_derived_cl1062])).
% 5.87/1.43 thf(zip_derived_cl1062, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl1050, zip_derived_cl893, zip_derived_cl443,
% 5.87/1.43 zip_derived_cl934, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl3, plain,
% 5.87/1.43 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 5.87/1.43 inference('cnf', [status(esa)], [identity])).
% 5.87/1.43 thf(zip_derived_cl1, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ X1 @ X0)
% 5.87/1.43 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 5.87/1.43 inference('cnf', [status(esa)], [multiply])).
% 5.87/1.43 thf(zip_derived_cl8, plain,
% 5.87/1.43 (![X0 : $i]:
% 5.87/1.43 ((multiply @ (inverse @ X0) @ X0)
% 5.87/1.43 = (double_divide @ identity @ identity))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 5.87/1.43 thf(zip_derived_cl6, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 5.87/1.43 thf(zip_derived_cl47, plain,
% 5.87/1.43 (![X0 : $i]:
% 5.87/1.43 ((multiply @ identity @ identity)
% 5.87/1.43 = (inverse @ (multiply @ (inverse @ X0) @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl6])).
% 5.87/1.43 thf(zip_derived_cl13, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.43 ((double_divide @
% 5.87/1.43 (double_divide @ X1 @
% 5.87/1.43 (double_divide @
% 5.87/1.43 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @ (inverse @ X2))) @
% 5.87/1.43 (inverse @ identity)) = (X0))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 5.87/1.43 thf(zip_derived_cl70, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.43 ((double_divide @
% 5.87/1.43 (double_divide @ X2 @
% 5.87/1.43 (double_divide @
% 5.87/1.43 (double_divide @ X0 @
% 5.87/1.43 (double_divide @ (multiply @ (inverse @ X1) @ X1) @ X2)) @
% 5.87/1.43 (multiply @ identity @ identity))) @
% 5.87/1.43 (inverse @ identity)) = (X0))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl13])).
% 5.87/1.43 thf(zip_derived_cl10, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 5.87/1.43 thf(zip_derived_cl89, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.87/1.43 ((double_divide @
% 5.87/1.43 (double_divide @ X2 @
% 5.87/1.43 (double_divide @
% 5.87/1.43 (double_divide @ X0 @
% 5.87/1.43 (double_divide @ (multiply @ (inverse @ X1) @ X1) @ X2)) @
% 5.87/1.43 (inverse @ (inverse @ identity)))) @
% 5.87/1.43 (inverse @ identity)) = (X0))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl10])).
% 5.87/1.43 thf(zip_derived_cl446, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl26, zip_derived_cl443])).
% 5.87/1.43 thf(zip_derived_cl943, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((double_divide @ X0 @ X1) = (inverse @ (multiply @ X1 @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl934, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl522, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl943, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((double_divide @ X0 @ X1) = (inverse @ (multiply @ X1 @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.43 zip_derived_cl415])).
% 5.87/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.43 zip_derived_cl415])).
% 5.87/1.43 thf(zip_derived_cl934, plain,
% 5.87/1.43 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl522, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl531, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((multiply @ (double_divide @ (inverse @ X1) @ X0) @ X0) = (X1))),
% 5.87/1.43 inference('demod', [status(thm)], [zip_derived_cl519, zip_derived_cl504])).
% 5.87/1.43 thf(zip_derived_cl957, plain,
% 5.87/1.43 (![X0 : $i]: ((double_divide @ (inverse @ X0) @ identity) = (X0))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl934, zip_derived_cl531])).
% 5.87/1.43 thf(zip_derived_cl943, plain,
% 5.87/1.43 (![X0 : $i, X1 : $i]:
% 5.87/1.43 ((double_divide @ X0 @ X1) = (inverse @ (multiply @ X1 @ X0)))),
% 5.87/1.43 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl893])).
% 5.87/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 5.87/1.43 inference('demod', [status(thm)],
% 5.87/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 5.87/1.43 zip_derived_cl415])).
% 5.87/1.43 thf(zip_derived_cl957, plain,
% 5.87/1.43 (![X0 : $i]: ((double_divide @ (inverse @ X0) @ identity) = (X0))),
% 6.00/1.43 inference('sup+', [status(thm)], [zip_derived_cl934, zip_derived_cl531])).
% 6.00/1.43 thf(zip_derived_cl1027, plain,
% 6.00/1.43 (![X0 : $i, X2 : $i]:
% 6.00/1.43 ((multiply @ (multiply @ (inverse @ X2) @ X0) @ X2) = (X0))),
% 6.00/1.43 inference('demod', [status(thm)],
% 6.00/1.43 [zip_derived_cl89, zip_derived_cl446, zip_derived_cl943,
% 6.00/1.43 zip_derived_cl934, zip_derived_cl943, zip_derived_cl443,
% 6.00/1.43 zip_derived_cl443, zip_derived_cl957, zip_derived_cl943,
% 6.00/1.43 zip_derived_cl443, zip_derived_cl957])).
% 6.00/1.43 thf(zip_derived_cl1079, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]:
% 6.00/1.43 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 6.00/1.43 inference('sup+', [status(thm)], [zip_derived_cl1062, zip_derived_cl1027])).
% 6.00/1.43 thf(zip_derived_cl1173, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]:
% 6.00/1.43 ((multiply @ (inverse @ X0) @ (multiply @ X1 @ X0)) = (X1))),
% 6.00/1.43 inference('sup+', [status(thm)], [zip_derived_cl1110, zip_derived_cl1079])).
% 6.00/1.43 thf(zip_derived_cl13, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.00/1.43 ((double_divide @
% 6.00/1.43 (double_divide @ X1 @
% 6.00/1.43 (double_divide @
% 6.00/1.43 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @ (inverse @ X2))) @
% 6.00/1.43 (inverse @ identity)) = (X0))),
% 6.00/1.43 inference('demod', [status(thm)],
% 6.00/1.43 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 6.00/1.43 thf(zip_derived_cl443, plain, (((identity) = (inverse @ identity))),
% 6.00/1.43 inference('demod', [status(thm)],
% 6.00/1.43 [zip_derived_cl436, zip_derived_cl3, zip_derived_cl2,
% 6.00/1.43 zip_derived_cl415])).
% 6.00/1.43 thf(zip_derived_cl1, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]:
% 6.00/1.43 ((multiply @ X1 @ X0)
% 6.00/1.43 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.00/1.43 inference('cnf', [status(esa)], [multiply])).
% 6.00/1.43 thf(zip_derived_cl444, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.00/1.43 ((multiply @
% 6.00/1.43 (double_divide @ (double_divide @ X0 @ (double_divide @ X2 @ X1)) @
% 6.00/1.43 (inverse @ X2)) @
% 6.00/1.43 X1) = (X0))),
% 6.00/1.43 inference('demod', [status(thm)],
% 6.00/1.43 [zip_derived_cl13, zip_derived_cl443, zip_derived_cl1])).
% 6.00/1.43 thf(zip_derived_cl943, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]:
% 6.00/1.43 ((double_divide @ X0 @ X1) = (inverse @ (multiply @ X1 @ X0)))),
% 6.00/1.43 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl893])).
% 6.00/1.43 thf(zip_derived_cl943, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]:
% 6.00/1.43 ((double_divide @ X0 @ X1) = (inverse @ (multiply @ X1 @ X0)))),
% 6.00/1.43 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl893])).
% 6.00/1.43 thf(zip_derived_cl1062, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 6.00/1.43 inference('demod', [status(thm)],
% 6.00/1.43 [zip_derived_cl1050, zip_derived_cl893, zip_derived_cl443,
% 6.00/1.43 zip_derived_cl934, zip_derived_cl893])).
% 6.00/1.43 thf(zip_derived_cl1027, plain,
% 6.00/1.43 (![X0 : $i, X2 : $i]:
% 6.00/1.43 ((multiply @ (multiply @ (inverse @ X2) @ X0) @ X2) = (X0))),
% 6.00/1.43 inference('demod', [status(thm)],
% 6.00/1.43 [zip_derived_cl89, zip_derived_cl446, zip_derived_cl943,
% 6.00/1.43 zip_derived_cl934, zip_derived_cl943, zip_derived_cl443,
% 6.00/1.43 zip_derived_cl443, zip_derived_cl957, zip_derived_cl943,
% 6.00/1.43 zip_derived_cl443, zip_derived_cl957])).
% 6.00/1.43 thf(zip_derived_cl1077, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]:
% 6.00/1.43 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 6.00/1.43 inference('sup+', [status(thm)], [zip_derived_cl1062, zip_derived_cl1027])).
% 6.00/1.43 thf(zip_derived_cl1110, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]:
% 6.00/1.43 ((multiply @ X1 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X0))),
% 6.00/1.43 inference('demod', [status(thm)],
% 6.00/1.43 [zip_derived_cl896, zip_derived_cl943, zip_derived_cl1062])).
% 6.00/1.43 thf(zip_derived_cl1138, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]:
% 6.00/1.43 ((multiply @ X1 @ (inverse @ X0))
% 6.00/1.43 = (inverse @ (multiply @ (inverse @ X1) @ X0)))),
% 6.00/1.43 inference('sup+', [status(thm)], [zip_derived_cl1077, zip_derived_cl1110])).
% 6.00/1.43 thf(zip_derived_cl943, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]:
% 6.00/1.43 ((double_divide @ X0 @ X1) = (inverse @ (multiply @ X1 @ X0)))),
% 6.00/1.43 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl893])).
% 6.00/1.43 thf(zip_derived_cl1138, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]:
% 6.00/1.43 ((multiply @ X1 @ (inverse @ X0))
% 6.00/1.43 = (inverse @ (multiply @ (inverse @ X1) @ X0)))),
% 6.00/1.43 inference('sup+', [status(thm)], [zip_derived_cl1077, zip_derived_cl1110])).
% 6.00/1.43 thf(zip_derived_cl893, plain,
% 6.00/1.43 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.00/1.43 inference('demod', [status(thm)], [zip_derived_cl504, zip_derived_cl887])).
% 6.00/1.43 thf(zip_derived_cl1027, plain,
% 6.00/1.43 (![X0 : $i, X2 : $i]:
% 6.00/1.43 ((multiply @ (multiply @ (inverse @ X2) @ X0) @ X2) = (X0))),
% 6.00/1.43 inference('demod', [status(thm)],
% 6.00/1.43 [zip_derived_cl89, zip_derived_cl446, zip_derived_cl943,
% 6.00/1.43 zip_derived_cl934, zip_derived_cl943, zip_derived_cl443,
% 6.00/1.43 zip_derived_cl443, zip_derived_cl957, zip_derived_cl943,
% 6.00/1.43 zip_derived_cl443, zip_derived_cl957])).
% 6.00/1.43 thf(zip_derived_cl1033, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]:
% 6.00/1.43 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X0)) = (X1))),
% 6.00/1.43 inference('sup+', [status(thm)], [zip_derived_cl893, zip_derived_cl1027])).
% 6.00/1.43 thf(zip_derived_cl1033, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]:
% 6.00/1.43 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X0)) = (X1))),
% 6.00/1.43 inference('sup+', [status(thm)], [zip_derived_cl893, zip_derived_cl1027])).
% 6.00/1.43 thf(zip_derived_cl1090, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]:
% 6.00/1.43 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))) = (inverse @ X1))),
% 6.00/1.43 inference('sup+', [status(thm)], [zip_derived_cl1033, zip_derived_cl1033])).
% 6.00/1.43 thf(zip_derived_cl1027, plain,
% 6.00/1.43 (![X0 : $i, X2 : $i]:
% 6.00/1.43 ((multiply @ (multiply @ (inverse @ X2) @ X0) @ X2) = (X0))),
% 6.00/1.43 inference('demod', [status(thm)],
% 6.00/1.43 [zip_derived_cl89, zip_derived_cl446, zip_derived_cl943,
% 6.00/1.43 zip_derived_cl934, zip_derived_cl943, zip_derived_cl443,
% 6.00/1.43 zip_derived_cl443, zip_derived_cl957, zip_derived_cl943,
% 6.00/1.43 zip_derived_cl443, zip_derived_cl957])).
% 6.00/1.43 thf(zip_derived_cl1375, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]:
% 6.00/1.43 ((multiply @ (inverse @ X0) @ X1)
% 6.00/1.43 = (inverse @ (multiply @ X0 @ (inverse @ X1))))),
% 6.00/1.43 inference('sup+', [status(thm)], [zip_derived_cl1090, zip_derived_cl1027])).
% 6.00/1.43 thf(zip_derived_cl1062, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 6.00/1.43 inference('demod', [status(thm)],
% 6.00/1.43 [zip_derived_cl1050, zip_derived_cl893, zip_derived_cl443,
% 6.00/1.43 zip_derived_cl934, zip_derived_cl893])).
% 6.00/1.43 thf(zip_derived_cl4509, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.00/1.43 ((multiply @ X1 @
% 6.00/1.43 (multiply @ X2 @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)))
% 6.00/1.43 = (X0))),
% 6.00/1.43 inference('demod', [status(thm)],
% 6.00/1.43 [zip_derived_cl444, zip_derived_cl943, zip_derived_cl943,
% 6.00/1.43 zip_derived_cl1138, zip_derived_cl943, zip_derived_cl1138,
% 6.00/1.43 zip_derived_cl1375, zip_derived_cl1062])).
% 6.00/1.43 thf(zip_derived_cl4571, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.00/1.43 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 6.00/1.43 = (multiply @ X0 @ (multiply @ X2 @ X1)))),
% 6.00/1.43 inference('sup+', [status(thm)], [zip_derived_cl1173, zip_derived_cl4509])).
% 6.00/1.43 thf(zip_derived_cl1062, plain,
% 6.00/1.43 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 6.00/1.43 inference('demod', [status(thm)],
% 6.00/1.43 [zip_derived_cl1050, zip_derived_cl893, zip_derived_cl443,
% 6.00/1.43 zip_derived_cl934, zip_derived_cl893])).
% 6.00/1.43 thf(zip_derived_cl4674, plain,
% 6.00/1.43 (((multiply @ a3 @ (multiply @ c3 @ b3))
% 6.00/1.43 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 6.00/1.43 inference('demod', [status(thm)],
% 6.00/1.43 [zip_derived_cl1073, zip_derived_cl4571, zip_derived_cl1062])).
% 6.00/1.43 thf(zip_derived_cl4675, plain, ($false),
% 6.00/1.43 inference('simplify', [status(thm)], [zip_derived_cl4674])).
% 6.00/1.43
% 6.00/1.43 % SZS output end Refutation
% 6.00/1.43
% 6.00/1.43
% 6.00/1.43 % Terminating...
% 6.00/1.46 % Runner terminated.
% 6.00/1.47 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------