TSTP Solution File: GRP079-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP079-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Hgntp0tpB7 true
% Computer : n027.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 01:49:50 EDT 2023
% Result : Unsatisfiable 3.14s 1.01s
% Output : Refutation 3.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP079-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Hgntp0tpB7 true
% 0.17/0.34 % Computer : n027.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon Aug 28 21:43:37 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.17/0.34 % Running portfolio for 300 s
% 0.17/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.34 % Number of cores: 8
% 0.21/0.35 % Python version: Python 3.6.8
% 0.21/0.35 % Running in FO mode
% 0.21/0.65 % Total configuration time : 435
% 0.21/0.65 % Estimated wc time : 1092
% 0.21/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 3.14/1.01 % Solved by fo/fo5.sh.
% 3.14/1.01 % done 503 iterations in 0.247s
% 3.14/1.01 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 3.14/1.01 % SZS output start Refutation
% 3.14/1.01 thf(a3_type, type, a3: $i).
% 3.14/1.01 thf(multiply_type, type, multiply: $i > $i > $i).
% 3.14/1.01 thf(c3_type, type, c3: $i).
% 3.14/1.01 thf(a2_type, type, a2: $i).
% 3.14/1.01 thf(a1_type, type, a1: $i).
% 3.14/1.01 thf(identity_type, type, identity: $i).
% 3.14/1.01 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 3.14/1.01 thf(inverse_type, type, inverse: $i > $i).
% 3.14/1.01 thf(b3_type, type, b3: $i).
% 3.14/1.01 thf(prove_these_axioms, conjecture,
% 3.14/1.01 (~( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 3.14/1.01 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 3.14/1.01 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 3.14/1.01 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) ) ))).
% 3.14/1.01 thf(zf_stmt_0, negated_conjecture,
% 3.14/1.01 (( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 3.14/1.01 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 3.14/1.01 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 3.14/1.01 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) )),
% 3.14/1.01 inference('cnf.neg', [status(esa)], [prove_these_axioms])).
% 3.14/1.01 thf(zip_derived_cl4, plain,
% 3.14/1.01 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.14/1.01 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 3.14/1.01 | ((multiply @ identity @ a2) != (a2))
% 3.14/1.01 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 3.14/1.01 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.14/1.01 thf(inverse, axiom, (( inverse @ X ) = ( double_divide @ X @ identity ))).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(multiply, axiom,
% 3.14/1.01 (( multiply @ X @ Y ) =
% 3.14/1.01 ( double_divide @ ( double_divide @ Y @ X ) @ identity ))).
% 3.14/1.01 thf(zip_derived_cl1, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X1 @ X0)
% 3.14/1.01 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [multiply])).
% 3.14/1.01 thf(zip_derived_cl7, plain,
% 3.14/1.01 (![X0 : $i]:
% 3.14/1.01 ((multiply @ identity @ X0)
% 3.14/1.01 = (double_divide @ (inverse @ X0) @ identity))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl10, plain,
% 3.14/1.01 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl34, plain,
% 3.14/1.01 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.14/1.01 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 3.14/1.01 | ((inverse @ (inverse @ a2)) != (a2))
% 3.14/1.01 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl10])).
% 3.14/1.01 thf(identity, axiom,
% 3.14/1.01 (( identity ) = ( double_divide @ X @ ( inverse @ X ) ))).
% 3.14/1.01 thf(zip_derived_cl3, plain,
% 3.14/1.01 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.14/1.01 inference('cnf', [status(esa)], [identity])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl1, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X1 @ X0)
% 3.14/1.01 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [multiply])).
% 3.14/1.01 thf(zip_derived_cl6, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.14/1.01 thf(zip_derived_cl37, plain,
% 3.14/1.01 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 3.14/1.01 thf(zip_derived_cl82, plain,
% 3.14/1.01 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.14/1.01 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 3.14/1.01 | ((inverse @ (inverse @ a2)) != (a2))
% 3.14/1.01 | ((inverse @ identity) != (identity)))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl34, zip_derived_cl37])).
% 3.14/1.01 thf(zip_derived_cl37, plain,
% 3.14/1.01 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 3.14/1.01 thf(zip_derived_cl3, plain,
% 3.14/1.01 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.14/1.01 inference('cnf', [status(esa)], [identity])).
% 3.14/1.01 thf(zip_derived_cl40, plain,
% 3.14/1.01 (![X0 : $i]:
% 3.14/1.01 ((identity)
% 3.14/1.01 = (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0)))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl37, zip_derived_cl3])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(single_axiom, axiom,
% 3.14/1.01 (( double_divide @
% 3.14/1.01 ( double_divide @ identity @ X ) @
% 3.14/1.01 ( double_divide @
% 3.14/1.01 ( double_divide @
% 3.14/1.01 ( double_divide @ Y @ Z ) @ ( double_divide @ identity @ identity ) ) @
% 3.14/1.01 ( double_divide @ X @ Z ) ) ) =
% 3.14/1.01 ( Y ))).
% 3.14/1.01 thf(zip_derived_cl0, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X0 @ X2) @
% 3.14/1.01 (double_divide @ identity @ identity)) @
% 3.14/1.01 (double_divide @ X1 @ X2)))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('cnf', [status(esa)], [single_axiom])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl13, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X0 @ X2) @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ X1 @ X2)))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl25, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (inverse @ identity) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X0 @ X1) @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ identity @ X1)))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 3.14/1.01 thf(zip_derived_cl495, plain,
% 3.14/1.01 (![X0 : $i]:
% 3.14/1.01 ((double_divide @ (inverse @ identity) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ identity @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0))))
% 3.14/1.01 = (identity))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl25])).
% 3.14/1.01 thf(zip_derived_cl3, plain,
% 3.14/1.01 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.14/1.01 inference('cnf', [status(esa)], [identity])).
% 3.14/1.01 thf(zip_derived_cl40, plain,
% 3.14/1.01 (![X0 : $i]:
% 3.14/1.01 ((identity)
% 3.14/1.01 = (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0)))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl37, zip_derived_cl3])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl510, plain,
% 3.14/1.01 (((double_divide @ (inverse @ identity) @ (inverse @ identity))
% 3.14/1.01 = (identity))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl495, zip_derived_cl3, zip_derived_cl40,
% 3.14/1.01 zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl25, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (inverse @ identity) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X0 @ X1) @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ identity @ X1)))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 3.14/1.01 thf(zip_derived_cl528, plain,
% 3.14/1.01 (((double_divide @ (inverse @ identity) @
% 3.14/1.01 (double_divide @ (double_divide @ identity @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ identity @ (inverse @ identity))))
% 3.14/1.01 = (inverse @ identity))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl510, zip_derived_cl25])).
% 3.14/1.01 thf(zip_derived_cl3, plain,
% 3.14/1.01 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.14/1.01 inference('cnf', [status(esa)], [identity])).
% 3.14/1.01 thf(zip_derived_cl3, plain,
% 3.14/1.01 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.14/1.01 inference('cnf', [status(esa)], [identity])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl510, plain,
% 3.14/1.01 (((double_divide @ (inverse @ identity) @ (inverse @ identity))
% 3.14/1.01 = (identity))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl495, zip_derived_cl3, zip_derived_cl40,
% 3.14/1.01 zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl543, plain, (((identity) = (inverse @ identity))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl528, zip_derived_cl3, zip_derived_cl3,
% 3.14/1.01 zip_derived_cl2, zip_derived_cl510])).
% 3.14/1.01 thf(zip_derived_cl553, plain,
% 3.14/1.01 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.14/1.01 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 3.14/1.01 | ((inverse @ (inverse @ a2)) != (a2))
% 3.14/1.01 | ((identity) != (identity)))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl82, zip_derived_cl543])).
% 3.14/1.01 thf(zip_derived_cl554, plain,
% 3.14/1.01 ((((inverse @ (inverse @ a2)) != (a2))
% 3.14/1.01 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.14/1.01 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 3.14/1.01 inference('simplify', [status(thm)], [zip_derived_cl553])).
% 3.14/1.01 thf(zip_derived_cl37, plain,
% 3.14/1.01 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 3.14/1.01 thf(zip_derived_cl543, plain, (((identity) = (inverse @ identity))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl528, zip_derived_cl3, zip_derived_cl3,
% 3.14/1.01 zip_derived_cl2, zip_derived_cl510])).
% 3.14/1.01 thf(zip_derived_cl549, plain,
% 3.14/1.01 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl37, zip_derived_cl543])).
% 3.14/1.01 thf(zip_derived_cl3, plain,
% 3.14/1.01 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.14/1.01 inference('cnf', [status(esa)], [identity])).
% 3.14/1.01 thf(zip_derived_cl13, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X0 @ X2) @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ X1 @ X2)))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl18, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X0 @ (inverse @ X1)) @
% 3.14/1.01 (inverse @ identity)) @
% 3.14/1.01 identity))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 3.14/1.01 thf(zip_derived_cl1, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X1 @ X0)
% 3.14/1.01 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [multiply])).
% 3.14/1.01 thf(zip_derived_cl28, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (multiply @ (inverse @ identity) @
% 3.14/1.01 (double_divide @ X0 @ (inverse @ X1))))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl1])).
% 3.14/1.01 thf(zip_derived_cl543, plain, (((identity) = (inverse @ identity))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl528, zip_derived_cl3, zip_derived_cl3,
% 3.14/1.01 zip_derived_cl2, zip_derived_cl510])).
% 3.14/1.01 thf(zip_derived_cl1, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X1 @ X0)
% 3.14/1.01 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [multiply])).
% 3.14/1.01 thf(zip_derived_cl1, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X1 @ X0)
% 3.14/1.01 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [multiply])).
% 3.14/1.01 thf(zip_derived_cl9, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 3.14/1.01 = (double_divide @ (multiply @ X1 @ X0) @ identity))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl1])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl11, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 3.14/1.01 = (inverse @ (multiply @ X1 @ X0)))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl685, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (inverse @ (multiply @ (inverse @ X1) @ X0))) = (X0))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl28, zip_derived_cl543, zip_derived_cl11])).
% 3.14/1.01 thf(zip_derived_cl690, plain,
% 3.14/1.01 (![X0 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X0) @
% 3.14/1.01 (inverse @ identity)) = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl549, zip_derived_cl685])).
% 3.14/1.01 thf(zip_derived_cl543, plain, (((identity) = (inverse @ identity))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl528, zip_derived_cl3, zip_derived_cl3,
% 3.14/1.01 zip_derived_cl2, zip_derived_cl510])).
% 3.14/1.01 thf(zip_derived_cl1, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X1 @ X0)
% 3.14/1.01 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [multiply])).
% 3.14/1.01 thf(zip_derived_cl699, plain,
% 3.14/1.01 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl690, zip_derived_cl543, zip_derived_cl1])).
% 3.14/1.01 thf(zip_derived_cl3, plain,
% 3.14/1.01 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.14/1.01 inference('cnf', [status(esa)], [identity])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl13, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X0 @ X2) @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ X1 @ X2)))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl17, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X0) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X1 @ identity) @
% 3.14/1.01 (inverse @ identity)) @
% 3.14/1.01 (inverse @ X0)))
% 3.14/1.01 = (X1))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl27, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X0) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (inverse @ X1) @ (inverse @ identity)) @
% 3.14/1.01 (inverse @ X0)))
% 3.14/1.01 = (X1))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl543, plain, (((identity) = (inverse @ identity))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl528, zip_derived_cl3, zip_derived_cl3,
% 3.14/1.01 zip_derived_cl2, zip_derived_cl510])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl594, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X0) @
% 3.14/1.01 (double_divide @ (inverse @ (inverse @ X1)) @ (inverse @ X0)))
% 3.14/1.01 = (X1))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl27, zip_derived_cl543, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl599, plain,
% 3.14/1.01 (![X0 : $i]:
% 3.14/1.01 ((double_divide @
% 3.14/1.01 (double_divide @ identity @ (inverse @ (inverse @ X0))) @ identity)
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl594])).
% 3.14/1.01 thf(zip_derived_cl1, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X1 @ X0)
% 3.14/1.01 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [multiply])).
% 3.14/1.01 thf(zip_derived_cl640, plain,
% 3.14/1.01 (![X0 : $i]: ((multiply @ (inverse @ (inverse @ X0)) @ identity) = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl599, zip_derived_cl1])).
% 3.14/1.01 thf(zip_derived_cl711, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl699, zip_derived_cl640])).
% 3.14/1.01 thf(zip_derived_cl714, plain,
% 3.14/1.01 ((((a2) != (a2))
% 3.14/1.01 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.14/1.01 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl554, zip_derived_cl711])).
% 3.14/1.01 thf(zip_derived_cl715, plain,
% 3.14/1.01 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.14/1.01 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 3.14/1.01 inference('simplify', [status(thm)], [zip_derived_cl714])).
% 3.14/1.01 thf(zip_derived_cl711, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl699, zip_derived_cl640])).
% 3.14/1.01 thf(zip_derived_cl3, plain,
% 3.14/1.01 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.14/1.01 inference('cnf', [status(esa)], [identity])).
% 3.14/1.01 thf(zip_derived_cl13, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X0 @ X2) @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ X1 @ X2)))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl22, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ identity @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ X1 @ (inverse @ X0))))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 3.14/1.01 thf(zip_derived_cl3, plain,
% 3.14/1.01 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.14/1.01 inference('cnf', [status(esa)], [identity])).
% 3.14/1.01 thf(zip_derived_cl31, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (double_divide @ identity @ (double_divide @ X1 @ (inverse @ X0))))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl22, zip_derived_cl3])).
% 3.14/1.01 thf(zip_derived_cl711, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl699, zip_derived_cl640])).
% 3.14/1.01 thf(zip_derived_cl543, plain, (((identity) = (inverse @ identity))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl528, zip_derived_cl3, zip_derived_cl3,
% 3.14/1.01 zip_derived_cl2, zip_derived_cl510])).
% 3.14/1.01 thf(zip_derived_cl594, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X0) @
% 3.14/1.01 (double_divide @ (inverse @ (inverse @ X1)) @ (inverse @ X0)))
% 3.14/1.01 = (X1))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl27, zip_derived_cl543, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl601, plain,
% 3.14/1.01 (![X0 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ identity) @
% 3.14/1.01 (double_divide @ (inverse @ (inverse @ X0)) @ identity)) = (
% 3.14/1.01 X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl543, zip_derived_cl594])).
% 3.14/1.01 thf(zip_derived_cl543, plain, (((identity) = (inverse @ identity))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl528, zip_derived_cl3, zip_derived_cl3,
% 3.14/1.01 zip_derived_cl2, zip_derived_cl510])).
% 3.14/1.01 thf(zip_derived_cl3, plain,
% 3.14/1.01 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.14/1.01 inference('cnf', [status(esa)], [identity])).
% 3.14/1.01 thf(zip_derived_cl561, plain,
% 3.14/1.01 (((identity) = (double_divide @ identity @ identity))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl543, zip_derived_cl3])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl607, plain,
% 3.14/1.01 (![X0 : $i]:
% 3.14/1.01 ((double_divide @ identity @ (inverse @ (inverse @ (inverse @ X0))))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl601, zip_derived_cl561, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl711, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl699, zip_derived_cl640])).
% 3.14/1.01 thf(zip_derived_cl717, plain,
% 3.14/1.01 (![X0 : $i]: ((double_divide @ identity @ (inverse @ X0)) = (X0))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl607, zip_derived_cl711])).
% 3.14/1.01 thf(zip_derived_cl744, plain,
% 3.14/1.01 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl711, zip_derived_cl717])).
% 3.14/1.01 thf(zip_derived_cl744, plain,
% 3.14/1.01 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl711, zip_derived_cl717])).
% 3.14/1.01 thf(zip_derived_cl6, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.14/1.01 thf(zip_derived_cl872, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X1))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl31, zip_derived_cl744, zip_derived_cl744,
% 3.14/1.01 zip_derived_cl6])).
% 3.14/1.01 thf(zip_derived_cl699, plain,
% 3.14/1.01 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl690, zip_derived_cl543, zip_derived_cl1])).
% 3.14/1.01 thf(zip_derived_cl1, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X1 @ X0)
% 3.14/1.01 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [multiply])).
% 3.14/1.01 thf(zip_derived_cl13, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X0 @ X2) @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ X1 @ X2)))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl20, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((double_divide @
% 3.14/1.01 (double_divide @ identity @ (double_divide @ X0 @ X1)) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X2 @ identity) @
% 3.14/1.01 (inverse @ identity)) @
% 3.14/1.01 (multiply @ X1 @ X0)))
% 3.14/1.01 = (X2))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl13])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl29, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((double_divide @
% 3.14/1.01 (double_divide @ identity @ (double_divide @ X0 @ X1)) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (inverse @ X2) @ (inverse @ identity)) @
% 3.14/1.01 (multiply @ X1 @ X0)))
% 3.14/1.01 = (X2))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl744, plain,
% 3.14/1.01 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl711, zip_derived_cl717])).
% 3.14/1.01 thf(zip_derived_cl6, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.14/1.01 thf(zip_derived_cl543, plain, (((identity) = (inverse @ identity))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl528, zip_derived_cl3, zip_derived_cl3,
% 3.14/1.01 zip_derived_cl2, zip_derived_cl510])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl711, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl699, zip_derived_cl640])).
% 3.14/1.01 thf(zip_derived_cl759, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((double_divide @ (multiply @ X1 @ X0) @
% 3.14/1.01 (double_divide @ X2 @ (multiply @ X1 @ X0))) = (X2))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl29, zip_derived_cl744, zip_derived_cl6,
% 3.14/1.01 zip_derived_cl543, zip_derived_cl2, zip_derived_cl711])).
% 3.14/1.01 thf(zip_derived_cl765, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (multiply @ X0 @ identity) @
% 3.14/1.01 (double_divide @ X1 @ X0)) = (X1))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl699, zip_derived_cl759])).
% 3.14/1.01 thf(zip_derived_cl699, plain,
% 3.14/1.01 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl690, zip_derived_cl543, zip_derived_cl1])).
% 3.14/1.01 thf(zip_derived_cl773, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ X0 @ (double_divide @ X1 @ X0)) = (X1))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl765, zip_derived_cl699])).
% 3.14/1.01 thf(zip_derived_cl6, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.14/1.01 thf(zip_derived_cl857, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ (double_divide @ X0 @ X1) @ X1) = (inverse @ X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl773, zip_derived_cl6])).
% 3.14/1.01 thf(zip_derived_cl932, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1))
% 3.14/1.01 = (inverse @ (inverse @ X1)))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl872, zip_derived_cl857])).
% 3.14/1.01 thf(zip_derived_cl711, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl699, zip_derived_cl640])).
% 3.14/1.01 thf(zip_derived_cl940, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)) = (X1))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl932, zip_derived_cl711])).
% 3.14/1.01 thf(zip_derived_cl955, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)) = (X1))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl711, zip_derived_cl940])).
% 3.14/1.01 thf(zip_derived_cl711, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl699, zip_derived_cl640])).
% 3.14/1.01 thf(zip_derived_cl872, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X1))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl31, zip_derived_cl744, zip_derived_cl744,
% 3.14/1.01 zip_derived_cl6])).
% 3.14/1.01 thf(zip_derived_cl883, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (inverse @ X1) @ (multiply @ X0 @ X1))
% 3.14/1.01 = (inverse @ X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl711, zip_derived_cl872])).
% 3.14/1.01 thf(zip_derived_cl1, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X1 @ X0)
% 3.14/1.01 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [multiply])).
% 3.14/1.01 thf(zip_derived_cl13, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X0 @ X2) @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ X1 @ X2)))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl13, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X0 @ X2) @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ X1 @ X2)))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl14, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X3) @
% 3.14/1.01 (double_divide @ (double_divide @ X0 @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ X3 @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X0 @ X2) @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ X1 @ X2)))))
% 3.14/1.01 = (double_divide @ identity @ X1))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 3.14/1.01 thf(zip_derived_cl166, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X3) @
% 3.14/1.01 (double_divide @ (double_divide @ X2 @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ X3 @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X2 @ identity) @
% 3.14/1.01 (inverse @ identity)) @
% 3.14/1.01 (multiply @ X1 @ X0)))))
% 3.14/1.01 = (double_divide @ identity @ (double_divide @ X0 @ X1)))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl14])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl187, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X3) @
% 3.14/1.01 (double_divide @ (double_divide @ X2 @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ X3 @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (inverse @ X2) @ (inverse @ identity)) @
% 3.14/1.01 (multiply @ X1 @ X0)))))
% 3.14/1.01 = (double_divide @ identity @ (double_divide @ X0 @ X1)))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl166, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl744, plain,
% 3.14/1.01 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl711, zip_derived_cl717])).
% 3.14/1.01 thf(zip_derived_cl543, plain, (((identity) = (inverse @ identity))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl528, zip_derived_cl3, zip_derived_cl3,
% 3.14/1.01 zip_derived_cl2, zip_derived_cl510])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl543, plain, (((identity) = (inverse @ identity))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl528, zip_derived_cl3, zip_derived_cl3,
% 3.14/1.01 zip_derived_cl2, zip_derived_cl510])).
% 3.14/1.01 thf(zip_derived_cl3, plain,
% 3.14/1.01 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.14/1.01 inference('cnf', [status(esa)], [identity])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl13, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (double_divide @ X0 @ X2) @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ X1 @ X2)))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl21, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (inverse @ X0) @ (inverse @ identity)) @
% 3.14/1.01 (double_divide @ X1 @ identity)))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl30, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ identity @ X1) @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (double_divide @ (inverse @ X0) @ (inverse @ identity)) @
% 3.14/1.01 (inverse @ X1)))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl21, zip_derived_cl2])).
% 3.14/1.01 thf(zip_derived_cl744, plain,
% 3.14/1.01 (![X0 : $i]: ((double_divide @ identity @ X0) = (inverse @ X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl711, zip_derived_cl717])).
% 3.14/1.01 thf(zip_derived_cl543, plain, (((identity) = (inverse @ identity))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl528, zip_derived_cl3, zip_derived_cl3,
% 3.14/1.01 zip_derived_cl2, zip_derived_cl510])).
% 3.14/1.01 thf(zip_derived_cl2, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.14/1.01 inference('cnf', [status(esa)], [inverse])).
% 3.14/1.01 thf(zip_derived_cl711, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl699, zip_derived_cl640])).
% 3.14/1.01 thf(zip_derived_cl812, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (inverse @ X1) @
% 3.14/1.01 (double_divide @ X0 @ (inverse @ X1))) = (X0))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl30, zip_derived_cl744, zip_derived_cl543,
% 3.14/1.01 zip_derived_cl2, zip_derived_cl711])).
% 3.14/1.01 thf(zip_derived_cl816, plain,
% 3.14/1.01 (![X0 : $i]: ((double_divide @ (inverse @ X0) @ identity) = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl812])).
% 3.14/1.01 thf(zip_derived_cl6, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.14/1.01 thf(zip_derived_cl711, plain,
% 3.14/1.01 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl699, zip_derived_cl640])).
% 3.14/1.01 thf(zip_derived_cl723, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl711])).
% 3.14/1.01 thf(zip_derived_cl872, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X1))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl31, zip_derived_cl744, zip_derived_cl744,
% 3.14/1.01 zip_derived_cl6])).
% 3.14/1.01 thf(zip_derived_cl773, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ X0 @ (double_divide @ X1 @ X0)) = (X1))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl765, zip_derived_cl699])).
% 3.14/1.01 thf(zip_derived_cl773, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ X0 @ (double_divide @ X1 @ X0)) = (X1))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl765, zip_derived_cl699])).
% 3.14/1.01 thf(zip_derived_cl858, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ X0 @ X1) @ X0) = (X1))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl773, zip_derived_cl773])).
% 3.14/1.01 thf(zip_derived_cl914, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ X0 @ (inverse @ X1))
% 3.14/1.01 = (multiply @ (inverse @ X0) @ X1))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl872, zip_derived_cl858])).
% 3.14/1.01 thf(zip_derived_cl1162, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((double_divide @ X2 @ (double_divide @ X1 @ X0))
% 3.14/1.01 = (multiply @ (inverse @ X2) @ (multiply @ X0 @ X1)))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl723, zip_derived_cl914])).
% 3.14/1.01 thf(zip_derived_cl858, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (double_divide @ X0 @ X1) @ X0) = (X1))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl773, zip_derived_cl773])).
% 3.14/1.01 thf(zip_derived_cl6, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.14/1.01 thf(zip_derived_cl899, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X1 @ (double_divide @ X1 @ X0)) = (inverse @ X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl858, zip_derived_cl6])).
% 3.14/1.01 thf(zip_derived_cl940, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)) = (X1))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl932, zip_derived_cl711])).
% 3.14/1.01 thf(zip_derived_cl1095, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X1 @ (inverse @ X0))
% 3.14/1.01 = (double_divide @ (inverse @ X1) @ X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl899, zip_derived_cl940])).
% 3.14/1.01 thf(zip_derived_cl872, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X1))
% 3.14/1.01 = (X0))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl31, zip_derived_cl744, zip_derived_cl744,
% 3.14/1.01 zip_derived_cl6])).
% 3.14/1.01 thf(zip_derived_cl899, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X1 @ (double_divide @ X1 @ X0)) = (inverse @ X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl858, zip_derived_cl6])).
% 3.14/1.01 thf(zip_derived_cl1107, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ (inverse @ X1) @ X0)
% 3.14/1.01 = (inverse @ (multiply @ (inverse @ X0) @ X1)))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl872, zip_derived_cl899])).
% 3.14/1.01 thf(zip_derived_cl723, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl711])).
% 3.14/1.01 thf(zip_derived_cl1095, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ X1 @ (inverse @ X0))
% 3.14/1.01 = (double_divide @ (inverse @ X1) @ X0))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl899, zip_derived_cl940])).
% 3.14/1.01 thf(zip_derived_cl723, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl711])).
% 3.14/1.01 thf(zip_derived_cl723, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl711])).
% 3.14/1.01 thf(zip_derived_cl717, plain,
% 3.14/1.01 (![X0 : $i]: ((double_divide @ identity @ (inverse @ X0)) = (X0))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl607, zip_derived_cl711])).
% 3.14/1.01 thf(zip_derived_cl803, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ identity @ (double_divide @ X1 @ X0))
% 3.14/1.01 = (multiply @ X0 @ X1))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl723, zip_derived_cl717])).
% 3.14/1.01 thf(zip_derived_cl2855, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.14/1.01 ((multiply @ X3 @
% 3.14/1.01 (double_divide @
% 3.14/1.01 (multiply @ (double_divide @ X2 @ (multiply @ X1 @ X0)) @ X3) @ X2))
% 3.14/1.01 = (multiply @ X1 @ X0))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl187, zip_derived_cl744, zip_derived_cl543,
% 3.14/1.01 zip_derived_cl2, zip_derived_cl543, zip_derived_cl816,
% 3.14/1.01 zip_derived_cl1162, zip_derived_cl1095, zip_derived_cl1107,
% 3.14/1.01 zip_derived_cl723, zip_derived_cl1095, zip_derived_cl723,
% 3.14/1.01 zip_derived_cl803])).
% 3.14/1.01 thf(zip_derived_cl2909, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((multiply @ X2 @
% 3.14/1.01 (double_divide @ (multiply @ (inverse @ X0) @ X2) @ (inverse @ X1)))
% 3.14/1.01 = (multiply @ X0 @ X1))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl883, zip_derived_cl2855])).
% 3.14/1.01 thf(zip_derived_cl914, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((double_divide @ X0 @ (inverse @ X1))
% 3.14/1.01 = (multiply @ (inverse @ X0) @ X1))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl872, zip_derived_cl858])).
% 3.14/1.01 thf(zip_derived_cl1107, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i]:
% 3.14/1.01 ((multiply @ (inverse @ X1) @ X0)
% 3.14/1.01 = (inverse @ (multiply @ (inverse @ X0) @ X1)))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl872, zip_derived_cl899])).
% 3.14/1.01 thf(zip_derived_cl2952, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((multiply @ X2 @ (multiply @ (multiply @ (inverse @ X2) @ X0) @ X1))
% 3.14/1.01 = (multiply @ X0 @ X1))),
% 3.14/1.01 inference('demod', [status(thm)],
% 3.14/1.01 [zip_derived_cl2909, zip_derived_cl914, zip_derived_cl1107])).
% 3.14/1.01 thf(zip_derived_cl3041, plain,
% 3.14/1.01 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.14/1.01 ((multiply @ X2 @ (multiply @ X0 @ X1))
% 3.14/1.01 = (multiply @ (multiply @ X2 @ X0) @ X1))),
% 3.14/1.01 inference('sup+', [status(thm)], [zip_derived_cl955, zip_derived_cl2952])).
% 3.14/1.01 thf(zip_derived_cl3088, plain,
% 3.14/1.01 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 3.14/1.01 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 3.14/1.01 inference('demod', [status(thm)], [zip_derived_cl715, zip_derived_cl3041])).
% 3.14/1.01 thf(zip_derived_cl3089, plain, ($false),
% 3.14/1.01 inference('simplify', [status(thm)], [zip_derived_cl3088])).
% 3.14/1.01
% 3.14/1.01 % SZS output end Refutation
% 3.14/1.01
% 3.14/1.01
% 3.14/1.01 % Terminating...
% 3.38/1.09 % Runner terminated.
% 3.38/1.10 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------