%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP078-1 : TPTP v9.2.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.6AFSqYGkUx true
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:35:35 PM UTC 2025
% Result : Unsatisfiable 3.87s 1.14s
% Output : Refutation 3.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP078-1 : TPTP v9.2.0. Bugfixed v2.3.0.
% 0.00/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.6AFSqYGkUx true
% 0.11/0.31 % Computer : n023.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Wed Oct 1 14:04:38 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % Running portfolio for 300 s
% 0.11/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Number of cores: 8
% 0.11/0.32 % Python version: Python 3.6.8
% 0.11/0.32 % Running in FO mode
% 0.51/0.58 % Total configuration time : 435
% 0.51/0.58 % Estimated wc time : 1092
% 0.51/0.58 % Estimated cpu time (7 cpus) : 156.0
% 0.90/0.67 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.90/0.67 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.90/0.67 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.90/0.68 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.90/0.68 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.90/0.68 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.90/0.68 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 3.87/1.14 % Solved by fo/fo5.sh.
% 3.87/1.14 % done 528 iterations in 0.428s
% 3.87/1.14 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 3.87/1.14 % SZS output start Refutation
% 3.87/1.14 thf(a3_type, type, a3: $i).
% 3.87/1.14 thf(multiply_type, type, multiply: $i > $i > $i).
% 3.87/1.14 thf(c3_type, type, c3: $i).
% 3.87/1.14 thf(a2_type, type, a2: $i).
% 3.87/1.14 thf(a1_type, type, a1: $i).
% 3.87/1.14 thf(identity_type, type, identity: $i).
% 3.87/1.14 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 3.87/1.14 thf(inverse_type, type, inverse: $i > $i).
% 3.87/1.14 thf(b3_type, type, b3: $i).
% 3.87/1.14 thf(prove_these_axioms, conjecture,
% 3.87/1.14 (~( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 3.87/1.14 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 3.87/1.14 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 3.87/1.14 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) ) ))).
% 3.87/1.14 thf(zf_stmt_0, negated_conjecture,
% 3.87/1.14 (( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 3.87/1.14 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 3.87/1.14 ( ( multiply @ identity @ a2 ) != ( a2 ) ) |
% 3.87/1.14 ( ( multiply @ ( inverse @ a1 ) @ a1 ) != ( identity ) )),
% 3.87/1.14 inference('cnf.neg', [status(esa)], [prove_these_axioms])).
% 3.87/1.14 thf(zip_derived_cl4, plain,
% 3.87/1.14 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.87/1.14 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 3.87/1.14 | ((multiply @ identity @ a2) != (a2))
% 3.87/1.14 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 3.87/1.14 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.87/1.14 thf(inverse, axiom, (( inverse @ X ) = ( double_divide @ X @ identity ))).
% 3.87/1.14 thf(zip_derived_cl2, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [inverse])).
% 3.87/1.14 thf(multiply, axiom,
% 3.87/1.14 (( multiply @ X @ Y ) =
% 3.87/1.14 ( double_divide @ ( double_divide @ Y @ X ) @ identity ))).
% 3.87/1.14 thf(zip_derived_cl1, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X1 @ X0)
% 3.87/1.14 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [multiply])).
% 3.87/1.14 thf(zip_derived_cl7, plain,
% 3.87/1.14 (![X0 : $i]:
% 3.87/1.14 ((multiply @ identity @ X0)
% 3.87/1.14 = (double_divide @ (inverse @ X0) @ identity))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl2, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [inverse])).
% 3.87/1.14 thf(zip_derived_cl10, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl24, plain,
% 3.87/1.14 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.87/1.14 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 3.87/1.14 | ((inverse @ (inverse @ a2)) != (a2))
% 3.87/1.14 | ((multiply @ (inverse @ a1) @ a1) != (identity)))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl10])).
% 3.87/1.14 thf(identity, axiom,
% 3.87/1.14 (( identity ) = ( double_divide @ X @ ( inverse @ X ) ))).
% 3.87/1.14 thf(zip_derived_cl3, plain,
% 3.87/1.14 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.87/1.14 inference('cnf', [status(esa)], [identity])).
% 3.87/1.14 thf(zip_derived_cl2, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [inverse])).
% 3.87/1.14 thf(zip_derived_cl1, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X1 @ X0)
% 3.87/1.14 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [multiply])).
% 3.87/1.14 thf(zip_derived_cl6, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl29, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 3.87/1.14 thf(zip_derived_cl74, plain,
% 3.87/1.14 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.87/1.14 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 3.87/1.14 | ((inverse @ (inverse @ a2)) != (a2))
% 3.87/1.14 | ((inverse @ identity) != (identity)))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl24, zip_derived_cl29])).
% 3.87/1.14 thf(zip_derived_cl3, plain,
% 3.87/1.14 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.87/1.14 inference('cnf', [status(esa)], [identity])).
% 3.87/1.14 thf(zip_derived_cl1, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X1 @ X0)
% 3.87/1.14 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [multiply])).
% 3.87/1.14 thf(zip_derived_cl8, plain,
% 3.87/1.14 (![X0 : $i]:
% 3.87/1.14 ((multiply @ (inverse @ X0) @ X0)
% 3.87/1.14 = (double_divide @ identity @ identity))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl6, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl50, plain,
% 3.87/1.14 (![X0 : $i]:
% 3.87/1.14 ((multiply @ identity @ identity)
% 3.87/1.14 = (inverse @ (multiply @ (inverse @ X0) @ X0)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl6])).
% 3.87/1.14 thf(zip_derived_cl8, plain,
% 3.87/1.14 (![X0 : $i]:
% 3.87/1.14 ((multiply @ (inverse @ X0) @ X0)
% 3.87/1.14 = (double_divide @ identity @ identity))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl76, plain,
% 3.87/1.14 (![X0 : $i]:
% 3.87/1.14 ((multiply @ (multiply @ identity @ identity) @
% 3.87/1.14 (multiply @ (inverse @ X0) @ X0))
% 3.87/1.14 = (double_divide @ identity @ identity))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl8])).
% 3.87/1.14 thf(zip_derived_cl10, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl2, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [inverse])).
% 3.87/1.14 thf(zip_derived_cl95, plain,
% 3.87/1.14 (![X0 : $i]:
% 3.87/1.14 ((multiply @ (inverse @ (inverse @ identity)) @
% 3.87/1.14 (multiply @ (inverse @ X0) @ X0)) = (inverse @ identity))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl76, zip_derived_cl10, zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl2, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [inverse])).
% 3.87/1.14 thf(zip_derived_cl3, plain,
% 3.87/1.14 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.87/1.14 inference('cnf', [status(esa)], [identity])).
% 3.87/1.14 thf(zip_derived_cl2, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [inverse])).
% 3.87/1.14 thf(single_axiom, axiom,
% 3.87/1.14 (( double_divide @
% 3.87/1.14 ( double_divide @ identity @ X ) @
% 3.87/1.14 ( double_divide @
% 3.87/1.14 identity @
% 3.87/1.14 ( double_divide @
% 3.87/1.14 ( double_divide @ ( double_divide @ X @ Y ) @ identity ) @
% 3.87/1.14 ( double_divide @ Z @ Y ) ) ) ) =
% 3.87/1.14 ( Z ))).
% 3.87/1.14 thf(zip_derived_cl0, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X1) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @
% 3.87/1.14 (double_divide @ (double_divide @ X1 @ X2) @ identity) @
% 3.87/1.14 (double_divide @ X0 @ X2))))
% 3.87/1.14 = (X0))),
% 3.87/1.14 inference('cnf', [status(esa)], [single_axiom])).
% 3.87/1.14 thf(zip_derived_cl1, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X1 @ X0)
% 3.87/1.14 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [multiply])).
% 3.87/1.14 thf(zip_derived_cl13, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X1) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (multiply @ X2 @ X1) @ (double_divide @ X0 @ X2))))
% 3.87/1.14 = (X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl16, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X1) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (multiply @ identity @ X1) @ (inverse @ X0))))
% 3.87/1.14 = (X0))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 3.87/1.14 thf(zip_derived_cl10, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl298, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X1) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (inverse @ (inverse @ X1)) @ (inverse @ X0))))
% 3.87/1.14 = (X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl10])).
% 3.87/1.14 thf(zip_derived_cl305, plain,
% 3.87/1.14 (![X0 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X0) @
% 3.87/1.14 (double_divide @ identity @ identity)) = (inverse @ (inverse @ X0)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl298])).
% 3.87/1.14 thf(zip_derived_cl2, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [inverse])).
% 3.87/1.14 thf(zip_derived_cl316, plain,
% 3.87/1.14 (![X0 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X0) @
% 3.87/1.14 (inverse @ identity)) = (inverse @ (inverse @ X0)))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl305, zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl352, plain,
% 3.87/1.14 (((double_divide @ (inverse @ identity) @ (inverse @ identity))
% 3.87/1.14 = (inverse @ (inverse @ identity)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl316])).
% 3.87/1.14 thf(zip_derived_cl2, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [inverse])).
% 3.87/1.14 thf(zip_derived_cl13, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X1) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (multiply @ X2 @ X1) @ (double_divide @ X0 @ X2))))
% 3.87/1.14 = (X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl20, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((double_divide @ (inverse @ identity) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (multiply @ X1 @ identity) @
% 3.87/1.14 (double_divide @ X0 @ X1))))
% 3.87/1.14 = (X0))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 3.87/1.14 thf(zip_derived_cl650, plain,
% 3.87/1.14 (((double_divide @ (inverse @ identity) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (multiply @ (inverse @ identity) @ identity) @
% 3.87/1.14 (inverse @ (inverse @ identity)))))
% 3.87/1.14 = (inverse @ identity))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl352, zip_derived_cl20])).
% 3.87/1.14 thf(zip_derived_cl8, plain,
% 3.87/1.14 (![X0 : $i]:
% 3.87/1.14 ((multiply @ (inverse @ X0) @ X0)
% 3.87/1.14 = (double_divide @ identity @ identity))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl2, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [inverse])).
% 3.87/1.14 thf(zip_derived_cl3, plain,
% 3.87/1.14 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.87/1.14 inference('cnf', [status(esa)], [identity])).
% 3.87/1.14 thf(zip_derived_cl2, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [inverse])).
% 3.87/1.14 thf(zip_derived_cl352, plain,
% 3.87/1.14 (((double_divide @ (inverse @ identity) @ (inverse @ identity))
% 3.87/1.14 = (inverse @ (inverse @ identity)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl316])).
% 3.87/1.14 thf(zip_derived_cl671, plain,
% 3.87/1.14 (((inverse @ (inverse @ identity)) = (inverse @ identity))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl650, zip_derived_cl8, zip_derived_cl2,
% 3.87/1.14 zip_derived_cl3, zip_derived_cl2, zip_derived_cl352])).
% 3.87/1.14 thf(zip_derived_cl29, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 3.87/1.14 thf(zip_derived_cl352, plain,
% 3.87/1.14 (((double_divide @ (inverse @ identity) @ (inverse @ identity))
% 3.87/1.14 = (inverse @ (inverse @ identity)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl316])).
% 3.87/1.14 thf(zip_derived_cl1, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X1 @ X0)
% 3.87/1.14 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [multiply])).
% 3.87/1.14 thf(zip_derived_cl454, plain,
% 3.87/1.14 (((multiply @ (inverse @ identity) @ (inverse @ identity))
% 3.87/1.14 = (double_divide @ (inverse @ (inverse @ identity)) @ identity))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl352, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl3, plain,
% 3.87/1.14 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.87/1.14 inference('cnf', [status(esa)], [identity])).
% 3.87/1.14 thf(zip_derived_cl316, plain,
% 3.87/1.14 (![X0 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X0) @
% 3.87/1.14 (inverse @ identity)) = (inverse @ (inverse @ X0)))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl305, zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl353, plain,
% 3.87/1.14 (((double_divide @ identity @ (inverse @ identity))
% 3.87/1.14 = (inverse @ (inverse @ (inverse @ identity))))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl316])).
% 3.87/1.14 thf(zip_derived_cl3, plain,
% 3.87/1.14 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.87/1.14 inference('cnf', [status(esa)], [identity])).
% 3.87/1.14 thf(zip_derived_cl356, plain,
% 3.87/1.14 (((identity) = (inverse @ (inverse @ (inverse @ identity))))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl353, zip_derived_cl3])).
% 3.87/1.14 thf(zip_derived_cl3, plain,
% 3.87/1.14 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.87/1.14 inference('cnf', [status(esa)], [identity])).
% 3.87/1.14 thf(zip_derived_cl361, plain,
% 3.87/1.14 (((identity)
% 3.87/1.14 = (double_divide @ (inverse @ (inverse @ identity)) @ identity))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl356, zip_derived_cl3])).
% 3.87/1.14 thf(zip_derived_cl460, plain,
% 3.87/1.14 (((multiply @ (inverse @ identity) @ (inverse @ identity)) = (identity))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl454, zip_derived_cl361])).
% 3.87/1.14 thf(zip_derived_cl466, plain,
% 3.87/1.14 (![X0 : $i]:
% 3.87/1.14 ((multiply @ (inverse @ identity) @ (multiply @ (inverse @ X0) @ X0))
% 3.87/1.14 = (identity))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl460])).
% 3.87/1.14 thf(zip_derived_cl679, plain, (((identity) = (inverse @ identity))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl95, zip_derived_cl671, zip_derived_cl466])).
% 3.87/1.14 thf(zip_derived_cl725, plain,
% 3.87/1.14 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.87/1.14 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 3.87/1.14 | ((inverse @ (inverse @ a2)) != (a2))
% 3.87/1.14 | ((identity) != (identity)))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl74, zip_derived_cl679])).
% 3.87/1.14 thf(zip_derived_cl726, plain,
% 3.87/1.14 ((((inverse @ (inverse @ a2)) != (a2))
% 3.87/1.14 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.87/1.14 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 3.87/1.14 inference('simplify', [status(thm)], [zip_derived_cl725])).
% 3.87/1.14 thf(zip_derived_cl671, plain,
% 3.87/1.14 (((inverse @ (inverse @ identity)) = (inverse @ identity))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl650, zip_derived_cl8, zip_derived_cl2,
% 3.87/1.14 zip_derived_cl3, zip_derived_cl2, zip_derived_cl352])).
% 3.87/1.14 thf(zip_derived_cl29, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 3.87/1.14 thf(zip_derived_cl29, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 3.87/1.14 thf(zip_derived_cl34, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X0) @ X0))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl29])).
% 3.87/1.14 thf(zip_derived_cl689, plain,
% 3.87/1.14 (![X0 : $i]:
% 3.87/1.14 ((multiply @ (inverse @ X0) @ X0)
% 3.87/1.14 = (multiply @ (inverse @ identity) @ (inverse @ identity)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl671, zip_derived_cl34])).
% 3.87/1.14 thf(zip_derived_cl460, plain,
% 3.87/1.14 (((multiply @ (inverse @ identity) @ (inverse @ identity)) = (identity))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl454, zip_derived_cl361])).
% 3.87/1.14 thf(zip_derived_cl708, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl689, zip_derived_cl460])).
% 3.87/1.14 thf(zip_derived_cl3, plain,
% 3.87/1.14 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.87/1.14 inference('cnf', [status(esa)], [identity])).
% 3.87/1.14 thf(zip_derived_cl13, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X1) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (multiply @ X2 @ X1) @ (double_divide @ X0 @ X2))))
% 3.87/1.14 = (X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl17, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X1) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (multiply @ (inverse @ X0) @ X1) @ identity)))
% 3.87/1.14 = (X0))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 3.87/1.14 thf(zip_derived_cl2, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [inverse])).
% 3.87/1.14 thf(zip_derived_cl22, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X1) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (inverse @ (multiply @ (inverse @ X0) @ X1))))
% 3.87/1.14 = (X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl316, plain,
% 3.87/1.14 (![X0 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X0) @
% 3.87/1.14 (inverse @ identity)) = (inverse @ (inverse @ X0)))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl305, zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl679, plain, (((identity) = (inverse @ identity))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl95, zip_derived_cl671, zip_derived_cl466])).
% 3.87/1.14 thf(zip_derived_cl1, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X1 @ X0)
% 3.87/1.14 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [multiply])).
% 3.87/1.14 thf(zip_derived_cl728, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl316, zip_derived_cl679, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl1, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X1 @ X0)
% 3.87/1.14 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [multiply])).
% 3.87/1.14 thf(zip_derived_cl13, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X1) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (multiply @ X2 @ X1) @ (double_divide @ X0 @ X2))))
% 3.87/1.14 = (X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl19, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X2) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (multiply @ identity @ X2) @ (multiply @ X1 @ X0))))
% 3.87/1.14 = (double_divide @ X0 @ X1))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl13])).
% 3.87/1.14 thf(zip_derived_cl10, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl501, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X2) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (inverse @ (inverse @ X2)) @ (multiply @ X1 @ X0))))
% 3.87/1.14 = (double_divide @ X0 @ X1))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl10])).
% 3.87/1.14 thf(zip_derived_cl853, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X1) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (inverse @ (inverse @ X1)) @
% 3.87/1.14 (inverse @ (inverse @ X0)))))
% 3.87/1.14 = (double_divide @ identity @ X0))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl728, zip_derived_cl501])).
% 3.87/1.14 thf(zip_derived_cl298, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X1) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (inverse @ (inverse @ X1)) @ (inverse @ X0))))
% 3.87/1.14 = (X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl10])).
% 3.87/1.14 thf(zip_derived_cl860, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl853, zip_derived_cl298])).
% 3.87/1.14 thf(zip_derived_cl860, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl853, zip_derived_cl298])).
% 3.87/1.14 thf(zip_derived_cl879, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((double_divide @ (inverse @ X1) @
% 3.87/1.14 (inverse @ (inverse @ (multiply @ (inverse @ X0) @ X1)))) = (
% 3.87/1.14 X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl22, zip_derived_cl860, zip_derived_cl860])).
% 3.87/1.14 thf(zip_derived_cl885, plain,
% 3.87/1.14 (![X0 : $i]:
% 3.87/1.14 ((double_divide @ (inverse @ X0) @ (inverse @ (inverse @ identity)))
% 3.87/1.14 = (X0))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl708, zip_derived_cl879])).
% 3.87/1.14 thf(zip_derived_cl679, plain, (((identity) = (inverse @ identity))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl95, zip_derived_cl671, zip_derived_cl466])).
% 3.87/1.14 thf(zip_derived_cl679, plain, (((identity) = (inverse @ identity))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl95, zip_derived_cl671, zip_derived_cl466])).
% 3.87/1.14 thf(zip_derived_cl2, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [inverse])).
% 3.87/1.14 thf(zip_derived_cl891, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl885, zip_derived_cl679, zip_derived_cl679,
% 3.87/1.14 zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl897, plain,
% 3.87/1.14 ((((a2) != (a2))
% 3.87/1.14 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.87/1.14 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl726, zip_derived_cl891])).
% 3.87/1.14 thf(zip_derived_cl898, plain,
% 3.87/1.14 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.87/1.14 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 3.87/1.14 inference('simplify', [status(thm)], [zip_derived_cl897])).
% 3.87/1.14 thf(zip_derived_cl10, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl13, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X1) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (multiply @ X2 @ X1) @ (double_divide @ X0 @ X2))))
% 3.87/1.14 = (X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl25, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X0) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (inverse @ (inverse @ X0)) @
% 3.87/1.14 (double_divide @ X1 @ identity))))
% 3.87/1.14 = (X1))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl13])).
% 3.87/1.14 thf(zip_derived_cl2, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [inverse])).
% 3.87/1.14 thf(zip_derived_cl26, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X0) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (inverse @ (inverse @ X0)) @ (inverse @ X1))))
% 3.87/1.14 = (X1))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl25, zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl860, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl853, zip_derived_cl298])).
% 3.87/1.14 thf(zip_derived_cl891, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl885, zip_derived_cl679, zip_derived_cl679,
% 3.87/1.14 zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl860, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl853, zip_derived_cl298])).
% 3.87/1.14 thf(zip_derived_cl6, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl989, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((double_divide @ (inverse @ X0) @ (multiply @ (inverse @ X1) @ X0))
% 3.87/1.14 = (X1))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl26, zip_derived_cl860, zip_derived_cl891,
% 3.87/1.14 zip_derived_cl860, zip_derived_cl6])).
% 3.87/1.14 thf(zip_derived_cl679, plain, (((identity) = (inverse @ identity))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl95, zip_derived_cl671, zip_derived_cl466])).
% 3.87/1.14 thf(zip_derived_cl13, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ identity @ X1) @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (multiply @ X2 @ X1) @ (double_divide @ X0 @ X2))))
% 3.87/1.14 = (X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl1, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X1 @ X0)
% 3.87/1.14 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [multiply])).
% 3.87/1.14 thf(zip_derived_cl15, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((multiply @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (multiply @ X1 @ X2) @ (double_divide @ X0 @ X1))) @
% 3.87/1.14 (double_divide @ identity @ X2)) = (double_divide @ X0 @ identity))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl2, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.87/1.14 inference('cnf', [status(esa)], [inverse])).
% 3.87/1.14 thf(zip_derived_cl23, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((multiply @
% 3.87/1.14 (double_divide @ identity @
% 3.87/1.14 (double_divide @ (multiply @ X1 @ X2) @ (double_divide @ X0 @ X1))) @
% 3.87/1.14 (double_divide @ identity @ X2)) = (inverse @ X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl860, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl853, zip_derived_cl298])).
% 3.87/1.14 thf(zip_derived_cl6, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl860, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl853, zip_derived_cl298])).
% 3.87/1.14 thf(zip_derived_cl932, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((multiply @
% 3.87/1.14 (multiply @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ X2)) @
% 3.87/1.14 (inverse @ X2)) = (inverse @ X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl23, zip_derived_cl860, zip_derived_cl6,
% 3.87/1.14 zip_derived_cl860])).
% 3.87/1.14 thf(zip_derived_cl936, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @
% 3.87/1.14 (multiply @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ identity)) @
% 3.87/1.14 identity) = (inverse @ X0))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl679, zip_derived_cl932])).
% 3.87/1.14 thf(zip_derived_cl728, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl316, zip_derived_cl679, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl891, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl885, zip_derived_cl679, zip_derived_cl679,
% 3.87/1.14 zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl899, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl728, zip_derived_cl891])).
% 3.87/1.14 thf(zip_derived_cl899, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl728, zip_derived_cl891])).
% 3.87/1.14 thf(zip_derived_cl950, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ (double_divide @ X0 @ X1) @ X1) = (inverse @ X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl936, zip_derived_cl899, zip_derived_cl899])).
% 3.87/1.14 thf(zip_derived_cl1080, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1))
% 3.87/1.14 = (inverse @ (inverse @ X1)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl989, zip_derived_cl950])).
% 3.87/1.14 thf(zip_derived_cl891, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl885, zip_derived_cl679, zip_derived_cl679,
% 3.87/1.14 zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl1087, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)) = (X1))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl1080, zip_derived_cl891])).
% 3.87/1.14 thf(zip_derived_cl989, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((double_divide @ (inverse @ X0) @ (multiply @ (inverse @ X1) @ X0))
% 3.87/1.14 = (X1))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl26, zip_derived_cl860, zip_derived_cl891,
% 3.87/1.14 zip_derived_cl860, zip_derived_cl6])).
% 3.87/1.14 thf(zip_derived_cl1096, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((double_divide @
% 3.87/1.14 (inverse @ (multiply @ (inverse @ (inverse @ X1)) @ X0)) @ X0)
% 3.87/1.14 = (X1))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl1087, zip_derived_cl989])).
% 3.87/1.14 thf(zip_derived_cl891, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl885, zip_derived_cl679, zip_derived_cl679,
% 3.87/1.14 zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl6, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl891, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl885, zip_derived_cl679, zip_derived_cl679,
% 3.87/1.14 zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl904, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((inverse @ (multiply @ X1 @ X0)) = (double_divide @ X0 @ X1))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl891])).
% 3.87/1.14 thf(zip_derived_cl1112, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((double_divide @ (double_divide @ X0 @ X1) @ X0) = (X1))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl1096, zip_derived_cl891, zip_derived_cl904])).
% 3.87/1.14 thf(zip_derived_cl932, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((multiply @
% 3.87/1.14 (multiply @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ X2)) @
% 3.87/1.14 (inverse @ X2)) = (inverse @ X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl23, zip_derived_cl860, zip_derived_cl6,
% 3.87/1.14 zip_derived_cl860])).
% 3.87/1.14 thf(zip_derived_cl1260, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((multiply @ (multiply @ X0 @ (multiply @ X1 @ X2)) @ (inverse @ X2))
% 3.87/1.14 = (inverse @ (double_divide @ X1 @ X0)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl1112, zip_derived_cl932])).
% 3.87/1.14 thf(zip_derived_cl6, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.87/1.14 thf(zip_derived_cl1282, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((multiply @ (multiply @ X0 @ (multiply @ X1 @ X2)) @ (inverse @ X2))
% 3.87/1.14 = (multiply @ X0 @ X1))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl1260, zip_derived_cl6])).
% 3.87/1.14 thf(zip_derived_cl891, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl885, zip_derived_cl679, zip_derived_cl679,
% 3.87/1.14 zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl891, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl885, zip_derived_cl679, zip_derived_cl679,
% 3.87/1.14 zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl3, plain,
% 3.87/1.14 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.87/1.14 inference('cnf', [status(esa)], [identity])).
% 3.87/1.14 thf(zip_derived_cl901, plain,
% 3.87/1.14 (![X0 : $i]: ((identity) = (double_divide @ (inverse @ X0) @ X0))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl891, zip_derived_cl3])).
% 3.87/1.14 thf(zip_derived_cl932, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((multiply @
% 3.87/1.14 (multiply @ (double_divide @ X0 @ X1) @ (multiply @ X1 @ X2)) @
% 3.87/1.14 (inverse @ X2)) = (inverse @ X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl23, zip_derived_cl860, zip_derived_cl6,
% 3.87/1.14 zip_derived_cl860])).
% 3.87/1.14 thf(zip_derived_cl949, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ (multiply @ identity @ (multiply @ X0 @ X1)) @
% 3.87/1.14 (inverse @ X1)) = (inverse @ (inverse @ X0)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl901, zip_derived_cl932])).
% 3.87/1.14 thf(zip_derived_cl10, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl891, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl885, zip_derived_cl679, zip_derived_cl679,
% 3.87/1.14 zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl896, plain,
% 3.87/1.14 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl891])).
% 3.87/1.14 thf(zip_derived_cl891, plain,
% 3.87/1.14 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl885, zip_derived_cl679, zip_derived_cl679,
% 3.87/1.14 zip_derived_cl2])).
% 3.87/1.14 thf(zip_derived_cl962, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X1)) = (X0))),
% 3.87/1.14 inference('demod', [status(thm)],
% 3.87/1.14 [zip_derived_cl949, zip_derived_cl896, zip_derived_cl891])).
% 3.87/1.14 thf(zip_derived_cl1030, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i]:
% 3.87/1.14 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl891, zip_derived_cl962])).
% 3.87/1.14 thf(zip_derived_cl3350, plain,
% 3.87/1.14 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.87/1.14 ((multiply @ (multiply @ X1 @ X0) @ X2)
% 3.87/1.14 = (multiply @ X1 @ (multiply @ X0 @ X2)))),
% 3.87/1.14 inference('sup+', [status(thm)], [zip_derived_cl1282, zip_derived_cl1030])).
% 3.87/1.14 thf(zip_derived_cl3458, plain,
% 3.87/1.14 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 3.87/1.14 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 3.87/1.14 inference('demod', [status(thm)], [zip_derived_cl898, zip_derived_cl3350])).
% 3.87/1.14 thf(zip_derived_cl3459, plain, ($false),
% 3.87/1.14 inference('simplify', [status(thm)], [zip_derived_cl3458])).
% 3.87/1.14
% 3.87/1.14 % SZS output end Refutation
% 3.87/1.14
% 3.87/1.14
% 3.87/1.14 % Terminating...
% 4.58/1.21 % Runner terminated.
% 4.58/1.21 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------