%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP567-1 : TPTP v9.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.EDYdnzZfm6 true
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:36:41 PM UTC 2025
% Result : Unsatisfiable 3.86s 1.21s
% Output : Refutation 3.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP567-1 : TPTP v9.2.0. Released v2.6.0.
% 0.04/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.EDYdnzZfm6 true
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 14:16:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.57/0.66 % Total configuration time : 435
% 0.57/0.66 % Estimated wc time : 1092
% 0.57/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.60/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.60/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.61/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.61/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.61/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.61/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.61/0.81 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 3.86/1.21 % Solved by fo/fo5.sh.
% 3.86/1.21 % done 588 iterations in 0.392s
% 3.86/1.21 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 3.86/1.21 % SZS output start Refutation
% 3.86/1.21 thf(c3_type, type, c3: $i).
% 3.86/1.21 thf(identity_type, type, identity: $i).
% 3.86/1.21 thf(multiply_type, type, multiply: $i > $i > $i).
% 3.86/1.21 thf(b3_type, type, b3: $i).
% 3.86/1.21 thf(a3_type, type, a3: $i).
% 3.86/1.21 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 3.86/1.21 thf(inverse_type, type, inverse: $i > $i).
% 3.86/1.21 thf(prove_these_axioms_3, conjecture,
% 3.86/1.21 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 3.86/1.21 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 3.86/1.21 thf(zf_stmt_0, negated_conjecture,
% 3.86/1.21 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 3.86/1.21 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 3.86/1.21 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 3.86/1.21 thf(zip_derived_cl4, plain,
% 3.86/1.21 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 3.86/1.21 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 3.86/1.21 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.86/1.21 thf(identity, axiom,
% 3.86/1.21 (( identity ) = ( double_divide @ A @ ( inverse @ A ) ))).
% 3.86/1.21 thf(zip_derived_cl3, plain,
% 3.86/1.21 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.86/1.21 inference('cnf', [status(esa)], [identity])).
% 3.86/1.21 thf(inverse, axiom, (( inverse @ A ) = ( double_divide @ A @ identity ))).
% 3.86/1.21 thf(zip_derived_cl2, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [inverse])).
% 3.86/1.21 thf(single_axiom, axiom,
% 3.86/1.21 (( double_divide @
% 3.86/1.21 ( double_divide @
% 3.86/1.21 A @
% 3.86/1.21 ( double_divide @
% 3.86/1.21 ( double_divide @ B @ ( double_divide @ A @ C ) ) @
% 3.86/1.21 ( double_divide @ identity @ C ) ) ) @
% 3.86/1.21 ( double_divide @ identity @ identity ) ) =
% 3.86/1.21 ( B ))).
% 3.86/1.21 thf(zip_derived_cl0, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ X1 @
% 3.86/1.21 (double_divide @
% 3.86/1.21 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @
% 3.86/1.21 (double_divide @ identity @ X2))) @
% 3.86/1.21 (double_divide @ identity @ identity)) = (X0))),
% 3.86/1.21 inference('cnf', [status(esa)], [single_axiom])).
% 3.86/1.21 thf(zip_derived_cl2, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [inverse])).
% 3.86/1.21 thf(zip_derived_cl13, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ X1 @
% 3.86/1.21 (double_divide @
% 3.86/1.21 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @
% 3.86/1.21 (double_divide @ identity @ X2))) @
% 3.86/1.21 (inverse @ identity)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl16, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ X1 @
% 3.86/1.21 (double_divide @
% 3.86/1.21 (double_divide @ X0 @ (double_divide @ X1 @ identity)) @
% 3.86/1.21 (inverse @ identity))) @
% 3.86/1.21 (inverse @ identity)) = (X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 3.86/1.21 thf(zip_derived_cl2, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [inverse])).
% 3.86/1.21 thf(zip_derived_cl22, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ X1 @
% 3.86/1.21 (double_divide @ (double_divide @ X0 @ (inverse @ X1)) @
% 3.86/1.21 (inverse @ identity))) @
% 3.86/1.21 (inverse @ identity)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl115, plain,
% 3.86/1.21 (![X0 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ X0 @
% 3.86/1.21 (double_divide @ identity @ (inverse @ identity))) @
% 3.86/1.21 (inverse @ identity)) = (X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl22])).
% 3.86/1.21 thf(zip_derived_cl3, plain,
% 3.86/1.21 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.86/1.21 inference('cnf', [status(esa)], [identity])).
% 3.86/1.21 thf(zip_derived_cl2, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [inverse])).
% 3.86/1.21 thf(zip_derived_cl120, plain,
% 3.86/1.21 (![X0 : $i]:
% 3.86/1.21 ((double_divide @ (inverse @ X0) @ (inverse @ identity)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl115, zip_derived_cl3, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl3, plain,
% 3.86/1.21 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.86/1.21 inference('cnf', [status(esa)], [identity])).
% 3.86/1.21 thf(zip_derived_cl2, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [inverse])).
% 3.86/1.21 thf(multiply, axiom,
% 3.86/1.21 (( multiply @ A @ B ) =
% 3.86/1.21 ( double_divide @ ( double_divide @ B @ A ) @ identity ))).
% 3.86/1.21 thf(zip_derived_cl1, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X1 @ X0)
% 3.86/1.21 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [multiply])).
% 3.86/1.21 thf(zip_derived_cl6, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.86/1.21 thf(zip_derived_cl32, plain,
% 3.86/1.21 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 3.86/1.21 thf(zip_derived_cl32, plain,
% 3.86/1.21 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 3.86/1.21 thf(zip_derived_cl120, plain,
% 3.86/1.21 (![X0 : $i]:
% 3.86/1.21 ((double_divide @ (inverse @ X0) @ (inverse @ identity)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl115, zip_derived_cl3, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl131, plain,
% 3.86/1.21 (![X0 : $i]:
% 3.86/1.21 ((double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 3.86/1.21 (inverse @ identity)) = (identity))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl120])).
% 3.86/1.21 thf(zip_derived_cl22, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ X1 @
% 3.86/1.21 (double_divide @ (double_divide @ X0 @ (inverse @ X1)) @
% 3.86/1.21 (inverse @ identity))) @
% 3.86/1.21 (inverse @ identity)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl217, plain,
% 3.86/1.21 (![X0 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ identity @
% 3.86/1.21 (double_divide @ identity @ (inverse @ identity))) @
% 3.86/1.21 (inverse @ identity)) = (multiply @ (inverse @ X0) @ X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl131, zip_derived_cl22])).
% 3.86/1.21 thf(zip_derived_cl3, plain,
% 3.86/1.21 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.86/1.21 inference('cnf', [status(esa)], [identity])).
% 3.86/1.21 thf(zip_derived_cl2, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [inverse])).
% 3.86/1.21 thf(zip_derived_cl120, plain,
% 3.86/1.21 (![X0 : $i]:
% 3.86/1.21 ((double_divide @ (inverse @ X0) @ (inverse @ identity)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl115, zip_derived_cl3, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl233, plain,
% 3.86/1.21 (![X0 : $i]: ((identity) = (multiply @ (inverse @ X0) @ X0))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl217, zip_derived_cl3, zip_derived_cl2,
% 3.86/1.21 zip_derived_cl120])).
% 3.86/1.21 thf(zip_derived_cl235, plain, (((identity) = (inverse @ identity))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl233])).
% 3.86/1.21 thf(zip_derived_cl2, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [inverse])).
% 3.86/1.21 thf(zip_derived_cl247, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl120, zip_derived_cl235, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl2, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [inverse])).
% 3.86/1.21 thf(zip_derived_cl13, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ X1 @
% 3.86/1.21 (double_divide @
% 3.86/1.21 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @
% 3.86/1.21 (double_divide @ identity @ X2))) @
% 3.86/1.21 (inverse @ identity)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl18, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ X0 @
% 3.86/1.21 (double_divide @ (double_divide @ X1 @ (inverse @ X0)) @
% 3.86/1.21 (double_divide @ identity @ identity))) @
% 3.86/1.21 (inverse @ identity)) = (X1))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 3.86/1.21 thf(zip_derived_cl2, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [inverse])).
% 3.86/1.21 thf(zip_derived_cl24, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ X0 @
% 3.86/1.21 (double_divide @ (double_divide @ X1 @ (inverse @ X0)) @
% 3.86/1.21 (inverse @ identity))) @
% 3.86/1.21 (inverse @ identity)) = (X1))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl235, plain, (((identity) = (inverse @ identity))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl233])).
% 3.86/1.21 thf(zip_derived_cl1, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X1 @ X0)
% 3.86/1.21 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [multiply])).
% 3.86/1.21 thf(zip_derived_cl235, plain, (((identity) = (inverse @ identity))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl233])).
% 3.86/1.21 thf(zip_derived_cl1, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X1 @ X0)
% 3.86/1.21 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [multiply])).
% 3.86/1.21 thf(zip_derived_cl259, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ (multiply @ (inverse @ X0) @ X1) @ X0) = (X1))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl24, zip_derived_cl235, zip_derived_cl1,
% 3.86/1.21 zip_derived_cl235, zip_derived_cl1])).
% 3.86/1.21 thf(zip_derived_cl271, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X0)) = (X1))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl247, zip_derived_cl259])).
% 3.86/1.21 thf(zip_derived_cl1, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X1 @ X0)
% 3.86/1.21 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [multiply])).
% 3.86/1.21 thf(zip_derived_cl13, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ X1 @
% 3.86/1.21 (double_divide @
% 3.86/1.21 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @
% 3.86/1.21 (double_divide @ identity @ X2))) @
% 3.86/1.21 (inverse @ identity)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl20, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ (double_divide @ X0 @ X1) @
% 3.86/1.21 (double_divide @ (double_divide @ X2 @ (multiply @ X1 @ X0)) @
% 3.86/1.21 (double_divide @ identity @ identity))) @
% 3.86/1.21 (inverse @ identity)) = (X2))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl13])).
% 3.86/1.21 thf(zip_derived_cl2, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [inverse])).
% 3.86/1.21 thf(zip_derived_cl26, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ (double_divide @ X0 @ X1) @
% 3.86/1.21 (double_divide @ (double_divide @ X2 @ (multiply @ X1 @ X0)) @
% 3.86/1.21 (inverse @ identity))) @
% 3.86/1.21 (inverse @ identity)) = (X2))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl20, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl235, plain, (((identity) = (inverse @ identity))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl233])).
% 3.86/1.21 thf(zip_derived_cl1, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X1 @ X0)
% 3.86/1.21 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [multiply])).
% 3.86/1.21 thf(zip_derived_cl235, plain, (((identity) = (inverse @ identity))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl233])).
% 3.86/1.21 thf(zip_derived_cl1, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X1 @ X0)
% 3.86/1.21 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [multiply])).
% 3.86/1.21 thf(zip_derived_cl341, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((multiply @ (multiply @ (multiply @ X1 @ X0) @ X2) @
% 3.86/1.21 (double_divide @ X0 @ X1)) = (X2))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl26, zip_derived_cl235, zip_derived_cl1,
% 3.86/1.21 zip_derived_cl235, zip_derived_cl1])).
% 3.86/1.21 thf(zip_derived_cl377, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X0 @ (double_divide @ X0 @ X1)) = (inverse @ X1))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl271, zip_derived_cl341])).
% 3.86/1.21 thf(zip_derived_cl1, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X1 @ X0)
% 3.86/1.21 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [multiply])).
% 3.86/1.21 thf(zip_derived_cl1, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X1 @ X0)
% 3.86/1.21 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [multiply])).
% 3.86/1.21 thf(zip_derived_cl9, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 3.86/1.21 = (double_divide @ (multiply @ X1 @ X0) @ identity))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl1])).
% 3.86/1.21 thf(zip_derived_cl2, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [inverse])).
% 3.86/1.21 thf(zip_derived_cl11, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 3.86/1.21 = (inverse @ (multiply @ X1 @ X0)))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl233, plain,
% 3.86/1.21 (![X0 : $i]: ((identity) = (multiply @ (inverse @ X0) @ X0))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl217, zip_derived_cl3, zip_derived_cl2,
% 3.86/1.21 zip_derived_cl120])).
% 3.86/1.21 thf(zip_derived_cl259, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ (multiply @ (inverse @ X0) @ X1) @ X0) = (X1))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl24, zip_derived_cl235, zip_derived_cl1,
% 3.86/1.21 zip_derived_cl235, zip_derived_cl1])).
% 3.86/1.21 thf(zip_derived_cl260, plain,
% 3.86/1.21 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl233, zip_derived_cl259])).
% 3.86/1.21 thf(zip_derived_cl267, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((double_divide @ X0 @ X1) = (inverse @ (multiply @ X1 @ X0)))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl11, zip_derived_cl260])).
% 3.86/1.21 thf(zip_derived_cl540, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((double_divide @ (double_divide @ X1 @ X0) @ X1)
% 3.86/1.21 = (inverse @ (inverse @ X0)))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl377, zip_derived_cl267])).
% 3.86/1.21 thf(zip_derived_cl247, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl120, zip_derived_cl235, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl564, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((double_divide @ (double_divide @ X1 @ X0) @ X1) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl540, zip_derived_cl247])).
% 3.86/1.21 thf(zip_derived_cl13, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ X1 @
% 3.86/1.21 (double_divide @
% 3.86/1.21 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @
% 3.86/1.21 (double_divide @ identity @ X2))) @
% 3.86/1.21 (inverse @ identity)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl1, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X1 @ X0)
% 3.86/1.21 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [multiply])).
% 3.86/1.21 thf(zip_derived_cl15, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((multiply @ (inverse @ identity) @
% 3.86/1.21 (double_divide @ X2 @
% 3.86/1.21 (double_divide @
% 3.86/1.21 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @
% 3.86/1.21 (double_divide @ identity @ X1))))
% 3.86/1.21 = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 3.86/1.21 thf(zip_derived_cl2, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [inverse])).
% 3.86/1.21 thf(zip_derived_cl29, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((multiply @ (inverse @ identity) @
% 3.86/1.21 (double_divide @ X2 @
% 3.86/1.21 (double_divide @
% 3.86/1.21 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @
% 3.86/1.21 (double_divide @ identity @ X1))))
% 3.86/1.21 = (inverse @ X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl235, plain, (((identity) = (inverse @ identity))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl233])).
% 3.86/1.21 thf(zip_derived_cl247, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl120, zip_derived_cl235, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl247, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl120, zip_derived_cl235, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl3, plain,
% 3.86/1.21 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.86/1.21 inference('cnf', [status(esa)], [identity])).
% 3.86/1.21 thf(zip_derived_cl268, plain,
% 3.86/1.21 (![X0 : $i]: ((identity) = (double_divide @ (inverse @ X0) @ X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl247, zip_derived_cl3])).
% 3.86/1.21 thf(zip_derived_cl3, plain,
% 3.86/1.21 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 3.86/1.21 inference('cnf', [status(esa)], [identity])).
% 3.86/1.21 thf(zip_derived_cl13, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ X1 @
% 3.86/1.21 (double_divide @
% 3.86/1.21 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @
% 3.86/1.21 (double_divide @ identity @ X2))) @
% 3.86/1.21 (inverse @ identity)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl19, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ X1 @
% 3.86/1.21 (double_divide @ (double_divide @ X0 @ identity) @
% 3.86/1.21 (double_divide @ identity @ (inverse @ X1)))) @
% 3.86/1.21 (inverse @ identity)) = (X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 3.86/1.21 thf(zip_derived_cl2, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [inverse])).
% 3.86/1.21 thf(zip_derived_cl25, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ X1 @
% 3.86/1.21 (double_divide @ (inverse @ X0) @
% 3.86/1.21 (double_divide @ identity @ (inverse @ X1)))) @
% 3.86/1.21 (inverse @ identity)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl235, plain, (((identity) = (inverse @ identity))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl233])).
% 3.86/1.21 thf(zip_derived_cl1, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X1 @ X0)
% 3.86/1.21 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [multiply])).
% 3.86/1.21 thf(zip_derived_cl293, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @
% 3.86/1.21 (double_divide @ (inverse @ X0) @
% 3.86/1.21 (double_divide @ identity @ (inverse @ X1))) @
% 3.86/1.21 X1) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl25, zip_derived_cl235, zip_derived_cl1])).
% 3.86/1.21 thf(zip_derived_cl294, plain,
% 3.86/1.21 (![X0 : $i]:
% 3.86/1.21 ((multiply @ identity @ X0)
% 3.86/1.21 = (double_divide @ identity @ (inverse @ X0)))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl268, zip_derived_cl293])).
% 3.86/1.21 thf(zip_derived_cl260, plain,
% 3.86/1.21 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl233, zip_derived_cl259])).
% 3.86/1.21 thf(zip_derived_cl302, plain,
% 3.86/1.21 (![X0 : $i]: ((X0) = (double_divide @ identity @ (inverse @ X0)))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl294, zip_derived_cl260])).
% 3.86/1.21 thf(zip_derived_cl316, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl247, zip_derived_cl302])).
% 3.86/1.21 thf(zip_derived_cl260, plain,
% 3.86/1.21 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl233, zip_derived_cl259])).
% 3.86/1.21 thf(zip_derived_cl615, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((double_divide @ X2 @
% 3.86/1.21 (double_divide @ (double_divide @ X0 @ (double_divide @ X2 @ X1)) @
% 3.86/1.21 (inverse @ X1)))
% 3.86/1.21 = (inverse @ X0))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl29, zip_derived_cl235, zip_derived_cl316,
% 3.86/1.21 zip_derived_cl260])).
% 3.86/1.21 thf(zip_derived_cl628, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((double_divide @ X1 @ (double_divide @ X1 @ X0))
% 3.86/1.21 = (inverse @ (inverse @ X0)))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl564, zip_derived_cl615])).
% 3.86/1.21 thf(zip_derived_cl247, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl120, zip_derived_cl235, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl649, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((double_divide @ X1 @ (double_divide @ X1 @ X0)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl628, zip_derived_cl247])).
% 3.86/1.21 thf(zip_derived_cl377, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X0 @ (double_divide @ X0 @ X1)) = (inverse @ X1))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl271, zip_derived_cl341])).
% 3.86/1.21 thf(zip_derived_cl672, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl649, zip_derived_cl377])).
% 3.86/1.21 thf(zip_derived_cl6, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.86/1.21 thf(zip_derived_cl834, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl672, zip_derived_cl6])).
% 3.86/1.21 thf(zip_derived_cl834, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl672, zip_derived_cl6])).
% 3.86/1.21 thf(zip_derived_cl858, plain,
% 3.86/1.21 (((multiply @ c3 @ (multiply @ a3 @ b3))
% 3.86/1.21 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl4, zip_derived_cl834, zip_derived_cl834])).
% 3.86/1.21 thf(zip_derived_cl834, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl672, zip_derived_cl6])).
% 3.86/1.21 thf(zip_derived_cl259, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ (multiply @ (inverse @ X0) @ X1) @ X0) = (X1))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl24, zip_derived_cl235, zip_derived_cl1,
% 3.86/1.21 zip_derived_cl235, zip_derived_cl1])).
% 3.86/1.21 thf(zip_derived_cl873, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl834, zip_derived_cl259])).
% 3.86/1.21 thf(zip_derived_cl13, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((double_divide @
% 3.86/1.21 (double_divide @ X1 @
% 3.86/1.21 (double_divide @
% 3.86/1.21 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @
% 3.86/1.21 (double_divide @ identity @ X2))) @
% 3.86/1.21 (inverse @ identity)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl11, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 3.86/1.21 = (inverse @ (multiply @ X1 @ X0)))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl99, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((multiply @ identity @ X0)
% 3.86/1.21 = (inverse @
% 3.86/1.21 (multiply @ (inverse @ identity) @
% 3.86/1.21 (double_divide @ X2 @
% 3.86/1.21 (double_divide @
% 3.86/1.21 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @
% 3.86/1.21 (double_divide @ identity @ X1))))))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl11])).
% 3.86/1.21 thf(zip_derived_cl2, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [inverse])).
% 3.86/1.21 thf(zip_derived_cl1, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X1 @ X0)
% 3.86/1.21 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [multiply])).
% 3.86/1.21 thf(zip_derived_cl7, plain,
% 3.86/1.21 (![X0 : $i]:
% 3.86/1.21 ((multiply @ identity @ X0)
% 3.86/1.21 = (double_divide @ (inverse @ X0) @ identity))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.86/1.21 thf(zip_derived_cl2, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 3.86/1.21 inference('cnf', [status(esa)], [inverse])).
% 3.86/1.21 thf(zip_derived_cl10, plain,
% 3.86/1.21 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl104, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((inverse @ (inverse @ X0))
% 3.86/1.21 = (inverse @
% 3.86/1.21 (multiply @ (inverse @ identity) @
% 3.86/1.21 (double_divide @ X2 @
% 3.86/1.21 (double_divide @
% 3.86/1.21 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @
% 3.86/1.21 (double_divide @ identity @ X1))))))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl99, zip_derived_cl10])).
% 3.86/1.21 thf(zip_derived_cl247, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl120, zip_derived_cl235, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl235, plain, (((identity) = (inverse @ identity))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl32, zip_derived_cl233])).
% 3.86/1.21 thf(zip_derived_cl316, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl247, zip_derived_cl302])).
% 3.86/1.21 thf(zip_derived_cl649, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((double_divide @ X1 @ (double_divide @ X1 @ X0)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl628, zip_derived_cl247])).
% 3.86/1.21 thf(zip_derived_cl564, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((double_divide @ (double_divide @ X1 @ X0) @ X1) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl540, zip_derived_cl247])).
% 3.86/1.21 thf(zip_derived_cl674, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((double_divide @ X0 @ X1) = (double_divide @ X1 @ X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl649, zip_derived_cl564])).
% 3.86/1.21 thf(zip_derived_cl293, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @
% 3.86/1.21 (double_divide @ (inverse @ X0) @
% 3.86/1.21 (double_divide @ identity @ (inverse @ X1))) @
% 3.86/1.21 X1) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl25, zip_derived_cl235, zip_derived_cl1])).
% 3.86/1.21 thf(zip_derived_cl302, plain,
% 3.86/1.21 (![X0 : $i]: ((X0) = (double_divide @ identity @ (inverse @ X0)))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl294, zip_derived_cl260])).
% 3.86/1.21 thf(zip_derived_cl311, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ (double_divide @ (inverse @ X0) @ X1) @ X1) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl293, zip_derived_cl302])).
% 3.86/1.21 thf(zip_derived_cl247, plain,
% 3.86/1.21 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl120, zip_derived_cl235, zip_derived_cl2])).
% 3.86/1.21 thf(zip_derived_cl311, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ (double_divide @ (inverse @ X0) @ X1) @ X1) = (X0))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl293, zip_derived_cl302])).
% 3.86/1.21 thf(zip_derived_cl271, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ (multiply @ X0 @ X1) @ (inverse @ X0)) = (X1))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl247, zip_derived_cl259])).
% 3.86/1.21 thf(zip_derived_cl398, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X0 @ (inverse @ (double_divide @ (inverse @ X0) @ X1)))
% 3.86/1.21 = (X1))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl311, zip_derived_cl271])).
% 3.86/1.21 thf(zip_derived_cl6, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 3.86/1.21 thf(zip_derived_cl410, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X0 @ (multiply @ X1 @ (inverse @ X0))) = (X1))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl398, zip_derived_cl6])).
% 3.86/1.21 thf(zip_derived_cl482, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ (inverse @ X0) @ (multiply @ X1 @ X0)) = (X1))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl247, zip_derived_cl410])).
% 3.86/1.21 thf(zip_derived_cl498, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ (inverse @ X1) @ X0)
% 3.86/1.21 = (double_divide @ (inverse @ X0) @ X1))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl311, zip_derived_cl482])).
% 3.86/1.21 thf(zip_derived_cl672, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl649, zip_derived_cl377])).
% 3.86/1.21 thf(zip_derived_cl834, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl672, zip_derived_cl6])).
% 3.86/1.21 thf(zip_derived_cl260, plain,
% 3.86/1.21 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl233, zip_derived_cl259])).
% 3.86/1.21 thf(zip_derived_cl672, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl649, zip_derived_cl377])).
% 3.86/1.21 thf(zip_derived_cl1258, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((X0)
% 3.86/1.21 = (multiply @ X2 @
% 3.86/1.21 (multiply @ X1 @ (multiply @ X0 @ (double_divide @ X2 @ X1)))))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl104, zip_derived_cl247, zip_derived_cl235,
% 3.86/1.21 zip_derived_cl316, zip_derived_cl674, zip_derived_cl498,
% 3.86/1.21 zip_derived_cl672, zip_derived_cl834, zip_derived_cl260,
% 3.86/1.21 zip_derived_cl672])).
% 3.86/1.21 thf(zip_derived_cl1283, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((multiply @ X0 @ (inverse @ (double_divide @ X2 @ X1)))
% 3.86/1.21 = (multiply @ X2 @ (multiply @ X1 @ X0)))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl873, zip_derived_cl1258])).
% 3.86/1.21 thf(zip_derived_cl672, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]:
% 3.86/1.21 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X1 @ X0)))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl649, zip_derived_cl377])).
% 3.86/1.21 thf(zip_derived_cl1307, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.86/1.21 ((multiply @ X0 @ (multiply @ X2 @ X1))
% 3.86/1.21 = (multiply @ X2 @ (multiply @ X1 @ X0)))),
% 3.86/1.21 inference('demod', [status(thm)], [zip_derived_cl1283, zip_derived_cl672])).
% 3.86/1.21 thf(zip_derived_cl834, plain,
% 3.86/1.21 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 3.86/1.21 inference('sup+', [status(thm)], [zip_derived_cl672, zip_derived_cl6])).
% 3.86/1.21 thf(zip_derived_cl2957, plain,
% 3.86/1.21 (((multiply @ a3 @ (multiply @ c3 @ b3))
% 3.86/1.21 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 3.86/1.21 inference('demod', [status(thm)],
% 3.86/1.21 [zip_derived_cl858, zip_derived_cl1307, zip_derived_cl834])).
% 3.86/1.21 thf(zip_derived_cl2958, plain, ($false),
% 3.86/1.21 inference('simplify', [status(thm)], [zip_derived_cl2957])).
% 3.86/1.21
% 3.86/1.21 % SZS output end Refutation
% 3.86/1.21
% 3.86/1.21
% 3.86/1.21 % Terminating...
% 4.54/1.31 % Runner terminated.
% 4.54/1.32 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------