%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP575-1 : TPTP v9.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ZbPTGajQeY true
% Computer : n001.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 04:36:42 PM UTC 2025
% Result : Unsatisfiable 6.84s 1.58s
% Output : Refutation 6.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP575-1 : TPTP v9.2.0. Released v2.6.0.
% 0.04/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ZbPTGajQeY true
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 14:10:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.56/0.63 % Total configuration time : 435
% 0.56/0.63 % Estimated wc time : 1092
% 0.56/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 6.84/1.58 % Solved by fo/fo5.sh.
% 6.84/1.58 % done 1259 iterations in 0.806s
% 6.84/1.58 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 6.84/1.58 % SZS output start Refutation
% 6.84/1.58 thf(c3_type, type, c3: $i).
% 6.84/1.58 thf(identity_type, type, identity: $i).
% 6.84/1.58 thf(multiply_type, type, multiply: $i > $i > $i).
% 6.84/1.58 thf(b3_type, type, b3: $i).
% 6.84/1.58 thf(a3_type, type, a3: $i).
% 6.84/1.58 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 6.84/1.58 thf(inverse_type, type, inverse: $i > $i).
% 6.84/1.58 thf(prove_these_axioms_3, conjecture,
% 6.84/1.58 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 6.84/1.58 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 6.84/1.58 thf(zf_stmt_0, negated_conjecture,
% 6.84/1.58 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 6.84/1.58 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 6.84/1.58 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 6.84/1.58 thf(zip_derived_cl4, plain,
% 6.84/1.58 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 6.84/1.58 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 6.84/1.58 inference('cnf', [status(esa)], [zf_stmt_0])).
% 6.84/1.58 thf(identity, axiom,
% 6.84/1.58 (( identity ) = ( double_divide @ A @ ( inverse @ A ) ))).
% 6.84/1.58 thf(zip_derived_cl3, plain,
% 6.84/1.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.84/1.58 inference('cnf', [status(esa)], [identity])).
% 6.84/1.58 thf(zip_derived_cl3, plain,
% 6.84/1.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.84/1.58 inference('cnf', [status(esa)], [identity])).
% 6.84/1.58 thf(single_axiom, axiom,
% 6.84/1.58 (( double_divide @
% 6.84/1.58 ( double_divide @
% 6.84/1.58 A @
% 6.84/1.58 ( double_divide @
% 6.84/1.58 ( double_divide @ B @ ( double_divide @ C @ A ) ) @
% 6.84/1.58 ( double_divide @ C @ identity ) ) ) @
% 6.84/1.58 ( double_divide @ identity @ identity ) ) =
% 6.84/1.58 ( B ))).
% 6.84/1.58 thf(zip_derived_cl0, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ X1 @
% 6.84/1.58 (double_divide @
% 6.84/1.58 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @
% 6.84/1.58 (double_divide @ X2 @ identity))) @
% 6.84/1.58 (double_divide @ identity @ identity)) = (X0))),
% 6.84/1.58 inference('cnf', [status(esa)], [single_axiom])).
% 6.84/1.58 thf(inverse, axiom, (( inverse @ A ) = ( double_divide @ A @ identity ))).
% 6.84/1.58 thf(zip_derived_cl2, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [inverse])).
% 6.84/1.58 thf(zip_derived_cl2, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [inverse])).
% 6.84/1.58 thf(zip_derived_cl13, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ X1 @
% 6.84/1.58 (double_divide @
% 6.84/1.58 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @ (inverse @ X2))) @
% 6.84/1.58 (inverse @ identity)) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl17, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ (inverse @ X1) @
% 6.84/1.58 (double_divide @ (double_divide @ X0 @ identity) @ (inverse @ X1))) @
% 6.84/1.58 (inverse @ identity)) = (X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl13])).
% 6.84/1.58 thf(zip_derived_cl2, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [inverse])).
% 6.84/1.58 thf(zip_derived_cl20, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ (inverse @ X1) @
% 6.84/1.58 (double_divide @ (inverse @ X0) @ (inverse @ X1))) @
% 6.84/1.58 (inverse @ identity)) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl3, plain,
% 6.84/1.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.84/1.58 inference('cnf', [status(esa)], [identity])).
% 6.84/1.58 thf(zip_derived_cl2, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [inverse])).
% 6.84/1.58 thf(multiply, axiom,
% 6.84/1.58 (( multiply @ A @ B ) =
% 6.84/1.58 ( double_divide @ ( double_divide @ B @ A ) @ identity ))).
% 6.84/1.58 thf(zip_derived_cl1, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X1 @ X0)
% 6.84/1.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [multiply])).
% 6.84/1.58 thf(zip_derived_cl6, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl25, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 6.84/1.58 thf(zip_derived_cl3, plain,
% 6.84/1.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.84/1.58 inference('cnf', [status(esa)], [identity])).
% 6.84/1.58 thf(zip_derived_cl28, plain,
% 6.84/1.58 (![X0 : $i]:
% 6.84/1.58 ((identity)
% 6.84/1.58 = (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl3])).
% 6.84/1.58 thf(zip_derived_cl1, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X1 @ X0)
% 6.84/1.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [multiply])).
% 6.84/1.58 thf(zip_derived_cl13, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ X1 @
% 6.84/1.58 (double_divide @
% 6.84/1.58 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @ (inverse @ X2))) @
% 6.84/1.58 (inverse @ identity)) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl18, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ identity @
% 6.84/1.58 (double_divide @ (double_divide @ X2 @ (multiply @ X1 @ X0)) @
% 6.84/1.58 (inverse @ (double_divide @ X0 @ X1)))) @
% 6.84/1.58 (inverse @ identity)) = (X2))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl13])).
% 6.84/1.58 thf(zip_derived_cl6, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl291, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ identity @
% 6.84/1.58 (double_divide @ (double_divide @ X2 @ (multiply @ X1 @ X0)) @
% 6.84/1.58 (multiply @ X1 @ X0))) @
% 6.84/1.58 (inverse @ identity)) = (X2))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl6])).
% 6.84/1.58 thf(zip_derived_cl312, plain,
% 6.84/1.58 (![X0 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ identity @
% 6.84/1.58 (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0))) @
% 6.84/1.58 (inverse @ identity)) = (identity))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl291])).
% 6.84/1.58 thf(zip_derived_cl28, plain,
% 6.84/1.58 (![X0 : $i]:
% 6.84/1.58 ((identity)
% 6.84/1.58 = (double_divide @ identity @ (multiply @ (inverse @ X0) @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl3])).
% 6.84/1.58 thf(zip_derived_cl2, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [inverse])).
% 6.84/1.58 thf(zip_derived_cl328, plain,
% 6.84/1.58 (((double_divide @ (inverse @ identity) @ (inverse @ identity))
% 6.84/1.58 = (identity))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl312, zip_derived_cl28, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl2, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [inverse])).
% 6.84/1.58 thf(zip_derived_cl13, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ X1 @
% 6.84/1.58 (double_divide @
% 6.84/1.58 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @ (inverse @ X2))) @
% 6.84/1.58 (inverse @ identity)) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl16, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ identity @
% 6.84/1.58 (double_divide @ (double_divide @ X1 @ (inverse @ X0)) @
% 6.84/1.58 (inverse @ X0))) @
% 6.84/1.58 (inverse @ identity)) = (X1))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl13])).
% 6.84/1.58 thf(zip_derived_cl347, plain,
% 6.84/1.58 (((double_divide @
% 6.84/1.58 (double_divide @ identity @
% 6.84/1.58 (double_divide @ identity @ (inverse @ identity))) @
% 6.84/1.58 (inverse @ identity)) = (inverse @ identity))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl328, zip_derived_cl16])).
% 6.84/1.58 thf(zip_derived_cl3, plain,
% 6.84/1.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.84/1.58 inference('cnf', [status(esa)], [identity])).
% 6.84/1.58 thf(zip_derived_cl2, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [inverse])).
% 6.84/1.58 thf(zip_derived_cl328, plain,
% 6.84/1.58 (((double_divide @ (inverse @ identity) @ (inverse @ identity))
% 6.84/1.58 = (identity))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl312, zip_derived_cl28, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl354, plain, (((identity) = (inverse @ identity))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl347, zip_derived_cl3, zip_derived_cl2,
% 6.84/1.58 zip_derived_cl328])).
% 6.84/1.58 thf(zip_derived_cl1, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X1 @ X0)
% 6.84/1.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [multiply])).
% 6.84/1.58 thf(zip_derived_cl422, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ (double_divide @ (inverse @ X0) @ (inverse @ X1)) @
% 6.84/1.58 (inverse @ X1)) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl20, zip_derived_cl354, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl427, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ identity @ (inverse @ (inverse @ X0))) = (X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl422])).
% 6.84/1.58 thf(zip_derived_cl2, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [inverse])).
% 6.84/1.58 thf(zip_derived_cl1, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X1 @ X0)
% 6.84/1.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [multiply])).
% 6.84/1.58 thf(zip_derived_cl7, plain,
% 6.84/1.58 (![X0 : $i]:
% 6.84/1.58 ((multiply @ identity @ X0)
% 6.84/1.58 = (double_divide @ (inverse @ X0) @ identity))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl2, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [inverse])).
% 6.84/1.58 thf(zip_derived_cl10, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl438, plain,
% 6.84/1.58 (![X0 : $i]: ((X0) = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl427, zip_derived_cl10])).
% 6.84/1.58 thf(zip_derived_cl354, plain, (((identity) = (inverse @ identity))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl347, zip_derived_cl3, zip_derived_cl2,
% 6.84/1.58 zip_derived_cl328])).
% 6.84/1.58 thf(zip_derived_cl422, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ (double_divide @ (inverse @ X0) @ (inverse @ X1)) @
% 6.84/1.58 (inverse @ X1)) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl20, zip_derived_cl354, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl426, plain,
% 6.84/1.58 (![X0 : $i]:
% 6.84/1.58 ((multiply @
% 6.84/1.58 (double_divide @ (inverse @ X0) @ (inverse @ identity)) @ identity)
% 6.84/1.58 = (X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl354, zip_derived_cl422])).
% 6.84/1.58 thf(zip_derived_cl354, plain, (((identity) = (inverse @ identity))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl347, zip_derived_cl3, zip_derived_cl2,
% 6.84/1.58 zip_derived_cl328])).
% 6.84/1.58 thf(zip_derived_cl2, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [inverse])).
% 6.84/1.58 thf(zip_derived_cl433, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ (inverse @ (inverse @ X0)) @ identity) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl426, zip_derived_cl354, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl458, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl438, zip_derived_cl433])).
% 6.84/1.58 thf(zip_derived_cl427, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ identity @ (inverse @ (inverse @ X0))) = (X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl422])).
% 6.84/1.58 thf(zip_derived_cl6, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl25, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 6.84/1.58 thf(zip_derived_cl33, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ (multiply @ X1 @ X0) @ (double_divide @ X0 @ X1))
% 6.84/1.58 = (inverse @ identity))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl25])).
% 6.84/1.58 thf(zip_derived_cl354, plain, (((identity) = (inverse @ identity))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl347, zip_derived_cl3, zip_derived_cl2,
% 6.84/1.58 zip_derived_cl328])).
% 6.84/1.58 thf(zip_derived_cl359, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ (multiply @ X1 @ X0) @ (double_divide @ X0 @ X1))
% 6.84/1.58 = (identity))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl354])).
% 6.84/1.58 thf(zip_derived_cl437, plain,
% 6.84/1.58 (![X0 : $i]:
% 6.84/1.58 ((multiply @ X0 @
% 6.84/1.58 (double_divide @ (inverse @ (inverse @ X0)) @ identity))
% 6.84/1.58 = (identity))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl427, zip_derived_cl359])).
% 6.84/1.58 thf(zip_derived_cl2, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [inverse])).
% 6.84/1.58 thf(zip_derived_cl443, plain,
% 6.84/1.58 (![X0 : $i]:
% 6.84/1.58 ((multiply @ X0 @ (inverse @ (inverse @ (inverse @ X0)))) = (identity))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl437, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl458, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (inverse @ (inverse @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl438, zip_derived_cl433])).
% 6.84/1.58 thf(zip_derived_cl6, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl427, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ identity @ (inverse @ (inverse @ X0))) = (X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl422])).
% 6.84/1.58 thf(zip_derived_cl439, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ identity @ (inverse @ (multiply @ X1 @ X0)))
% 6.84/1.58 = (double_divide @ X0 @ X1))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl427])).
% 6.84/1.58 thf(zip_derived_cl627, plain,
% 6.84/1.58 (![X0 : $i]:
% 6.84/1.58 ((multiply @ identity @ (inverse @ (inverse @ (inverse @ X0))))
% 6.84/1.58 = (double_divide @ identity @ X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl458, zip_derived_cl439])).
% 6.84/1.58 thf(zip_derived_cl427, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ identity @ (inverse @ (inverse @ X0))) = (X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl422])).
% 6.84/1.58 thf(zip_derived_cl644, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl627, zip_derived_cl427])).
% 6.84/1.58 thf(zip_derived_cl13, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ X1 @
% 6.84/1.58 (double_divide @
% 6.84/1.58 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @ (inverse @ X2))) @
% 6.84/1.58 (inverse @ identity)) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl1, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X1 @ X0)
% 6.84/1.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [multiply])).
% 6.84/1.58 thf(zip_derived_cl15, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((multiply @ (inverse @ identity) @
% 6.84/1.58 (double_divide @ X2 @
% 6.84/1.58 (double_divide @
% 6.84/1.58 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @ (inverse @ X1))))
% 6.84/1.58 = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl2, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [inverse])).
% 6.84/1.58 thf(zip_derived_cl21, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((multiply @ (inverse @ identity) @
% 6.84/1.58 (double_divide @ X2 @
% 6.84/1.58 (double_divide @
% 6.84/1.58 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @ (inverse @ X1))))
% 6.84/1.58 = (inverse @ X0))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl354, plain, (((identity) = (inverse @ identity))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl347, zip_derived_cl3, zip_derived_cl2,
% 6.84/1.58 zip_derived_cl328])).
% 6.84/1.58 thf(zip_derived_cl1, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X1 @ X0)
% 6.84/1.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [multiply])).
% 6.84/1.58 thf(zip_derived_cl1, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X1 @ X0)
% 6.84/1.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [multiply])).
% 6.84/1.58 thf(zip_derived_cl9, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 6.84/1.58 = (double_divide @ (multiply @ X1 @ X0) @ identity))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl2, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [inverse])).
% 6.84/1.58 thf(zip_derived_cl11, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ identity @ (double_divide @ X0 @ X1))
% 6.84/1.58 = (inverse @ (multiply @ X1 @ X0)))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl505, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((inverse @
% 6.84/1.58 (multiply @
% 6.84/1.58 (double_divide @
% 6.84/1.58 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @ (inverse @ X1)) @
% 6.84/1.58 X2))
% 6.84/1.58 = (inverse @ X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl21, zip_derived_cl354, zip_derived_cl11])).
% 6.84/1.58 thf(zip_derived_cl672, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((inverse @
% 6.84/1.58 (multiply @
% 6.84/1.58 (double_divide @ (double_divide @ X1 @ (inverse @ X0)) @
% 6.84/1.58 (inverse @ identity)) @
% 6.84/1.58 X0))
% 6.84/1.58 = (inverse @ X1))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl644, zip_derived_cl505])).
% 6.84/1.58 thf(zip_derived_cl354, plain, (((identity) = (inverse @ identity))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl347, zip_derived_cl3, zip_derived_cl2,
% 6.84/1.58 zip_derived_cl328])).
% 6.84/1.58 thf(zip_derived_cl1, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X1 @ X0)
% 6.84/1.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [multiply])).
% 6.84/1.58 thf(zip_derived_cl681, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((inverse @ (multiply @ (multiply @ (inverse @ X0) @ X1) @ X0))
% 6.84/1.58 = (inverse @ X1))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl672, zip_derived_cl354, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl427, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ identity @ (inverse @ (inverse @ X0))) = (X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl422])).
% 6.84/1.58 thf(zip_derived_cl756, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ identity @ (inverse @ (inverse @ X0)))
% 6.84/1.58 = (multiply @ (multiply @ (inverse @ X1) @ X0) @ X1))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl681, zip_derived_cl427])).
% 6.84/1.58 thf(zip_derived_cl427, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ identity @ (inverse @ (inverse @ X0))) = (X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl422])).
% 6.84/1.58 thf(zip_derived_cl784, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X0) = (multiply @ (multiply @ (inverse @ X1) @ X0) @ X1))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl756, zip_derived_cl427])).
% 6.84/1.58 thf(zip_derived_cl796, plain,
% 6.84/1.58 (![X0 : $i]:
% 6.84/1.58 ((inverse @ (inverse @ (inverse @ (inverse @ X0))))
% 6.84/1.58 = (multiply @ identity @ X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl443, zip_derived_cl784])).
% 6.84/1.58 thf(zip_derived_cl438, plain,
% 6.84/1.58 (![X0 : $i]: ((X0) = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl427, zip_derived_cl10])).
% 6.84/1.58 thf(zip_derived_cl10, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl804, plain,
% 6.84/1.58 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl796, zip_derived_cl438, zip_derived_cl10])).
% 6.84/1.58 thf(zip_derived_cl830, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl458, zip_derived_cl804])).
% 6.84/1.58 thf(zip_derived_cl438, plain,
% 6.84/1.58 (![X0 : $i]: ((X0) = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl427, zip_derived_cl10])).
% 6.84/1.58 thf(zip_derived_cl422, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ (double_divide @ (inverse @ X0) @ (inverse @ X1)) @
% 6.84/1.58 (inverse @ X1)) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl20, zip_derived_cl354, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl455, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @
% 6.84/1.58 (double_divide @ (inverse @ X1) @
% 6.84/1.58 (inverse @ (inverse @ (inverse @ (inverse @ X0))))) @
% 6.84/1.58 X0) = (X1))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl438, zip_derived_cl422])).
% 6.84/1.58 thf(zip_derived_cl438, plain,
% 6.84/1.58 (![X0 : $i]: ((X0) = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl427, zip_derived_cl10])).
% 6.84/1.58 thf(zip_derived_cl467, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ (double_divide @ (inverse @ X1) @ X0) @ X0) = (X1))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl455, zip_derived_cl438])).
% 6.84/1.58 thf(zip_derived_cl849, plain,
% 6.84/1.58 (![X0 : $i]: ((double_divide @ (inverse @ X0) @ identity) = (X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl830, zip_derived_cl467])).
% 6.84/1.58 thf(zip_derived_cl505, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((inverse @
% 6.84/1.58 (multiply @
% 6.84/1.58 (double_divide @
% 6.84/1.58 (double_divide @ X0 @ (double_divide @ X1 @ X2)) @ (inverse @ X1)) @
% 6.84/1.58 X2))
% 6.84/1.58 = (inverse @ X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl21, zip_derived_cl354, zip_derived_cl11])).
% 6.84/1.58 thf(zip_derived_cl897, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((inverse @
% 6.84/1.58 (multiply @
% 6.84/1.58 (double_divide @ (double_divide @ X1 @ X0) @
% 6.84/1.58 (inverse @ (inverse @ X0))) @
% 6.84/1.58 identity))
% 6.84/1.58 = (inverse @ X1))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl849, zip_derived_cl505])).
% 6.84/1.58 thf(zip_derived_cl804, plain,
% 6.84/1.58 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl796, zip_derived_cl438, zip_derived_cl10])).
% 6.84/1.58 thf(zip_derived_cl830, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl458, zip_derived_cl804])).
% 6.84/1.58 thf(zip_derived_cl6, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl908, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X0 @ (double_divide @ X1 @ X0)) = (inverse @ X1))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl897, zip_derived_cl804, zip_derived_cl830,
% 6.84/1.58 zip_derived_cl6])).
% 6.84/1.58 thf(zip_derived_cl804, plain,
% 6.84/1.58 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl796, zip_derived_cl438, zip_derived_cl10])).
% 6.84/1.58 thf(zip_derived_cl467, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ (double_divide @ (inverse @ X1) @ X0) @ X0) = (X1))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl455, zip_derived_cl438])).
% 6.84/1.58 thf(zip_derived_cl804, plain,
% 6.84/1.58 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl796, zip_derived_cl438, zip_derived_cl10])).
% 6.84/1.58 thf(zip_derived_cl784, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X0) = (multiply @ (multiply @ (inverse @ X1) @ X0) @ X1))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl756, zip_derived_cl427])).
% 6.84/1.58 thf(zip_derived_cl838, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X1) = (multiply @ (multiply @ X0 @ X1) @ (inverse @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl804, zip_derived_cl784])).
% 6.84/1.58 thf(zip_derived_cl955, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X1)
% 6.84/1.58 = (multiply @ X0 @ (inverse @ (double_divide @ (inverse @ X0) @ X1))))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl467, zip_derived_cl838])).
% 6.84/1.58 thf(zip_derived_cl6, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl964, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X1) = (multiply @ X0 @ (multiply @ X1 @ (inverse @ X0))))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl955, zip_derived_cl6])).
% 6.84/1.58 thf(zip_derived_cl1118, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X1) = (multiply @ (inverse @ X0) @ (multiply @ X1 @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl804, zip_derived_cl964])).
% 6.84/1.58 thf(zip_derived_cl1833, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X1)
% 6.84/1.58 = (multiply @ (inverse @ (double_divide @ X0 @ X1)) @ (inverse @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl908, zip_derived_cl1118])).
% 6.84/1.58 thf(zip_derived_cl6, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl1865, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X1) = (multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl1833, zip_derived_cl6])).
% 6.84/1.58 thf(zip_derived_cl964, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X1) = (multiply @ X0 @ (multiply @ X1 @ (inverse @ X0))))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl955, zip_derived_cl6])).
% 6.84/1.58 thf(zip_derived_cl1874, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl1865, zip_derived_cl964])).
% 6.84/1.58 thf(zip_derived_cl1874, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl1865, zip_derived_cl964])).
% 6.84/1.58 thf(zip_derived_cl1908, plain,
% 6.84/1.58 (((multiply @ c3 @ (multiply @ a3 @ b3))
% 6.84/1.58 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl4, zip_derived_cl1874, zip_derived_cl1874])).
% 6.84/1.58 thf(zip_derived_cl6, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl784, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X0) = (multiply @ (multiply @ (inverse @ X1) @ X0) @ X1))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl756, zip_derived_cl427])).
% 6.84/1.58 thf(zip_derived_cl800, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((X2)
% 6.84/1.58 = (multiply @ (multiply @ (multiply @ X1 @ X0) @ X2) @
% 6.84/1.58 (double_divide @ X0 @ X1)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl784])).
% 6.84/1.58 thf(zip_derived_cl1865, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X1) = (multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl1833, zip_derived_cl6])).
% 6.84/1.58 thf(zip_derived_cl5724, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((multiply @ (multiply @ X1 @ X2) @ X0)
% 6.84/1.58 = (multiply @ X0 @ (inverse @ (double_divide @ X2 @ X1))))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl800, zip_derived_cl1865])).
% 6.84/1.58 thf(zip_derived_cl3, plain,
% 6.84/1.58 (![X0 : $i]: ((identity) = (double_divide @ X0 @ (inverse @ X0)))),
% 6.84/1.58 inference('cnf', [status(esa)], [identity])).
% 6.84/1.58 thf(zip_derived_cl13, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ X1 @
% 6.84/1.58 (double_divide @
% 6.84/1.58 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @ (inverse @ X2))) @
% 6.84/1.58 (inverse @ identity)) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl13, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ X1 @
% 6.84/1.58 (double_divide @
% 6.84/1.58 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @ (inverse @ X2))) @
% 6.84/1.58 (inverse @ identity)) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl14, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ (inverse @ identity) @
% 6.84/1.58 (double_divide @ (double_divide @ X1 @ X0) @
% 6.84/1.58 (inverse @
% 6.84/1.58 (double_divide @ X3 @
% 6.84/1.58 (double_divide @
% 6.84/1.58 (double_divide @ X0 @ (double_divide @ X2 @ X3)) @
% 6.84/1.58 (inverse @ X2)))))) @
% 6.84/1.58 (inverse @ identity)) = (X1))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 6.84/1.58 thf(zip_derived_cl6, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl97, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ (inverse @ identity) @
% 6.84/1.58 (double_divide @ (double_divide @ X1 @ X0) @
% 6.84/1.58 (multiply @
% 6.84/1.58 (double_divide @
% 6.84/1.58 (double_divide @ X0 @ (double_divide @ X2 @ X3)) @
% 6.84/1.58 (inverse @ X2)) @
% 6.84/1.58 X3))) @
% 6.84/1.58 (inverse @ identity)) = (X1))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl14, zip_derived_cl6])).
% 6.84/1.58 thf(zip_derived_cl108, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ (inverse @ identity) @
% 6.84/1.58 (double_divide @ (double_divide @ X0 @ X2) @
% 6.84/1.58 (multiply @
% 6.84/1.58 (double_divide @ (double_divide @ X2 @ identity) @ (inverse @ X1)) @
% 6.84/1.58 (inverse @ X1)))) @
% 6.84/1.58 (inverse @ identity)) = (X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl97])).
% 6.84/1.58 thf(zip_derived_cl2, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [inverse])).
% 6.84/1.58 thf(zip_derived_cl122, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ (inverse @ identity) @
% 6.84/1.58 (double_divide @ (double_divide @ X0 @ X2) @
% 6.84/1.58 (multiply @ (double_divide @ (inverse @ X2) @ (inverse @ X1)) @
% 6.84/1.58 (inverse @ X1)))) @
% 6.84/1.58 (inverse @ identity)) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl108, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl354, plain, (((identity) = (inverse @ identity))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl347, zip_derived_cl3, zip_derived_cl2,
% 6.84/1.58 zip_derived_cl328])).
% 6.84/1.58 thf(zip_derived_cl467, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ (double_divide @ (inverse @ X1) @ X0) @ X0) = (X1))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl455, zip_derived_cl438])).
% 6.84/1.58 thf(zip_derived_cl644, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ identity @ X0))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl627, zip_derived_cl427])).
% 6.84/1.58 thf(zip_derived_cl6, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl354, plain, (((identity) = (inverse @ identity))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl347, zip_derived_cl3, zip_derived_cl2,
% 6.84/1.58 zip_derived_cl328])).
% 6.84/1.58 thf(zip_derived_cl2, plain,
% 6.84/1.58 (![X0 : $i]: ((inverse @ X0) = (double_divide @ X0 @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [inverse])).
% 6.84/1.58 thf(zip_derived_cl909, plain,
% 6.84/1.58 (![X0 : $i, X2 : $i]:
% 6.84/1.58 ((inverse @ (multiply @ X2 @ (double_divide @ X0 @ X2))) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl122, zip_derived_cl354, zip_derived_cl467,
% 6.84/1.58 zip_derived_cl644, zip_derived_cl6, zip_derived_cl354,
% 6.84/1.58 zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl439, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ identity @ (inverse @ (multiply @ X1 @ X0)))
% 6.84/1.58 = (double_divide @ X0 @ X1))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl427])).
% 6.84/1.58 thf(zip_derived_cl919, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ identity @ X0)
% 6.84/1.58 = (double_divide @ (double_divide @ X0 @ X1) @ X1))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl909, zip_derived_cl439])).
% 6.84/1.58 thf(zip_derived_cl25, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (inverse @ identity))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl6])).
% 6.84/1.58 thf(zip_derived_cl354, plain, (((identity) = (inverse @ identity))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl347, zip_derived_cl3, zip_derived_cl2,
% 6.84/1.58 zip_derived_cl328])).
% 6.84/1.58 thf(zip_derived_cl357, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl25, zip_derived_cl354])).
% 6.84/1.58 thf(zip_derived_cl784, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X0) = (multiply @ (multiply @ (inverse @ X1) @ X0) @ X1))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl756, zip_derived_cl427])).
% 6.84/1.58 thf(zip_derived_cl797, plain,
% 6.84/1.58 (![X0 : $i]: ((X0) = (multiply @ identity @ X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl357, zip_derived_cl784])).
% 6.84/1.58 thf(zip_derived_cl940, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X0) = (double_divide @ (double_divide @ X0 @ X1) @ X1))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl919, zip_derived_cl797])).
% 6.84/1.58 thf(zip_derived_cl438, plain,
% 6.84/1.58 (![X0 : $i]: ((X0) = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl427, zip_derived_cl10])).
% 6.84/1.58 thf(zip_derived_cl467, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ (double_divide @ (inverse @ X1) @ X0) @ X0) = (X1))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl455, zip_derived_cl438])).
% 6.84/1.58 thf(zip_derived_cl483, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ (double_divide @ X0 @ X1) @ X1)
% 6.84/1.58 = (inverse @ (inverse @ (inverse @ X0))))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl438, zip_derived_cl467])).
% 6.84/1.58 thf(zip_derived_cl439, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ identity @ (inverse @ (multiply @ X1 @ X0)))
% 6.84/1.58 = (double_divide @ X0 @ X1))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl427])).
% 6.84/1.58 thf(zip_derived_cl629, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ identity @
% 6.84/1.58 (inverse @ (inverse @ (inverse @ (inverse @ X0)))))
% 6.84/1.58 = (double_divide @ X1 @ (double_divide @ X0 @ X1)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl483, zip_derived_cl439])).
% 6.84/1.58 thf(zip_derived_cl438, plain,
% 6.84/1.58 (![X0 : $i]: ((X0) = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl427, zip_derived_cl10])).
% 6.84/1.58 thf(zip_derived_cl10, plain,
% 6.84/1.58 (![X0 : $i]: ((multiply @ identity @ X0) = (inverse @ (inverse @ X0)))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl7, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl646, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((inverse @ (inverse @ X0))
% 6.84/1.58 = (double_divide @ X1 @ (double_divide @ X0 @ X1)))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl629, zip_derived_cl438, zip_derived_cl10])).
% 6.84/1.58 thf(zip_derived_cl804, plain,
% 6.84/1.58 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl796, zip_derived_cl438, zip_derived_cl10])).
% 6.84/1.58 thf(zip_derived_cl832, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X0) = (double_divide @ X1 @ (double_divide @ X0 @ X1)))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl646, zip_derived_cl804])).
% 6.84/1.58 thf(zip_derived_cl1132, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((double_divide @ X0 @ X1) = (double_divide @ X1 @ X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl940, zip_derived_cl832])).
% 6.84/1.58 thf(zip_derived_cl6, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X0 @ X1) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl1458, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl1132, zip_derived_cl6])).
% 6.84/1.58 thf(zip_derived_cl5902, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((multiply @ (multiply @ X1 @ X2) @ X0)
% 6.84/1.58 = (multiply @ X0 @ (multiply @ X2 @ X1)))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl5724, zip_derived_cl1458])).
% 6.84/1.58 thf(zip_derived_cl1874, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl1865, zip_derived_cl964])).
% 6.84/1.58 thf(zip_derived_cl6229, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((multiply @ (multiply @ X1 @ X2) @ X0)
% 6.84/1.58 = (multiply @ (multiply @ X2 @ X1) @ X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl5902, zip_derived_cl1874])).
% 6.84/1.58 thf(zip_derived_cl784, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X0) = (multiply @ (multiply @ (inverse @ X1) @ X0) @ X1))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl756, zip_derived_cl427])).
% 6.84/1.58 thf(zip_derived_cl13, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((double_divide @
% 6.84/1.58 (double_divide @ X1 @
% 6.84/1.58 (double_divide @
% 6.84/1.58 (double_divide @ X0 @ (double_divide @ X2 @ X1)) @ (inverse @ X2))) @
% 6.84/1.58 (inverse @ identity)) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl0, zip_derived_cl2, zip_derived_cl2])).
% 6.84/1.58 thf(zip_derived_cl354, plain, (((identity) = (inverse @ identity))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl347, zip_derived_cl3, zip_derived_cl2,
% 6.84/1.58 zip_derived_cl328])).
% 6.84/1.58 thf(zip_derived_cl1, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X1 @ X0)
% 6.84/1.58 = (double_divide @ (double_divide @ X0 @ X1) @ identity))),
% 6.84/1.58 inference('cnf', [status(esa)], [multiply])).
% 6.84/1.58 thf(zip_derived_cl355, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((multiply @
% 6.84/1.58 (double_divide @ (double_divide @ X0 @ (double_divide @ X2 @ X1)) @
% 6.84/1.58 (inverse @ X2)) @
% 6.84/1.58 X1) = (X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl13, zip_derived_cl354, zip_derived_cl1])).
% 6.84/1.58 thf(zip_derived_cl908, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X0 @ (double_divide @ X1 @ X0)) = (inverse @ X1))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl897, zip_derived_cl804, zip_derived_cl830,
% 6.84/1.58 zip_derived_cl6])).
% 6.84/1.58 thf(zip_derived_cl784, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((X0) = (multiply @ (multiply @ (inverse @ X1) @ X0) @ X1))),
% 6.84/1.58 inference('demod', [status(thm)], [zip_derived_cl756, zip_derived_cl427])).
% 6.84/1.58 thf(zip_derived_cl1837, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((double_divide @ X0 @ (inverse @ X1))
% 6.84/1.58 = (multiply @ (inverse @ X0) @ X1))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl908, zip_derived_cl784])).
% 6.84/1.58 thf(zip_derived_cl1458, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl1132, zip_derived_cl6])).
% 6.84/1.58 thf(zip_derived_cl1874, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl1865, zip_derived_cl964])).
% 6.84/1.58 thf(zip_derived_cl1874, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl1865, zip_derived_cl964])).
% 6.84/1.58 thf(zip_derived_cl6051, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((multiply @ X1 @
% 6.84/1.58 (multiply @ X2 @ (multiply @ X0 @ (double_divide @ X2 @ X1))))
% 6.84/1.58 = (X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl355, zip_derived_cl1837, zip_derived_cl1458,
% 6.84/1.58 zip_derived_cl1874, zip_derived_cl1874])).
% 6.84/1.58 thf(zip_derived_cl6107, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((multiply @ X1 @ (multiply @ X2 @ X0))
% 6.84/1.58 = (multiply @ (inverse @ (double_divide @ X2 @ X1)) @ X0))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl784, zip_derived_cl6051])).
% 6.84/1.58 thf(zip_derived_cl1458, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i]:
% 6.84/1.58 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X1 @ X0)))),
% 6.84/1.58 inference('sup+', [status(thm)], [zip_derived_cl1132, zip_derived_cl6])).
% 6.84/1.58 thf(zip_derived_cl6162, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((multiply @ X1 @ (multiply @ X2 @ X0))
% 6.84/1.58 = (multiply @ (multiply @ X2 @ X1) @ X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl6107, zip_derived_cl1458])).
% 6.84/1.58 thf(zip_derived_cl6162, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((multiply @ X1 @ (multiply @ X2 @ X0))
% 6.84/1.58 = (multiply @ (multiply @ X2 @ X1) @ X0))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl6107, zip_derived_cl1458])).
% 6.84/1.58 thf(zip_derived_cl7451, plain,
% 6.84/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.84/1.58 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 6.84/1.58 = (multiply @ X1 @ (multiply @ X2 @ X0)))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl6229, zip_derived_cl6162, zip_derived_cl6162])).
% 6.84/1.58 thf(zip_derived_cl7452, plain,
% 6.84/1.58 (((multiply @ a3 @ (multiply @ c3 @ b3))
% 6.84/1.58 != (multiply @ a3 @ (multiply @ c3 @ b3)))),
% 6.84/1.58 inference('demod', [status(thm)],
% 6.84/1.58 [zip_derived_cl1908, zip_derived_cl7451])).
% 6.84/1.58 thf(zip_derived_cl7453, plain, ($false),
% 6.84/1.58 inference('simplify', [status(thm)], [zip_derived_cl7452])).
% 6.84/1.58
% 6.84/1.58 % SZS output end Refutation
% 6.84/1.58
% 6.84/1.58
% 6.84/1.58 % Terminating...
% 7.44/1.66 % Runner terminated.
% 7.44/1.67 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------