%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP014-1 : TPTP v9.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.VWedmcbFfz true
% Computer : n007.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 04:35:25 PM UTC 2025
% Result : Unsatisfiable 118.60s 26.52s
% Output : Refutation 118.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GRP014-1 : TPTP v9.2.0. Released v1.0.0.
% 0.02/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.VWedmcbFfz true
% 0.10/0.32 % Computer : n007.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Wed Oct 1 14:04:53 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % Running portfolio for 300 s
% 0.10/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.32 % Number of cores: 8
% 0.10/0.33 % Python version: Python 3.6.8
% 0.10/0.33 % Running in FO mode
% 0.52/0.66 % Total configuration time : 435
% 0.52/0.66 % Estimated wc time : 1092
% 0.52/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.52/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.52/0.85 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.52/0.88 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.89 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.53/0.91 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.53/0.95 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.53/0.97 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 118.60/26.52 % Solved by fo/fo7.sh.
% 118.60/26.52 % done 1513 iterations in 25.491s
% 118.60/26.52 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 118.60/26.52 % SZS output start Refutation
% 118.60/26.52 thf(inverse_type, type, inverse: $i > $i).
% 118.60/26.52 thf(a_type, type, a: $i).
% 118.60/26.52 thf(b_type, type, b: $i).
% 118.60/26.52 thf(multiply_type, type, multiply: $i > $i > $i).
% 118.60/26.52 thf(c_type, type, c: $i).
% 118.60/26.52 thf(prove_associativity, conjecture,
% 118.60/26.52 (( multiply @ a @ ( multiply @ b @ c ) ) =
% 118.60/26.52 ( multiply @ ( multiply @ a @ b ) @ c ))).
% 118.60/26.52 thf(zf_stmt_0, negated_conjecture,
% 118.60/26.52 (( multiply @ a @ ( multiply @ b @ c ) ) !=
% 118.60/26.52 ( multiply @ ( multiply @ a @ b ) @ c )),
% 118.60/26.52 inference('cnf.neg', [status(esa)], [prove_associativity])).
% 118.60/26.52 thf(zip_derived_cl1, plain,
% 118.60/26.52 (((multiply @ a @ (multiply @ b @ c))
% 118.60/26.52 != (multiply @ (multiply @ a @ b) @ c))),
% 118.60/26.52 inference('cnf', [status(esa)], [zf_stmt_0])).
% 118.60/26.52 thf(group_axiom, axiom,
% 118.60/26.52 (( multiply @
% 118.60/26.52 X @
% 118.60/26.52 ( inverse @
% 118.60/26.52 ( multiply @
% 118.60/26.52 ( multiply @
% 118.60/26.52 ( inverse @
% 118.60/26.52 ( multiply @
% 118.60/26.52 ( inverse @ Y ) @ ( multiply @ ( inverse @ X ) @ W ) ) ) @
% 118.60/26.52 Z ) @
% 118.60/26.52 ( inverse @ ( multiply @ Y @ Z ) ) ) ) ) =
% 118.60/26.52 ( W ))).
% 118.60/26.52 thf(zip_derived_cl0, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 118.60/26.52 X3) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X3)))))
% 118.60/26.52 = (X0))),
% 118.60/26.52 inference('cnf', [status(esa)], [group_axiom])).
% 118.60/26.52 thf(zip_derived_cl0, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 118.60/26.52 X3) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X3)))))
% 118.60/26.52 = (X0))),
% 118.60/26.52 inference('cnf', [status(esa)], [group_axiom])).
% 118.60/26.52 thf(zip_derived_cl3, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X5) @ X0)) @ X4) @
% 118.60/26.52 (inverse @ (multiply @ X5 @ X4)))))
% 118.60/26.52 = (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X2) @
% 118.60/26.52 (multiply @ (inverse @ (inverse @ X3)) @ X0))) @
% 118.60/26.52 X1) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X1)))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl0, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 118.60/26.52 X3) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X3)))))
% 118.60/26.52 = (X0))),
% 118.60/26.52 inference('cnf', [status(esa)], [group_axiom])).
% 118.60/26.52 thf(zip_derived_cl64, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ X1 @ X0))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl3, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X5) @ X0)) @ X4) @
% 118.60/26.52 (inverse @ (multiply @ X5 @ X4)))))
% 118.60/26.52 = (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X2) @
% 118.60/26.52 (multiply @ (inverse @ (inverse @ X3)) @ X0))) @
% 118.60/26.52 X1) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X1)))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl0, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 118.60/26.52 X3) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X3)))))
% 118.60/26.52 = (X0))),
% 118.60/26.52 inference('cnf', [status(esa)], [group_axiom])).
% 118.60/26.52 thf(zip_derived_cl74, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X1) @
% 118.60/26.52 (multiply @ (inverse @ (inverse @ X3)) @
% 118.60/26.52 (multiply @ (inverse @ X3) @ X2)))) @
% 118.60/26.52 X0) @
% 118.60/26.52 (inverse @ (multiply @ X1 @ X0))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl64, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ X1 @ X0))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl217, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X0))
% 118.60/26.52 = (multiply @ (inverse @ (inverse @ X1)) @
% 118.60/26.52 (multiply @ (inverse @ X1) @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl64])).
% 118.60/26.52 thf(zip_derived_cl217, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X0))
% 118.60/26.52 = (multiply @ (inverse @ (inverse @ X1)) @
% 118.60/26.52 (multiply @ (inverse @ X1) @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl64])).
% 118.60/26.52 thf(zip_derived_cl283, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ X0))
% 118.60/26.52 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl217])).
% 118.60/26.52 thf(zip_derived_cl283, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ X0))
% 118.60/26.52 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl217])).
% 118.60/26.52 thf(zip_derived_cl0, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 118.60/26.52 X3) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X3)))))
% 118.60/26.52 = (X0))),
% 118.60/26.52 inference('cnf', [status(esa)], [group_axiom])).
% 118.60/26.52 thf(zip_derived_cl384, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))) @
% 118.60/26.52 X2) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X3) @ X2)))))
% 118.60/26.52 = (X0))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl283, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl717, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X4) @ (multiply @ X4 @ X2))) @
% 118.60/26.52 (multiply @ X3 @ X0)) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl283, zip_derived_cl384])).
% 118.60/26.52 thf(zip_derived_cl5044, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ (multiply @ (inverse @ X5) @ (multiply @ X5 @ X1)) @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ X0 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X4) @
% 118.60/26.52 (multiply @ X4 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X3) @ X0)) @ X2) @
% 118.60/26.52 (inverse @ (multiply @ X3 @ X2))))))))))
% 118.60/26.52 = (X1))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl717])).
% 118.60/26.52 thf(zip_derived_cl64, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ X1 @ X0))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl5138, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ (multiply @ (inverse @ X5) @ (multiply @ X5 @ X1)) @
% 118.60/26.52 (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)], [zip_derived_cl5044, zip_derived_cl64])).
% 118.60/26.52 thf(zip_derived_cl283, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ X0))
% 118.60/26.52 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl217])).
% 118.60/26.52 thf(zip_derived_cl283, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ X0))
% 118.60/26.52 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl217])).
% 118.60/26.52 thf(zip_derived_cl366, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X3) @ (multiply @ X3 @ (multiply @ X2 @ X0)))
% 118.60/26.52 = (multiply @ (inverse @ (inverse @ X2)) @
% 118.60/26.52 (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl283, zip_derived_cl283])).
% 118.60/26.52 thf(zip_derived_cl5138, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ (multiply @ (inverse @ X5) @ (multiply @ X5 @ X1)) @
% 118.60/26.52 (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)], [zip_derived_cl5044, zip_derived_cl64])).
% 118.60/26.52 thf(zip_derived_cl5222, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @
% 118.60/26.52 (multiply @ (inverse @ (inverse @ X2)) @
% 118.60/26.52 (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))) @
% 118.60/26.52 (inverse @ (multiply @ X3 @ (inverse @ X3)))) = (multiply @ X2 @ X0))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl366, zip_derived_cl5138])).
% 118.60/26.52 thf(zip_derived_cl5982, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @
% 118.60/26.52 (multiply @ (inverse @ (inverse @ X2)) @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X4) @ (multiply @ X4 @ X0))) @
% 118.60/26.52 X0)) @
% 118.60/26.52 (inverse @ (multiply @ X3 @ (inverse @ X3))))
% 118.60/26.52 = (multiply @ X2 @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl5138, zip_derived_cl5222])).
% 118.60/26.52 thf(zip_derived_cl5138, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ (multiply @ (inverse @ X5) @ (multiply @ X5 @ X1)) @
% 118.60/26.52 (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)], [zip_derived_cl5044, zip_derived_cl64])).
% 118.60/26.52 thf(zip_derived_cl74, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X1) @
% 118.60/26.52 (multiply @ (inverse @ (inverse @ X3)) @
% 118.60/26.52 (multiply @ (inverse @ X3) @ X2)))) @
% 118.60/26.52 X0) @
% 118.60/26.52 (inverse @ (multiply @ X1 @ X0))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl74, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X1) @
% 118.60/26.52 (multiply @ (inverse @ (inverse @ X3)) @
% 118.60/26.52 (multiply @ (inverse @ X3) @ X2)))) @
% 118.60/26.52 X0) @
% 118.60/26.52 (inverse @ (multiply @ X1 @ X0))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl237, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 118.60/26.52 ((inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X5) @
% 118.60/26.52 (multiply @ (inverse @ (inverse @ X6)) @
% 118.60/26.52 (multiply @ (inverse @ X6) @ X0)))) @
% 118.60/26.52 X4) @
% 118.60/26.52 (inverse @ (multiply @ X5 @ X4))))) @
% 118.60/26.52 (multiply @ X0 @ X1)))) @
% 118.60/26.52 X2) @
% 118.60/26.52 (inverse @ (multiply @ X3 @ X2))))
% 118.60/26.52 = (X1))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl74])).
% 118.60/26.52 thf(zip_derived_cl3, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X5) @ X0)) @ X4) @
% 118.60/26.52 (inverse @ (multiply @ X5 @ X4)))))
% 118.60/26.52 = (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X2) @
% 118.60/26.52 (multiply @ (inverse @ (inverse @ X3)) @ X0))) @
% 118.60/26.52 X1) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X1)))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl0, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 118.60/26.52 X3) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X3)))))
% 118.60/26.52 = (X0))),
% 118.60/26.52 inference('cnf', [status(esa)], [group_axiom])).
% 118.60/26.52 thf(zip_derived_cl248, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)))) @
% 118.60/26.52 X2) @
% 118.60/26.52 (inverse @ (multiply @ X3 @ X2))))
% 118.60/26.52 = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl237, zip_derived_cl3, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl64, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ X1 @ X0))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl0, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 118.60/26.52 X3) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X3)))))
% 118.60/26.52 = (X0))),
% 118.60/26.52 inference('cnf', [status(esa)], [group_axiom])).
% 118.60/26.52 thf(zip_derived_cl155, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ X4 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X0) @ X3) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X4) @ X3)))))
% 118.60/26.52 = (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X0)) @ X1) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X1)))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl366, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X3) @ (multiply @ X3 @ (multiply @ X2 @ X0)))
% 118.60/26.52 = (multiply @ (inverse @ (inverse @ X2)) @
% 118.60/26.52 (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl283, zip_derived_cl283])).
% 118.60/26.52 thf(zip_derived_cl1108, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X6) @
% 118.60/26.52 (multiply @ X6 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ X1 @ X0))))))
% 118.60/26.52 = (multiply @ (inverse @ (inverse @ X4)) @
% 118.60/26.52 (multiply @ (inverse @ X5) @
% 118.60/26.52 (multiply @ X5 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X2) @ X3) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X4) @ X3))))))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl366])).
% 118.60/26.52 thf(zip_derived_cl64, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ X1 @ X0))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl1251, plain,
% 118.60/26.52 (![X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 118.60/26.52 ((X2)
% 118.60/26.52 = (multiply @ (inverse @ (inverse @ X4)) @
% 118.60/26.52 (multiply @ (inverse @ X5) @
% 118.60/26.52 (multiply @ X5 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X2) @ X3) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X4) @ X3))))))))),
% 118.60/26.52 inference('demod', [status(thm)], [zip_derived_cl1108, zip_derived_cl64])).
% 118.60/26.52 thf(zip_derived_cl3045, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 118.60/26.52 ((X5)
% 118.60/26.52 = (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ (inverse @ X4) @ (multiply @ X4 @ X0)))) @
% 118.60/26.52 X2) @
% 118.60/26.52 (inverse @ (multiply @ X3 @ X2))))) @
% 118.60/26.52 (multiply @ (inverse @ X6) @
% 118.60/26.52 (multiply @ X6 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X5) @ X1) @
% 118.60/26.52 (inverse @ (multiply @ X0 @ X1))))))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl248, zip_derived_cl1251])).
% 118.60/26.52 thf(zip_derived_cl155, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ X4 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X0) @ X3) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X4) @ X3)))))
% 118.60/26.52 = (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X0)) @ X1) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X1)))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl384, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))) @
% 118.60/26.52 X2) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X3) @ X2)))))
% 118.60/26.52 = (X0))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl283, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl3097, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X5 : $i, X6 : $i]:
% 118.60/26.52 ((X5)
% 118.60/26.52 = (multiply @ (inverse @ X0) @
% 118.60/26.52 (multiply @ (inverse @ X6) @
% 118.60/26.52 (multiply @ X6 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X5) @ X1) @
% 118.60/26.52 (inverse @ (multiply @ X0 @ X1))))))))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl3045, zip_derived_cl155, zip_derived_cl384])).
% 118.60/26.52 thf(zip_derived_cl5202, plain,
% 118.60/26.52 (![X0 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((X2)
% 118.60/26.52 = (multiply @ (inverse @ (inverse @ X2)) @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X3) @ (multiply @ X3 @ X0))) @
% 118.60/26.52 X0)))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl5138, zip_derived_cl3097])).
% 118.60/26.52 thf(zip_derived_cl6030, plain,
% 118.60/26.52 (![X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X2 @ (inverse @ (multiply @ X3 @ (inverse @ X3))))
% 118.60/26.52 = (multiply @ X2 @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl5982, zip_derived_cl5202])).
% 118.60/26.52 thf(zip_derived_cl0, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 118.60/26.52 X3) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X3)))))
% 118.60/26.52 = (X0))),
% 118.60/26.52 inference('cnf', [status(esa)], [group_axiom])).
% 118.60/26.52 thf(zip_derived_cl6121, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X4) @
% 118.60/26.52 (multiply @ (inverse @ X1) @
% 118.60/26.52 (inverse @ (multiply @ X0 @ (inverse @ X0)))))) @
% 118.60/26.52 X3) @
% 118.60/26.52 (inverse @ (multiply @ X4 @ X3)))))
% 118.60/26.52 = (inverse @ (multiply @ X2 @ (inverse @ X2))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl6030, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl155, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ X4 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X0) @ X3) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X4) @ X3)))))
% 118.60/26.52 = (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X0)) @ X1) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X1)))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl155, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ X4 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X0) @ X3) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X4) @ X3)))))
% 118.60/26.52 = (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X0)) @ X1) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X1)))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl0, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 118.60/26.52 X3) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X3)))))
% 118.60/26.52 = (X0))),
% 118.60/26.52 inference('cnf', [status(esa)], [group_axiom])).
% 118.60/26.52 thf(zip_derived_cl1081, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X3 @
% 118.60/26.52 (multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X3) @ X2)) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X1) @ X0))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl6320, plain,
% 118.60/26.52 (![X0 : $i, X2 : $i]:
% 118.60/26.52 ((inverse @ (multiply @ X0 @ (inverse @ X0)))
% 118.60/26.52 = (inverse @ (multiply @ X2 @ (inverse @ X2))))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl6121, zip_derived_cl155, zip_derived_cl1081])).
% 118.60/26.52 thf(zip_derived_cl283, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ X0))
% 118.60/26.52 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl217])).
% 118.60/26.52 thf(zip_derived_cl6337, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ (multiply @ X0 @ (inverse @ X0))) @
% 118.60/26.52 (multiply @ (multiply @ X3 @ (inverse @ X3)) @ X1))
% 118.60/26.52 = (multiply @ (inverse @ X2) @ (multiply @ X2 @ X1)))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl6320, zip_derived_cl283])).
% 118.60/26.52 thf(zip_derived_cl0, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X0))) @
% 118.60/26.52 X3) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X3)))))
% 118.60/26.52 = (X0))),
% 118.60/26.52 inference('cnf', [status(esa)], [group_axiom])).
% 118.60/26.52 thf(zip_derived_cl9432, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X4) @
% 118.60/26.52 (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))) @
% 118.60/26.52 X3) @
% 118.60/26.52 (inverse @ (multiply @ X4 @ X3)))))
% 118.60/26.52 = (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl6337, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl155, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ X4 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X0) @ X3) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X4) @ X3)))))
% 118.60/26.52 = (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X0)) @ X1) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X1)))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl384, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))) @
% 118.60/26.52 X2) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X3) @ X2)))))
% 118.60/26.52 = (X0))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl283, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl9767, plain,
% 118.60/26.52 (![X0 : $i, X2 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ (multiply @ X5 @ (inverse @ X5)) @ X0)
% 118.60/26.52 = (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl9432, zip_derived_cl155, zip_derived_cl384])).
% 118.60/26.52 thf(zip_derived_cl6320, plain,
% 118.60/26.52 (![X0 : $i, X2 : $i]:
% 118.60/26.52 ((inverse @ (multiply @ X0 @ (inverse @ X0)))
% 118.60/26.52 = (inverse @ (multiply @ X2 @ (inverse @ X2))))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl6121, zip_derived_cl155, zip_derived_cl1081])).
% 118.60/26.52 thf(zip_derived_cl1081, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X3 @
% 118.60/26.52 (multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X3) @ X2)) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X1) @ X0))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl6433, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X3 @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X3) @ X1) @
% 118.60/26.52 (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 118.60/26.52 = (X1))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl6320, zip_derived_cl1081])).
% 118.60/26.52 thf(zip_derived_cl9900, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ X2 @
% 118.60/26.52 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 118.60/26.52 (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 118.60/26.52 = (inverse @ (inverse @ X2)))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl9767, zip_derived_cl6433])).
% 118.60/26.52 thf(zip_derived_cl155, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ X4 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X0) @ X3) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X4) @ X3)))))
% 118.60/26.52 = (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X0)) @ X1) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X1)))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl64, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ X1 @ X0))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl1087, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X5) @
% 118.60/26.52 (multiply @ X5 @
% 118.60/26.52 (multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X2) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X1) @ X0)))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl64])).
% 118.60/26.52 thf(zip_derived_cl10156, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X0) @ (inverse @ (inverse @ X0)))
% 118.60/26.52 = (multiply @ X1 @ (inverse @ X1)))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl9900, zip_derived_cl1087])).
% 118.60/26.52 thf(zip_derived_cl10156, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X0) @ (inverse @ (inverse @ X0)))
% 118.60/26.52 = (multiply @ X1 @ (inverse @ X1)))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl9900, zip_derived_cl1087])).
% 118.60/26.52 thf(zip_derived_cl10625, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X1 @ (inverse @ X1)))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl10156, zip_derived_cl10156])).
% 118.60/26.52 thf(zip_derived_cl5138, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ (multiply @ (inverse @ X5) @ (multiply @ X5 @ X1)) @
% 118.60/26.52 (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)], [zip_derived_cl5044, zip_derived_cl64])).
% 118.60/26.52 thf(zip_derived_cl248, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)))) @
% 118.60/26.52 X2) @
% 118.60/26.52 (inverse @ (multiply @ X3 @ X2))))
% 118.60/26.52 = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl237, zip_derived_cl3, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl10625, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X1 @ (inverse @ X1)))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl10156, zip_derived_cl10156])).
% 118.60/26.52 thf(zip_derived_cl9900, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ X2 @
% 118.60/26.52 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 118.60/26.52 (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 118.60/26.52 = (inverse @ (inverse @ X2)))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl9767, zip_derived_cl6433])).
% 118.60/26.52 thf(zip_derived_cl10821, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0)))
% 118.60/26.52 = (inverse @ (inverse @ X1)))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl10625, zip_derived_cl9900])).
% 118.60/26.52 thf(zip_derived_cl283, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ X0))
% 118.60/26.52 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl217])).
% 118.60/26.52 thf(zip_derived_cl11154, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X1) @ (multiply @ X1 @ (inverse @ X0)))
% 118.60/26.52 = (inverse @ (inverse @ (inverse @ X0))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl10821, zip_derived_cl283])).
% 118.60/26.52 thf(zip_derived_cl11455, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X0))
% 118.60/26.52 = (inverse @
% 118.60/26.52 (inverse @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X2) @
% 118.60/26.52 (multiply @ (inverse @ X3) @ (multiply @ X3 @ X0)))) @
% 118.60/26.52 X1) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ X1)))))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl248, zip_derived_cl11154])).
% 118.60/26.52 thf(zip_derived_cl248, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ (inverse @ X0) @ (multiply @ X0 @ X1)))) @
% 118.60/26.52 X2) @
% 118.60/26.52 (inverse @ (multiply @ X3 @ X2))))
% 118.60/26.52 = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl237, zip_derived_cl3, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl11488, plain,
% 118.60/26.52 (![X0 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X0))
% 118.60/26.52 = (inverse @ (inverse @ X0)))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11455, zip_derived_cl248])).
% 118.60/26.52 thf(zip_derived_cl11530, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ (inverse @ X1)) @
% 118.60/26.52 (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl5138, zip_derived_cl11488])).
% 118.60/26.52 thf(zip_derived_cl6320, plain,
% 118.60/26.52 (![X0 : $i, X2 : $i]:
% 118.60/26.52 ((inverse @ (multiply @ X0 @ (inverse @ X0)))
% 118.60/26.52 = (inverse @ (multiply @ X2 @ (inverse @ X2))))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl6121, zip_derived_cl155, zip_derived_cl1081])).
% 118.60/26.52 thf(zip_derived_cl1087, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X5) @
% 118.60/26.52 (multiply @ X5 @
% 118.60/26.52 (multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X2) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X1) @ X0)))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl64])).
% 118.60/26.52 thf(zip_derived_cl6432, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ X3 @
% 118.60/26.52 (multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 118.60/26.52 = (X1))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl6320, zip_derived_cl1087])).
% 118.60/26.52 thf(zip_derived_cl366, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X3) @ (multiply @ X3 @ (multiply @ X2 @ X0)))
% 118.60/26.52 = (multiply @ (inverse @ (inverse @ X2)) @
% 118.60/26.52 (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl283, zip_derived_cl283])).
% 118.60/26.52 thf(zip_derived_cl283, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X2) @ (multiply @ X2 @ X0))
% 118.60/26.52 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl217])).
% 118.60/26.52 thf(zip_derived_cl468, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X4) @
% 118.60/26.52 (multiply @ X4 @ (multiply @ (inverse @ X3) @ (multiply @ X3 @ X0))))
% 118.60/26.52 = (multiply @ (inverse @ (inverse @ (inverse @ X1))) @
% 118.60/26.52 (multiply @ (inverse @ X2) @
% 118.60/26.52 (multiply @ X2 @ (multiply @ X1 @ X0)))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl366, zip_derived_cl283])).
% 118.60/26.52 thf(zip_derived_cl6652, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ (inverse @ (inverse @ X0))) @ X0)
% 118.60/26.52 = (multiply @ (inverse @ (inverse @ (inverse @ X2))) @
% 118.60/26.52 (multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ X3 @
% 118.60/26.52 (multiply @ X2 @ (inverse @ (multiply @ X1 @ (inverse @ X1))))))))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl6432, zip_derived_cl468])).
% 118.60/26.52 thf(zip_derived_cl6432, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ X3 @
% 118.60/26.52 (multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 118.60/26.52 = (X1))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl6320, zip_derived_cl1087])).
% 118.60/26.52 thf(zip_derived_cl6785, plain,
% 118.60/26.52 (![X0 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ (inverse @ (inverse @ X0))) @ X0)
% 118.60/26.52 = (multiply @ (inverse @ (inverse @ (inverse @ X2))) @ X2))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl6652, zip_derived_cl6432])).
% 118.60/26.52 thf(zip_derived_cl6433, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X3 @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X3) @ X1) @
% 118.60/26.52 (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 118.60/26.52 = (X1))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl6320, zip_derived_cl1081])).
% 118.60/26.52 thf(zip_derived_cl7164, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ (inverse @ X1)) @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (inverse @ (inverse @ X0))) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ (inverse @ X2)))))
% 118.60/26.52 = (X1))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl6785, zip_derived_cl6433])).
% 118.60/26.52 thf(zip_derived_cl11664, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ (inverse @ X1)) @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 118.60/26.52 (inverse @ (multiply @ X2 @ (inverse @ X2)))))
% 118.60/26.52 = (X1))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl11530, zip_derived_cl7164])).
% 118.60/26.52 thf(zip_derived_cl11530, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ (inverse @ X1)) @
% 118.60/26.52 (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl5138, zip_derived_cl11488])).
% 118.60/26.52 thf(zip_derived_cl10821, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0)))
% 118.60/26.52 = (inverse @ (inverse @ X1)))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl10625, zip_derived_cl9900])).
% 118.60/26.52 thf(zip_derived_cl11700, plain,
% 118.60/26.52 (![X1 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X1)))) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11664, zip_derived_cl11530, zip_derived_cl10821])).
% 118.60/26.52 thf(zip_derived_cl11530, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ (inverse @ X1)) @
% 118.60/26.52 (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl5138, zip_derived_cl11488])).
% 118.60/26.52 thf(zip_derived_cl11752, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ (inverse @ X1))))
% 118.60/26.52 = (inverse @ (inverse @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl11700, zip_derived_cl11530])).
% 118.60/26.52 thf(zip_derived_cl1087, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X5) @
% 118.60/26.52 (multiply @ X5 @
% 118.60/26.52 (multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X2) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X1) @ X0)))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl64])).
% 118.60/26.52 thf(zip_derived_cl11799, plain,
% 118.60/26.52 (![X0 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X2) @
% 118.60/26.52 (multiply @ X2 @ (inverse @ (inverse @ X0)))) = (X0))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl11752, zip_derived_cl1087])).
% 118.60/26.52 thf(zip_derived_cl12033, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ (inverse @ X1)) @
% 118.60/26.52 (multiply @ X0 @ (inverse @ X0))) = (X1))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl10625, zip_derived_cl11799])).
% 118.60/26.52 thf(zip_derived_cl1087, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X5) @
% 118.60/26.52 (multiply @ X5 @
% 118.60/26.52 (multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X2) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X1) @ X0)))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl64])).
% 118.60/26.52 thf(zip_derived_cl12089, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ X3 @
% 118.60/26.52 (multiply @ X2 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ X0 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ X2) @ (multiply @ X1 @ (inverse @ X1)))))))))
% 118.60/26.52 = (inverse @ X0))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl12033, zip_derived_cl1087])).
% 118.60/26.52 thf(zip_derived_cl10821, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0)))
% 118.60/26.52 = (inverse @ (inverse @ X1)))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl10625, zip_derived_cl9900])).
% 118.60/26.52 thf(zip_derived_cl11700, plain,
% 118.60/26.52 (![X1 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X1)))) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11664, zip_derived_cl11530, zip_derived_cl10821])).
% 118.60/26.52 thf(zip_derived_cl11488, plain,
% 118.60/26.52 (![X0 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X0))
% 118.60/26.52 = (inverse @ (inverse @ X0)))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11455, zip_derived_cl248])).
% 118.60/26.52 thf(zip_derived_cl12145, plain,
% 118.60/26.52 (![X0 : $i, X2 : $i]:
% 118.60/26.52 ((inverse @
% 118.60/26.52 (inverse @ (multiply @ X2 @ (inverse @ (multiply @ X0 @ X2)))))
% 118.60/26.52 = (inverse @ X0))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl12089, zip_derived_cl10821,
% 118.60/26.52 zip_derived_cl11700, zip_derived_cl11488])).
% 118.60/26.52 thf(zip_derived_cl1087, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X5) @
% 118.60/26.52 (multiply @ X5 @
% 118.60/26.52 (multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X2) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X1) @ X0)))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl64])).
% 118.60/26.52 thf(zip_derived_cl12519, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X4) @
% 118.60/26.52 (multiply @ X4 @
% 118.60/26.52 (multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X0) @ X2) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X3) @ X2)))))))
% 118.60/26.52 = (inverse @ (multiply @ X1 @ (inverse @ (multiply @ X0 @ X1)))))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl12145, zip_derived_cl1087])).
% 118.60/26.52 thf(zip_derived_cl1087, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X5 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X5) @
% 118.60/26.52 (multiply @ X5 @
% 118.60/26.52 (multiply @ X1 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X2) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ (inverse @ X1) @ X0)))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl155, zip_derived_cl64])).
% 118.60/26.52 thf(zip_derived_cl12597, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((X0) = (inverse @ (multiply @ X1 @ (inverse @ (multiply @ X0 @ X1)))))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl12519, zip_derived_cl1087])).
% 118.60/26.52 thf(zip_derived_cl12597, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((X0) = (inverse @ (multiply @ X1 @ (inverse @ (multiply @ X0 @ X1)))))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl12519, zip_derived_cl1087])).
% 118.60/26.52 thf(zip_derived_cl12650, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((X1) = (inverse @ (multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl12597, zip_derived_cl12597])).
% 118.60/26.52 thf(zip_derived_cl11700, plain,
% 118.60/26.52 (![X1 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X1)))) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11664, zip_derived_cl11530, zip_derived_cl10821])).
% 118.60/26.52 thf(zip_derived_cl12650, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((X1) = (inverse @ (multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl12597, zip_derived_cl12597])).
% 118.60/26.52 thf(zip_derived_cl6433, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X3 @
% 118.60/26.52 (multiply @ (multiply @ (inverse @ X3) @ X1) @
% 118.60/26.52 (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 118.60/26.52 = (X1))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl6320, zip_derived_cl1081])).
% 118.60/26.52 thf(zip_derived_cl11752, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ X0 @ (inverse @ (multiply @ X1 @ (inverse @ X1))))
% 118.60/26.52 = (inverse @ (inverse @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl11700, zip_derived_cl11530])).
% 118.60/26.52 thf(zip_derived_cl11781, plain,
% 118.60/26.52 (![X1 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X3 @
% 118.60/26.52 (inverse @ (inverse @ (multiply @ (inverse @ X3) @ X1)))) = (
% 118.60/26.52 X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl6433, zip_derived_cl11752])).
% 118.60/26.52 thf(zip_derived_cl12757, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl12650, zip_derived_cl11781])).
% 118.60/26.52 thf(zip_derived_cl12650, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((X1) = (inverse @ (multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl12597, zip_derived_cl12597])).
% 118.60/26.52 thf(zip_derived_cl12827, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((inverse @ X1)
% 118.60/26.52 = (inverse @ (multiply @ (inverse @ X0) @ (multiply @ X0 @ X1))))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl12757, zip_derived_cl12650])).
% 118.60/26.52 thf(zip_derived_cl11488, plain,
% 118.60/26.52 (![X0 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X0))
% 118.60/26.52 = (inverse @ (inverse @ X0)))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11455, zip_derived_cl248])).
% 118.60/26.52 thf(zip_derived_cl12867, plain,
% 118.60/26.52 (![X1 : $i]: ((inverse @ X1) = (inverse @ (inverse @ (inverse @ X1))))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl12827, zip_derived_cl11488])).
% 118.60/26.52 thf(zip_derived_cl12870, plain,
% 118.60/26.52 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11700, zip_derived_cl12867])).
% 118.60/26.52 thf(zip_derived_cl12987, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((inverse @ X0) = (multiply @ (inverse @ (multiply @ X1 @ X0)) @ X1))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl12650, zip_derived_cl12870])).
% 118.60/26.52 thf(zip_derived_cl64, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X2)) @ X0) @
% 118.60/26.52 (inverse @ (multiply @ X1 @ X0))))))
% 118.60/26.52 = (X2))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 118.60/26.52 thf(zip_derived_cl14013, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X3) @
% 118.60/26.52 (multiply @ X3 @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @
% 118.60/26.52 (inverse @
% 118.60/26.52 (multiply @ (inverse @ (inverse @ (multiply @ X2 @ X0))) @ X1)) @
% 118.60/26.52 X2) @
% 118.60/26.52 (inverse @ (inverse @ X0))))))
% 118.60/26.52 = (X1))),
% 118.60/26.52 inference('sup+', [status(thm)], [zip_derived_cl12987, zip_derived_cl64])).
% 118.60/26.52 thf(zip_derived_cl12870, plain,
% 118.60/26.52 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11700, zip_derived_cl12867])).
% 118.60/26.52 thf(zip_derived_cl12870, plain,
% 118.60/26.52 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11700, zip_derived_cl12867])).
% 118.60/26.52 thf(zip_derived_cl11488, plain,
% 118.60/26.52 (![X0 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X0))
% 118.60/26.52 = (inverse @ (inverse @ X0)))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11455, zip_derived_cl248])).
% 118.60/26.52 thf(zip_derived_cl12870, plain,
% 118.60/26.52 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11700, zip_derived_cl12867])).
% 118.60/26.52 thf(zip_derived_cl12949, plain,
% 118.60/26.52 (![X0 : $i, X4 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X4) @ (multiply @ X4 @ X0)) = (X0))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11488, zip_derived_cl12870])).
% 118.60/26.52 thf(zip_derived_cl14104, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 118.60/26.52 ((inverse @
% 118.60/26.52 (multiply @
% 118.60/26.52 (multiply @ (inverse @ (multiply @ (multiply @ X2 @ X0) @ X1)) @ X2) @
% 118.60/26.52 X0))
% 118.60/26.52 = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl14013, zip_derived_cl12870,
% 118.60/26.52 zip_derived_cl12870, zip_derived_cl12949])).
% 118.60/26.52 thf(zip_derived_cl12987, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((inverse @ X0) = (multiply @ (inverse @ (multiply @ X1 @ X0)) @ X1))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl12650, zip_derived_cl12870])).
% 118.60/26.52 thf(zip_derived_cl12870, plain,
% 118.60/26.52 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11700, zip_derived_cl12867])).
% 118.60/26.52 thf(zip_derived_cl12757, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ (multiply @ X1 @ X0) @ (inverse @ X0)) = (X1))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl12650, zip_derived_cl11781])).
% 118.60/26.52 thf(zip_derived_cl12979, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ (multiply @ X1 @ (inverse @ X0)) @ X0) = (X1))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl12870, zip_derived_cl12757])).
% 118.60/26.52 thf(zip_derived_cl14024, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X0) @ X1)
% 118.60/26.52 = (inverse @ (multiply @ (inverse @ X1) @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl12987, zip_derived_cl12979])).
% 118.60/26.52 thf(zip_derived_cl14024, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X0) @ X1)
% 118.60/26.52 = (inverse @ (multiply @ (inverse @ X1) @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl12987, zip_derived_cl12979])).
% 118.60/26.52 thf(zip_derived_cl12870, plain,
% 118.60/26.52 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11700, zip_derived_cl12867])).
% 118.60/26.52 thf(zip_derived_cl17510, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ (inverse @ X0) @
% 118.60/26.52 (multiply @ (inverse @ X2) @ (multiply @ (multiply @ X2 @ X0) @ X1)))
% 118.60/26.52 = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl14104, zip_derived_cl14024,
% 118.60/26.52 zip_derived_cl14024, zip_derived_cl12870])).
% 118.60/26.52 thf(zip_derived_cl11781, plain,
% 118.60/26.52 (![X1 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X3 @
% 118.60/26.52 (inverse @ (inverse @ (multiply @ (inverse @ X3) @ X1)))) = (
% 118.60/26.52 X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl6433, zip_derived_cl11752])).
% 118.60/26.52 thf(zip_derived_cl12870, plain,
% 118.60/26.52 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11700, zip_derived_cl12867])).
% 118.60/26.52 thf(zip_derived_cl12951, plain,
% 118.60/26.52 (![X1 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X3 @ (multiply @ (inverse @ X3) @ X1)) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11781, zip_derived_cl12870])).
% 118.60/26.52 thf(zip_derived_cl17532, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ X1 @ X0)
% 118.60/26.52 = (multiply @ (inverse @ X2) @
% 118.60/26.52 (multiply @ (multiply @ X2 @ X1) @ X0)))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl17510, zip_derived_cl12951])).
% 118.60/26.52 thf(zip_derived_cl12951, plain,
% 118.60/26.52 (![X1 : $i, X3 : $i]:
% 118.60/26.52 ((multiply @ X3 @ (multiply @ (inverse @ X3) @ X1)) = (X1))),
% 118.60/26.52 inference('demod', [status(thm)],
% 118.60/26.52 [zip_derived_cl11781, zip_derived_cl12870])).
% 118.60/26.52 thf(zip_derived_cl17703, plain,
% 118.60/26.52 (![X0 : $i, X1 : $i, X2 : $i]:
% 118.60/26.52 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 118.60/26.52 = (multiply @ (multiply @ X2 @ X1) @ X0))),
% 118.60/26.52 inference('sup+', [status(thm)],
% 118.60/26.52 [zip_derived_cl17532, zip_derived_cl12951])).
% 118.60/26.52 thf(zip_derived_cl17820, plain,
% 118.60/26.52 (((multiply @ a @ (multiply @ b @ c))
% 118.60/26.52 != (multiply @ a @ (multiply @ b @ c)))),
% 118.60/26.52 inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl17703])).
% 118.60/26.52 thf(zip_derived_cl17821, plain, ($false),
% 118.60/26.52 inference('simplify', [status(thm)], [zip_derived_cl17820])).
% 118.60/26.52
% 118.60/26.52 % SZS output end Refutation
% 118.60/26.52
% 118.60/26.52
% 118.60/26.52 % Terminating...
% 119.57/26.71 % Runner terminated.
% 119.57/26.73 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------