%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP430-1 : TPTP v9.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.xjYMRiBhNO true
% Computer : n002.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 04:36:26 PM UTC 2025
% Result : Unsatisfiable 6.87s 4.37s
% Output : Refutation 6.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/1.01 % Problem : GRP430-1 : TPTP v9.2.0. Released v2.6.0.
% 0.10/1.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.xjYMRiBhNO true
% 0.13/1.45 % Computer : n002.cluster.edu
% 0.13/1.45 % Model : x86_64 x86_64
% 0.13/1.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/1.45 % Memory : 8042.1875MB
% 0.13/1.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/1.45 % CPULimit : 300
% 0.13/1.45 % WCLimit : 300
% 0.13/1.45 % DateTime : Wed Oct 1 14:09:09 EDT 2025
% 0.16/1.46 % CPUTime :
% 0.16/1.46 % Running portfolio for 300 s
% 0.16/1.46 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/1.48 % Number of cores: 8
% 0.16/1.49 % Python version: Python 3.6.8
% 0.16/1.51 % Running in FO mode
% 0.36/1.89 % Total configuration time : 435
% 0.36/1.89 % Estimated wc time : 1092
% 0.36/1.89 % Estimated cpu time (7 cpus) : 156.0
% 0.38/2.17 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.38/2.18 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.85/2.22 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.85/2.23 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.85/2.25 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.85/2.25 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.85/2.26 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 6.87/4.37 % Solved by fo/fo7.sh.
% 6.87/4.37 % done 499 iterations in 1.975s
% 6.87/4.37 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 6.87/4.37 % SZS output start Refutation
% 6.87/4.37 thf(inverse_type, type, inverse: $i > $i).
% 6.87/4.37 thf(a1_type, type, a1: $i).
% 6.87/4.37 thf(b1_type, type, b1: $i).
% 6.87/4.37 thf(multiply_type, type, multiply: $i > $i > $i).
% 6.87/4.37 thf(single_axiom, axiom,
% 6.87/4.37 (( multiply @
% 6.87/4.37 A @
% 6.87/4.37 ( inverse @
% 6.87/4.37 ( multiply @
% 6.87/4.37 B @
% 6.87/4.37 ( multiply @
% 6.87/4.37 ( multiply @
% 6.87/4.37 ( multiply @ C @ ( inverse @ C ) ) @
% 6.87/4.37 ( inverse @ ( multiply @ D @ B ) ) ) @
% 6.87/4.37 A ) ) ) ) =
% 6.87/4.37 ( D ))).
% 6.87/4.37 thf(zip_derived_cl0, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @ X1 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ X2 @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (multiply @ X0 @ X2))) @
% 6.87/4.37 X1))))
% 6.87/4.37 = (X0))),
% 6.87/4.37 inference('cnf', [status(esa)], [single_axiom])).
% 6.87/4.37 thf(zip_derived_cl0, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @ X1 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ X2 @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (multiply @ X0 @ X2))) @
% 6.87/4.37 X1))))
% 6.87/4.37 = (X0))),
% 6.87/4.37 inference('cnf', [status(esa)], [single_axiom])).
% 6.87/4.37 thf(zip_derived_cl0, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @ X1 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ X2 @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (multiply @ X0 @ X2))) @
% 6.87/4.37 X1))))
% 6.87/4.37 = (X0))),
% 6.87/4.37 inference('cnf', [status(esa)], [single_axiom])).
% 6.87/4.37 thf(zip_derived_cl4, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/4.37 ((multiply @ X2 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 6.87/4.37 (inverse @ (multiply @ X0 @ X1))) @
% 6.87/4.37 (multiply @ X3 @ (inverse @ X3))) @
% 6.87/4.37 (multiply @ X0 @ X2))))
% 6.87/4.37 = (X1))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 6.87/4.37 thf(zip_derived_cl0, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @ X1 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ X2 @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (multiply @ X0 @ X2))) @
% 6.87/4.37 X1))))
% 6.87/4.37 = (X0))),
% 6.87/4.37 inference('cnf', [status(esa)], [single_axiom])).
% 6.87/4.37 thf(zip_derived_cl12, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.87/4.37 ((multiply @ X4 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ (multiply @ X2 @ (multiply @ X5 @ (inverse @ X5))) @
% 6.87/4.37 (multiply @ X0 @ X4))))
% 6.87/4.37 = (multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (multiply @ X2 @ X0))) @
% 6.87/4.37 (multiply @ X1 @ (inverse @ X1))))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 6.87/4.37 thf(zip_derived_cl4, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/4.37 ((multiply @ X2 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 6.87/4.37 (inverse @ (multiply @ X0 @ X1))) @
% 6.87/4.37 (multiply @ X3 @ (inverse @ X3))) @
% 6.87/4.37 (multiply @ X0 @ X2))))
% 6.87/4.37 = (X1))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 6.87/4.37 thf(zip_derived_cl36, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/4.37 ((multiply @
% 6.87/4.37 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (multiply @ X1 @ X2))) @
% 6.87/4.37 X1))) @
% 6.87/4.37 (multiply @ X0 @ (inverse @ X0))) = (X2))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl4])).
% 6.87/4.37 thf(zip_derived_cl0, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @ X1 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ X2 @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (multiply @ X0 @ X2))) @
% 6.87/4.37 X1))))
% 6.87/4.37 = (X0))),
% 6.87/4.37 inference('cnf', [status(esa)], [single_axiom])).
% 6.87/4.37 thf(zip_derived_cl78, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (multiply @ X1 @ X0)))
% 6.87/4.37 = (multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 6.87/4.37 (inverse @ (multiply @ X1 @ X0))))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl0])).
% 6.87/4.37 thf(zip_derived_cl172, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.87/4.37 ((multiply @ (multiply @ X5 @ (inverse @ X5)) @ (inverse @ X0))
% 6.87/4.37 = (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ X1 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ X2 @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (multiply @ X0 @ X2))) @
% 6.87/4.37 X1)))))))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl78])).
% 6.87/4.37 thf(zip_derived_cl0, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @ X1 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ X2 @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (multiply @ X0 @ X2))) @
% 6.87/4.37 X1))))
% 6.87/4.37 = (X0))),
% 6.87/4.37 inference('cnf', [status(esa)], [single_axiom])).
% 6.87/4.37 thf(zip_derived_cl194, plain,
% 6.87/4.37 (![X0 : $i, X4 : $i, X5 : $i]:
% 6.87/4.37 ((multiply @ (multiply @ X5 @ (inverse @ X5)) @ (inverse @ X0))
% 6.87/4.37 = (multiply @ (multiply @ X4 @ (inverse @ X4)) @ (inverse @ X0)))),
% 6.87/4.37 inference('demod', [status(thm)], [zip_derived_cl172, zip_derived_cl0])).
% 6.87/4.37 thf(zip_derived_cl36, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/4.37 ((multiply @
% 6.87/4.37 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (multiply @ X1 @ X2))) @
% 6.87/4.37 X1))) @
% 6.87/4.37 (multiply @ X0 @ (inverse @ X0))) = (X2))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl4])).
% 6.87/4.37 thf(zip_derived_cl227, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ (multiply @ X1 @ (inverse @ X1)) @ (inverse @ X0)))) @
% 6.87/4.37 (multiply @ X2 @ (inverse @ X2))) = (inverse @ (inverse @ X0)))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl194, zip_derived_cl36])).
% 6.87/4.37 thf(zip_derived_cl4, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/4.37 ((multiply @ X2 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 6.87/4.37 (inverse @ (multiply @ X0 @ X1))) @
% 6.87/4.37 (multiply @ X3 @ (inverse @ X3))) @
% 6.87/4.37 (multiply @ X0 @ X2))))
% 6.87/4.37 = (X1))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 6.87/4.37 thf(zip_derived_cl330, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 6.87/4.37 ((multiply @ X2 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X6 @ (inverse @ X6)) @
% 6.87/4.37 (inverse @ (inverse @ (inverse @ X0)))) @
% 6.87/4.37 (multiply @ X5 @ (inverse @ X5))) @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @ (inverse @ X0)))) @
% 6.87/4.37 X2))))
% 6.87/4.37 = (multiply @ X1 @ (inverse @ X1)))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl227, zip_derived_cl4])).
% 6.87/4.37 thf(zip_derived_cl36, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/4.37 ((multiply @
% 6.87/4.37 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (multiply @ X1 @ X2))) @
% 6.87/4.37 X1))) @
% 6.87/4.37 (multiply @ X0 @ (inverse @ X0))) = (X2))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl4])).
% 6.87/4.37 thf(zip_derived_cl36, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/4.37 ((multiply @
% 6.87/4.37 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (multiply @ X1 @ X2))) @
% 6.87/4.37 X1))) @
% 6.87/4.37 (multiply @ X0 @ (inverse @ X0))) = (X2))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl4])).
% 6.87/4.37 thf(zip_derived_cl79, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (inverse @ X0))) @
% 6.87/4.37 (multiply @ X1 @ (inverse @ X1))) = (X0))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl36])).
% 6.87/4.37 thf(zip_derived_cl0, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @ X1 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ X2 @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (multiply @ X0 @ X2))) @
% 6.87/4.37 X1))))
% 6.87/4.37 = (X0))),
% 6.87/4.37 inference('cnf', [status(esa)], [single_axiom])).
% 6.87/4.37 thf(zip_derived_cl351, plain,
% 6.87/4.37 (![X1 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @ X3 @ (inverse @ X3)) = (multiply @ X1 @ (inverse @ X1)))),
% 6.87/4.37 inference('demod', [status(thm)],
% 6.87/4.37 [zip_derived_cl330, zip_derived_cl79, zip_derived_cl0])).
% 6.87/4.37 thf(zip_derived_cl227, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ (multiply @ X1 @ (inverse @ X1)) @ (inverse @ X0)))) @
% 6.87/4.37 (multiply @ X2 @ (inverse @ X2))) = (inverse @ (inverse @ X0)))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl194, zip_derived_cl36])).
% 6.87/4.37 thf(zip_derived_cl391, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.37 ((multiply @ (multiply @ X0 @ (inverse @ X0)) @
% 6.87/4.37 (multiply @ X2 @ (inverse @ X2)))
% 6.87/4.37 = (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl227])).
% 6.87/4.37 thf(zip_derived_cl4, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/4.37 ((multiply @ X2 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 6.87/4.37 (inverse @ (multiply @ X0 @ X1))) @
% 6.87/4.37 (multiply @ X3 @ (inverse @ X3))) @
% 6.87/4.37 (multiply @ X0 @ X2))))
% 6.87/4.37 = (X1))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 6.87/4.37 thf(zip_derived_cl518, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.37 ((multiply @ X2 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @
% 6.87/4.37 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 6.87/4.37 (multiply @ X1 @ X2))))
% 6.87/4.37 = (inverse @ X1))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl391, zip_derived_cl4])).
% 6.87/4.37 thf(zip_derived_cl0, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @ X1 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ X2 @
% 6.87/4.37 (multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (multiply @ X0 @ X2))) @
% 6.87/4.37 X1))))
% 6.87/4.37 = (X0))),
% 6.87/4.37 inference('cnf', [status(esa)], [single_axiom])).
% 6.87/4.37 thf(zip_derived_cl541, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.37 ((inverse @
% 6.87/4.37 (multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ X1 @
% 6.87/4.37 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))))
% 6.87/4.37 = (X1))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl518, zip_derived_cl0])).
% 6.87/4.37 thf(zip_derived_cl541, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.37 ((inverse @
% 6.87/4.37 (multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ X1 @
% 6.87/4.37 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))))
% 6.87/4.37 = (X1))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl518, zip_derived_cl0])).
% 6.87/4.37 thf(zip_derived_cl79, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (inverse @ X0))) @
% 6.87/4.37 (multiply @ X1 @ (inverse @ X1))) = (X0))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl36])).
% 6.87/4.37 thf(zip_derived_cl518, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.37 ((multiply @ X2 @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @
% 6.87/4.37 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 6.87/4.37 (multiply @ X1 @ X2))))
% 6.87/4.37 = (inverse @ X1))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl391, zip_derived_cl4])).
% 6.87/4.37 thf(zip_derived_cl227, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @ (multiply @ X1 @ (inverse @ X1)) @ (inverse @ X0)))) @
% 6.87/4.37 (multiply @ X2 @ (inverse @ X2))) = (inverse @ (inverse @ X0)))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl194, zip_derived_cl36])).
% 6.87/4.37 thf(zip_derived_cl549, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/4.37 ((multiply @
% 6.87/4.37 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 6.87/4.37 (inverse @ (inverse @ X0))) @
% 6.87/4.37 (multiply @ X3 @ (inverse @ X3)))
% 6.87/4.37 = (inverse @
% 6.87/4.37 (inverse @
% 6.87/4.37 (multiply @
% 6.87/4.37 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2)))) @
% 6.87/4.37 (multiply @ X0 @ (multiply @ X1 @ (inverse @ X1)))))))),
% 6.87/4.37 inference('sup+', [status(thm)], [zip_derived_cl518, zip_derived_cl227])).
% 6.87/4.37 thf(zip_derived_cl79, plain,
% 6.87/4.37 (![X0 : $i, X1 : $i, X3 : $i]:
% 6.87/4.37 ((multiply @
% 6.87/4.37 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.37 (inverse @ (inverse @ X0))) @
% 6.87/4.37 (multiply @ X1 @ (inverse @ X1))) = (X0))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl36])).
% 6.87/4.38 thf(zip_derived_cl573, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.38 ((X0)
% 6.87/4.38 = (inverse @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @
% 6.87/4.38 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2)))) @
% 6.87/4.38 (multiply @ X0 @ (multiply @ X1 @ (inverse @ X1)))))))),
% 6.87/4.38 inference('demod', [status(thm)], [zip_derived_cl549, zip_derived_cl79])).
% 6.87/4.38 thf(zip_derived_cl1025, plain,
% 6.87/4.38 (![X0 : $i, X2 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 6.87/4.38 (inverse @ (inverse @ X0)))
% 6.87/4.38 = (inverse @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @
% 6.87/4.38 (inverse @ (inverse @ (multiply @ X3 @ (inverse @ X3)))) @ X0))))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl79, zip_derived_cl573])).
% 6.87/4.38 thf(zip_derived_cl36, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/4.38 ((multiply @
% 6.87/4.38 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @
% 6.87/4.38 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.38 (inverse @ (multiply @ X1 @ X2))) @
% 6.87/4.38 X1))) @
% 6.87/4.38 (multiply @ X0 @ (inverse @ X0))) = (X2))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl4])).
% 6.87/4.38 thf(zip_derived_cl1117, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.87/4.38 ((multiply @
% 6.87/4.38 (multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @
% 6.87/4.38 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 6.87/4.38 (inverse @
% 6.87/4.38 (inverse @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @
% 6.87/4.38 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1)))) @
% 6.87/4.38 X0))))) @
% 6.87/4.38 (multiply @ X3 @ (inverse @ X3))))) @
% 6.87/4.38 (multiply @ X2 @ (inverse @ X2))) = (inverse @ (inverse @ X0)))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1025, zip_derived_cl36])).
% 6.87/4.38 thf(zip_derived_cl79, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @
% 6.87/4.38 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.38 (inverse @ (inverse @ X0))) @
% 6.87/4.38 (multiply @ X1 @ (inverse @ X1))) = (X0))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl36])).
% 6.87/4.38 thf(zip_derived_cl79, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @
% 6.87/4.38 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.38 (inverse @ (inverse @ X0))) @
% 6.87/4.38 (multiply @ X1 @ (inverse @ X1))) = (X0))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl36])).
% 6.87/4.38 thf(zip_derived_cl1175, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((multiply @
% 6.87/4.38 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1)))) @ X0)
% 6.87/4.38 = (inverse @ (inverse @ X0)))),
% 6.87/4.38 inference('demod', [status(thm)],
% 6.87/4.38 [zip_derived_cl1117, zip_derived_cl79, zip_derived_cl79])).
% 6.87/4.38 thf(zip_derived_cl1025, plain,
% 6.87/4.38 (![X0 : $i, X2 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 6.87/4.38 (inverse @ (inverse @ X0)))
% 6.87/4.38 = (inverse @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @
% 6.87/4.38 (inverse @ (inverse @ (multiply @ X3 @ (inverse @ X3)))) @ X0))))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl79, zip_derived_cl573])).
% 6.87/4.38 thf(zip_derived_cl1255, plain,
% 6.87/4.38 (![X0 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 6.87/4.38 (inverse @ (inverse @ X0)))
% 6.87/4.38 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1175, zip_derived_cl1025])).
% 6.87/4.38 thf(zip_derived_cl1452, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @ (inverse @ X0))
% 6.87/4.38 = (inverse @
% 6.87/4.38 (inverse @
% 6.87/4.38 (inverse @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @ X0 @
% 6.87/4.38 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1))))))))))))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl541, zip_derived_cl1255])).
% 6.87/4.38 thf(zip_derived_cl541, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.38 ((inverse @
% 6.87/4.38 (multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @ X1 @
% 6.87/4.38 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))))
% 6.87/4.38 = (X1))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl518, zip_derived_cl0])).
% 6.87/4.38 thf(zip_derived_cl1485, plain,
% 6.87/4.38 (![X0 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @ (inverse @ X0))
% 6.87/4.38 = (inverse @ (inverse @ (inverse @ X0))))),
% 6.87/4.38 inference('demod', [status(thm)], [zip_derived_cl1452, zip_derived_cl541])).
% 6.87/4.38 thf(zip_derived_cl1670, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @ X0)
% 6.87/4.38 = (inverse @
% 6.87/4.38 (inverse @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @ X0 @
% 6.87/4.38 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))))))))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl541, zip_derived_cl1485])).
% 6.87/4.38 thf(zip_derived_cl541, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.38 ((inverse @
% 6.87/4.38 (multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @ X1 @
% 6.87/4.38 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))))
% 6.87/4.38 = (X1))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl518, zip_derived_cl0])).
% 6.87/4.38 thf(zip_derived_cl1699, plain,
% 6.87/4.38 (![X0 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @ X0)
% 6.87/4.38 = (inverse @ (inverse @ X0)))),
% 6.87/4.38 inference('demod', [status(thm)], [zip_derived_cl1670, zip_derived_cl541])).
% 6.87/4.38 thf(zip_derived_cl391, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X0 @ (inverse @ X0)) @
% 6.87/4.38 (multiply @ X2 @ (inverse @ X2)))
% 6.87/4.38 = (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl227])).
% 6.87/4.38 thf(zip_derived_cl2020, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))
% 6.87/4.38 = (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1699, zip_derived_cl391])).
% 6.87/4.38 thf(zip_derived_cl1485, plain,
% 6.87/4.38 (![X0 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @ (inverse @ X0))
% 6.87/4.38 = (inverse @ (inverse @ (inverse @ X0))))),
% 6.87/4.38 inference('demod', [status(thm)], [zip_derived_cl1452, zip_derived_cl541])).
% 6.87/4.38 thf(zip_derived_cl351, plain,
% 6.87/4.38 (![X1 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @ X3 @ (inverse @ X3)) = (multiply @ X1 @ (inverse @ X1)))),
% 6.87/4.38 inference('demod', [status(thm)],
% 6.87/4.38 [zip_derived_cl330, zip_derived_cl79, zip_derived_cl0])).
% 6.87/4.38 thf(zip_derived_cl227, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @
% 6.87/4.38 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @ (multiply @ X1 @ (inverse @ X1)) @ (inverse @ X0)))) @
% 6.87/4.38 (multiply @ X2 @ (inverse @ X2))) = (inverse @ (inverse @ X0)))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl194, zip_derived_cl36])).
% 6.87/4.38 thf(zip_derived_cl351, plain,
% 6.87/4.38 (![X1 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @ X3 @ (inverse @ X3)) = (multiply @ X1 @ (inverse @ X1)))),
% 6.87/4.38 inference('demod', [status(thm)],
% 6.87/4.38 [zip_derived_cl330, zip_derived_cl79, zip_derived_cl0])).
% 6.87/4.38 thf(zip_derived_cl0, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @ X1 @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @ X2 @
% 6.87/4.38 (multiply @
% 6.87/4.38 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.38 (inverse @ (multiply @ X0 @ X2))) @
% 6.87/4.38 X1))))
% 6.87/4.38 = (X0))),
% 6.87/4.38 inference('cnf', [status(esa)], [single_axiom])).
% 6.87/4.38 thf(zip_derived_cl383, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ X2 @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @ (inverse @ X1) @
% 6.87/4.38 (multiply @ (multiply @ X0 @ (inverse @ X0)) @ X2))))
% 6.87/4.38 = (X1))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl0])).
% 6.87/4.38 thf(zip_derived_cl455, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @ (inverse @ X1) @
% 6.87/4.38 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))))
% 6.87/4.38 = (X1))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl227, zip_derived_cl383])).
% 6.87/4.38 thf(zip_derived_cl678, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 6.87/4.38 (inverse @ (multiply @ X0 @ (inverse @ X0))))
% 6.87/4.38 = (multiply @ X1 @ (inverse @ X1)))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl455])).
% 6.87/4.38 thf(zip_derived_cl1667, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 6.87/4.38 = (multiply @ X1 @ (inverse @ X1)))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1485, zip_derived_cl678])).
% 6.87/4.38 thf(zip_derived_cl1175, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((multiply @
% 6.87/4.38 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1)))) @ X0)
% 6.87/4.38 = (inverse @ (inverse @ X0)))),
% 6.87/4.38 inference('demod', [status(thm)],
% 6.87/4.38 [zip_derived_cl1117, zip_derived_cl79, zip_derived_cl79])).
% 6.87/4.38 thf(zip_derived_cl1667, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 6.87/4.38 = (multiply @ X1 @ (inverse @ X1)))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1485, zip_derived_cl678])).
% 6.87/4.38 thf(zip_derived_cl1699, plain,
% 6.87/4.38 (![X0 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @ X0)
% 6.87/4.38 = (inverse @ (inverse @ X0)))),
% 6.87/4.38 inference('demod', [status(thm)], [zip_derived_cl1670, zip_derived_cl541])).
% 6.87/4.38 thf(zip_derived_cl383, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ X2 @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @ (inverse @ X1) @
% 6.87/4.38 (multiply @ (multiply @ X0 @ (inverse @ X0)) @ X2))))
% 6.87/4.38 = (X1))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl0])).
% 6.87/4.38 thf(zip_derived_cl2016, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((multiply @ X0 @
% 6.87/4.38 (inverse @ (multiply @ (inverse @ X1) @ (inverse @ (inverse @ X0)))))
% 6.87/4.38 = (X1))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1699, zip_derived_cl383])).
% 6.87/4.38 thf(zip_derived_cl2117, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((multiply @ X1 @
% 6.87/4.38 (inverse @
% 6.87/4.38 (inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))))
% 6.87/4.38 = (X1))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1667, zip_derived_cl2016])).
% 6.87/4.38 thf(zip_derived_cl2308, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ X2 @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @
% 6.87/4.38 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1)))) @
% 6.87/4.38 (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 6.87/4.38 = (X2))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1175, zip_derived_cl2117])).
% 6.87/4.38 thf(zip_derived_cl351, plain,
% 6.87/4.38 (![X1 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @ X3 @ (inverse @ X3)) = (multiply @ X1 @ (inverse @ X1)))),
% 6.87/4.38 inference('demod', [status(thm)],
% 6.87/4.38 [zip_derived_cl330, zip_derived_cl79, zip_derived_cl0])).
% 6.87/4.38 thf(zip_derived_cl2016, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((multiply @ X0 @
% 6.87/4.38 (inverse @ (multiply @ (inverse @ X1) @ (inverse @ (inverse @ X0)))))
% 6.87/4.38 = (X1))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1699, zip_derived_cl383])).
% 6.87/4.38 thf(zip_derived_cl2114, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl2016])).
% 6.87/4.38 thf(zip_derived_cl1667, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 6.87/4.38 = (multiply @ X1 @ (inverse @ X1)))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1485, zip_derived_cl678])).
% 6.87/4.38 thf(zip_derived_cl2331, plain,
% 6.87/4.38 (![X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ X2 @ (multiply @ X1 @ (inverse @ X1))) = (X2))),
% 6.87/4.38 inference('demod', [status(thm)],
% 6.87/4.38 [zip_derived_cl2308, zip_derived_cl2114, zip_derived_cl1667])).
% 6.87/4.38 thf(zip_derived_cl1255, plain,
% 6.87/4.38 (![X0 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 6.87/4.38 (inverse @ (inverse @ X0)))
% 6.87/4.38 = (inverse @ (inverse @ (inverse @ (inverse @ X0)))))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1175, zip_derived_cl1025])).
% 6.87/4.38 thf(zip_derived_cl79, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @
% 6.87/4.38 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.38 (inverse @ (inverse @ X0))) @
% 6.87/4.38 (multiply @ X1 @ (inverse @ X1))) = (X0))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl36])).
% 6.87/4.38 thf(zip_derived_cl1441, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((multiply @ (inverse @ (inverse @ (inverse @ (inverse @ X0)))) @
% 6.87/4.38 (multiply @ X1 @ (inverse @ X1))) = (X0))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1255, zip_derived_cl79])).
% 6.87/4.38 thf(zip_derived_cl2379, plain,
% 6.87/4.38 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X0)))) = (X0))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl2331, zip_derived_cl1441])).
% 6.87/4.38 thf(zip_derived_cl2455, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((inverse @ (multiply @ X0 @ (inverse @ X0)))
% 6.87/4.38 = (multiply @ X1 @ (inverse @ X1)))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1667, zip_derived_cl2379])).
% 6.87/4.38 thf(zip_derived_cl2455, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((inverse @ (multiply @ X0 @ (inverse @ X0)))
% 6.87/4.38 = (multiply @ X1 @ (inverse @ X1)))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1667, zip_derived_cl2379])).
% 6.87/4.38 thf(zip_derived_cl3347, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))
% 6.87/4.38 = (multiply @ X1 @ (inverse @ X1)))),
% 6.87/4.38 inference('demod', [status(thm)],
% 6.87/4.38 [zip_derived_cl2020, zip_derived_cl2455, zip_derived_cl2455])).
% 6.87/4.38 thf(zip_derived_cl0, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @ X1 @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @ X2 @
% 6.87/4.38 (multiply @
% 6.87/4.38 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.38 (inverse @ (multiply @ X0 @ X2))) @
% 6.87/4.38 X1))))
% 6.87/4.38 = (X0))),
% 6.87/4.38 inference('cnf', [status(esa)], [single_axiom])).
% 6.87/4.38 thf(zip_derived_cl3391, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 6.87/4.38 (inverse @ (multiply @ X1 @ X2)))) @
% 6.87/4.38 (inverse @
% 6.87/4.38 (multiply @ X2 @
% 6.87/4.38 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))))
% 6.87/4.38 = (X1))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl3347, zip_derived_cl0])).
% 6.87/4.38 thf(zip_derived_cl1699, plain,
% 6.87/4.38 (![X0 : $i, X3 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @ X0)
% 6.87/4.38 = (inverse @ (inverse @ X0)))),
% 6.87/4.38 inference('demod', [status(thm)], [zip_derived_cl1670, zip_derived_cl541])).
% 6.87/4.38 thf(zip_derived_cl2379, plain,
% 6.87/4.38 (![X0 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X0)))) = (X0))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl2331, zip_derived_cl1441])).
% 6.87/4.38 thf(zip_derived_cl2454, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((inverse @
% 6.87/4.38 (multiply @ (multiply @ X1 @ (inverse @ X1)) @ (inverse @ X0)))
% 6.87/4.38 = (X0))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1699, zip_derived_cl2379])).
% 6.87/4.38 thf(zip_derived_cl1667, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 6.87/4.38 = (multiply @ X1 @ (inverse @ X1)))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1485, zip_derived_cl678])).
% 6.87/4.38 thf(zip_derived_cl2331, plain,
% 6.87/4.38 (![X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ X2 @ (multiply @ X1 @ (inverse @ X1))) = (X2))),
% 6.87/4.38 inference('demod', [status(thm)],
% 6.87/4.38 [zip_derived_cl2308, zip_derived_cl2114, zip_derived_cl1667])).
% 6.87/4.38 thf(zip_derived_cl2393, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ X1 @
% 6.87/4.38 (multiply @
% 6.87/4.38 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2)))) @
% 6.87/4.38 (multiply @ X0 @ (inverse @ X0))))
% 6.87/4.38 = (X1))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1667, zip_derived_cl2331])).
% 6.87/4.38 thf(zip_derived_cl2331, plain,
% 6.87/4.38 (![X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ X2 @ (multiply @ X1 @ (inverse @ X1))) = (X2))),
% 6.87/4.38 inference('demod', [status(thm)],
% 6.87/4.38 [zip_derived_cl2308, zip_derived_cl2114, zip_derived_cl1667])).
% 6.87/4.38 thf(zip_derived_cl2397, plain,
% 6.87/4.38 (![X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ X1 @
% 6.87/4.38 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2))))) = (
% 6.87/4.38 X1))),
% 6.87/4.38 inference('demod', [status(thm)],
% 6.87/4.38 [zip_derived_cl2393, zip_derived_cl2331])).
% 6.87/4.38 thf(zip_derived_cl3521, plain,
% 6.87/4.38 (![X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X1 @ X2) @ (inverse @ X2)) = (X1))),
% 6.87/4.38 inference('demod', [status(thm)],
% 6.87/4.38 [zip_derived_cl3391, zip_derived_cl2454, zip_derived_cl2397])).
% 6.87/4.38 thf(zip_derived_cl3521, plain,
% 6.87/4.38 (![X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X1 @ X2) @ (inverse @ X2)) = (X1))),
% 6.87/4.38 inference('demod', [status(thm)],
% 6.87/4.38 [zip_derived_cl3391, zip_derived_cl2454, zip_derived_cl2397])).
% 6.87/4.38 thf(zip_derived_cl3568, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((multiply @ X0 @ (inverse @ (inverse @ X1))) = (multiply @ X0 @ X1))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl3521, zip_derived_cl3521])).
% 6.87/4.38 thf(zip_derived_cl678, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 6.87/4.38 (inverse @ (multiply @ X0 @ (inverse @ X0))))
% 6.87/4.38 = (multiply @ X1 @ (inverse @ X1)))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl455])).
% 6.87/4.38 thf(zip_derived_cl3652, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 6.87/4.38 (inverse @ (multiply @ X1 @ (inverse @ X1))))
% 6.87/4.38 = (multiply @ (inverse @ X0) @ X0))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl3568, zip_derived_cl678])).
% 6.87/4.38 thf(zip_derived_cl2455, plain,
% 6.87/4.38 (![X0 : $i, X1 : $i]:
% 6.87/4.38 ((inverse @ (multiply @ X0 @ (inverse @ X0)))
% 6.87/4.38 = (multiply @ X1 @ (inverse @ X1)))),
% 6.87/4.38 inference('sup+', [status(thm)], [zip_derived_cl1667, zip_derived_cl2379])).
% 6.87/4.38 thf(zip_derived_cl2331, plain,
% 6.87/4.38 (![X1 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ X2 @ (multiply @ X1 @ (inverse @ X1))) = (X2))),
% 6.87/4.38 inference('demod', [status(thm)],
% 6.87/4.38 [zip_derived_cl2308, zip_derived_cl2114, zip_derived_cl1667])).
% 6.87/4.38 thf(zip_derived_cl3712, plain,
% 6.87/4.38 (![X0 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ X2 @ (inverse @ X2)) = (multiply @ (inverse @ X0) @ X0))),
% 6.87/4.38 inference('demod', [status(thm)],
% 6.87/4.38 [zip_derived_cl3652, zip_derived_cl2455, zip_derived_cl2331])).
% 6.87/4.38 thf(prove_these_axioms_1, conjecture,
% 6.87/4.38 (( multiply @ ( inverse @ a1 ) @ a1 ) =
% 6.87/4.38 ( multiply @ ( inverse @ b1 ) @ b1 ))).
% 6.87/4.38 thf(zf_stmt_0, negated_conjecture,
% 6.87/4.38 (( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 6.87/4.38 ( multiply @ ( inverse @ b1 ) @ b1 )),
% 6.87/4.38 inference('cnf.neg', [status(esa)], [prove_these_axioms_1])).
% 6.87/4.38 thf(zip_derived_cl1, plain,
% 6.87/4.38 (((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ b1) @ b1))),
% 6.87/4.38 inference('cnf', [status(esa)], [zf_stmt_0])).
% 6.87/4.38 thf(zip_derived_cl3969, plain,
% 6.87/4.38 (![X0 : $i]:
% 6.87/4.38 ((multiply @ (inverse @ a1) @ a1) != (multiply @ X0 @ (inverse @ X0)))),
% 6.87/4.38 inference('sup-', [status(thm)], [zip_derived_cl3712, zip_derived_cl1])).
% 6.87/4.38 thf(zip_derived_cl3712, plain,
% 6.87/4.38 (![X0 : $i, X2 : $i]:
% 6.87/4.38 ((multiply @ X2 @ (inverse @ X2)) = (multiply @ (inverse @ X0) @ X0))),
% 6.87/4.38 inference('demod', [status(thm)],
% 6.87/4.38 [zip_derived_cl3652, zip_derived_cl2455, zip_derived_cl2331])).
% 6.87/4.38 thf(zip_derived_cl4007, plain, ($false),
% 6.87/4.38 inference('simplify_reflect+', [status(thm)],
% 6.87/4.38 [zip_derived_cl3969, zip_derived_cl3712])).
% 6.87/4.38
% 6.87/4.38 % SZS output end Refutation
% 6.87/4.38
% 6.87/4.38
% 6.87/4.38 % Terminating...
% 7.49/4.63 % Runner terminated.
% 7.49/4.64 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------