%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP443-1 : 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.vlLSiojGXv true
% Computer : n022.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 04:36:27 PM UTC 2025
% Result : Unsatisfiable 22.55s 3.86s
% Output : Refutation 22.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP443-1 : TPTP v9.2.0. Released v2.6.0.
% 0.11/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.vlLSiojGXv true
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 14:15:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.57/0.65 % Total configuration time : 435
% 0.57/0.65 % Estimated wc time : 1092
% 0.57/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.57/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.57/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.58/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.58/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.58/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.58/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.58/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 22.55/3.86 % Solved by fo/fo7.sh.
% 22.55/3.86 % done 965 iterations in 3.068s
% 22.55/3.86 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 22.55/3.86 % SZS output start Refutation
% 22.55/3.86 thf(b2_type, type, b2: $i).
% 22.55/3.86 thf(a2_type, type, a2: $i).
% 22.55/3.86 thf(inverse_type, type, inverse: $i > $i).
% 22.55/3.86 thf(multiply_type, type, multiply: $i > $i > $i).
% 22.55/3.86 thf(single_axiom, axiom,
% 22.55/3.86 (( inverse @
% 22.55/3.86 ( multiply @
% 22.55/3.86 A @
% 22.55/3.86 ( multiply @
% 22.55/3.86 B @
% 22.55/3.86 ( multiply @
% 22.55/3.86 ( multiply @ C @ ( inverse @ C ) ) @
% 22.55/3.86 ( inverse @ ( multiply @ D @ ( multiply @ A @ B ) ) ) ) ) ) ) =
% 22.55/3.86 ( D ))).
% 22.55/3.86 thf(zip_derived_cl0, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('cnf', [status(esa)], [single_axiom])).
% 22.55/3.86 thf(zip_derived_cl0, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('cnf', [status(esa)], [single_axiom])).
% 22.55/3.86 thf(zip_derived_cl3, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))) @
% 22.55/3.86 (multiply @ (multiply @ X4 @ (inverse @ X4)) @ X0))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl3, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))) @
% 22.55/3.86 (multiply @ (multiply @ X4 @ (inverse @ X4)) @ X0))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl3, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))) @
% 22.55/3.86 (multiply @ (multiply @ X4 @ (inverse @ X4)) @ X0))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl10, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (multiply @ (multiply @ X5 @ (inverse @ X5)) @ X2) @
% 22.55/3.86 (multiply @ (multiply @ (multiply @ X6 @ (inverse @ X6)) @ X0) @
% 22.55/3.86 (multiply @ (multiply @ X4 @ (inverse @ X4)) @ X1))))
% 22.55/3.86 = (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X2 @ (multiply @ X0 @ X1)))))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3])).
% 22.55/3.86 thf(zip_derived_cl3, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))) @
% 22.55/3.86 (multiply @ (multiply @ X4 @ (inverse @ X4)) @ X0))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl0, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('cnf', [status(esa)], [single_axiom])).
% 22.55/3.86 thf(zip_derived_cl9, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @
% 22.55/3.86 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.55/3.86 (inverse @ (multiply @ X2 @ (multiply @ X0 @ X1)))) @
% 22.55/3.86 (multiply @ (multiply @ (multiply @ X3 @ (inverse @ X3)) @ X2) @
% 22.55/3.86 (multiply @ (multiply @ X5 @ (inverse @ X5)) @ X0))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl98, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @ (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 22.55/3.86 (multiply @ X1 @ X0))))
% 22.55/3.86 = (X2))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl9])).
% 22.55/3.86 thf(zip_derived_cl154, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @ X0 @
% 22.55/3.86 (multiply @ X3 @
% 22.55/3.86 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.55/3.86 (inverse @ (multiply @ X1 @ (multiply @ X0 @ X3))))))))
% 22.55/3.86 = (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl98])).
% 22.55/3.86 thf(zip_derived_cl0, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('cnf', [status(esa)], [single_axiom])).
% 22.55/3.86 thf(zip_derived_cl164, plain,
% 22.55/3.86 (![X1 : $i, X2 : $i, X5 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X5 @ (inverse @ X5)) @ X1)
% 22.55/3.86 = (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X1))),
% 22.55/3.86 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl164, plain,
% 22.55/3.86 (![X1 : $i, X2 : $i, X5 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X5 @ (inverse @ X5)) @ X1)
% 22.55/3.86 = (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X1))),
% 22.55/3.86 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl188, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @
% 22.55/3.86 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 22.55/3.86 X2) = (multiply @ (multiply @ X3 @ (inverse @ X3)) @ X2))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl164, zip_derived_cl164])).
% 22.55/3.86 thf(zip_derived_cl0, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('cnf', [status(esa)], [single_axiom])).
% 22.55/3.86 thf(zip_derived_cl317, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X0 @
% 22.55/3.86 (multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X2 @ (inverse @ X2)))) @
% 22.55/3.86 (multiply @ X1 @ X0)))))))
% 22.55/3.86 = (multiply @ X4 @ (inverse @ X4)))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl188, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl188, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @
% 22.55/3.86 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 22.55/3.86 X2) = (multiply @ (multiply @ X3 @ (inverse @ X3)) @ X2))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl164, zip_derived_cl164])).
% 22.55/3.86 thf(zip_derived_cl0, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('cnf', [status(esa)], [single_axiom])).
% 22.55/3.86 thf(zip_derived_cl445, plain,
% 22.55/3.86 (![X3 : $i, X4 : $i]:
% 22.55/3.86 ((multiply @ X3 @ (inverse @ X3)) = (multiply @ X4 @ (inverse @ X4)))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl317, zip_derived_cl188, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl0, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('cnf', [status(esa)], [single_axiom])).
% 22.55/3.86 thf(zip_derived_cl445, plain,
% 22.55/3.86 (![X3 : $i, X4 : $i]:
% 22.55/3.86 ((multiply @ X3 @ (inverse @ X3)) = (multiply @ X4 @ (inverse @ X4)))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl317, zip_derived_cl188, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl534, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.55/3.86 ((multiply @
% 22.55/3.86 (multiply @ X3 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X3 @ X2)))))) @
% 22.55/3.86 X0) = (multiply @ X1 @ (inverse @ X1)))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl445])).
% 22.55/3.86 thf(zip_derived_cl445, plain,
% 22.55/3.86 (![X3 : $i, X4 : $i]:
% 22.55/3.86 ((multiply @ X3 @ (inverse @ X3)) = (multiply @ X4 @ (inverse @ X4)))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl317, zip_derived_cl188, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl98, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @ (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 22.55/3.86 (multiply @ X1 @ X0))))
% 22.55/3.86 = (X2))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl9])).
% 22.55/3.86 thf(zip_derived_cl469, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @
% 22.55/3.86 (inverse @ (multiply @ X2 @ (multiply @ X0 @ (inverse @ X0)))) @
% 22.55/3.86 (multiply @ X2 @ X1))))
% 22.55/3.86 = (inverse @ X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl98])).
% 22.55/3.86 thf(zip_derived_cl445, plain,
% 22.55/3.86 (![X3 : $i, X4 : $i]:
% 22.55/3.86 ((multiply @ X3 @ (inverse @ X3)) = (multiply @ X4 @ (inverse @ X4)))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl317, zip_derived_cl188, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl0, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('cnf', [status(esa)], [single_axiom])).
% 22.55/3.86 thf(zip_derived_cl462, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (inverse @ X2) @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl1176, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X3 @
% 22.55/3.86 (multiply @ (inverse @ X3) @ (inverse @ (inverse @ X0)))))
% 22.55/3.86 = (inverse @ (multiply @ X0 @ (multiply @ X1 @ (inverse @ X1)))))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl469, zip_derived_cl462])).
% 22.55/3.86 thf(zip_derived_cl3338, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X5 @
% 22.55/3.86 (multiply @ (inverse @ X5) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @ X3 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 22.55/3.86 (multiply @ X3 @ X2)))))))))))
% 22.55/3.86 = (inverse @ (multiply @ X0 @ (inverse @ X0))))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl534, zip_derived_cl1176])).
% 22.55/3.86 thf(zip_derived_cl0, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('cnf', [status(esa)], [single_axiom])).
% 22.55/3.86 thf(zip_derived_cl3530, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X5 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X5 @
% 22.55/3.86 (multiply @ (inverse @ X5) @
% 22.55/3.86 (inverse @ (multiply @ X1 @ (inverse @ X1))))))
% 22.55/3.86 = (inverse @ (multiply @ X0 @ (inverse @ X0))))),
% 22.55/3.86 inference('demod', [status(thm)], [zip_derived_cl3338, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl3530, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X5 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X5 @
% 22.55/3.86 (multiply @ (inverse @ X5) @
% 22.55/3.86 (inverse @ (multiply @ X1 @ (inverse @ X1))))))
% 22.55/3.86 = (inverse @ (multiply @ X0 @ (inverse @ X0))))),
% 22.55/3.86 inference('demod', [status(thm)], [zip_derived_cl3338, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl3606, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X3 @
% 22.55/3.86 (multiply @ (inverse @ X3) @
% 22.55/3.86 (inverse @ (multiply @ X2 @ (inverse @ X2))))))
% 22.55/3.86 = (inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (inverse @ X0)))))))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl3530, zip_derived_cl3530])).
% 22.55/3.86 thf(zip_derived_cl98, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @ (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 22.55/3.86 (multiply @ X1 @ X0))))
% 22.55/3.86 = (X2))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl9])).
% 22.55/3.86 thf(zip_derived_cl462, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (inverse @ X2) @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl1175, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @ (multiply @ X3 @ (multiply @ (inverse @ X3) @ X0)))
% 22.55/3.86 = (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0))))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl98, zip_derived_cl462])).
% 22.55/3.86 thf(zip_derived_cl0, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('cnf', [status(esa)], [single_axiom])).
% 22.55/3.86 thf(zip_derived_cl1235, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X2) @
% 22.55/3.86 (multiply @ X0 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))))))
% 22.55/3.86 = (X2))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl1175, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl4096, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (inverse @ X0)))))) @
% 22.55/3.86 (multiply @ X4 @
% 22.55/3.86 (multiply @ (multiply @ X6 @ (inverse @ X6)) @
% 22.55/3.86 (inverse @ (multiply @ X5 @ (multiply @ (inverse @ X5) @ X4)))))))
% 22.55/3.86 = (multiply @ X3 @
% 22.55/3.86 (multiply @ (inverse @ X3) @
% 22.55/3.86 (inverse @ (multiply @ X2 @ (inverse @ X2))))))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl3606, zip_derived_cl1235])).
% 22.55/3.86 thf(zip_derived_cl3530, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X5 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X5 @
% 22.55/3.86 (multiply @ (inverse @ X5) @
% 22.55/3.86 (inverse @ (multiply @ X1 @ (inverse @ X1))))))
% 22.55/3.86 = (inverse @ (multiply @ X0 @ (inverse @ X0))))),
% 22.55/3.86 inference('demod', [status(thm)], [zip_derived_cl3338, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl1235, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X2) @
% 22.55/3.86 (multiply @ X0 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))))))
% 22.55/3.86 = (X2))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl1175, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl4419, plain,
% 22.55/3.86 (![X0 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @ X0 @ (inverse @ X0))
% 22.55/3.86 = (multiply @ X3 @
% 22.55/3.86 (multiply @ (inverse @ X3) @
% 22.55/3.86 (inverse @ (multiply @ X2 @ (inverse @ X2))))))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl4096, zip_derived_cl3530, zip_derived_cl1235])).
% 22.55/3.86 thf(zip_derived_cl98, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @ (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 22.55/3.86 (multiply @ X1 @ X0))))
% 22.55/3.86 = (X2))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl9])).
% 22.55/3.86 thf(zip_derived_cl4570, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @
% 22.55/3.86 (inverse @ (multiply @ X3 @ (multiply @ X0 @ (inverse @ X0)))) @
% 22.55/3.86 (multiply @ X3 @ X2))))
% 22.55/3.86 = (multiply @ (inverse @ X2) @
% 22.55/3.86 (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl4419, zip_derived_cl98])).
% 22.55/3.86 thf(zip_derived_cl469, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @
% 22.55/3.86 (inverse @ (multiply @ X2 @ (multiply @ X0 @ (inverse @ X0)))) @
% 22.55/3.86 (multiply @ X2 @ X1))))
% 22.55/3.86 = (inverse @ X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl98])).
% 22.55/3.86 thf(zip_derived_cl4781, plain,
% 22.55/3.86 (![X1 : $i, X2 : $i]:
% 22.55/3.86 ((inverse @ X2)
% 22.55/3.86 = (multiply @ (inverse @ X2) @
% 22.55/3.86 (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 22.55/3.86 inference('demod', [status(thm)], [zip_derived_cl4570, zip_derived_cl469])).
% 22.55/3.86 thf(zip_derived_cl445, plain,
% 22.55/3.86 (![X3 : $i, X4 : $i]:
% 22.55/3.86 ((multiply @ X3 @ (inverse @ X3)) = (multiply @ X4 @ (inverse @ X4)))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl317, zip_derived_cl188, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl98, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @ (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 22.55/3.86 (multiply @ X1 @ X0))))
% 22.55/3.86 = (X2))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl9])).
% 22.55/3.86 thf(zip_derived_cl468, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @
% 22.55/3.86 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X1))) @
% 22.55/3.86 (multiply @ X0 @ (inverse @ X0)))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl98])).
% 22.55/3.86 thf(zip_derived_cl1235, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X2) @
% 22.55/3.86 (multiply @ X0 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))))))
% 22.55/3.86 = (X2))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl1175, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl1802, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (multiply @
% 22.55/3.86 (inverse @
% 22.55/3.86 (inverse @
% 22.55/3.86 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X0))))) @
% 22.55/3.86 X0)))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl468, zip_derived_cl1235])).
% 22.55/3.86 thf(zip_derived_cl4887, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (multiply @
% 22.55/3.86 (inverse @
% 22.55/3.86 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))) @
% 22.55/3.86 (inverse @ (multiply @ X2 @ (inverse @ X2))))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl4781, zip_derived_cl1802])).
% 22.55/3.86 thf(zip_derived_cl4781, plain,
% 22.55/3.86 (![X1 : $i, X2 : $i]:
% 22.55/3.86 ((inverse @ X2)
% 22.55/3.86 = (multiply @ (inverse @ X2) @
% 22.55/3.86 (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 22.55/3.86 inference('demod', [status(thm)], [zip_derived_cl4570, zip_derived_cl469])).
% 22.55/3.86 thf(zip_derived_cl4951, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl4887, zip_derived_cl4781])).
% 22.55/3.86 thf(zip_derived_cl4951, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl4887, zip_derived_cl4781])).
% 22.55/3.86 thf(zip_derived_cl5136, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X0 @
% 22.55/3.86 (inverse @ (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2)))))))
% 22.55/3.86 = (multiply @ (inverse @ X0) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl4951, zip_derived_cl4951])).
% 22.55/3.86 thf(zip_derived_cl4951, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl4887, zip_derived_cl4781])).
% 22.55/3.86 thf(zip_derived_cl5358, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((multiply @ (inverse @ (inverse @ X1)) @
% 22.55/3.86 (inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl5136, zip_derived_cl4951])).
% 22.55/3.86 thf(zip_derived_cl1802, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (multiply @
% 22.55/3.86 (inverse @
% 22.55/3.86 (inverse @
% 22.55/3.86 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X0))))) @
% 22.55/3.86 X0)))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl468, zip_derived_cl1235])).
% 22.55/3.86 thf(zip_derived_cl5821, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (multiply @
% 22.55/3.86 (inverse @
% 22.55/3.86 (inverse @ (inverse @ (multiply @ (inverse @ X0) @ X0)))) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2))))))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl5358, zip_derived_cl1802])).
% 22.55/3.86 thf(zip_derived_cl5358, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((multiply @ (inverse @ (inverse @ X1)) @
% 22.55/3.86 (inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl5136, zip_derived_cl4951])).
% 22.55/3.86 thf(zip_derived_cl5891, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl5821, zip_derived_cl5358])).
% 22.55/3.86 thf(zip_derived_cl5891, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl5821, zip_derived_cl5358])).
% 22.55/3.86 thf(zip_derived_cl5953, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X0 @ (inverse @ (multiply @ (inverse @ X2) @ X2))))
% 22.55/3.86 = (multiply @ (inverse @ X0) @
% 22.55/3.86 (inverse @ (multiply @ (inverse @ X1) @ X1))))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl5891, zip_derived_cl5891])).
% 22.55/3.86 thf(zip_derived_cl5891, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl5821, zip_derived_cl5358])).
% 22.55/3.86 thf(zip_derived_cl6223, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @ X1 @ (inverse @ (multiply @ (inverse @ X0) @ X0)))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl5953, zip_derived_cl5891])).
% 22.55/3.86 thf(zip_derived_cl7423, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))
% 22.55/3.86 = (multiply @ (inverse @ X1) @ X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl6223])).
% 22.55/3.86 thf(prove_these_axioms_2, conjecture,
% 22.55/3.86 (( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) = ( a2 ))).
% 22.55/3.86 thf(zf_stmt_0, negated_conjecture,
% 22.55/3.86 (( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) != ( a2 )),
% 22.55/3.86 inference('cnf.neg', [status(esa)], [prove_these_axioms_2])).
% 22.55/3.86 thf(zip_derived_cl1, plain,
% 22.55/3.86 (((multiply @ (multiply @ (inverse @ b2) @ b2) @ a2) != (a2))),
% 22.55/3.86 inference('cnf', [status(esa)], [zf_stmt_0])).
% 22.55/3.86 thf(zip_derived_cl7657, plain,
% 22.55/3.86 (![X0 : $i]:
% 22.55/3.86 ((multiply @
% 22.55/3.86 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) @ a2)
% 22.55/3.86 != (a2))),
% 22.55/3.86 inference('sup-', [status(thm)], [zip_derived_cl7423, zip_derived_cl1])).
% 22.55/3.86 thf(zip_derived_cl7423, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))
% 22.55/3.86 = (multiply @ (inverse @ X1) @ X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl6223])).
% 22.55/3.86 thf(zip_derived_cl3530, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X5 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X5 @
% 22.55/3.86 (multiply @ (inverse @ X5) @
% 22.55/3.86 (inverse @ (multiply @ X1 @ (inverse @ X1))))))
% 22.55/3.86 = (inverse @ (multiply @ X0 @ (inverse @ X0))))),
% 22.55/3.86 inference('demod', [status(thm)], [zip_derived_cl3338, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl0, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('cnf', [status(esa)], [single_axiom])).
% 22.55/3.86 thf(zip_derived_cl3683, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X2))) @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (inverse @ X0)))))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl3530, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl188, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @
% 22.55/3.86 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 22.55/3.86 X2) = (multiply @ (multiply @ X3 @ (inverse @ X3)) @ X2))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl164, zip_derived_cl164])).
% 22.55/3.86 thf(zip_derived_cl188, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @
% 22.55/3.86 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 22.55/3.86 X2) = (multiply @ (multiply @ X3 @ (inverse @ X3)) @ X2))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl164, zip_derived_cl164])).
% 22.55/3.86 thf(zip_derived_cl333, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.55/3.86 ((multiply @
% 22.55/3.86 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.55/3.86 (inverse @ (multiply @ X3 @ (inverse @ X3)))) @
% 22.55/3.86 X0)
% 22.55/3.86 = (multiply @
% 22.55/3.86 (multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 22.55/3.86 (inverse @ (multiply @ X1 @ (inverse @ X1)))) @
% 22.55/3.86 X0))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl188, zip_derived_cl188])).
% 22.55/3.86 thf(zip_derived_cl0, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('cnf', [status(esa)], [single_axiom])).
% 22.55/3.86 thf(zip_derived_cl630, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X0 @
% 22.55/3.86 (multiply @ (multiply @ X6 @ (inverse @ X6)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X2 @ (inverse @ X2)))) @
% 22.55/3.86 (multiply @ X1 @ X0)))))))
% 22.55/3.86 = (multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 22.55/3.86 (inverse @ (multiply @ X4 @ (inverse @ X4)))))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl188, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @
% 22.55/3.86 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 22.55/3.86 X2) = (multiply @ (multiply @ X3 @ (inverse @ X3)) @ X2))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl164, zip_derived_cl164])).
% 22.55/3.86 thf(zip_derived_cl0, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('cnf', [status(esa)], [single_axiom])).
% 22.55/3.86 thf(zip_derived_cl830, plain,
% 22.55/3.86 (![X3 : $i, X4 : $i, X5 : $i]:
% 22.55/3.86 ((multiply @ X3 @ (inverse @ X3))
% 22.55/3.86 = (multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 22.55/3.86 (inverse @ (multiply @ X4 @ (inverse @ X4)))))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl630, zip_derived_cl188, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl3873, plain,
% 22.55/3.86 (![X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X2))) @
% 22.55/3.86 (multiply @ X3 @ (inverse @ X3)))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('demod', [status(thm)], [zip_derived_cl3683, zip_derived_cl830])).
% 22.55/3.86 thf(zip_derived_cl7656, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl7423, zip_derived_cl3873])).
% 22.55/3.86 thf(zip_derived_cl7656, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl7423, zip_derived_cl3873])).
% 22.55/3.86 thf(zip_derived_cl9767, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ (inverse @ X1) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl7656, zip_derived_cl7656])).
% 22.55/3.86 thf(zip_derived_cl0, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('cnf', [status(esa)], [single_axiom])).
% 22.55/3.86 thf(zip_derived_cl4781, plain,
% 22.55/3.86 (![X1 : $i, X2 : $i]:
% 22.55/3.86 ((inverse @ X2)
% 22.55/3.86 = (multiply @ (inverse @ X2) @
% 22.55/3.86 (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 22.55/3.86 inference('demod', [status(thm)], [zip_derived_cl4570, zip_derived_cl469])).
% 22.55/3.86 thf(zip_derived_cl4917, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X3 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X3 @ X2)))))))
% 22.55/3.86 = (multiply @ X0 @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl4781])).
% 22.55/3.86 thf(zip_derived_cl0, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ X2 @
% 22.55/3.86 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('cnf', [status(esa)], [single_axiom])).
% 22.55/3.86 thf(zip_derived_cl4936, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((X0) = (multiply @ X0 @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 22.55/3.86 inference('demod', [status(thm)], [zip_derived_cl4917, zip_derived_cl0])).
% 22.55/3.86 thf(zip_derived_cl9837, plain,
% 22.55/3.86 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl9767, zip_derived_cl4936])).
% 22.55/3.86 thf(zip_derived_cl9868, plain,
% 22.55/3.86 (![X0 : $i]: ((multiply @ (multiply @ X0 @ (inverse @ X0)) @ a2) != (a2))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl7657, zip_derived_cl9837])).
% 22.55/3.86 thf(zip_derived_cl469, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @
% 22.55/3.86 (inverse @ (multiply @ X2 @ (multiply @ X0 @ (inverse @ X0)))) @
% 22.55/3.86 (multiply @ X2 @ X1))))
% 22.55/3.86 = (inverse @ X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl98])).
% 22.55/3.86 thf(zip_derived_cl6223, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @ X1 @ (inverse @ (multiply @ (inverse @ X0) @ X0)))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl5953, zip_derived_cl5891])).
% 22.55/3.86 thf(zip_derived_cl7433, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 22.55/3.86 = (multiply @ X1 @ (inverse @ X1)))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl469, zip_derived_cl6223])).
% 22.55/3.86 thf(zip_derived_cl5358, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((multiply @ (inverse @ (inverse @ X1)) @
% 22.55/3.86 (inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 22.55/3.86 = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl5136, zip_derived_cl4951])).
% 22.55/3.86 thf(zip_derived_cl8787, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((multiply @ (inverse @ (inverse @ X1)) @
% 22.55/3.86 (multiply @ X0 @ (inverse @ X0))) = (X1))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl7433, zip_derived_cl5358])).
% 22.55/3.86 thf(zip_derived_cl9837, plain,
% 22.55/3.86 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl9767, zip_derived_cl4936])).
% 22.55/3.86 thf(zip_derived_cl9870, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))) = (X1))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl8787, zip_derived_cl9837])).
% 22.55/3.86 thf(zip_derived_cl1175, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X3 : $i]:
% 22.55/3.86 ((inverse @ (multiply @ X3 @ (multiply @ (inverse @ X3) @ X0)))
% 22.55/3.86 = (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0))))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl98, zip_derived_cl462])).
% 22.55/3.86 thf(zip_derived_cl10076, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @
% 22.55/3.86 (multiply @ X1 @
% 22.55/3.86 (multiply @ (inverse @ X1) @ (inverse @ (inverse @ X0)))))
% 22.55/3.86 = (inverse @ X0))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl9870, zip_derived_cl1175])).
% 22.55/3.86 thf(zip_derived_cl9837, plain,
% 22.55/3.86 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl9767, zip_derived_cl4936])).
% 22.55/3.86 thf(zip_derived_cl10147, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))
% 22.55/3.86 = (inverse @ X0))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl10076, zip_derived_cl9837])).
% 22.55/3.86 thf(zip_derived_cl98, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @ (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 22.55/3.86 (multiply @ X1 @ X0))))
% 22.55/3.86 = (X2))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl9])).
% 22.55/3.86 thf(zip_derived_cl10590, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 22.55/3.86 (inverse @
% 22.55/3.86 (multiply @ (inverse @ X0) @ (multiply @ X1 @ (inverse @ X1)))))
% 22.55/3.86 = (X0))),
% 22.55/3.86 inference('sup+', [status(thm)], [zip_derived_cl10147, zip_derived_cl98])).
% 22.55/3.86 thf(zip_derived_cl9870, plain,
% 22.55/3.86 (![X0 : $i, X1 : $i]:
% 22.55/3.86 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))) = (X1))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl8787, zip_derived_cl9837])).
% 22.55/3.86 thf(zip_derived_cl9837, plain,
% 22.55/3.86 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl9767, zip_derived_cl4936])).
% 22.55/3.86 thf(zip_derived_cl10628, plain,
% 22.55/3.86 (![X0 : $i, X2 : $i]:
% 22.55/3.86 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0) = (X0))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl10590, zip_derived_cl9870, zip_derived_cl9837])).
% 22.55/3.86 thf(zip_derived_cl10706, plain, (((a2) != (a2))),
% 22.55/3.86 inference('demod', [status(thm)],
% 22.55/3.86 [zip_derived_cl9868, zip_derived_cl10628])).
% 22.55/3.86 thf(zip_derived_cl10707, plain, ($false),
% 22.55/3.86 inference('simplify', [status(thm)], [zip_derived_cl10706])).
% 22.55/3.86
% 22.55/3.86 % SZS output end Refutation
% 22.55/3.86
% 22.55/3.86
% 22.55/3.86 % Terminating...
% 23.06/3.96 % Runner terminated.
% 23.06/3.97 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------