%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP060-1 : 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.oEBh3mbgfX true
% Computer : n017.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 04:35:33 PM UTC 2025
% Result : Unsatisfiable 37.41s 5.99s
% Output : Refutation 37.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP060-1 : TPTP v9.2.0. Released v1.0.0.
% 0.04/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.oEBh3mbgfX true
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 14:11:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.56/0.66 % Total configuration time : 435
% 0.56/0.66 % Estimated wc time : 1092
% 0.56/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.59/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.60/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.60/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.60/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.60/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.60/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.60/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 37.41/5.99 % Solved by fo/fo7.sh.
% 37.41/5.99 % done 942 iterations in 5.152s
% 37.41/5.99 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 37.41/5.99 % SZS output start Refutation
% 37.41/5.99 thf(inverse_type, type, inverse: $i > $i).
% 37.41/5.99 thf(a1_type, type, a1: $i).
% 37.41/5.99 thf(a3_type, type, a3: $i).
% 37.41/5.99 thf(b1_type, type, b1: $i).
% 37.41/5.99 thf(c3_type, type, c3: $i).
% 37.41/5.99 thf(multiply_type, type, multiply: $i > $i > $i).
% 37.41/5.99 thf(a2_type, type, a2: $i).
% 37.41/5.99 thf(b3_type, type, b3: $i).
% 37.41/5.99 thf(b2_type, type, b2: $i).
% 37.41/5.99 thf(single_axiom, axiom,
% 37.41/5.99 (( multiply @
% 37.41/5.99 X @
% 37.41/5.99 ( inverse @
% 37.41/5.99 ( multiply @
% 37.41/5.99 Y @
% 37.41/5.99 ( multiply @
% 37.41/5.99 Z @
% 37.41/5.99 ( multiply @
% 37.41/5.99 ( multiply @
% 37.41/5.99 ( inverse @ Z ) @ ( inverse @ ( multiply @ U @ Y ) ) ) @
% 37.41/5.99 X ) ) ) ) ) =
% 37.41/5.99 ( U ))).
% 37.41/5.99 thf(zip_derived_cl0, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X1 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 37.41/5.99 X1)))))
% 37.41/5.99 = (X0))),
% 37.41/5.99 inference('cnf', [status(esa)], [single_axiom])).
% 37.41/5.99 thf(zip_derived_cl0, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X1 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 37.41/5.99 X1)))))
% 37.41/5.99 = (X0))),
% 37.41/5.99 inference('cnf', [status(esa)], [single_axiom])).
% 37.41/5.99 thf(zip_derived_cl4, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X2 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X4 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X1))) @
% 37.41/5.99 (inverse @ X3))) @
% 37.41/5.99 (multiply @ X3 @ (multiply @ X0 @ X2)))))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl0, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X1 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 37.41/5.99 X1)))))
% 37.41/5.99 = (X0))),
% 37.41/5.99 inference('cnf', [status(esa)], [single_axiom])).
% 37.41/5.99 thf(zip_derived_cl13, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ (multiply @ X1 @ (multiply @ X2 @ (inverse @ X5))) @
% 37.41/5.99 (multiply @ X5 @ (multiply @ X0 @ X4)))))
% 37.41/5.99 = (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X0))) @
% 37.41/5.99 (inverse @ X1))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl4, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X2 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X4 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X1))) @
% 37.41/5.99 (inverse @ X3))) @
% 37.41/5.99 (multiply @ X3 @ (multiply @ X0 @ X2)))))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl41, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 37.41/5.99 X1))) @
% 37.41/5.99 (inverse @ X0)))
% 37.41/5.99 = (X2))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 37.41/5.99 thf(zip_derived_cl13, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ (multiply @ X1 @ (multiply @ X2 @ (inverse @ X5))) @
% 37.41/5.99 (multiply @ X5 @ (multiply @ X0 @ X4)))))
% 37.41/5.99 = (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X0))) @
% 37.41/5.99 (inverse @ X1))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl0, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X1 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 37.41/5.99 X1)))))
% 37.41/5.99 = (X0))),
% 37.41/5.99 inference('cnf', [status(esa)], [single_axiom])).
% 37.41/5.99 thf(zip_derived_cl40, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X4) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ (inverse @ X1) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @ X0 @ (multiply @ X2 @ (inverse @ X1))))))))) @
% 37.41/5.99 (inverse @ X0)))
% 37.41/5.99 = (X3))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl4, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X2 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X4 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X1))) @
% 37.41/5.99 (inverse @ X3))) @
% 37.41/5.99 (multiply @ X3 @ (multiply @ X0 @ X2)))))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl109, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (inverse @ (multiply @ X0 @ (multiply @ X3 @ (multiply @ X2 @ X4)))))
% 37.41/5.99 = (multiply @ (inverse @ X1) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (multiply @ X3 @ (multiply @ X2 @ (inverse @ X1)))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl4])).
% 37.41/5.99 thf(zip_derived_cl109, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (inverse @ (multiply @ X0 @ (multiply @ X3 @ (multiply @ X2 @ X4)))))
% 37.41/5.99 = (multiply @ (inverse @ X1) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (multiply @ X3 @ (multiply @ X2 @ (inverse @ X1)))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl4])).
% 37.41/5.99 thf(zip_derived_cl177, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (inverse @ (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X4)))))
% 37.41/5.99 = (multiply @ X0 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl109, zip_derived_cl109])).
% 37.41/5.99 thf(zip_derived_cl330, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.41/5.99 ((multiply @ (inverse @ X3) @ (inverse @ (multiply @ X5 @ X0)))
% 37.41/5.99 = (multiply @ X1 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X5 @
% 37.41/5.99 (multiply @ X4 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X4) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @ (multiply @ X2 @ X0))) @
% 37.41/5.99 X2))) @
% 37.41/5.99 X1))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl177])).
% 37.41/5.99 thf(zip_derived_cl109, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (inverse @ (multiply @ X0 @ (multiply @ X3 @ (multiply @ X2 @ X4)))))
% 37.41/5.99 = (multiply @ (inverse @ X1) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (multiply @ X3 @ (multiply @ X2 @ (inverse @ X1)))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl4])).
% 37.41/5.99 thf(zip_derived_cl40, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X4) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ (inverse @ X1) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @ X0 @ (multiply @ X2 @ (inverse @ X1))))))))) @
% 37.41/5.99 (inverse @ X0)))
% 37.41/5.99 = (X3))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl0, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X1 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 37.41/5.99 X1)))))
% 37.41/5.99 = (X0))),
% 37.41/5.99 inference('cnf', [status(esa)], [single_axiom])).
% 37.41/5.99 thf(zip_derived_cl108, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ (inverse @ X2) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (multiply @ X2 @ (multiply @ X1 @ (inverse @ X3)))))) @
% 37.41/5.99 X0)))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl175, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ (inverse @ X2) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))) @
% 37.41/5.99 X3)))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl109, zip_derived_cl108])).
% 37.41/5.99 thf(zip_derived_cl41, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 37.41/5.99 X1))) @
% 37.41/5.99 (inverse @ X0)))
% 37.41/5.99 = (X2))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 37.41/5.99 thf(zip_derived_cl248, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X4) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X1 @ (multiply @ X2 @ (multiply @ X0 @ X3)))))))) @
% 37.41/5.99 (inverse @ X2)))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl175, zip_derived_cl41])).
% 37.41/5.99 thf(zip_derived_cl41, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 37.41/5.99 X1))) @
% 37.41/5.99 (inverse @ X0)))
% 37.41/5.99 = (X2))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 37.41/5.99 thf(zip_derived_cl41, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 37.41/5.99 X1))) @
% 37.41/5.99 (inverse @ X0)))
% 37.41/5.99 = (X2))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 37.41/5.99 thf(zip_derived_cl13, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ (multiply @ X1 @ (multiply @ X2 @ (inverse @ X5))) @
% 37.41/5.99 (multiply @ X5 @ (multiply @ X0 @ X4)))))
% 37.41/5.99 = (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X0))) @
% 37.41/5.99 (inverse @ X1))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl13, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ (multiply @ X1 @ (multiply @ X2 @ (inverse @ X5))) @
% 37.41/5.99 (multiply @ X5 @ (multiply @ X0 @ X4)))))
% 37.41/5.99 = (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X0))) @
% 37.41/5.99 (inverse @ X1))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl43, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X1))) @
% 37.41/5.99 (inverse @ X0)))
% 37.41/5.99 = (multiply @ X4 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X2 @ X1))) @
% 37.41/5.99 (inverse @ X0))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 37.41/5.99 thf(zip_derived_cl553, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 37.41/5.99 ((multiply @ X6 @
% 37.41/5.99 (multiply @ (multiply @ (inverse @ X6) @ (inverse @ X0)) @
% 37.41/5.99 (inverse @ X1)))
% 37.41/5.99 = (multiply @ X5 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X5) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X4 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X4) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X2) @
% 37.41/5.99 (inverse @ (multiply @ X3 @ X0))) @
% 37.41/5.99 X3))) @
% 37.41/5.99 (inverse @ X2))))) @
% 37.41/5.99 (inverse @ X1))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl43])).
% 37.41/5.99 thf(zip_derived_cl41, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 37.41/5.99 X1))) @
% 37.41/5.99 (inverse @ X0)))
% 37.41/5.99 = (X2))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 37.41/5.99 thf(zip_derived_cl593, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X5 : $i, X6 : $i]:
% 37.41/5.99 ((multiply @ X6 @
% 37.41/5.99 (multiply @ (multiply @ (inverse @ X6) @ (inverse @ X0)) @
% 37.41/5.99 (inverse @ X1)))
% 37.41/5.99 = (multiply @ X5 @
% 37.41/5.99 (multiply @ (multiply @ (inverse @ X5) @ (inverse @ X0)) @
% 37.41/5.99 (inverse @ X1))))),
% 37.41/5.99 inference('demod', [status(thm)], [zip_derived_cl553, zip_derived_cl41])).
% 37.41/5.99 thf(zip_derived_cl175, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ (inverse @ X2) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))) @
% 37.41/5.99 X3)))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl109, zip_derived_cl108])).
% 37.41/5.99 thf(zip_derived_cl630, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X0) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X4 @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ (multiply @ (inverse @ X2) @ (inverse @ X1)) @
% 37.41/5.99 (inverse @ X0)))))) @
% 37.41/5.99 X4)))
% 37.41/5.99 = (multiply @ (inverse @ X3) @ (inverse @ X1)))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl593, zip_derived_cl175])).
% 37.41/5.99 thf(zip_derived_cl177, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (inverse @ (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X4)))))
% 37.41/5.99 = (multiply @ X0 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl109, zip_derived_cl109])).
% 37.41/5.99 thf(zip_derived_cl704, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X4 @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ (multiply @ (inverse @ X2) @ (inverse @ X1)) @ X0))))) @
% 37.41/5.99 X4)))
% 37.41/5.99 = (multiply @ (inverse @ X3) @ (inverse @ X1)))),
% 37.41/5.99 inference('demod', [status(thm)], [zip_derived_cl630, zip_derived_cl177])).
% 37.41/5.99 thf(zip_derived_cl41, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 37.41/5.99 X1))) @
% 37.41/5.99 (inverse @ X0)))
% 37.41/5.99 = (X2))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 37.41/5.99 thf(zip_derived_cl714, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 37.41/5.99 ((multiply @ X6 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X6) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X5) @
% 37.41/5.99 (inverse @ (multiply @ (inverse @ X1) @ (inverse @ X0)))) @
% 37.41/5.99 (inverse @ X1)))) @
% 37.41/5.99 (inverse @ X5)))
% 37.41/5.99 = (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X4 @
% 37.41/5.99 (multiply @ (multiply @ (inverse @ X4) @ (inverse @ X0)) @
% 37.41/5.99 X3))))) @
% 37.41/5.99 X2)))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl704, zip_derived_cl41])).
% 37.41/5.99 thf(zip_derived_cl41, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 37.41/5.99 X1))) @
% 37.41/5.99 (inverse @ X0)))
% 37.41/5.99 = (X2))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 37.41/5.99 thf(zip_derived_cl775, plain,
% 37.41/5.99 (![X0 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((inverse @ X0)
% 37.41/5.99 = (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X4 @
% 37.41/5.99 (multiply @ (multiply @ (inverse @ X4) @ (inverse @ X0)) @
% 37.41/5.99 X3))))) @
% 37.41/5.99 X2)))),
% 37.41/5.99 inference('demod', [status(thm)], [zip_derived_cl714, zip_derived_cl41])).
% 37.41/5.99 thf(zip_derived_cl175, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ (inverse @ X2) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))) @
% 37.41/5.99 X3)))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl109, zip_derived_cl108])).
% 37.41/5.99 thf(zip_derived_cl4, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X2 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X4 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X1))) @
% 37.41/5.99 (inverse @ X3))) @
% 37.41/5.99 (multiply @ X3 @ (multiply @ X0 @ X2)))))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl247, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.41/5.99 ((multiply @ X2 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ (multiply @ X4 @ (multiply @ X0 @ (inverse @ X5))) @
% 37.41/5.99 (multiply @ X5 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X1 @ (multiply @ X4 @ (multiply @ X0 @ X3))))) @
% 37.41/5.99 X2)))))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl175, zip_derived_cl4])).
% 37.41/5.99 thf(zip_derived_cl808, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 37.41/5.99 ((multiply @ X6 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ (multiply @ X5 @ (multiply @ X4 @ (inverse @ X7))) @
% 37.41/5.99 (multiply @ X7 @
% 37.41/5.99 (multiply @ (multiply @ X3 @ (inverse @ X0)) @ X6)))))
% 37.41/5.99 = (multiply @ X1 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ (multiply @ X5 @ (multiply @ X4 @ X3)) @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ (multiply @ (inverse @ X2) @ (inverse @ X0)) @ X1))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl775, zip_derived_cl247])).
% 37.41/5.99 thf(zip_derived_cl13, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ (multiply @ X1 @ (multiply @ X2 @ (inverse @ X5))) @
% 37.41/5.99 (multiply @ X5 @ (multiply @ X0 @ X4)))))
% 37.41/5.99 = (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X0))) @
% 37.41/5.99 (inverse @ X1))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl859, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @ (multiply @ X4 @ (multiply @ X3 @ (inverse @ X0))))) @
% 37.41/5.99 (inverse @ X5)))
% 37.41/5.99 = (multiply @ X1 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ (multiply @ X5 @ (multiply @ X4 @ X3)) @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ (multiply @ (inverse @ X2) @ (inverse @ X0)) @ X1))))))),
% 37.41/5.99 inference('demod', [status(thm)], [zip_derived_cl808, zip_derived_cl13])).
% 37.41/5.99 thf(zip_derived_cl775, plain,
% 37.41/5.99 (![X0 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((inverse @ X0)
% 37.41/5.99 = (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X4 @
% 37.41/5.99 (multiply @ (multiply @ (inverse @ X4) @ (inverse @ X0)) @
% 37.41/5.99 X3))))) @
% 37.41/5.99 X2)))),
% 37.41/5.99 inference('demod', [status(thm)], [zip_derived_cl714, zip_derived_cl41])).
% 37.41/5.99 thf(zip_derived_cl2082, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((inverse @ X1)
% 37.41/5.99 = (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X2) @
% 37.41/5.99 (inverse @ (multiply @ X3 @ (multiply @ X2 @ (inverse @ X1))))) @
% 37.41/5.99 (inverse @ X0))) @
% 37.41/5.99 (multiply @ X0 @ (multiply @ X3 @ X2)))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl859, zip_derived_cl775])).
% 37.41/5.99 thf(zip_derived_cl2278, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((inverse @ X2)
% 37.41/5.99 = (inverse @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @ (multiply @ (multiply @ X1 @ (inverse @ X2)) @ X0))) @
% 37.41/5.99 X1)))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl2082])).
% 37.41/5.99 thf(zip_derived_cl248, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X4) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X1 @ (multiply @ X2 @ (multiply @ X0 @ X3)))))))) @
% 37.41/5.99 (inverse @ X2)))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl175, zip_derived_cl41])).
% 37.41/5.99 thf(zip_derived_cl775, plain,
% 37.41/5.99 (![X0 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((inverse @ X0)
% 37.41/5.99 = (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X4 @
% 37.41/5.99 (multiply @ (multiply @ (inverse @ X4) @ (inverse @ X0)) @
% 37.41/5.99 X3))))) @
% 37.41/5.99 X2)))),
% 37.41/5.99 inference('demod', [status(thm)], [zip_derived_cl714, zip_derived_cl41])).
% 37.41/5.99 thf(zip_derived_cl825, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((inverse @
% 37.41/5.99 (multiply @ X4 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X0 @ (multiply @ X2 @ (multiply @ X4 @ X3)))))))
% 37.41/5.99 = (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X1 @ X0))) @
% 37.41/5.99 X1)))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl248, zip_derived_cl775])).
% 37.41/5.99 thf(zip_derived_cl177, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (inverse @ (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X4)))))
% 37.41/5.99 = (multiply @ X0 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl109, zip_derived_cl109])).
% 37.41/5.99 thf(zip_derived_cl41, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 37.41/5.99 X1))) @
% 37.41/5.99 (inverse @ X0)))
% 37.41/5.99 = (X2))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 37.41/5.99 thf(zip_derived_cl298, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.41/5.99 ((multiply @ X5 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X5) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))) @
% 37.41/5.99 X3))) @
% 37.41/5.99 (inverse @ X4)))
% 37.41/5.99 = (multiply @ X2 @ (multiply @ X1 @ (inverse @ X4))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl177, zip_derived_cl41])).
% 37.41/5.99 thf(zip_derived_cl1625, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X7 : $i]:
% 37.41/5.99 ((multiply @ X7 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X7) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X1 @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ X4 @ (multiply @ X3 @ (inverse @ X2))) @
% 37.41/5.99 (multiply @ X2 @ (multiply @ X1 @ X0)))))))) @
% 37.41/5.99 (inverse @ X5)))
% 37.41/5.99 = (multiply @ X4 @ (multiply @ X3 @ (inverse @ X5))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl825, zip_derived_cl298])).
% 37.41/5.99 thf(zip_derived_cl13, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ (multiply @ X1 @ (multiply @ X2 @ (inverse @ X5))) @
% 37.41/5.99 (multiply @ X5 @ (multiply @ X0 @ X4)))))
% 37.41/5.99 = (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X0))) @
% 37.41/5.99 (inverse @ X1))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl1672, plain,
% 37.41/5.99 (![X1 : $i, X3 : $i, X4 : $i, X5 : $i, X7 : $i]:
% 37.41/5.99 ((multiply @ X7 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X7) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X1 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X3 @ X1))) @
% 37.41/5.99 (inverse @ X4)))))) @
% 37.41/5.99 (inverse @ X5)))
% 37.41/5.99 = (multiply @ X4 @ (multiply @ X3 @ (inverse @ X5))))),
% 37.41/5.99 inference('demod', [status(thm)], [zip_derived_cl1625, zip_derived_cl13])).
% 37.41/5.99 thf(zip_derived_cl3301, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 37.41/5.99 ((multiply @ X7 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X7) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X6 @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X2 @ X6))) @
% 37.41/5.99 (inverse @ X0)))))) @
% 37.41/5.99 (inverse @ X1)))
% 37.41/5.99 = (multiply @
% 37.41/5.99 (multiply @ X4 @
% 37.41/5.99 (multiply @ X5 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X5) @
% 37.41/5.99 (inverse @ (multiply @ (multiply @ X3 @ (inverse @ X0)) @ X4))) @
% 37.41/5.99 X3))) @
% 37.41/5.99 (multiply @ X2 @ (inverse @ X1))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl2278, zip_derived_cl1672])).
% 37.41/5.99 thf(zip_derived_cl1672, plain,
% 37.41/5.99 (![X1 : $i, X3 : $i, X4 : $i, X5 : $i, X7 : $i]:
% 37.41/5.99 ((multiply @ X7 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X7) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X1 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X3 @ X1))) @
% 37.41/5.99 (inverse @ X4)))))) @
% 37.41/5.99 (inverse @ X5)))
% 37.41/5.99 = (multiply @ X4 @ (multiply @ X3 @ (inverse @ X5))))),
% 37.41/5.99 inference('demod', [status(thm)], [zip_derived_cl1625, zip_derived_cl13])).
% 37.41/5.99 thf(zip_derived_cl3381, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (multiply @ X2 @ (inverse @ X1)))
% 37.41/5.99 = (multiply @
% 37.41/5.99 (multiply @ X4 @
% 37.41/5.99 (multiply @ X5 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X5) @
% 37.41/5.99 (inverse @ (multiply @ (multiply @ X3 @ (inverse @ X0)) @ X4))) @
% 37.41/5.99 X3))) @
% 37.41/5.99 (multiply @ X2 @ (inverse @ X1))))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl3301, zip_derived_cl1672])).
% 37.41/5.99 thf(zip_derived_cl0, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X1 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 37.41/5.99 X1)))))
% 37.41/5.99 = (X0))),
% 37.41/5.99 inference('cnf', [status(esa)], [single_axiom])).
% 37.41/5.99 thf(zip_derived_cl3406, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 37.41/5.99 ((multiply @ X6 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ (multiply @ X1 @ (inverse @ X0)) @
% 37.41/5.99 (multiply @ X7 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X7) @
% 37.41/5.99 (inverse @ (multiply @ X2 @ (multiply @ X1 @ (inverse @ X0))))) @
% 37.41/5.99 X6)))))
% 37.41/5.99 = (multiply @ X4 @
% 37.41/5.99 (multiply @ X5 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X5) @
% 37.41/5.99 (inverse @ (multiply @ (multiply @ X3 @ (inverse @ X2)) @ X4))) @
% 37.41/5.99 X3))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl3381, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl0, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X1 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 37.41/5.99 X1)))))
% 37.41/5.99 = (X0))),
% 37.41/5.99 inference('cnf', [status(esa)], [single_axiom])).
% 37.41/5.99 thf(zip_derived_cl3586, plain,
% 37.41/5.99 (![X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.41/5.99 ((X2)
% 37.41/5.99 = (multiply @ X4 @
% 37.41/5.99 (multiply @ X5 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X5) @
% 37.41/5.99 (inverse @ (multiply @ (multiply @ X3 @ (inverse @ X2)) @ X4))) @
% 37.41/5.99 X3))))),
% 37.41/5.99 inference('demod', [status(thm)], [zip_derived_cl3406, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl3710, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((X3)
% 37.41/5.99 = (multiply @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (multiply @ X1 @
% 37.41/5.99 (multiply @ (multiply @ (inverse @ X1) @ (inverse @ X3)) @ X2))))) @
% 37.41/5.99 X0))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl248, zip_derived_cl3586])).
% 37.41/5.99 thf(zip_derived_cl3878, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @
% 37.41/5.99 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X4 @ X0))) @ X4)
% 37.41/5.99 = (multiply @
% 37.41/5.99 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X1 @ X0))) @
% 37.41/5.99 X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl330, zip_derived_cl3710])).
% 37.41/5.99 thf(zip_derived_cl0, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X1 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 37.41/5.99 X1)))))
% 37.41/5.99 = (X0))),
% 37.41/5.99 inference('cnf', [status(esa)], [single_axiom])).
% 37.41/5.99 thf(zip_derived_cl4048, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X1 @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X0 @ X1))) @
% 37.41/5.99 X0)))))
% 37.41/5.99 = (X3))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl3878, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl4048, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X1 @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X0 @ X1))) @
% 37.41/5.99 X0)))))
% 37.41/5.99 = (X3))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl3878, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl1672, plain,
% 37.41/5.99 (![X1 : $i, X3 : $i, X4 : $i, X5 : $i, X7 : $i]:
% 37.41/5.99 ((multiply @ X7 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X7) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X1 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X3 @ X1))) @
% 37.41/5.99 (inverse @ X4)))))) @
% 37.41/5.99 (inverse @ X5)))
% 37.41/5.99 = (multiply @ X4 @ (multiply @ X3 @ (inverse @ X5))))),
% 37.41/5.99 inference('demod', [status(thm)], [zip_derived_cl1625, zip_derived_cl13])).
% 37.41/5.99 thf(zip_derived_cl4357, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ (inverse @ X1)))
% 37.41/5.99 = (multiply @ X2 @ (multiply @ (inverse @ X2) @ (inverse @ X1))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4048, zip_derived_cl1672])).
% 37.41/5.99 thf(zip_derived_cl4560, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (inverse @ X0))
% 37.41/5.99 = (multiply @ X4 @
% 37.41/5.99 (multiply @ (inverse @ X4) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @ (multiply @ X1 @ X2))) @
% 37.41/5.99 X1)))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4048, zip_derived_cl4357])).
% 37.41/5.99 thf(zip_derived_cl4048, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X1 @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X0 @ X1))) @
% 37.41/5.99 X0)))))
% 37.41/5.99 = (X3))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl3878, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl4610, plain,
% 37.41/5.99 (![X0 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X4 @ (inverse @ X4)))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl4560, zip_derived_cl4048])).
% 37.41/5.99 thf(zip_derived_cl3586, plain,
% 37.41/5.99 (![X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 37.41/5.99 ((X2)
% 37.41/5.99 = (multiply @ X4 @
% 37.41/5.99 (multiply @ X5 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X5) @
% 37.41/5.99 (inverse @ (multiply @ (multiply @ X3 @ (inverse @ X2)) @ X4))) @
% 37.41/5.99 X3))))),
% 37.41/5.99 inference('demod', [status(thm)], [zip_derived_cl3406, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl4659, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((X1)
% 37.41/5.99 = (multiply @ X2 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @ (multiply @ (multiply @ X0 @ (inverse @ X0)) @ X2))) @
% 37.41/5.99 X1))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4610, zip_derived_cl3586])).
% 37.41/5.99 thf(zip_derived_cl4048, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X1 @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X0 @ X1))) @
% 37.41/5.99 X0)))))
% 37.41/5.99 = (X3))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl3878, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl6128, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4659, zip_derived_cl4048])).
% 37.41/5.99 thf(zip_derived_cl4610, plain,
% 37.41/5.99 (![X0 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X4 @ (inverse @ X4)))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl4560, zip_derived_cl4048])).
% 37.41/5.99 thf(zip_derived_cl6128, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4659, zip_derived_cl4048])).
% 37.41/5.99 thf(zip_derived_cl0, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X1 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 37.41/5.99 X1)))))
% 37.41/5.99 = (X0))),
% 37.41/5.99 inference('cnf', [status(esa)], [single_axiom])).
% 37.41/5.99 thf(zip_derived_cl6348, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X2 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ (inverse @ X1) @
% 37.41/5.99 (multiply @ X0 @ (multiply @ (inverse @ X0) @ X2)))))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6128, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl248, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X4) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X1 @ (multiply @ X2 @ (multiply @ X0 @ X3)))))))) @
% 37.41/5.99 (inverse @ X2)))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl175, zip_derived_cl41])).
% 37.41/5.99 thf(zip_derived_cl6438, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @
% 37.41/5.99 (inverse @ (multiply @ (inverse @ X1) @ X0))) @
% 37.41/5.99 (inverse @ X1)))
% 37.41/5.99 = (inverse @ X0))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6348, zip_derived_cl248])).
% 37.41/5.99 thf(zip_derived_cl3878, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @
% 37.41/5.99 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X4 @ X0))) @ X4)
% 37.41/5.99 = (multiply @
% 37.41/5.99 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X1 @ X0))) @
% 37.41/5.99 X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl330, zip_derived_cl3710])).
% 37.41/5.99 thf(zip_derived_cl6548, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X1 @ X0))) @ X1))
% 37.41/5.99 = (inverse @ X0))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl6438, zip_derived_cl3878])).
% 37.41/5.99 thf(zip_derived_cl3710, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((X3)
% 37.41/5.99 = (multiply @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (multiply @ X1 @
% 37.41/5.99 (multiply @ (multiply @ (inverse @ X1) @ (inverse @ X3)) @ X2))))) @
% 37.41/5.99 X0))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl248, zip_derived_cl3586])).
% 37.41/5.99 thf(zip_derived_cl6614, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X2 @ X0)
% 37.41/5.99 = (multiply @
% 37.41/5.99 (multiply @ X2 @ (inverse @ (multiply @ X1 @ (inverse @ X0)))) @
% 37.41/5.99 X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6548, zip_derived_cl3710])).
% 37.41/5.99 thf(zip_derived_cl7097, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ (multiply @ X1 @ (inverse @ X2)) @ X2)
% 37.41/5.99 = (multiply @ (multiply @ X0 @ (inverse @ X0)) @ X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4610, zip_derived_cl6614])).
% 37.41/5.99 thf(zip_derived_cl8272, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (multiply @ X2 @ (inverse @ X2)))
% 37.41/5.99 = (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6128, zip_derived_cl7097])).
% 37.41/5.99 thf(zip_derived_cl6128, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4659, zip_derived_cl4048])).
% 37.41/5.99 thf(zip_derived_cl6128, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4659, zip_derived_cl4048])).
% 37.41/5.99 thf(zip_derived_cl6548, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X1 @ X0))) @ X1))
% 37.41/5.99 = (inverse @ X0))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl6438, zip_derived_cl3878])).
% 37.41/5.99 thf(zip_derived_cl6656, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1))
% 37.41/5.99 = (inverse @ (inverse @ X1)))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6128, zip_derived_cl6548])).
% 37.41/5.99 thf(zip_derived_cl6881, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (inverse @ X0))
% 37.41/5.99 = (inverse @
% 37.41/5.99 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6128, zip_derived_cl6656])).
% 37.41/5.99 thf(zip_derived_cl6881, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (inverse @ X0))
% 37.41/5.99 = (inverse @
% 37.41/5.99 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6128, zip_derived_cl6656])).
% 37.41/5.99 thf(zip_derived_cl4610, plain,
% 37.41/5.99 (![X0 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X4 @ (inverse @ X4)))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl4560, zip_derived_cl4048])).
% 37.41/5.99 thf(zip_derived_cl6128, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4659, zip_derived_cl4048])).
% 37.41/5.99 thf(zip_derived_cl6614, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X2 @ X0)
% 37.41/5.99 = (multiply @
% 37.41/5.99 (multiply @ X2 @ (inverse @ (multiply @ X1 @ (inverse @ X0)))) @
% 37.41/5.99 X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6548, zip_derived_cl3710])).
% 37.41/5.99 thf(zip_derived_cl7124, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X2 @ (multiply @ X1 @ (inverse @ X1)))
% 37.41/5.99 = (multiply @ (multiply @ X2 @ (inverse @ X0)) @ X0))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6128, zip_derived_cl6614])).
% 37.41/5.99 thf(zip_derived_cl4610, plain,
% 37.41/5.99 (![X0 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X4 @ (inverse @ X4)))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl4560, zip_derived_cl4048])).
% 37.41/5.99 thf(zip_derived_cl3710, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((X3)
% 37.41/5.99 = (multiply @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (multiply @ X1 @
% 37.41/5.99 (multiply @ (multiply @ (inverse @ X1) @ (inverse @ X3)) @ X2))))) @
% 37.41/5.99 X0))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl248, zip_derived_cl3586])).
% 37.41/5.99 thf(zip_derived_cl4684, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((inverse @ X3)
% 37.41/5.99 = (multiply @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X1 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @ (multiply @ X0 @ (inverse @ X0)) @ X2))))) @
% 37.41/5.99 X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4610, zip_derived_cl3710])).
% 37.41/5.99 thf(zip_derived_cl6548, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X1 @ X0))) @ X1))
% 37.41/5.99 = (inverse @ X0))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl6438, zip_derived_cl3878])).
% 37.41/5.99 thf(zip_derived_cl6644, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ X0))
% 37.41/5.99 = (inverse @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (multiply @ (multiply @ X2 @ (inverse @ X2)) @ (inverse @ X1)))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4684, zip_derived_cl6548])).
% 37.41/5.99 thf(zip_derived_cl8424, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ X2))
% 37.41/5.99 = (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ (inverse @ X1) @ (multiply @ X0 @ (inverse @ X0))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl7124, zip_derived_cl6644])).
% 37.41/5.99 thf(zip_derived_cl6548, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X1 @ X0))) @ X1))
% 37.41/5.99 = (inverse @ X0))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl6438, zip_derived_cl3878])).
% 37.41/5.99 thf(zip_derived_cl248, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 37.41/5.99 ((multiply @ X4 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X4) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X1 @ (multiply @ X2 @ (multiply @ X0 @ X3)))))))) @
% 37.41/5.99 (inverse @ X2)))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl175, zip_derived_cl41])).
% 37.41/5.99 thf(zip_derived_cl6607, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((inverse @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0))))))
% 37.41/5.99 = (X2))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6548, zip_derived_cl248])).
% 37.41/5.99 thf(zip_derived_cl10299, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((inverse @
% 37.41/5.99 (multiply @ (inverse @ (inverse @ (inverse @ X1))) @
% 37.41/5.99 (multiply @ X1 @ (inverse @ X0))))
% 37.41/5.99 = (X0))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl8424, zip_derived_cl6607])).
% 37.41/5.99 thf(zip_derived_cl10517, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((inverse @
% 37.41/5.99 (multiply @ (inverse @ (inverse @ (inverse @ X1))) @
% 37.41/5.99 (multiply @ X0 @ (inverse @ X0))))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)],
% 37.41/5.99 [zip_derived_cl4610, zip_derived_cl10299])).
% 37.41/5.99 thf(zip_derived_cl8272, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (multiply @ X2 @ (inverse @ X2)))
% 37.41/5.99 = (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6128, zip_derived_cl7097])).
% 37.41/5.99 thf(zip_derived_cl10571, plain,
% 37.41/5.99 (![X1 : $i]:
% 37.41/5.99 ((inverse @
% 37.41/5.99 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 37.41/5.99 (inverse @ (inverse @ (inverse @ X1)))))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl10517, zip_derived_cl8272])).
% 37.41/5.99 thf(zip_derived_cl10719, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 37.41/5.99 (inverse @ (multiply @ X1 @ (inverse @ X1)))) @
% 37.41/5.99 (multiply @ X0 @ (inverse @ X0))))
% 37.41/5.99 = (multiply @ X1 @ (inverse @ X1)))),
% 37.41/5.99 inference('sup+', [status(thm)],
% 37.41/5.99 [zip_derived_cl6881, zip_derived_cl10571])).
% 37.41/5.99 thf(zip_derived_cl6128, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4659, zip_derived_cl4048])).
% 37.41/5.99 thf(zip_derived_cl10761, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((inverse @
% 37.41/5.99 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 37.41/5.99 (multiply @ X0 @ (inverse @ X0))))
% 37.41/5.99 = (multiply @ X1 @ (inverse @ X1)))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl10719, zip_derived_cl6128])).
% 37.41/5.99 thf(zip_derived_cl11327, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @
% 37.41/5.99 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1)))) @
% 37.41/5.99 (multiply @ X0 @ (inverse @ X0))) @
% 37.41/5.99 (multiply @ X2 @ (inverse @ X2))))
% 37.41/5.99 = (multiply @
% 37.41/5.99 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1)))) @
% 37.41/5.99 (inverse @
% 37.41/5.99 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))))),
% 37.41/5.99 inference('sup+', [status(thm)],
% 37.41/5.99 [zip_derived_cl6881, zip_derived_cl10761])).
% 37.41/5.99 thf(zip_derived_cl8272, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (multiply @ X2 @ (inverse @ X2)))
% 37.41/5.99 = (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6128, zip_derived_cl7097])).
% 37.41/5.99 thf(zip_derived_cl8272, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (multiply @ X2 @ (inverse @ X2)))
% 37.41/5.99 = (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6128, zip_derived_cl7097])).
% 37.41/5.99 thf(zip_derived_cl6644, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ X0))
% 37.41/5.99 = (inverse @
% 37.41/5.99 (multiply @ X0 @
% 37.41/5.99 (multiply @ (multiply @ X2 @ (inverse @ X2)) @ (inverse @ X1)))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4684, zip_derived_cl6548])).
% 37.41/5.99 thf(zip_derived_cl6128, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4659, zip_derived_cl4048])).
% 37.41/5.99 thf(zip_derived_cl6881, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (inverse @ X0))
% 37.41/5.99 = (inverse @
% 37.41/5.99 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6128, zip_derived_cl6656])).
% 37.41/5.99 thf(zip_derived_cl11361, plain,
% 37.41/5.99 (![X1 : $i]:
% 37.41/5.99 ((inverse @ (multiply @ X1 @ (inverse @ X1)))
% 37.41/5.99 = (inverse @
% 37.41/5.99 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1))))))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl11327, zip_derived_cl8272, zip_derived_cl8272,
% 37.41/5.99 zip_derived_cl6644, zip_derived_cl6128, zip_derived_cl6881])).
% 37.41/5.99 thf(zip_derived_cl6128, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4659, zip_derived_cl4048])).
% 37.41/5.99 thf(zip_derived_cl11426, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @
% 37.41/5.99 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 37.41/5.99 (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)],
% 37.41/5.99 [zip_derived_cl11361, zip_derived_cl6128])).
% 37.41/5.99 thf(zip_derived_cl6656, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1))
% 37.41/5.99 = (inverse @ (inverse @ X1)))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6128, zip_derived_cl6548])).
% 37.41/5.99 thf(zip_derived_cl6128, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4659, zip_derived_cl4048])).
% 37.41/5.99 thf(zip_derived_cl8424, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ X2))
% 37.41/5.99 = (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ (inverse @ X1) @ (multiply @ X0 @ (inverse @ X0))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl7124, zip_derived_cl6644])).
% 37.41/5.99 thf(zip_derived_cl11567, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))) = (X1))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl11426, zip_derived_cl6656, zip_derived_cl6128,
% 37.41/5.99 zip_derived_cl8424])).
% 37.41/5.99 thf(zip_derived_cl11625, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((X0) = (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl8272, zip_derived_cl11567])).
% 37.41/5.99 thf(zip_derived_cl7124, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X2 @ (multiply @ X1 @ (inverse @ X1)))
% 37.41/5.99 = (multiply @ (multiply @ X2 @ (inverse @ X0)) @ X0))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6128, zip_derived_cl6614])).
% 37.41/5.99 thf(zip_derived_cl11567, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))) = (X1))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl11426, zip_derived_cl6656, zip_derived_cl6128,
% 37.41/5.99 zip_derived_cl8424])).
% 37.41/5.99 thf(zip_derived_cl11624, plain,
% 37.41/5.99 (![X0 : $i, X2 : $i]:
% 37.41/5.99 ((X2) = (multiply @ (multiply @ X2 @ (inverse @ X0)) @ X0))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl7124, zip_derived_cl11567])).
% 37.41/5.99 thf(zip_derived_cl12227, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ X1)) = (multiply @ (inverse @ X0) @ X0))),
% 37.41/5.99 inference('sup+', [status(thm)],
% 37.41/5.99 [zip_derived_cl11625, zip_derived_cl11624])).
% 37.41/5.99 thf(prove_these_axioms, conjecture,
% 37.41/5.99 (~( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 37.41/5.99 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 37.41/5.99 ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) != ( a2 ) ) |
% 37.41/5.99 ( ( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 37.41/5.99 ( multiply @ ( inverse @ b1 ) @ b1 ) ) ))).
% 37.41/5.99 thf(zf_stmt_0, negated_conjecture,
% 37.41/5.99 (( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 37.41/5.99 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 37.41/5.99 ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) != ( a2 ) ) |
% 37.41/5.99 ( ( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 37.41/5.99 ( multiply @ ( inverse @ b1 ) @ b1 ) )),
% 37.41/5.99 inference('cnf.neg', [status(esa)], [prove_these_axioms])).
% 37.41/5.99 thf(zip_derived_cl1, plain,
% 37.41/5.99 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 37.41/5.99 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 37.41/5.99 | ((multiply @ (multiply @ (inverse @ b2) @ b2) @ a2) != (a2))
% 37.41/5.99 | ((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ b1) @ b1)))),
% 37.41/5.99 inference('cnf', [status(esa)], [zf_stmt_0])).
% 37.41/5.99 thf(zip_derived_cl11625, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((X0) = (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl8272, zip_derived_cl11567])).
% 37.41/5.99 thf(zip_derived_cl6656, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1))
% 37.41/5.99 = (inverse @ (inverse @ X1)))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6128, zip_derived_cl6548])).
% 37.41/5.99 thf(zip_derived_cl12195, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ (inverse @ (multiply @ X1 @ (inverse @ X1))) @ X0)
% 37.41/5.99 = (inverse @ (inverse @ X0)))),
% 37.41/5.99 inference('sup+', [status(thm)],
% 37.41/5.99 [zip_derived_cl11625, zip_derived_cl6656])).
% 37.41/5.99 thf(zip_derived_cl6128, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4659, zip_derived_cl4048])).
% 37.41/5.99 thf(zip_derived_cl11361, plain,
% 37.41/5.99 (![X1 : $i]:
% 37.41/5.99 ((inverse @ (multiply @ X1 @ (inverse @ X1)))
% 37.41/5.99 = (inverse @
% 37.41/5.99 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1))))))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl11327, zip_derived_cl8272, zip_derived_cl8272,
% 37.41/5.99 zip_derived_cl6644, zip_derived_cl6128, zip_derived_cl6881])).
% 37.41/5.99 thf(zip_derived_cl11489, plain,
% 37.41/5.99 (![X0 : $i]:
% 37.41/5.99 ((inverse @
% 37.41/5.99 (multiply @ (multiply @ X0 @ (inverse @ X0)) @
% 37.41/5.99 (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 37.41/5.99 = (inverse @
% 37.41/5.99 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))),
% 37.41/5.99 inference('sup+', [status(thm)],
% 37.41/5.99 [zip_derived_cl6128, zip_derived_cl11361])).
% 37.41/5.99 thf(zip_derived_cl6128, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl4659, zip_derived_cl4048])).
% 37.41/5.99 thf(zip_derived_cl6656, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1))
% 37.41/5.99 = (inverse @ (inverse @ X1)))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6128, zip_derived_cl6548])).
% 37.41/5.99 thf(zip_derived_cl8424, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ X2))
% 37.41/5.99 = (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ (inverse @ X1) @ (multiply @ X0 @ (inverse @ X0))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl7124, zip_derived_cl6644])).
% 37.41/5.99 thf(zip_derived_cl11512, plain,
% 37.41/5.99 (![X0 : $i]:
% 37.41/5.99 ((inverse @ (multiply @ X0 @ (inverse @ X0)))
% 37.41/5.99 = (multiply @ X0 @ (inverse @ X0)))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl11489, zip_derived_cl6128, zip_derived_cl6656,
% 37.41/5.99 zip_derived_cl8424])).
% 37.41/5.99 thf(zip_derived_cl11625, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((X0) = (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl8272, zip_derived_cl11567])).
% 37.41/5.99 thf(zip_derived_cl12347, plain,
% 37.41/5.99 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl12195, zip_derived_cl11512, zip_derived_cl11625])).
% 37.41/5.99 thf(zip_derived_cl11625, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((X0) = (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl8272, zip_derived_cl11567])).
% 37.41/5.99 thf(zip_derived_cl12446, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((X1) = (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1))),
% 37.41/5.99 inference('sup+', [status(thm)],
% 37.41/5.99 [zip_derived_cl12347, zip_derived_cl11625])).
% 37.41/5.99 thf(zip_derived_cl13021, plain,
% 37.41/5.99 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 37.41/5.99 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 37.41/5.99 | ((a2) != (a2))
% 37.41/5.99 | ((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ b1) @ b1)))),
% 37.41/5.99 inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl12446])).
% 37.41/5.99 thf(zip_derived_cl13022, plain,
% 37.41/5.99 ((((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ b1) @ b1))
% 37.41/5.99 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 37.41/5.99 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 37.41/5.99 inference('simplify', [status(thm)], [zip_derived_cl13021])).
% 37.41/5.99 thf(zip_derived_cl13362, plain,
% 37.41/5.99 (![X0 : $i]:
% 37.41/5.99 (((multiply @ (inverse @ a1) @ a1) != (multiply @ X0 @ (inverse @ X0)))
% 37.41/5.99 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 37.41/5.99 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 37.41/5.99 inference('sup-', [status(thm)],
% 37.41/5.99 [zip_derived_cl12227, zip_derived_cl13022])).
% 37.41/5.99 thf(zip_derived_cl12227, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ X1)) = (multiply @ (inverse @ X0) @ X0))),
% 37.41/5.99 inference('sup+', [status(thm)],
% 37.41/5.99 [zip_derived_cl11625, zip_derived_cl11624])).
% 37.41/5.99 thf(zip_derived_cl13535, plain,
% 37.41/5.99 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 37.41/5.99 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 37.41/5.99 inference('simplify_reflect+', [status(thm)],
% 37.41/5.99 [zip_derived_cl13362, zip_derived_cl12227])).
% 37.41/5.99 thf(zip_derived_cl11624, plain,
% 37.41/5.99 (![X0 : $i, X2 : $i]:
% 37.41/5.99 ((X2) = (multiply @ (multiply @ X2 @ (inverse @ X0)) @ X0))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl7124, zip_derived_cl11567])).
% 37.41/5.99 thf(zip_derived_cl0, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 37.41/5.99 ((multiply @ X1 @
% 37.41/5.99 (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ X3 @
% 37.41/5.99 (multiply @
% 37.41/5.99 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 37.41/5.99 X1)))))
% 37.41/5.99 = (X0))),
% 37.41/5.99 inference('cnf', [status(esa)], [single_axiom])).
% 37.41/5.99 thf(zip_derived_cl11869, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ (multiply @ X1 @ X2) @
% 37.41/5.99 (inverse @ (multiply @ X2 @ (multiply @ X0 @ (inverse @ X0)))))
% 37.41/5.99 = (X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl11624, zip_derived_cl0])).
% 37.41/5.99 thf(zip_derived_cl11567, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))) = (X1))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl11426, zip_derived_cl6656, zip_derived_cl6128,
% 37.41/5.99 zip_derived_cl8424])).
% 37.41/5.99 thf(zip_derived_cl11924, plain,
% 37.41/5.99 (![X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ (multiply @ X1 @ X2) @ (inverse @ X2)) = (X1))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl11869, zip_derived_cl11567])).
% 37.41/5.99 thf(zip_derived_cl6614, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X2 @ X0)
% 37.41/5.99 = (multiply @
% 37.41/5.99 (multiply @ X2 @ (inverse @ (multiply @ X1 @ (inverse @ X0)))) @
% 37.41/5.99 X1))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl6548, zip_derived_cl3710])).
% 37.41/5.99 thf(zip_derived_cl8424, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ X2))
% 37.41/5.99 = (inverse @
% 37.41/5.99 (multiply @ X2 @
% 37.41/5.99 (multiply @ (inverse @ X1) @ (multiply @ X0 @ (inverse @ X0))))))),
% 37.41/5.99 inference('sup+', [status(thm)], [zip_derived_cl7124, zip_derived_cl6644])).
% 37.41/5.99 thf(zip_derived_cl11567, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))) = (X1))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl11426, zip_derived_cl6656, zip_derived_cl6128,
% 37.41/5.99 zip_derived_cl8424])).
% 37.41/5.99 thf(zip_derived_cl11626, plain,
% 37.41/5.99 (![X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X1 @ (inverse @ X2))
% 37.41/5.99 = (inverse @ (multiply @ X2 @ (inverse @ X1))))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl8424, zip_derived_cl11567])).
% 37.41/5.99 thf(zip_derived_cl14122, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X2 @ X0)
% 37.41/5.99 = (multiply @ (multiply @ X2 @ (multiply @ X0 @ (inverse @ X1))) @
% 37.41/5.99 X1))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl6614, zip_derived_cl11626])).
% 37.41/5.99 thf(zip_derived_cl15300, plain,
% 37.41/5.99 (![X0 : $i, X1 : $i, X2 : $i]:
% 37.41/5.99 ((multiply @ X2 @ (multiply @ X0 @ X1))
% 37.41/5.99 = (multiply @ (multiply @ X2 @ X0) @ X1))),
% 37.41/5.99 inference('sup+', [status(thm)],
% 37.41/5.99 [zip_derived_cl11924, zip_derived_cl14122])).
% 37.41/5.99 thf(zip_derived_cl15362, plain,
% 37.41/5.99 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 37.41/5.99 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 37.41/5.99 inference('demod', [status(thm)],
% 37.41/5.99 [zip_derived_cl13535, zip_derived_cl15300])).
% 37.41/5.99 thf(zip_derived_cl15363, plain, ($false),
% 37.41/5.99 inference('simplify', [status(thm)], [zip_derived_cl15362])).
% 37.41/5.99
% 37.41/5.99 % SZS output end Refutation
% 37.41/5.99
% 37.41/5.99
% 37.41/5.99 % Terminating...
% 38.19/6.09 % Runner terminated.
% 38.19/6.11 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------