%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP412-1 : TPTP v9.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.KSc9vTaIGo true
% Computer : n027.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 04:36:24 PM UTC 2025
% Result : Unsatisfiable 51.65s 7.98s
% Output : Refutation 51.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP412-1 : TPTP v9.2.0. Released v2.6.0.
% 0.09/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.KSc9vTaIGo true
% 0.09/0.31 % Computer : n027.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Wed Oct 1 14:16:08 EDT 2025
% 0.09/0.31 % CPUTime :
% 0.09/0.31 % Running portfolio for 300 s
% 0.09/0.31 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.31 % Number of cores: 8
% 0.09/0.32 % Python version: Python 3.6.8
% 0.09/0.32 % Running in FO mode
% 0.16/0.56 % Total configuration time : 435
% 0.16/0.56 % Estimated wc time : 1092
% 0.16/0.56 % Estimated cpu time (7 cpus) : 156.0
% 0.80/0.66 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.80/0.67 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.80/0.67 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.80/0.67 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.80/0.67 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.80/0.68 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.80/0.68 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 51.65/7.98 % Solved by fo/fo7.sh.
% 51.65/7.98 % done 775 iterations in 7.271s
% 51.65/7.98 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 51.65/7.98 % SZS output start Refutation
% 51.65/7.98 thf(inverse_type, type, inverse: $i > $i).
% 51.65/7.98 thf(b1_type, type, b1: $i).
% 51.65/7.98 thf(multiply_type, type, multiply: $i > $i > $i).
% 51.65/7.98 thf(a1_type, type, a1: $i).
% 51.65/7.98 thf(single_axiom, axiom,
% 51.65/7.98 (( multiply @
% 51.65/7.98 A @
% 51.65/7.98 ( inverse @
% 51.65/7.98 ( multiply @
% 51.65/7.98 ( multiply @
% 51.65/7.98 ( multiply @ ( inverse @ B ) @ B ) @
% 51.65/7.98 ( inverse @
% 51.65/7.98 ( multiply @
% 51.65/7.98 ( inverse @ ( multiply @ A @ ( inverse @ B ) ) ) @ C ) ) ) @
% 51.65/7.98 B ) ) ) =
% 51.65/7.98 ( C ))).
% 51.65/7.98 thf(zip_derived_cl0, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ X1 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (X0))),
% 51.65/7.98 inference('cnf', [status(esa)], [single_axiom])).
% 51.65/7.98 thf(zip_derived_cl0, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ X1 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (X0))),
% 51.65/7.98 inference('cnf', [status(esa)], [single_axiom])).
% 51.65/7.98 thf(zip_derived_cl0, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ X1 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (X0))),
% 51.65/7.98 inference('cnf', [status(esa)], [single_axiom])).
% 51.65/7.98 thf(zip_derived_cl3, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ X3 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0)) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 51.65/7.98 (inverse @ X1))) @
% 51.65/7.98 X0))) @
% 51.65/7.98 X1)))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 51.65/7.98 thf(zip_derived_cl0, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ X1 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (X0))),
% 51.65/7.98 inference('cnf', [status(esa)], [single_axiom])).
% 51.65/7.98 thf(zip_derived_cl13, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X0) @ X0) @ (inverse @ X1)) @
% 51.65/7.98 X0))))
% 51.65/7.98 = (X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 51.65/7.98 thf(zip_derived_cl35, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 51.65/7.98 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 51.65/7.98 = (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 51.65/7.98 X0))) @
% 51.65/7.98 X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 51.65/7.98 thf(zip_derived_cl0, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ X1 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (X0))),
% 51.65/7.98 inference('cnf', [status(esa)], [single_axiom])).
% 51.65/7.98 thf(zip_derived_cl0, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ X1 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (X0))),
% 51.65/7.98 inference('cnf', [status(esa)], [single_axiom])).
% 51.65/7.98 thf(zip_derived_cl0, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ X1 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (X0))),
% 51.65/7.98 inference('cnf', [status(esa)], [single_axiom])).
% 51.65/7.98 thf(zip_derived_cl3, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ X3 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0)) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 51.65/7.98 (inverse @ X1))) @
% 51.65/7.98 X0))) @
% 51.65/7.98 X1)))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 51.65/7.98 thf(zip_derived_cl0, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ X1 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (X0))),
% 51.65/7.98 inference('cnf', [status(esa)], [single_axiom])).
% 51.65/7.98 thf(zip_derived_cl35, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 51.65/7.98 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 51.65/7.98 = (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 51.65/7.98 X0))) @
% 51.65/7.98 X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 51.65/7.98 thf(zip_derived_cl13, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X0) @ X0) @ (inverse @ X1)) @
% 51.65/7.98 X0))))
% 51.65/7.98 = (X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 51.65/7.98 thf(zip_derived_cl57, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))))) @
% 51.65/7.98 X0) = (X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl13])).
% 51.65/7.98 thf(zip_derived_cl35, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 51.65/7.98 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 51.65/7.98 = (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 51.65/7.98 X0))) @
% 51.65/7.98 X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 51.65/7.98 thf(zip_derived_cl35, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 51.65/7.98 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 51.65/7.98 = (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 51.65/7.98 X0))) @
% 51.65/7.98 X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 51.65/7.98 thf(zip_derived_cl52, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ X3 @ (inverse @ (multiply @ X1 @ X0))))
% 51.65/7.98 = (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0)))))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl35])).
% 51.65/7.98 thf(zip_derived_cl196, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ (multiply @ X4 @ (inverse @ X1))) @
% 51.65/7.98 (multiply @ X4 @ (inverse @ X0)))
% 51.65/7.98 = (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X1))) @
% 51.65/7.98 (multiply @ X3 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @ X1))) @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @ X0))))) @
% 51.65/7.98 X1)))))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl57, zip_derived_cl52])).
% 51.65/7.98 thf(zip_derived_cl57, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))))) @
% 51.65/7.98 X0) = (X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl13])).
% 51.65/7.98 thf(zip_derived_cl234, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ (multiply @ X4 @ (inverse @ X1))) @
% 51.65/7.98 (multiply @ X4 @ (inverse @ X0)))
% 51.65/7.98 = (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X1))) @
% 51.65/7.98 (multiply @ X3 @ (inverse @ X0))))),
% 51.65/7.98 inference('demod', [status(thm)], [zip_derived_cl196, zip_derived_cl57])).
% 51.65/7.98 thf(zip_derived_cl284, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ X0) @ (multiply @ X4 @ (inverse @ X1)))
% 51.65/7.98 = (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @
% 51.65/7.98 X0))) @
% 51.65/7.98 X3)))) @
% 51.65/7.98 (multiply @ X2 @ (inverse @ X1))))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl234])).
% 51.65/7.98 thf(zip_derived_cl457, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ X1) @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 51.65/7.98 (inverse @ X3)))
% 51.65/7.98 = (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ X4 @
% 51.65/7.98 (multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 51.65/7.98 (inverse @ X1)) @
% 51.65/7.98 X0))))) @
% 51.65/7.98 (multiply @ X4 @ (inverse @ X3))))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl284])).
% 51.65/7.98 thf(zip_derived_cl657, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 51.65/7.98 ((multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @ X0)) @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @
% 51.65/7.98 (inverse @ X1)))
% 51.65/7.98 = (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 51.65/7.98 (multiply @ X2 @ (inverse @ X1))))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl457])).
% 51.65/7.98 thf(zip_derived_cl752, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 51.65/7.98 ((multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @ X5)) @
% 51.65/7.98 X0)
% 51.65/7.98 = (multiply @ (inverse @ (multiply @ X4 @ X5)) @
% 51.65/7.98 (multiply @ X4 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 51.65/7.98 (inverse @ X1))) @
% 51.65/7.98 X0))) @
% 51.65/7.98 X1)))))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl657])).
% 51.65/7.98 thf(zip_derived_cl3, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ X3 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0)) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 51.65/7.98 (inverse @ X1))) @
% 51.65/7.98 X0))) @
% 51.65/7.98 X1)))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 51.65/7.98 thf(zip_derived_cl804, plain,
% 51.65/7.98 (![X0 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 51.65/7.98 ((multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @ X5)) @
% 51.65/7.98 X0)
% 51.65/7.98 = (multiply @ (inverse @ (multiply @ X4 @ X5)) @
% 51.65/7.98 (multiply @ X4 @
% 51.65/7.98 (multiply @ X3 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0)) @
% 51.65/7.98 X2))))))),
% 51.65/7.98 inference('demod', [status(thm)], [zip_derived_cl752, zip_derived_cl3])).
% 51.65/7.98 thf(zip_derived_cl1086, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 51.65/7.98 ((multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X4)) @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X0))
% 51.65/7.98 = (multiply @ (inverse @ (multiply @ X3 @ X4)) @
% 51.65/7.98 (multiply @ X3 @ X0)))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl804])).
% 51.65/7.98 thf(zip_derived_cl3, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ X3 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0)) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 51.65/7.98 (inverse @ X1))) @
% 51.65/7.98 X0))) @
% 51.65/7.98 X1)))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 51.65/7.98 thf(zip_derived_cl1222, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 51.65/7.98 ((multiply @ X4 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @ X0))) @
% 51.65/7.98 X3)))
% 51.65/7.98 = (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 51.65/7.98 (multiply @ X1 @ X0)))) @
% 51.65/7.98 X2)))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl1086, zip_derived_cl3])).
% 51.65/7.98 thf(zip_derived_cl0, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ X1 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (X0))),
% 51.65/7.98 inference('cnf', [status(esa)], [single_axiom])).
% 51.65/7.98 thf(zip_derived_cl1344, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((X0)
% 51.65/7.98 = (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 51.65/7.98 (multiply @ X1 @ X0)))) @
% 51.65/7.98 X2)))),
% 51.65/7.98 inference('demod', [status(thm)], [zip_derived_cl1222, zip_derived_cl0])).
% 51.65/7.98 thf(zip_derived_cl1561, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((X1)
% 51.65/7.98 = (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl1344])).
% 51.65/7.98 thf(zip_derived_cl284, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ X0) @ (multiply @ X4 @ (inverse @ X1)))
% 51.65/7.98 = (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @
% 51.65/7.98 X0))) @
% 51.65/7.98 X3)))) @
% 51.65/7.98 (multiply @ X2 @ (inverse @ X1))))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl234])).
% 51.65/7.98 thf(zip_derived_cl234, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ (multiply @ X4 @ (inverse @ X1))) @
% 51.65/7.98 (multiply @ X4 @ (inverse @ X0)))
% 51.65/7.98 = (multiply @ (inverse @ (multiply @ X3 @ (inverse @ X1))) @
% 51.65/7.98 (multiply @ X3 @ (inverse @ X0))))),
% 51.65/7.98 inference('demod', [status(thm)], [zip_derived_cl196, zip_derived_cl57])).
% 51.65/7.98 thf(zip_derived_cl57, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))))) @
% 51.65/7.98 X0) = (X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl13])).
% 51.65/7.98 thf(zip_derived_cl252, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 51.65/7.98 (multiply @ X1 @ (inverse @ X0))))) @
% 51.65/7.98 X2) = (X0))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl234, zip_derived_cl57])).
% 51.65/7.98 thf(zip_derived_cl1086, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 51.65/7.98 ((multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X4)) @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X0))
% 51.65/7.98 = (multiply @ (inverse @ (multiply @ X3 @ X4)) @
% 51.65/7.98 (multiply @ X3 @ X0)))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl804])).
% 51.65/7.98 thf(zip_derived_cl1086, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 51.65/7.98 ((multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X4)) @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @ X0))
% 51.65/7.98 = (multiply @ (inverse @ (multiply @ X3 @ X4)) @
% 51.65/7.98 (multiply @ X3 @ X0)))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl804])).
% 51.65/7.98 thf(zip_derived_cl1241, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ (multiply @ X1 @ X2)) @ (multiply @ X1 @ X0))
% 51.65/7.98 = (multiply @ (inverse @ (multiply @ X3 @ X2)) @
% 51.65/7.98 (multiply @ X3 @ X0)))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl1086, zip_derived_cl1086])).
% 51.65/7.98 thf(zip_derived_cl0, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ X1 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (X0))),
% 51.65/7.98 inference('cnf', [status(esa)], [single_axiom])).
% 51.65/7.98 thf(zip_derived_cl1357, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 51.65/7.98 ((multiply @ X4 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ X0)) @
% 51.65/7.98 (multiply @ X1 @ X0)) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @ (multiply @ X4 @ (inverse @ (multiply @ X3 @ X0)))) @
% 51.65/7.98 X2))) @
% 51.65/7.98 (multiply @ X3 @ X0))))
% 51.65/7.98 = (X2))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl1241, zip_derived_cl0])).
% 51.65/7.98 thf(zip_derived_cl3469, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 51.65/7.98 ((multiply @ X4 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X5 @ X2)) @
% 51.65/7.98 (multiply @ X5 @ X2)) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ X4 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 51.65/7.98 (multiply @ X3 @ (inverse @ X0))))) @
% 51.65/7.98 X2)))) @
% 51.65/7.98 X1))) @
% 51.65/7.98 X0)))
% 51.65/7.98 = (X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl252, zip_derived_cl1357])).
% 51.65/7.98 thf(zip_derived_cl252, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @
% 51.65/7.98 (multiply @ X1 @ (inverse @ X0))))) @
% 51.65/7.98 X2) = (X0))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl234, zip_derived_cl57])).
% 51.65/7.98 thf(zip_derived_cl3596, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i, X5 : $i]:
% 51.65/7.98 ((multiply @ X4 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X5 @ X2)) @
% 51.65/7.98 (multiply @ X5 @ X2)) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X0))) @ X1))) @
% 51.65/7.98 X0)))
% 51.65/7.98 = (X1))),
% 51.65/7.98 inference('demod', [status(thm)], [zip_derived_cl3469, zip_derived_cl252])).
% 51.65/7.98 thf(zip_derived_cl3755, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 51.65/7.98 ((multiply @ X5 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (inverse @ X1) @
% 51.65/7.98 (multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 51.65/7.98 X1))) @
% 51.65/7.98 X0)))) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X5 @ (inverse @ X4))) @ X3))) @
% 51.65/7.98 X4)))
% 51.65/7.98 = (X3))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl284, zip_derived_cl3596])).
% 51.65/7.98 thf(zip_derived_cl0, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ X1 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (X0))),
% 51.65/7.98 inference('cnf', [status(esa)], [single_axiom])).
% 51.65/7.98 thf(zip_derived_cl3815, plain,
% 51.65/7.98 (![X1 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 51.65/7.98 ((multiply @ X5 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X5 @ (inverse @ X4))) @ X3))) @
% 51.65/7.98 X4)))
% 51.65/7.98 = (X3))),
% 51.65/7.98 inference('demod', [status(thm)], [zip_derived_cl3755, zip_derived_cl0])).
% 51.65/7.98 thf(zip_derived_cl3923, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (multiply @ (multiply @ (inverse @ X3) @ X3) @ X0) @ X1)))
% 51.65/7.98 = (multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0) @ X1))))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl1561, zip_derived_cl3815])).
% 51.65/7.98 thf(zip_derived_cl35, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ (multiply @ X3 @ (inverse @ X2))) @
% 51.65/7.98 (multiply @ X3 @ (inverse @ (multiply @ X0 @ X2))))
% 51.65/7.98 = (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X1) @ X1) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @ (inverse @ X1))) @
% 51.65/7.98 X0))) @
% 51.65/7.98 X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl13])).
% 51.65/7.98 thf(zip_derived_cl0, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ X1 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X1 @ (inverse @ X2))) @ X0))) @
% 51.65/7.98 X2)))
% 51.65/7.98 = (X0))),
% 51.65/7.98 inference('cnf', [status(esa)], [single_axiom])).
% 51.65/7.98 thf(zip_derived_cl50, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ (multiply @ (inverse @ X0) @ X0) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 51.65/7.98 = (X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl0])).
% 51.65/7.98 thf(zip_derived_cl4120, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ (multiply @ (inverse @ X0) @ X0) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))
% 51.65/7.98 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl3923, zip_derived_cl50])).
% 51.65/7.98 thf(zip_derived_cl1561, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((X1)
% 51.65/7.98 = (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl1344])).
% 51.65/7.98 thf(zip_derived_cl4275, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 51.65/7.98 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 51.65/7.98 inference('demod', [status(thm)],
% 51.65/7.98 [zip_derived_cl4120, zip_derived_cl1561])).
% 51.65/7.98 thf(zip_derived_cl4275, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 51.65/7.98 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 51.65/7.98 inference('demod', [status(thm)],
% 51.65/7.98 [zip_derived_cl4120, zip_derived_cl1561])).
% 51.65/7.98 thf(zip_derived_cl4275, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 51.65/7.98 = (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))),
% 51.65/7.98 inference('demod', [status(thm)],
% 51.65/7.98 [zip_derived_cl4120, zip_derived_cl1561])).
% 51.65/7.98 thf(zip_derived_cl50, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ (multiply @ (inverse @ X0) @ X0) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 51.65/7.98 = (X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl0])).
% 51.65/7.98 thf(zip_derived_cl4350, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ (multiply @ (inverse @ X3) @ X3) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 51.65/7.98 = (X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl4275, zip_derived_cl50])).
% 51.65/7.98 thf(zip_derived_cl4824, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 51.65/7.98 ((multiply @ (multiply @ (inverse @ X4) @ X4) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X3) @ X3) @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 51.65/7.98 (inverse @ (multiply @ X1 @ X0))))))
% 51.65/7.98 = (X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl4275, zip_derived_cl4350])).
% 51.65/7.98 thf(zip_derived_cl8370, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 51.65/7.98 ((multiply @ (multiply @ (inverse @ X5) @ X5) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X4) @ X4) @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X3) @ X3) @
% 51.65/7.98 (inverse @ (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0))))))
% 51.65/7.98 = (multiply @ (inverse @ X2) @ X2))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl4275, zip_derived_cl4824])).
% 51.65/7.98 thf(zip_derived_cl3923, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (multiply @ (multiply @ (inverse @ X3) @ X3) @ X0) @ X1)))
% 51.65/7.98 = (multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0) @ X1))))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl1561, zip_derived_cl3815])).
% 51.65/7.98 thf(zip_derived_cl50, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ (multiply @ (inverse @ X0) @ X0) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 51.65/7.98 = (X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl0])).
% 51.65/7.98 thf(zip_derived_cl1241, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ (multiply @ X1 @ X2)) @ (multiply @ X1 @ X0))
% 51.65/7.98 = (multiply @ (inverse @ (multiply @ X3 @ X2)) @
% 51.65/7.98 (multiply @ X3 @ X0)))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl1086, zip_derived_cl1086])).
% 51.65/7.98 thf(zip_derived_cl1452, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ X0) @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))
% 51.65/7.98 = (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X4 @ (inverse @ X3))) @
% 51.65/7.98 (multiply @ X4 @ (inverse @ (multiply @ X0 @ X3))))))) @
% 51.65/7.98 (multiply @ X2 @ X1)))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl50, zip_derived_cl1241])).
% 51.65/7.98 thf(zip_derived_cl4122, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 51.65/7.98 ((multiply @
% 51.65/7.98 (inverse @ (multiply @ (multiply @ (inverse @ X5) @ X5) @ X1)) @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X3))
% 51.65/7.98 = (multiply @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ X4 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))) @
% 51.65/7.98 (multiply @ X4 @ X3)))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl3923, zip_derived_cl1452])).
% 51.65/7.98 thf(zip_derived_cl1561, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 51.65/7.98 ((X1)
% 51.65/7.98 = (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ X2 @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1) @ X0))))))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl1344])).
% 51.65/7.98 thf(zip_derived_cl4277, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 51.65/7.98 ((multiply @
% 51.65/7.98 (inverse @ (multiply @ (multiply @ (inverse @ X5) @ X5) @ X1)) @
% 51.65/7.98 (multiply @ (multiply @ (inverse @ X0) @ X0) @ X3))
% 51.65/7.98 = (multiply @ (inverse @ (multiply @ X4 @ X1)) @
% 51.65/7.98 (multiply @ X4 @ X3)))),
% 51.65/7.98 inference('demod', [status(thm)],
% 51.65/7.98 [zip_derived_cl4122, zip_derived_cl1561])).
% 51.65/7.98 thf(zip_derived_cl4350, plain,
% 51.65/7.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 51.65/7.98 ((multiply @ (multiply @ (inverse @ X3) @ X3) @
% 51.65/7.98 (inverse @
% 51.65/7.98 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X0))) @
% 51.65/7.98 (multiply @ X2 @ (inverse @ (multiply @ X1 @ X0))))))
% 51.65/7.98 = (X1))),
% 51.65/7.98 inference('sup+', [status(thm)], [zip_derived_cl4275, zip_derived_cl50])).
% 51.65/7.98 thf(zip_derived_cl8481, plain,
% 51.65/7.98 (![X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X2) @ X2))),
% 51.65/7.98 inference('demod', [status(thm)],
% 51.65/7.98 [zip_derived_cl8370, zip_derived_cl4277, zip_derived_cl4350])).
% 51.65/7.98 thf(prove_these_axioms_1, conjecture,
% 51.65/7.98 (( multiply @ ( inverse @ a1 ) @ a1 ) =
% 51.65/7.98 ( multiply @ ( inverse @ b1 ) @ b1 ))).
% 51.65/7.98 thf(zf_stmt_0, negated_conjecture,
% 51.65/7.98 (( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 51.65/7.98 ( multiply @ ( inverse @ b1 ) @ b1 )),
% 51.65/7.98 inference('cnf.neg', [status(esa)], [prove_these_axioms_1])).
% 51.65/7.98 thf(zip_derived_cl1, plain,
% 51.65/7.98 (((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ b1) @ b1))),
% 51.65/7.98 inference('cnf', [status(esa)], [zf_stmt_0])).
% 51.65/7.98 thf(zip_derived_cl8701, plain,
% 51.65/7.98 (![X0 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ X0) @ X0))),
% 51.65/7.98 inference('sup-', [status(thm)], [zip_derived_cl8481, zip_derived_cl1])).
% 51.65/7.98 thf(zip_derived_cl8481, plain,
% 51.65/7.98 (![X1 : $i, X2 : $i]:
% 51.65/7.98 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X2) @ X2))),
% 51.65/7.98 inference('demod', [status(thm)],
% 51.65/7.98 [zip_derived_cl8370, zip_derived_cl4277, zip_derived_cl4350])).
% 51.65/7.98 thf(zip_derived_cl8878, plain, ($false),
% 51.65/7.98 inference('simplify_reflect+', [status(thm)],
% 51.65/7.98 [zip_derived_cl8701, zip_derived_cl8481])).
% 51.65/7.98
% 51.65/7.98 % SZS output end Refutation
% 51.65/7.98
% 51.65/7.98
% 51.65/7.98 % Terminating...
% 52.23/8.10 % Runner terminated.
% 52.23/8.12 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------