TSTP Solution File: GRP438-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP438-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.JYQIzK7S8V true
% Computer : n008.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 Aug 31 01:51:39 EDT 2023
% Result : Unsatisfiable 31.61s 5.09s
% Output : Refutation 31.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP438-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.JYQIzK7S8V true
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 23:05:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.21/0.64 % Total configuration time : 435
% 0.21/0.64 % Estimated wc time : 1092
% 0.21/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 31.61/5.09 % Solved by fo/fo7.sh.
% 31.61/5.09 % done 878 iterations in 4.305s
% 31.61/5.09 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 31.61/5.09 % SZS output start Refutation
% 31.61/5.09 thf(inverse_type, type, inverse: $i > $i).
% 31.61/5.09 thf(a3_type, type, a3: $i).
% 31.61/5.09 thf(b3_type, type, b3: $i).
% 31.61/5.09 thf(multiply_type, type, multiply: $i > $i > $i).
% 31.61/5.09 thf(c3_type, type, c3: $i).
% 31.61/5.09 thf(prove_these_axioms_3, conjecture,
% 31.61/5.09 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 31.61/5.09 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 31.61/5.09 thf(zf_stmt_0, negated_conjecture,
% 31.61/5.09 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 31.61/5.09 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 31.61/5.09 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 31.61/5.09 thf(zip_derived_cl1, plain,
% 31.61/5.09 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 31.61/5.09 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 31.61/5.09 inference('cnf', [status(esa)], [zf_stmt_0])).
% 31.61/5.09 thf(single_axiom, axiom,
% 31.61/5.09 (( multiply @
% 31.61/5.09 A @
% 31.61/5.09 ( inverse @
% 31.61/5.09 ( multiply @
% 31.61/5.09 B @
% 31.61/5.09 ( multiply @
% 31.61/5.09 C @
% 31.61/5.09 ( multiply @
% 31.61/5.09 ( multiply @
% 31.61/5.10 ( inverse @ C ) @ ( inverse @ ( multiply @ D @ B ) ) ) @
% 31.61/5.10 A ) ) ) ) ) =
% 31.61/5.10 ( D ))).
% 31.61/5.10 thf(zip_derived_cl0, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 31.61/5.10 X1)))))
% 31.61/5.10 = (X0))),
% 31.61/5.10 inference('cnf', [status(esa)], [single_axiom])).
% 31.61/5.10 thf(zip_derived_cl0, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 31.61/5.10 X1)))))
% 31.61/5.10 = (X0))),
% 31.61/5.10 inference('cnf', [status(esa)], [single_axiom])).
% 31.61/5.10 thf(zip_derived_cl4, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X2 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X1))) @
% 31.61/5.10 (inverse @ X3))) @
% 31.61/5.10 (multiply @ X3 @ (multiply @ X0 @ X2)))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl0, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 31.61/5.10 X1)))))
% 31.61/5.10 = (X0))),
% 31.61/5.10 inference('cnf', [status(esa)], [single_axiom])).
% 31.61/5.10 thf(zip_derived_cl13, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 31.61/5.10 ((multiply @ X4 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ (multiply @ X1 @ (multiply @ X2 @ (inverse @ X5))) @
% 31.61/5.10 (multiply @ X5 @ (multiply @ X0 @ X4)))))
% 31.61/5.10 = (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X0))) @
% 31.61/5.10 (inverse @ X1))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl4, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X2 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X1))) @
% 31.61/5.10 (inverse @ X3))) @
% 31.61/5.10 (multiply @ X3 @ (multiply @ X0 @ X2)))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl41, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 31.61/5.10 X1))) @
% 31.61/5.10 (inverse @ X0)))
% 31.61/5.10 = (X2))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 31.61/5.10 thf(zip_derived_cl13, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 31.61/5.10 ((multiply @ X4 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ (multiply @ X1 @ (multiply @ X2 @ (inverse @ X5))) @
% 31.61/5.10 (multiply @ X5 @ (multiply @ X0 @ X4)))))
% 31.61/5.10 = (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X0))) @
% 31.61/5.10 (inverse @ X1))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl13, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 31.61/5.10 ((multiply @ X4 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ (multiply @ X1 @ (multiply @ X2 @ (inverse @ X5))) @
% 31.61/5.10 (multiply @ X5 @ (multiply @ X0 @ X4)))))
% 31.61/5.10 = (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X0))) @
% 31.61/5.10 (inverse @ X1))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl43, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X1))) @
% 31.61/5.10 (inverse @ X0)))
% 31.61/5.10 = (multiply @ X4 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X2 @ X1))) @
% 31.61/5.10 (inverse @ X0))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl13])).
% 31.61/5.10 thf(zip_derived_cl460, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 31.61/5.10 ((multiply @ X6 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X6) @ (inverse @ X0)) @
% 31.61/5.10 (inverse @ X1)))
% 31.61/5.10 = (multiply @ X5 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X5) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X4) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X2) @
% 31.61/5.10 (inverse @ (multiply @ X3 @ X0))) @
% 31.61/5.10 X3))) @
% 31.61/5.10 (inverse @ X2))))) @
% 31.61/5.10 (inverse @ X1))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl43])).
% 31.61/5.10 thf(zip_derived_cl41, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 31.61/5.10 X1))) @
% 31.61/5.10 (inverse @ X0)))
% 31.61/5.10 = (X2))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 31.61/5.10 thf(zip_derived_cl498, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X5 : $i, X6 : $i]:
% 31.61/5.10 ((multiply @ X6 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X6) @ (inverse @ X0)) @
% 31.61/5.10 (inverse @ X1)))
% 31.61/5.10 = (multiply @ X5 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X5) @ (inverse @ X0)) @
% 31.61/5.10 (inverse @ X1))))),
% 31.61/5.10 inference('demod', [status(thm)], [zip_derived_cl460, zip_derived_cl41])).
% 31.61/5.10 thf(zip_derived_cl0, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 31.61/5.10 X1)))))
% 31.61/5.10 = (X0))),
% 31.61/5.10 inference('cnf', [status(esa)], [single_axiom])).
% 31.61/5.10 thf(zip_derived_cl13, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 31.61/5.10 ((multiply @ X4 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ (multiply @ X1 @ (multiply @ X2 @ (inverse @ X5))) @
% 31.61/5.10 (multiply @ X5 @ (multiply @ X0 @ X4)))))
% 31.61/5.10 = (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X0))) @
% 31.61/5.10 (inverse @ X1))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl0, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 31.61/5.10 X1)))))
% 31.61/5.10 = (X0))),
% 31.61/5.10 inference('cnf', [status(esa)], [single_axiom])).
% 31.61/5.10 thf(zip_derived_cl28, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ X4) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X1 @
% 31.61/5.10 (multiply @ X0 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X4 @ (multiply @ X3 @ (inverse @ X2))) @
% 31.61/5.10 (multiply @ X2 @ (multiply @ X1 @ X0))))))))
% 31.61/5.10 = (X3))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl101, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ X4) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X0 @
% 31.61/5.10 (multiply @ X4 @ (multiply @ X1 @ (inverse @ X3)))))) @
% 31.61/5.10 X0)))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl28])).
% 31.61/5.10 thf(zip_derived_cl0, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 31.61/5.10 X1)))))
% 31.61/5.10 = (X0))),
% 31.61/5.10 inference('cnf', [status(esa)], [single_axiom])).
% 31.61/5.10 thf(zip_derived_cl128, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X4 @
% 31.61/5.10 (inverse @ (multiply @ X3 @ (multiply @ X2 @ (multiply @ X0 @ X4)))))
% 31.61/5.10 = (multiply @ (inverse @ X1) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @ X2 @ (multiply @ X0 @ (inverse @ X1)))))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl101, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ X4) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X0 @
% 31.61/5.10 (multiply @ X4 @ (multiply @ X1 @ (inverse @ X3)))))) @
% 31.61/5.10 X0)))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl28])).
% 31.61/5.10 thf(zip_derived_cl167, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ X2) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X0 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))) @
% 31.61/5.10 X3)))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl128, zip_derived_cl101])).
% 31.61/5.10 thf(zip_derived_cl535, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X0) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X2) @ (inverse @ X1)) @
% 31.61/5.10 (inverse @ X0)))))) @
% 31.61/5.10 X4)))
% 31.61/5.10 = (multiply @ (inverse @ X3) @ (inverse @ X1)))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl498, zip_derived_cl167])).
% 31.61/5.10 thf(zip_derived_cl128, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X4 @
% 31.61/5.10 (inverse @ (multiply @ X3 @ (multiply @ X2 @ (multiply @ X0 @ X4)))))
% 31.61/5.10 = (multiply @ (inverse @ X1) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @ X2 @ (multiply @ X0 @ (inverse @ X1)))))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl128, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X4 @
% 31.61/5.10 (inverse @ (multiply @ X3 @ (multiply @ X2 @ (multiply @ X0 @ X4)))))
% 31.61/5.10 = (multiply @ (inverse @ X1) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @ X2 @ (multiply @ X0 @ (inverse @ X1)))))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl169, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X4 @
% 31.61/5.10 (inverse @ (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X4)))))
% 31.61/5.10 = (multiply @ X0 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl128, zip_derived_cl128])).
% 31.61/5.10 thf(zip_derived_cl605, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X0 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X2) @ (inverse @ X1)) @ X0))))) @
% 31.61/5.10 X4)))
% 31.61/5.10 = (multiply @ (inverse @ X3) @ (inverse @ X1)))),
% 31.61/5.10 inference('demod', [status(thm)], [zip_derived_cl535, zip_derived_cl169])).
% 31.61/5.10 thf(zip_derived_cl41, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 31.61/5.10 X1))) @
% 31.61/5.10 (inverse @ X0)))
% 31.61/5.10 = (X2))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 31.61/5.10 thf(zip_derived_cl728, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 31.61/5.10 ((multiply @ X6 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X6) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X5) @
% 31.61/5.10 (inverse @ (multiply @ (inverse @ X1) @ (inverse @ X0)))) @
% 31.61/5.10 (inverse @ X1)))) @
% 31.61/5.10 (inverse @ X5)))
% 31.61/5.10 = (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X4) @ (inverse @ X0)) @
% 31.61/5.10 X3))))) @
% 31.61/5.10 X2)))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl605, zip_derived_cl41])).
% 31.61/5.10 thf(zip_derived_cl41, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 31.61/5.10 X1))) @
% 31.61/5.10 (inverse @ X0)))
% 31.61/5.10 = (X2))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 31.61/5.10 thf(zip_derived_cl167, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ X2) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X0 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))) @
% 31.61/5.10 X3)))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl128, zip_derived_cl101])).
% 31.61/5.10 thf(zip_derived_cl248, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X4 @ X0))) @
% 31.61/5.10 X4)))
% 31.61/5.10 = (multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X1 @ X0))) @
% 31.61/5.10 X1))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl167])).
% 31.61/5.10 thf(zip_derived_cl41, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 31.61/5.10 X1))) @
% 31.61/5.10 (inverse @ X0)))
% 31.61/5.10 = (X2))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 31.61/5.10 thf(zip_derived_cl794, plain,
% 31.61/5.10 (![X0 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((inverse @ X0)
% 31.61/5.10 = (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X4) @ (inverse @ X0)) @
% 31.61/5.10 X3))))) @
% 31.61/5.10 X2)))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl728, zip_derived_cl248, zip_derived_cl41])).
% 31.61/5.10 thf(zip_derived_cl4, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X2 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X1))) @
% 31.61/5.10 (inverse @ X3))) @
% 31.61/5.10 (multiply @ X3 @ (multiply @ X0 @ X2)))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl41, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 31.61/5.10 X1))) @
% 31.61/5.10 (inverse @ X0)))
% 31.61/5.10 = (X2))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 31.61/5.10 thf(zip_derived_cl81, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 31.61/5.10 ((multiply @ X5 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X5) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X0 @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X2 @ X0))) @
% 31.61/5.10 (inverse @ X3)))))) @
% 31.61/5.10 (inverse @ X1)))
% 31.61/5.10 = (multiply @ X3 @ (multiply @ X2 @ (inverse @ X1))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl41])).
% 31.61/5.10 thf(zip_derived_cl2728, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i,
% 31.61/5.10 X7 : $i, X8 : $i]:
% 31.61/5.10 ((multiply @ X8 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X8) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X6 @
% 31.61/5.10 (multiply @ X7 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X7) @ (inverse @ (multiply @ X2 @ X6))) @
% 31.61/5.10 (inverse @ X0)))))) @
% 31.61/5.10 (inverse @ X1)))
% 31.61/5.10 = (multiply @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @ X5 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X5) @ (inverse @ X0)) @
% 31.61/5.10 X4))))) @
% 31.61/5.10 X3) @
% 31.61/5.10 (multiply @ X2 @ (inverse @ X1))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl794, zip_derived_cl81])).
% 31.61/5.10 thf(zip_derived_cl81, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 31.61/5.10 ((multiply @ X5 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X5) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X0 @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X2 @ X0))) @
% 31.61/5.10 (inverse @ X3)))))) @
% 31.61/5.10 (inverse @ X1)))
% 31.61/5.10 = (multiply @ X3 @ (multiply @ X2 @ (inverse @ X1))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl41])).
% 31.61/5.10 thf(zip_derived_cl2807, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 31.61/5.10 ((multiply @ X0 @ (multiply @ X2 @ (inverse @ X1)))
% 31.61/5.10 = (multiply @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @ X5 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X5) @ (inverse @ X0)) @
% 31.61/5.10 X4))))) @
% 31.61/5.10 X3) @
% 31.61/5.10 (multiply @ X2 @ (inverse @ X1))))),
% 31.61/5.10 inference('demod', [status(thm)], [zip_derived_cl2728, zip_derived_cl81])).
% 31.61/5.10 thf(zip_derived_cl0, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 31.61/5.10 X1)))))
% 31.61/5.10 = (X0))),
% 31.61/5.10 inference('cnf', [status(esa)], [single_axiom])).
% 31.61/5.10 thf(zip_derived_cl2827, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 31.61/5.10 ((multiply @ X6 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ (multiply @ X1 @ (inverse @ X0)) @
% 31.61/5.10 (multiply @ X7 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X7) @
% 31.61/5.10 (inverse @ (multiply @ X2 @ (multiply @ X1 @ (inverse @ X0))))) @
% 31.61/5.10 X6)))))
% 31.61/5.10 = (multiply @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @ X5 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X5) @ (inverse @ X2)) @ X4))))) @
% 31.61/5.10 X3))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl2807, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl0, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 31.61/5.10 X1)))))
% 31.61/5.10 = (X0))),
% 31.61/5.10 inference('cnf', [status(esa)], [single_axiom])).
% 31.61/5.10 thf(zip_derived_cl3019, plain,
% 31.61/5.10 (![X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 31.61/5.10 ((X2)
% 31.61/5.10 = (multiply @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @ X5 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X5) @ (inverse @ X2)) @ X4))))) @
% 31.61/5.10 X3))),
% 31.61/5.10 inference('demod', [status(thm)], [zip_derived_cl2827, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl167, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ X2) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X0 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X3 @ (multiply @ X2 @ (multiply @ X1 @ X0))))) @
% 31.61/5.10 X3)))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl128, zip_derived_cl101])).
% 31.61/5.10 thf(zip_derived_cl4, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X2 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X4) @ (inverse @ (multiply @ X0 @ X1))) @
% 31.61/5.10 (inverse @ X3))) @
% 31.61/5.10 (multiply @ X3 @ (multiply @ X0 @ X2)))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl236, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 31.61/5.10 ((multiply @ X2 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ (multiply @ X4 @ (multiply @ X0 @ (inverse @ X5))) @
% 31.61/5.10 (multiply @ X5 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X1 @ (multiply @ X4 @ (multiply @ X0 @ X3))))) @
% 31.61/5.10 X2)))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl167, zip_derived_cl4])).
% 31.61/5.10 thf(zip_derived_cl3141, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X3) @ (inverse @ X0)) @
% 31.61/5.10 (inverse @ X4))) @
% 31.61/5.10 (multiply @ X4 @ X0))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl3019, zip_derived_cl236])).
% 31.61/5.10 thf(zip_derived_cl3141, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X3) @ (inverse @ X0)) @
% 31.61/5.10 (inverse @ X4))) @
% 31.61/5.10 (multiply @ X4 @ X0))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl3019, zip_derived_cl236])).
% 31.61/5.10 thf(zip_derived_cl498, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X5 : $i, X6 : $i]:
% 31.61/5.10 ((multiply @ X6 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X6) @ (inverse @ X0)) @
% 31.61/5.10 (inverse @ X1)))
% 31.61/5.10 = (multiply @ X5 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X5) @ (inverse @ X0)) @
% 31.61/5.10 (inverse @ X1))))),
% 31.61/5.10 inference('demod', [status(thm)], [zip_derived_cl460, zip_derived_cl41])).
% 31.61/5.10 thf(zip_derived_cl3310, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 31.61/5.10 ((multiply @ X5 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X5) @ (inverse @ X0)) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X4) @ (inverse @ X2)) @
% 31.61/5.10 (inverse @ X3))) @
% 31.61/5.10 (multiply @ X3 @ X2)))))
% 31.61/5.10 = (multiply @ X1 @ (multiply @ (inverse @ X1) @ (inverse @ X0))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl3141, zip_derived_cl498])).
% 31.61/5.10 thf(zip_derived_cl3141, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X3) @ (inverse @ X0)) @
% 31.61/5.10 (inverse @ X4))) @
% 31.61/5.10 (multiply @ X4 @ X0))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl3019, zip_derived_cl236])).
% 31.61/5.10 thf(zip_derived_cl3423, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X5 : $i]:
% 31.61/5.10 ((multiply @ X5 @ (multiply @ (inverse @ X5) @ (inverse @ X0)))
% 31.61/5.10 = (multiply @ X1 @ (multiply @ (inverse @ X1) @ (inverse @ X0))))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl3310, zip_derived_cl3141])).
% 31.61/5.10 thf(zip_derived_cl3568, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X0 @ (inverse @ X0))
% 31.61/5.10 = (multiply @ X4 @
% 31.61/5.10 (multiply @ (inverse @ X4) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X3) @ (inverse @ X1)) @
% 31.61/5.10 (inverse @ X2))) @
% 31.61/5.10 (multiply @ X2 @ X1))))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl3141, zip_derived_cl3423])).
% 31.61/5.10 thf(zip_derived_cl3141, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X3) @ (inverse @ X0)) @
% 31.61/5.10 (inverse @ X4))) @
% 31.61/5.10 (multiply @ X4 @ X0))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl3019, zip_derived_cl236])).
% 31.61/5.10 thf(zip_derived_cl3631, plain,
% 31.61/5.10 (![X0 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X4 @ (inverse @ X4)))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl3568, zip_derived_cl3141])).
% 31.61/5.10 thf(zip_derived_cl41, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 31.61/5.10 X1))) @
% 31.61/5.10 (inverse @ X0)))
% 31.61/5.10 = (X2))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 31.61/5.10 thf(zip_derived_cl3141, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X3) @ (inverse @ X0)) @
% 31.61/5.10 (inverse @ X4))) @
% 31.61/5.10 (multiply @ X4 @ X0))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl3019, zip_derived_cl236])).
% 31.61/5.10 thf(zip_derived_cl3355, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X0 @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X2 @ X0))) @
% 31.61/5.10 X2)))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl3141])).
% 31.61/5.10 thf(zip_derived_cl4847, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X0 @ (inverse @ X0))
% 31.61/5.10 = (multiply @ X2 @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X1 @ X2))) @
% 31.61/5.10 X1))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl3631, zip_derived_cl3355])).
% 31.61/5.10 thf(zip_derived_cl0, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 31.61/5.10 X1)))))
% 31.61/5.10 = (X0))),
% 31.61/5.10 inference('cnf', [status(esa)], [single_axiom])).
% 31.61/5.10 thf(zip_derived_cl5197, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl4847, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl5197, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl4847, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl41, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 31.61/5.10 X1))) @
% 31.61/5.10 (inverse @ X0)))
% 31.61/5.10 = (X2))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 31.61/5.10 thf(zip_derived_cl794, plain,
% 31.61/5.10 (![X0 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((inverse @ X0)
% 31.61/5.10 = (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X4) @ (inverse @ X0)) @
% 31.61/5.10 X3))))) @
% 31.61/5.10 X2)))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl728, zip_derived_cl248, zip_derived_cl41])).
% 31.61/5.10 thf(zip_derived_cl850, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X3 @ X0))) @ X3))
% 31.61/5.10 = (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X2) @ (inverse @ (multiply @ X1 @ X0))) @
% 31.61/5.10 X1)))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl794])).
% 31.61/5.10 thf(zip_derived_cl5583, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X0) @
% 31.61/5.10 (inverse @ (multiply @ X2 @ (inverse @ X1)))) @
% 31.61/5.10 X2))
% 31.61/5.10 = (inverse @ (multiply @ (inverse @ X0) @ X1)))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl5197, zip_derived_cl850])).
% 31.61/5.10 thf(zip_derived_cl5197, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl4847, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl0, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 31.61/5.10 X1)))))
% 31.61/5.10 = (X0))),
% 31.61/5.10 inference('cnf', [status(esa)], [single_axiom])).
% 31.61/5.10 thf(zip_derived_cl5572, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ X2 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ (inverse @ X1) @
% 31.61/5.10 (multiply @ X0 @ (multiply @ (inverse @ X0) @ X2)))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl5197, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl6345, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X3 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X0)) @
% 31.61/5.10 (multiply @ X4 @ (multiply @ (inverse @ X4) @ X3)))))
% 31.61/5.10 = (multiply @
% 31.61/5.10 (multiply @ (inverse @ X1) @
% 31.61/5.10 (inverse @ (multiply @ X2 @ (inverse @ X0)))) @
% 31.61/5.10 X2))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl5583, zip_derived_cl5572])).
% 31.61/5.10 thf(zip_derived_cl5572, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ X2 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ (inverse @ X1) @
% 31.61/5.10 (multiply @ X0 @ (multiply @ (inverse @ X0) @ X2)))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl5197, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl6511, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ X1) @ X0)
% 31.61/5.10 = (multiply @
% 31.61/5.10 (multiply @ (inverse @ X1) @
% 31.61/5.10 (inverse @ (multiply @ X2 @ (inverse @ X0)))) @
% 31.61/5.10 X2))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl6345, zip_derived_cl5572])).
% 31.61/5.10 thf(zip_derived_cl5197, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl4847, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl41, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X0) @ (inverse @ (multiply @ X1 @ X2))) @
% 31.61/5.10 X1))) @
% 31.61/5.10 (inverse @ X0)))
% 31.61/5.10 = (X2))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl4])).
% 31.61/5.10 thf(zip_derived_cl5582, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ X2 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X2) @
% 31.61/5.10 (inverse @ (multiply @ (inverse @ X0) @ X1))) @
% 31.61/5.10 (inverse @ X0)))
% 31.61/5.10 = (inverse @ X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl5197, zip_derived_cl41])).
% 31.61/5.10 thf(zip_derived_cl7115, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0))
% 31.61/5.10 = (inverse @ (inverse @ X0)))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl6511, zip_derived_cl5582])).
% 31.61/5.10 thf(zip_derived_cl7352, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X0 @ (inverse @ X0))
% 31.61/5.10 = (inverse @
% 31.61/5.10 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1))))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl5197, zip_derived_cl7115])).
% 31.61/5.10 thf(zip_derived_cl5572, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ X2 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ (inverse @ X1) @
% 31.61/5.10 (multiply @ X0 @ (multiply @ (inverse @ X0) @ X2)))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl5197, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl7115, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0))
% 31.61/5.10 = (inverse @ (inverse @ X0)))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl6511, zip_derived_cl5582])).
% 31.61/5.10 thf(zip_derived_cl7240, plain,
% 31.61/5.10 (![X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ X2 @
% 31.61/5.10 (inverse @ (multiply @ (inverse @ X1) @ (inverse @ (inverse @ X2)))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl5572, zip_derived_cl7115])).
% 31.61/5.10 thf(zip_derived_cl8085, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @
% 31.61/5.10 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2)))) @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ (inverse @ X1) @
% 31.61/5.10 (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl7352, zip_derived_cl7240])).
% 31.61/5.10 thf(zip_derived_cl5197, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl4847, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl8107, plain,
% 31.61/5.10 (![X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @
% 31.61/5.10 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2)))) @
% 31.61/5.10 (inverse @ (inverse @ X1))) = (X1))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl8085, zip_derived_cl5197])).
% 31.61/5.10 thf(zip_derived_cl3631, plain,
% 31.61/5.10 (![X0 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X4 @ (inverse @ X4)))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl3568, zip_derived_cl3141])).
% 31.61/5.10 thf(zip_derived_cl8158, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((inverse @ (multiply @ X0 @ (inverse @ X0)))
% 31.61/5.10 = (multiply @ X1 @ (inverse @ X1)))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl8107, zip_derived_cl3631])).
% 31.61/5.10 thf(zip_derived_cl6511, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ X1) @ X0)
% 31.61/5.10 = (multiply @
% 31.61/5.10 (multiply @ (inverse @ X1) @
% 31.61/5.10 (inverse @ (multiply @ X2 @ (inverse @ X0)))) @
% 31.61/5.10 X2))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl6345, zip_derived_cl5572])).
% 31.61/5.10 thf(zip_derived_cl8652, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ X3) @ (multiply @ X2 @ (inverse @ X2)))
% 31.61/5.10 = (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @ (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))) @
% 31.61/5.10 X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl8158, zip_derived_cl6511])).
% 31.61/5.10 thf(zip_derived_cl3631, plain,
% 31.61/5.10 (![X0 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X4 @ (inverse @ X4)))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl3568, zip_derived_cl3141])).
% 31.61/5.10 thf(zip_derived_cl3423, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X5 : $i]:
% 31.61/5.10 ((multiply @ X5 @ (multiply @ (inverse @ X5) @ (inverse @ X0)))
% 31.61/5.10 = (multiply @ X1 @ (multiply @ (inverse @ X1) @ (inverse @ X0))))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl3310, zip_derived_cl3141])).
% 31.61/5.10 thf(zip_derived_cl3719, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0)))
% 31.61/5.10 = (multiply @ X2 @
% 31.61/5.10 (multiply @ (inverse @ X2) @ (inverse @ (inverse @ X1)))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl3631, zip_derived_cl3423])).
% 31.61/5.10 thf(zip_derived_cl7115, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0))
% 31.61/5.10 = (inverse @ (inverse @ X0)))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl6511, zip_derived_cl5582])).
% 31.61/5.10 thf(zip_derived_cl7238, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0)))
% 31.61/5.10 = (inverse @ (inverse @ (inverse @ (inverse @ X1)))))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl3719, zip_derived_cl7115])).
% 31.61/5.10 thf(zip_derived_cl8107, plain,
% 31.61/5.10 (![X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @
% 31.61/5.10 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2)))) @
% 31.61/5.10 (inverse @ (inverse @ X1))) = (X1))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl8085, zip_derived_cl5197])).
% 31.61/5.10 thf(zip_derived_cl7238, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0)))
% 31.61/5.10 = (inverse @ (inverse @ (inverse @ (inverse @ X1)))))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl3719, zip_derived_cl7115])).
% 31.61/5.10 thf(zip_derived_cl8163, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0))))
% 31.61/5.10 = (inverse @ (inverse @ (inverse @ (inverse @ X1)))))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl8107, zip_derived_cl7238])).
% 31.61/5.10 thf(zip_derived_cl5197, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl4847, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl8242, plain,
% 31.61/5.10 (![X1 : $i]: ((X1) = (inverse @ (inverse @ (inverse @ (inverse @ X1)))))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl8163, zip_derived_cl5197])).
% 31.61/5.10 thf(zip_derived_cl8245, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))) = (X1))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl7238, zip_derived_cl8242])).
% 31.61/5.10 thf(zip_derived_cl8245, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))) = (X1))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl7238, zip_derived_cl8242])).
% 31.61/5.10 thf(zip_derived_cl8833, plain,
% 31.61/5.10 (![X1 : $i, X3 : $i]:
% 31.61/5.10 ((inverse @ X3)
% 31.61/5.10 = (multiply @ (multiply @ (inverse @ X3) @ (inverse @ X1)) @ X1))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl8652, zip_derived_cl8245, zip_derived_cl8245])).
% 31.61/5.10 thf(zip_derived_cl0, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 31.61/5.10 X1)))))
% 31.61/5.10 = (X0))),
% 31.61/5.10 inference('cnf', [status(esa)], [single_axiom])).
% 31.61/5.10 thf(zip_derived_cl8957, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ (multiply @ X1 @ X2) @
% 31.61/5.10 (inverse @ (multiply @ X2 @ (multiply @ X0 @ (inverse @ X0)))))
% 31.61/5.10 = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl8833, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl8245, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))) = (X1))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl7238, zip_derived_cl8242])).
% 31.61/5.10 thf(zip_derived_cl9029, plain,
% 31.61/5.10 (![X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ (multiply @ X1 @ X2) @ (inverse @ X2)) = (X1))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl8957, zip_derived_cl8245])).
% 31.61/5.10 thf(zip_derived_cl3019, plain,
% 31.61/5.10 (![X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 31.61/5.10 ((X2)
% 31.61/5.10 = (multiply @
% 31.61/5.10 (multiply @ X4 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @ X5 @
% 31.61/5.10 (multiply @ (multiply @ (inverse @ X5) @ (inverse @ X2)) @ X4))))) @
% 31.61/5.10 X3))),
% 31.61/5.10 inference('demod', [status(thm)], [zip_derived_cl2827, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl9221, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((X2)
% 31.61/5.10 = (multiply @
% 31.61/5.10 (multiply @ (inverse @ (inverse @ X2)) @
% 31.61/5.10 (inverse @ (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))) @
% 31.61/5.10 X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl9029, zip_derived_cl3019])).
% 31.61/5.10 thf(zip_derived_cl8245, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))) = (X1))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl7238, zip_derived_cl8242])).
% 31.61/5.10 thf(zip_derived_cl8242, plain,
% 31.61/5.10 (![X1 : $i]: ((X1) = (inverse @ (inverse @ (inverse @ (inverse @ X1)))))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl8163, zip_derived_cl5197])).
% 31.61/5.10 thf(zip_derived_cl8833, plain,
% 31.61/5.10 (![X1 : $i, X3 : $i]:
% 31.61/5.10 ((inverse @ X3)
% 31.61/5.10 = (multiply @ (multiply @ (inverse @ X3) @ (inverse @ X1)) @ X1))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl8652, zip_derived_cl8245, zip_derived_cl8245])).
% 31.61/5.10 thf(zip_derived_cl9014, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((inverse @ (inverse @ (inverse @ (inverse @ X0))))
% 31.61/5.10 = (multiply @ (multiply @ X0 @ (inverse @ X1)) @ X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl8242, zip_derived_cl8833])).
% 31.61/5.10 thf(zip_derived_cl8242, plain,
% 31.61/5.10 (![X1 : $i]: ((X1) = (inverse @ (inverse @ (inverse @ (inverse @ X1)))))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl8163, zip_derived_cl5197])).
% 31.61/5.10 thf(zip_derived_cl9025, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((X0) = (multiply @ (multiply @ X0 @ (inverse @ X1)) @ X1))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl9014, zip_derived_cl8242])).
% 31.61/5.10 thf(zip_derived_cl9295, plain,
% 31.61/5.10 (![X2 : $i]: ((X2) = (inverse @ (inverse @ X2)))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl9221, zip_derived_cl8245, zip_derived_cl9025])).
% 31.61/5.10 thf(zip_derived_cl9295, plain,
% 31.61/5.10 (![X2 : $i]: ((X2) = (inverse @ (inverse @ X2)))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl9221, zip_derived_cl8245, zip_derived_cl9025])).
% 31.61/5.10 thf(zip_derived_cl3631, plain,
% 31.61/5.10 (![X0 : $i, X4 : $i]:
% 31.61/5.10 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X4 @ (inverse @ X4)))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl3568, zip_derived_cl3141])).
% 31.61/5.10 thf(zip_derived_cl9324, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (inverse @ X1)) = (multiply @ (inverse @ X0) @ X0))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl9295, zip_derived_cl3631])).
% 31.61/5.10 thf(zip_derived_cl0, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X1 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X2 @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @ (inverse @ (multiply @ X0 @ X2))) @
% 31.61/5.10 X1)))))
% 31.61/5.10 = (X0))),
% 31.61/5.10 inference('cnf', [status(esa)], [single_axiom])).
% 31.61/5.10 thf(zip_derived_cl10313, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 31.61/5.10 ((multiply @ X2 @
% 31.61/5.10 (inverse @
% 31.61/5.10 (multiply @ X1 @
% 31.61/5.10 (multiply @ X3 @
% 31.61/5.10 (multiply @
% 31.61/5.10 (multiply @ (inverse @ X3) @
% 31.61/5.10 (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 31.61/5.10 X2)))))
% 31.61/5.10 = (inverse @ X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl9324, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl5197, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) = (X1))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl4847, zip_derived_cl0])).
% 31.61/5.10 thf(zip_derived_cl7115, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0))
% 31.61/5.10 = (inverse @ (inverse @ X0)))),
% 31.61/5.10 inference('sup+', [status(thm)], [zip_derived_cl6511, zip_derived_cl5582])).
% 31.61/5.10 thf(zip_derived_cl9295, plain,
% 31.61/5.10 (![X2 : $i]: ((X2) = (inverse @ (inverse @ X2)))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl9221, zip_derived_cl8245, zip_derived_cl9025])).
% 31.61/5.10 thf(zip_derived_cl9299, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i]:
% 31.61/5.10 ((multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)) = (X0))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl7115, zip_derived_cl9295])).
% 31.61/5.10 thf(zip_derived_cl10527, plain,
% 31.61/5.10 (![X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ X2 @ (inverse @ (multiply @ X1 @ X2))) = (inverse @ X1))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl10313, zip_derived_cl5197, zip_derived_cl9299])).
% 31.61/5.10 thf(zip_derived_cl6511, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ X1) @ X0)
% 31.61/5.10 = (multiply @
% 31.61/5.10 (multiply @ (inverse @ X1) @
% 31.61/5.10 (inverse @ (multiply @ X2 @ (inverse @ X0)))) @
% 31.61/5.10 X2))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl6345, zip_derived_cl5572])).
% 31.61/5.10 thf(zip_derived_cl10902, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ X2) @ (multiply @ X0 @ X1))
% 31.61/5.10 = (multiply @
% 31.61/5.10 (multiply @ (inverse @ X2) @ (inverse @ (inverse @ X0))) @ X1))),
% 31.61/5.10 inference('sup+', [status(thm)],
% 31.61/5.10 [zip_derived_cl10527, zip_derived_cl6511])).
% 31.61/5.10 thf(zip_derived_cl9295, plain,
% 31.61/5.10 (![X2 : $i]: ((X2) = (inverse @ (inverse @ X2)))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl9221, zip_derived_cl8245, zip_derived_cl9025])).
% 31.61/5.10 thf(zip_derived_cl11019, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ X2) @ (multiply @ X0 @ X1))
% 31.61/5.10 = (multiply @ (multiply @ (inverse @ X2) @ X0) @ X1))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl10902, zip_derived_cl9295])).
% 31.61/5.10 thf(zip_derived_cl13265, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ (inverse @ (inverse @ X0)) @ (multiply @ X2 @ X1))
% 31.61/5.10 = (multiply @ (multiply @ X0 @ X2) @ X1))),
% 31.61/5.10 inference('sup+', [status(thm)],
% 31.61/5.10 [zip_derived_cl9295, zip_derived_cl11019])).
% 31.61/5.10 thf(zip_derived_cl9295, plain,
% 31.61/5.10 (![X2 : $i]: ((X2) = (inverse @ (inverse @ X2)))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl9221, zip_derived_cl8245, zip_derived_cl9025])).
% 31.61/5.10 thf(zip_derived_cl13279, plain,
% 31.61/5.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 31.61/5.10 ((multiply @ X0 @ (multiply @ X2 @ X1))
% 31.61/5.10 = (multiply @ (multiply @ X0 @ X2) @ X1))),
% 31.61/5.10 inference('demod', [status(thm)],
% 31.61/5.10 [zip_derived_cl13265, zip_derived_cl9295])).
% 31.61/5.10 thf(zip_derived_cl13333, plain,
% 31.61/5.10 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 31.61/5.10 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 31.61/5.10 inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl13279])).
% 31.61/5.10 thf(zip_derived_cl13334, plain, ($false),
% 31.61/5.10 inference('simplify', [status(thm)], [zip_derived_cl13333])).
% 31.61/5.10
% 31.61/5.10 % SZS output end Refutation
% 31.61/5.10
% 31.61/5.10
% 31.61/5.10 % Terminating...
% 31.61/5.16 % Runner terminated.
% 31.61/5.17 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------