%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP417-1 : TPTP v9.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.NiIa91x4Ox true
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:36:24 PM UTC 2025
% Result : Unsatisfiable 14.61s 2.67s
% Output : Refutation 14.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP417-1 : TPTP v9.2.0. Released v2.6.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.NiIa91x4Ox true
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 1 14:14:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35 % Number of cores: 8
% 0.12/0.35 % Python version: Python 3.6.8
% 0.12/0.35 % Running in FO mode
% 0.57/0.65 % Total configuration time : 435
% 0.57/0.65 % Estimated wc time : 1092
% 0.57/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.57/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.57/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.57/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.57/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.57/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.57/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 14.61/2.67 % Solved by fo/fo7.sh.
% 14.61/2.67 % done 871 iterations in 1.889s
% 14.61/2.67 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 14.61/2.67 % SZS output start Refutation
% 14.61/2.67 thf(b3_type, type, b3: $i).
% 14.61/2.67 thf(c3_type, type, c3: $i).
% 14.61/2.67 thf(inverse_type, type, inverse: $i > $i).
% 14.61/2.67 thf(multiply_type, type, multiply: $i > $i > $i).
% 14.61/2.67 thf(a3_type, type, a3: $i).
% 14.61/2.67 thf(prove_these_axioms_3, conjecture,
% 14.61/2.67 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 14.61/2.67 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 14.61/2.67 thf(zf_stmt_0, negated_conjecture,
% 14.61/2.67 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 14.61/2.67 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 14.61/2.67 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 14.61/2.67 thf(zip_derived_cl1, plain,
% 14.61/2.67 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 14.61/2.67 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 14.61/2.67 inference('cnf', [status(esa)], [zf_stmt_0])).
% 14.61/2.67 thf(single_axiom, axiom,
% 14.61/2.67 (( inverse @
% 14.61/2.67 ( multiply @
% 14.61/2.67 A @
% 14.61/2.67 ( inverse @
% 14.61/2.67 ( multiply @
% 14.61/2.67 ( inverse @
% 14.61/2.67 ( multiply @
% 14.61/2.67 ( inverse @ ( multiply @ B @ A ) ) @
% 14.61/2.67 ( multiply @ B @ ( inverse @ C ) ) ) ) @
% 14.61/2.67 ( inverse @ ( multiply @ ( inverse @ A ) @ A ) ) ) ) ) ) =
% 14.61/2.67 ( C ))).
% 14.61/2.67 thf(zip_derived_cl0, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ X0)))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))))
% 14.61/2.67 = (X0))),
% 14.61/2.67 inference('cnf', [status(esa)], [single_axiom])).
% 14.61/2.67 thf(zip_derived_cl0, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ X0)))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))))
% 14.61/2.67 = (X0))),
% 14.61/2.67 inference('cnf', [status(esa)], [single_axiom])).
% 14.61/2.67 thf(zip_derived_cl0, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ X0)))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))))
% 14.61/2.67 = (X0))),
% 14.61/2.67 inference('cnf', [status(esa)], [single_axiom])).
% 14.61/2.67 thf(zip_derived_cl2, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X3 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X4 @ X3)) @
% 14.61/2.67 (multiply @ X4 @ X0))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X3) @ X3))))))
% 14.61/2.67 = (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ X0)))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl0, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ X0)))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))))
% 14.61/2.67 = (X0))),
% 14.61/2.67 inference('cnf', [status(esa)], [single_axiom])).
% 14.61/2.67 thf(zip_derived_cl25, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @ X0 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (inverse @ X1))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0)))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl0, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ X0)))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))))
% 14.61/2.67 = (X0))),
% 14.61/2.67 inference('cnf', [status(esa)], [single_axiom])).
% 14.61/2.67 thf(zip_derived_cl69, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X3 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X3)) @ X0)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X3) @ X3))))))
% 14.61/2.67 = (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (inverse @ X0))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl25, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @ X0 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (inverse @ X1))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0)))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl103, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @ X2 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X0 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ (multiply @ X2 @ X0)) @ X1)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl69, zip_derived_cl25])).
% 14.61/2.67 thf(zip_derived_cl196, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 14.61/2.67 ((multiply @ X2 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X0 @ (inverse @ (multiply @ (inverse @ X1) @ X1))))))))
% 14.61/2.67 = (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @ (multiply @ X3 @ (inverse @ (multiply @ X2 @ X1)))) @
% 14.61/2.67 (multiply @ X3 @ (inverse @ X0)))) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (inverse @ (multiply @ X2 @ X1))) @
% 14.61/2.67 (inverse @ (multiply @ X2 @ X1)))))))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl103])).
% 14.61/2.67 thf(zip_derived_cl25, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @ X0 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (inverse @ X1))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0)))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl1121, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X0 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ X1) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0)))))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl196, zip_derived_cl25])).
% 14.61/2.67 thf(zip_derived_cl69, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X3 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X3)) @ X0)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X3) @ X3))))))
% 14.61/2.67 = (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (inverse @ X0))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl2, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X3 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X4 @ X3)) @
% 14.61/2.67 (multiply @ X4 @ X0))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X3) @ X3))))))
% 14.61/2.67 = (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ X0)))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl0, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ X0)))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))))
% 14.61/2.67 = (X0))),
% 14.61/2.67 inference('cnf', [status(esa)], [single_axiom])).
% 14.61/2.67 thf(zip_derived_cl14, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X0 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @ X1))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0)))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl126, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (inverse @ (multiply @ X0 @ X1)))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl69, zip_derived_cl14])).
% 14.61/2.67 thf(zip_derived_cl69, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X3 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X3)) @ X0)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X3) @ X3))))))
% 14.61/2.67 = (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (inverse @ X0))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl0, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ X0)))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))))
% 14.61/2.67 = (X0))),
% 14.61/2.67 inference('cnf', [status(esa)], [single_axiom])).
% 14.61/2.67 thf(zip_derived_cl124, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @
% 14.61/2.67 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X1))))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))) = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl69, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl0, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ X0)))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))))
% 14.61/2.67 = (X0))),
% 14.61/2.67 inference('cnf', [status(esa)], [single_axiom])).
% 14.61/2.67 thf(zip_derived_cl228, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X2 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X3 @ X1)) @
% 14.61/2.67 (multiply @ X3 @
% 14.61/2.67 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X0))))))) @
% 14.61/2.67 X2)) @
% 14.61/2.67 X0)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X2) @ X2))))))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl124, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl683, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X1)) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @ (inverse @ (multiply @ (inverse @ X1) @ X1))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))))))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl228])).
% 14.61/2.67 thf(zip_derived_cl103, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @ X2 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X0 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ (multiply @ X2 @ X0)) @ X1)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl69, zip_derived_cl25])).
% 14.61/2.67 thf(zip_derived_cl788, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ X0) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X0 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))))))))
% 14.61/2.67 = (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X1)) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @ (inverse @ (multiply @ (inverse @ X0) @ X0))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0)))))))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl683, zip_derived_cl103])).
% 14.61/2.67 thf(zip_derived_cl1121, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X0 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ X1) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0)))))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl196, zip_derived_cl25])).
% 14.61/2.67 thf(zip_derived_cl1668, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (multiply @ (inverse @ X0) @ X0)))) @
% 14.61/2.67 (multiply @ X2 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 14.61/2.67 (multiply @ (inverse @ X0) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X0 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0)))))))))))))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl788, zip_derived_cl1121])).
% 14.61/2.67 thf(zip_derived_cl196, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 14.61/2.67 ((multiply @ X2 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X0 @ (inverse @ (multiply @ (inverse @ X1) @ X1))))))))
% 14.61/2.67 = (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @ (multiply @ X3 @ (inverse @ (multiply @ X2 @ X1)))) @
% 14.61/2.67 (multiply @ X3 @ (inverse @ X0)))) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (inverse @ (multiply @ X2 @ X1))) @
% 14.61/2.67 (inverse @ (multiply @ X2 @ X1)))))))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl103])).
% 14.61/2.67 thf(zip_derived_cl0, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ X0)))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))))
% 14.61/2.67 = (X0))),
% 14.61/2.67 inference('cnf', [status(esa)], [single_axiom])).
% 14.61/2.67 thf(zip_derived_cl1118, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X0 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X1 @ (inverse @ (multiply @ (inverse @ X0) @ X0))))))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl196, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl1716, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (multiply @ (inverse @ X0) @ X0)))) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl1668, zip_derived_cl1118])).
% 14.61/2.67 thf(zip_derived_cl1716, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (multiply @ (inverse @ X0) @ X0)))) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl1668, zip_derived_cl1118])).
% 14.61/2.67 thf(zip_derived_cl2055, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl1716, zip_derived_cl1716])).
% 14.61/2.67 thf(zip_derived_cl2055, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl1716, zip_derived_cl1716])).
% 14.61/2.67 thf(zip_derived_cl0, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ X0)))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))))
% 14.61/2.67 = (X0))),
% 14.61/2.67 inference('cnf', [status(esa)], [single_axiom])).
% 14.61/2.67 thf(zip_derived_cl2287, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ (inverse @ X1) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (inverse @ X1)) @ (inverse @ X1)))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl2055, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl1716, zip_derived_cl1716])).
% 14.61/2.67 thf(zip_derived_cl2407, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ (inverse @ X1) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl2287, zip_derived_cl2055])).
% 14.61/2.67 thf(zip_derived_cl2588, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ (inverse @ X1) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl2407])).
% 14.61/2.67 thf(zip_derived_cl2055, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl1716, zip_derived_cl1716])).
% 14.61/2.67 thf(zip_derived_cl1716, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (multiply @ (inverse @ X0) @ X0)))) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl1668, zip_derived_cl1118])).
% 14.61/2.67 thf(zip_derived_cl14, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X0 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @ X1))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0)))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl1993, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X2 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X1 @ (inverse @ (multiply @ (inverse @ X0) @ X0)))) @
% 14.61/2.67 (multiply @ X1 @ (inverse @ (multiply @ (inverse @ X0) @ X0))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X2) @ X2)))))))
% 14.61/2.67 = (X2))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl1716, zip_derived_cl14])).
% 14.61/2.67 thf(zip_derived_cl1716, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (multiply @ (inverse @ X0) @ X0)))) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl1668, zip_derived_cl1118])).
% 14.61/2.67 thf(zip_derived_cl2198, plain,
% 14.61/2.67 (![X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X2 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X1)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X2) @ X2)))))))
% 14.61/2.67 = (X2))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl1993, zip_derived_cl1716])).
% 14.61/2.67 thf(zip_derived_cl2475, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0)))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl2198])).
% 14.61/2.67 thf(zip_derived_cl3019, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X2 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X3) @ X3)) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X1)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0)))))))))
% 14.61/2.67 = (X2))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2588, zip_derived_cl2475])).
% 14.61/2.67 thf(zip_derived_cl2588, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ (inverse @ X1) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl2407])).
% 14.61/2.67 thf(zip_derived_cl3136, plain,
% 14.61/2.67 (![X2 : $i, X3 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X3) @ X3))))
% 14.61/2.67 = (X2))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl3019, zip_derived_cl2588])).
% 14.61/2.67 thf(zip_derived_cl3728, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ (inverse @ X0))
% 14.61/2.67 = (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X1 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ X0) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1)))))))) @
% 14.61/2.67 X1)))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl1121, zip_derived_cl3136])).
% 14.61/2.67 thf(zip_derived_cl2055, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl1716, zip_derived_cl1716])).
% 14.61/2.67 thf(zip_derived_cl2588, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ (inverse @ X1) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl2407])).
% 14.61/2.67 thf(zip_derived_cl2588, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ (inverse @ X1) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl2407])).
% 14.61/2.67 thf(zip_derived_cl3038, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ (inverse @ X2) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X3) @ X3)) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X1) @ X1)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))))))))
% 14.61/2.67 = (X2))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2588, zip_derived_cl2588])).
% 14.61/2.67 thf(zip_derived_cl2588, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ (inverse @ X1) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl2407])).
% 14.61/2.67 thf(zip_derived_cl3081, plain,
% 14.61/2.67 (![X2 : $i, X3 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X3) @ X3)))
% 14.61/2.67 = (X2))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl3038, zip_derived_cl2588])).
% 14.61/2.67 thf(zip_derived_cl3242, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ (multiply @ (inverse @ X0) @ X0))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl3081])).
% 14.61/2.67 thf(zip_derived_cl3081, plain,
% 14.61/2.67 (![X2 : $i, X3 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X3) @ X3)))
% 14.61/2.67 = (X2))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl3038, zip_derived_cl2588])).
% 14.61/2.67 thf(zip_derived_cl3750, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ (inverse @ X0))
% 14.61/2.67 = (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @ (inverse @ (inverse @ (multiply @ X1 @ X0)))) @ X1)))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl3728, zip_derived_cl3242, zip_derived_cl3081])).
% 14.61/2.67 thf(zip_derived_cl124, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @
% 14.61/2.67 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X1))))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))) = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl69, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl4199, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 14.61/2.67 ((multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X3 @ X2)) @
% 14.61/2.67 (multiply @ X3 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (inverse @ (multiply @ X2 @ (inverse @ (inverse @ X0)))))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X2) @ X2)))
% 14.61/2.67 = (multiply @
% 14.61/2.67 (inverse @ (inverse @ (inverse @ (multiply @ X1 @ X0)))) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl3750, zip_derived_cl124])).
% 14.61/2.67 thf(zip_derived_cl124, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @
% 14.61/2.67 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X1))))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))) = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl69, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl4253, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ X0)
% 14.61/2.67 = (multiply @
% 14.61/2.67 (inverse @ (inverse @ (inverse @ (multiply @ X1 @ X0)))) @ X1))),
% 14.61/2.67 inference('demod', [status(thm)], [zip_derived_cl4199, zip_derived_cl124])).
% 14.61/2.67 thf(zip_derived_cl3242, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ (multiply @ (inverse @ X0) @ X0))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl3081])).
% 14.61/2.67 thf(zip_derived_cl3242, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ (multiply @ (inverse @ X0) @ X0))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl3081])).
% 14.61/2.67 thf(zip_derived_cl3395, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ (inverse @ (multiply @ (inverse @ X0) @ X0)))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl3242, zip_derived_cl3242])).
% 14.61/2.67 thf(zip_derived_cl4253, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ X0)
% 14.61/2.67 = (multiply @
% 14.61/2.67 (inverse @ (inverse @ (inverse @ (multiply @ X1 @ X0)))) @ X1))),
% 14.61/2.67 inference('demod', [status(thm)], [zip_derived_cl4199, zip_derived_cl124])).
% 14.61/2.67 thf(zip_derived_cl3242, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ (multiply @ (inverse @ X0) @ X0))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl3081])).
% 14.61/2.67 thf(zip_derived_cl2055, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl1716, zip_derived_cl1716])).
% 14.61/2.67 thf(zip_derived_cl25, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @ X0 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (inverse @ X1))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0)))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl2290, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ (inverse @ X1)) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (inverse @ (inverse @ X1))) @
% 14.61/2.67 (inverse @ (inverse @ X1)))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl25])).
% 14.61/2.67 thf(zip_derived_cl2055, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ X0) @ X0) = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl1716, zip_derived_cl1716])).
% 14.61/2.67 thf(zip_derived_cl2409, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ (inverse @ X1)) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X1) @ X1)))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl2290, zip_derived_cl2055])).
% 14.61/2.67 thf(zip_derived_cl3486, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ (inverse @ X1)) @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 14.61/2.67 (multiply @ (inverse @ X0) @ X0))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl3242, zip_derived_cl2409])).
% 14.61/2.67 thf(zip_derived_cl3081, plain,
% 14.61/2.67 (![X2 : $i, X3 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X3) @ X3)))
% 14.61/2.67 = (X2))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl3038, zip_derived_cl2588])).
% 14.61/2.67 thf(zip_derived_cl3644, plain,
% 14.61/2.67 (![X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ (inverse @ X1)) @
% 14.61/2.67 (multiply @ (inverse @ X2) @ X2)) = (X1))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl3486, zip_derived_cl3081])).
% 14.61/2.67 thf(zip_derived_cl4282, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ X0)
% 14.61/2.67 = (inverse @ (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0)))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl4253, zip_derived_cl3644])).
% 14.61/2.67 thf(zip_derived_cl124, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @
% 14.61/2.67 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X1))))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))) = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl69, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl4322, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 14.61/2.67 ((multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X3 @ X2)) @
% 14.61/2.67 (multiply @ X3 @
% 14.61/2.67 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X0))))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X2) @ X2)))
% 14.61/2.67 = (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl4282, zip_derived_cl124])).
% 14.61/2.67 thf(zip_derived_cl124, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @
% 14.61/2.67 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X1))))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))) = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl69, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl4364, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((X0) = (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0))),
% 14.61/2.67 inference('demod', [status(thm)], [zip_derived_cl4322, zip_derived_cl124])).
% 14.61/2.67 thf(zip_derived_cl4391, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((X1)
% 14.61/2.67 = (multiply @
% 14.61/2.67 (inverse @ (inverse @ (multiply @ (inverse @ X0) @ X0))) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl3395, zip_derived_cl4364])).
% 14.61/2.67 thf(zip_derived_cl4364, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((X0) = (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0))),
% 14.61/2.67 inference('demod', [status(thm)], [zip_derived_cl4322, zip_derived_cl124])).
% 14.61/2.67 thf(zip_derived_cl126, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @ (inverse @ (inverse @ (multiply @ X0 @ X1)))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl69, zip_derived_cl14])).
% 14.61/2.67 thf(zip_derived_cl4374, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ X0) @
% 14.61/2.67 (multiply @ (multiply @ (inverse @ X2) @ X2) @
% 14.61/2.67 (inverse @ (inverse @ (multiply @ X0 @ X1)))))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl4364, zip_derived_cl126])).
% 14.61/2.67 thf(zip_derived_cl4364, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((X0) = (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0))),
% 14.61/2.67 inference('demod', [status(thm)], [zip_derived_cl4322, zip_derived_cl124])).
% 14.61/2.67 thf(zip_derived_cl3242, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ (multiply @ (inverse @ X0) @ X0))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl3081])).
% 14.61/2.67 thf(zip_derived_cl3081, plain,
% 14.61/2.67 (![X2 : $i, X3 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X3) @ X3)))
% 14.61/2.67 = (X2))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl3038, zip_derived_cl2588])).
% 14.61/2.67 thf(zip_derived_cl3378, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (multiply @ (inverse @ X1) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl3242, zip_derived_cl3081])).
% 14.61/2.67 thf(zip_derived_cl4410, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ X0) @
% 14.61/2.67 (inverse @ (inverse @ (multiply @ X0 @ X1)))) = (X1))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl4374, zip_derived_cl4364, zip_derived_cl3378])).
% 14.61/2.67 thf(zip_derived_cl4621, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((multiply @
% 14.61/2.67 (inverse @ (inverse @ (inverse @ (multiply @ (inverse @ X1) @ X1)))) @
% 14.61/2.67 (inverse @ (inverse @ X0))) = (X0))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl4391, zip_derived_cl4410])).
% 14.61/2.67 thf(zip_derived_cl3242, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ (multiply @ (inverse @ X0) @ X0))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl3081])).
% 14.61/2.67 thf(zip_derived_cl3242, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ (multiply @ (inverse @ X0) @ X0))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl3081])).
% 14.61/2.67 thf(zip_derived_cl3242, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ (multiply @ (inverse @ X0) @ X0))
% 14.61/2.67 = (multiply @ (inverse @ X1) @ X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2055, zip_derived_cl3081])).
% 14.61/2.67 thf(zip_derived_cl4364, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((X0) = (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0))),
% 14.61/2.67 inference('demod', [status(thm)], [zip_derived_cl4322, zip_derived_cl124])).
% 14.61/2.67 thf(zip_derived_cl4641, plain,
% 14.61/2.67 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl4621, zip_derived_cl3242, zip_derived_cl3242,
% 14.61/2.67 zip_derived_cl3242, zip_derived_cl4364])).
% 14.61/2.67 thf(zip_derived_cl4662, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ X0) = (multiply @ (inverse @ (multiply @ X1 @ X0)) @ X1))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl4253, zip_derived_cl4641])).
% 14.61/2.67 thf(zip_derived_cl4662, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ X0) = (multiply @ (inverse @ (multiply @ X1 @ X0)) @ X1))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl4253, zip_derived_cl4641])).
% 14.61/2.67 thf(zip_derived_cl5050, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ X1)
% 14.61/2.67 = (multiply @ (inverse @ (inverse @ X0)) @
% 14.61/2.67 (inverse @ (multiply @ X1 @ X0))))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl4662, zip_derived_cl4662])).
% 14.61/2.67 thf(zip_derived_cl4641, plain,
% 14.61/2.67 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl4621, zip_derived_cl3242, zip_derived_cl3242,
% 14.61/2.67 zip_derived_cl3242, zip_derived_cl4364])).
% 14.61/2.67 thf(zip_derived_cl5067, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((inverse @ X1) = (multiply @ X0 @ (inverse @ (multiply @ X1 @ X0))))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl5050, zip_derived_cl4641])).
% 14.61/2.67 thf(zip_derived_cl4364, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((X0) = (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0))),
% 14.61/2.67 inference('demod', [status(thm)], [zip_derived_cl4322, zip_derived_cl124])).
% 14.61/2.67 thf(zip_derived_cl14, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X0 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @ X1))) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0)))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 14.61/2.67 thf(zip_derived_cl1121, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ X0 @
% 14.61/2.67 (inverse @
% 14.61/2.67 (multiply @ (inverse @ X1) @
% 14.61/2.67 (inverse @ (multiply @ (inverse @ X0) @ X0)))))))))
% 14.61/2.67 = (X1))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl196, zip_derived_cl25])).
% 14.61/2.67 thf(zip_derived_cl1656, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ (multiply @ X3 @ X2)) @ (multiply @ X3 @ X0))
% 14.61/2.67 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 14.61/2.67 (multiply @ X1 @ X0)))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl1121])).
% 14.61/2.67 thf(zip_derived_cl4372, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ X0) @
% 14.61/2.67 (multiply @ (multiply @ (inverse @ X3) @ X3) @ X1))
% 14.61/2.67 = (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @ X1)))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl4364, zip_derived_cl1656])).
% 14.61/2.67 thf(zip_derived_cl4364, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i]:
% 14.61/2.67 ((X0) = (multiply @ (multiply @ (inverse @ X1) @ X1) @ X0))),
% 14.61/2.67 inference('demod', [status(thm)], [zip_derived_cl4322, zip_derived_cl124])).
% 14.61/2.67 thf(zip_derived_cl4408, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ X0) @ X1)
% 14.61/2.67 = (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 14.61/2.67 (multiply @ X2 @ X1)))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl4372, zip_derived_cl4364])).
% 14.61/2.67 thf(zip_derived_cl6899, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @ (inverse @ (inverse @ (multiply @ X0 @ X2))) @ X1)
% 14.61/2.67 = (multiply @ (inverse @ (inverse @ X0)) @ (multiply @ X2 @ X1)))),
% 14.61/2.67 inference('sup+', [status(thm)], [zip_derived_cl5067, zip_derived_cl4408])).
% 14.61/2.67 thf(zip_derived_cl4641, plain,
% 14.61/2.67 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl4621, zip_derived_cl3242, zip_derived_cl3242,
% 14.61/2.67 zip_derived_cl3242, zip_derived_cl4364])).
% 14.61/2.67 thf(zip_derived_cl4641, plain,
% 14.61/2.67 (![X0 : $i]: ((inverse @ (inverse @ X0)) = (X0))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl4621, zip_derived_cl3242, zip_derived_cl3242,
% 14.61/2.67 zip_derived_cl3242, zip_derived_cl4364])).
% 14.61/2.67 thf(zip_derived_cl6945, plain,
% 14.61/2.67 (![X0 : $i, X1 : $i, X2 : $i]:
% 14.61/2.67 ((multiply @ (multiply @ X0 @ X2) @ X1)
% 14.61/2.67 = (multiply @ X0 @ (multiply @ X2 @ X1)))),
% 14.61/2.67 inference('demod', [status(thm)],
% 14.61/2.67 [zip_derived_cl6899, zip_derived_cl4641, zip_derived_cl4641])).
% 14.61/2.67 thf(zip_derived_cl6967, plain,
% 14.61/2.67 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 14.61/2.67 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 14.61/2.67 inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl6945])).
% 14.61/2.67 thf(zip_derived_cl6968, plain, ($false),
% 14.61/2.67 inference('simplify', [status(thm)], [zip_derived_cl6967])).
% 14.61/2.67
% 14.61/2.67 % SZS output end Refutation
% 14.61/2.67
% 14.61/2.67
% 14.61/2.67 % Terminating...
% 15.04/2.76 % Runner terminated.
% 15.04/2.77 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------