%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP444-1 : TPTP v9.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.AXaJ3Iqpes true
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:36:27 PM UTC 2025
% Result : Unsatisfiable 26.31s 4.90s
% Output : Refutation 26.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP444-1 : TPTP v9.2.0. Released v2.6.0.
% 0.13/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.AXaJ3Iqpes true
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 1 14:08:38 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running portfolio for 300 s
% 0.14/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34 % Number of cores: 8
% 0.14/0.34 % Python version: Python 3.6.8
% 0.20/0.35 % Running in FO mode
% 0.54/0.66 % Total configuration time : 435
% 0.54/0.66 % Estimated wc time : 1092
% 0.54/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.70 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.55/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.55/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.55/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.55/0.80 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.55/0.83 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 26.31/4.90 % Solved by fo/fo7.sh.
% 26.31/4.90 % done 1152 iterations in 4.078s
% 26.31/4.90 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 26.31/4.90 % SZS output start Refutation
% 26.31/4.90 thf(a3_type, type, a3: $i).
% 26.31/4.90 thf(b3_type, type, b3: $i).
% 26.31/4.90 thf(inverse_type, type, inverse: $i > $i).
% 26.31/4.90 thf(multiply_type, type, multiply: $i > $i > $i).
% 26.31/4.90 thf(c3_type, type, c3: $i).
% 26.31/4.90 thf(prove_these_axioms_3, conjecture,
% 26.31/4.90 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 26.31/4.90 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 26.31/4.90 thf(zf_stmt_0, negated_conjecture,
% 26.31/4.90 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 26.31/4.90 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 26.31/4.90 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 26.31/4.90 thf(zip_derived_cl1, plain,
% 26.31/4.90 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 26.31/4.90 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 26.31/4.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 26.31/4.90 thf(single_axiom, axiom,
% 26.31/4.90 (( inverse @
% 26.31/4.90 ( multiply @
% 26.31/4.90 A @
% 26.31/4.90 ( multiply @
% 26.31/4.90 B @
% 26.31/4.90 ( multiply @
% 26.31/4.90 ( multiply @ C @ ( inverse @ C ) ) @
% 26.31/4.90 ( inverse @ ( multiply @ D @ ( multiply @ A @ B ) ) ) ) ) ) ) =
% 26.31/4.90 ( D ))).
% 26.31/4.90 thf(zip_derived_cl0, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 26.31/4.90 = (X0))),
% 26.31/4.90 inference('cnf', [status(esa)], [single_axiom])).
% 26.31/4.90 thf(zip_derived_cl0, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 26.31/4.90 = (X0))),
% 26.31/4.90 inference('cnf', [status(esa)], [single_axiom])).
% 26.31/4.90 thf(zip_derived_cl3, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))) @
% 26.31/4.90 (multiply @ (multiply @ X4 @ (inverse @ X4)) @ X0))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl3, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))) @
% 26.31/4.90 (multiply @ (multiply @ X4 @ (inverse @ X4)) @ X0))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl10, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (multiply @ (multiply @ X5 @ (inverse @ X5)) @ X2) @
% 26.31/4.90 (multiply @ (multiply @ (multiply @ X6 @ (inverse @ X6)) @ X0) @
% 26.31/4.90 (multiply @ (multiply @ X4 @ (inverse @ X4)) @ X1))))
% 26.31/4.90 = (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X2 @ (multiply @ X0 @ X1)))))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3])).
% 26.31/4.90 thf(zip_derived_cl3, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))) @
% 26.31/4.90 (multiply @ (multiply @ X4 @ (inverse @ X4)) @ X0))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl0, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 26.31/4.90 = (X0))),
% 26.31/4.90 inference('cnf', [status(esa)], [single_axiom])).
% 26.31/4.90 thf(zip_derived_cl9, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @
% 26.31/4.90 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 26.31/4.90 (inverse @ (multiply @ X2 @ (multiply @ X0 @ X1)))) @
% 26.31/4.90 (multiply @ (multiply @ (multiply @ X3 @ (inverse @ X3)) @ X2) @
% 26.31/4.90 (multiply @ (multiply @ X5 @ (inverse @ X5)) @ X0))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl98, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @ (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 26.31/4.90 (multiply @ X1 @ X0))))
% 26.31/4.90 = (X2))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl9])).
% 26.31/4.90 thf(zip_derived_cl3, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))) @
% 26.31/4.90 (multiply @ (multiply @ X4 @ (inverse @ X4)) @ X0))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl98, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @ (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 26.31/4.90 (multiply @ X1 @ X0))))
% 26.31/4.90 = (X2))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl9])).
% 26.31/4.90 thf(zip_derived_cl154, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 26.31/4.90 ((multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @ X0 @
% 26.31/4.90 (multiply @ X3 @
% 26.31/4.90 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 26.31/4.90 (inverse @ (multiply @ X1 @ (multiply @ X0 @ X3))))))))
% 26.31/4.90 = (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl98])).
% 26.31/4.90 thf(zip_derived_cl0, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 26.31/4.90 = (X0))),
% 26.31/4.90 inference('cnf', [status(esa)], [single_axiom])).
% 26.31/4.90 thf(zip_derived_cl164, plain,
% 26.31/4.90 (![X1 : $i, X2 : $i, X5 : $i]:
% 26.31/4.90 ((multiply @ (multiply @ X5 @ (inverse @ X5)) @ X1)
% 26.31/4.90 = (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X1))),
% 26.31/4.90 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl164, plain,
% 26.31/4.90 (![X1 : $i, X2 : $i, X5 : $i]:
% 26.31/4.90 ((multiply @ (multiply @ X5 @ (inverse @ X5)) @ X1)
% 26.31/4.90 = (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X1))),
% 26.31/4.90 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl188, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @
% 26.31/4.90 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 26.31/4.90 X2) = (multiply @ (multiply @ X3 @ (inverse @ X3)) @ X2))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl164, zip_derived_cl164])).
% 26.31/4.90 thf(zip_derived_cl188, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @
% 26.31/4.90 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 26.31/4.90 X2) = (multiply @ (multiply @ X3 @ (inverse @ X3)) @ X2))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl164, zip_derived_cl164])).
% 26.31/4.90 thf(zip_derived_cl333, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 26.31/4.90 ((multiply @
% 26.31/4.90 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 26.31/4.90 (inverse @ (multiply @ X3 @ (inverse @ X3)))) @
% 26.31/4.90 X0)
% 26.31/4.90 = (multiply @
% 26.31/4.90 (multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 26.31/4.90 (inverse @ (multiply @ X1 @ (inverse @ X1)))) @
% 26.31/4.90 X0))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl188, zip_derived_cl188])).
% 26.31/4.90 thf(zip_derived_cl0, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 26.31/4.90 = (X0))),
% 26.31/4.90 inference('cnf', [status(esa)], [single_axiom])).
% 26.31/4.90 thf(zip_derived_cl630, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X0 @
% 26.31/4.90 (multiply @ (multiply @ X6 @ (inverse @ X6)) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X2 @ (inverse @ X2)))) @
% 26.31/4.90 (multiply @ X1 @ X0)))))))
% 26.31/4.90 = (multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 26.31/4.90 (inverse @ (multiply @ X4 @ (inverse @ X4)))))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl188, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @
% 26.31/4.90 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 26.31/4.90 X2) = (multiply @ (multiply @ X3 @ (inverse @ X3)) @ X2))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl164, zip_derived_cl164])).
% 26.31/4.90 thf(zip_derived_cl0, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 26.31/4.90 = (X0))),
% 26.31/4.90 inference('cnf', [status(esa)], [single_axiom])).
% 26.31/4.90 thf(zip_derived_cl830, plain,
% 26.31/4.90 (![X3 : $i, X4 : $i, X5 : $i]:
% 26.31/4.90 ((multiply @ X3 @ (inverse @ X3))
% 26.31/4.90 = (multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 26.31/4.90 (inverse @ (multiply @ X4 @ (inverse @ X4)))))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl630, zip_derived_cl188, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl188, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @
% 26.31/4.90 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 26.31/4.90 X2) = (multiply @ (multiply @ X3 @ (inverse @ X3)) @ X2))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl164, zip_derived_cl164])).
% 26.31/4.90 thf(zip_derived_cl0, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 26.31/4.90 = (X0))),
% 26.31/4.90 inference('cnf', [status(esa)], [single_axiom])).
% 26.31/4.90 thf(zip_derived_cl317, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X0 @
% 26.31/4.90 (multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X2 @ (inverse @ X2)))) @
% 26.31/4.90 (multiply @ X1 @ X0)))))))
% 26.31/4.90 = (multiply @ X4 @ (inverse @ X4)))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl188, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl188, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @
% 26.31/4.90 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 26.31/4.90 X2) = (multiply @ (multiply @ X3 @ (inverse @ X3)) @ X2))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl164, zip_derived_cl164])).
% 26.31/4.90 thf(zip_derived_cl0, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 26.31/4.90 = (X0))),
% 26.31/4.90 inference('cnf', [status(esa)], [single_axiom])).
% 26.31/4.90 thf(zip_derived_cl445, plain,
% 26.31/4.90 (![X3 : $i, X4 : $i]:
% 26.31/4.90 ((multiply @ X3 @ (inverse @ X3)) = (multiply @ X4 @ (inverse @ X4)))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl317, zip_derived_cl188, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl0, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 26.31/4.90 = (X0))),
% 26.31/4.90 inference('cnf', [status(esa)], [single_axiom])).
% 26.31/4.90 thf(zip_derived_cl445, plain,
% 26.31/4.90 (![X3 : $i, X4 : $i]:
% 26.31/4.90 ((multiply @ X3 @ (inverse @ X3)) = (multiply @ X4 @ (inverse @ X4)))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl317, zip_derived_cl188, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl534, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 26.31/4.90 ((multiply @
% 26.31/4.90 (multiply @ X3 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X3 @ X2)))))) @
% 26.31/4.90 X0) = (multiply @ X1 @ (inverse @ X1)))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl445])).
% 26.31/4.90 thf(zip_derived_cl445, plain,
% 26.31/4.90 (![X3 : $i, X4 : $i]:
% 26.31/4.90 ((multiply @ X3 @ (inverse @ X3)) = (multiply @ X4 @ (inverse @ X4)))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl317, zip_derived_cl188, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl98, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @ (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 26.31/4.90 (multiply @ X1 @ X0))))
% 26.31/4.90 = (X2))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl9])).
% 26.31/4.90 thf(zip_derived_cl469, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @
% 26.31/4.90 (inverse @ (multiply @ X2 @ (multiply @ X0 @ (inverse @ X0)))) @
% 26.31/4.90 (multiply @ X2 @ X1))))
% 26.31/4.90 = (inverse @ X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl98])).
% 26.31/4.90 thf(zip_derived_cl445, plain,
% 26.31/4.90 (![X3 : $i, X4 : $i]:
% 26.31/4.90 ((multiply @ X3 @ (inverse @ X3)) = (multiply @ X4 @ (inverse @ X4)))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl317, zip_derived_cl188, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl0, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 26.31/4.90 = (X0))),
% 26.31/4.90 inference('cnf', [status(esa)], [single_axiom])).
% 26.31/4.90 thf(zip_derived_cl462, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (inverse @ X2) @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl1176, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X3 @
% 26.31/4.90 (multiply @ (inverse @ X3) @ (inverse @ (inverse @ X0)))))
% 26.31/4.90 = (inverse @ (multiply @ X0 @ (multiply @ X1 @ (inverse @ X1)))))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl469, zip_derived_cl462])).
% 26.31/4.90 thf(zip_derived_cl3339, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X5 @
% 26.31/4.90 (multiply @ (inverse @ X5) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @ X3 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 26.31/4.90 (multiply @ X3 @ X2)))))))))))
% 26.31/4.90 = (inverse @ (multiply @ X0 @ (inverse @ X0))))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl534, zip_derived_cl1176])).
% 26.31/4.90 thf(zip_derived_cl0, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 26.31/4.90 = (X0))),
% 26.31/4.90 inference('cnf', [status(esa)], [single_axiom])).
% 26.31/4.90 thf(zip_derived_cl3531, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X5 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X5 @
% 26.31/4.90 (multiply @ (inverse @ X5) @
% 26.31/4.90 (inverse @ (multiply @ X1 @ (inverse @ X1))))))
% 26.31/4.90 = (inverse @ (multiply @ X0 @ (inverse @ X0))))),
% 26.31/4.90 inference('demod', [status(thm)], [zip_derived_cl3339, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl3531, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X5 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X5 @
% 26.31/4.90 (multiply @ (inverse @ X5) @
% 26.31/4.90 (inverse @ (multiply @ X1 @ (inverse @ X1))))))
% 26.31/4.90 = (inverse @ (multiply @ X0 @ (inverse @ X0))))),
% 26.31/4.90 inference('demod', [status(thm)], [zip_derived_cl3339, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl3606, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X3 @
% 26.31/4.90 (multiply @ (inverse @ X3) @
% 26.31/4.90 (inverse @ (multiply @ X2 @ (inverse @ X2))))))
% 26.31/4.90 = (inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (inverse @ X0)))))))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl3531, zip_derived_cl3531])).
% 26.31/4.90 thf(zip_derived_cl98, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @ (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 26.31/4.90 (multiply @ X1 @ X0))))
% 26.31/4.90 = (X2))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl9])).
% 26.31/4.90 thf(zip_derived_cl462, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (inverse @ X2) @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl1175, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @ (multiply @ X3 @ (multiply @ (inverse @ X3) @ X0)))
% 26.31/4.90 = (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0))))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl98, zip_derived_cl462])).
% 26.31/4.90 thf(zip_derived_cl0, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 26.31/4.90 = (X0))),
% 26.31/4.90 inference('cnf', [status(esa)], [single_axiom])).
% 26.31/4.90 thf(zip_derived_cl1235, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X2) @
% 26.31/4.90 (multiply @ X0 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))))))
% 26.31/4.90 = (X2))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl1175, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl4096, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (inverse @ X0)))))) @
% 26.31/4.90 (multiply @ X4 @
% 26.31/4.90 (multiply @ (multiply @ X6 @ (inverse @ X6)) @
% 26.31/4.90 (inverse @ (multiply @ X5 @ (multiply @ (inverse @ X5) @ X4)))))))
% 26.31/4.90 = (multiply @ X3 @
% 26.31/4.90 (multiply @ (inverse @ X3) @
% 26.31/4.90 (inverse @ (multiply @ X2 @ (inverse @ X2))))))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl3606, zip_derived_cl1235])).
% 26.31/4.90 thf(zip_derived_cl3531, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X5 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X5 @
% 26.31/4.90 (multiply @ (inverse @ X5) @
% 26.31/4.90 (inverse @ (multiply @ X1 @ (inverse @ X1))))))
% 26.31/4.90 = (inverse @ (multiply @ X0 @ (inverse @ X0))))),
% 26.31/4.90 inference('demod', [status(thm)], [zip_derived_cl3339, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl1235, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X2) @
% 26.31/4.90 (multiply @ X0 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))))))
% 26.31/4.90 = (X2))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl1175, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl4419, plain,
% 26.31/4.90 (![X0 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @ X0 @ (inverse @ X0))
% 26.31/4.90 = (multiply @ X3 @
% 26.31/4.90 (multiply @ (inverse @ X3) @
% 26.31/4.90 (inverse @ (multiply @ X2 @ (inverse @ X2))))))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl4096, zip_derived_cl3531, zip_derived_cl1235])).
% 26.31/4.90 thf(zip_derived_cl98, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @ (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 26.31/4.90 (multiply @ X1 @ X0))))
% 26.31/4.90 = (X2))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl9])).
% 26.31/4.90 thf(zip_derived_cl4570, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 26.31/4.90 ((multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @
% 26.31/4.90 (inverse @ (multiply @ X3 @ (multiply @ X0 @ (inverse @ X0)))) @
% 26.31/4.90 (multiply @ X3 @ X2))))
% 26.31/4.90 = (multiply @ (inverse @ X2) @
% 26.31/4.90 (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl4419, zip_derived_cl98])).
% 26.31/4.90 thf(zip_derived_cl469, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @
% 26.31/4.90 (inverse @ (multiply @ X2 @ (multiply @ X0 @ (inverse @ X0)))) @
% 26.31/4.90 (multiply @ X2 @ X1))))
% 26.31/4.90 = (inverse @ X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl98])).
% 26.31/4.90 thf(zip_derived_cl4781, plain,
% 26.31/4.90 (![X1 : $i, X2 : $i]:
% 26.31/4.90 ((inverse @ X2)
% 26.31/4.90 = (multiply @ (inverse @ X2) @
% 26.31/4.90 (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 26.31/4.90 inference('demod', [status(thm)], [zip_derived_cl4570, zip_derived_cl469])).
% 26.31/4.90 thf(zip_derived_cl445, plain,
% 26.31/4.90 (![X3 : $i, X4 : $i]:
% 26.31/4.90 ((multiply @ X3 @ (inverse @ X3)) = (multiply @ X4 @ (inverse @ X4)))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl317, zip_derived_cl188, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl98, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @ (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 26.31/4.90 (multiply @ X1 @ X0))))
% 26.31/4.90 = (X2))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl9])).
% 26.31/4.90 thf(zip_derived_cl468, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @
% 26.31/4.90 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X1))) @
% 26.31/4.90 (multiply @ X0 @ (inverse @ X0)))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl98])).
% 26.31/4.90 thf(zip_derived_cl1235, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X2) @
% 26.31/4.90 (multiply @ X0 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))))))
% 26.31/4.90 = (X2))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl1175, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl1802, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (multiply @
% 26.31/4.90 (inverse @
% 26.31/4.90 (inverse @
% 26.31/4.90 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X0))))) @
% 26.31/4.90 X0)))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl468, zip_derived_cl1235])).
% 26.31/4.90 thf(zip_derived_cl4887, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (multiply @
% 26.31/4.90 (inverse @
% 26.31/4.90 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))) @
% 26.31/4.90 (inverse @ (multiply @ X2 @ (inverse @ X2))))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl4781, zip_derived_cl1802])).
% 26.31/4.90 thf(zip_derived_cl4781, plain,
% 26.31/4.90 (![X1 : $i, X2 : $i]:
% 26.31/4.90 ((inverse @ X2)
% 26.31/4.90 = (multiply @ (inverse @ X2) @
% 26.31/4.90 (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 26.31/4.90 inference('demod', [status(thm)], [zip_derived_cl4570, zip_derived_cl469])).
% 26.31/4.90 thf(zip_derived_cl4951, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl4887, zip_derived_cl4781])).
% 26.31/4.90 thf(zip_derived_cl4951, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl4887, zip_derived_cl4781])).
% 26.31/4.90 thf(zip_derived_cl5136, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X0 @
% 26.31/4.90 (inverse @ (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2)))))))
% 26.31/4.90 = (multiply @ (inverse @ X0) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl4951, zip_derived_cl4951])).
% 26.31/4.90 thf(zip_derived_cl4951, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl4887, zip_derived_cl4781])).
% 26.31/4.90 thf(zip_derived_cl5358, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((multiply @ (inverse @ (inverse @ X1)) @
% 26.31/4.90 (inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl5136, zip_derived_cl4951])).
% 26.31/4.90 thf(zip_derived_cl1802, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (multiply @
% 26.31/4.90 (inverse @
% 26.31/4.90 (inverse @
% 26.31/4.90 (inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X0))))) @
% 26.31/4.90 X0)))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl468, zip_derived_cl1235])).
% 26.31/4.90 thf(zip_derived_cl5821, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (multiply @
% 26.31/4.90 (inverse @
% 26.31/4.90 (inverse @ (inverse @ (multiply @ (inverse @ X0) @ X0)))) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2))))))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl5358, zip_derived_cl1802])).
% 26.31/4.90 thf(zip_derived_cl5358, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((multiply @ (inverse @ (inverse @ X1)) @
% 26.31/4.90 (inverse @ (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl5136, zip_derived_cl4951])).
% 26.31/4.90 thf(zip_derived_cl5891, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl5821, zip_derived_cl5358])).
% 26.31/4.90 thf(zip_derived_cl5891, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl5821, zip_derived_cl5358])).
% 26.31/4.90 thf(zip_derived_cl5953, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X0 @ (inverse @ (multiply @ (inverse @ X2) @ X2))))
% 26.31/4.90 = (multiply @ (inverse @ X0) @
% 26.31/4.90 (inverse @ (multiply @ (inverse @ X1) @ X1))))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl5891, zip_derived_cl5891])).
% 26.31/4.90 thf(zip_derived_cl5891, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (inverse @ (multiply @ (inverse @ X0) @ X0))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl5821, zip_derived_cl5358])).
% 26.31/4.90 thf(zip_derived_cl6223, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @ X1 @ (inverse @ (multiply @ (inverse @ X0) @ X0)))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl5953, zip_derived_cl5891])).
% 26.31/4.90 thf(zip_derived_cl7423, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))
% 26.31/4.90 = (multiply @ (inverse @ X1) @ X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl6223])).
% 26.31/4.90 thf(zip_derived_cl3531, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X5 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X5 @
% 26.31/4.90 (multiply @ (inverse @ X5) @
% 26.31/4.90 (inverse @ (multiply @ X1 @ (inverse @ X1))))))
% 26.31/4.90 = (inverse @ (multiply @ X0 @ (inverse @ X0))))),
% 26.31/4.90 inference('demod', [status(thm)], [zip_derived_cl3339, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl0, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 26.31/4.90 = (X0))),
% 26.31/4.90 inference('cnf', [status(esa)], [single_axiom])).
% 26.31/4.90 thf(zip_derived_cl3683, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X2))) @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (inverse @ X0)))))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl3531, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl830, plain,
% 26.31/4.90 (![X3 : $i, X4 : $i, X5 : $i]:
% 26.31/4.90 ((multiply @ X3 @ (inverse @ X3))
% 26.31/4.90 = (multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 26.31/4.90 (inverse @ (multiply @ X4 @ (inverse @ X4)))))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl630, zip_derived_cl188, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl3873, plain,
% 26.31/4.90 (![X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (multiply @ (inverse @ (multiply @ X2 @ (inverse @ X2))) @
% 26.31/4.90 (multiply @ X3 @ (inverse @ X3)))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('demod', [status(thm)], [zip_derived_cl3683, zip_derived_cl830])).
% 26.31/4.90 thf(zip_derived_cl7656, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl7423, zip_derived_cl3873])).
% 26.31/4.90 thf(zip_derived_cl8336, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 26.31/4.90 = (multiply @ X2 @ (inverse @ X2)))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl830, zip_derived_cl7656])).
% 26.31/4.90 thf(zip_derived_cl0, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 26.31/4.90 = (X0))),
% 26.31/4.90 inference('cnf', [status(esa)], [single_axiom])).
% 26.31/4.90 thf(zip_derived_cl4781, plain,
% 26.31/4.90 (![X1 : $i, X2 : $i]:
% 26.31/4.90 ((inverse @ X2)
% 26.31/4.90 = (multiply @ (inverse @ X2) @
% 26.31/4.90 (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 26.31/4.90 inference('demod', [status(thm)], [zip_derived_cl4570, zip_derived_cl469])).
% 26.31/4.90 thf(zip_derived_cl4917, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X3 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X3 @ X2)))))))
% 26.31/4.90 = (multiply @ X0 @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl4781])).
% 26.31/4.90 thf(zip_derived_cl0, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X1 @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X2)))))))
% 26.31/4.90 = (X0))),
% 26.31/4.90 inference('cnf', [status(esa)], [single_axiom])).
% 26.31/4.90 thf(zip_derived_cl4936, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((X0) = (multiply @ X0 @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 26.31/4.90 inference('demod', [status(thm)], [zip_derived_cl4917, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl8405, plain,
% 26.31/4.90 (![X1 : $i, X2 : $i]:
% 26.31/4.90 ((inverse @ (multiply @ X1 @ (inverse @ X1)))
% 26.31/4.90 = (multiply @ X2 @ (inverse @ X2)))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl8336, zip_derived_cl4936])).
% 26.31/4.90 thf(zip_derived_cl1175, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X3 : $i]:
% 26.31/4.90 ((inverse @ (multiply @ X3 @ (multiply @ (inverse @ X3) @ X0)))
% 26.31/4.90 = (inverse @ (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0))))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl98, zip_derived_cl462])).
% 26.31/4.90 thf(zip_derived_cl9022, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ X2 @
% 26.31/4.90 (multiply @ (inverse @ X2) @ (inverse @ (inverse @ X1)))))
% 26.31/4.90 = (inverse @
% 26.31/4.90 (multiply @ X1 @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl8405, zip_derived_cl1175])).
% 26.31/4.90 thf(zip_derived_cl7656, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl7423, zip_derived_cl3873])).
% 26.31/4.90 thf(zip_derived_cl7656, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl7423, zip_derived_cl3873])).
% 26.31/4.90 thf(zip_derived_cl8347, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((inverse @
% 26.31/4.90 (multiply @ (inverse @ X1) @
% 26.31/4.90 (inverse @ (multiply @ X0 @ (inverse @ X0)))))
% 26.31/4.90 = (X1))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl7656, zip_derived_cl7656])).
% 26.31/4.90 thf(zip_derived_cl4936, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((X0) = (multiply @ X0 @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 26.31/4.90 inference('demod', [status(thm)], [zip_derived_cl4917, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl8412, plain,
% 26.31/4.90 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl8347, zip_derived_cl4936])).
% 26.31/4.90 thf(zip_derived_cl4936, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((X0) = (multiply @ X0 @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 26.31/4.90 inference('demod', [status(thm)], [zip_derived_cl4917, zip_derived_cl0])).
% 26.31/4.90 thf(zip_derived_cl9185, plain,
% 26.31/4.90 (![X1 : $i, X2 : $i]:
% 26.31/4.90 ((inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X1)))
% 26.31/4.90 = (inverse @ X1))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl9022, zip_derived_cl8412, zip_derived_cl4936])).
% 26.31/4.90 thf(zip_derived_cl8412, plain,
% 26.31/4.90 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl8347, zip_derived_cl4936])).
% 26.31/4.90 thf(zip_derived_cl9344, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((inverse @ (inverse @ X0))
% 26.31/4.90 = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 26.31/4.90 inference('sup+', [status(thm)], [zip_derived_cl9185, zip_derived_cl8412])).
% 26.31/4.90 thf(zip_derived_cl8412, plain,
% 26.31/4.90 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl8347, zip_derived_cl4936])).
% 26.31/4.90 thf(zip_derived_cl9398, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i]:
% 26.31/4.90 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl9344, zip_derived_cl8412])).
% 26.31/4.90 thf(zip_derived_cl9185, plain,
% 26.31/4.90 (![X1 : $i, X2 : $i]:
% 26.31/4.90 ((inverse @ (multiply @ X2 @ (multiply @ (inverse @ X2) @ X1)))
% 26.31/4.90 = (inverse @ X1))),
% 26.31/4.90 inference('demod', [status(thm)],
% 26.31/4.90 [zip_derived_cl9022, zip_derived_cl8412, zip_derived_cl4936])).
% 26.31/4.90 thf(zip_derived_cl98, plain,
% 26.31/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.90 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.90 (inverse @
% 26.31/4.90 (multiply @ (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 26.31/4.91 (multiply @ X1 @ X0))))
% 26.31/4.91 = (X2))),
% 26.31/4.91 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl9])).
% 26.31/4.91 thf(zip_derived_cl9359, plain,
% 26.31/4.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.31/4.91 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 26.31/4.91 (inverse @
% 26.31/4.91 (multiply @ (inverse @ X0) @ (multiply @ X1 @ (inverse @ X1)))))
% 26.31/4.91 = (X0))),
% 26.31/4.91 inference('sup+', [status(thm)], [zip_derived_cl9185, zip_derived_cl98])).
% 26.31/4.91 thf(zip_derived_cl8405, plain,
% 26.31/4.91 (![X1 : $i, X2 : $i]:
% 26.31/4.91 ((inverse @ (multiply @ X1 @ (inverse @ X1)))
% 26.31/4.91 = (multiply @ X2 @ (inverse @ X2)))),
% 26.31/4.91 inference('demod', [status(thm)],
% 26.31/4.91 [zip_derived_cl8336, zip_derived_cl4936])).
% 26.31/4.91 thf(zip_derived_cl4936, plain,
% 26.31/4.91 (![X0 : $i, X1 : $i]:
% 26.31/4.91 ((X0) = (multiply @ X0 @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))),
% 26.31/4.91 inference('demod', [status(thm)], [zip_derived_cl4917, zip_derived_cl0])).
% 26.31/4.91 thf(zip_derived_cl9103, plain,
% 26.31/4.91 (![X0 : $i, X2 : $i]:
% 26.31/4.91 ((X2) = (multiply @ X2 @ (multiply @ X0 @ (inverse @ X0))))),
% 26.31/4.91 inference('sup+', [status(thm)], [zip_derived_cl8405, zip_derived_cl4936])).
% 26.31/4.91 thf(zip_derived_cl8412, plain,
% 26.31/4.91 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 26.31/4.91 inference('demod', [status(thm)],
% 26.31/4.91 [zip_derived_cl8347, zip_derived_cl4936])).
% 26.31/4.91 thf(zip_derived_cl9401, plain,
% 26.31/4.91 (![X0 : $i, X2 : $i]:
% 26.31/4.91 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0) = (X0))),
% 26.31/4.91 inference('demod', [status(thm)],
% 26.31/4.91 [zip_derived_cl9359, zip_derived_cl9103, zip_derived_cl8412])).
% 26.31/4.91 thf(zip_derived_cl98, plain,
% 26.31/4.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.91 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.91 (inverse @
% 26.31/4.91 (multiply @ (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2))) @
% 26.31/4.91 (multiply @ X1 @ X0))))
% 26.31/4.91 = (X2))),
% 26.31/4.91 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl9])).
% 26.31/4.91 thf(zip_derived_cl9481, plain,
% 26.31/4.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 26.31/4.91 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 26.31/4.91 (inverse @
% 26.31/4.91 (multiply @
% 26.31/4.91 (inverse @
% 26.31/4.91 (multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 26.31/4.91 (multiply @ X0 @ X1))) @
% 26.31/4.91 X0)))
% 26.31/4.91 = (X1))),
% 26.31/4.91 inference('sup+', [status(thm)], [zip_derived_cl9401, zip_derived_cl98])).
% 26.31/4.91 thf(zip_derived_cl9401, plain,
% 26.31/4.91 (![X0 : $i, X2 : $i]:
% 26.31/4.91 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0) = (X0))),
% 26.31/4.91 inference('demod', [status(thm)],
% 26.31/4.91 [zip_derived_cl9359, zip_derived_cl9103, zip_derived_cl8412])).
% 26.31/4.91 thf(zip_derived_cl9401, plain,
% 26.31/4.91 (![X0 : $i, X2 : $i]:
% 26.31/4.91 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0) = (X0))),
% 26.31/4.91 inference('demod', [status(thm)],
% 26.31/4.91 [zip_derived_cl9359, zip_derived_cl9103, zip_derived_cl8412])).
% 26.31/4.91 thf(zip_derived_cl9521, plain,
% 26.31/4.91 (![X0 : $i, X1 : $i]:
% 26.31/4.91 ((inverse @ (multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0)) = (X1))),
% 26.31/4.91 inference('demod', [status(thm)],
% 26.31/4.91 [zip_derived_cl9481, zip_derived_cl9401, zip_derived_cl9401])).
% 26.31/4.91 thf(zip_derived_cl8412, plain,
% 26.31/4.91 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 26.31/4.91 inference('demod', [status(thm)],
% 26.31/4.91 [zip_derived_cl8347, zip_derived_cl4936])).
% 26.31/4.91 thf(zip_derived_cl9646, plain,
% 26.31/4.91 (![X0 : $i, X1 : $i]:
% 26.31/4.91 ((inverse @ X0) = (multiply @ (inverse @ (multiply @ X1 @ X0)) @ X1))),
% 26.31/4.91 inference('sup+', [status(thm)], [zip_derived_cl9521, zip_derived_cl8412])).
% 26.31/4.91 thf(zip_derived_cl9722, plain,
% 26.31/4.91 (![X0 : $i, X1 : $i]:
% 26.31/4.91 ((inverse @ (multiply @ (inverse @ X1) @ X0))
% 26.31/4.91 = (multiply @ (inverse @ X0) @ X1))),
% 26.31/4.91 inference('sup+', [status(thm)], [zip_derived_cl9398, zip_derived_cl9646])).
% 26.31/4.91 thf(zip_derived_cl8412, plain,
% 26.31/4.91 (![X1 : $i]: ((inverse @ (inverse @ X1)) = (X1))),
% 26.31/4.91 inference('demod', [status(thm)],
% 26.31/4.91 [zip_derived_cl8347, zip_derived_cl4936])).
% 26.31/4.91 thf(zip_derived_cl9401, plain,
% 26.31/4.91 (![X0 : $i, X2 : $i]:
% 26.31/4.91 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0) = (X0))),
% 26.31/4.91 inference('demod', [status(thm)],
% 26.31/4.91 [zip_derived_cl9359, zip_derived_cl9103, zip_derived_cl8412])).
% 26.31/4.91 thf(zip_derived_cl10164, plain,
% 26.31/4.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.31/4.91 ((multiply @ (inverse @ (multiply @ X1 @ X0)) @
% 26.31/4.91 (multiply @ X1 @ (multiply @ X0 @ X2))) = (X2))),
% 26.31/4.91 inference('demod', [status(thm)],
% 26.31/4.91 [zip_derived_cl98, zip_derived_cl9722, zip_derived_cl8412,
% 26.31/4.91 zip_derived_cl9401])).
% 26.31/4.91 thf(zip_derived_cl9398, plain,
% 26.31/4.91 (![X0 : $i, X1 : $i]:
% 26.31/4.91 ((X0) = (multiply @ X1 @ (multiply @ (inverse @ X1) @ X0)))),
% 26.31/4.91 inference('demod', [status(thm)],
% 26.31/4.91 [zip_derived_cl9344, zip_derived_cl8412])).
% 26.31/4.91 thf(zip_derived_cl10726, plain,
% 26.31/4.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 26.31/4.91 ((multiply @ X2 @ (multiply @ X1 @ X0))
% 26.31/4.91 = (multiply @ (multiply @ X2 @ X1) @ X0))),
% 26.31/4.91 inference('sup+', [status(thm)],
% 26.31/4.91 [zip_derived_cl10164, zip_derived_cl9398])).
% 26.31/4.91 thf(zip_derived_cl10845, plain,
% 26.31/4.91 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 26.31/4.91 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 26.31/4.91 inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl10726])).
% 26.31/4.91 thf(zip_derived_cl10846, plain, ($false),
% 26.31/4.91 inference('simplify', [status(thm)], [zip_derived_cl10845])).
% 26.31/4.91
% 26.31/4.91 % SZS output end Refutation
% 26.31/4.91
% 26.31/4.91
% 26.31/4.91 % Terminating...
% 27.07/5.11 % Runner terminated.
% 27.12/5.12 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------