%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP591-1 : 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.VyUV8lee0D true
% Computer : n031.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 04:36:44 PM UTC 2025
% Result : Unsatisfiable 48.13s 7.41s
% Output : Refutation 48.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : GRP591-1 : TPTP v9.2.0. Released v2.6.0.
% 0.05/0.10 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.VyUV8lee0D true
% 0.10/0.30 % Computer : n031.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Wed Oct 1 14:23:08 EDT 2025
% 0.10/0.30 % CPUTime :
% 0.10/0.30 % Running portfolio for 300 s
% 0.10/0.30 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.31 % Number of cores: 8
% 0.10/0.31 % Python version: Python 3.6.8
% 0.10/0.31 % Running in FO mode
% 0.44/0.56 % Total configuration time : 435
% 0.44/0.56 % Estimated wc time : 1092
% 0.44/0.56 % Estimated cpu time (7 cpus) : 156.0
% 0.45/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.45/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.45/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.45/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.45/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.45/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.45/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 48.13/7.41 % Solved by fo/fo13.sh.
% 48.13/7.41 % done 1747 iterations in 6.701s
% 48.13/7.41 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 48.13/7.41 % SZS output start Refutation
% 48.13/7.41 thf(multiply_type, type, multiply: $i > $i > $i).
% 48.13/7.41 thf(b3_type, type, b3: $i).
% 48.13/7.41 thf(inverse_type, type, inverse: $i > $i).
% 48.13/7.41 thf(double_divide_type, type, double_divide: $i > $i > $i).
% 48.13/7.41 thf(a3_type, type, a3: $i).
% 48.13/7.41 thf(c3_type, type, c3: $i).
% 48.13/7.41 thf(prove_these_axioms_3, conjecture,
% 48.13/7.41 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 48.13/7.41 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 48.13/7.41 thf(zf_stmt_0, negated_conjecture,
% 48.13/7.41 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 48.13/7.41 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 48.13/7.41 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 48.13/7.41 thf(zip_derived_cl2, plain,
% 48.13/7.41 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 48.13/7.41 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 48.13/7.41 inference('cnf', [status(esa)], [zf_stmt_0])).
% 48.13/7.41 thf(single_axiom, axiom,
% 48.13/7.41 (( double_divide @
% 48.13/7.41 ( inverse @
% 48.13/7.41 ( double_divide @
% 48.13/7.41 ( double_divide @ A @ B ) @
% 48.13/7.41 ( inverse @ ( double_divide @ A @ ( inverse @ C ) ) ) ) ) @
% 48.13/7.41 B ) =
% 48.13/7.41 ( C ))).
% 48.13/7.41 thf(zip_derived_cl0, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.41 ((double_divide @
% 48.13/7.41 (inverse @
% 48.13/7.41 (double_divide @ (double_divide @ X1 @ X2) @
% 48.13/7.41 (inverse @ (double_divide @ X1 @ (inverse @ X0))))) @
% 48.13/7.41 X2) = (X0))),
% 48.13/7.41 inference('cnf', [status(esa)], [single_axiom])).
% 48.13/7.41 thf(multiply, axiom,
% 48.13/7.41 (( multiply @ A @ B ) = ( inverse @ ( double_divide @ B @ A ) ))).
% 48.13/7.41 thf(zip_derived_cl1, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i]:
% 48.13/7.41 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 48.13/7.41 inference('cnf', [status(esa)], [multiply])).
% 48.13/7.41 thf(zip_derived_cl1, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i]:
% 48.13/7.41 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 48.13/7.41 inference('cnf', [status(esa)], [multiply])).
% 48.13/7.41 thf(zip_derived_cl3, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.41 ((double_divide @
% 48.13/7.41 (multiply @ (multiply @ (inverse @ X0) @ X1) @
% 48.13/7.41 (double_divide @ X1 @ X2)) @
% 48.13/7.41 X2) = (X0))),
% 48.13/7.41 inference('demod', [status(thm)],
% 48.13/7.41 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 48.13/7.41 thf(zip_derived_cl1, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i]:
% 48.13/7.41 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 48.13/7.41 inference('cnf', [status(esa)], [multiply])).
% 48.13/7.41 thf(zip_derived_cl5, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.41 ((multiply @ X1 @
% 48.13/7.41 (multiply @ (multiply @ (inverse @ X0) @ X2) @
% 48.13/7.41 (double_divide @ X2 @ X1)))
% 48.13/7.41 = (inverse @ X0))),
% 48.13/7.41 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 48.13/7.41 thf(zip_derived_cl3, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.41 ((double_divide @
% 48.13/7.41 (multiply @ (multiply @ (inverse @ X0) @ X1) @
% 48.13/7.41 (double_divide @ X1 @ X2)) @
% 48.13/7.41 X2) = (X0))),
% 48.13/7.41 inference('demod', [status(thm)],
% 48.13/7.41 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 48.13/7.41 thf(zip_derived_cl5, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.41 ((multiply @ X1 @
% 48.13/7.41 (multiply @ (multiply @ (inverse @ X0) @ X2) @
% 48.13/7.41 (double_divide @ X2 @ X1)))
% 48.13/7.41 = (inverse @ X0))),
% 48.13/7.41 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 48.13/7.41 thf(zip_derived_cl10, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 48.13/7.41 ((multiply @ X2 @
% 48.13/7.41 (multiply @
% 48.13/7.41 (multiply @ (inverse @ X1) @
% 48.13/7.41 (multiply @ (multiply @ (inverse @ X0) @ X3) @
% 48.13/7.41 (double_divide @ X3 @ X2))) @
% 48.13/7.41 X0))
% 48.13/7.41 = (inverse @ X1))),
% 48.13/7.41 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl5])).
% 48.13/7.41 thf(zip_derived_cl43, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i]:
% 48.13/7.41 ((multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X0))
% 48.13/7.41 = (inverse @ X1))),
% 48.13/7.41 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl10])).
% 48.13/7.41 thf(zip_derived_cl43, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i]:
% 48.13/7.41 ((multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X0))
% 48.13/7.41 = (inverse @ X1))),
% 48.13/7.41 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl10])).
% 48.13/7.41 thf(zip_derived_cl1, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i]:
% 48.13/7.41 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 48.13/7.41 inference('cnf', [status(esa)], [multiply])).
% 48.13/7.41 thf(zip_derived_cl3, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.41 ((double_divide @
% 48.13/7.41 (multiply @ (multiply @ (inverse @ X0) @ X1) @
% 48.13/7.41 (double_divide @ X1 @ X2)) @
% 48.13/7.41 X2) = (X0))),
% 48.13/7.41 inference('demod', [status(thm)],
% 48.13/7.41 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 48.13/7.41 thf(zip_derived_cl7, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 48.13/7.41 ((double_divide @
% 48.13/7.41 (multiply @ (multiply @ (multiply @ X1 @ X0) @ X3) @
% 48.13/7.41 (double_divide @ X3 @ X2)) @
% 48.13/7.41 X2) = (double_divide @ X0 @ X1))),
% 48.13/7.41 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 48.13/7.41 thf(zip_derived_cl52, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 48.13/7.41 ((double_divide @
% 48.13/7.41 (multiply @ (multiply @ (inverse @ X0) @ X3) @
% 48.13/7.41 (double_divide @ X3 @ X2)) @
% 48.13/7.41 X2)
% 48.13/7.41 = (double_divide @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0)))),
% 48.13/7.41 inference('s_sup+', [status(thm)], [zip_derived_cl43, zip_derived_cl7])).
% 48.13/7.41 thf(zip_derived_cl3, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.41 ((double_divide @
% 48.13/7.41 (multiply @ (multiply @ (inverse @ X0) @ X1) @
% 48.13/7.41 (double_divide @ X1 @ X2)) @
% 48.13/7.41 X2) = (X0))),
% 48.13/7.41 inference('demod', [status(thm)],
% 48.13/7.41 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 48.13/7.41 thf(zip_derived_cl61, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i]:
% 48.13/7.41 ((X0)
% 48.13/7.41 = (double_divide @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0)))),
% 48.13/7.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl3])).
% 48.13/7.41 thf(zip_derived_cl3, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.41 ((double_divide @
% 48.13/7.41 (multiply @ (multiply @ (inverse @ X0) @ X1) @
% 48.13/7.41 (double_divide @ X1 @ X2)) @
% 48.13/7.41 X2) = (X0))),
% 48.13/7.41 inference('demod', [status(thm)],
% 48.13/7.41 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 48.13/7.41 thf(zip_derived_cl94, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.41 ((double_divide @
% 48.13/7.41 (multiply @
% 48.13/7.41 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X2) @ X2)) @ X0) @
% 48.13/7.41 (inverse @ X0)) = (X1))),
% 48.13/7.41 inference('s_sup+', [status(thm)], [zip_derived_cl61, zip_derived_cl3])).
% 48.13/7.41 thf(zip_derived_cl43, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i]:
% 48.13/7.41 ((multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X0))
% 48.13/7.41 = (inverse @ X1))),
% 48.13/7.41 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl10])).
% 48.13/7.41 thf(zip_derived_cl104, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i]:
% 48.13/7.41 ((double_divide @ (multiply @ (inverse @ X1) @ X0) @ (inverse @ X0))
% 48.13/7.41 = (X1))),
% 48.13/7.41 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl43])).
% 48.13/7.41 thf(zip_derived_cl121, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i]:
% 48.13/7.41 ((double_divide @ (inverse @ X0) @
% 48.13/7.41 (inverse @ (multiply @ (inverse @ X1) @ X1))) = (X0))),
% 48.13/7.41 inference('s_sup+', [status(thm)], [zip_derived_cl43, zip_derived_cl104])).
% 48.13/7.41 thf(zip_derived_cl43, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i]:
% 48.13/7.41 ((multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X0))
% 48.13/7.41 = (inverse @ X1))),
% 48.13/7.41 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl10])).
% 48.13/7.41 thf(zip_derived_cl61, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i]:
% 48.13/7.41 ((X0)
% 48.13/7.41 = (double_divide @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0)))),
% 48.13/7.41 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl3])).
% 48.13/7.41 thf(zip_derived_cl102, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i]:
% 48.13/7.41 ((X1)
% 48.13/7.41 = (double_divide @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 48.13/7.41 (inverse @ X1)))),
% 48.13/7.41 inference('s_sup+', [status(thm)], [zip_derived_cl43, zip_derived_cl61])).
% 48.13/7.41 thf(zip_derived_cl157, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i]:
% 48.13/7.41 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X0) @ X0))),
% 48.13/7.41 inference('s_sup+', [status(thm)], [zip_derived_cl121, zip_derived_cl102])).
% 48.13/7.41 thf(zip_derived_cl43, plain,
% 48.13/7.41 (![X0 : $i, X1 : $i]:
% 48.13/7.41 ((multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X0))
% 48.13/7.42 = (inverse @ X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl10])).
% 48.13/7.42 thf(zip_derived_cl179, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X0) @ X0)
% 48.13/7.42 = (inverse @ (multiply @ (inverse @ X1) @ X1)))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl157, zip_derived_cl43])).
% 48.13/7.42 thf(zip_derived_cl7, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 48.13/7.42 ((double_divide @
% 48.13/7.42 (multiply @ (multiply @ (multiply @ X1 @ X0) @ X3) @
% 48.13/7.42 (double_divide @ X3 @ X2)) @
% 48.13/7.42 X2) = (double_divide @ X0 @ X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 48.13/7.42 thf(zip_derived_cl263, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 48.13/7.42 ((double_divide @
% 48.13/7.42 (multiply @
% 48.13/7.42 (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @ X3) @
% 48.13/7.42 (double_divide @ X3 @ X2)) @
% 48.13/7.42 X2) = (double_divide @ X1 @ (inverse @ X1)))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl7])).
% 48.13/7.42 thf(zip_derived_cl179, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X0) @ X0)
% 48.13/7.42 = (inverse @ (multiply @ (inverse @ X1) @ X1)))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl157, zip_derived_cl43])).
% 48.13/7.42 thf(zip_derived_cl7, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 48.13/7.42 ((double_divide @
% 48.13/7.42 (multiply @ (multiply @ (multiply @ X1 @ X0) @ X3) @
% 48.13/7.42 (double_divide @ X3 @ X2)) @
% 48.13/7.42 X2) = (double_divide @ X0 @ X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl3])).
% 48.13/7.42 thf(zip_derived_cl308, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ X0 @ (inverse @ X0))
% 48.13/7.42 = (double_divide @ X1 @ (inverse @ X1)))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl263, zip_derived_cl179, zip_derived_cl7])).
% 48.13/7.42 thf(zip_derived_cl1, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 48.13/7.42 inference('cnf', [status(esa)], [multiply])).
% 48.13/7.42 thf(zip_derived_cl386, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X1) @ X1)
% 48.13/7.42 = (inverse @ (double_divide @ X0 @ (inverse @ X0))))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl308, zip_derived_cl1])).
% 48.13/7.42 thf(zip_derived_cl61, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((X0)
% 48.13/7.42 = (double_divide @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0)))),
% 48.13/7.42 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl3])).
% 48.13/7.42 thf(zip_derived_cl5, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.42 ((multiply @ X1 @
% 48.13/7.42 (multiply @ (multiply @ (inverse @ X0) @ X2) @
% 48.13/7.42 (double_divide @ X2 @ X1)))
% 48.13/7.42 = (inverse @ X0))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 48.13/7.42 thf(zip_derived_cl100, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X0) @
% 48.13/7.42 (multiply @
% 48.13/7.42 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X2) @ X2)) @ X0))
% 48.13/7.42 = (inverse @ X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl61, zip_derived_cl5])).
% 48.13/7.42 thf(zip_derived_cl43, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X0))
% 48.13/7.42 = (inverse @ X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl10])).
% 48.13/7.42 thf(zip_derived_cl109, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X0) @ (multiply @ (inverse @ X1) @ X0))
% 48.13/7.42 = (inverse @ X1))),
% 48.13/7.42 inference('demod', [status(thm)], [zip_derived_cl100, zip_derived_cl43])).
% 48.13/7.42 thf(zip_derived_cl104, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (multiply @ (inverse @ X1) @ X0) @ (inverse @ X0))
% 48.13/7.42 = (X1))),
% 48.13/7.42 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl43])).
% 48.13/7.42 thf(zip_derived_cl130, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (inverse @ X0) @
% 48.13/7.42 (inverse @ (multiply @ (inverse @ X0) @ X1))) = (X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl109, zip_derived_cl104])).
% 48.13/7.42 thf(zip_derived_cl102, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((X1)
% 48.13/7.42 = (double_divide @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 48.13/7.42 (inverse @ X1)))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl43, zip_derived_cl61])).
% 48.13/7.42 thf(zip_derived_cl3351, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ (multiply @ (inverse @ X1) @ X1)) @ X0) = (X0))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl130, zip_derived_cl102])).
% 48.13/7.42 thf(zip_derived_cl4641, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.42 ((multiply @
% 48.13/7.42 (inverse @
% 48.13/7.42 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 48.13/7.42 (double_divide @ X2 @ (inverse @ X2)))) @
% 48.13/7.42 X1) = (X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl386, zip_derived_cl3351])).
% 48.13/7.42 thf(zip_derived_cl308, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ X0 @ (inverse @ X0))
% 48.13/7.42 = (double_divide @ X1 @ (inverse @ X1)))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl263, zip_derived_cl179, zip_derived_cl7])).
% 48.13/7.42 thf(zip_derived_cl61, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((X0)
% 48.13/7.42 = (double_divide @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0)))),
% 48.13/7.42 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl3])).
% 48.13/7.42 thf(zip_derived_cl399, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X1) @ X1)
% 48.13/7.42 = (double_divide @ X0 @ (inverse @ X0)))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl308, zip_derived_cl61])).
% 48.13/7.42 thf(zip_derived_cl386, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X1) @ X1)
% 48.13/7.42 = (inverse @ (double_divide @ X0 @ (inverse @ X0))))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl308, zip_derived_cl1])).
% 48.13/7.42 thf(zip_derived_cl130, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (inverse @ X0) @
% 48.13/7.42 (inverse @ (multiply @ (inverse @ X0) @ X1))) = (X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl109, zip_derived_cl104])).
% 48.13/7.42 thf(zip_derived_cl3376, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (multiply @ (inverse @ X0) @ X0) @
% 48.13/7.42 (inverse @ (multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)))
% 48.13/7.42 = (X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl386, zip_derived_cl130])).
% 48.13/7.42 thf(zip_derived_cl399, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X1) @ X1)
% 48.13/7.42 = (double_divide @ X0 @ (inverse @ X0)))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl308, zip_derived_cl61])).
% 48.13/7.42 thf(zip_derived_cl399, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X1) @ X1)
% 48.13/7.42 = (double_divide @ X0 @ (inverse @ X0)))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl308, zip_derived_cl61])).
% 48.13/7.42 thf(zip_derived_cl399, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X1) @ X1)
% 48.13/7.42 = (double_divide @ X0 @ (inverse @ X0)))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl308, zip_derived_cl61])).
% 48.13/7.42 thf(zip_derived_cl61, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((X0)
% 48.13/7.42 = (double_divide @ (multiply @ (inverse @ X1) @ X1) @ (inverse @ X0)))),
% 48.13/7.42 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl3])).
% 48.13/7.42 thf(zip_derived_cl453, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((X1)
% 48.13/7.42 = (double_divide @ (double_divide @ X0 @ (inverse @ X0)) @
% 48.13/7.42 (inverse @ X1)))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl399, zip_derived_cl61])).
% 48.13/7.42 thf(zip_derived_cl3391, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (double_divide @ X0 @ (inverse @ X0)) @ X1) = (X1))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl3376, zip_derived_cl399, zip_derived_cl399,
% 48.13/7.42 zip_derived_cl453])).
% 48.13/7.42 thf(zip_derived_cl1, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 48.13/7.42 inference('cnf', [status(esa)], [multiply])).
% 48.13/7.42 thf(zip_derived_cl4656, plain,
% 48.13/7.42 (![X1 : $i, X2 : $i]:
% 48.13/7.42 ((multiply @ (multiply @ (inverse @ X2) @ X2) @ X1) = (X1))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl4641, zip_derived_cl399, zip_derived_cl3391,
% 48.13/7.42 zip_derived_cl1])).
% 48.13/7.42 thf(zip_derived_cl5, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.42 ((multiply @ X1 @
% 48.13/7.42 (multiply @ (multiply @ (inverse @ X0) @ X2) @
% 48.13/7.42 (double_divide @ X2 @ X1)))
% 48.13/7.42 = (inverse @ X0))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl1])).
% 48.13/7.42 thf(zip_derived_cl4781, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ X0 @ (double_divide @ X1 @ X0)) = (inverse @ X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl4656, zip_derived_cl5])).
% 48.13/7.42 thf(zip_derived_cl399, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X1) @ X1)
% 48.13/7.42 = (double_divide @ X0 @ (inverse @ X0)))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl308, zip_derived_cl61])).
% 48.13/7.42 thf(zip_derived_cl179, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X0) @ X0)
% 48.13/7.42 = (inverse @ (multiply @ (inverse @ X1) @ X1)))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl157, zip_derived_cl43])).
% 48.13/7.42 thf(zip_derived_cl121, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (inverse @ X0) @
% 48.13/7.42 (inverse @ (multiply @ (inverse @ X1) @ X1))) = (X0))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl43, zip_derived_cl104])).
% 48.13/7.42 thf(zip_derived_cl261, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (inverse @ X1) @ (multiply @ (inverse @ X0) @ X0))
% 48.13/7.42 = (X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl121])).
% 48.13/7.42 thf(zip_derived_cl452, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (inverse @ X1) @
% 48.13/7.42 (double_divide @ X0 @ (inverse @ X0))) = (X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl399, zip_derived_cl261])).
% 48.13/7.42 thf(zip_derived_cl4781, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ X0 @ (double_divide @ X1 @ X0)) = (inverse @ X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl4656, zip_derived_cl5])).
% 48.13/7.42 thf(zip_derived_cl5218, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (double_divide @ X1 @ (inverse @ X1)) @ X0)
% 48.13/7.42 = (inverse @ (inverse @ X0)))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl452, zip_derived_cl4781])).
% 48.13/7.42 thf(zip_derived_cl3391, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (double_divide @ X0 @ (inverse @ X0)) @ X1) = (X1))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl3376, zip_derived_cl399, zip_derived_cl399,
% 48.13/7.42 zip_derived_cl453])).
% 48.13/7.42 thf(zip_derived_cl5240, plain,
% 48.13/7.42 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl5218, zip_derived_cl3391])).
% 48.13/7.42 thf(zip_derived_cl104, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (multiply @ (inverse @ X1) @ X0) @ (inverse @ X0))
% 48.13/7.42 = (X1))),
% 48.13/7.42 inference('demod', [status(thm)], [zip_derived_cl94, zip_derived_cl43])).
% 48.13/7.42 thf(zip_derived_cl4656, plain,
% 48.13/7.42 (![X1 : $i, X2 : $i]:
% 48.13/7.42 ((multiply @ (multiply @ (inverse @ X2) @ X2) @ X1) = (X1))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl4641, zip_derived_cl399, zip_derived_cl3391,
% 48.13/7.42 zip_derived_cl1])).
% 48.13/7.42 thf(zip_derived_cl3, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.42 ((double_divide @
% 48.13/7.42 (multiply @ (multiply @ (inverse @ X0) @ X1) @
% 48.13/7.42 (double_divide @ X1 @ X2)) @
% 48.13/7.42 X2) = (X0))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 48.13/7.42 thf(zip_derived_cl4778, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (double_divide @ X1 @ X0) @ X0) = (X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl4656, zip_derived_cl3])).
% 48.13/7.42 thf(zip_derived_cl4907, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ X0 @ (inverse @ X1))
% 48.13/7.42 = (multiply @ (inverse @ X0) @ X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl104, zip_derived_cl4778])).
% 48.13/7.42 thf(zip_derived_cl6247, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (inverse @ X0) @ (inverse @ X1))
% 48.13/7.42 = (multiply @ X0 @ X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl5240, zip_derived_cl4907])).
% 48.13/7.42 thf(zip_derived_cl4781, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ X0 @ (double_divide @ X1 @ X0)) = (inverse @ X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl4656, zip_derived_cl5])).
% 48.13/7.42 thf(zip_derived_cl6569, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X0) @ (multiply @ X1 @ X0))
% 48.13/7.42 = (inverse @ (inverse @ X1)))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl6247, zip_derived_cl4781])).
% 48.13/7.42 thf(zip_derived_cl5240, plain,
% 48.13/7.42 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl5218, zip_derived_cl3391])).
% 48.13/7.42 thf(zip_derived_cl6610, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X0) @ (multiply @ X1 @ X0)) = (X1))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl6569, zip_derived_cl5240])).
% 48.13/7.42 thf(zip_derived_cl6807, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ (double_divide @ X0 @ X1)) @ (inverse @ X0))
% 48.13/7.42 = (X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl4781, zip_derived_cl6610])).
% 48.13/7.42 thf(zip_derived_cl1, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 48.13/7.42 inference('cnf', [status(esa)], [multiply])).
% 48.13/7.42 thf(zip_derived_cl5240, plain,
% 48.13/7.42 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl5218, zip_derived_cl3391])).
% 48.13/7.42 thf(zip_derived_cl6247, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (inverse @ X0) @ (inverse @ X1))
% 48.13/7.42 = (multiply @ X0 @ X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl5240, zip_derived_cl4907])).
% 48.13/7.42 thf(zip_derived_cl6595, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (inverse @ X1) @ X0)
% 48.13/7.42 = (multiply @ X1 @ (inverse @ X0)))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl5240, zip_derived_cl6247])).
% 48.13/7.42 thf(zip_derived_cl1, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 48.13/7.42 inference('cnf', [status(esa)], [multiply])).
% 48.13/7.42 thf(zip_derived_cl5240, plain,
% 48.13/7.42 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl5218, zip_derived_cl3391])).
% 48.13/7.42 thf(zip_derived_cl5346, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ X0 @ X1) = (inverse @ (multiply @ X1 @ X0)))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl5240])).
% 48.13/7.42 thf(zip_derived_cl6834, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (double_divide @ X0 @ X1) @ X0) = (X1))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl6807, zip_derived_cl1, zip_derived_cl6595,
% 48.13/7.42 zip_derived_cl5346])).
% 48.13/7.42 thf(zip_derived_cl4781, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ X0 @ (double_divide @ X1 @ X0)) = (inverse @ X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl4656, zip_derived_cl5])).
% 48.13/7.42 thf(zip_derived_cl6862, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X1 @ X0)))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl6834, zip_derived_cl4781])).
% 48.13/7.42 thf(zip_derived_cl1, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 48.13/7.42 inference('cnf', [status(esa)], [multiply])).
% 48.13/7.42 thf(zip_derived_cl8023, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl6862, zip_derived_cl1])).
% 48.13/7.42 thf(zip_derived_cl8069, plain,
% 48.13/7.42 (((multiply @ c3 @ (multiply @ a3 @ b3))
% 48.13/7.42 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 48.13/7.42 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl8023])).
% 48.13/7.42 thf(zip_derived_cl6834, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (double_divide @ X0 @ X1) @ X0) = (X1))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl6807, zip_derived_cl1, zip_derived_cl6595,
% 48.13/7.42 zip_derived_cl5346])).
% 48.13/7.42 thf(zip_derived_cl179, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X0) @ X0)
% 48.13/7.42 = (inverse @ (multiply @ (inverse @ X1) @ X1)))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl157, zip_derived_cl43])).
% 48.13/7.42 thf(zip_derived_cl3, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.42 ((double_divide @
% 48.13/7.42 (multiply @ (multiply @ (inverse @ X0) @ X1) @
% 48.13/7.42 (double_divide @ X1 @ X2)) @
% 48.13/7.42 X2) = (X0))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 48.13/7.42 thf(zip_derived_cl3, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.42 ((double_divide @
% 48.13/7.42 (multiply @ (multiply @ (inverse @ X0) @ X1) @
% 48.13/7.42 (double_divide @ X1 @ X2)) @
% 48.13/7.42 X2) = (X0))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl0, zip_derived_cl1, zip_derived_cl1])).
% 48.13/7.42 thf(zip_derived_cl4, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 48.13/7.42 ((double_divide @
% 48.13/7.42 (multiply @
% 48.13/7.42 (multiply @ (inverse @ X1) @
% 48.13/7.42 (multiply @ (multiply @ (inverse @ X0) @ X3) @
% 48.13/7.42 (double_divide @ X3 @ X2))) @
% 48.13/7.42 X0) @
% 48.13/7.42 X2) = (X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl3])).
% 48.13/7.42 thf(zip_derived_cl267, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 48.13/7.42 ((double_divide @
% 48.13/7.42 (multiply @
% 48.13/7.42 (multiply @ (inverse @ X1) @
% 48.13/7.42 (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 48.13/7.42 (double_divide @ X3 @ X2))) @
% 48.13/7.42 X3) @
% 48.13/7.42 X2) = (X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl4])).
% 48.13/7.42 thf(zip_derived_cl179, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (inverse @ X0) @ X0)
% 48.13/7.42 = (inverse @ (multiply @ (inverse @ X1) @ X1)))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl157, zip_derived_cl43])).
% 48.13/7.42 thf(zip_derived_cl312, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 48.13/7.42 ((double_divide @
% 48.13/7.42 (multiply @
% 48.13/7.42 (multiply @ (inverse @ X1) @
% 48.13/7.42 (multiply @ (multiply @ (inverse @ X0) @ X0) @
% 48.13/7.42 (double_divide @ X3 @ X2))) @
% 48.13/7.42 X3) @
% 48.13/7.42 X2) = (X1))),
% 48.13/7.42 inference('demod', [status(thm)], [zip_derived_cl267, zip_derived_cl179])).
% 48.13/7.42 thf(zip_derived_cl4907, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ X0 @ (inverse @ X1))
% 48.13/7.42 = (multiply @ (inverse @ X0) @ X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl104, zip_derived_cl4778])).
% 48.13/7.42 thf(zip_derived_cl3391, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ (double_divide @ X0 @ (inverse @ X0)) @ X1) = (X1))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl3376, zip_derived_cl399, zip_derived_cl399,
% 48.13/7.42 zip_derived_cl453])).
% 48.13/7.42 thf(zip_derived_cl4907, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ X0 @ (inverse @ X1))
% 48.13/7.42 = (multiply @ (inverse @ X0) @ X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl104, zip_derived_cl4778])).
% 48.13/7.42 thf(zip_derived_cl1, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X0 @ X1)))),
% 48.13/7.42 inference('cnf', [status(esa)], [multiply])).
% 48.13/7.42 thf(zip_derived_cl8023, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl6862, zip_derived_cl1])).
% 48.13/7.42 thf(zip_derived_cl6834, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (double_divide @ X0 @ X1) @ X0) = (X1))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl6807, zip_derived_cl1, zip_derived_cl6595,
% 48.13/7.42 zip_derived_cl5346])).
% 48.13/7.42 thf(zip_derived_cl4778, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ (double_divide @ X1 @ X0) @ X0) = (X1))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl4656, zip_derived_cl3])).
% 48.13/7.42 thf(zip_derived_cl6861, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((double_divide @ X0 @ X1) = (double_divide @ X1 @ X0))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl6834, zip_derived_cl4778])).
% 48.13/7.42 thf(zip_derived_cl8421, plain,
% 48.13/7.42 (![X1 : $i, X2 : $i, X3 : $i]:
% 48.13/7.42 ((double_divide @ X2 @
% 48.13/7.42 (multiply @ X3 @ (double_divide @ X1 @ (multiply @ X2 @ X3))))
% 48.13/7.42 = (X1))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl312, zip_derived_cl4907, zip_derived_cl3391,
% 48.13/7.42 zip_derived_cl4907, zip_derived_cl1, zip_derived_cl8023,
% 48.13/7.42 zip_derived_cl6861])).
% 48.13/7.42 thf(zip_derived_cl8449, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.42 ((double_divide @ X2 @ (multiply @ X1 @ X0))
% 48.13/7.42 = (double_divide @ (multiply @ X2 @ X1) @ X0))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl6834, zip_derived_cl8421])).
% 48.13/7.42 thf(zip_derived_cl6862, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X1 @ X0)))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl6834, zip_derived_cl4781])).
% 48.13/7.42 thf(zip_derived_cl17087, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.42 ((multiply @ (multiply @ X2 @ X1) @ X0)
% 48.13/7.42 = (inverse @ (double_divide @ X2 @ (multiply @ X1 @ X0))))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl8449, zip_derived_cl6862])).
% 48.13/7.42 thf(zip_derived_cl6862, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]:
% 48.13/7.42 ((multiply @ X1 @ X0) = (inverse @ (double_divide @ X1 @ X0)))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl6834, zip_derived_cl4781])).
% 48.13/7.42 thf(zip_derived_cl17227, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.42 ((multiply @ (multiply @ X2 @ X1) @ X0)
% 48.13/7.42 = (multiply @ X2 @ (multiply @ X1 @ X0)))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl17087, zip_derived_cl6862])).
% 48.13/7.42 thf(zip_derived_cl8023, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i]: ((multiply @ X0 @ X1) = (multiply @ X1 @ X0))),
% 48.13/7.42 inference('s_sup+', [status(thm)], [zip_derived_cl6862, zip_derived_cl1])).
% 48.13/7.42 thf(zip_derived_cl17512, plain,
% 48.13/7.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 48.13/7.42 ((multiply @ X0 @ (multiply @ X2 @ X1))
% 48.13/7.42 = (multiply @ X2 @ (multiply @ X1 @ X0)))),
% 48.13/7.42 inference('s_sup+', [status(thm)],
% 48.13/7.42 [zip_derived_cl17227, zip_derived_cl8023])).
% 48.13/7.42 thf(zip_derived_cl17660, plain,
% 48.13/7.42 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 48.13/7.42 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 48.13/7.42 inference('demod', [status(thm)],
% 48.13/7.42 [zip_derived_cl8069, zip_derived_cl17512])).
% 48.13/7.42 thf(zip_derived_cl17661, plain, ($false),
% 48.13/7.42 inference('simplify', [status(thm)], [zip_derived_cl17660])).
% 48.13/7.42
% 48.13/7.42 % SZS output end Refutation
% 48.13/7.42
% 48.13/7.42
% 48.13/7.42 % Terminating...
% 48.54/7.50 % Runner terminated.
% 48.54/7.51 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------