%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP050-1 : TPTP v9.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.5HPoSyBdpq true
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:35:32 PM UTC 2025
% Result : Unsatisfiable 13.61s 3.69s
% Output : Refutation 13.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : GRP050-1 : TPTP v9.2.0. Released v1.0.0.
% 0.02/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.5HPoSyBdpq true
% 0.07/0.36 % Computer : n027.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8042.1875MB
% 0.07/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Wed Oct 1 14:23:23 EDT 2025
% 0.07/0.36 % CPUTime :
% 0.07/0.36 % Running portfolio for 300 s
% 0.07/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36 % Number of cores: 8
% 0.07/0.36 % Python version: Python 3.6.8
% 0.07/0.37 % Running in FO mode
% 0.40/0.57 % Total configuration time : 435
% 0.40/0.57 % Estimated wc time : 1092
% 0.40/0.57 % Estimated cpu time (7 cpus) : 156.0
% 0.63/0.64 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.63/0.65 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.73/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.73/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.83/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.83/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.83/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 13.61/3.69 % Solved by fo/fo7.sh.
% 13.61/3.69 % done 552 iterations in 2.879s
% 13.61/3.69 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 13.61/3.69 % SZS output start Refutation
% 13.61/3.69 thf(inverse_type, type, inverse: $i > $i).
% 13.61/3.69 thf(b1_type, type, b1: $i).
% 13.61/3.69 thf(b3_type, type, b3: $i).
% 13.61/3.69 thf(b2_type, type, b2: $i).
% 13.61/3.69 thf(multiply_type, type, multiply: $i > $i > $i).
% 13.61/3.69 thf(a3_type, type, a3: $i).
% 13.61/3.69 thf(c3_type, type, c3: $i).
% 13.61/3.69 thf(a2_type, type, a2: $i).
% 13.61/3.69 thf(a1_type, type, a1: $i).
% 13.61/3.69 thf(single_axiom, axiom,
% 13.61/3.69 (( multiply @
% 13.61/3.69 Z @
% 13.61/3.69 ( inverse @
% 13.61/3.69 ( multiply @
% 13.61/3.69 ( inverse @ ( multiply @ ( inverse @ ( multiply @ Z @ Y ) ) @ X ) ) @
% 13.61/3.69 ( multiply @ ( inverse @ Y ) @ ( multiply @ ( inverse @ Y ) @ Y ) ) ) ) ) =
% 13.61/3.69 ( X ))).
% 13.61/3.69 thf(zip_derived_cl0, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ X1 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))
% 13.61/3.69 = (X0))),
% 13.61/3.69 inference('cnf', [status(esa)], [single_axiom])).
% 13.61/3.69 thf(zip_derived_cl0, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ X1 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))
% 13.61/3.69 = (X0))),
% 13.61/3.69 inference('cnf', [status(esa)], [single_axiom])).
% 13.61/3.69 thf(zip_derived_cl0, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ X1 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))
% 13.61/3.69 = (X0))),
% 13.61/3.69 inference('cnf', [status(esa)], [single_axiom])).
% 13.61/3.69 thf(zip_derived_cl3, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.61/3.69 ((multiply @ X3 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ X0) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X3 @ X2)) @ X1)) @
% 13.61/3.69 X0)) @
% 13.61/3.69 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X1) @ X1)))))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl3, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.61/3.69 ((multiply @ X3 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ X0) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X3 @ X2)) @ X1)) @
% 13.61/3.69 X0)) @
% 13.61/3.69 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X1) @ X1)))))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl0, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ X1 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))
% 13.61/3.69 = (X0))),
% 13.61/3.69 inference('cnf', [status(esa)], [single_axiom])).
% 13.61/3.69 thf(zip_derived_cl15, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 13.61/3.69 (multiply @ X2 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ X1) @
% 13.61/3.69 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X0) @ X0))))))
% 13.61/3.69 = (X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl39, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @
% 13.61/3.69 (multiply @ X4 @
% 13.61/3.69 (multiply @ X2 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ X1) @
% 13.61/3.69 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X0) @ X0)))))))
% 13.61/3.69 = (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X2 @ X0)) @ X3)) @
% 13.61/3.69 X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl15])).
% 13.61/3.69 thf(zip_derived_cl83, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @ (multiply @ X4 @ X0))
% 13.61/3.69 = (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X3)) @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X0)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl39])).
% 13.61/3.69 thf(zip_derived_cl3, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.61/3.69 ((multiply @ X3 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ X0) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X3 @ X2)) @ X1)) @
% 13.61/3.69 X0)) @
% 13.61/3.69 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X1) @ X1)))))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl140, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ X4 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X4 @ X3)) @ X0)) @
% 13.61/3.69 (multiply @ (inverse @ X3) @ (multiply @ (inverse @ X3) @ X3)))))
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 13.61/3.69 (multiply @ X1 @ X0))) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl3])).
% 13.61/3.69 thf(zip_derived_cl0, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ X1 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))
% 13.61/3.69 = (X0))),
% 13.61/3.69 inference('cnf', [status(esa)], [single_axiom])).
% 13.61/3.69 thf(zip_derived_cl237, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((X0)
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 13.61/3.69 (multiply @ X1 @ X0))) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))),
% 13.61/3.69 inference('demod', [status(thm)], [zip_derived_cl140, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl0, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ X1 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))
% 13.61/3.69 = (X0))),
% 13.61/3.69 inference('cnf', [status(esa)], [single_axiom])).
% 13.61/3.69 thf(zip_derived_cl346, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ X0 @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 13.61/3.69 (multiply @ X2 @ X0))))))
% 13.61/3.69 = (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X1) @ X1)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl237, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl15, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 13.61/3.69 (multiply @ X2 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ X1) @
% 13.61/3.69 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X0) @ X0))))))
% 13.61/3.69 = (X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl840, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 13.61/3.69 (multiply @ X2 @ (inverse @ X1)))) @
% 13.61/3.69 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X0) @ X0)))
% 13.61/3.69 = (X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl346, zip_derived_cl15])).
% 13.61/3.69 thf(zip_derived_cl237, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((X0)
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 13.61/3.69 (multiply @ X1 @ X0))) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))),
% 13.61/3.69 inference('demod', [status(thm)], [zip_derived_cl140, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl83, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @ (multiply @ X4 @ X0))
% 13.61/3.69 = (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X3)) @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X0)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl39])).
% 13.61/3.69 thf(zip_derived_cl83, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @ (multiply @ X4 @ X0))
% 13.61/3.69 = (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X3)) @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X2 @ X1)) @ X0)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl39])).
% 13.61/3.69 thf(zip_derived_cl149, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X3 @ X2)) @ (multiply @ X3 @ X0))
% 13.61/3.69 = (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 13.61/3.69 (multiply @ X1 @ X0)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl83])).
% 13.61/3.69 thf(zip_derived_cl339, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ X4 @
% 13.61/3.69 (multiply @ (inverse @ X3) @ (multiply @ (inverse @ X3) @ X3)))) @
% 13.61/3.69 (multiply @ X4 @ X1))
% 13.61/3.69 = (multiply @ X0 @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X2 @ X3)) @
% 13.61/3.69 (multiply @ X2 @ X0))) @
% 13.61/3.69 X1)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl237, zip_derived_cl149])).
% 13.61/3.69 thf(zip_derived_cl339, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ X4 @
% 13.61/3.69 (multiply @ (inverse @ X3) @ (multiply @ (inverse @ X3) @ X3)))) @
% 13.61/3.69 (multiply @ X4 @ X1))
% 13.61/3.69 = (multiply @ X0 @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X2 @ X3)) @
% 13.61/3.69 (multiply @ X2 @ X0))) @
% 13.61/3.69 X1)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl237, zip_derived_cl149])).
% 13.61/3.69 thf(zip_derived_cl536, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 13.61/3.69 ((multiply @ X1 @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X2 @ X3)) @
% 13.61/3.69 (multiply @ X2 @ X1))) @
% 13.61/3.69 X0))
% 13.61/3.69 = (multiply @ X4 @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X5 @ X3)) @
% 13.61/3.69 (multiply @ X5 @ X4))) @
% 13.61/3.69 X0)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl339, zip_derived_cl339])).
% 13.61/3.69 thf(zip_derived_cl980, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X0) @ X0)
% 13.61/3.69 = (multiply @ X2 @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X3 @ X1)) @
% 13.61/3.69 (multiply @ X3 @ X2))) @
% 13.61/3.69 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X1) @ X1)))))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl840, zip_derived_cl536])).
% 13.61/3.69 thf(zip_derived_cl980, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X0) @ X0)
% 13.61/3.69 = (multiply @ X2 @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X3 @ X1)) @
% 13.61/3.69 (multiply @ X3 @ X2))) @
% 13.61/3.69 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X1) @ X1)))))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl840, zip_derived_cl536])).
% 13.61/3.69 thf(zip_derived_cl1075, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X0) @ X0))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl980, zip_derived_cl980])).
% 13.61/3.69 thf(prove_these_axioms, conjecture,
% 13.61/3.69 (~( ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 13.61/3.69 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 13.61/3.69 ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) != ( a2 ) ) |
% 13.61/3.69 ( ( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 13.61/3.69 ( multiply @ ( inverse @ b1 ) @ b1 ) ) ))).
% 13.61/3.69 thf(zf_stmt_0, negated_conjecture,
% 13.61/3.69 (( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 13.61/3.69 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) ) |
% 13.61/3.69 ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) != ( a2 ) ) |
% 13.61/3.69 ( ( multiply @ ( inverse @ a1 ) @ a1 ) !=
% 13.61/3.69 ( multiply @ ( inverse @ b1 ) @ b1 ) )),
% 13.61/3.69 inference('cnf.neg', [status(esa)], [prove_these_axioms])).
% 13.61/3.69 thf(zip_derived_cl1, plain,
% 13.61/3.69 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 13.61/3.69 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 13.61/3.69 | ((multiply @ (multiply @ (inverse @ b2) @ b2) @ a2) != (a2))
% 13.61/3.69 | ((multiply @ (inverse @ a1) @ a1) != (multiply @ (inverse @ b1) @ b1)))),
% 13.61/3.69 inference('cnf', [status(esa)], [zf_stmt_0])).
% 13.61/3.69 thf(zip_derived_cl1375, plain,
% 13.61/3.69 (![X0 : $i]:
% 13.61/3.69 (((multiply @ (multiply @ (inverse @ X0) @ X0) @ a2) != (a2))
% 13.61/3.69 | ((multiply @ (inverse @ a1) @ a1)
% 13.61/3.69 != (multiply @ (inverse @ b1) @ b1))
% 13.61/3.69 | ((multiply @ (multiply @ a3 @ b3) @ c3)
% 13.61/3.69 != (multiply @ a3 @ (multiply @ b3 @ c3))))),
% 13.61/3.69 inference('sup-', [status(thm)], [zip_derived_cl1075, zip_derived_cl1])).
% 13.61/3.69 thf(zip_derived_cl1075, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X0) @ X0))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl980, zip_derived_cl980])).
% 13.61/3.69 thf(zip_derived_cl1458, plain,
% 13.61/3.69 (![X0 : $i]:
% 13.61/3.69 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 13.61/3.69 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 13.61/3.69 | ((multiply @ (multiply @ (inverse @ X0) @ X0) @ a2) != (a2)))),
% 13.61/3.69 inference('simplify_reflect+', [status(thm)],
% 13.61/3.69 [zip_derived_cl1375, zip_derived_cl1075])).
% 13.61/3.69 thf(zip_derived_cl237, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((X0)
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 13.61/3.69 (multiply @ X1 @ X0))) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))),
% 13.61/3.69 inference('demod', [status(thm)], [zip_derived_cl140, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl237, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((X0)
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 13.61/3.69 (multiply @ X1 @ X0))) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))),
% 13.61/3.69 inference('demod', [status(thm)], [zip_derived_cl140, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl1075, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X0) @ X0))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl980, zip_derived_cl980])).
% 13.61/3.69 thf(zip_derived_cl980, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X0) @ X0)
% 13.61/3.69 = (multiply @ X2 @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X3 @ X1)) @
% 13.61/3.69 (multiply @ X3 @ X2))) @
% 13.61/3.69 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X1) @ X1)))))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl840, zip_derived_cl536])).
% 13.61/3.69 thf(zip_derived_cl3, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 13.61/3.69 ((multiply @ X3 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ X0) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X3 @ X2)) @ X1)) @
% 13.61/3.69 X0)) @
% 13.61/3.69 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X1) @ X1)))))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl1078, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 13.61/3.69 ((multiply @ X4 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X5 @ X2)) @
% 13.61/3.69 (multiply @ X5 @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X4 @ X3)) @ X1))))) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))) @
% 13.61/3.69 (multiply @ (inverse @ X3) @ (multiply @ (inverse @ X3) @ X3)))))
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 13.61/3.69 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X1) @ X1)))))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl980, zip_derived_cl3])).
% 13.61/3.69 thf(zip_derived_cl840, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 13.61/3.69 (multiply @ X2 @ (inverse @ X1)))) @
% 13.61/3.69 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X0) @ X0)))
% 13.61/3.69 = (X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl346, zip_derived_cl15])).
% 13.61/3.69 thf(zip_derived_cl0, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ X1 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X1 @ X2)) @ X0)) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))
% 13.61/3.69 = (X0))),
% 13.61/3.69 inference('cnf', [status(esa)], [single_axiom])).
% 13.61/3.69 thf(zip_derived_cl1241, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((X1)
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ (inverse @ X0) @ X0)) @
% 13.61/3.69 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X1) @ X1)))))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl1078, zip_derived_cl840, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl237, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((X0)
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 13.61/3.69 (multiply @ X1 @ X0))) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))),
% 13.61/3.69 inference('demod', [status(thm)], [zip_derived_cl140, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl1521, plain,
% 13.61/3.69 (![X0 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X0) @ X0)
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @ X0 @
% 13.61/3.69 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X0) @ X0)))))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl1241, zip_derived_cl237])).
% 13.61/3.69 thf(zip_derived_cl15, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 13.61/3.69 (multiply @ X2 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ X1) @
% 13.61/3.69 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X0) @ X0))))))
% 13.61/3.69 = (X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl1662, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X1 @ (inverse @ X0))) @
% 13.61/3.69 (multiply @ X1 @
% 13.61/3.69 (multiply @ (inverse @ (inverse @ X0)) @ (inverse @ X0))))
% 13.61/3.69 = (X0))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl1521, zip_derived_cl15])).
% 13.61/3.69 thf(zip_derived_cl1075, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X0) @ X0))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl980, zip_derived_cl980])).
% 13.61/3.69 thf(zip_derived_cl1730, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X1 @ (inverse @ X0))) @
% 13.61/3.69 (multiply @ X1 @ (multiply @ (inverse @ X0) @ X0))) = (X0))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl1662, zip_derived_cl1075])).
% 13.61/3.69 thf(zip_derived_cl2742, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X2 @ (inverse @ X1))) @
% 13.61/3.69 (multiply @ X2 @ (multiply @ (inverse @ X0) @ X0))) = (X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl1075, zip_derived_cl1730])).
% 13.61/3.69 thf(zip_derived_cl15, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 13.61/3.69 (multiply @ X2 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ X1) @
% 13.61/3.69 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X0) @ X0))))))
% 13.61/3.69 = (X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl3236, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 13.61/3.69 (multiply @ X2 @ (inverse @ X0)))
% 13.61/3.69 = (multiply @ (inverse @ X1) @ (inverse @ X0)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl2742, zip_derived_cl15])).
% 13.61/3.69 thf(zip_derived_cl3422, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @ (multiply @ X4 @ X0))
% 13.61/3.69 = (multiply @ (inverse @ X3) @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X2 @ X1)) @
% 13.61/3.69 (multiply @ X2 @ X0))) @
% 13.61/3.69 (multiply @ (inverse @ X1) @ (multiply @ (inverse @ X1) @ X1))))))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl237, zip_derived_cl3236])).
% 13.61/3.69 thf(zip_derived_cl237, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((X0)
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ X1 @ X2)) @
% 13.61/3.69 (multiply @ X1 @ X0))) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X2) @ X2)))))),
% 13.61/3.69 inference('demod', [status(thm)], [zip_derived_cl140, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl3460, plain,
% 13.61/3.69 (![X0 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @ (multiply @ X4 @ X0))
% 13.61/3.69 = (multiply @ (inverse @ X3) @ X0))),
% 13.61/3.69 inference('demod', [status(thm)], [zip_derived_cl3422, zip_derived_cl237])).
% 13.61/3.69 thf(zip_derived_cl3460, plain,
% 13.61/3.69 (![X0 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @ (multiply @ X4 @ X0))
% 13.61/3.69 = (multiply @ (inverse @ X3) @ X0))),
% 13.61/3.69 inference('demod', [status(thm)], [zip_derived_cl3422, zip_derived_cl237])).
% 13.61/3.69 thf(zip_derived_cl3508, plain,
% 13.61/3.69 (![X0 : $i, X2 : $i]:
% 13.61/3.69 ((X0)
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X2) @ X2))))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl237, zip_derived_cl3460, zip_derived_cl3460])).
% 13.61/3.69 thf(zip_derived_cl15, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X2 @ X0)) @
% 13.61/3.69 (multiply @ X2 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ X1) @
% 13.61/3.69 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X0) @ X0))))))
% 13.61/3.69 = (X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl0])).
% 13.61/3.69 thf(zip_derived_cl3631, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ X0 @
% 13.61/3.69 (multiply @ (inverse @ X0) @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ X1) @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ (inverse @ X2) @ X2)) @
% 13.61/3.69 (multiply @ (inverse @ X2) @ X2)))))))
% 13.61/3.69 = (X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3508, zip_derived_cl15])).
% 13.61/3.69 thf(zip_derived_cl3460, plain,
% 13.61/3.69 (![X0 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @ (multiply @ X4 @ X0))
% 13.61/3.69 = (multiply @ (inverse @ X3) @ X0))),
% 13.61/3.69 inference('demod', [status(thm)], [zip_derived_cl3422, zip_derived_cl237])).
% 13.61/3.69 thf(zip_derived_cl3460, plain,
% 13.61/3.69 (![X0 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @ (multiply @ X4 @ X0))
% 13.61/3.69 = (multiply @ (inverse @ X3) @ X0))),
% 13.61/3.69 inference('demod', [status(thm)], [zip_derived_cl3422, zip_derived_cl237])).
% 13.61/3.69 thf(zip_derived_cl3508, plain,
% 13.61/3.69 (![X0 : $i, X2 : $i]:
% 13.61/3.69 ((X0)
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X2) @ X2))))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl237, zip_derived_cl3460, zip_derived_cl3460])).
% 13.61/3.69 thf(zip_derived_cl3700, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)) = (X1))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl3631, zip_derived_cl3460, zip_derived_cl3460,
% 13.61/3.69 zip_derived_cl3508])).
% 13.61/3.69 thf(zip_derived_cl3508, plain,
% 13.61/3.69 (![X0 : $i, X2 : $i]:
% 13.61/3.69 ((X0)
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X2) @ X2))))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl237, zip_derived_cl3460, zip_derived_cl3460])).
% 13.61/3.69 thf(zip_derived_cl3777, plain,
% 13.61/3.69 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3700, zip_derived_cl3508])).
% 13.61/3.69 thf(zip_derived_cl1075, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X0) @ X0))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl980, zip_derived_cl980])).
% 13.61/3.69 thf(zip_derived_cl3821, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X1) @ X1) = (multiply @ X0 @ (inverse @ X0)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3777, zip_derived_cl1075])).
% 13.61/3.69 thf(zip_derived_cl1075, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X0) @ X0))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl980, zip_derived_cl980])).
% 13.61/3.69 thf(zip_derived_cl1075, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X1) @ X1) = (multiply @ (inverse @ X0) @ X0))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl980, zip_derived_cl980])).
% 13.61/3.69 thf(zip_derived_cl3700, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)) = (X1))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl3631, zip_derived_cl3460, zip_derived_cl3460,
% 13.61/3.69 zip_derived_cl3508])).
% 13.61/3.69 thf(zip_derived_cl3782, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ X1 @ (multiply @ (inverse @ X0) @ X0)) = (X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl1075, zip_derived_cl3700])).
% 13.61/3.69 thf(zip_derived_cl3460, plain,
% 13.61/3.69 (![X0 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @ (multiply @ X4 @ X0))
% 13.61/3.69 = (multiply @ (inverse @ X3) @ X0))),
% 13.61/3.69 inference('demod', [status(thm)], [zip_derived_cl3422, zip_derived_cl237])).
% 13.61/3.69 thf(zip_derived_cl3865, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X0 @ X2)) @ X0)
% 13.61/3.69 = (multiply @ (inverse @ X2) @ (multiply @ (inverse @ X1) @ X1)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3782, zip_derived_cl3460])).
% 13.61/3.69 thf(zip_derived_cl3782, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ X1 @ (multiply @ (inverse @ X0) @ X0)) = (X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl1075, zip_derived_cl3700])).
% 13.61/3.69 thf(zip_derived_cl3893, plain,
% 13.61/3.69 (![X0 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X0 @ X2)) @ X0) = (inverse @ X2))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl3865, zip_derived_cl3782])).
% 13.61/3.69 thf(zip_derived_cl3777, plain,
% 13.61/3.69 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3700, zip_derived_cl3508])).
% 13.61/3.69 thf(zip_derived_cl3782, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ X1 @ (multiply @ (inverse @ X0) @ X0)) = (X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl1075, zip_derived_cl3700])).
% 13.61/3.69 thf(zip_derived_cl3888, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))) = (X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3777, zip_derived_cl3782])).
% 13.61/3.69 thf(zip_derived_cl3460, plain,
% 13.61/3.69 (![X0 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @ (multiply @ X4 @ X0))
% 13.61/3.69 = (multiply @ (inverse @ X3) @ X0))),
% 13.61/3.69 inference('demod', [status(thm)], [zip_derived_cl3422, zip_derived_cl237])).
% 13.61/3.69 thf(zip_derived_cl3915, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((inverse @ (multiply @ X1 @ X0))
% 13.61/3.69 = (multiply @ (inverse @ X0) @ (inverse @ X1)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3888, zip_derived_cl3460])).
% 13.61/3.69 thf(zip_derived_cl4044, plain,
% 13.61/3.69 (![X0 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (multiply @ (inverse @ X2) @ (inverse @ X0)) @ X0)
% 13.61/3.69 = (inverse @ X2))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl3893, zip_derived_cl3915])).
% 13.61/3.69 thf(zip_derived_cl4051, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ (multiply @ (inverse @ X0) @ X0) @ X1)
% 13.61/3.69 = (inverse @ (inverse @ X1)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl1075, zip_derived_cl4044])).
% 13.61/3.69 thf(zip_derived_cl3821, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X1) @ X1) = (multiply @ X0 @ (inverse @ X0)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3777, zip_derived_cl1075])).
% 13.61/3.69 thf(zip_derived_cl3777, plain,
% 13.61/3.69 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3700, zip_derived_cl3508])).
% 13.61/3.69 thf(zip_derived_cl4061, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((multiply @ (multiply @ X0 @ (inverse @ X0)) @ X1) = (X1))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl4051, zip_derived_cl3821, zip_derived_cl3777])).
% 13.61/3.69 thf(zip_derived_cl4164, plain,
% 13.61/3.69 ((((multiply @ (multiply @ a3 @ b3) @ c3)
% 13.61/3.69 != (multiply @ a3 @ (multiply @ b3 @ c3)))
% 13.61/3.69 | ((a2) != (a2)))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl1458, zip_derived_cl3821, zip_derived_cl4061])).
% 13.61/3.69 thf(zip_derived_cl4165, plain,
% 13.61/3.69 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 13.61/3.69 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 13.61/3.69 inference('simplify', [status(thm)], [zip_derived_cl4164])).
% 13.61/3.69 thf(zip_derived_cl3777, plain,
% 13.61/3.69 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3700, zip_derived_cl3508])).
% 13.61/3.69 thf(zip_derived_cl3777, plain,
% 13.61/3.69 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3700, zip_derived_cl3508])).
% 13.61/3.69 thf(zip_derived_cl3508, plain,
% 13.61/3.69 (![X0 : $i, X2 : $i]:
% 13.61/3.69 ((X0)
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X2) @ X2))))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl237, zip_derived_cl3460, zip_derived_cl3460])).
% 13.61/3.69 thf(zip_derived_cl39, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @
% 13.61/3.69 (multiply @ X4 @
% 13.61/3.69 (multiply @ X2 @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ X1) @
% 13.61/3.69 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X0) @ X0)))))))
% 13.61/3.69 = (multiply @
% 13.61/3.69 (inverse @ (multiply @ (inverse @ (multiply @ X2 @ X0)) @ X3)) @
% 13.61/3.69 X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl15])).
% 13.61/3.69 thf(zip_derived_cl3632, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X2)) @
% 13.61/3.69 (multiply @ X4 @
% 13.61/3.69 (multiply @ (inverse @ X0) @
% 13.61/3.69 (inverse @
% 13.61/3.69 (multiply @ (inverse @ X1) @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ (inverse @ X3) @ X3)) @
% 13.61/3.69 (multiply @ (inverse @ (multiply @ (inverse @ X3) @ X3)) @
% 13.61/3.69 (multiply @ (inverse @ X3) @ X3))))))))
% 13.61/3.69 = (multiply @ (inverse @ (multiply @ X0 @ X2)) @ X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3508, zip_derived_cl39])).
% 13.61/3.69 thf(zip_derived_cl3460, plain,
% 13.61/3.69 (![X0 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @ (multiply @ X4 @ X0))
% 13.61/3.69 = (multiply @ (inverse @ X3) @ X0))),
% 13.61/3.69 inference('demod', [status(thm)], [zip_derived_cl3422, zip_derived_cl237])).
% 13.61/3.69 thf(zip_derived_cl3460, plain,
% 13.61/3.69 (![X0 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @ (multiply @ X4 @ X0))
% 13.61/3.69 = (multiply @ (inverse @ X3) @ X0))),
% 13.61/3.69 inference('demod', [status(thm)], [zip_derived_cl3422, zip_derived_cl237])).
% 13.61/3.69 thf(zip_derived_cl3508, plain,
% 13.61/3.69 (![X0 : $i, X2 : $i]:
% 13.61/3.69 ((X0)
% 13.61/3.69 = (inverse @
% 13.61/3.69 (multiply @ (inverse @ X0) @ (multiply @ (inverse @ X2) @ X2))))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl237, zip_derived_cl3460, zip_derived_cl3460])).
% 13.61/3.69 thf(zip_derived_cl3460, plain,
% 13.61/3.69 (![X0 : $i, X3 : $i, X4 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (multiply @ X4 @ X3)) @ (multiply @ X4 @ X0))
% 13.61/3.69 = (multiply @ (inverse @ X3) @ X0))),
% 13.61/3.69 inference('demod', [status(thm)], [zip_derived_cl3422, zip_derived_cl237])).
% 13.61/3.69 thf(zip_derived_cl3701, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X2) @ (multiply @ (inverse @ X0) @ X1))
% 13.61/3.69 = (multiply @ (inverse @ (multiply @ X0 @ X2)) @ X1))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl3632, zip_derived_cl3460, zip_derived_cl3460,
% 13.61/3.69 zip_derived_cl3508, zip_derived_cl3460])).
% 13.61/3.69 thf(zip_derived_cl3915, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i]:
% 13.61/3.69 ((inverse @ (multiply @ X1 @ X0))
% 13.61/3.69 = (multiply @ (inverse @ X0) @ (inverse @ X1)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3888, zip_derived_cl3460])).
% 13.61/3.69 thf(zip_derived_cl4860, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X2) @ (multiply @ (inverse @ X0) @ X1))
% 13.61/3.69 = (multiply @ (multiply @ (inverse @ X2) @ (inverse @ X0)) @ X1))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl3701, zip_derived_cl3915])).
% 13.61/3.69 thf(zip_derived_cl4900, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X2) @
% 13.61/3.69 (multiply @ (inverse @ (inverse @ X0)) @ X1))
% 13.61/3.69 = (multiply @ (multiply @ (inverse @ X2) @ X0) @ X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3777, zip_derived_cl4860])).
% 13.61/3.69 thf(zip_derived_cl3777, plain,
% 13.61/3.69 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3700, zip_derived_cl3508])).
% 13.61/3.69 thf(zip_derived_cl4928, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ X2) @ (multiply @ X0 @ X1))
% 13.61/3.69 = (multiply @ (multiply @ (inverse @ X2) @ X0) @ X1))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl4900, zip_derived_cl3777])).
% 13.61/3.69 thf(zip_derived_cl5000, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ (inverse @ (inverse @ X0)) @ (multiply @ X2 @ X1))
% 13.61/3.69 = (multiply @ (multiply @ X0 @ X2) @ X1))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3777, zip_derived_cl4928])).
% 13.61/3.69 thf(zip_derived_cl3777, plain,
% 13.61/3.69 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 13.61/3.69 inference('sup+', [status(thm)], [zip_derived_cl3700, zip_derived_cl3508])).
% 13.61/3.69 thf(zip_derived_cl5022, plain,
% 13.61/3.69 (![X0 : $i, X1 : $i, X2 : $i]:
% 13.61/3.69 ((multiply @ X0 @ (multiply @ X2 @ X1))
% 13.61/3.69 = (multiply @ (multiply @ X0 @ X2) @ X1))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl5000, zip_derived_cl3777])).
% 13.61/3.69 thf(zip_derived_cl5040, plain,
% 13.61/3.69 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 13.61/3.69 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 13.61/3.69 inference('demod', [status(thm)],
% 13.61/3.69 [zip_derived_cl4165, zip_derived_cl5022])).
% 13.61/3.69 thf(zip_derived_cl5041, plain, ($false),
% 13.61/3.69 inference('simplify', [status(thm)], [zip_derived_cl5040])).
% 13.61/3.69
% 13.61/3.69 % SZS output end Refutation
% 13.61/3.69
% 13.61/3.69
% 13.61/3.69 % Terminating...
% 14.04/3.86 % Runner terminated.
% 14.04/3.87 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------