TSTP Solution File: GRP495-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP495-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% 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 : 600s
% DateTime : Sat Jul 16 10:55:49 EDT 2022
% Result : Unsatisfiable 210.40s 210.24s
% Output : Proof 210.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP495-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.13 % Command : moca.sh %s
% 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 : 600
% 0.14/0.34 % DateTime : Tue Jun 14 13:48:54 EDT 2022
% 0.14/0.35 % CPUTime :
% 210.40/210.24 % SZS status Unsatisfiable
% 210.40/210.24 % SZS output start Proof
% 210.40/210.24 The input problem is unsatisfiable because
% 210.40/210.24
% 210.40/210.24 [1] the following set of Horn clauses is unsatisfiable:
% 210.40/210.24
% 210.40/210.24 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) = B
% 210.40/210.24 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 210.40/210.24 inverse(A) = double_divide(A, identity)
% 210.40/210.24 identity = double_divide(A, inverse(A))
% 210.40/210.24 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom
% 210.40/210.24
% 210.40/210.24 This holds because
% 210.40/210.24
% 210.40/210.24 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 210.40/210.24
% 210.40/210.24 E:
% 210.40/210.24 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) = B
% 210.40/210.24 f1(multiply(a3, multiply(b3, c3))) = false__
% 210.40/210.24 f1(multiply(multiply(a3, b3), c3)) = true__
% 210.40/210.24 identity = double_divide(A, inverse(A))
% 210.40/210.24 inverse(A) = double_divide(A, identity)
% 210.40/210.24 multiply(A, B) = double_divide(double_divide(B, A), identity)
% 210.40/210.24 G:
% 210.40/210.24 true__ = false__
% 210.40/210.24
% 210.40/210.24 This holds because
% 210.40/210.24
% 210.40/210.24 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 210.40/210.24
% 210.40/210.24 double_divide(X0, inverse(identity)) = double_divide(identity, double_divide(inverse(identity), inverse(X0)))
% 210.40/210.24 double_divide(X1, inverse(X0)) = inverse(double_divide(X0, inverse(X1)))
% 210.40/210.24 double_divide(Y0, double_divide(X1, X0)) = inverse(double_divide(X1, inverse(double_divide(X0, inverse(Y0)))))
% 210.40/210.24 double_divide(Y0, double_divide(X1, X0)) = inverse(double_divide(double_divide(inverse(X0), inverse(X1)), inverse(Y0)))
% 210.40/210.24 double_divide(Y0, double_divide(X1, inverse(X0))) = inverse(double_divide(double_divide(X0, inverse(X1)), inverse(Y0)))
% 210.40/210.24 double_divide(Y0, double_divide(X2, double_divide(inverse(X1), inverse(X0)))) = inverse(double_divide(double_divide(double_divide(X0, X1), inverse(X2)), inverse(Y0)))
% 210.40/210.24 double_divide(Y0, double_divide(Y1, double_divide(X1, X0))) = inverse(double_divide(double_divide(double_divide(inverse(X0), inverse(X1)), inverse(Y1)), inverse(Y0)))
% 210.40/210.24 double_divide(Y0, double_divide(Y1, double_divide(X1, inverse(X0)))) = inverse(double_divide(double_divide(double_divide(X0, inverse(X1)), inverse(Y1)), inverse(Y0)))
% 210.40/210.24 double_divide(Y0, double_divide(double_divide(X2, inverse(X1)), X0)) = inverse(double_divide(double_divide(inverse(X0), double_divide(X1, inverse(X2))), inverse(Y0)))
% 210.40/210.24 double_divide(Y0, double_divide(double_divide(inverse(X2), inverse(X1)), X0)) = inverse(double_divide(double_divide(inverse(X0), double_divide(X1, X2)), inverse(Y0)))
% 210.40/210.24 double_divide(Y0, double_divide(inverse(X1), X0)) = inverse(double_divide(double_divide(inverse(X0), X1), inverse(Y0)))
% 210.40/210.24 double_divide(double_divide(X1, X0), Y1) = inverse(double_divide(inverse(Y1), double_divide(inverse(X0), inverse(X1))))
% 210.40/210.24 double_divide(double_divide(X1, X0), inverse(Y1)) = inverse(double_divide(Y1, double_divide(inverse(X0), inverse(X1))))
% 210.40/210.24 double_divide(double_divide(X1, inverse(X0)), double_divide(Y1, Y2)) = inverse(double_divide(double_divide(inverse(Y2), inverse(Y1)), double_divide(X0, inverse(X1))))
% 210.40/210.24 double_divide(double_divide(X1, inverse(X0)), inverse(Y1)) = inverse(double_divide(Y1, double_divide(X0, inverse(X1))))
% 210.40/210.24 double_divide(double_divide(X2, double_divide(inverse(X1), inverse(X0))), Y1) = inverse(double_divide(inverse(Y1), double_divide(double_divide(X0, X1), inverse(X2))))
% 210.40/210.24 double_divide(double_divide(X2, double_divide(inverse(X1), inverse(X0))), inverse(Y1)) = inverse(double_divide(Y1, double_divide(double_divide(X0, X1), inverse(X2))))
% 210.40/210.24 double_divide(double_divide(Y0, Y1), double_divide(X1, X0)) = inverse(double_divide(double_divide(inverse(X0), inverse(X1)), double_divide(inverse(Y1), inverse(Y0))))
% 210.40/210.24 double_divide(double_divide(Y0, Y1), double_divide(X1, inverse(X0))) = inverse(double_divide(double_divide(X0, inverse(X1)), double_divide(inverse(Y1), inverse(Y0))))
% 210.40/210.24 double_divide(double_divide(Y0, Y1), double_divide(inverse(X1), X0)) = inverse(double_divide(double_divide(inverse(X0), X1), double_divide(inverse(Y1), inverse(Y0))))
% 210.40/210.24 double_divide(double_divide(Y0, Y1), double_divide(inverse(X1), inverse(X0))) = inverse(double_divide(double_divide(X0, X1), double_divide(inverse(Y1), inverse(Y0))))
% 210.40/210.24 double_divide(double_divide(Y0, double_divide(X1, X0)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(double_divide(inverse(X0), inverse(X1)), inverse(Y0))))
% 210.40/210.24 double_divide(double_divide(Y0, double_divide(X1, inverse(X0))), inverse(Y2)) = inverse(double_divide(Y2, double_divide(double_divide(X0, inverse(X1)), inverse(Y0))))
% 210.40/210.24 double_divide(double_divide(Y0, double_divide(inverse(X1), X0)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(double_divide(inverse(X0), X1), inverse(Y0))))
% 210.40/210.24 double_divide(double_divide(Y0, inverse(Y1)), double_divide(X1, inverse(X0))) = inverse(double_divide(double_divide(X0, inverse(X1)), double_divide(Y1, inverse(Y0))))
% 210.40/210.24 double_divide(double_divide(Y0, inverse(Y1)), double_divide(inverse(X1), X0)) = inverse(double_divide(double_divide(inverse(X0), X1), double_divide(Y1, inverse(Y0))))
% 210.40/210.24 double_divide(double_divide(double_divide(X1, X0), Y1), inverse(Y2)) = inverse(double_divide(Y2, double_divide(inverse(Y1), double_divide(inverse(X0), inverse(X1)))))
% 210.40/210.24 double_divide(double_divide(double_divide(X1, X0), inverse(Y1)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(Y1, double_divide(inverse(X0), inverse(X1)))))
% 210.40/210.24 double_divide(double_divide(double_divide(X1, inverse(X0)), inverse(Y1)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(Y1, double_divide(X0, inverse(X1)))))
% 210.40/210.24 double_divide(double_divide(double_divide(X2, inverse(X1)), X0), Y1) = inverse(double_divide(inverse(Y1), double_divide(inverse(X0), double_divide(X1, inverse(X2)))))
% 210.40/210.24 double_divide(double_divide(double_divide(X2, inverse(X1)), X0), inverse(Y1)) = inverse(double_divide(Y1, double_divide(inverse(X0), double_divide(X1, inverse(X2)))))
% 210.40/210.24 double_divide(double_divide(double_divide(inverse(X1), X0), inverse(Y1)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(Y1, double_divide(inverse(X0), X1))))
% 210.40/210.24 double_divide(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y1)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(Y1, double_divide(X0, X1))))
% 210.40/210.24 double_divide(double_divide(double_divide(inverse(X2), inverse(X1)), X0), Y1) = inverse(double_divide(inverse(Y1), double_divide(inverse(X0), double_divide(X1, X2))))
% 210.40/210.24 double_divide(double_divide(double_divide(inverse(X2), inverse(X1)), X0), inverse(Y1)) = inverse(double_divide(Y1, double_divide(inverse(X0), double_divide(X1, X2))))
% 210.40/210.24 double_divide(double_divide(inverse(X1), X0), double_divide(Y1, Y2)) = inverse(double_divide(double_divide(inverse(Y2), inverse(Y1)), double_divide(inverse(X0), X1)))
% 210.40/210.24 double_divide(double_divide(inverse(X1), X0), inverse(Y1)) = inverse(double_divide(Y1, double_divide(inverse(X0), X1)))
% 210.40/210.24 double_divide(double_divide(inverse(X1), inverse(X0)), double_divide(Y1, Y2)) = inverse(double_divide(double_divide(inverse(Y2), inverse(Y1)), double_divide(X0, X1)))
% 210.40/210.24 double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y1)) = inverse(double_divide(Y1, double_divide(X0, X1)))
% 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(X1, X0)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(double_divide(inverse(X0), inverse(X1)), Y0)))
% 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(X1, inverse(X0))), inverse(Y2)) = inverse(double_divide(Y2, double_divide(double_divide(X0, inverse(X1)), Y0)))
% 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(inverse(X1), X0)), inverse(Y2)) = inverse(double_divide(Y2, double_divide(double_divide(inverse(X0), X1), Y0)))
% 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(inverse(X1), inverse(X0))), inverse(Y2)) = inverse(double_divide(Y2, double_divide(double_divide(X0, X1), Y0)))
% 210.40/210.24 double_divide(inverse(X0), inverse(double_divide(inverse(X1), inverse(Y1)))) = inverse(double_divide(Y1, double_divide(inverse(X0), inverse(X1))))
% 210.40/210.24 double_divide(inverse(X1), Y0) = inverse(double_divide(inverse(Y0), X1))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(X1, X0)) = inverse(double_divide(X1, inverse(double_divide(X0, Y0))))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(X1, X0)) = inverse(double_divide(double_divide(inverse(X0), inverse(X1)), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(X1, inverse(X0))) = inverse(double_divide(double_divide(X0, inverse(X1)), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(X2, double_divide(inverse(X1), inverse(X0)))) = inverse(double_divide(double_divide(double_divide(X0, X1), inverse(X2)), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(Y1, double_divide(X1, X0))) = inverse(double_divide(double_divide(double_divide(inverse(X0), inverse(X1)), inverse(Y1)), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(Y1, double_divide(X1, inverse(X0)))) = inverse(double_divide(double_divide(double_divide(X0, inverse(X1)), inverse(Y1)), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(X1, X0), Y2)) = inverse(double_divide(double_divide(inverse(Y2), double_divide(inverse(X0), inverse(X1))), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(X1, X0), inverse(Y2))) = inverse(double_divide(double_divide(Y2, double_divide(inverse(X0), inverse(X1))), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(X1, inverse(X0)), inverse(Y2))) = inverse(double_divide(double_divide(Y2, double_divide(X0, inverse(X1))), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(X2, inverse(X1)), X0)) = inverse(double_divide(double_divide(inverse(X0), double_divide(X1, inverse(X2))), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(inverse(X1), X0), inverse(Y2))) = inverse(double_divide(double_divide(Y2, double_divide(inverse(X0), X1)), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y2))) = inverse(double_divide(double_divide(Y2, double_divide(X0, X1)), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(inverse(X2), inverse(X1)), X0)) = inverse(double_divide(double_divide(inverse(X0), double_divide(X1, X2)), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(inverse(X1), X0)) = inverse(double_divide(double_divide(inverse(X0), X1), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(inverse(X1), inverse(X0))) = inverse(double_divide(double_divide(X0, X1), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(inverse(Y1), double_divide(X1, X0))) = inverse(double_divide(double_divide(double_divide(inverse(X0), inverse(X1)), Y1), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(inverse(Y1), double_divide(X1, inverse(X0)))) = inverse(double_divide(double_divide(double_divide(X0, inverse(X1)), Y1), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(inverse(Y1), double_divide(inverse(X1), X0))) = inverse(double_divide(double_divide(double_divide(inverse(X0), X1), Y1), Y0))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(inverse(Y1), double_divide(inverse(X1), inverse(X0)))) = inverse(double_divide(double_divide(double_divide(X0, X1), Y1), Y0))
% 210.40/210.24 double_divide(inverse(Y0), inverse(X1)) = inverse(double_divide(X1, Y0))
% 210.40/210.24 double_divide(inverse(double_divide(X0, X1)), inverse(X2)) = inverse(double_divide(X2, inverse(double_divide(inverse(X1), inverse(X0)))))
% 210.40/210.24 double_divide(inverse(double_divide(inverse(X0), inverse(X1))), inverse(X2)) = inverse(double_divide(X2, inverse(double_divide(X1, X0))))
% 210.40/210.24 inverse(double_divide(double_divide(X1, X0), inverse(Y1))) = double_divide(Y1, double_divide(inverse(X0), inverse(X1)))
% 210.40/210.24 inverse(double_divide(double_divide(X1, inverse(X0)), double_divide(Y1, Y2))) = double_divide(double_divide(inverse(Y2), inverse(Y1)), double_divide(X0, inverse(X1)))
% 210.40/210.24 inverse(double_divide(double_divide(X2, double_divide(inverse(X1), inverse(X0))), inverse(Y1))) = double_divide(Y1, double_divide(double_divide(X0, X1), inverse(X2)))
% 210.40/210.24 inverse(double_divide(double_divide(Y0, Y1), double_divide(X1, X0))) = double_divide(double_divide(inverse(X0), inverse(X1)), double_divide(inverse(Y1), inverse(Y0)))
% 210.40/210.24 inverse(double_divide(double_divide(Y0, Y1), double_divide(X1, inverse(X0)))) = double_divide(double_divide(X0, inverse(X1)), double_divide(inverse(Y1), inverse(Y0)))
% 210.40/210.24 inverse(double_divide(double_divide(Y0, Y1), double_divide(inverse(X1), X0))) = double_divide(double_divide(inverse(X0), X1), double_divide(inverse(Y1), inverse(Y0)))
% 210.40/210.24 inverse(double_divide(double_divide(double_divide(X2, inverse(X1)), X0), inverse(Y1))) = double_divide(Y1, double_divide(inverse(X0), double_divide(X1, inverse(X2))))
% 210.40/210.24 inverse(double_divide(double_divide(double_divide(inverse(X2), inverse(X1)), X0), inverse(Y1))) = double_divide(Y1, double_divide(inverse(X0), double_divide(X1, X2)))
% 210.40/210.24 inverse(double_divide(double_divide(inverse(X1), X0), double_divide(Y1, Y2))) = double_divide(double_divide(inverse(Y2), inverse(Y1)), double_divide(inverse(X0), X1))
% 210.40/210.24 inverse(double_divide(inverse(X1), inverse(Y1))) = double_divide(Y1, X1)
% 210.40/210.24 inverse(double_divide(inverse(Y0), double_divide(X1, X0))) = double_divide(double_divide(inverse(X0), inverse(X1)), Y0)
% 210.40/210.24 inverse(double_divide(inverse(Y0), double_divide(X1, inverse(X0)))) = double_divide(double_divide(X0, inverse(X1)), Y0)
% 210.40/210.24 inverse(double_divide(inverse(Y0), double_divide(X2, double_divide(inverse(X1), inverse(X0))))) = double_divide(double_divide(double_divide(X0, X1), inverse(X2)), Y0)
% 210.40/210.24 inverse(double_divide(inverse(Y0), double_divide(Y1, double_divide(X1, X0)))) = double_divide(double_divide(double_divide(inverse(X0), inverse(X1)), inverse(Y1)), Y0)
% 210.40/210.24 inverse(double_divide(inverse(Y0), double_divide(double_divide(X2, inverse(X1)), X0))) = double_divide(double_divide(inverse(X0), double_divide(X1, inverse(X2))), Y0)
% 210.40/210.24 inverse(double_divide(inverse(Y0), double_divide(double_divide(inverse(X2), inverse(X1)), X0))) = double_divide(double_divide(inverse(X0), double_divide(X1, X2)), Y0)
% 210.40/210.24 inverse(double_divide(inverse(Y0), double_divide(inverse(X1), X0))) = double_divide(double_divide(inverse(X0), X1), Y0)
% 210.40/210.24 double_divide(A, identity) -> inverse(A)
% 210.40/210.24 double_divide(A, inverse(A)) -> identity
% 210.40/210.24 double_divide(X0, double_divide(Y1, X0)) -> Y1
% 210.40/210.24 double_divide(X0, double_divide(double_divide(inverse(Y1), inverse(Y2)), double_divide(inverse(X0), Y1))) -> Y2
% 210.40/210.24 double_divide(X0, double_divide(inverse(double_divide(X0, inverse(X1))), X1)) -> identity
% 210.40/210.24 double_divide(X0, inverse(double_divide(X1, double_divide(Y1, inverse(double_divide(X0, X1)))))) -> Y1
% 210.40/210.24 double_divide(X0, inverse(double_divide(inverse(X0), Y1))) -> inverse(Y1)
% 210.40/210.24 double_divide(X0, inverse(double_divide(inverse(X0), inverse(Y1)))) -> Y1
% 210.40/210.24 double_divide(X0, inverse(double_divide(inverse(X1), double_divide(Y1, inverse(double_divide(X0, inverse(X1))))))) -> Y1
% 210.40/210.24 double_divide(X0, inverse(double_divide(inverse(Y1), double_divide(Y2, double_divide(Y1, inverse(X0)))))) -> Y2
% 210.40/210.24 double_divide(Y0, double_divide(X1, double_divide(inverse(Y0), Y1))) -> inverse(double_divide(X1, inverse(Y1)))
% 210.40/210.24 double_divide(Y0, double_divide(double_divide(X0, inverse(Y2)), double_divide(inverse(Y0), inverse(X0)))) -> Y2
% 210.40/210.24 double_divide(Y0, double_divide(double_divide(Y1, X0), double_divide(inverse(Y0), inverse(Y1)))) -> inverse(X0)
% 210.40/210.24 double_divide(Y0, double_divide(double_divide(inverse(Y1), X0), double_divide(inverse(Y0), Y1))) -> inverse(X0)
% 210.40/210.24 double_divide(Y0, inverse(double_divide(X0, double_divide(Y2, double_divide(inverse(X0), inverse(Y0)))))) -> Y2
% 210.40/210.24 double_divide(double_divide(X0, X1), double_divide(inverse(X1), inverse(X0))) -> identity
% 210.40/210.24 double_divide(double_divide(X0, inverse(Y1)), double_divide(Y2, inverse(X0))) -> double_divide(Y1, inverse(Y2))
% 210.40/210.24 double_divide(double_divide(X1, X0), double_divide(Y1, inverse(double_divide(inverse(X0), inverse(X1))))) -> Y1
% 210.40/210.24 double_divide(double_divide(X1, X0), inverse(double_divide(double_divide(inverse(X0), inverse(X1)), Y1))) -> inverse(Y1)
% 210.40/210.24 double_divide(double_divide(X1, X0), inverse(double_divide(double_divide(inverse(X0), inverse(X1)), inverse(Y1)))) -> Y1
% 210.40/210.24 double_divide(double_divide(X1, Y1), X1) -> Y1
% 210.40/210.24 double_divide(double_divide(X1, inverse(X0)), X1) -> inverse(X0)
% 210.40/210.24 double_divide(double_divide(Y0, X0), double_divide(Y2, inverse(Y0))) -> double_divide(inverse(X0), inverse(Y2))
% 210.40/210.24 double_divide(double_divide(Y0, double_divide(X0, X1)), double_divide(Y2, inverse(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y0))))) -> Y2
% 210.40/210.24 double_divide(double_divide(Y0, double_divide(X0, X1)), double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y0))) -> identity
% 210.40/210.24 double_divide(double_divide(Y0, double_divide(X0, inverse(X1))), double_divide(Y2, inverse(double_divide(double_divide(X1, inverse(X0)), inverse(Y0))))) -> Y2
% 210.40/210.24 double_divide(double_divide(Y0, double_divide(X0, inverse(X1))), double_divide(double_divide(X1, inverse(X0)), inverse(Y0))) -> identity
% 210.40/210.24 double_divide(double_divide(Y0, double_divide(inverse(X0), X1)), double_divide(Y2, inverse(double_divide(double_divide(inverse(X1), X0), inverse(Y0))))) -> Y2
% 210.40/210.24 double_divide(double_divide(Y0, double_divide(inverse(X0), X1)), double_divide(double_divide(inverse(X1), X0), inverse(Y0))) -> identity
% 210.40/210.24 double_divide(double_divide(Y0, double_divide(inverse(X0), inverse(X1))), double_divide(Y2, inverse(double_divide(double_divide(X1, X0), inverse(Y0))))) -> Y2
% 210.40/210.24 double_divide(double_divide(Y0, double_divide(inverse(X0), inverse(X1))), double_divide(double_divide(X1, X0), inverse(Y0))) -> identity
% 210.40/210.24 double_divide(double_divide(Y1, Y0), X1) -> double_divide(inverse(Y0), inverse(double_divide(inverse(Y1), X1)))
% 210.40/210.24 double_divide(double_divide(double_divide(X0, X1), Y1), double_divide(Y2, inverse(double_divide(inverse(Y1), double_divide(inverse(X1), inverse(X0)))))) -> Y2
% 210.40/210.24 double_divide(double_divide(double_divide(X0, X1), Y1), double_divide(inverse(Y1), double_divide(inverse(X1), inverse(X0)))) -> identity
% 210.40/210.24 double_divide(double_divide(double_divide(X0, X1), inverse(X2)), double_divide(X2, double_divide(inverse(X1), inverse(X0)))) -> identity
% 210.40/210.24 double_divide(double_divide(double_divide(X0, inverse(X1)), Y1), double_divide(Y2, inverse(double_divide(inverse(Y1), double_divide(X1, inverse(X0)))))) -> Y2
% 210.40/210.24 double_divide(double_divide(double_divide(X0, inverse(X1)), Y1), double_divide(inverse(Y1), double_divide(X1, inverse(X0)))) -> identity
% 210.40/210.24 double_divide(double_divide(double_divide(X1, X0), inverse(Y1)), double_divide(Y2, inverse(double_divide(Y1, double_divide(inverse(X0), inverse(X1)))))) -> Y2
% 210.40/210.24 double_divide(double_divide(double_divide(X1, inverse(X0)), inverse(Y1)), double_divide(Y1, double_divide(X0, inverse(X1)))) -> identity
% 210.40/210.24 double_divide(double_divide(double_divide(X1, inverse(X0)), inverse(Y1)), double_divide(Y2, inverse(double_divide(Y1, double_divide(X0, inverse(X1)))))) -> Y2
% 210.40/210.24 double_divide(double_divide(double_divide(inverse(X0), X1), Y1), double_divide(Y2, inverse(double_divide(inverse(Y1), double_divide(inverse(X1), X0))))) -> Y2
% 210.40/210.24 double_divide(double_divide(double_divide(inverse(X0), X1), Y1), double_divide(inverse(Y1), double_divide(inverse(X1), X0))) -> identity
% 210.40/210.24 double_divide(double_divide(double_divide(inverse(X0), inverse(X1)), Y1), double_divide(Y2, inverse(double_divide(inverse(Y1), double_divide(X1, X0))))) -> Y2
% 210.40/210.24 double_divide(double_divide(double_divide(inverse(X0), inverse(X1)), Y1), double_divide(inverse(Y1), double_divide(X1, X0))) -> identity
% 210.40/210.24 double_divide(double_divide(double_divide(inverse(X1), X0), inverse(Y1)), double_divide(Y1, double_divide(inverse(X0), X1))) -> identity
% 210.40/210.24 double_divide(double_divide(double_divide(inverse(X1), X0), inverse(Y1)), double_divide(Y2, inverse(double_divide(Y1, double_divide(inverse(X0), X1))))) -> Y2
% 210.40/210.24 double_divide(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y1)), double_divide(Y1, double_divide(X0, X1))) -> identity
% 210.40/210.24 double_divide(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y1)), double_divide(Y2, inverse(double_divide(Y1, double_divide(X0, X1))))) -> Y2
% 210.40/210.24 double_divide(double_divide(identity, A), double_divide(double_divide(double_divide(B, C), double_divide(identity, identity)), double_divide(A, C))) -> B
% 210.40/210.24 double_divide(double_divide(identity, X0), X0) -> identity
% 210.40/210.24 double_divide(double_divide(identity, Y0), double_divide(double_divide(double_divide(Y1, Y2), inverse(identity)), double_divide(Y0, Y2))) -> Y1
% 210.40/210.24 double_divide(double_divide(identity, Y0), double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(Y0))) -> Y1
% 210.40/210.24 double_divide(double_divide(identity, Y0), double_divide(identity, double_divide(Y0, inverse(Y1)))) -> Y1
% 210.40/210.24 double_divide(double_divide(identity, Y0), double_divide(identity, inverse(Y0))) -> identity
% 210.40/210.24 double_divide(double_divide(identity, Y0), inverse(double_divide(double_divide(Y1, inverse(Y0)), inverse(identity)))) -> Y1
% 210.40/210.24 double_divide(double_divide(identity, Y1), inverse(identity)) -> Y1
% 210.40/210.24 double_divide(double_divide(identity, double_divide(identity, X0)), double_divide(identity, X0)) -> identity
% 210.40/210.24 double_divide(double_divide(identity, inverse(X0)), double_divide(identity, X0)) -> identity
% 210.40/210.24 double_divide(double_divide(identity, inverse(inverse(X0))), X0) -> identity
% 210.40/210.24 double_divide(double_divide(inverse(X0), inverse(X1)), double_divide(X1, X0)) -> identity
% 210.40/210.24 double_divide(double_divide(inverse(X0), inverse(X2)), X1) -> double_divide(X2, inverse(double_divide(X0, X1)))
% 210.40/210.24 double_divide(double_divide(inverse(X1), inverse(X0)), double_divide(Y1, inverse(double_divide(X0, X1)))) -> Y1
% 210.40/210.24 double_divide(double_divide(inverse(X1), inverse(X0)), inverse(double_divide(double_divide(X0, X1), Y1))) -> inverse(Y1)
% 210.40/210.24 double_divide(double_divide(inverse(X1), inverse(X0)), inverse(double_divide(double_divide(X0, X1), inverse(Y1)))) -> Y1
% 210.40/210.24 double_divide(double_divide(inverse(X1), inverse(X2)), double_divide(X0, X1)) -> double_divide(X2, inverse(X0))
% 210.40/210.24 double_divide(double_divide(inverse(Y0), X0), double_divide(Y2, Y0)) -> double_divide(inverse(X0), inverse(Y2))
% 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(X1, X0)), double_divide(Y2, inverse(double_divide(double_divide(inverse(X0), inverse(X1)), Y0)))) -> Y2
% 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(X1, X0)), double_divide(double_divide(inverse(X0), inverse(X1)), Y0)) -> identity
% 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(X1, inverse(X0))), double_divide(Y2, inverse(double_divide(double_divide(X0, inverse(X1)), Y0)))) -> Y2
% 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(X1, inverse(X0))), double_divide(double_divide(X0, inverse(X1)), Y0)) -> identity
% 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(inverse(X1), X0)), double_divide(Y2, inverse(double_divide(double_divide(inverse(X0), X1), Y0)))) -> Y2
% 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(inverse(X1), X0)), double_divide(double_divide(inverse(X0), X1), Y0)) -> identity
% 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(inverse(X1), inverse(X0))), double_divide(Y2, inverse(double_divide(double_divide(X0, X1), Y0)))) -> Y2
% 210.40/210.24 double_divide(double_divide(inverse(Y0), double_divide(inverse(X1), inverse(X0))), double_divide(double_divide(X0, X1), Y0)) -> identity
% 210.40/210.24 double_divide(double_divide(inverse(double_divide(X0, X1)), inverse(X1)), X0) -> identity
% 210.40/210.24 double_divide(double_divide(inverse(double_divide(X0, inverse(X1))), X1), X0) -> identity
% 210.40/210.24 double_divide(identity, X0) -> inverse(X0)
% 210.40/210.24 double_divide(identity, double_divide(double_divide(double_divide(Y1, Y2), inverse(identity)), double_divide(inverse(identity), Y2))) -> Y1
% 210.40/210.24 double_divide(identity, double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(inverse(identity)))) -> Y1
% 210.40/210.24 double_divide(identity, double_divide(identity, X0)) -> X0
% 210.40/210.24 double_divide(identity, double_divide(identity, X0)) -> double_divide(identity, inverse(X0))
% 210.40/210.24 double_divide(identity, double_divide(identity, double_divide(identity, inverse(Y0)))) -> Y0
% 210.40/210.24 double_divide(identity, double_divide(identity, double_divide(inverse(identity), inverse(Y1)))) -> Y1
% 210.40/210.24 double_divide(identity, double_divide(identity, inverse(Y0))) -> inverse(Y0)
% 210.40/210.24 double_divide(identity, inverse(X0)) -> inverse(inverse(X0))
% 210.40/210.24 double_divide(identity, inverse(double_divide(double_divide(Y1, inverse(inverse(identity))), inverse(identity)))) -> Y1
% 210.40/210.24 double_divide(identity, inverse(inverse(Y0))) -> double_divide(identity, Y0)
% 210.40/210.24 double_divide(inverse(X0), X0) -> identity
% 210.40/210.24 double_divide(inverse(X0), inverse(double_divide(inverse(X1), double_divide(Y1, inverse(double_divide(inverse(X0), inverse(X1))))))) -> Y1
% 210.40/210.24 double_divide(inverse(Y0), double_divide(X1, double_divide(Y0, Y1))) -> inverse(double_divide(X1, inverse(Y1)))
% 210.40/210.24 double_divide(inverse(Y0), double_divide(X1, double_divide(Y0, inverse(double_divide(inverse(Y2), X1))))) -> Y2
% 210.40/210.24 double_divide(inverse(Y0), double_divide(Y1, inverse(Y0))) -> Y1
% 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(X0, inverse(Y2)), double_divide(Y0, inverse(X0)))) -> Y2
% 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(Y1, X0), double_divide(Y0, inverse(Y1)))) -> inverse(X0)
% 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(inverse(Y1), X0), double_divide(Y0, Y1))) -> inverse(X0)
% 210.40/210.24 double_divide(inverse(Y0), double_divide(double_divide(inverse(Y2), inverse(Y1)), double_divide(Y0, Y2))) -> Y1
% 210.40/210.24 double_divide(inverse(Y0), double_divide(inverse(X0), inverse(Y0))) -> inverse(X0)
% 210.40/210.24 double_divide(inverse(Y0), inverse(double_divide(X0, double_divide(Y2, double_divide(inverse(X0), Y0))))) -> Y2
% 210.40/210.24 double_divide(inverse(Y0), inverse(double_divide(Y0, X0))) -> inverse(X0)
% 210.40/210.24 double_divide(inverse(Y0), inverse(double_divide(Y0, inverse(Y1)))) -> Y1
% 210.40/210.24 double_divide(inverse(Y0), inverse(double_divide(inverse(X1), double_divide(Y2, double_divide(X1, Y0))))) -> Y2
% 210.40/210.24 double_divide(inverse(Y0), inverse(double_divide(inverse(double_divide(Y0, X1)), double_divide(Y2, X1)))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(X0, X1)), double_divide(Y1, double_divide(inverse(X1), inverse(X0)))) -> Y1
% 210.40/210.24 double_divide(inverse(double_divide(X0, X1)), inverse(X1)) -> inverse(X0)
% 210.40/210.24 double_divide(inverse(double_divide(X0, X1)), inverse(double_divide(inverse(double_divide(inverse(X1), inverse(X0))), inverse(Y1)))) -> Y1
% 210.40/210.24 double_divide(inverse(double_divide(X0, inverse(X1))), X1) -> inverse(X0)
% 210.40/210.24 double_divide(inverse(double_divide(X1, Y1)), inverse(double_divide(inverse(Y1), double_divide(Y2, X1)))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(X2, inverse(double_divide(X1, X0)))), inverse(double_divide(inverse(X0), inverse(X1)))) -> inverse(X2)
% 210.40/210.24 double_divide(inverse(double_divide(X2, inverse(double_divide(inverse(X1), inverse(X0))))), inverse(double_divide(X0, X1))) -> inverse(X2)
% 210.40/210.24 double_divide(inverse(double_divide(Y0, Y1)), double_divide(double_divide(inverse(Y0), X0), Y1)) -> inverse(X0)
% 210.40/210.24 double_divide(inverse(double_divide(Y0, Y1)), inverse(double_divide(inverse(Y1), inverse(Y0)))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(Y0, Y1)), inverse(double_divide(inverse(double_divide(inverse(Y1), inverse(Y0))), X0))) -> inverse(X0)
% 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(X0, X1))), double_divide(Y2, double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y0)))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(X0, X1))), inverse(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y0)))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(X0, inverse(X1)))), double_divide(Y2, double_divide(double_divide(X1, inverse(X0)), inverse(Y0)))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(X0, inverse(X1)))), inverse(double_divide(double_divide(X1, inverse(X0)), inverse(Y0)))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(inverse(X0), X1))), double_divide(Y2, double_divide(double_divide(inverse(X1), X0), inverse(Y0)))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(inverse(X0), X1))), inverse(double_divide(double_divide(inverse(X1), X0), inverse(Y0)))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(inverse(X0), inverse(X1)))), double_divide(Y2, double_divide(double_divide(X1, X0), inverse(Y0)))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(Y0, double_divide(inverse(X0), inverse(X1)))), inverse(double_divide(double_divide(X1, X0), inverse(Y0)))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(Y1, X1)), double_divide(double_divide(inverse(Y1), inverse(Y2)), X1)) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(X0, X1), Y1)), double_divide(Y2, double_divide(inverse(Y1), double_divide(inverse(X1), inverse(X0))))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(X0, X1), Y1)), inverse(double_divide(inverse(Y1), double_divide(inverse(X1), inverse(X0))))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(X0, inverse(X1)), Y1)), double_divide(Y2, double_divide(inverse(Y1), double_divide(X1, inverse(X0))))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(X0, inverse(X1)), Y1)), inverse(double_divide(inverse(Y1), double_divide(X1, inverse(X0))))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(X1, X0), inverse(Y1))), double_divide(Y2, double_divide(Y1, double_divide(inverse(X0), inverse(X1))))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(X1, X0), inverse(Y1))), inverse(double_divide(Y1, double_divide(inverse(X0), inverse(X1))))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(X1, inverse(X0)), inverse(Y1))), double_divide(Y2, double_divide(Y1, double_divide(X0, inverse(X1))))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(X1, inverse(X0)), inverse(Y1))), inverse(double_divide(Y1, double_divide(X0, inverse(X1))))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X0), X1), Y1)), double_divide(Y2, double_divide(inverse(Y1), double_divide(inverse(X1), X0)))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X0), X1), Y1)), inverse(double_divide(inverse(Y1), double_divide(inverse(X1), X0)))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X0), inverse(X1)), Y1)), double_divide(Y2, double_divide(inverse(Y1), double_divide(X1, X0)))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X0), inverse(X1)), Y1)), inverse(double_divide(inverse(Y1), double_divide(X1, X0)))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X1), X0), inverse(Y1))), double_divide(Y2, double_divide(Y1, double_divide(inverse(X0), X1)))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X1), X0), inverse(Y1))), inverse(double_divide(Y1, double_divide(inverse(X0), X1)))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y1))), double_divide(Y2, double_divide(Y1, double_divide(X0, X1)))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(double_divide(inverse(X1), inverse(X0)), inverse(Y1))), inverse(double_divide(Y1, double_divide(X0, X1)))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(inverse(X0), Y1)), double_divide(double_divide(X0, inverse(Y2)), Y1)) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(inverse(X0), inverse(X1))), double_divide(Y1, double_divide(X1, X0))) -> Y1
% 210.40/210.24 double_divide(inverse(double_divide(inverse(X0), inverse(X1))), inverse(double_divide(inverse(double_divide(X1, X0)), inverse(Y1)))) -> Y1
% 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), Y1)), double_divide(double_divide(Y0, X0), Y1)) -> inverse(X0)
% 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(X1, X0))), double_divide(Y2, double_divide(double_divide(inverse(X0), inverse(X1)), Y0))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(X1, X0))), inverse(double_divide(double_divide(inverse(X0), inverse(X1)), Y0))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(X1, inverse(X0)))), double_divide(Y2, double_divide(double_divide(X0, inverse(X1)), Y0))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(X1, inverse(X0)))), inverse(double_divide(double_divide(X0, inverse(X1)), Y0))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(inverse(X1), X0))), double_divide(Y2, double_divide(double_divide(inverse(X0), X1), Y0))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(inverse(X1), X0))), inverse(double_divide(double_divide(inverse(X0), X1), Y0))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(inverse(X1), inverse(X0)))), double_divide(Y2, double_divide(double_divide(X0, X1), Y0))) -> Y2
% 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), double_divide(inverse(X1), inverse(X0)))), inverse(double_divide(double_divide(X0, X1), Y0))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), inverse(Y1))), inverse(double_divide(Y1, Y0))) -> identity
% 210.40/210.24 double_divide(inverse(double_divide(inverse(Y0), inverse(Y1))), inverse(double_divide(inverse(double_divide(Y1, Y0)), X0))) -> inverse(X0)
% 210.40/210.24 double_divide(inverse(identity), double_divide(double_divide(double_divide(Y1, Y2), inverse(identity)), double_divide(identity, Y2))) -> Y1
% 210.40/210.24 double_divide(inverse(identity), double_divide(double_divide(inverse(Y1), inverse(identity)), inverse(identity))) -> Y1
% 210.40/210.24 double_divide(inverse(identity), double_divide(identity, double_divide(identity, inverse(Y1)))) -> Y1
% 210.40/210.24 double_divide(inverse(identity), inverse(double_divide(X0, inverse(identity)))) -> double_divide(identity, X0)
% 210.40/210.24 double_divide(inverse(identity), inverse(double_divide(double_divide(Y1, inverse(identity)), inverse(identity)))) -> Y1
% 210.40/210.24 double_divide(inverse(identity), inverse(identity)) -> identity
% 210.40/210.24 f1(double_divide(inverse(a3), inverse(double_divide(inverse(b3), inverse(c3))))) -> false__
% 210.40/210.24 f1(double_divide(inverse(double_divide(inverse(a3), inverse(b3))), inverse(c3))) -> true__
% 210.40/210.24 f1(inverse(double_divide(c3, inverse(double_divide(b3, a3))))) -> true__
% 210.40/210.24 f1(inverse(double_divide(inverse(double_divide(c3, b3)), a3))) -> false__
% 210.40/210.24 f1(multiply(a3, multiply(b3, c3))) -> false__
% 210.40/210.24 f1(multiply(multiply(a3, b3), c3)) -> true__
% 210.40/210.24 inverse(double_divide(X2, double_divide(inverse(double_divide(X0, X1)), double_divide(inverse(X2), X1)))) -> inverse(X0)
% 210.40/210.24 inverse(double_divide(identity, Y0)) -> Y0
% 210.40/210.24 inverse(double_divide(identity, double_divide(inverse(Y1), inverse(identity)))) -> Y1
% 210.40/210.24 inverse(double_divide(identity, inverse(inverse(Y0)))) -> Y0
% 210.40/210.24 inverse(double_divide(inverse(X2), double_divide(inverse(double_divide(X0, X1)), double_divide(X2, X1)))) -> inverse(X0)
% 210.40/210.24 inverse(double_divide(inverse(double_divide(Y0, Y1)), inverse(Y1))) -> Y0
% 210.40/210.24 inverse(double_divide(inverse(double_divide(Y0, inverse(X0))), X0)) -> Y0
% 210.40/210.24 inverse(identity) -> identity
% 210.40/210.24 inverse(inverse(Y0)) -> Y0
% 210.40/210.24 multiply(A, B) -> double_divide(double_divide(B, A), identity)
% 210.40/210.24 true__ -> false__
% 210.40/210.24 with the LPO induced by
% 210.40/210.24 c3 > b3 > a3 > f1 > multiply > double_divide > inverse > identity > true__ > false__
% 210.40/210.24
% 210.40/210.24 % SZS output end Proof
% 210.40/210.24
%------------------------------------------------------------------------------