TSTP Solution File: GRP206-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP206-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n028.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 10:54:06 EDT 2022
% Result : Unsatisfiable 1.11s 1.32s
% Output : Proof 1.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP206-1 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 15:17:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.11/1.32 % SZS status Unsatisfiable
% 1.11/1.32 % SZS output start Proof
% 1.11/1.32 The input problem is unsatisfiable because
% 1.11/1.32
% 1.11/1.32 [1] the following set of Horn clauses is unsatisfiable:
% 1.11/1.32
% 1.11/1.32 multiply(identity, X) = X
% 1.11/1.32 multiply(X, identity) = X
% 1.11/1.32 multiply(X, left_division(X, Y)) = Y
% 1.11/1.32 left_division(X, multiply(X, Y)) = Y
% 1.11/1.32 multiply(right_division(X, Y), Y) = X
% 1.11/1.32 right_division(multiply(X, Y), Y) = X
% 1.11/1.32 multiply(X, right_inverse(X)) = identity
% 1.11/1.32 multiply(left_inverse(X), X) = identity
% 1.11/1.32 multiply(X, multiply(multiply(Y, Z), X)) = multiply(multiply(X, Y), multiply(Z, X))
% 1.11/1.32 multiply(multiply(a, multiply(b, c)), a) = multiply(multiply(a, b), multiply(c, a)) ==> \bottom
% 1.11/1.32
% 1.11/1.32 This holds because
% 1.11/1.32
% 1.11/1.32 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.11/1.32
% 1.11/1.32 E:
% 1.11/1.32 f1(multiply(multiply(a, b), multiply(c, a))) = false__
% 1.11/1.32 f1(multiply(multiply(a, multiply(b, c)), a)) = true__
% 1.11/1.32 left_division(X, multiply(X, Y)) = Y
% 1.11/1.32 multiply(X, identity) = X
% 1.11/1.32 multiply(X, left_division(X, Y)) = Y
% 1.11/1.32 multiply(X, multiply(multiply(Y, Z), X)) = multiply(multiply(X, Y), multiply(Z, X))
% 1.11/1.32 multiply(X, right_inverse(X)) = identity
% 1.11/1.32 multiply(identity, X) = X
% 1.11/1.32 multiply(left_inverse(X), X) = identity
% 1.11/1.32 multiply(right_division(X, Y), Y) = X
% 1.11/1.32 right_division(multiply(X, Y), Y) = X
% 1.11/1.32 G:
% 1.11/1.32 true__ = false__
% 1.11/1.32
% 1.11/1.32 This holds because
% 1.11/1.32
% 1.11/1.32 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.11/1.32
% 1.11/1.32 left_division(X0, X0) = left_division(Y0, Y0)
% 1.11/1.32 left_division(X0, X0) = right_division(Y0, Y0)
% 1.11/1.32 left_division(Y0, Y0) = identity
% 1.11/1.32 left_division(Y0, Y0) = right_division(false__, false__)
% 1.11/1.32 left_division(Y0, multiply(Y2, Y0)) = multiply(multiply(left_division(Y0, right_division(false__, false__)), Y2), Y0)
% 1.11/1.32 left_division(Y0, multiply(multiply(Y0, Y1), X0)) = multiply(multiply(Y1, right_division(X0, Y0)), Y0)
% 1.11/1.32 left_division(multiply(X0, X1), multiply(X0, X0)) = multiply(left_division(X1, right_division(false__, false__)), X0)
% 1.11/1.32 multiply(X, multiply(multiply(Y, Z), X)) = multiply(multiply(X, Y), multiply(Z, X))
% 1.11/1.32 multiply(X0, multiply(left_division(Y1, Y2), right_division(X0, Y1))) = multiply(right_division(X0, Y1), multiply(Y2, right_division(X0, Y1)))
% 1.11/1.32 multiply(X0, multiply(left_division(Y1, right_division(false__, false__)), right_division(X0, Y1))) = multiply(right_division(X0, Y1), right_division(X0, Y1))
% 1.11/1.32 multiply(Y0, multiply(multiply(X0, multiply(multiply(X1, X2), X0)), Y0)) = multiply(multiply(Y0, multiply(X0, X1)), multiply(multiply(X2, X0), Y0))
% 1.11/1.32 multiply(Y0, multiply(multiply(Y1, multiply(Y2, Y1)), Y0)) = multiply(multiply(Y0, multiply(Y1, Y2)), multiply(Y1, Y0))
% 1.11/1.32 multiply(Y0, multiply(multiply(left_division(Y3, right_division(false__, false__)), Y2), Y0)) = multiply(multiply(Y0, left_division(Y3, right_division(false__, false__))), multiply(multiply(multiply(Y2, Y3), left_division(Y3, right_division(false__, false__))), Y0))
% 1.11/1.32 multiply(Y0, multiply(multiply(multiply(Y1, X1), multiply(X2, Y1)), Y0)) = multiply(multiply(Y0, Y1), multiply(multiply(multiply(X1, X2), Y1), Y0))
% 1.11/1.32 multiply(left_division(Y1, Y2), right_division(right_division(false__, false__), Y1)) = multiply(right_division(right_division(false__, false__), Y1), multiply(Y2, right_division(right_division(false__, false__), Y1)))
% 1.11/1.32 multiply(left_division(Y2, right_division(false__, false__)), right_division(Y1, Y2)) = multiply(left_division(Y2, right_division(false__, false__)), multiply(Y1, left_division(Y2, right_division(false__, false__))))
% 1.11/1.32 multiply(multiply(X0, X0), multiply(X0, X1)) = multiply(multiply(X0, X1), multiply(multiply(left_division(X1, right_division(false__, false__)), X0), multiply(X0, X1)))
% 1.11/1.32 multiply(multiply(X0, X0), multiply(X0, right_division(right_division(false__, false__), X1))) = multiply(multiply(X0, right_division(right_division(false__, false__), X1)), multiply(multiply(X1, X0), multiply(X0, right_division(right_division(false__, false__), X1))))
% 1.11/1.32 multiply(multiply(X0, X0), multiply(left_division(multiply(X1, X0), right_division(false__, false__)), multiply(X0, right_division(right_division(false__, false__), X1)))) = multiply(multiply(X0, right_division(right_division(false__, false__), X1)), multiply(X0, right_division(right_division(false__, false__), X1)))
% 1.11/1.32 multiply(multiply(X0, multiply(multiply(X1, X2), X0)), multiply(Y2, multiply(X0, X1))) = multiply(multiply(X0, X1), multiply(multiply(multiply(X2, X0), Y2), multiply(X0, X1)))
% 1.11/1.32 multiply(multiply(X2, Y1), multiply(Y1, multiply(multiply(Y2, X2), Y1))) = multiply(multiply(multiply(X2, Y1), Y1), multiply(Y2, multiply(X2, Y1)))
% 1.11/1.32 multiply(multiply(Y2, Y1), left_division(Y1, Y1)) = multiply(multiply(left_division(Y1, Y1), Y2), Y1)
% 1.11/1.32 multiply(multiply(left_division(Y2, X1), Y1), X1) = multiply(left_division(Y2, X1), multiply(multiply(Y1, Y2), left_division(Y2, X1)))
% 1.11/1.32 multiply(multiply(multiply(X2, X0), Y1), multiply(X0, multiply(multiply(X1, X2), X0))) = multiply(multiply(X2, X0), multiply(multiply(Y1, multiply(X0, X1)), multiply(X2, X0)))
% 1.11/1.32 multiply(multiply(multiply(multiply(X1, X2), Y2), Y1), multiply(multiply(Y2, X1), multiply(X2, Y2))) = multiply(multiply(multiply(X1, X2), Y2), multiply(multiply(Y1, Y2), multiply(multiply(X1, X2), Y2)))
% 1.11/1.32 multiply(right_division(Y1, Y1), multiply(Y1, Y2)) = multiply(Y1, multiply(Y2, right_division(Y1, Y1)))
% 1.11/1.32 right_division(X0, X0) = right_division(Y0, Y0)
% 1.11/1.32 right_division(Y1, Y1) = identity
% 1.11/1.32 right_division(Y1, Y1) = right_division(false__, false__)
% 1.11/1.32 right_division(multiply(X0, X0), multiply(X1, X0)) = multiply(X0, right_division(right_division(false__, false__), X1))
% 1.11/1.32 f1(multiply(multiply(a, b), multiply(c, a))) -> false__
% 1.11/1.32 f1(multiply(multiply(a, multiply(b, c)), a)) -> true__
% 1.11/1.32 left_division(X, multiply(X, Y)) -> Y
% 1.11/1.32 left_division(Y0, multiply(X1, multiply(Y2, Y0))) -> multiply(multiply(left_division(Y0, X1), Y2), Y0)
% 1.11/1.32 left_division(Y0, multiply(multiply(Y0, X1), multiply(X2, Y0))) -> multiply(multiply(X1, X2), Y0)
% 1.11/1.32 left_division(identity, Y1) -> Y1
% 1.11/1.32 left_division(left_division(X0, X0), Y0) -> Y0
% 1.11/1.32 left_division(left_division(X0, X0), right_division(false__, false__)) -> right_division(false__, false__)
% 1.11/1.32 left_division(left_division(Y2, X1), multiply(multiply(left_division(Y2, X1), Y1), X1)) -> multiply(multiply(Y1, Y2), left_division(Y2, X1))
% 1.11/1.32 left_division(left_inverse(Y1), identity) -> Y1
% 1.11/1.32 left_division(multiply(X0, X1), multiply(X0, multiply(X2, X0))) -> multiply(left_division(X1, X2), X0)
% 1.11/1.32 left_division(multiply(X0, X1), multiply(X0, multiply(multiply(X1, X2), X0))) -> multiply(X2, X0)
% 1.11/1.32 left_division(multiply(X0, right_division(X1, X2)), multiply(X0, multiply(X1, X0))) -> multiply(X2, X0)
% 1.11/1.32 left_division(multiply(X0, right_division(right_division(false__, false__), X1)), multiply(X0, X0)) -> multiply(X1, X0)
% 1.11/1.32 left_division(multiply(Y0, Y1), multiply(Y0, multiply(Y1, Y0))) -> Y0
% 1.11/1.32 left_division(multiply(left_division(multiply(Y1, Y2), X1), Y1), multiply(left_division(multiply(Y1, Y2), X1), X1)) -> multiply(Y2, left_division(multiply(Y1, Y2), X1))
% 1.11/1.32 left_division(multiply(left_division(multiply(Y1, Y2), right_division(false__, false__)), Y1), left_division(multiply(Y1, Y2), right_division(false__, false__))) -> multiply(Y2, left_division(multiply(Y1, Y2), right_division(false__, false__)))
% 1.11/1.32 left_division(right_division(X0, X0), Y0) -> Y0
% 1.11/1.32 left_division(right_division(X0, X0), right_division(false__, false__)) -> right_division(false__, false__)
% 1.11/1.32 left_division(right_division(X0, Y1), X0) -> Y1
% 1.11/1.32 left_division(right_division(X0, Y1), multiply(X0, multiply(Y2, right_division(X0, Y1)))) -> multiply(multiply(Y1, Y2), right_division(X0, Y1))
% 1.11/1.32 left_division(right_division(right_division(false__, false__), Y0), left_division(X0, X0)) -> Y0
% 1.11/1.32 left_division(right_division(right_division(false__, false__), Y0), right_division(X0, X0)) -> Y0
% 1.11/1.32 left_division(right_division(right_division(false__, false__), Y1), multiply(Y2, right_division(right_division(false__, false__), Y1))) -> multiply(multiply(Y1, Y2), right_division(right_division(false__, false__), Y1))
% 1.11/1.32 left_inverse(Y1) -> right_division(identity, Y1)
% 1.11/1.32 left_inverse(identity) -> identity
% 1.11/1.32 multiply(X, identity) -> X
% 1.11/1.32 multiply(X, left_division(X, Y)) -> Y
% 1.11/1.32 multiply(X, right_inverse(X)) -> identity
% 1.11/1.32 multiply(X1, multiply(left_division(left_division(Y0, X1), Y2), Y0)) -> multiply(Y0, multiply(Y2, Y0))
% 1.11/1.32 multiply(X1, multiply(left_division(left_division(Y0, X1), right_division(false__, false__)), Y0)) -> multiply(Y0, Y0)
% 1.11/1.32 multiply(Y0, left_division(X0, X0)) -> Y0
% 1.11/1.32 multiply(Y0, multiply(left_division(Y0, X1), Y0)) -> multiply(X1, Y0)
% 1.11/1.32 multiply(Y0, multiply(left_division(Y0, right_division(false__, false__)), Y0)) -> Y0
% 1.11/1.32 multiply(Y0, multiply(multiply(Y1, right_division(right_division(false__, false__), Y0)), Y0)) -> multiply(Y0, Y1)
% 1.11/1.32 multiply(Y0, right_division(X0, X0)) -> Y0
% 1.11/1.32 multiply(Y0, right_division(Y1, right_division(right_division(false__, false__), Y0))) -> multiply(Y0, multiply(Y1, Y0))
% 1.11/1.32 multiply(Y0, right_division(right_division(false__, false__), right_division(right_division(false__, false__), Y0))) -> multiply(Y0, Y0)
% 1.11/1.32 multiply(identity, X) -> X
% 1.11/1.32 multiply(left_division(X0, X0), Y0) -> Y0
% 1.11/1.32 multiply(left_division(X0, right_division(false__, false__)), multiply(multiply(multiply(X1, X0), left_division(X0, right_division(false__, false__))), left_division(X0, right_division(false__, false__)))) -> multiply(left_division(X0, right_division(false__, false__)), multiply(X1, left_division(X0, right_division(false__, false__))))
% 1.11/1.32 multiply(left_division(Y0, right_division(false__, false__)), multiply(multiply(Y0, multiply(X1, Y0)), left_division(Y0, right_division(false__, false__)))) -> multiply(left_division(Y0, right_division(false__, false__)), multiply(Y0, X1))
% 1.11/1.32 multiply(left_division(Y0, right_division(false__, false__)), multiply(multiply(Y1, Y0), left_division(Y0, right_division(false__, false__)))) -> multiply(left_division(Y0, right_division(false__, false__)), Y1)
% 1.11/1.32 multiply(left_division(Y1, Y1), multiply(multiply(Y2, Y1), left_division(Y1, Y1))) -> multiply(Y2, Y1)
% 1.11/1.32 multiply(left_division(Y1, right_division(false__, false__)), right_division(right_division(false__, false__), Y1)) -> multiply(left_division(Y1, right_division(false__, false__)), left_division(Y1, right_division(false__, false__)))
% 1.11/1.32 multiply(left_division(left_division(Y0, right_division(false__, false__)), Y2), Y0) -> multiply(Y0, multiply(Y2, Y0))
% 1.11/1.32 multiply(left_division(left_division(Y0, right_division(false__, false__)), right_division(false__, false__)), Y0) -> multiply(Y0, Y0)
% 1.11/1.32 multiply(left_division(left_division(Y1, Y2), right_division(false__, false__)), multiply(Y2, left_division(left_division(Y1, Y2), right_division(false__, false__)))) -> multiply(left_division(left_division(Y1, Y2), right_division(false__, false__)), Y1)
% 1.11/1.32 multiply(left_division(left_division(Y1, right_division(false__, false__)), right_division(false__, false__)), left_division(left_division(Y1, right_division(false__, false__)), right_division(false__, false__))) -> multiply(left_division(left_division(Y1, right_division(false__, false__)), right_division(false__, false__)), Y1)
% 1.11/1.32 multiply(left_inverse(X), X) -> identity
% 1.11/1.32 multiply(left_inverse(Y1), multiply(multiply(Y1, Y2), left_inverse(Y1))) -> multiply(Y2, left_inverse(Y1))
% 1.11/1.32 multiply(multiply(X0, X0), multiply(left_division(multiply(left_division(X1, right_division(false__, false__)), X0), right_division(false__, false__)), multiply(X0, X1))) -> multiply(multiply(X0, X1), multiply(X0, X1))
% 1.11/1.32 multiply(multiply(Y0, Y1), Y0) -> multiply(Y0, multiply(Y1, Y0))
% 1.11/1.32 multiply(multiply(Y0, Y1), multiply(left_division(Y1, X1), Y0)) -> multiply(Y0, multiply(X1, Y0))
% 1.11/1.32 multiply(multiply(Y0, Y1), multiply(multiply(multiply(Y2, right_division(right_division(false__, false__), Y1)), Y1), Y0)) -> multiply(Y0, multiply(multiply(Y1, Y2), Y0))
% 1.11/1.32 multiply(multiply(Y0, Y1), multiply(right_inverse(Y1), Y0)) -> multiply(Y0, Y0)
% 1.11/1.32 multiply(multiply(Y0, left_inverse(Y2)), multiply(Y2, Y0)) -> multiply(Y0, Y0)
% 1.11/1.32 multiply(multiply(Y0, multiply(multiply(Y1, Y2), Y0)), multiply(Y0, Y1)) -> multiply(multiply(Y0, Y1), multiply(multiply(Y2, Y0), multiply(Y0, Y1)))
% 1.11/1.32 multiply(multiply(Y0, right_division(X0, Y2)), multiply(Y2, Y0)) -> multiply(Y0, multiply(X0, Y0))
% 1.11/1.32 multiply(multiply(Y0, right_division(Y1, right_division(X0, Y0))), X0) -> multiply(Y0, multiply(Y1, Y0))
% 1.11/1.32 multiply(multiply(Y0, right_division(right_division(false__, false__), Y2)), multiply(multiply(multiply(Y2, Y3), right_division(right_division(false__, false__), Y2)), Y0)) -> multiply(Y0, multiply(multiply(Y3, right_division(right_division(false__, false__), Y2)), Y0))
% 1.11/1.32 multiply(multiply(Y0, right_division(right_division(false__, false__), multiply(Y0, X1))), multiply(Y0, multiply(X1, Y0))) -> multiply(Y0, Y0)
% 1.11/1.32 multiply(multiply(Y0, right_division(right_division(false__, false__), right_division(X0, Y0))), X0) -> multiply(Y0, Y0)
% 1.11/1.32 multiply(multiply(Y1, Y1), multiply(Y2, Y1)) -> multiply(Y1, multiply(Y1, multiply(Y2, Y1)))
% 1.11/1.32 multiply(multiply(Y1, Y2), left_division(Y2, right_division(false__, false__))) -> Y1
% 1.11/1.32 multiply(multiply(Y1, Y2), right_division(Y1, Y1)) -> multiply(Y1, multiply(Y2, right_division(Y1, Y1)))
% 1.11/1.32 multiply(multiply(Y1, multiply(X1, Y1)), multiply(Y1, X1)) -> multiply(multiply(Y1, X1), multiply(Y1, multiply(Y1, X1)))
% 1.11/1.32 multiply(multiply(Y1, multiply(X1, Y1)), multiply(left_division(Y1, right_division(false__, false__)), multiply(Y1, X1))) -> multiply(multiply(Y1, X1), multiply(Y1, X1))
% 1.11/1.32 multiply(multiply(Y1, right_division(right_division(false__, false__), Y0)), Y0) -> Y1
% 1.11/1.32 multiply(multiply(left_division(Y1, X1), right_division(right_division(false__, false__), Y1)), X1) -> multiply(left_division(Y1, X1), left_division(Y1, X1))
% 1.11/1.32 multiply(multiply(left_division(Y1, Y1), Y2), Y1) -> multiply(left_division(Y1, Y1), multiply(Y2, Y1))
% 1.11/1.32 multiply(multiply(left_division(Y2, X1), right_division(Y1, Y2)), X1) -> multiply(left_division(Y2, X1), multiply(Y1, left_division(Y2, X1)))
% 1.11/1.32 multiply(multiply(multiply(left_division(X1, right_division(false__, false__)), X0), right_division(right_division(false__, false__), multiply(X0, X1))), multiply(X0, X0)) -> multiply(multiply(left_division(X1, right_division(false__, false__)), X0), multiply(left_division(X1, right_division(false__, false__)), X0))
% 1.11/1.32 multiply(multiply(right_division(right_division(false__, false__), Y1), multiply(X1, right_division(right_division(false__, false__), Y1))), multiply(Y1, multiply(right_division(right_division(false__, false__), Y1), X1))) -> multiply(multiply(right_division(right_division(false__, false__), Y1), X1), multiply(right_division(right_division(false__, false__), Y1), X1))
% 1.11/1.32 multiply(right_division(X, Y), Y) -> X
% 1.11/1.32 multiply(right_division(X0, X0), Y0) -> Y0
% 1.11/1.32 multiply(right_division(X0, Y1), multiply(Y1, right_division(X0, Y1))) -> multiply(X0, right_division(X0, Y1))
% 1.11/1.32 multiply(right_division(X0, Y1), multiply(multiply(Y1, Y2), right_division(X0, Y1))) -> multiply(X0, multiply(Y2, right_division(X0, Y1)))
% 1.11/1.32 multiply(right_division(X0, right_division(Y1, Y2)), multiply(Y1, right_division(X0, right_division(Y1, Y2)))) -> multiply(X0, multiply(Y2, right_division(X0, right_division(Y1, Y2))))
% 1.11/1.32 multiply(right_division(X0, right_division(right_division(false__, false__), Y1)), right_division(X0, right_division(right_division(false__, false__), Y1))) -> multiply(X0, multiply(Y1, right_division(X0, right_division(right_division(false__, false__), Y1))))
% 1.11/1.32 multiply(right_division(false__, false__), multiply(Y1, right_division(right_division(false__, false__), Y0))) -> multiply(Y1, right_division(right_division(false__, false__), Y0))
% 1.11/1.32 multiply(right_division(right_division(false__, false__), Y0), multiply(Y0, right_division(right_division(false__, false__), Y0))) -> right_division(right_division(false__, false__), Y0)
% 1.11/1.32 multiply(right_division(right_division(false__, false__), Y1), right_division(right_division(false__, false__), Y1)) -> multiply(left_division(Y1, right_division(false__, false__)), right_division(right_division(false__, false__), Y1))
% 1.11/1.32 multiply(right_division(right_division(false__, false__), right_division(Y1, Y2)), multiply(Y1, right_division(right_division(false__, false__), right_division(Y1, Y2)))) -> multiply(Y2, right_division(right_division(false__, false__), right_division(Y1, Y2)))
% 1.11/1.32 multiply(right_division(right_division(false__, false__), right_division(right_division(false__, false__), Y1)), right_division(right_division(false__, false__), right_division(right_division(false__, false__), Y1))) -> multiply(Y1, right_division(right_division(false__, false__), right_division(right_division(false__, false__), Y1)))
% 1.11/1.32 multiply(right_inverse(Y2), multiply(multiply(Y1, Y2), right_inverse(Y2))) -> multiply(right_inverse(Y2), Y1)
% 1.11/1.32 right_division(X1, left_division(Y0, X1)) -> Y0
% 1.11/1.32 right_division(Y0, identity) -> Y0
% 1.11/1.32 right_division(Y0, left_division(X0, X0)) -> Y0
% 1.11/1.32 right_division(Y0, right_division(X0, X0)) -> Y0
% 1.11/1.32 right_division(identity, right_inverse(Y0)) -> Y0
% 1.11/1.32 right_division(left_division(X0, X0), left_division(Y0, right_division(false__, false__))) -> Y0
% 1.11/1.32 right_division(left_division(multiply(Y1, Y2), right_division(false__, false__)), multiply(Y2, left_division(multiply(Y1, Y2), right_division(false__, false__)))) -> multiply(left_division(multiply(Y1, Y2), right_division(false__, false__)), Y1)
% 1.11/1.32 right_division(multiply(X, Y), Y) -> X
% 1.11/1.32 right_division(multiply(X0, X0), multiply(left_division(X1, right_division(false__, false__)), X0)) -> multiply(X0, X1)
% 1.11/1.32 right_division(multiply(X0, multiply(X2, X0)), multiply(left_division(X1, X2), X0)) -> multiply(X0, X1)
% 1.11/1.32 right_division(multiply(X0, multiply(multiply(X1, X2), X0)), multiply(X2, X0)) -> multiply(X0, X1)
% 1.11/1.32 right_division(multiply(X1, multiply(Y2, Y0)), multiply(multiply(left_division(Y0, X1), Y2), Y0)) -> Y0
% 1.11/1.32 right_division(multiply(Y0, Y1), multiply(multiply(Y1, right_division(right_division(false__, false__), Y0)), Y0)) -> Y0
% 1.11/1.32 right_division(multiply(Y0, multiply(Y1, Y0)), Y0) -> multiply(Y0, Y1)
% 1.11/1.32 right_division(multiply(Y1, Y2), multiply(Y1, Y2)) -> right_division(false__, false__)
% 1.11/1.32 right_division(multiply(Y2, Y0), multiply(multiply(left_division(Y0, right_division(false__, false__)), Y2), Y0)) -> Y0
% 1.11/1.32 right_division(multiply(Y2, right_division(right_division(false__, false__), Y1)), multiply(multiply(Y1, Y2), right_division(right_division(false__, false__), Y1))) -> right_division(right_division(false__, false__), Y1)
% 1.11/1.32 right_division(multiply(left_division(Y2, right_division(false__, false__)), Y1), multiply(multiply(Y1, Y2), left_division(Y2, right_division(false__, false__)))) -> left_division(Y2, right_division(false__, false__))
% 1.11/1.32 right_division(multiply(multiply(Y0, X1), multiply(X2, Y0)), multiply(multiply(X1, X2), Y0)) -> Y0
% 1.11/1.32 right_division(multiply(multiply(left_division(Y2, X1), Y1), X1), multiply(multiply(Y1, Y2), left_division(Y2, X1))) -> left_division(Y2, X1)
% 1.11/1.32 right_division(right_division(X0, X0), left_division(Y0, right_division(false__, false__))) -> Y0
% 1.11/1.32 right_division(right_division(false__, false__), left_division(X0, X0)) -> right_division(false__, false__)
% 1.11/1.32 right_division(right_division(false__, false__), right_division(X0, X0)) -> right_division(false__, false__)
% 1.11/1.32 right_inverse(Y0) -> left_division(Y0, identity)
% 1.11/1.32 right_inverse(identity) -> identity
% 1.11/1.32 true__ -> false__
% 1.11/1.32 with the LPO induced by
% 1.11/1.32 c > b > a > f1 > left_inverse > right_inverse > identity > right_division > left_division > multiply > true__ > false__
% 1.11/1.32
% 1.11/1.32 % SZS output end Proof
% 1.11/1.32
%------------------------------------------------------------------------------