TSTP Solution File: BOO010-2 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : BOO010-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% 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 : 600s
% DateTime : Thu Jul 14 23:46:21 EDT 2022
% Result : Unsatisfiable 15.21s 15.27s
% Output : Proof 15.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO010-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 1 18:31:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 15.21/15.27 % SZS status Unsatisfiable
% 15.21/15.27 % SZS output start Proof
% 15.21/15.27 The input problem is unsatisfiable because
% 15.21/15.27
% 15.21/15.27 [1] the following set of Horn clauses is unsatisfiable:
% 15.21/15.27
% 15.21/15.27 add(X, Y) = add(Y, X)
% 15.21/15.27 multiply(X, Y) = multiply(Y, X)
% 15.21/15.27 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z))
% 15.21/15.27 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 15.21/15.27 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 15.21/15.27 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 15.21/15.27 add(X, inverse(X)) = multiplicative_identity
% 15.21/15.27 add(inverse(X), X) = multiplicative_identity
% 15.21/15.27 multiply(X, inverse(X)) = additive_identity
% 15.21/15.27 multiply(inverse(X), X) = additive_identity
% 15.21/15.27 multiply(X, multiplicative_identity) = X
% 15.21/15.27 multiply(multiplicative_identity, X) = X
% 15.21/15.27 add(X, additive_identity) = X
% 15.21/15.27 add(additive_identity, X) = X
% 15.21/15.27 add(a, multiply(a, b)) = a ==> \bottom
% 15.21/15.27
% 15.21/15.27 This holds because
% 15.21/15.27
% 15.21/15.27 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 15.21/15.27
% 15.21/15.27 E:
% 15.21/15.27 add(X, Y) = add(Y, X)
% 15.21/15.27 add(X, additive_identity) = X
% 15.21/15.27 add(X, inverse(X)) = multiplicative_identity
% 15.21/15.27 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 15.21/15.27 add(additive_identity, X) = X
% 15.21/15.27 add(inverse(X), X) = multiplicative_identity
% 15.21/15.27 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z))
% 15.21/15.27 f1(a) = false__
% 15.21/15.27 f1(add(a, multiply(a, b))) = true__
% 15.21/15.27 multiply(X, Y) = multiply(Y, X)
% 15.21/15.27 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 15.21/15.27 multiply(X, inverse(X)) = additive_identity
% 15.21/15.27 multiply(X, multiplicative_identity) = X
% 15.21/15.27 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 15.21/15.27 multiply(inverse(X), X) = additive_identity
% 15.21/15.27 multiply(multiplicative_identity, X) = X
% 15.21/15.27 G:
% 15.21/15.27 true__ = false__
% 15.21/15.27
% 15.21/15.27 This holds because
% 15.21/15.27
% 15.21/15.27 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 15.21/15.27
% 15.21/15.27 add(X, Y) = add(Y, X)
% 15.21/15.27 add(X1, Y1) = multiply(add(Y1, X1), add(Y1, add(Y1, X1)))
% 15.21/15.27 add(Y0, Y0) = multiply(Y0, add(multiplicative_identity, multiplicative_identity))
% 15.21/15.27 add(Y1, Y1) = multiply(add(multiplicative_identity, multiplicative_identity), Y1)
% 15.21/15.27 multiply(X, Y) = multiply(Y, X)
% 15.21/15.27 multiply(X0, add(add(Y1, Y1), add(Y1, Y1))) = multiply(add(add(X0, X0), add(X0, X0)), Y1)
% 15.21/15.27 multiply(Y0, multiply(add(X0, inverse(Y0)), add(X1, inverse(Y0)))) = multiply(multiply(X0, X1), Y0)
% 15.21/15.27 multiply(Y0, multiply(add(multiplicative_identity, multiplicative_identity), inverse(Y2))) = multiply(inverse(Y2), Y0)
% 15.21/15.27 multiply(Y1, add(Y0, Y0)) = multiply(Y0, add(Y1, Y1))
% 15.21/15.27 multiply(add(X0, Y2), add(X0, add(X0, inverse(X1)))) = multiply(add(add(X0, X1), Y2), add(X0, inverse(X1)))
% 15.21/15.27 multiply(add(X0, add(X0, X1)), add(Y1, X0)) = multiply(add(X0, X1), add(Y1, add(X0, inverse(X1))))
% 15.21/15.27 multiply(add(X1, Y2), add(X1, add(inverse(X0), X1))) = multiply(add(add(X0, X1), Y2), add(inverse(X0), X1))
% 15.21/15.27 multiply(add(X1, add(X0, X1)), add(Y1, X1)) = multiply(add(X0, X1), add(Y1, add(inverse(X0), X1)))
% 15.21/15.27 multiply(add(Y0, X0), add(X0, add(X0, inverse(X1)))) = multiply(add(Y0, add(X0, X1)), add(X0, inverse(X1)))
% 15.21/15.27 multiply(add(Y0, X1), add(X1, add(inverse(X0), X1))) = multiply(add(Y0, add(X0, X1)), add(inverse(X0), X1))
% 15.21/15.27 multiply(add(Y0, Y0), Y2) = multiply(Y0, add(Y2, Y2))
% 15.21/15.27 multiply(add(Y0, Y0), Y2) = multiply(Y2, Y0)
% 15.21/15.27 multiply(add(Y0, Y0), add(Y0, Y1)) = multiply(Y0, add(Y1, multiplicative_identity))
% 15.21/15.27 multiply(add(Y0, Y0), add(Y0, Y1)) = multiply(add(multiplicative_identity, Y1), Y0)
% 15.21/15.27 multiply(add(Y0, Y0), add(Y0, Y2)) = multiply(Y0, add(multiplicative_identity, Y2))
% 15.21/15.27 multiply(add(Y0, Y0), add(Y1, Y0)) = multiply(Y0, add(Y1, multiplicative_identity))
% 15.21/15.27 multiply(add(Y0, Y0), add(Y1, Y0)) = multiply(Y0, add(multiplicative_identity, Y1))
% 15.21/15.27 multiply(add(Y0, Y1), add(Y0, Y0)) = multiply(Y0, add(multiplicative_identity, Y1))
% 15.21/15.27 multiply(add(Y0, Y1), add(Y1, Y1)) = multiply(add(Y0, multiplicative_identity), Y1)
% 15.21/15.27 multiply(add(Y0, multiplicative_identity), add(Y1, Y0)) = add(Y0, Y1)
% 15.21/15.27 multiply(add(Y1, Y0), add(Y0, Y0)) = multiply(Y0, add(Y1, multiplicative_identity))
% 15.21/15.27 multiply(add(Y1, Y0), add(Y0, Y0)) = multiply(add(multiplicative_identity, Y1), Y0)
% 15.21/15.27 multiply(add(Y1, Y0), add(Y0, multiplicative_identity)) = add(Y0, Y1)
% 15.21/15.27 multiply(add(Y1, Y0), add(Y1, Y1)) = multiply(add(Y0, multiplicative_identity), Y1)
% 15.21/15.27 multiply(add(Y1, Y0), add(multiplicative_identity, Y1)) = add(Y0, Y1)
% 15.21/15.27 multiply(add(Y1, Y1), Y0) = multiply(add(Y0, Y0), Y1)
% 15.21/15.27 multiply(add(Y1, Y1), add(Y0, Y1)) = multiply(add(Y0, multiplicative_identity), Y1)
% 15.21/15.27 multiply(add(Y1, Y2), add(Y1, Y1)) = multiply(add(multiplicative_identity, Y2), Y1)
% 15.21/15.27 multiply(add(Y2, Y1), multiply(add(multiplicative_identity, Y1), inverse(Y2))) = multiply(inverse(Y2), Y1)
% 15.21/15.27 multiply(add(multiplicative_identity, Y0), add(Y0, Y1)) = add(Y1, Y0)
% 15.21/15.27 multiply(additive_identity, Y0) = multiply(add(Y0, multiplicative_identity), additive_identity)
% 15.21/15.27 multiply(additive_identity, Y1) = multiply(add(multiplicative_identity, Y1), additive_identity)
% 15.21/15.27 multiply(additive_identity, add(Y1, multiplicative_identity)) = multiply(Y1, additive_identity)
% 15.21/15.27 multiply(additive_identity, add(multiplicative_identity, Y1)) = multiply(Y1, additive_identity)
% 15.21/15.27 multiply(multiply(Y0, add(Y0, Y2)), multiply(additive_identity, Y2)) = multiply(additive_identity, add(Y0, Y2))
% 15.21/15.27 multiply(multiply(Y0, add(Y0, Y2)), multiply(additive_identity, add(multiplicative_identity, Y2))) = multiply(additive_identity, add(Y0, Y2))
% 15.21/15.27 multiply(multiply(Y1, additive_identity), multiply(Y2, add(Y2, Y1))) = multiply(add(Y2, Y1), additive_identity)
% 15.21/15.27 multiply(multiply(add(X0, Y1), add(X0, Y2)), multiply(add(X1, Y1), add(X1, Y2))) = multiply(multiply(add(X0, Y1), add(X1, Y1)), multiply(add(X0, Y2), add(X1, Y2)))
% 15.21/15.27 multiply(multiply(add(multiplicative_identity, Y1), additive_identity), multiply(Y2, add(Y2, Y1))) = multiply(add(Y2, Y1), additive_identity)
% 15.21/15.27 multiply(multiply(add(multiplicative_identity, multiplicative_identity), inverse(Y1)), Y2) = multiply(Y2, inverse(Y1))
% 15.21/15.27 multiply(multiply(additive_identity, Y1), multiply(Y2, add(Y2, Y1))) = multiply(add(Y2, Y1), additive_identity)
% 15.21/15.27 multiply(multiply(multiply(X0, add(X0, X1)), multiply(X1, add(X1, X0))), Y1) = multiply(Y1, multiply(X0, X1))
% 15.21/15.27 multiply(multiply(multiply(X1, add(X2, X1)), multiply(X2, add(X1, X2))), Y1) = multiply(Y1, multiply(X1, X2))
% 15.21/15.27 add(X, additive_identity) -> X
% 15.21/15.27 add(X, inverse(X)) -> multiplicative_identity
% 15.21/15.27 add(X, multiply(Y, Z)) -> multiply(add(X, Y), add(X, Z))
% 15.21/15.27 add(Y0, inverse(add(Y0, multiplicative_identity))) -> multiply(Y0, add(Y0, multiplicative_identity))
% 15.21/15.27 add(Y0, inverse(add(multiplicative_identity, Y0))) -> multiply(Y0, add(multiplicative_identity, Y0))
% 15.21/15.27 add(Y0, inverse(inverse(Y0))) -> Y0
% 15.21/15.27 add(Y0, inverse(inverse(Y0))) -> inverse(inverse(Y0))
% 15.21/15.27 add(Y0, inverse(inverse(Y2))) -> add(Y0, Y2)
% 15.21/15.27 add(Y0, inverse(inverse(inverse(Y0)))) -> multiplicative_identity
% 15.21/15.27 add(Y0, multiplicative_identity) -> multiplicative_identity
% 15.21/15.27 add(Y1, Y1) -> Y1
% 15.21/15.27 add(add(Y0, Y1), inverse(add(Y0, inverse(Y1)))) -> add(Y0, inverse(add(Y0, inverse(Y1))))
% 15.21/15.27 add(add(Y0, Y1), inverse(add(inverse(Y0), Y1))) -> add(Y1, inverse(add(inverse(Y0), Y1)))
% 15.21/15.27 add(add(Y0, inverse(Y1)), inverse(add(Y0, Y1))) -> add(Y0, inverse(add(Y0, Y1)))
% 15.21/15.27 add(add(inverse(Y0), Y1), inverse(add(Y0, Y1))) -> add(Y1, inverse(add(Y0, Y1)))
% 15.21/15.27 add(additive_identity, X) -> X
% 15.21/15.27 add(inverse(X), X) -> multiplicative_identity
% 15.21/15.27 add(inverse(inverse(Y1)), Y2) -> add(Y1, Y2)
% 15.21/15.27 add(multiplicative_identity, Y1) -> multiplicative_identity
% 15.21/15.27 add(multiplicative_identity, inverse(Y0)) -> multiplicative_identity
% 15.21/15.27 add(multiply(X, Y), Z) -> multiply(add(X, Z), add(Y, Z))
% 15.21/15.27 add(multiply(X, Y), multiply(X, Z)) -> multiply(X, add(Y, Z))
% 15.21/15.27 add(multiply(X, Z), multiply(Y, Z)) -> multiply(add(X, Y), Z)
% 15.21/15.27 f1(a) -> false__
% 15.21/15.27 f1(add(a, multiply(a, b))) -> true__
% 15.21/15.27 f1(multiply(a, add(a, b))) -> true__
% 15.21/15.27 f1(multiply(a, add(multiplicative_identity, b))) -> true__
% 15.21/15.27 f1(multiply(add(a, a), add(a, b))) -> true__
% 15.21/15.27 inverse(additive_identity) -> multiplicative_identity
% 15.21/15.27 inverse(inverse(Y0)) -> Y0
% 15.21/15.27 inverse(multiplicative_identity) -> additive_identity
% 15.21/15.27 multiply(X, inverse(X)) -> additive_identity
% 15.21/15.27 multiply(X, multiplicative_identity) -> X
% 15.21/15.27 multiply(Y0, Y0) -> Y0
% 15.21/15.27 multiply(Y0, add(Y0, Y0)) -> Y0
% 15.21/15.27 multiply(Y0, add(Y0, Y1)) -> Y0
% 15.21/15.27 multiply(Y0, add(Y0, inverse(X0))) -> Y0
% 15.21/15.27 multiply(Y0, add(Y0, inverse(inverse(inverse(Y0))))) -> Y0
% 15.21/15.27 multiply(Y0, add(Y0, multiplicative_identity)) -> Y0
% 15.21/15.27 multiply(Y0, add(Y1, Y0)) -> Y0
% 15.21/15.27 multiply(Y0, add(Y1, add(inverse(Y0), X1))) -> multiply(Y0, add(Y1, X1))
% 15.21/15.27 multiply(Y0, add(Y1, inverse(Y0))) -> multiply(Y0, Y1)
% 15.21/15.27 multiply(Y0, add(Y1, inverse(inverse(Y0)))) -> multiply(Y0, add(Y1, Y0))
% 15.21/15.27 multiply(Y0, add(add(inverse(Y0), X1), Y2)) -> multiply(Y0, add(X1, Y2))
% 15.21/15.27 multiply(Y0, add(inverse(Y0), Y2)) -> multiply(Y0, Y2)
% 15.21/15.27 multiply(Y0, add(inverse(inverse(Y0)), Y2)) -> multiply(Y0, add(Y0, Y2))
% 15.21/15.27 multiply(Y0, add(multiplicative_identity, inverse(add(Y0, Y0)))) -> multiply(Y0, add(Y0, Y0))
% 15.21/15.27 multiply(Y0, additive_identity) -> additive_identity
% 15.21/15.27 multiply(Y0, inverse(inverse(Y0))) -> Y0
% 15.21/15.27 multiply(Y0, inverse(inverse(Y0))) -> inverse(inverse(Y0))
% 15.21/15.27 multiply(Y0, inverse(inverse(inverse(Y0)))) -> additive_identity
% 15.21/15.27 multiply(Y0, multiply(Y1, add(Y0, Y1))) -> multiply(Y1, Y0)
% 15.21/15.27 multiply(Y0, multiply(Y1, add(Y1, Y0))) -> multiply(Y1, Y0)
% 15.21/15.27 multiply(Y0, multiply(add(X0, inverse(Y0)), add(X1, inverse(Y0)))) -> multiply(Y0, multiply(X0, X1))
% 15.21/15.27 multiply(Y0, multiply(add(inverse(Y0), X1), add(inverse(Y0), X2))) -> multiply(Y0, multiply(X1, X2))
% 15.21/15.27 multiply(Y0, multiply(add(multiplicative_identity, multiplicative_identity), inverse(Y2))) -> multiply(Y0, inverse(Y2))
% 15.21/15.27 multiply(Y1, add(Y0, inverse(Y1))) -> multiply(Y0, Y1)
% 15.21/15.27 multiply(Y1, add(inverse(Y1), Y2)) -> multiply(Y2, Y1)
% 15.21/15.27 multiply(Y1, add(multiplicative_identity, Y1)) -> Y1
% 15.21/15.27 multiply(Y1, multiply(Y0, add(Y0, Y1))) -> multiply(Y1, Y0)
% 15.21/15.27 multiply(Y1, multiply(Y0, add(Y1, Y0))) -> multiply(Y1, Y0)
% 15.21/15.27 multiply(Y2, add(inverse(X0), Y2)) -> Y2
% 15.21/15.27 multiply(add(X0, X1), add(add(X0, inverse(X1)), Y2)) -> multiply(add(X0, add(X0, X1)), add(X0, Y2))
% 15.21/15.27 multiply(add(X0, X1), add(add(inverse(X0), X1), Y2)) -> multiply(add(X1, add(X0, X1)), add(X1, Y2))
% 15.21/15.27 multiply(add(X0, Y1), add(Y1, add(X0, Y1))) -> add(Y1, X0)
% 15.21/15.27 multiply(add(Y0, Y0), additive_identity) -> multiply(Y0, additive_identity)
% 15.21/15.27 multiply(add(Y0, Y1), add(Y0, add(X1, inverse(Y1)))) -> multiply(add(Y0, Y1), add(Y0, X1))
% 15.21/15.27 multiply(add(Y0, Y1), add(Y0, add(inverse(Y1), X1))) -> multiply(add(Y0, X1), add(Y0, Y1))
% 15.21/15.27 multiply(add(Y0, Y1), add(Y0, add(inverse(Y1), X1))) -> multiply(add(Y0, Y1), add(Y0, X1))
% 15.21/15.27 multiply(add(Y0, Y1), add(Y0, inverse(Y1))) -> Y0
% 15.21/15.27 multiply(add(Y0, Y1), add(Y0, inverse(inverse(Y1)))) -> add(Y0, Y1)
% 15.21/15.27 multiply(add(Y0, Y1), add(Y0, inverse(inverse(Y1)))) -> add(Y0, inverse(inverse(Y1)))
% 15.21/15.27 multiply(add(Y0, Y1), add(Y0, multiplicative_identity)) -> add(Y0, Y1)
% 15.21/15.27 multiply(add(Y0, Y1), add(Y1, inverse(Y0))) -> Y1
% 15.21/15.27 multiply(add(Y0, Y1), add(Y1, inverse(multiply(Y0, inverse(Y1))))) -> Y1
% 15.21/15.27 multiply(add(Y0, Y1), add(Y1, multiplicative_identity)) -> add(Y0, Y1)
% 15.21/15.27 multiply(add(Y0, Y1), add(add(Y0, Y1), add(Y0, inverse(Y1)))) -> add(Y0, add(Y0, Y1))
% 15.21/15.27 multiply(add(Y0, Y1), add(add(Y0, Y1), add(inverse(Y0), Y1))) -> add(Y1, add(Y0, Y1))
% 15.21/15.27 multiply(add(Y0, Y1), add(multiplicative_identity, Y0)) -> add(Y0, Y1)
% 15.21/15.27 multiply(add(Y0, Y1), multiply(Y0, add(Y0, inverse(Y1)))) -> Y0
% 15.21/15.27 multiply(add(Y0, Y1), multiply(Y1, add(Y1, inverse(Y0)))) -> Y1
% 15.21/15.27 multiply(add(Y0, Y1), multiply(add(Y1, Y1), add(Y1, inverse(Y0)))) -> Y1
% 15.21/15.27 multiply(add(Y0, Y2), add(add(X1, inverse(Y0)), Y2)) -> multiply(add(X1, Y2), add(Y0, Y2))
% 15.21/15.27 multiply(add(Y0, Y2), add(add(X1, inverse(Y0)), Y2)) -> multiply(add(Y0, Y2), add(X1, Y2))
% 15.21/15.27 multiply(add(Y0, Y2), add(add(inverse(Y0), X1), Y2)) -> multiply(add(X1, Y2), add(Y0, Y2))
% 15.21/15.27 multiply(add(Y0, Y2), add(add(inverse(Y0), X1), Y2)) -> multiply(add(Y0, Y2), add(X1, Y2))
% 15.21/15.27 multiply(add(Y0, Y2), add(inverse(Y0), Y2)) -> Y2
% 15.21/15.27 multiply(add(Y0, Y2), add(inverse(inverse(Y0)), Y2)) -> add(Y0, Y2)
% 15.21/15.27 multiply(add(Y0, Y2), add(inverse(inverse(Y0)), Y2)) -> add(inverse(inverse(Y0)), Y2)
% 15.21/15.27 multiply(add(Y0, Y2), add(multiplicative_identity, Y2)) -> add(Y0, Y2)
% 15.21/15.27 multiply(add(Y0, Y2), inverse(Y0)) -> multiply(Y2, inverse(Y0))
% 15.21/15.27 multiply(add(Y0, Y2), inverse(Y2)) -> multiply(Y0, inverse(Y2))
% 15.21/15.27 multiply(add(Y0, Y2), inverse(inverse(Y0))) -> inverse(inverse(Y0))
% 15.21/15.27 multiply(add(Y0, Y2), inverse(inverse(Y2))) -> inverse(inverse(Y2))
% 15.21/15.27 multiply(add(Y0, Y2), multiply(inverse(Y0), add(multiplicative_identity, Y2))) -> multiply(Y2, inverse(Y0))
% 15.21/15.27 multiply(add(Y0, Y2), multiply(inverse(Y0), add(multiplicative_identity, Y2))) -> multiply(inverse(Y0), Y2)
% 15.21/15.27 multiply(add(Y0, add(X0, X1)), add(Y0, add(X0, inverse(X1)))) -> add(Y0, X0)
% 15.21/15.27 multiply(add(Y0, add(X0, X1)), add(Y0, add(inverse(X0), X1))) -> add(Y0, X1)
% 15.21/15.27 multiply(add(Y0, inverse(Y1)), add(add(Y0, Y1), add(Y0, inverse(Y1)))) -> add(Y0, add(Y0, inverse(Y1)))
% 15.21/15.27 multiply(add(Y0, inverse(Y2)), add(inverse(Y2), inverse(multiply(Y0, Y2)))) -> inverse(Y2)
% 15.21/15.27 multiply(add(Y0, inverse(inverse(multiply(Y0, Y1)))), add(Y1, inverse(inverse(multiply(Y0, Y1))))) -> inverse(inverse(multiply(Y0, Y1)))
% 15.21/15.27 multiply(add(Y0, inverse(inverse(multiply(Y0, Y1)))), add(Y1, inverse(inverse(multiply(Y0, Y1))))) -> multiply(Y0, Y1)
% 15.21/15.27 multiply(add(Y0, inverse(multiply(Y0, Y1))), add(Y1, inverse(multiply(Y0, Y1)))) -> multiplicative_identity
% 15.21/15.27 multiply(add(Y0, multiplicative_identity), add(Y0, Y2)) -> add(Y0, Y2)
% 15.21/15.27 multiply(add(Y0, multiplicative_identity), add(Y1, Y0)) -> add(Y1, Y0)
% 15.21/15.27 multiply(add(Y0, multiplicative_identity), add(multiplicative_identity, inverse(Y0))) -> multiplicative_identity
% 15.21/15.27 multiply(add(Y0, multiplicative_identity), additive_identity) -> multiply(Y0, additive_identity)
% 15.21/15.27 multiply(add(Y2, Y1), add(Y1, inverse(multiply(inverse(Y1), Y2)))) -> Y1
% 15.21/15.27 multiply(add(Y2, Y1), multiply(add(multiplicative_identity, Y1), inverse(Y2))) -> multiply(Y1, inverse(Y2))
% 15.21/15.27 multiply(add(Y2, inverse(Y0)), add(inverse(Y0), inverse(multiply(Y0, Y2)))) -> inverse(Y0)
% 15.21/15.27 multiply(add(add(X0, X1), Y2), add(add(X0, inverse(X1)), Y2)) -> add(X0, Y2)
% 15.21/15.27 multiply(add(add(X0, X1), Y2), add(add(inverse(X0), X1), Y2)) -> add(X1, Y2)
% 15.21/15.27 multiply(add(inverse(Y0), Y1), add(add(Y0, Y1), add(inverse(Y0), Y1))) -> add(Y1, add(inverse(Y0), Y1))
% 15.21/15.27 multiply(add(inverse(Y0), Y1), multiply(Y1, add(Y1, Y0))) -> Y1
% 15.21/15.27 multiply(add(inverse(Y2), Y1), multiply(add(Y1, Y1), add(Y1, Y2))) -> Y1
% 15.21/15.27 multiply(add(multiplicative_identity, Y0), add(Y0, Y1)) -> add(Y0, Y1)
% 15.21/15.27 multiply(add(multiplicative_identity, Y1), additive_identity) -> multiply(Y1, additive_identity)
% 15.21/15.27 multiply(add(multiplicative_identity, Y2), add(Y1, Y2)) -> add(Y1, Y2)
% 15.21/15.27 multiply(add(multiplicative_identity, multiplicative_identity), inverse(Y0)) -> inverse(Y0)
% 15.21/15.27 multiply(additive_identity, Y0) -> additive_identity
% 15.21/15.27 multiply(additive_identity, add(Y1, Y1)) -> multiply(additive_identity, Y1)
% 15.21/15.27 multiply(additive_identity, add(Y1, multiplicative_identity)) -> multiply(additive_identity, Y1)
% 15.21/15.27 multiply(additive_identity, add(multiplicative_identity, Y1)) -> multiply(additive_identity, Y1)
% 15.21/15.27 multiply(additive_identity, inverse(Y0)) -> additive_identity
% 15.21/15.27 multiply(inverse(X), X) -> additive_identity
% 15.21/15.27 multiply(inverse(X0), add(Y0, inverse(X0))) -> inverse(X0)
% 15.21/15.27 multiply(inverse(X0), add(inverse(X0), Y2)) -> inverse(X0)
% 15.21/15.27 multiply(inverse(Y0), inverse(Y0)) -> inverse(Y0)
% 15.21/15.27 multiply(inverse(Y1), add(Y1, Y2)) -> multiply(inverse(Y1), Y2)
% 15.21/15.27 multiply(inverse(Y2), add(Y1, Y2)) -> multiply(inverse(Y2), Y1)
% 15.21/15.27 multiply(inverse(inverse(Y0)), add(Y1, inverse(inverse(Y0)))) -> multiply(Y0, add(Y1, inverse(inverse(Y0))))
% 15.21/15.27 multiply(inverse(inverse(Y0)), add(inverse(inverse(Y0)), Y2)) -> multiply(Y0, add(inverse(inverse(Y0)), Y2))
% 15.21/15.27 multiply(inverse(inverse(inverse(Y0))), add(Y0, inverse(inverse(inverse(Y0))))) -> inverse(inverse(inverse(Y0)))
% 15.21/15.27 multiply(inverse(multiply(Y0, additive_identity)), add(Y0, inverse(multiply(Y0, additive_identity)))) -> multiplicative_identity
% 15.21/15.27 multiply(inverse(multiply(additive_identity, Y1)), add(Y1, inverse(multiply(additive_identity, Y1)))) -> multiplicative_identity
% 15.21/15.27 multiply(multiplicative_identity, X) -> X
% 15.21/15.27 multiply(multiply(X0, X1), multiply(multiply(X0, add(X0, X1)), multiply(X1, add(X1, X0)))) -> multiply(X0, X1)
% 15.21/15.27 multiply(multiply(X0, add(X1, X2)), multiply(add(X0, inverse(multiply(X0, X1))), add(inverse(multiply(X0, X1)), X2))) -> multiply(X0, X2)
% 15.21/15.27 multiply(multiply(X0, add(X1, X2)), multiply(add(X0, inverse(multiply(X0, X2))), add(X1, inverse(multiply(X0, X2))))) -> multiply(X0, X1)
% 15.21/15.27 multiply(multiply(X1, X2), multiply(multiply(X1, add(X2, X1)), multiply(X2, add(X1, X2)))) -> multiply(X1, X2)
% 15.21/15.27 multiply(multiply(Y0, Y1), multiply(Y0, add(Y0, Y1))) -> multiply(Y0, Y1)
% 15.21/15.27 multiply(multiply(Y0, Y1), multiply(Y0, add(Y0, Y1))) -> multiply(Y1, Y0)
% 15.21/15.27 multiply(multiply(Y0, Y1), multiply(Y0, add(Y1, Y0))) -> multiply(Y0, Y1)
% 15.21/15.27 multiply(multiply(Y0, Y1), multiply(Y0, add(Y1, Y0))) -> multiply(Y1, Y0)
% 15.21/15.27 multiply(multiply(Y0, Y1), multiply(Y1, add(Y0, Y1))) -> multiply(Y0, Y1)
% 15.21/15.27 multiply(multiply(Y0, Y1), multiply(Y1, add(Y1, Y0))) -> multiply(Y0, Y1)
% 15.21/15.27 multiply(multiply(Y0, Y1), multiply(Y1, add(Y1, Y0))) -> multiply(Y1, Y0)
% 15.21/15.27 multiply(multiply(Y0, Y2), multiply(add(Y0, Y2), add(Y2, Y2))) -> multiply(Y0, Y2)
% 15.21/15.27 multiply(multiply(Y0, add(Y0, Y0)), multiply(Y2, add(Y2, Y0))) -> multiply(Y0, Y2)
% 15.21/15.27 multiply(multiply(Y0, add(Y0, Y0)), multiply(Y2, add(Y2, Y0))) -> multiply(Y2, Y0)
% 15.21/15.27 multiply(multiply(Y0, add(Y0, Y1)), add(Y0, inverse(Y1))) -> Y0
% 15.21/15.27 multiply(multiply(Y0, add(Y0, Y1)), add(inverse(Y0), Y1)) -> multiply(Y1, Y0)
% 15.21/15.27 multiply(multiply(Y0, add(Y0, Y1)), add(inverse(Y1), Y0)) -> Y0
% 15.21/15.27 multiply(multiply(Y0, add(Y0, Y1)), multiply(Y1, add(Y1, Y0))) -> multiply(Y0, Y1)
% 15.21/15.27 multiply(multiply(Y0, add(Y0, Y1)), multiply(Y1, add(Y1, Y1))) -> multiply(Y0, Y1)
% 15.21/15.27 multiply(multiply(Y0, add(Y0, Y1)), multiply(Y1, add(Y1, Y1))) -> multiply(Y1, Y0)
% 15.21/15.27 multiply(multiply(Y0, add(Y0, Y1)), multiply(Y1, additive_identity)) -> multiply(add(Y0, Y1), additive_identity)
% 15.21/15.27 multiply(multiply(Y0, add(Y0, Y1)), multiply(add(multiplicative_identity, Y1), additive_identity)) -> multiply(add(Y0, Y1), additive_identity)
% 15.21/15.27 multiply(multiply(Y0, add(Y0, Y2)), multiply(add(Y1, Y2), add(Y1, Y0))) -> multiply(Y0, add(Y1, Y2))
% 15.21/15.27 multiply(multiply(Y0, add(Y0, Y2)), multiply(additive_identity, Y2)) -> multiply(add(Y0, Y2), additive_identity)
% 15.21/15.27 multiply(multiply(Y0, add(Y0, Y2)), multiply(additive_identity, add(multiplicative_identity, Y2))) -> multiply(add(Y0, Y2), additive_identity)
% 15.21/15.27 multiply(multiply(Y0, add(Y0, inverse(Y1))), add(Y1, Y0)) -> Y0
% 15.21/15.27 multiply(multiply(Y0, add(Y1, Y0)), add(inverse(Y1), Y0)) -> Y0
% 15.21/15.27 multiply(multiply(Y1, Y0), multiply(add(Y0, Y1), add(Y0, Y0))) -> multiply(Y0, Y1)
% 15.21/15.27 multiply(multiply(Y1, Y0), multiply(add(Y0, Y1), add(Y0, Y0))) -> multiply(Y1, Y0)
% 15.21/15.27 multiply(multiply(Y1, Y2), multiply(add(Y1, Y1), add(Y1, Y2))) -> multiply(Y1, Y2)
% 15.21/15.27 multiply(multiply(Y1, Y2), multiply(add(Y1, Y1), add(Y1, Y2))) -> multiply(Y2, Y1)
% 15.21/15.27 multiply(multiply(Y1, add(Y0, Y1)), add(Y1, inverse(multiply(Y0, Y1)))) -> Y1
% 15.21/15.27 multiply(multiply(Y1, add(Y0, Y1)), multiply(Y0, additive_identity)) -> multiply(add(Y0, Y1), additive_identity)
% 15.21/15.27 multiply(multiply(Y1, add(Y0, Y1)), multiply(additive_identity, Y0)) -> multiply(add(Y0, Y1), additive_identity)
% 15.21/15.27 multiply(multiply(Y1, add(Y1, Y2)), multiply(add(Y0, Y2), add(Y0, Y1))) -> multiply(add(Y0, Y2), Y1)
% 15.21/15.27 multiply(multiply(Y1, add(Y2, Y1)), add(Y1, inverse(multiply(Y1, Y2)))) -> Y1
% 15.21/15.27 multiply(multiply(Y1, add(Y2, Y1)), multiply(Y2, add(Y1, Y2))) -> multiply(Y1, Y2)
% 15.21/15.27 multiply(multiply(Y1, additive_identity), multiply(Y2, add(Y2, Y1))) -> multiply(additive_identity, add(Y2, Y1))
% 15.21/15.27 multiply(multiply(add(X0, X2), X1), multiply(add(X0, inverse(multiply(X2, X1))), add(X1, inverse(multiply(X2, X1))))) -> multiply(X0, X1)
% 15.21/15.27 multiply(multiply(add(X0, X2), X1), multiply(add(X1, inverse(multiply(X0, X1))), add(inverse(multiply(X0, X1)), X2))) -> multiply(X2, X1)
% 15.21/15.27 multiply(multiply(add(X0, Y1), add(X1, Y1)), add(inverse(multiply(X0, X1)), Y1)) -> Y1
% 15.21/15.27 multiply(multiply(add(X0, Y1), add(X1, Y1)), multiply(add(X0, inverse(Y1)), add(X1, inverse(Y1)))) -> multiply(X0, X1)
% 15.21/15.27 multiply(multiply(add(Y0, X1), add(Y0, X2)), add(Y0, inverse(multiply(X1, X2)))) -> Y0
% 15.21/15.27 multiply(multiply(add(Y0, X1), add(Y0, X2)), multiply(add(inverse(Y0), X1), add(inverse(Y0), X2))) -> multiply(X1, X2)
% 15.21/15.27 multiply(multiply(add(Y0, Y0), add(Y0, Y2)), multiply(add(Y1, Y0), add(Y1, Y2))) -> multiply(Y0, add(Y1, Y2))
% 15.21/15.27 multiply(multiply(add(Y0, Y0), add(Y1, Y0)), multiply(add(Y0, Y2), add(Y1, Y2))) -> multiply(Y0, add(Y1, Y2))
% 15.21/15.27 multiply(multiply(add(Y0, Y1), add(Y0, Y0)), add(inverse(Y0), Y1)) -> multiply(Y1, Y0)
% 15.21/15.27 multiply(multiply(add(Y0, Y1), add(Y0, Y0)), add(inverse(Y1), Y0)) -> Y0
% 15.21/15.27 multiply(multiply(add(Y0, Y1), add(Y0, Y2)), multiply(add(Y1, Y1), add(Y1, Y2))) -> multiply(add(Y0, Y2), Y1)
% 15.21/15.27 multiply(multiply(add(Y0, Y2), add(Y0, X1)), multiply(add(Y2, add(X1, inverse(Y2))), add(X1, add(X1, inverse(Y2))))) -> multiply(add(Y0, Y2), add(X1, inverse(Y2)))
% 15.21/15.27 multiply(multiply(add(Y0, Y2), add(Y0, X1)), multiply(add(Y2, add(inverse(Y2), X1)), add(X1, add(inverse(Y2), X1)))) -> multiply(add(Y0, Y2), add(inverse(Y2), X1))
% 15.21/15.27 multiply(multiply(add(Y0, Y2), add(Y0, Y0)), multiply(add(Y1, Y2), add(Y1, Y0))) -> multiply(Y0, add(Y1, Y2))
% 15.21/15.27 multiply(multiply(add(Y0, Y2), add(Y0, Y1)), multiply(add(Y1, Y2), add(Y1, Y1))) -> multiply(add(Y0, Y2), Y1)
% 15.21/15.27 multiply(multiply(add(Y0, Y2), add(Y0, add(X1, inverse(Y0)))), multiply(add(X1, Y2), add(X1, add(X1, inverse(Y0))))) -> multiply(add(Y0, Y2), add(X1, inverse(Y0)))
% 15.21/15.27 multiply(multiply(add(Y0, Y2), add(Y0, add(inverse(Y0), X1))), multiply(add(X1, Y2), add(X1, add(inverse(Y0), X1)))) -> multiply(add(Y0, Y2), add(inverse(Y0), X1))
% 15.21/15.27 multiply(multiply(add(Y0, Y2), add(Y1, Y2)), multiply(add(Y0, Y1), add(Y1, Y1))) -> multiply(add(Y0, Y2), Y1)
% 15.21/15.27 multiply(multiply(add(Y0, inverse(Y2)), add(Y0, Y0)), add(Y2, Y0)) -> Y0
% 15.21/15.27 multiply(multiply(add(Y1, Y0), add(Y1, Y2)), multiply(add(Y0, Y0), add(Y0, Y2))) -> multiply(Y0, add(Y1, Y2))
% 15.21/15.27 multiply(multiply(add(Y1, Y1), add(Y1, Y2)), add(inverse(Y1), Y2)) -> multiply(Y2, Y1)
% 15.21/15.27 multiply(multiply(add(Y1, Y2), add(Y1, Y1)), multiply(add(Y0, Y2), add(Y0, Y1))) -> multiply(add(Y0, Y2), Y1)
% 15.21/15.27 multiply(multiply(add(multiplicative_identity, Y1), additive_identity), multiply(Y2, add(Y2, Y1))) -> multiply(additive_identity, add(Y2, Y1))
% 15.21/15.27 multiply(multiply(additive_identity, Y1), multiply(Y2, add(Y2, Y1))) -> multiply(additive_identity, add(Y2, Y1))
% 15.21/15.27 multiply(multiply(additive_identity, add(multiplicative_identity, Y1)), multiply(Y2, add(Y2, Y1))) -> multiply(additive_identity, add(Y2, Y1))
% 15.21/15.27 true__ -> false__
% 15.21/15.27 with the LPO induced by
% 15.21/15.27 b > a > f1 > inverse > additive_identity > multiplicative_identity > add > multiply > true__ > false__
% 15.21/15.27
% 15.21/15.27 % SZS output end Proof
% 15.21/15.27
%------------------------------------------------------------------------------