TSTP Solution File: NUM020-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : NUM020-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n021.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 : Mon Jul 18 12:32:14 EDT 2022
% Result : Unsatisfiable 9.56s 9.46s
% Output : Proof 9.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM020-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n021.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 : Thu Jul 7 21:32:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 9.56/9.46 % SZS status Unsatisfiable
% 9.56/9.46 % SZS output start Proof
% 9.56/9.46 The input problem is unsatisfiable because
% 9.56/9.46
% 9.56/9.46 [1] the following set of Horn clauses is unsatisfiable:
% 9.56/9.46
% 9.56/9.46 equalish(add(A, n0), A)
% 9.56/9.46 equalish(add(A, successor(B)), successor(add(A, B)))
% 9.56/9.46 equalish(multiply(A, n0), n0)
% 9.56/9.46 equalish(multiply(A, successor(B)), add(multiply(A, B), A))
% 9.56/9.46 equalish(successor(A), successor(B)) ==> equalish(A, B)
% 9.56/9.46 equalish(A, B) ==> equalish(successor(A), successor(B))
% 9.56/9.46 equalish(X, X)
% 9.56/9.46 equalish(X, Y) ==> equalish(Y, X)
% 9.56/9.46 equalish(X, Y) & equalish(Y, Z) ==> equalish(X, Z)
% 9.56/9.46 equalish(n1, successor(n0))
% 9.56/9.46 equalish(add(a, successor(n0)), successor(a)) ==> \bottom
% 9.56/9.46 equalish(successor(A), n0) ==> \bottom
% 9.56/9.46
% 9.56/9.46 This holds because
% 9.56/9.46
% 9.56/9.46 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 9.56/9.46
% 9.56/9.46 E:
% 9.56/9.46 equalish(X, X) = true__
% 9.56/9.46 equalish(add(A, n0), A) = true__
% 9.56/9.46 equalish(add(A, successor(B)), successor(add(A, B))) = true__
% 9.56/9.46 equalish(multiply(A, n0), n0) = true__
% 9.56/9.46 equalish(multiply(A, successor(B)), add(multiply(A, B), A)) = true__
% 9.56/9.46 equalish(n1, successor(n0)) = true__
% 9.56/9.46 f1(equalish(successor(A), successor(B)), A, B) = true__
% 9.56/9.46 f1(true__, A, B) = equalish(A, B)
% 9.56/9.46 f2(equalish(A, B), A, B) = true__
% 9.56/9.46 f2(true__, A, B) = equalish(successor(A), successor(B))
% 9.56/9.46 f3(equalish(X, Y), Y, X) = true__
% 9.56/9.46 f3(true__, Y, X) = equalish(Y, X)
% 9.56/9.46 f4(true__, X, Z) = equalish(X, Z)
% 9.56/9.46 f5(equalish(Y, Z), X, Y, Z) = true__
% 9.56/9.46 f5(true__, X, Y, Z) = f4(equalish(X, Y), X, Z)
% 9.56/9.46 f6(equalish(add(a, successor(n0)), successor(a))) = true__
% 9.56/9.46 f6(true__) = false__
% 9.56/9.46 f7(equalish(successor(A), n0)) = true__
% 9.56/9.46 f7(true__) = false__
% 9.56/9.46 G:
% 9.56/9.46 true__ = false__
% 9.56/9.46
% 9.56/9.46 This holds because
% 9.56/9.46
% 9.56/9.46 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 9.56/9.46
% 9.56/9.46
% 9.56/9.46 equalish(A, B) -> f1(true__, A, B)
% 9.56/9.46 equalish(X, X) -> true__
% 9.56/9.46 equalish(add(A, n0), A) -> true__
% 9.56/9.46 equalish(add(A, successor(B)), successor(add(A, B))) -> true__
% 9.56/9.46 equalish(multiply(A, n0), n0) -> true__
% 9.56/9.46 equalish(multiply(A, successor(B)), add(multiply(A, B), A)) -> true__
% 9.56/9.46 equalish(n1, successor(n0)) -> true__
% 9.56/9.46 f1(equalish(successor(A), successor(B)), A, B) -> true__
% 9.56/9.46 f1(f1(true__, successor(Y0), successor(Y1)), Y0, Y1) -> true__
% 9.56/9.46 f1(true__, Y0, add(add(Y0, n0), n0)) -> true__
% 9.56/9.46 f1(true__, Y0, add(add(add(Y0, n0), n0), n0)) -> true__
% 9.56/9.46 f1(true__, Y1, Y1) -> true__
% 9.56/9.46 f1(true__, Y1, add(Y1, n0)) -> true__
% 9.56/9.46 f1(true__, add(X0, successor(X1)), add(successor(add(X0, X1)), n0)) -> true__
% 9.56/9.46 f1(true__, add(X0, successor(n0)), add(successor(X0), n0)) -> true__
% 9.56/9.46 f1(true__, add(Y0, successor(Y1)), successor(add(Y0, Y1))) -> true__
% 9.56/9.46 f1(true__, add(Y1, n0), Y1) -> true__
% 9.56/9.46 f1(true__, add(Y1, successor(n0)), successor(Y1)) -> true__
% 9.56/9.46 f1(true__, add(Y1, successor(successor(Y2))), successor(successor(add(Y1, Y2)))) -> true__
% 9.56/9.46 f1(true__, add(add(X0, successor(X1)), n0), add(successor(add(X0, X1)), n0)) -> true__
% 9.56/9.46 f1(true__, add(add(Y1, n0), n0), Y1) -> true__
% 9.56/9.46 f1(true__, add(add(Y1, successor(Y2)), n0), successor(add(Y1, Y2))) -> true__
% 9.56/9.46 f1(true__, add(add(Y1, successor(n0)), n0), successor(Y1)) -> true__
% 9.56/9.46 f1(true__, add(add(add(Y1, n0), n0), n0), Y1) -> true__
% 9.56/9.46 f1(true__, add(add(add(Y1, successor(Y2)), n0), n0), successor(add(Y1, Y2))) -> true__
% 9.56/9.46 f1(true__, add(add(add(multiply(Y1, Y2), Y1), n0), n0), multiply(Y1, successor(Y2))) -> true__
% 9.56/9.46 f1(true__, add(add(add(n1, n0), n0), n0), successor(n0)) -> true__
% 9.56/9.46 f1(true__, add(add(multiply(Y1, Y2), Y1), n0), multiply(Y1, successor(Y2))) -> true__
% 9.56/9.46 f1(true__, add(add(multiply(Y1, n0), n0), n0), n0) -> true__
% 9.56/9.46 f1(true__, add(add(multiply(Y1, successor(Y2)), n0), n0), add(multiply(Y1, Y2), Y1)) -> true__
% 9.56/9.46 f1(true__, add(add(n0, n0), n0), multiply(Y1, n0)) -> true__
% 9.56/9.46 f1(true__, add(add(n1, n0), n0), add(successor(n0), n0)) -> true__
% 9.56/9.46 f1(true__, add(add(n1, n0), n0), successor(n0)) -> true__
% 9.56/9.46 f1(true__, add(add(successor(add(Y1, Y2)), n0), n0), add(Y1, successor(Y2))) -> true__
% 9.56/9.46 f1(true__, add(add(successor(add(Y1, n0)), n0), n0), successor(Y1)) -> true__
% 9.56/9.46 f1(true__, add(add(successor(add(Y1, successor(Y2))), n0), n0), successor(successor(add(Y1, Y2)))) -> true__
% 9.56/9.46 f1(true__, add(add(successor(multiply(Y1, n0)), n0), n0), successor(n0)) -> true__
% 9.56/9.46 f1(true__, add(add(successor(multiply(Y1, successor(Y2))), n0), n0), successor(add(multiply(Y1, Y2), Y1))) -> true__
% 9.56/9.46 f1(true__, add(add(successor(n0), n0), n0), n1) -> true__
% 9.56/9.46 f1(true__, add(add(successor(n1), n0), n0), successor(successor(n0))) -> true__
% 9.56/9.46 f1(true__, add(add(successor(successor(n0)), n0), n0), successor(n1)) -> true__
% 9.56/9.46 f1(true__, add(multiply(X0, X1), X0), add(multiply(X0, successor(X1)), n0)) -> true__
% 9.56/9.46 f1(true__, add(multiply(X0, X1), X0), multiply(X0, successor(X1))) -> true__
% 9.56/9.46 f1(true__, add(multiply(X0, n0), n0), add(n0, n0)) -> true__
% 9.56/9.46 f1(true__, add(multiply(X0, n0), n0), multiply(Y1, n0)) -> true__
% 9.56/9.46 f1(true__, add(multiply(X0, successor(X1)), n0), add(add(multiply(X0, X1), X0), n0)) -> true__
% 9.56/9.46 f1(true__, add(multiply(Y1, n0), n0), n0) -> true__
% 9.56/9.46 f1(true__, add(multiply(Y1, successor(Y2)), n0), add(multiply(Y1, Y2), Y1)) -> true__
% 9.56/9.46 f1(true__, add(multiply(n0, successor(X1)), n0), multiply(n0, X1)) -> true__
% 9.56/9.46 f1(true__, add(n0, n0), add(multiply(X0, n0), n0)) -> true__
% 9.56/9.46 f1(true__, add(n0, n0), multiply(Y1, n0)) -> true__
% 9.56/9.46 f1(true__, add(n0, successor(n0)), n1) -> true__
% 9.56/9.46 f1(true__, add(n1, n0), add(successor(n0), n0)) -> true__
% 9.56/9.46 f1(true__, add(n1, n0), successor(n0)) -> true__
% 9.56/9.46 f1(true__, add(successor(X0), n0), successor(add(X0, n0))) -> true__
% 9.56/9.46 f1(true__, add(successor(add(Y1, Y2)), n0), add(Y1, successor(Y2))) -> true__
% 9.56/9.46 f1(true__, add(successor(add(Y1, n0)), n0), successor(Y1)) -> true__
% 9.56/9.46 f1(true__, add(successor(add(Y1, successor(Y2))), n0), successor(successor(add(Y1, Y2)))) -> true__
% 9.56/9.46 f1(true__, add(successor(add(n0, n0)), n0), n1) -> true__
% 9.56/9.46 f1(true__, add(successor(multiply(Y1, n0)), n0), successor(n0)) -> true__
% 9.56/9.46 f1(true__, add(successor(multiply(Y1, successor(Y2))), n0), successor(add(multiply(Y1, Y2), Y1))) -> true__
% 9.56/9.46 f1(true__, add(successor(n0), n0), add(n1, n0)) -> true__
% 9.56/9.46 f1(true__, add(successor(n0), n0), n1) -> true__
% 9.56/9.46 f1(true__, add(successor(n0), n0), successor(multiply(X0, n0))) -> true__
% 9.56/9.46 f1(true__, add(successor(n1), n0), add(successor(successor(n0)), n0)) -> true__
% 9.56/9.46 f1(true__, add(successor(n1), n0), successor(successor(n0))) -> true__
% 9.56/9.46 f1(true__, add(successor(successor(n0)), n0), successor(n1)) -> true__
% 9.56/9.46 f1(true__, multiply(X0, n0), add(add(n0, n0), n0)) -> true__
% 9.56/9.46 f1(true__, multiply(X0, n0), add(multiply(X1, n0), n0)) -> true__
% 9.56/9.46 f1(true__, multiply(X0, n0), add(n0, n0)) -> true__
% 9.56/9.46 f1(true__, multiply(X0, n0), multiply(Y1, n0)) -> true__
% 9.56/9.46 f1(true__, multiply(X0, n0), n0) -> true__
% 9.56/9.46 f1(true__, multiply(X0, successor(X1)), add(add(multiply(X0, X1), X0), n0)) -> true__
% 9.56/9.46 f1(true__, multiply(Y0, successor(Y1)), add(multiply(Y0, Y1), Y0)) -> true__
% 9.56/9.46 f1(true__, multiply(n0, X0), multiply(n0, successor(X0))) -> true__
% 9.56/9.46 f1(true__, multiply(n0, successor(X1)), multiply(n0, X1)) -> true__
% 9.56/9.46 f1(true__, multiply(n0, successor(n0)), add(n0, n0)) -> true__
% 9.56/9.46 f1(true__, multiply(n0, successor(n0)), multiply(Y1, n0)) -> true__
% 9.56/9.46 f1(true__, multiply(n0, successor(n0)), n0) -> true__
% 9.56/9.46 f1(true__, multiply(n0, successor(successor(Y2))), add(multiply(n0, Y2), n0)) -> true__
% 9.56/9.46 f1(true__, multiply(successor(X0), successor(X1)), add(successor(add(multiply(successor(X0), X1), X0)), n0)) -> true__
% 9.56/9.46 f1(true__, multiply(successor(Y2), successor(X1)), successor(add(multiply(successor(Y2), X1), Y2))) -> true__
% 9.56/9.46 f1(true__, n0, add(add(multiply(X0, n0), n0), n0)) -> true__
% 9.56/9.46 f1(true__, n0, add(multiply(X0, n0), n0)) -> true__
% 9.56/9.46 f1(true__, n0, multiply(X0, n0)) -> true__
% 9.56/9.46 f1(true__, n0, multiply(n0, successor(n0))) -> true__
% 9.56/9.46 f1(true__, n1, add(add(successor(n0), n0), n0)) -> true__
% 9.56/9.46 f1(true__, n1, add(successor(n0), n0)) -> true__
% 9.56/9.46 f1(true__, n1, successor(add(n0, n0))) -> true__
% 9.56/9.46 f1(true__, n1, successor(multiply(X0, n0))) -> true__
% 9.56/9.46 f1(true__, n1, successor(n0)) -> true__
% 9.56/9.46 f1(true__, successor(X0), add(add(X0, successor(n0)), n0)) -> true__
% 9.56/9.46 f1(true__, successor(X0), add(successor(add(X0, n0)), n0)) -> true__
% 9.56/9.46 f1(true__, successor(Y0), successor(add(Y0, n0))) -> true__
% 9.56/9.46 f1(true__, successor(Y0), successor(add(add(Y0, n0), n0))) -> true__
% 9.56/9.46 f1(true__, successor(Y1), add(Y1, successor(n0))) -> true__
% 9.56/9.46 f1(true__, successor(Y1), successor(Y1)) -> true__
% 9.56/9.46 f1(true__, successor(add(X0, X1)), add(X0, successor(X1))) -> true__
% 9.56/9.46 f1(true__, successor(add(X0, X1)), add(add(X0, successor(X1)), n0)) -> true__
% 9.56/9.46 f1(true__, successor(add(X0, n0)), add(successor(X0), n0)) -> true__
% 9.56/9.46 f1(true__, successor(add(X0, successor(X1))), add(successor(successor(add(X0, X1))), n0)) -> true__
% 9.56/9.46 f1(true__, successor(add(X0, successor(X1))), successor(successor(add(X0, X1)))) -> true__
% 9.56/9.46 f1(true__, successor(add(X0, successor(n0))), successor(successor(X0))) -> true__
% 9.56/9.46 f1(true__, successor(add(Y1, n0)), successor(Y1)) -> true__
% 9.56/9.46 f1(true__, successor(add(add(X0, successor(X1)), n0)), successor(successor(add(X0, X1)))) -> true__
% 9.56/9.46 f1(true__, successor(add(add(X0, successor(n0)), n0)), successor(successor(X0))) -> true__
% 9.56/9.46 f1(true__, successor(add(add(Y1, Y2), n0)), add(Y1, successor(Y2))) -> true__
% 9.56/9.46 f1(true__, successor(add(add(Y1, n0), n0)), successor(Y1)) -> true__
% 9.56/9.46 f1(true__, successor(add(add(add(Y1, n0), n0), n0)), successor(Y1)) -> true__
% 9.56/9.46 f1(true__, successor(add(add(multiply(X0, n0), n0), n0)), successor(n0)) -> true__
% 9.56/9.46 f1(true__, successor(add(add(n0, n0), n0)), n1) -> true__
% 9.56/9.46 f1(true__, successor(add(add(n0, n0), n0)), successor(multiply(X0, n0))) -> true__
% 9.56/9.46 f1(true__, successor(add(add(n1, n0), n0)), successor(successor(n0))) -> true__
% 9.56/9.46 f1(true__, successor(add(add(successor(n0), n0), n0)), successor(n1)) -> true__
% 9.56/9.46 f1(true__, successor(add(multiply(X0, X1), X0)), add(successor(multiply(X0, successor(X1))), n0)) -> true__
% 9.56/9.46 f1(true__, successor(add(multiply(X0, X1), X0)), successor(multiply(X0, successor(X1)))) -> true__
% 9.56/9.46 f1(true__, successor(add(multiply(X0, n0), n0)), n1) -> true__
% 9.56/9.46 f1(true__, successor(add(multiply(X0, n0), n0)), successor(add(n0, n0))) -> true__
% 9.56/9.46 f1(true__, successor(add(multiply(X0, n0), n0)), successor(multiply(X1, n0))) -> true__
% 9.56/9.46 f1(true__, successor(add(multiply(X0, n0), n0)), successor(n0)) -> true__
% 9.56/9.46 f1(true__, successor(add(multiply(X0, successor(X1)), n0)), successor(add(multiply(X0, X1), X0))) -> true__
% 9.56/9.46 f1(true__, successor(add(multiply(successor(X0), X1), X0)), multiply(successor(X0), successor(X1))) -> true__
% 9.56/9.46 f1(true__, successor(add(n0, n0)), add(n1, n0)) -> true__
% 9.56/9.46 f1(true__, successor(add(n0, n0)), n1) -> true__
% 9.56/9.46 f1(true__, successor(add(n0, n0)), successor(multiply(X0, n0))) -> true__
% 9.56/9.46 f1(true__, successor(add(n1, n0)), add(successor(successor(n0)), n0)) -> true__
% 9.56/9.46 f1(true__, successor(add(n1, n0)), successor(add(successor(n0), n0))) -> true__
% 9.56/9.46 f1(true__, successor(add(n1, n0)), successor(successor(n0))) -> true__
% 9.56/9.46 f1(true__, successor(add(successor(add(X0, n0)), n0)), successor(successor(X0))) -> true__
% 9.56/9.46 f1(true__, successor(add(successor(multiply(X0, n0)), n0)), successor(successor(n0))) -> true__
% 9.56/9.46 f1(true__, successor(add(successor(n0), n0)), successor(n1)) -> true__
% 9.56/9.46 f1(true__, successor(add(successor(n1), n0)), successor(successor(successor(n0)))) -> true__
% 9.56/9.46 f1(true__, successor(multiply(X0, n0)), add(n1, n0)) -> true__
% 9.56/9.46 f1(true__, successor(multiply(X0, n0)), add(successor(n0), n0)) -> true__
% 9.56/9.46 f1(true__, successor(multiply(X0, n0)), n1) -> true__
% 9.56/9.46 f1(true__, successor(multiply(X0, n0)), successor(add(n0, n0))) -> true__
% 9.56/9.46 f1(true__, successor(multiply(X0, n0)), successor(multiply(X1, n0))) -> true__
% 9.56/9.46 f1(true__, successor(multiply(X0, n0)), successor(n0)) -> true__
% 9.56/9.46 f1(true__, successor(multiply(X0, successor(X1))), add(successor(add(multiply(X0, X1), X0)), n0)) -> true__
% 9.56/9.46 f1(true__, successor(multiply(X0, successor(X1))), successor(add(multiply(X0, X1), X0))) -> true__
% 9.56/9.46 f1(true__, successor(multiply(n0, X0)), successor(multiply(n0, successor(X0)))) -> true__
% 9.56/9.46 f1(true__, successor(multiply(n0, successor(X0))), successor(multiply(n0, X0))) -> true__
% 9.56/9.46 f1(true__, successor(multiply(n0, successor(n0))), successor(n0)) -> true__
% 9.56/9.46 f1(true__, successor(multiply(successor(X0), successor(X1))), successor(successor(add(multiply(successor(X0), X1), X0)))) -> true__
% 9.56/9.46 f1(true__, successor(n0), add(add(n1, n0), n0)) -> true__
% 9.56/9.46 f1(true__, successor(n0), add(n1, n0)) -> true__
% 9.56/9.46 f1(true__, successor(n0), add(successor(multiply(X0, n0)), n0)) -> true__
% 9.56/9.46 f1(true__, successor(n0), n1) -> true__
% 9.56/9.46 f1(true__, successor(n0), successor(add(multiply(X0, n0), n0))) -> true__
% 9.56/9.46 f1(true__, successor(n0), successor(multiply(X0, n0))) -> true__
% 9.56/9.46 f1(true__, successor(n1), add(add(successor(successor(n0)), n0), n0)) -> true__
% 9.56/9.46 f1(true__, successor(n1), add(successor(successor(n0)), n0)) -> true__
% 9.56/9.46 f1(true__, successor(n1), successor(add(successor(n0), n0))) -> true__
% 9.56/9.46 f1(true__, successor(n1), successor(successor(n0))) -> true__
% 9.56/9.46 f1(true__, successor(successor(X0)), successor(add(X0, successor(n0)))) -> true__
% 9.56/9.46 f1(true__, successor(successor(X0)), successor(add(successor(add(X0, n0)), n0))) -> true__
% 9.56/9.46 f1(true__, successor(successor(X0)), successor(successor(add(X0, n0)))) -> true__
% 9.56/9.46 f1(true__, successor(successor(add(X0, X1))), add(successor(add(X0, successor(X1))), n0)) -> true__
% 9.56/9.46 f1(true__, successor(successor(add(X0, X1))), successor(add(X0, successor(X1)))) -> true__
% 9.56/9.46 f1(true__, successor(successor(add(X0, n0))), add(successor(successor(X0)), n0)) -> true__
% 9.56/9.46 f1(true__, successor(successor(add(X0, n0))), successor(add(successor(X0), n0))) -> true__
% 9.56/9.46 f1(true__, successor(successor(add(X0, n0))), successor(successor(X0))) -> true__
% 9.56/9.46 f1(true__, successor(successor(add(X0, successor(X1)))), add(successor(successor(successor(add(X0, X1)))), n0)) -> true__
% 9.56/9.46 f1(true__, successor(successor(add(X0, successor(X1)))), successor(successor(successor(add(X0, X1))))) -> true__
% 9.56/9.46 f1(true__, successor(successor(add(add(X0, n0), n0))), successor(successor(X0))) -> true__
% 9.56/9.46 f1(true__, successor(successor(add(multiply(X0, X1), X0))), successor(successor(multiply(X0, successor(X1))))) -> true__
% 9.56/9.46 f1(true__, successor(successor(add(multiply(X0, n0), n0))), successor(successor(n0))) -> true__
% 9.56/9.46 f1(true__, successor(successor(add(n0, n0))), successor(n1)) -> true__
% 9.56/9.46 f1(true__, successor(successor(add(n1, n0))), successor(successor(successor(n0)))) -> true__
% 9.56/9.46 f1(true__, successor(successor(multiply(X0, n0))), add(successor(successor(n0)), n0)) -> true__
% 9.56/9.46 f1(true__, successor(successor(multiply(X0, n0))), successor(add(successor(n0), n0))) -> true__
% 9.56/9.46 f1(true__, successor(successor(multiply(X0, n0))), successor(n1)) -> true__
% 9.56/9.46 f1(true__, successor(successor(multiply(X0, n0))), successor(successor(n0))) -> true__
% 9.56/9.46 f1(true__, successor(successor(multiply(X0, successor(X1)))), add(successor(successor(add(multiply(X0, X1), X0))), n0)) -> true__
% 9.56/9.46 f1(true__, successor(successor(multiply(X0, successor(X1)))), successor(successor(add(multiply(X0, X1), X0)))) -> true__
% 9.56/9.46 f1(true__, successor(successor(n0)), add(add(successor(n1), n0), n0)) -> true__
% 9.56/9.46 f1(true__, successor(successor(n0)), add(successor(n1), n0)) -> true__
% 9.56/9.46 f1(true__, successor(successor(n0)), successor(add(n1, n0))) -> true__
% 9.56/9.46 f1(true__, successor(successor(n0)), successor(add(successor(multiply(X0, n0)), n0))) -> true__
% 9.56/9.46 f1(true__, successor(successor(n0)), successor(n1)) -> true__
% 9.56/9.46 f1(true__, successor(successor(n0)), successor(successor(multiply(X0, n0)))) -> true__
% 9.56/9.46 f1(true__, successor(successor(n1)), add(successor(successor(successor(n0))), n0)) -> true__
% 9.56/9.46 f1(true__, successor(successor(n1)), successor(add(successor(successor(n0)), n0))) -> true__
% 9.56/9.46 f1(true__, successor(successor(n1)), successor(successor(successor(n0)))) -> true__
% 9.56/9.46 f1(true__, successor(successor(successor(X0))), successor(successor(successor(add(X0, n0))))) -> true__
% 9.56/9.46 f1(true__, successor(successor(successor(add(X0, X1)))), successor(successor(add(X0, successor(X1))))) -> true__
% 9.56/9.46 f1(true__, successor(successor(successor(add(X0, n0)))), successor(successor(successor(X0)))) -> true__
% 9.56/9.46 f1(true__, successor(successor(successor(add(X0, successor(X1))))), successor(successor(successor(successor(add(X0, X1)))))) -> true__
% 9.56/9.46 f1(true__, successor(successor(successor(multiply(X0, n0)))), successor(successor(successor(n0)))) -> true__
% 9.56/9.46 f1(true__, successor(successor(successor(multiply(X0, successor(X1))))), successor(successor(successor(add(multiply(X0, X1), X0))))) -> true__
% 9.56/9.46 f1(true__, successor(successor(successor(n0))), add(successor(successor(n1)), n0)) -> true__
% 9.56/9.46 f1(true__, successor(successor(successor(n0))), successor(add(successor(n1), n0))) -> true__
% 9.56/9.46 f1(true__, successor(successor(successor(n0))), successor(successor(n1))) -> true__
% 9.56/9.46 f1(true__, successor(successor(successor(n0))), successor(successor(successor(multiply(X0, n0))))) -> true__
% 9.56/9.46 f1(true__, successor(successor(successor(n1))), successor(successor(successor(successor(n0))))) -> true__
% 9.56/9.46 f1(true__, successor(successor(successor(successor(n0)))), successor(successor(successor(n1)))) -> true__
% 9.56/9.46 f1(true__, successor(successor(successor(successor(n1)))), successor(successor(successor(successor(successor(n0)))))) -> true__
% 9.56/9.46 f2(equalish(A, B), A, B) -> true__
% 9.56/9.46 f2(f1(true__, Y0, Y1), Y0, Y1) -> true__
% 9.56/9.46 f2(true__, A, B) -> equalish(successor(A), successor(B))
% 9.56/9.46 f3(equalish(X, Y), Y, X) -> true__
% 9.56/9.46 f3(f1(true__, Y0, Y1), Y1, Y0) -> true__
% 9.56/9.46 f3(true__, Y, X) -> equalish(Y, X)
% 9.56/9.46 f4(f1(true__, Y2, Y0), Y2, add(Y0, n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, Y0), Y2, add(add(Y0, n0), n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, Y1), Y2, Y1) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(X0, successor(X1))), Y2, successor(add(X0, X1))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(X0, successor(n0))), Y2, successor(X0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(Y1, n0)), Y2, Y1) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(add(X0, successor(X1)), n0)), Y2, successor(add(X0, X1))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(add(Y1, n0), n0)), Y2, Y1) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(add(n1, n0), n0)), Y2, successor(n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(add(successor(n0), n0), n0)), Y2, n1) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(multiply(X0, X1), X0)), Y2, multiply(X0, successor(X1))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(multiply(X0, n0), n0)), Y2, n0) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(multiply(X0, successor(X1)), n0)), Y2, add(multiply(X0, X1), X0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(n0, n0)), Y2, multiply(X0, n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(n1, n0)), Y2, add(successor(n0), n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(n1, n0)), Y2, successor(n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(successor(add(X0, n0)), n0)), Y2, successor(X0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(successor(multiply(X0, n0)), n0)), Y2, successor(n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(successor(n0), n0)), Y2, n1) -> true__
% 9.56/9.46 f4(f1(true__, Y2, add(successor(n1), n0)), Y2, successor(successor(n0))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, multiply(X0, n0)), Y2, add(n0, n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, multiply(X0, n0)), Y2, multiply(X1, n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, multiply(X0, n0)), Y2, n0) -> true__
% 9.56/9.46 f4(f1(true__, Y2, multiply(X0, successor(X1))), Y2, add(multiply(X0, X1), X0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, multiply(n0, X0)), Y2, multiply(n0, successor(X0))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, multiply(n0, successor(X0))), Y2, multiply(n0, X0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, multiply(n0, successor(n0))), Y2, n0) -> true__
% 9.56/9.46 f4(f1(true__, Y2, multiply(successor(X0), successor(X1))), Y2, successor(add(multiply(successor(X0), X1), X0))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, n0), Y2, add(multiply(X0, n0), n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, n0), Y2, multiply(X0, n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, n1), Y2, add(successor(n0), n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, n1), Y2, successor(n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(X0)), Y2, add(X0, successor(n0))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(X0)), Y2, successor(add(X0, n0))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(add(X0, X1))), Y2, add(X0, successor(X1))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(add(X0, n0))), Y2, successor(X0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(add(X0, successor(X1)))), Y2, successor(successor(add(X0, X1)))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(add(add(X0, n0), n0))), Y2, successor(X0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(add(multiply(X0, X1), X0))), Y2, successor(multiply(X0, successor(X1)))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(add(multiply(X0, n0), n0))), Y2, successor(n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(add(n0, n0))), Y2, n1) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(add(n1, n0))), Y2, successor(successor(n0))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(multiply(X0, n0))), Y2, n1) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(multiply(X0, n0))), Y2, successor(n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(multiply(X0, successor(X1)))), Y2, successor(add(multiply(X0, X1), X0))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(n0)), Y2, add(n1, n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(n0)), Y2, n1) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(n0)), Y2, successor(multiply(X0, n0))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(n1)), Y2, add(successor(successor(n0)), n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(n1)), Y2, successor(successor(n0))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(successor(X0))), Y2, successor(successor(add(X0, n0)))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(successor(add(X0, X1)))), Y2, successor(add(X0, successor(X1)))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(successor(add(X0, n0)))), Y2, successor(successor(X0))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(successor(add(X0, successor(X1))))), Y2, successor(successor(successor(add(X0, X1))))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(successor(multiply(X0, n0)))), Y2, successor(successor(n0))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(successor(multiply(X0, successor(X1))))), Y2, successor(successor(add(multiply(X0, X1), X0)))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(successor(n0))), Y2, add(successor(n1), n0)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(successor(n0))), Y2, successor(n1)) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(successor(n0))), Y2, successor(successor(multiply(X0, n0)))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(successor(n1))), Y2, successor(successor(successor(n0)))) -> true__
% 9.56/9.46 f4(f1(true__, Y2, successor(successor(successor(n0)))), Y2, successor(successor(n1))) -> true__
% 9.56/9.46 f4(true__, X, Z) -> equalish(X, Z)
% 9.56/9.46 f5(equalish(Y, Z), X, Y, Z) -> true__
% 9.56/9.46 f5(f1(true__, Y0, Y1), Y2, Y0, Y1) -> true__
% 9.56/9.46 f5(true__, X, Y, Z) -> f4(equalish(X, Y), X, Z)
% 9.56/9.46 f6(equalish(add(a, successor(n0)), successor(a))) -> true__
% 9.56/9.46 f6(f1(true__, add(a, successor(n0)), successor(a))) -> true__
% 9.56/9.46 f6(true__) -> false__
% 9.56/9.46 f7(equalish(successor(A), n0)) -> true__
% 9.56/9.46 f7(f1(true__, successor(Y0), n0)) -> true__
% 9.56/9.46 f7(true__) -> false__
% 9.56/9.46 false__ -> true__
% 9.56/9.46 with the LPO induced by
% 9.56/9.46 f7 > a > f6 > n1 > multiply > f5 > f4 > f3 > f2 > equalish > f1 > successor > n0 > add > false__ > true__
% 9.56/9.46
% 9.56/9.46 % SZS output end Proof
% 9.56/9.46
%------------------------------------------------------------------------------