%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP560-1 : TPTP v8.1.0. Bugfixed v2.7.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n026.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 10:56:16 EDT 2022 % Result : Unsatisfiable 62.93s 63.06s % Output : Proof 62.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : GRP560-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 0.11/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n026.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 : Tue Jun 14 00:03:21 EDT 2022 % 0.12/0.33 % CPUTime : % 62.93/63.06 % SZS status Unsatisfiable % 62.93/63.06 % SZS output start Proof % 62.93/63.06 The input problem is unsatisfiable because % 62.93/63.06 % 62.93/63.06 [1] the following set of Horn clauses is unsatisfiable: % 62.93/63.06 % 62.93/63.06 divide(A, inverse(divide(divide(B, C), divide(A, C)))) = B % 62.93/63.06 multiply(A, B) = divide(A, inverse(B)) % 62.93/63.06 multiply(a, b) = multiply(b, a) ==> \bottom % 62.93/63.06 % 62.93/63.06 This holds because % 62.93/63.06 % 62.93/63.06 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 62.93/63.06 % 62.93/63.06 E: % 62.93/63.06 divide(A, inverse(divide(divide(B, C), divide(A, C)))) = B % 62.93/63.06 f1(multiply(a, b)) = true__ % 62.93/63.06 f1(multiply(b, a)) = false__ % 62.93/63.06 multiply(A, B) = divide(A, inverse(B)) % 62.93/63.06 G: % 62.93/63.06 true__ = false__ % 62.93/63.06 % 62.93/63.06 This holds because % 62.93/63.06 % 62.93/63.06 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 62.93/63.06 % 62.93/63.06 divide(X1, X1) = divide(Y1, Y1) % 62.93/63.06 divide(X1, X1) = divide(inverse(Y1), inverse(Y1)) % 62.93/63.06 divide(X1, Y0) = divide(divide(Y2, Y2), divide(Y0, X1)) % 62.93/63.06 divide(X1, Y2) = divide(divide(Y0, Y2), divide(divide(false__, false__), divide(X1, Y0))) % 62.93/63.06 divide(X1, divide(Y0, Y2)) = divide(Y2, divide(divide(false__, false__), divide(X1, Y0))) % 62.93/63.06 divide(X1, divide(divide(false__, false__), Y1)) = divide(Y1, divide(divide(X0, X0), X1)) % 62.93/63.06 divide(Y0, X0) = divide(Y2, divide(divide(X0, divide(divide(false__, false__), Y2)), Y0)) % 62.93/63.06 divide(Y0, X0) = divide(divide(divide(false__, false__), X1), divide(divide(X0, X1), Y0)) % 62.93/63.06 divide(Y0, X1) = divide(Y2, divide(divide(Y2, divide(divide(false__, false__), X1)), Y0)) % 62.93/63.06 divide(Y0, X1) = divide(divide(Y1, X1), divide(Y1, Y0)) % 62.93/63.06 divide(Y0, X1) = divide(divide(divide(false__, false__), X1), divide(divide(false__, false__), Y0)) % 62.93/63.06 divide(Y0, X1) = divide(divide(divide(false__, false__), divide(X1, Y1)), divide(Y1, Y0)) % 62.93/63.06 divide(Y0, X1) = divide(divide(false__, false__), divide(divide(X1, X2), divide(Y0, X2))) % 62.93/63.06 divide(Y0, X2) = divide(X1, divide(X2, divide(Y0, X1))) % 62.93/63.06 divide(Y0, Y2) = divide(inverse(Y2), inverse(Y0)) % 62.93/63.06 divide(Y0, divide(X1, divide(divide(false__, false__), Y0))) = divide(divide(X0, X0), X1) % 62.93/63.06 divide(Y0, divide(X2, X1)) = divide(X1, divide(X2, Y0)) % 62.93/63.06 divide(Y0, divide(divide(false__, divide(divide(false__, false__), X2)), divide(false__, divide(divide(false__, false__), divide(X2, Y0))))) = divide(X0, X0) % 62.93/63.06 divide(Y0, divide(divide(false__, divide(divide(false__, false__), false__)), divide(false__, divide(divide(false__, false__), divide(X0, Y0))))) = divide(X0, false__) % 62.93/63.06 divide(Y0, divide(divide(false__, false__), X0)) = divide(X0, divide(divide(false__, false__), Y0)) % 62.93/63.06 divide(Y0, divide(divide(false__, false__), false__)) = divide(false__, divide(divide(false__, false__), Y0)) % 62.93/63.06 divide(Y0, false__) = divide(Y2, divide(divide(false__, divide(divide(false__, false__), Y2)), Y0)) % 62.93/63.06 divide(Y0, false__) = divide(divide(Y1, false__), divide(Y1, Y0)) % 62.93/63.06 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(Y1))))) = inverse(divide(X1, X1)) % 62.93/63.06 divide(divide(X1, X1), divide(Y0, Y1)) = divide(divide(divide(false__, false__), Y0), divide(divide(false__, false__), Y1)) % 62.93/63.06 divide(divide(X1, X2), divide(divide(false__, false__), divide(X2, X1))) = divide(X0, X0) % 62.93/63.06 divide(divide(Y0, X1), Y0) = divide(divide(X0, X0), X1) % 62.93/63.06 divide(divide(Y0, Y1), X1) = divide(divide(Y0, X1), Y1) % 62.93/63.06 divide(divide(Y0, Y1), X1) = divide(divide(divide(false__, false__), divide(X1, Y0)), Y1) % 62.93/63.06 divide(divide(Y0, false__), X1) = divide(divide(Y0, X1), false__) % 62.93/63.06 divide(divide(divide(X0, X0), false__), divide(divide(false__, false__), Y1)) = divide(Y1, false__) % 62.93/63.06 divide(divide(divide(X1, X1), Y0), divide(divide(false__, false__), Y1)) = divide(Y1, Y0) % 62.93/63.06 divide(divide(divide(false__, false__), Y0), X1) = divide(divide(divide(X0, X0), X1), Y0) % 62.93/63.06 divide(divide(divide(false__, false__), Y0), divide(divide(X1, X1), Y1)) = divide(Y1, Y0) % 62.93/63.06 divide(divide(divide(false__, false__), false__), Y1) = divide(divide(false__, false__), divide(false__, divide(divide(X0, X0), Y1))) % 62.93/63.06 divide(divide(divide(false__, false__), false__), divide(divide(X1, X1), false__)) = divide(Y0, Y0) % 62.93/63.06 divide(divide(false__, false__), Y1) = divide(Y2, divide(Y1, divide(divide(X0, X0), Y2))) % 62.93/63.06 divide(divide(false__, false__), false__) = divide(Y2, divide(false__, divide(divide(X0, X0), Y2))) % 62.93/63.06 divide(false__, false__) = divide(Y1, Y1) % 62.93/63.06 divide(inverse(X1), inverse(X1)) = divide(inverse(Y1), inverse(Y1)) % 62.93/63.06 divide(inverse(Y0), inverse(Y0)) = inverse(divide(X1, X1)) % 62.93/63.06 divide(inverse(false__), inverse(false__)) = divide(Y1, Y1) % 62.93/63.06 inverse(X1) = divide(divide(Y0, Y0), X1) % 62.93/63.06 inverse(divide(Y0, Y0)) = divide(X1, X1) % 62.93/63.06 inverse(divide(Y0, Y0)) = inverse(divide(X1, X1)) % 62.93/63.06 inverse(false__) = divide(divide(Y0, Y0), false__) % 62.93/63.06 inverse(inverse(divide(Y0, Y0))) = divide(X1, X1) % 62.93/63.06 divide(A, inverse(divide(divide(B, C), divide(A, C)))) -> B % 62.93/63.06 divide(Y0, divide(X1, X1)) -> Y0 % 62.93/63.06 divide(Y0, divide(X1, divide(Y1, divide(Y0, X1)))) -> Y1 % 62.93/63.06 divide(Y0, divide(Y0, Y2)) -> Y2 % 62.93/63.06 divide(Y0, divide(Y0, false__)) -> false__ % 62.93/63.06 divide(Y0, divide(divide(X1, X1), divide(Y1, Y0))) -> Y1 % 62.93/63.06 divide(Y0, divide(divide(Y0, X1), divide(Y1, X1))) -> Y1 % 62.93/63.06 divide(Y0, divide(divide(Y0, divide(Y1, X1)), X1)) -> Y1 % 62.93/63.06 divide(Y0, divide(divide(Y0, false__), divide(Y1, false__))) -> Y1 % 62.93/63.06 divide(Y0, divide(divide(divide(X0, X0), false__), divide(divide(false__, false__), Y0))) -> false__ % 62.93/63.06 divide(Y0, divide(divide(divide(X1, X1), Y1), divide(divide(false__, false__), Y0))) -> Y1 % 62.93/63.06 divide(Y0, divide(divide(divide(false__, false__), Y1), divide(divide(X1, X1), Y0))) -> Y1 % 62.93/63.06 divide(Y0, divide(divide(false__, divide(divide(false__, false__), X1)), divide(false__, divide(divide(false__, false__), divide(Y1, divide(Y0, X1)))))) -> Y1 % 62.93/63.06 divide(Y0, divide(divide(false__, divide(divide(false__, false__), false__)), divide(false__, divide(divide(divide(false__, false__), Y1), divide(false__, Y0))))) -> Y1 % 62.93/63.06 divide(Y0, divide(divide(false__, false__), divide(Y1, divide(Y0, divide(divide(false__, false__), X1))))) -> divide(Y1, X1) % 62.93/63.06 divide(Y0, divide(divide(false__, false__), divide(divide(X0, Y0), X1))) -> divide(X0, X1) % 62.93/63.06 divide(Y0, divide(divide(false__, false__), divide(divide(X2, Y0), divide(X2, Y1)))) -> Y1 % 62.93/63.06 divide(Y0, divide(divide(false__, false__), divide(divide(divide(X1, X1), Y0), divide(divide(false__, false__), Y1)))) -> Y1 % 62.93/63.06 divide(Y0, divide(divide(false__, false__), divide(divide(divide(false__, false__), Y0), divide(divide(X1, X1), Y1)))) -> Y1 % 62.93/63.06 divide(Y0, divide(inverse(Y2), inverse(Y0))) -> Y2 % 62.93/63.06 divide(Y0, inverse(divide(X1, divide(Y0, inverse(divide(divide(X1, X2), divide(Y1, X2))))))) -> Y1 % 62.93/63.06 divide(Y0, inverse(divide(Y1, Y0))) -> Y1 % 62.93/63.06 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(X1, divide(Y3, inverse(divide(divide(X1, X2), divide(Y1, X2)))))))))) -> Y3 % 62.93/63.06 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(X3, divide(Y3, inverse(divide(X1, divide(Y1, inverse(divide(divide(X1, X2), divide(X3, X2))))))))))))) -> Y3 % 62.93/63.06 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(Y1, Y3)))))) -> Y3 % 62.93/63.06 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(Y1, inverse(divide(divide(inverse(divide(X1, X1)), Y3), divide(Y4, Y3))))))))) -> Y4 % 62.93/63.06 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(Y2, divide(Y3, inverse(divide(Y2, Y1))))))))) -> Y3 % 62.93/63.06 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(divide(Y1, inverse(divide(X1, divide(Y3, inverse(divide(divide(X1, X2), divide(X3, X2))))))), X3)))))) -> Y3 % 62.93/63.06 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(divide(Y1, inverse(divide(divide(X1, X2), divide(Y3, X2)))), X1)))))) -> Y3 % 62.93/63.06 divide(Y0, inverse(divide(Y1, inverse(divide(divide(inverse(divide(X1, X1)), Y3), divide(Y0, Y3)))))) -> Y1 % 62.93/63.06 divide(Y0, inverse(divide(divide(Y1, inverse(divide(X1, divide(Y0, inverse(divide(divide(X1, X2), divide(X3, X2))))))), X3))) -> Y1 % 62.93/63.06 divide(Y0, inverse(divide(divide(Y1, inverse(divide(Y2, Y0))), Y2))) -> Y1 % 62.93/63.06 divide(Y0, inverse(divide(divide(Y1, inverse(divide(divide(X1, X2), divide(Y0, X2)))), X1))) -> Y1 % 62.93/63.06 divide(Y0, inverse(divide(divide(Y1, inverse(divide(divide(Y2, inverse(divide(divide(X1, X2), divide(Y0, X2)))), X1))), Y2))) -> Y1 % 62.93/63.06 divide(Y0, inverse(inverse(divide(X1, X1)))) -> Y0 % 62.93/63.06 divide(Y0, inverse(inverse(inverse(divide(X1, X1))))) -> Y0 % 62.93/63.06 divide(Y0, inverse(inverse(inverse(inverse(divide(X1, X1)))))) -> Y0 % 62.93/63.06 divide(Y1, divide(divide(false__, false__), divide(divide(divide(false__, false__), Y1), divide(divide(false__, false__), Y0)))) -> Y0 % 62.93/63.06 divide(Y2, divide(Y1, divide(X0, divide(divide(false__, false__), divide(Y1, Y2))))) -> X0 % 62.93/63.06 divide(Y2, divide(Y1, divide(divide(X0, divide(divide(false__, false__), Y1)), Y2))) -> X0 % 62.93/63.06 divide(Y2, divide(Y1, divide(divide(Y1, Y2), divide(divide(false__, false__), X1)))) -> X1 % 62.93/63.06 divide(Y2, divide(divide(divide(false__, false__), X1), divide(divide(X0, X1), Y2))) -> X0 % 62.93/63.06 divide(Y3, inverse(divide(Y1, Y1))) -> Y3 % 62.93/63.06 divide(divide(X1, X1), divide(divide(Y0, Y0), Y1)) -> Y1 % 62.93/63.06 divide(divide(X1, X1), inverse(Y1)) -> Y1 % 62.93/63.06 divide(divide(X1, X2), divide(divide(false__, false__), divide(X2, divide(X1, Y1)))) -> Y1 % 62.93/63.06 divide(divide(X1, inverse(Y1)), X1) -> Y1 % 62.93/63.06 divide(divide(X2, Y0), divide(divide(divide(false__, false__), Y1), divide(Y0, X2))) -> Y1 % 62.93/63.06 divide(divide(X2, Y1), divide(divide(divide(false__, false__), Y1), divide(Y0, X2))) -> Y0 % 62.93/63.06 divide(divide(X2, divide(Y1, divide(Y0, X2))), divide(divide(false__, false__), Y1)) -> Y0 % 62.93/63.06 divide(divide(Y0, Y0), divide(divide(X0, X0), false__)) -> false__ % 62.93/63.06 divide(divide(Y0, Y1), divide(divide(X1, X1), Y1)) -> Y0 % 62.93/63.06 divide(divide(Y0, divide(X1, X2)), X2) -> divide(Y0, X1) % 62.93/63.06 divide(divide(Y0, divide(divide(X0, X0), false__)), false__) -> Y0 % 62.93/63.06 divide(divide(Y0, divide(divide(X1, X1), Y1)), Y1) -> Y0 % 62.93/63.06 divide(divide(Y0, false__), divide(divide(X1, X1), false__)) -> Y0 % 62.93/63.06 divide(divide(Y1, X1), inverse(X1)) -> Y1 % 62.93/63.06 divide(divide(Y1, false__), divide(Y1, divide(false__, divide(divide(false__, false__), X1)))) -> X1 % 62.93/63.06 divide(divide(Y1, false__), inverse(false__)) -> Y1 % 62.93/63.06 divide(divide(Y1, inverse(X1)), X1) -> Y1 % 62.93/63.06 divide(divide(Y2, X1), divide(Y1, X1)) -> divide(Y2, Y1) % 62.93/63.06 divide(divide(Y2, Y1), divide(Y2, divide(X0, divide(divide(false__, false__), Y1)))) -> X0 % 62.93/63.06 divide(divide(Y2, Y1), divide(Y2, divide(Y1, divide(divide(false__, false__), X1)))) -> X1 % 62.93/63.06 divide(divide(Y2, Y2), divide(Y1, divide(X0, divide(divide(false__, false__), Y1)))) -> X0 % 62.93/63.06 divide(divide(Y2, divide(divide(false__, false__), X1)), divide(Y2, divide(X0, X1))) -> X0 % 62.93/63.06 divide(divide(Y2, divide(divide(false__, false__), false__)), divide(Y2, divide(X0, false__))) -> X0 % 62.93/63.06 divide(divide(Y2, false__), divide(Y1, false__)) -> divide(Y2, Y1) % 62.93/63.06 divide(divide(divide(X0, X0), X1), divide(divide(divide(false__, false__), Y1), X1)) -> Y1 % 62.93/63.06 divide(divide(divide(X0, X0), false__), Y1) -> divide(divide(false__, false__), divide(false__, divide(divide(false__, false__), Y1))) % 62.93/63.06 divide(divide(divide(divide(false__, false__), Y0), divide(divide(false__, false__), Y1)), divide(divide(X1, X1), Y0)) -> Y1 % 62.93/63.06 divide(divide(divide(false__, false__), X0), divide(X1, X0)) -> divide(divide(false__, false__), X1) % 62.93/63.06 divide(divide(divide(false__, false__), X1), divide(divide(divide(X0, X0), X1), Y1)) -> Y1 % 62.93/63.06 divide(divide(divide(false__, false__), Y0), divide(divide(X0, X0), false__)) -> divide(false__, Y0) % 62.93/63.06 divide(divide(divide(false__, false__), Y1), divide(divide(false__, false__), divide(Y1, divide(divide(false__, false__), Y0)))) -> Y0 % 62.93/63.06 divide(divide(divide(false__, false__), divide(X1, Y2)), divide(Y1, X1)) -> divide(Y2, Y1) % 62.93/63.06 divide(divide(divide(false__, false__), false__), divide(divide(false__, false__), divide(false__, divide(divide(false__, false__), Y1)))) -> Y1 % 62.93/63.06 divide(divide(false__, divide(divide(X1, X1), Y0)), Y0) -> false__ % 62.93/63.06 divide(divide(false__, divide(divide(false__, false__), X1)), divide(false__, divide(divide(false__, false__), divide(X1, Y1)))) -> Y1 % 62.93/63.06 divide(divide(false__, divide(divide(false__, false__), Y0)), divide(false__, divide(Y1, Y0))) -> Y1 % 62.93/63.06 divide(divide(false__, divide(divide(false__, false__), Y0)), divide(false__, divide(divide(divide(X1, X1), Y0), divide(divide(false__, false__), Y1)))) -> Y1 % 62.93/63.06 divide(divide(false__, divide(divide(false__, false__), Y0)), divide(false__, divide(divide(divide(false__, false__), Y0), divide(divide(X1, X1), Y1)))) -> Y1 % 62.93/63.06 divide(divide(false__, divide(divide(false__, false__), Y1)), divide(false__, divide(divide(false__, false__), divide(X0, divide(divide(false__, false__), Y1))))) -> divide(divide(false__, false__), X0) % 62.93/63.06 divide(divide(false__, divide(divide(false__, false__), Y1)), divide(false__, divide(divide(false__, false__), divide(Y1, divide(divide(false__, false__), X1))))) -> divide(divide(false__, false__), X1) % 62.93/63.06 divide(divide(false__, divide(divide(false__, false__), false__)), divide(false__, divide(Y2, false__))) -> Y2 % 62.93/63.06 divide(divide(false__, divide(divide(false__, false__), false__)), divide(false__, divide(divide(divide(X0, X0), false__), divide(divide(false__, false__), Y1)))) -> Y1 % 62.93/63.06 divide(divide(false__, false__), divide(X1, divide(Y1, divide(divide(false__, false__), X1)))) -> Y1 % 62.93/63.06 divide(divide(false__, false__), divide(X1, divide(false__, divide(divide(false__, false__), X1)))) -> false__ % 62.93/63.06 divide(divide(false__, false__), divide(Y0, divide(false__, divide(divide(X1, X1), Y0)))) -> false__ % 62.93/63.06 divide(divide(false__, false__), divide(Y1, divide(Y0, divide(divide(X1, X1), Y1)))) -> Y0 % 62.93/63.06 divide(divide(false__, false__), divide(Y1, divide(divide(X2, divide(divide(false__, false__), Y1)), divide(X2, Y0)))) -> Y0 % 62.93/63.06 divide(divide(false__, false__), divide(Y1, divide(divide(Y1, divide(divide(false__, false__), X1)), Y2))) -> divide(X1, Y2) % 62.93/63.06 divide(divide(false__, false__), divide(divide(X1, X1), Y1)) -> Y1 % 62.93/63.06 divide(divide(false__, false__), divide(false__, divide(Y0, divide(divide(X0, X0), false__)))) -> Y0 % 62.93/63.06 divide(divide(false__, inverse(X1)), X1) -> false__ % 62.93/63.06 divide(divide(inverse(Y1), inverse(Y2)), inverse(Y1)) -> Y2 % 62.93/63.06 divide(false__, divide(divide(false__, X1), divide(divide(false__, false__), divide(X1, Y1)))) -> Y1 % 62.93/63.06 divide(false__, divide(divide(false__, Y0), divide(divide(divide(X1, X1), Y0), divide(divide(false__, false__), Y1)))) -> Y1 % 62.93/63.06 divide(false__, divide(divide(false__, Y1), divide(divide(false__, false__), divide(X0, divide(divide(false__, false__), Y1))))) -> divide(divide(false__, false__), X0) % 62.93/63.06 divide(false__, divide(divide(false__, Y1), divide(divide(false__, false__), divide(Y1, divide(divide(false__, false__), X1))))) -> divide(divide(false__, false__), X1) % 62.93/63.06 divide(false__, divide(divide(false__, Y1), divide(false__, divide(divide(false__, divide(divide(false__, false__), false__)), divide(divide(false__, false__), Y1))))) -> divide(divide(false__, false__), false__) % 62.93/63.06 divide(false__, divide(divide(false__, divide(divide(false__, false__), Y1)), divide(Y1, divide(divide(false__, false__), Y0)))) -> Y0 % 62.93/63.06 divide(false__, divide(divide(false__, false__), divide(divide(divide(X0, X0), false__), divide(divide(false__, false__), Y1)))) -> Y1 % 62.93/63.06 divide(inverse(Y1), inverse(Y1)) -> divide(false__, false__) % 62.93/63.06 divide(inverse(divide(X1, X1)), inverse(Y1)) -> Y1 % 62.93/63.06 divide(inverse(divide(X1, Y1)), inverse(X1)) -> Y1 % 62.93/63.06 divide(inverse(divide(divide(X1, X2), divide(Y1, X2))), inverse(X1)) -> Y1 % 62.93/63.06 divide(inverse(inverse(divide(X1, X1))), inverse(Y1)) -> Y1 % 62.93/63.06 divide(inverse(inverse(inverse(divide(X1, X1)))), inverse(Y1)) -> Y1 % 62.93/63.06 f1(divide(X2, divide(divide(divide(false__, false__), b), divide(a, X2)))) -> true__ % 62.93/63.06 f1(divide(a, divide(divide(X1, X1), b))) -> true__ % 62.93/63.06 f1(divide(a, inverse(b))) -> true__ % 62.93/63.06 f1(divide(b, divide(divide(X1, X1), a))) -> false__ % 62.93/63.06 f1(divide(b, inverse(a))) -> false__ % 62.93/63.06 f1(divide(divide(X2, X2), divide(divide(divide(false__, false__), b), a))) -> true__ % 62.93/63.06 f1(divide(divide(X2, divide(divide(false__, false__), b)), divide(X2, a))) -> true__ % 62.93/63.06 f1(divide(divide(Y0, Y0), divide(divide(divide(X1, X1), b), a))) -> true__ % 62.93/63.06 f1(multiply(a, b)) -> true__ % 62.93/63.06 f1(multiply(b, a)) -> false__ % 62.93/63.06 inverse(divide(X1, Y0)) -> divide(inverse(X1), inverse(Y0)) % 62.93/63.06 inverse(divide(divide(X1, X1), Y1)) -> Y1 % 62.93/63.06 multiply(A, B) -> divide(A, inverse(B)) % 62.93/63.06 true__ -> false__ % 62.93/63.06 with the LPO induced by % 62.93/63.06 a > b > f1 > multiply > inverse > divide > true__ > false__ % 62.93/63.06 % 62.93/63.06 % SZS output end Proof % 62.93/63.06 %------------------------------------------------------------------------------