%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP600-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 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 10:56:33 EDT 2022 % Result : Unsatisfiable 10.12s 10.26s % Output : Proof 10.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GRP600-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 0.07/0.14 % Command : moca.sh %s % 0.13/0.34 % Computer : n028.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Mon Jun 13 10:57:22 EDT 2022 % 0.13/0.35 % CPUTime : % 10.12/10.26 % SZS status Unsatisfiable % 10.12/10.26 % SZS output start Proof % 10.12/10.26 The input problem is unsatisfiable because % 10.12/10.26 % 10.12/10.26 [1] the following set of Horn clauses is unsatisfiable: % 10.12/10.26 % 10.12/10.26 double_divide(double_divide(A, B), inverse(double_divide(A, inverse(double_divide(inverse(C), B))))) = C % 10.12/10.26 multiply(A, B) = inverse(double_divide(B, A)) % 10.12/10.26 multiply(a, b) = multiply(b, a) ==> \bottom % 10.12/10.26 % 10.12/10.26 This holds because % 10.12/10.26 % 10.12/10.26 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 10.12/10.26 % 10.12/10.26 E: % 10.12/10.26 double_divide(double_divide(A, B), inverse(double_divide(A, inverse(double_divide(inverse(C), B))))) = C % 10.12/10.26 f1(multiply(a, b)) = true__ % 10.12/10.26 f1(multiply(b, a)) = false__ % 10.12/10.26 multiply(A, B) = inverse(double_divide(B, A)) % 10.12/10.26 G: % 10.12/10.26 true__ = false__ % 10.12/10.26 % 10.12/10.26 This holds because % 10.12/10.26 % 10.12/10.26 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 10.12/10.26 % 10.12/10.26 double_divide(X0, inverse(double_divide(X1, inverse(X1)))) = inverse(X0) % 10.12/10.26 double_divide(X1, inverse(X1)) = double_divide(double_divide(Y1, inverse(Y1)), double_divide(false__, inverse(false__))) % 10.12/10.26 double_divide(X1, inverse(X1)) = double_divide(double_divide(inverse(Y1), Y1), double_divide(false__, inverse(false__))) % 10.12/10.26 double_divide(X1, inverse(Y2)) = double_divide(inverse(Y2), inverse(inverse(X1))) % 10.12/10.26 double_divide(Y0, X0) = double_divide(X0, Y0) % 10.12/10.26 double_divide(Y0, double_divide(X1, inverse(X1))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(Y0, double_divide(X1, inverse(X1)))) = double_divide(Y1, inverse(Y1)) % 10.12/10.26 double_divide(Y0, double_divide(Y0, double_divide(X1, inverse(X1)))) = double_divide(inverse(Y1), Y1) % 10.12/10.26 double_divide(Y0, double_divide(Y0, double_divide(false__, inverse(false__)))) = double_divide(Y1, inverse(Y1)) % 10.12/10.26 double_divide(Y0, double_divide(Y0, double_divide(inverse(X1), X1))) = double_divide(Y1, inverse(Y1)) % 10.12/10.26 double_divide(Y0, double_divide(Y0, double_divide(inverse(X1), X1))) = double_divide(inverse(Y1), Y1) % 10.12/10.26 double_divide(Y0, double_divide(Y1, double_divide(Y1, double_divide(X1, inverse(X1))))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(Y1, double_divide(Y1, double_divide(inverse(X1), X1)))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(Y1, double_divide(double_divide(X1, inverse(X1)), Y1))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(Y1, double_divide(double_divide(inverse(X1), X1), Y1))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(double_divide(X0, inverse(X0)), double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__))))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(double_divide(X0, inverse(X0)), double_divide(false__, inverse(false__)))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(double_divide(X1, inverse(X1)), Y0)) = double_divide(Y1, inverse(Y1)) % 10.12/10.26 double_divide(Y0, double_divide(double_divide(X1, inverse(X1)), Y0)) = double_divide(inverse(Y1), Y1) % 10.12/10.26 double_divide(Y0, double_divide(double_divide(Y1, double_divide(X1, inverse(X1))), Y1)) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(double_divide(Y1, double_divide(inverse(X1), X1)), Y1)) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(double_divide(false__, inverse(false__)), double_divide(X0, inverse(X0)))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(double_divide(false__, inverse(false__)), double_divide(inverse(X0), X0))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(double_divide(inverse(X0), X0), double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__))))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(double_divide(inverse(X0), X0), double_divide(false__, inverse(false__)))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(double_divide(inverse(X1), X1), Y0)) = double_divide(Y1, inverse(Y1)) % 10.12/10.26 double_divide(Y0, double_divide(double_divide(inverse(X1), X1), Y0)) = double_divide(inverse(Y1), Y1) % 10.12/10.26 double_divide(Y0, double_divide(double_divide(inverse(Y0), X0), double_divide(false__, inverse(false__)))) = inverse(X0) % 10.12/10.26 double_divide(Y0, double_divide(false__, double_divide(double_divide(X1, inverse(X1)), false__))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(false__, double_divide(double_divide(inverse(X1), X1), false__))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(false__, double_divide(false__, double_divide(X1, inverse(X1))))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(false__, double_divide(false__, double_divide(inverse(X1), X1)))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(false__, inverse(false__))) = inverse(Y0) % 10.12/10.26 double_divide(Y0, double_divide(inverse(X1), X1)) = inverse(Y0) % 10.12/10.26 double_divide(Y0, inverse(double_divide(inverse(X0), X0))) = inverse(Y0) % 10.12/10.26 double_divide(Y1, inverse(Y1)) = double_divide(X0, inverse(X0)) % 10.12/10.26 double_divide(double_divide(X1, inverse(X1)), Y0) = double_divide(Y0, double_divide(Y1, inverse(Y1))) % 10.12/10.26 double_divide(double_divide(X1, inverse(X1)), Y0) = double_divide(Y0, double_divide(false__, inverse(false__))) % 10.12/10.26 double_divide(double_divide(X1, inverse(X1)), Y0) = double_divide(Y0, double_divide(inverse(Y1), Y1)) % 10.12/10.26 double_divide(double_divide(Y0, double_divide(X1, inverse(X1))), Y0) = double_divide(Y1, inverse(Y1)) % 10.12/10.26 double_divide(double_divide(Y0, double_divide(X1, inverse(X1))), Y0) = double_divide(inverse(Y1), Y1) % 10.12/10.26 double_divide(double_divide(Y0, double_divide(Y0, double_divide(X1, inverse(X1)))), Y1) = inverse(Y1) % 10.12/10.26 double_divide(double_divide(Y0, double_divide(Y0, double_divide(inverse(X1), X1))), Y1) = inverse(Y1) % 10.12/10.26 double_divide(double_divide(Y0, double_divide(double_divide(X1, inverse(X1)), Y0)), Y1) = inverse(Y1) % 10.12/10.26 double_divide(double_divide(Y0, double_divide(double_divide(inverse(X1), X1), Y0)), Y1) = inverse(Y1) % 10.12/10.26 double_divide(double_divide(Y0, double_divide(false__, inverse(false__))), Y0) = double_divide(Y1, inverse(Y1)) % 10.12/10.26 double_divide(double_divide(Y0, double_divide(inverse(X1), X1)), Y0) = double_divide(Y1, inverse(Y1)) % 10.12/10.26 double_divide(double_divide(Y0, double_divide(inverse(X1), X1)), Y0) = double_divide(inverse(Y1), Y1) % 10.12/10.26 double_divide(double_divide(Y0, inverse(Y0)), X0) = inverse(X0) % 10.12/10.26 double_divide(double_divide(double_divide(Y0, double_divide(X1, inverse(X1))), Y0), Y1) = inverse(Y1) % 10.12/10.26 double_divide(double_divide(double_divide(Y0, double_divide(inverse(X1), X1)), Y0), Y1) = inverse(Y1) % 10.12/10.26 double_divide(double_divide(double_divide(Y0, inverse(Y0)), double_divide(false__, inverse(false__))), X0) = inverse(X0) % 10.12/10.26 double_divide(double_divide(inverse(X0), X0), Y1) = inverse(Y1) % 10.12/10.26 double_divide(double_divide(inverse(X1), X1), Y0) = double_divide(Y0, double_divide(Y1, inverse(Y1))) % 10.12/10.26 double_divide(double_divide(inverse(X1), X1), Y0) = double_divide(Y0, double_divide(false__, inverse(false__))) % 10.12/10.26 double_divide(double_divide(inverse(X1), X1), Y0) = double_divide(Y0, double_divide(inverse(Y1), Y1)) % 10.12/10.26 double_divide(inverse(X0), X0) = double_divide(Y1, inverse(Y1)) % 10.12/10.26 double_divide(inverse(X0), X0) = double_divide(inverse(Y1), Y1) % 10.12/10.26 double_divide(inverse(X0), double_divide(double_divide(Y1, X0), double_divide(false__, inverse(false__)))) = inverse(Y1) % 10.12/10.26 double_divide(inverse(Y0), double_divide(double_divide(Y0, X0), double_divide(false__, inverse(false__)))) = inverse(X0) % 10.12/10.26 double_divide(inverse(Y0), inverse(X1)) = double_divide(inverse(X1), inverse(Y0)) % 10.12/10.26 double_divide(X0, inverse(double_divide(double_divide(double_divide(inverse(X0), X1), inverse(double_divide(inverse(X2), X1))), inverse(double_divide(inverse(Y2), inverse(X2)))))) -> Y2 % 10.12/10.26 double_divide(X0, inverse(double_divide(inverse(X0), inverse(Y2)))) -> Y2 % 10.12/10.26 double_divide(X1, inverse(double_divide(X0, inverse(X1)))) -> inverse(X0) % 10.12/10.26 double_divide(X1, inverse(double_divide(Y0, inverse(double_divide(inverse(Y2), inverse(double_divide(inverse(X1), inverse(Y0)))))))) -> Y2 % 10.12/10.26 double_divide(X1, inverse(double_divide(double_divide(inverse(X0), inverse(inverse(X1))), inverse(double_divide(inverse(Y2), inverse(X0)))))) -> Y2 % 10.12/10.26 double_divide(X2, inverse(double_divide(double_divide(X0, X1), inverse(double_divide(inverse(Y2), inverse(double_divide(X0, inverse(double_divide(inverse(X2), X1))))))))) -> Y2 % 10.12/10.26 double_divide(Y0, inverse(double_divide(X0, inverse(double_divide(inverse(Y3), inverse(double_divide(double_divide(double_divide(inverse(X0), X1), inverse(double_divide(inverse(X2), X1))), inverse(double_divide(inverse(Y0), inverse(X2)))))))))) -> Y3 % 10.12/10.26 double_divide(Y0, inverse(double_divide(X2, inverse(double_divide(inverse(Y3), inverse(double_divide(double_divide(X0, X1), inverse(double_divide(inverse(Y0), inverse(double_divide(X0, inverse(double_divide(inverse(X2), X1))))))))))))) -> Y3 % 10.12/10.26 double_divide(Y0, inverse(double_divide(X2, inverse(double_divide(inverse(Y3), inverse(double_divide(double_divide(double_divide(double_divide(inverse(X0), X1), inverse(double_divide(inverse(double_divide(inverse(X2), X3)), X1))), X3), inverse(double_divide(inverse(Y0), inverse(X0)))))))))) -> Y3 % 10.12/10.26 double_divide(Y0, inverse(double_divide(X3, inverse(double_divide(inverse(Y3), inverse(double_divide(Y1, inverse(double_divide(inverse(Y0), inverse(double_divide(double_divide(X1, X2), inverse(double_divide(inverse(X3), inverse(double_divide(X1, inverse(double_divide(inverse(Y1), X2))))))))))))))))) -> Y3 % 10.12/10.26 double_divide(Y0, inverse(double_divide(double_divide(Y1, inverse(double_divide(double_divide(X1, X2), inverse(double_divide(inverse(X3), inverse(double_divide(X1, inverse(double_divide(inverse(inverse(Y0)), X2))))))))), inverse(double_divide(inverse(Y3), inverse(double_divide(Y1, inverse(X3)))))))) -> Y3 % 10.12/10.26 double_divide(Y0, inverse(double_divide(double_divide(double_divide(double_divide(double_divide(inverse(double_divide(inverse(Y0), Y2)), X1), inverse(double_divide(inverse(double_divide(inverse(X2), X3)), X1))), X3), Y2), inverse(double_divide(inverse(Y3), inverse(X2)))))) -> Y3 % 10.12/10.26 double_divide(Y0, inverse(double_divide(double_divide(double_divide(double_divide(inverse(X0), X1), inverse(double_divide(inverse(double_divide(inverse(Y0), Y2)), X1))), Y2), inverse(double_divide(inverse(Y3), inverse(X0)))))) -> Y3 % 10.12/10.26 double_divide(Y0, inverse(double_divide(inverse(Y2), inverse(double_divide(inverse(Y0), inverse(double_divide(X0, inverse(X0)))))))) -> Y2 % 10.12/10.26 double_divide(Y0, inverse(double_divide(inverse(Y3), inverse(Y0)))) -> Y3 % 10.12/10.26 double_divide(Y1, double_divide(Y0, Y1)) -> Y0 % 10.12/10.26 double_divide(Y1, double_divide(Y1, Y0)) -> Y0 % 10.12/10.26 double_divide(Y1, inverse(double_divide(inverse(Y2), inverse(double_divide(inverse(double_divide(X0, inverse(X0))), inverse(Y1)))))) -> Y2 % 10.12/10.26 double_divide(double_divide(A, B), inverse(double_divide(A, inverse(double_divide(inverse(C), B))))) -> C % 10.12/10.26 double_divide(double_divide(X1, inverse(X0)), inverse(double_divide(inverse(X0), inverse(double_divide(inverse(Y2), inverse(inverse(X1))))))) -> Y2 % 10.12/10.26 double_divide(double_divide(X1, inverse(double_divide(inverse(Y2), inverse(double_divide(inverse(X1), inverse(inverse(Y0))))))), inverse(Y2)) -> Y0 % 10.12/10.26 double_divide(double_divide(X3, inverse(double_divide(inverse(Y2), inverse(double_divide(double_divide(X1, X2), inverse(double_divide(inverse(X3), inverse(double_divide(X1, inverse(double_divide(inverse(inverse(Y0)), X2))))))))))), inverse(Y2)) -> Y0 % 10.12/10.26 double_divide(double_divide(X3, inverse(double_divide(inverse(Y2), inverse(double_divide(double_divide(double_divide(inverse(inverse(Y0)), X1), inverse(double_divide(inverse(X2), X1))), inverse(double_divide(inverse(X3), inverse(X2)))))))), inverse(Y2)) -> Y0 % 10.12/10.26 double_divide(double_divide(Y0, X0), X0) -> Y0 % 10.12/10.26 double_divide(double_divide(Y0, double_divide(X1, inverse(X1))), double_divide(false__, inverse(false__))) -> Y0 % 10.12/10.26 double_divide(double_divide(Y0, double_divide(double_divide(X1, inverse(X1)), Y0)), inverse(Y1)) -> Y1 % 10.12/10.26 double_divide(double_divide(Y0, double_divide(double_divide(X1, inverse(X1)), Y1)), inverse(Y1)) -> Y0 % 10.12/10.26 double_divide(double_divide(Y0, double_divide(double_divide(X1, inverse(X1)), double_divide(false__, inverse(false__)))), double_divide(false__, inverse(false__))) -> Y0 % 10.12/10.26 double_divide(double_divide(Y0, double_divide(double_divide(inverse(X1), X1), Y0)), inverse(Y1)) -> Y1 % 10.12/10.26 double_divide(double_divide(Y0, double_divide(double_divide(inverse(X1), X1), double_divide(false__, inverse(false__)))), double_divide(false__, inverse(false__))) -> Y0 % 10.12/10.26 double_divide(double_divide(Y0, double_divide(inverse(X1), X1)), double_divide(false__, inverse(false__))) -> Y0 % 10.12/10.26 double_divide(double_divide(Y0, inverse(Y0)), double_divide(Y1, double_divide(false__, inverse(false__)))) -> Y1 % 10.12/10.26 double_divide(double_divide(Y0, inverse(Y0)), double_divide(double_divide(X1, inverse(X1)), Y1)) -> Y1 % 10.12/10.26 double_divide(double_divide(Y0, inverse(Y0)), double_divide(double_divide(inverse(X1), X1), Y1)) -> Y1 % 10.12/10.26 double_divide(double_divide(Y0, inverse(Y0)), inverse(Y2)) -> Y2 % 10.12/10.26 double_divide(double_divide(Y0, inverse(Y1)), double_divide(double_divide(X1, inverse(X1)), Y1)) -> Y0 % 10.12/10.26 double_divide(double_divide(Y0, inverse(double_divide(X1, inverse(X1)))), inverse(double_divide(Y0, inverse(Y2)))) -> Y2 % 10.12/10.26 double_divide(double_divide(Y0, inverse(double_divide(X1, inverse(X1)))), inverse(double_divide(false__, inverse(false__)))) -> Y0 % 10.12/10.26 double_divide(double_divide(Y0, inverse(double_divide(double_divide(X1, X2), inverse(double_divide(inverse(X3), inverse(double_divide(X1, inverse(double_divide(inverse(inverse(Y2)), X2))))))))), inverse(double_divide(Y0, inverse(X3)))) -> Y2 % 10.12/10.26 double_divide(double_divide(Y0, inverse(double_divide(double_divide(double_divide(inverse(inverse(Y2)), X1), inverse(double_divide(inverse(X2), X1))), inverse(double_divide(inverse(X3), inverse(X2)))))), inverse(double_divide(Y0, inverse(X3)))) -> Y2 % 10.12/10.26 double_divide(double_divide(Y0, inverse(double_divide(inverse(X1), inverse(inverse(Y2))))), inverse(double_divide(Y0, inverse(X1)))) -> Y2 % 10.12/10.26 double_divide(double_divide(Y0, inverse(inverse(X1))), inverse(double_divide(Y0, inverse(double_divide(X1, inverse(Y2)))))) -> Y2 % 10.12/10.26 double_divide(double_divide(Y1, inverse(Y0)), inverse(Y0)) -> Y1 % 10.12/10.26 double_divide(double_divide(double_divide(X0, inverse(X0)), Y1), inverse(double_divide(inverse(Y2), Y1))) -> Y2 % 10.12/10.26 double_divide(double_divide(double_divide(X1, inverse(X1)), Y0), double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__)))) -> Y0 % 10.12/10.26 double_divide(double_divide(double_divide(X1, inverse(X1)), Y0), double_divide(false__, inverse(false__))) -> Y0 % 10.12/10.26 double_divide(double_divide(double_divide(X1, inverse(double_divide(inverse(double_divide(inverse(Y2), Y3)), inverse(double_divide(inverse(X1), inverse(inverse(Y0))))))), Y3), inverse(Y0)) -> Y2 % 10.12/10.26 double_divide(double_divide(double_divide(X3, inverse(double_divide(inverse(double_divide(inverse(Y2), Y3)), inverse(double_divide(double_divide(X1, X2), inverse(double_divide(inverse(X3), inverse(double_divide(X1, inverse(double_divide(inverse(inverse(Y0)), X2))))))))))), Y3), inverse(Y0)) -> Y2 % 10.12/10.26 double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(inverse(double_divide(inverse(X0), X1)), X2), inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(Y2), Y1)), X4)), X2))), X4), X1), Y1), inverse(X0)) -> Y2 % 10.12/10.26 double_divide(double_divide(double_divide(double_divide(double_divide(inverse(double_divide(inverse(Y2), Y1)), X1), inverse(double_divide(inverse(double_divide(inverse(X2), X3)), X1))), X3), Y1), inverse(X2)) -> Y2 % 10.12/10.26 double_divide(double_divide(double_divide(double_divide(inverse(X0), X1), inverse(double_divide(inverse(double_divide(inverse(Y2), Y1)), X1))), Y1), inverse(X0)) -> Y2 % 10.12/10.26 double_divide(double_divide(double_divide(double_divide(inverse(Y0), Y1), inverse(double_divide(inverse(X3), Y1))), inverse(double_divide(double_divide(X1, X2), inverse(double_divide(inverse(X3), inverse(double_divide(X1, inverse(double_divide(inverse(inverse(Y2)), X2))))))))), inverse(Y0)) -> Y2 % 10.12/10.26 double_divide(double_divide(double_divide(double_divide(inverse(Y0), inverse(double_divide(double_divide(X1, X2), inverse(double_divide(inverse(X3), inverse(double_divide(X1, inverse(double_divide(inverse(inverse(double_divide(inverse(Y2), Y3))), X2))))))))), inverse(X3)), Y3), inverse(Y0)) -> Y2 % 10.12/10.26 double_divide(double_divide(double_divide(inverse(X0), X0), double_divide(false__, inverse(false__))), inverse(Y1)) -> Y1 % 10.12/10.26 double_divide(double_divide(double_divide(inverse(X0), inverse(Y1)), double_divide(false__, inverse(false__))), X0) -> Y1 % 10.12/10.26 double_divide(double_divide(double_divide(inverse(X1), X1), Y0), double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__)))) -> Y0 % 10.12/10.26 double_divide(double_divide(double_divide(inverse(X1), X1), Y0), double_divide(false__, inverse(false__))) -> Y0 % 10.12/10.26 double_divide(double_divide(double_divide(inverse(X1), inverse(inverse(Y2))), inverse(double_divide(inverse(X1), inverse(inverse(Y0))))), inverse(Y2)) -> Y0 % 10.12/10.26 double_divide(double_divide(double_divide(inverse(Y0), inverse(double_divide(double_divide(X1, X2), inverse(double_divide(inverse(X3), inverse(double_divide(X1, inverse(double_divide(inverse(inverse(Y2)), X2))))))))), inverse(X3)), inverse(Y2)) -> Y0 % 10.12/10.26 double_divide(double_divide(double_divide(inverse(Y0), inverse(double_divide(double_divide(double_divide(inverse(inverse(Y2)), X1), inverse(double_divide(inverse(X2), X1))), inverse(double_divide(inverse(X3), inverse(X2)))))), inverse(X3)), inverse(Y2)) -> Y0 % 10.12/10.26 double_divide(double_divide(double_divide(inverse(Y0), inverse(double_divide(inverse(X1), inverse(inverse(Y2))))), inverse(X1)), inverse(Y2)) -> Y0 % 10.12/10.26 double_divide(double_divide(double_divide(inverse(Y2), X1), inverse(double_divide(inverse(X2), X1))), inverse(X2)) -> Y2 % 10.12/10.26 double_divide(double_divide(double_divide(inverse(double_divide(inverse(Y2), Y1)), inverse(inverse(X1))), Y1), inverse(X1)) -> Y2 % 10.12/10.26 double_divide(double_divide(false__, inverse(false__)), double_divide(Y0, double_divide(false__, inverse(false__)))) -> Y0 % 10.12/10.26 double_divide(double_divide(false__, inverse(false__)), double_divide(double_divide(X1, inverse(X1)), Y0)) -> Y0 % 10.12/10.26 double_divide(double_divide(inverse(X0), X0), inverse(Y1)) -> Y1 % 10.12/10.26 double_divide(double_divide(inverse(X1), inverse(inverse(Y1))), inverse(X1)) -> Y1 % 10.12/10.26 double_divide(double_divide(inverse(Y0), Y0), double_divide(double_divide(X1, inverse(X1)), Y1)) -> Y1 % 10.12/10.26 double_divide(inverse(X0), double_divide(double_divide(inverse(Y1), Y1), double_divide(false__, inverse(false__)))) -> X0 % 10.12/10.26 double_divide(inverse(X0), double_divide(false__, inverse(false__))) -> X0 % 10.12/10.26 double_divide(inverse(X0), inverse(double_divide(inverse(Y1), X0))) -> Y1 % 10.12/10.26 double_divide(inverse(X1), inverse(double_divide(X1, inverse(Y1)))) -> Y1 % 10.12/10.26 double_divide(inverse(Y0), double_divide(X1, inverse(X1))) -> Y0 % 10.12/10.26 double_divide(inverse(Y0), double_divide(false__, double_divide(false__, double_divide(X1, inverse(X1))))) -> Y0 % 10.12/10.26 double_divide(inverse(Y0), double_divide(inverse(X1), X1)) -> Y0 % 10.12/10.26 double_divide(inverse(Y1), double_divide(Y0, inverse(Y1))) -> Y0 % 10.12/10.26 double_divide(inverse(Y1), double_divide(inverse(Y1), Y0)) -> Y0 % 10.12/10.26 double_divide(inverse(Y1), inverse(double_divide(X0, inverse(X0)))) -> Y1 % 10.12/10.26 double_divide(inverse(double_divide(X0, inverse(X0))), inverse(Y1)) -> Y1 % 10.12/10.26 double_divide(inverse(double_divide(X0, inverse(Y1))), inverse(X0)) -> Y1 % 10.12/10.26 f1(double_divide(double_divide(X1, inverse(X1)), double_divide(a, b))) -> false__ % 10.12/10.26 f1(double_divide(double_divide(X1, inverse(X1)), double_divide(b, a))) -> true__ % 10.12/10.26 f1(double_divide(double_divide(a, b), double_divide(X1, inverse(X1)))) -> false__ % 10.12/10.26 f1(double_divide(double_divide(a, b), double_divide(double_divide(X1, inverse(X1)), double_divide(false__, inverse(false__))))) -> false__ % 10.12/10.26 f1(double_divide(double_divide(a, b), double_divide(double_divide(inverse(X1), X1), double_divide(false__, inverse(false__))))) -> false__ % 10.12/10.26 f1(double_divide(double_divide(a, b), double_divide(false__, inverse(false__)))) -> false__ % 10.12/10.26 f1(double_divide(double_divide(a, b), double_divide(inverse(X1), X1))) -> false__ % 10.12/10.26 f1(double_divide(double_divide(b, a), double_divide(X1, inverse(X1)))) -> true__ % 10.12/10.26 f1(double_divide(double_divide(b, a), double_divide(double_divide(X1, inverse(X1)), double_divide(false__, inverse(false__))))) -> true__ % 10.12/10.26 f1(double_divide(double_divide(b, a), double_divide(double_divide(inverse(X1), X1), double_divide(false__, inverse(false__))))) -> true__ % 10.12/10.26 f1(double_divide(double_divide(b, a), double_divide(false__, inverse(false__)))) -> true__ % 10.12/10.26 f1(double_divide(double_divide(b, a), double_divide(inverse(X1), X1))) -> true__ % 10.12/10.26 f1(double_divide(double_divide(inverse(X1), X1), double_divide(a, b))) -> false__ % 10.12/10.26 f1(double_divide(double_divide(inverse(X1), X1), double_divide(b, a))) -> true__ % 10.12/10.26 f1(inverse(double_divide(a, b))) -> false__ % 10.12/10.26 f1(inverse(double_divide(b, a))) -> true__ % 10.12/10.26 f1(multiply(a, b)) -> true__ % 10.12/10.26 f1(multiply(b, a)) -> false__ % 10.12/10.26 inverse(inverse(X1)) -> X1 % 10.12/10.26 multiply(A, B) -> inverse(double_divide(B, A)) % 10.12/10.26 true__ -> false__ % 10.12/10.26 with the LPO induced by % 10.12/10.26 a > b > f1 > multiply > inverse > double_divide > true__ > false__ % 10.12/10.26 % 10.12/10.26 % SZS output end Proof % 10.12/10.26 %------------------------------------------------------------------------------