%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP597-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n032.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 10:56:32 EDT 2022 % Result : Unsatisfiable 8.79s 8.93s % Output : Proof 8.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : GRP597-1 : TPTP v8.1.0. Released v2.6.0. % 0.03/0.12 % Command : moca.sh %s % 0.12/0.31 % Computer : n032.cluster.edu % 0.12/0.31 % Model : x86_64 x86_64 % 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.31 % Memory : 8042.1875MB % 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.31 % CPULimit : 300 % 0.12/0.31 % WCLimit : 600 % 0.12/0.31 % DateTime : Mon Jun 13 04:13:41 EDT 2022 % 0.12/0.31 % CPUTime : % 8.79/8.93 % SZS status Unsatisfiable % 8.79/8.93 % SZS output start Proof % 8.79/8.93 The input problem is unsatisfiable because % 8.79/8.93 % 8.79/8.93 [1] the following set of Horn clauses is unsatisfiable: % 8.79/8.93 % 8.79/8.93 double_divide(double_divide(A, B), inverse(double_divide(A, inverse(double_divide(inverse(C), B))))) = C % 8.79/8.93 multiply(A, B) = inverse(double_divide(B, A)) % 8.79/8.93 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom % 8.79/8.93 % 8.79/8.93 This holds because % 8.79/8.93 % 8.79/8.93 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 8.79/8.93 % 8.79/8.93 E: % 8.79/8.93 double_divide(double_divide(A, B), inverse(double_divide(A, inverse(double_divide(inverse(C), B))))) = C % 8.79/8.93 f1(multiply(inverse(a1), a1)) = true__ % 8.79/8.93 f1(multiply(inverse(b1), b1)) = false__ % 8.79/8.93 multiply(A, B) = inverse(double_divide(B, A)) % 8.79/8.93 G: % 8.79/8.93 true__ = false__ % 8.79/8.93 % 8.79/8.93 This holds because % 8.79/8.93 % 8.79/8.93 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 8.79/8.93 % 8.79/8.93 double_divide(X0, inverse(double_divide(X1, inverse(X1)))) = inverse(X0) % 8.79/8.93 double_divide(X1, inverse(Y2)) = double_divide(inverse(Y2), inverse(inverse(X1))) % 8.79/8.93 double_divide(Y0, inverse(double_divide(inverse(X0), X0))) = inverse(Y0) % 8.79/8.93 double_divide(Y1, inverse(Y1)) = double_divide(X0, inverse(X0)) % 8.79/8.93 double_divide(double_divide(Y0, inverse(Y0)), X0) = inverse(X0) % 8.79/8.93 double_divide(double_divide(inverse(X0), X0), Y1) = inverse(Y1) % 8.79/8.93 double_divide(inverse(X0), X0) = double_divide(Y1, inverse(Y1)) % 8.79/8.93 double_divide(inverse(X0), X0) = double_divide(inverse(Y1), Y1) % 8.79/8.93 double_divide(inverse(Y0), inverse(X1)) = double_divide(inverse(X1), inverse(Y0)) % 8.79/8.93 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 % 8.79/8.93 double_divide(X0, inverse(double_divide(inverse(X0), inverse(Y2)))) -> Y2 % 8.79/8.93 double_divide(X1, inverse(double_divide(X0, inverse(X1)))) -> inverse(X0) % 8.79/8.93 double_divide(X1, inverse(double_divide(Y0, inverse(double_divide(inverse(Y2), inverse(double_divide(inverse(X1), inverse(Y0)))))))) -> Y2 % 8.79/8.93 double_divide(X1, inverse(double_divide(double_divide(inverse(X0), inverse(inverse(X1))), inverse(double_divide(inverse(Y2), inverse(X0)))))) -> Y2 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 double_divide(Y0, inverse(double_divide(inverse(Y2), inverse(double_divide(inverse(Y0), inverse(double_divide(X0, inverse(X0)))))))) -> Y2 % 8.79/8.93 double_divide(Y0, inverse(double_divide(inverse(Y3), inverse(Y0)))) -> Y3 % 8.79/8.93 double_divide(Y1, inverse(double_divide(inverse(Y2), inverse(double_divide(inverse(double_divide(X0, inverse(X0))), inverse(Y1)))))) -> Y2 % 8.79/8.93 double_divide(double_divide(A, B), inverse(double_divide(A, inverse(double_divide(inverse(C), B))))) -> C % 8.79/8.93 double_divide(double_divide(X1, inverse(X0)), inverse(double_divide(inverse(X0), inverse(double_divide(inverse(Y2), inverse(inverse(X1))))))) -> Y2 % 8.79/8.93 double_divide(double_divide(X1, inverse(double_divide(inverse(Y2), inverse(double_divide(inverse(X1), inverse(inverse(Y0))))))), inverse(Y2)) -> Y0 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 double_divide(double_divide(Y0, X0), X0) -> Y0 % 8.79/8.93 double_divide(double_divide(Y0, inverse(Y0)), inverse(Y2)) -> Y2 % 8.79/8.93 double_divide(double_divide(Y0, inverse(double_divide(X1, inverse(X1)))), inverse(double_divide(Y0, inverse(Y2)))) -> Y2 % 8.79/8.93 double_divide(double_divide(Y0, inverse(double_divide(X1, inverse(X1)))), inverse(double_divide(false__, inverse(false__)))) -> Y0 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 double_divide(double_divide(Y0, inverse(double_divide(inverse(X1), inverse(inverse(Y2))))), inverse(double_divide(Y0, inverse(X1)))) -> Y2 % 8.79/8.93 double_divide(double_divide(Y0, inverse(inverse(X1))), inverse(double_divide(Y0, inverse(double_divide(X1, inverse(Y2)))))) -> Y2 % 8.79/8.93 double_divide(double_divide(Y1, inverse(Y0)), inverse(Y0)) -> Y1 % 8.79/8.93 double_divide(double_divide(double_divide(X0, inverse(X0)), Y1), inverse(double_divide(inverse(Y2), Y1))) -> Y2 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 double_divide(double_divide(double_divide(inverse(X1), inverse(inverse(Y2))), inverse(double_divide(inverse(X1), inverse(inverse(Y0))))), inverse(Y2)) -> Y0 % 8.79/8.93 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 % 8.79/8.93 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 % 8.79/8.93 double_divide(double_divide(double_divide(inverse(Y0), inverse(double_divide(inverse(X1), inverse(inverse(Y2))))), inverse(X1)), inverse(Y2)) -> Y0 % 8.79/8.93 double_divide(double_divide(double_divide(inverse(Y2), X1), inverse(double_divide(inverse(X2), X1))), inverse(X2)) -> Y2 % 8.79/8.93 double_divide(double_divide(double_divide(inverse(double_divide(inverse(Y2), Y1)), inverse(inverse(X1))), Y1), inverse(X1)) -> Y2 % 8.79/8.93 double_divide(double_divide(false__, inverse(false__)), double_divide(double_divide(X1, inverse(X1)), Y0)) -> Y0 % 8.79/8.93 double_divide(double_divide(inverse(X0), X0), inverse(Y1)) -> Y1 % 8.79/8.93 double_divide(double_divide(inverse(X1), inverse(inverse(Y1))), inverse(X1)) -> Y1 % 8.79/8.93 double_divide(inverse(X1), inverse(double_divide(X1, inverse(Y1)))) -> Y1 % 8.79/8.93 double_divide(inverse(Y1), inverse(double_divide(X0, inverse(X0)))) -> Y1 % 8.79/8.93 double_divide(inverse(double_divide(X0, inverse(X0))), inverse(Y1)) -> Y1 % 8.79/8.93 double_divide(inverse(double_divide(X0, inverse(Y1))), inverse(X0)) -> Y1 % 8.79/8.93 f1(double_divide(double_divide(a1, double_divide(double_divide(X1, inverse(X1)), a1)), double_divide(false__, inverse(false__)))) -> true__ % 8.79/8.93 f1(double_divide(double_divide(b1, double_divide(double_divide(X1, inverse(X1)), b1)), double_divide(false__, inverse(false__)))) -> false__ % 8.79/8.93 f1(double_divide(double_divide(false__, inverse(false__)), double_divide(inverse(X0), X0))) -> false__ % 8.79/8.93 f1(inverse(double_divide(X1, inverse(X1)))) -> false__ % 8.79/8.93 f1(inverse(double_divide(a1, inverse(a1)))) -> true__ % 8.79/8.93 f1(inverse(double_divide(b1, inverse(b1)))) -> false__ % 8.79/8.93 f1(multiply(inverse(a1), a1)) -> true__ % 8.79/8.93 f1(multiply(inverse(b1), b1)) -> false__ % 8.79/8.93 inverse(inverse(X1)) -> X1 % 8.79/8.93 multiply(A, B) -> inverse(double_divide(B, A)) % 8.79/8.93 true__ -> false__ % 8.79/8.93 with the LPO induced by % 8.79/8.93 a1 > b1 > f1 > multiply > inverse > double_divide > true__ > false__ % 8.79/8.93 % 8.79/8.93 % SZS output end Proof % 8.79/8.93 %------------------------------------------------------------------------------