%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP466-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n008.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 10:55:39 EDT 2022 % Result : Unsatisfiable 0.46s 0.65s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : GRP466-1 : TPTP v8.1.0. Released v2.6.0. % 0.12/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n008.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 09:39:07 EDT 2022 % 0.12/0.33 % CPUTime : % 0.46/0.65 % SZS status Unsatisfiable % 0.46/0.65 % SZS output start Proof % 0.46/0.65 The input problem is unsatisfiable because % 0.46/0.65 % 0.46/0.65 [1] the following set of Horn clauses is unsatisfiable: % 0.46/0.65 % 0.46/0.65 divide(divide(A, A), divide(B, divide(divide(C, divide(D, B)), inverse(D)))) = C % 0.46/0.65 multiply(A, B) = divide(A, inverse(B)) % 0.46/0.65 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom % 0.46/0.65 % 0.46/0.65 This holds because % 0.46/0.65 % 0.46/0.65 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.46/0.65 % 0.46/0.65 E: % 0.46/0.65 divide(divide(A, A), divide(B, divide(divide(C, divide(D, B)), inverse(D)))) = C % 0.46/0.65 f1(multiply(inverse(a1), a1)) = true__ % 0.46/0.65 f1(multiply(inverse(b1), b1)) = false__ % 0.46/0.65 multiply(A, B) = divide(A, inverse(B)) % 0.46/0.65 G: % 0.46/0.65 true__ = false__ % 0.46/0.65 % 0.46/0.65 This holds because % 0.46/0.65 % 0.46/0.65 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.46/0.65 % 0.46/0.65 divide(X4, X4) = divide(Y4, Y4) % 0.46/0.65 divide(divide(Y0, Y0), divide(Y1, divide(divide(X1, X1), inverse(Y3)))) = divide(Y3, Y1) % 0.46/0.65 divide(divide(Y0, Y0), divide(divide(X2, inverse(Y2)), divide(divide(X0, X0), inverse(divide(divide(X2, divide(X3, Y2)), inverse(X3)))))) = divide(Y4, Y4) % 0.46/0.65 divide(divide(Y0, Y0), divide(divide(divide(X2, divide(X3, Y3)), inverse(X3)), divide(X2, inverse(Y3)))) = divide(X0, X0) % 0.46/0.65 divide(divide(Y0, Y0), divide(divide(divide(Y1, X2), inverse(divide(X0, X0))), divide(Y1, inverse(divide(X1, divide(divide(X2, divide(X3, X1)), inverse(X3))))))) = divide(Y4, Y4) % 0.46/0.65 divide(divide(Y0, Y0), divide(divide(divide(Y1, divide(X0, X0)), inverse(false__)), divide(Y1, inverse(false__)))) = divide(Y4, Y4) % 0.46/0.65 divide(false__, false__) = divide(X0, X0) % 0.46/0.65 divide(divide(A, A), divide(B, divide(divide(C, divide(D, B)), inverse(D)))) -> C % 0.46/0.65 divide(divide(Y0, Y0), divide(Y1, divide(divide(Y2, divide(X1, X1)), inverse(Y1)))) -> Y2 % 0.46/0.65 divide(divide(Y0, Y0), divide(divide(X1, divide(divide(X2, divide(X3, X1)), inverse(X3))), divide(divide(Y2, X2), inverse(divide(X0, X0))))) -> Y2 % 0.46/0.65 divide(divide(Y0, Y0), divide(divide(divide(divide(X1, divide(X2, X3)), inverse(X2)), divide(X1, inverse(X3))), divide(divide(Y2, divide(X4, X4)), inverse(divide(X0, X0))))) -> Y2 % 0.46/0.65 divide(divide(Y0, Y0), divide(false__, divide(divide(Y2, divide(X0, X0)), inverse(false__)))) -> Y2 % 0.46/0.65 f1(divide(X0, X0)) -> false__ % 0.46/0.65 f1(divide(X0, X0)) -> true__ % 0.46/0.65 f1(divide(false__, false__)) -> false__ % 0.46/0.65 f1(divide(false__, false__)) -> true__ % 0.46/0.65 f1(divide(inverse(a1), inverse(a1))) -> true__ % 0.46/0.65 f1(divide(inverse(b1), inverse(b1))) -> false__ % 0.46/0.65 f1(multiply(inverse(a1), a1)) -> true__ % 0.46/0.65 f1(multiply(inverse(b1), b1)) -> false__ % 0.46/0.65 multiply(A, B) -> divide(A, inverse(B)) % 0.46/0.65 true__ -> false__ % 0.46/0.65 with the LPO induced by % 0.46/0.65 a1 > b1 > f1 > multiply > inverse > divide > true__ > false__ % 0.46/0.65 % 0.46/0.65 % SZS output end Proof % 0.46/0.65 %------------------------------------------------------------------------------