%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP451-1 : 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 10:55:32 EDT 2022 % Result : Unsatisfiable 0.46s 0.63s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : GRP451-1 : TPTP v8.1.0. Released v2.6.0. % 0.06/0.11 % Command : moca.sh %s % 0.11/0.31 % Computer : n032.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 600 % 0.11/0.31 % DateTime : Mon Jun 13 22:31:27 EDT 2022 % 0.11/0.31 % CPUTime : % 0.46/0.63 % SZS status Unsatisfiable % 0.46/0.63 % SZS output start Proof % 0.46/0.63 The input problem is unsatisfiable because % 0.46/0.63 % 0.46/0.63 [1] the following set of Horn clauses is unsatisfiable: % 0.46/0.63 % 0.46/0.63 divide(divide(divide(A, A), divide(A, divide(B, divide(divide(divide(A, A), A), C)))), C) = B % 0.46/0.63 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 0.46/0.63 inverse(A) = divide(divide(B, B), A) % 0.46/0.63 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom % 0.46/0.63 % 0.46/0.63 This holds because % 0.46/0.63 % 0.46/0.63 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.46/0.63 % 0.46/0.63 E: % 0.46/0.63 divide(divide(divide(A, A), divide(A, divide(B, divide(divide(divide(A, A), A), C)))), C) = B % 0.46/0.63 f1(multiply(inverse(a1), a1)) = true__ % 0.46/0.63 f1(multiply(inverse(b1), b1)) = false__ % 0.46/0.63 inverse(A) = divide(divide(B, B), A) % 0.46/0.63 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 0.46/0.63 G: % 0.46/0.63 true__ = false__ % 0.46/0.63 % 0.46/0.63 This holds because % 0.46/0.63 % 0.46/0.63 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.46/0.63 % 0.46/0.63 divide(X0, X0) = divide(Y0, Y0) % 0.46/0.63 divide(X0, X0) = inverse(divide(Y0, Y0)) % 0.46/0.63 divide(false__, false__) = divide(X0, X0) % 0.46/0.63 divide(false__, false__) = inverse(inverse(inverse(divide(Y0, Y0)))) % 0.46/0.63 divide(inverse(divide(Y0, inverse(divide(inverse(Y0), Y2)))), Y2) = divide(X0, X0) % 0.46/0.63 divide(inverse(inverse(inverse(inverse(Y1)))), Y1) = divide(Y2, Y2) % 0.46/0.63 inverse(divide(X0, X0)) = divide(false__, false__) % 0.46/0.63 inverse(divide(X0, X0)) = inverse(divide(Y0, Y0)) % 0.46/0.63 inverse(inverse(divide(X0, X0))) = divide(false__, false__) % 0.46/0.63 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 0.46/0.63 divide(Y0, divide(inverse(inverse(divide(X0, X0))), Y2)) -> divide(Y0, inverse(Y2)) % 0.46/0.63 divide(divide(B, B), A) -> inverse(A) % 0.46/0.63 divide(divide(divide(A, A), divide(A, divide(B, divide(divide(divide(A, A), A), C)))), C) -> B % 0.46/0.63 divide(divide(inverse(divide(X0, X0)), inverse(divide(Y1, divide(inverse(divide(X0, X0)), Y2)))), Y2) -> Y1 % 0.46/0.63 divide(inverse(divide(X0, X0)), Y1) -> inverse(Y1) % 0.46/0.63 divide(inverse(divide(Y0, divide(Y1, divide(inverse(Y0), Y2)))), Y2) -> Y1 % 0.46/0.63 divide(inverse(inverse(divide(X0, X0))), Y1) -> inverse(Y1) % 0.46/0.63 divide(inverse(inverse(divide(Y0, divide(inverse(inverse(divide(X0, X0))), Y2)))), Y2) -> Y0 % 0.46/0.63 divide(inverse(inverse(divide(Y1, divide(inverse(divide(X0, X0)), Y2)))), Y2) -> Y1 % 0.46/0.63 divide(inverse(inverse(inverse(divide(X0, X0)))), Y1) -> inverse(Y1) % 0.46/0.63 f1(divide(X0, X0)) -> false__ % 0.46/0.63 f1(divide(X0, X0)) -> true__ % 0.46/0.63 f1(divide(false__, false__)) -> false__ % 0.46/0.63 f1(divide(false__, false__)) -> true__ % 0.46/0.63 f1(divide(inverse(a1), inverse(a1))) -> true__ % 0.46/0.63 f1(divide(inverse(b1), inverse(b1))) -> false__ % 0.46/0.63 f1(inverse(divide(X1, X1))) -> false__ % 0.46/0.63 f1(inverse(divide(X1, X1))) -> true__ % 0.46/0.63 f1(inverse(inverse(divide(X0, X0)))) -> false__ % 0.46/0.63 f1(inverse(inverse(divide(X0, X0)))) -> true__ % 0.46/0.63 f1(multiply(inverse(a1), a1)) -> true__ % 0.46/0.63 f1(multiply(inverse(b1), b1)) -> false__ % 0.46/0.63 true__ -> false__ % 0.46/0.63 with the LPO induced by % 0.46/0.63 a1 > b1 > f1 > multiply > divide > inverse > true__ > false__ % 0.46/0.63 % 0.46/0.63 % SZS output end Proof % 0.46/0.63 %------------------------------------------------------------------------------