%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP555-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n015.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 10:56:14 EDT 2022 % Result : Unsatisfiable 5.34s 5.45s % Output : Proof 5.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRP555-1 : TPTP v8.1.0. Released v2.6.0. % 0.12/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n015.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 07:34:23 EDT 2022 % 0.12/0.33 % CPUTime : % 5.34/5.45 % SZS status Unsatisfiable % 5.34/5.45 % SZS output start Proof % 5.34/5.45 The input problem is unsatisfiable because % 5.34/5.45 % 5.34/5.45 [1] the following set of Horn clauses is unsatisfiable: % 5.34/5.45 % 5.34/5.45 divide(divide(A, inverse(divide(B, divide(A, C)))), C) = B % 5.34/5.45 multiply(A, B) = divide(A, inverse(B)) % 5.34/5.45 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom % 5.34/5.45 % 5.34/5.45 This holds because % 5.34/5.45 % 5.34/5.45 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 5.34/5.45 % 5.34/5.45 E: % 5.34/5.45 divide(divide(A, inverse(divide(B, divide(A, C)))), C) = B % 5.34/5.45 f1(multiply(a3, multiply(b3, c3))) = false__ % 5.34/5.45 f1(multiply(multiply(a3, b3), c3)) = true__ % 5.34/5.45 multiply(A, B) = divide(A, inverse(B)) % 5.34/5.45 G: % 5.34/5.45 true__ = false__ % 5.34/5.45 % 5.34/5.45 This holds because % 5.34/5.45 % 5.34/5.45 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 5.34/5.45 % 5.34/5.45 divide(X1, divide(Y2, divide(inverse(X1), inverse(Y0)))) = divide(Y0, Y2) % 5.34/5.45 divide(X1, divide(Y2, inverse(X0))) = divide(divide(inverse(X0), inverse(X1)), Y2) % 5.34/5.45 divide(X1, divide(Y2, inverse(X0))) = divide(inverse(divide(X0, X1)), Y2) % 5.34/5.45 divide(X1, divide(Y2, inverse(divide(X1, Y0)))) = divide(Y0, Y2) % 5.34/5.45 divide(Y0, Y0) = divide(Y2, Y2) % 5.34/5.45 divide(Y0, inverse(divide(Y1, divide(Y0, X1)))) = divide(divide(divide(X0, inverse(divide(X1, divide(X0, Y3)))), inverse(Y1)), Y3) % 5.34/5.45 divide(divide(X0, X2), inverse(X1)) = divide(divide(X0, inverse(X1)), X2) % 5.34/5.45 divide(divide(X2, X1), divide(inverse(X0), inverse(X2))) = divide(X0, X1) % 5.34/5.45 divide(divide(X2, X1), inverse(divide(X0, X2))) = divide(X0, X1) % 5.34/5.45 divide(divide(Y0, inverse(X0)), X1) = divide(Y0, divide(inverse(X0), inverse(X1))) % 5.34/5.45 divide(divide(Y0, inverse(X0)), X1) = divide(Y0, inverse(divide(X0, X1))) % 5.34/5.45 divide(divide(divide(X2, inverse(X1)), inverse(Y1)), X3) = divide(divide(Y2, inverse(Y1)), inverse(divide(X1, divide(Y2, divide(X2, X3))))) % 5.34/5.45 divide(divide(divide(Y2, inverse(X1)), Y3), inverse(divide(Y1, X1))) = divide(divide(Y2, inverse(Y1)), Y3) % 5.34/5.45 divide(X0, inverse(divide(X1, divide(X0, Y0)))) -> divide(Y0, inverse(X1)) % 5.34/5.45 divide(X0, inverse(divide(X1, divide(X0, divide(Y0, Y2))))) -> divide(divide(Y0, inverse(X1)), Y2) % 5.34/5.45 divide(X1, divide(Y0, inverse(divide(X1, divide(Y0, inverse(Y1)))))) -> Y1 % 5.34/5.45 divide(Y0, divide(divide(inverse(X0), inverse(X1)), inverse(Y0))) -> divide(X0, X1) % 5.34/5.45 divide(Y0, divide(inverse(Y1), inverse(Y0))) -> Y1 % 5.34/5.45 divide(Y1, divide(divide(divide(inverse(X0), inverse(X1)), inverse(X0)), X1)) -> Y1 % 5.34/5.45 divide(Y1, inverse(divide(Y3, Y1))) -> Y3 % 5.34/5.45 divide(divide(A, inverse(divide(B, divide(A, C)))), C) -> B % 5.34/5.45 divide(divide(X0, X1), divide(inverse(Y1), divide(inverse(X0), inverse(X1)))) -> Y1 % 5.34/5.45 divide(divide(X1, Y2), divide(Y0, Y2)) -> divide(X1, Y0) % 5.34/5.45 divide(divide(X1, inverse(Y1)), X1) -> Y1 % 5.34/5.45 divide(divide(Y0, X1), inverse(divide(X1, Y2))) -> divide(Y0, Y2) % 5.34/5.45 divide(divide(Y0, divide(inverse(X1), inverse(Y2))), X1) -> divide(Y0, Y2) % 5.34/5.45 divide(divide(Y0, inverse(divide(Y1, X1))), inverse(divide(X1, Y0))) -> Y1 % 5.34/5.45 divide(divide(Y0, inverse(divide(Y1, divide(divide(X2, inverse(X1)), X3)))), inverse(divide(X1, divide(Y0, divide(X2, X3))))) -> Y1 % 5.34/5.45 divide(divide(divide(X0, inverse(divide(X1, divide(X0, Y2)))), inverse(divide(Y1, X1))), Y2) -> Y1 % 5.34/5.45 divide(divide(divide(X2, inverse(Y1)), X3), divide(X2, X3)) -> Y1 % 5.34/5.45 divide(divide(divide(Y0, inverse(Y1)), inverse(divide(X1, Y0))), X1) -> Y1 % 5.34/5.45 divide(divide(divide(divide(X0, inverse(divide(X1, divide(X0, Y2)))), inverse(divide(Y1, X1))), inverse(divide(Y3, Y1))), Y2) -> Y3 % 5.34/5.45 divide(divide(inverse(X0), inverse(X2)), divide(inverse(X0), inverse(X1))) -> divide(X2, X1) % 5.34/5.45 divide(divide(inverse(Y0), inverse(Y1)), inverse(Y0)) -> Y1 % 5.34/5.45 divide(inverse(X1), inverse(inverse(divide(X0, X1)))) -> inverse(X0) % 5.34/5.45 divide(inverse(divide(X1, Y1)), inverse(X1)) -> Y1 % 5.34/5.45 f1(divide(a3, inverse(divide(b3, inverse(c3))))) -> false__ % 5.34/5.45 f1(divide(divide(a3, inverse(b3)), inverse(c3))) -> true__ % 5.34/5.45 f1(multiply(a3, multiply(b3, c3))) -> false__ % 5.34/5.45 f1(multiply(multiply(a3, b3), c3)) -> true__ % 5.34/5.45 inverse(divide(X1, Y0)) -> divide(inverse(X1), inverse(Y0)) % 5.34/5.45 multiply(A, B) -> divide(A, inverse(B)) % 5.34/5.45 true__ -> false__ % 5.34/5.45 with the LPO induced by % 5.34/5.45 c3 > b3 > a3 > f1 > multiply > inverse > divide > true__ > false__ % 5.34/5.45 % 5.34/5.45 % SZS output end Proof % 5.34/5.45 %------------------------------------------------------------------------------