%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP561-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n004.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 10:56:17 EDT 2022 % Result : Unsatisfiable 3.02s 3.19s % Output : Proof 3.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : GRP561-1 : TPTP v8.1.0. Released v2.6.0. % 0.00/0.09 % Command : moca.sh %s % 0.08/0.29 % Computer : n004.cluster.edu % 0.08/0.29 % Model : x86_64 x86_64 % 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.29 % Memory : 8042.1875MB % 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.29 % CPULimit : 300 % 0.08/0.29 % WCLimit : 600 % 0.08/0.29 % DateTime : Tue Jun 14 05:57:09 EDT 2022 % 0.08/0.29 % CPUTime : % 3.02/3.19 % SZS status Unsatisfiable % 3.02/3.19 % SZS output start Proof % 3.02/3.19 The input problem is unsatisfiable because % 3.02/3.19 % 3.02/3.19 [1] the following set of Horn clauses is unsatisfiable: % 3.02/3.19 % 3.02/3.19 divide(divide(divide(A, inverse(B)), C), divide(A, C)) = B % 3.02/3.19 multiply(A, B) = divide(A, inverse(B)) % 3.02/3.19 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom % 3.02/3.19 % 3.02/3.19 This holds because % 3.02/3.19 % 3.02/3.19 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 3.02/3.19 % 3.02/3.19 E: % 3.02/3.19 divide(divide(divide(A, inverse(B)), C), divide(A, C)) = B % 3.02/3.19 f1(multiply(inverse(a1), a1)) = true__ % 3.02/3.19 f1(multiply(inverse(b1), b1)) = false__ % 3.02/3.19 multiply(A, B) = divide(A, inverse(B)) % 3.02/3.19 G: % 3.02/3.19 true__ = false__ % 3.02/3.19 % 3.02/3.19 This holds because % 3.02/3.19 % 3.02/3.19 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 3.02/3.19 % 3.02/3.19 divide(Y0, X1) = multiply(inverse(X1), Y0) % 3.02/3.19 divide(A, inverse(B)) -> multiply(A, B) % 3.02/3.19 divide(X1, divide(Y0, divide(inverse(X1), inverse(divide(Y0, inverse(Y1)))))) -> Y1 % 3.02/3.19 divide(X1, divide(divide(X0, inverse(X1)), divide(X0, inverse(Y1)))) -> Y1 % 3.02/3.19 divide(X1, divide(divide(inverse(Y2), inverse(divide(Y1, inverse(X1)))), Y1)) -> Y2 % 3.02/3.19 divide(X1, divide(inverse(Y1), inverse(X1))) -> Y1 % 3.02/3.19 divide(X2, divide(Y0, divide(divide(X1, inverse(divide(Y0, inverse(Y1)))), divide(X1, inverse(X2))))) -> Y1 % 3.02/3.19 divide(X2, divide(divide(divide(X0, inverse(inverse(Y1))), inverse(X2)), X0)) -> Y1 % 3.02/3.19 divide(Y0, Y0) -> g2 % 3.02/3.19 divide(Y0, divide(X1, divide(divide(inverse(Y0), inverse(X1)), inverse(Y2)))) -> Y2 % 3.02/3.19 divide(Y0, divide(Y0, Y2)) -> Y2 % 3.02/3.19 divide(Y0, divide(divide(divide(inverse(Y2), inverse(X1)), inverse(Y0)), X1)) -> Y2 % 3.02/3.19 divide(Y0, divide(divide(inverse(Y1), inverse(divide(X1, X1))), inverse(Y0))) -> Y1 % 3.02/3.19 divide(Y0, g2) -> Y0 % 3.02/3.19 divide(Y0, multiply(inverse(Y1), Y0)) -> Y1 % 3.02/3.19 divide(Y1, divide(Y2, Y2)) -> Y1 % 3.02/3.19 divide(divide(X1, X1), inverse(Y1)) -> Y1 % 3.02/3.19 divide(divide(X1, Y2), divide(divide(inverse(Y1), inverse(X1)), Y2)) -> Y1 % 3.02/3.19 divide(divide(X1, inverse(Y2)), divide(inverse(divide(Y1, Y1)), inverse(X1))) -> Y2 % 3.02/3.19 divide(divide(Y1, Y2), divide(divide(X0, X0), Y2)) -> Y1 % 3.02/3.19 divide(divide(Y1, inverse(X1)), X1) -> Y1 % 3.02/3.19 divide(divide(Y1, inverse(Y3)), Y1) -> Y3 % 3.02/3.19 divide(divide(divide(A, inverse(B)), C), divide(A, C)) -> B % 3.02/3.19 divide(divide(divide(Y0, inverse(Y1)), divide(divide(X1, inverse(Y0)), divide(X1, inverse(X2)))), X2) -> Y1 % 3.02/3.19 divide(divide(divide(Y0, inverse(Y1)), divide(inverse(X1), inverse(Y0))), X1) -> Y1 % 3.02/3.19 divide(divide(divide(Y0, inverse(divide(X1, X1))), inverse(Y2)), Y0) -> Y2 % 3.02/3.19 divide(divide(divide(divide(X1, X1), inverse(Y1)), inverse(Y2)), Y1) -> Y2 % 3.02/3.19 divide(divide(divide(divide(Y0, inverse(divide(X1, X1))), Y2), inverse(Y3)), divide(Y0, Y2)) -> Y3 % 3.02/3.19 divide(divide(divide(divide(Y2, inverse(X1)), inverse(Y1)), Y2), X1) -> Y1 % 3.02/3.19 divide(divide(divide(divide(divide(X0, inverse(X1)), X2), inverse(Y1)), divide(X0, X2)), X1) -> Y1 % 3.02/3.19 f1(divide(a1, a1)) -> true__ % 3.02/3.19 f1(divide(b1, b1)) -> false__ % 3.02/3.19 f1(divide(inverse(a1), inverse(a1))) -> true__ % 3.02/3.19 f1(divide(inverse(b1), inverse(b1))) -> false__ % 3.02/3.19 f1(g1) -> false__ % 3.02/3.19 f1(g1) -> true__ % 3.02/3.19 f1(g2) -> false__ % 3.02/3.19 f1(g2) -> true__ % 3.02/3.19 f1(multiply(inverse(a1), a1)) -> true__ % 3.02/3.19 g1 -> g2 % 3.02/3.19 inverse(Y1) -> divide(g2, Y1) % 3.02/3.19 multiply(Y0, multiply(inverse(X1), X1)) -> Y0 % 3.02/3.19 multiply(g2, Y1) -> Y1 % 3.02/3.19 multiply(inverse(Y0), Y0) -> g1 % 3.02/3.19 multiply(inverse(Y0), multiply(Y0, Y1)) -> Y1 % 3.02/3.19 multiply(inverse(Y0), multiply(inverse(inverse(Y1)), Y0)) -> Y1 % 3.02/3.19 multiply(inverse(divide(X1, X1)), Y0) -> Y0 % 3.02/3.19 multiply(inverse(multiply(inverse(X1), X1)), Y0) -> Y0 % 3.02/3.19 multiply(inverse(multiply(inverse(X1), Y0)), Y0) -> X1 % 3.02/3.19 true__ -> false__ % 3.02/3.19 with the LPO induced by % 3.02/3.19 inverse > g1 > divide > g2 > a1 > b1 > multiply > f1 > true__ > false__ % 3.02/3.19 % 3.02/3.19 % SZS output end Proof % 3.02/3.19 %------------------------------------------------------------------------------