%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP557-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n025.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 10:56:15 EDT 2022 % Result : Unsatisfiable 2.80s 2.95s % Output : Proof 2.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP557-1 : TPTP v8.1.0. Released v2.6.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n025.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Tue Jun 14 00:40:24 EDT 2022 % 0.13/0.34 % CPUTime : % 2.80/2.95 % SZS status Unsatisfiable % 2.80/2.95 % SZS output start Proof % 2.80/2.95 The input problem is unsatisfiable because % 2.80/2.95 % 2.80/2.95 [1] the following set of Horn clauses is unsatisfiable: % 2.80/2.95 % 2.80/2.95 divide(A, inverse(divide(divide(B, C), divide(A, C)))) = B % 2.80/2.95 multiply(A, B) = divide(A, inverse(B)) % 2.80/2.95 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom % 2.80/2.95 % 2.80/2.95 This holds because % 2.80/2.95 % 2.80/2.95 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 2.80/2.95 % 2.80/2.95 E: % 2.80/2.95 divide(A, inverse(divide(divide(B, C), divide(A, C)))) = B % 2.80/2.95 f1(multiply(inverse(a1), a1)) = true__ % 2.80/2.95 f1(multiply(inverse(b1), b1)) = false__ % 2.80/2.95 multiply(A, B) = divide(A, inverse(B)) % 2.80/2.95 G: % 2.80/2.95 true__ = false__ % 2.80/2.95 % 2.80/2.95 This holds because % 2.80/2.95 % 2.80/2.95 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 2.80/2.95 % 2.80/2.95 multiply(Y0, divide(Y1, multiply(Y0, Y1))) = inverse(g1) % 2.80/2.95 divide(A, inverse(B)) -> multiply(A, B) % 2.80/2.95 divide(A, inverse(divide(divide(B, C), divide(A, C)))) -> B % 2.80/2.95 divide(X1, X1) -> g1 % 2.80/2.95 divide(Y0, g1) -> Y0 % 2.80/2.95 divide(Y0, inverse(divide(X1, divide(Y0, inverse(divide(divide(X1, X2), divide(Y1, X2))))))) -> Y1 % 2.80/2.95 divide(Y0, inverse(divide(Y1, divide(Y0, inverse(divide(Y1, Y3)))))) -> Y3 % 2.80/2.95 divide(Y0, inverse(divide(Y1, inverse(divide(divide(inverse(divide(X1, X1)), Y3), divide(Y0, Y3)))))) -> Y1 % 2.80/2.95 divide(Y0, inverse(divide(divide(Y1, inverse(divide(Y2, Y0))), Y2))) -> Y1 % 2.80/2.95 divide(Y0, inverse(divide(divide(Y1, inverse(divide(divide(X1, X2), divide(Y0, X2)))), X1))) -> Y1 % 2.80/2.95 divide(Y0, inverse(inverse(inverse(divide(X1, X1))))) -> Y0 % 2.80/2.95 divide(Y0, inverse(inverse(inverse(inverse(divide(X1, X1)))))) -> Y0 % 2.80/2.95 divide(inverse(divide(divide(X1, X2), divide(Y1, X2))), inverse(X1)) -> Y1 % 2.80/2.95 f1(divide(inverse(a1), inverse(a1))) -> true__ % 2.80/2.95 f1(g1) -> false__ % 2.80/2.95 f1(g1) -> true__ % 2.80/2.95 f1(multiply(inverse(a1), a1)) -> true__ % 2.80/2.95 f1(multiply(inverse(b1), b1)) -> false__ % 2.80/2.95 g2 -> inverse(g1) % 2.80/2.95 inverse(divide(divide(X1, X1), Y1)) -> Y1 % 2.80/2.95 inverse(divide(g1, Y1)) -> Y1 % 2.80/2.95 inverse(g1) -> g1 % 2.80/2.95 inverse(inverse(g1)) -> g1 % 2.80/2.95 multiply(Y0, divide(X1, Y0)) -> X1 % 2.80/2.95 multiply(Y0, divide(Y1, multiply(Y0, Y1))) -> g1 % 2.80/2.95 multiply(Y0, g1) -> Y0 % 2.80/2.95 multiply(Y0, inverse(divide(X1, X1))) -> Y0 % 2.80/2.95 multiply(Y0, multiply(false__, divide(false__, multiply(false__, false__)))) -> Y0 % 2.80/2.95 multiply(Y0, multiply(inverse(X1), X1)) -> Y0 % 2.80/2.95 multiply(false__, divide(false__, multiply(false__, false__))) -> g1 % 2.80/2.95 multiply(g1, Y1) -> Y1 % 2.80/2.95 multiply(inverse(X1), multiply(Y1, X1)) -> Y1 % 2.80/2.95 multiply(inverse(Y1), Y1) -> g1 % 2.80/2.95 multiply(inverse(divide(X1, X1)), Y1) -> Y1 % 2.80/2.95 multiply(inverse(divide(X1, Y1)), X1) -> Y1 % 2.80/2.95 multiply(inverse(inverse(divide(X1, X1))), Y1) -> Y1 % 2.80/2.95 multiply(multiply(false__, divide(false__, multiply(false__, false__))), Y1) -> Y1 % 2.80/2.95 true__ -> false__ % 2.80/2.95 with the LPO induced by % 2.80/2.95 a1 > b1 > g2 > inverse > divide > multiply > g1 > f1 > true__ > false__ % 2.80/2.95 % 2.80/2.95 % SZS output end Proof % 2.80/2.95 %------------------------------------------------------------------------------