%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP526-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n009.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 10:56:02 EDT 2022 % Result : Unsatisfiable 2.55s 2.70s % Output : Proof 2.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP526-1 : TPTP v8.1.0. Released v2.6.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n009.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 09:25:53 EDT 2022 % 0.13/0.34 % CPUTime : % 2.55/2.70 % SZS status Unsatisfiable % 2.55/2.70 % SZS output start Proof % 2.55/2.70 The input problem is unsatisfiable because % 2.55/2.70 % 2.55/2.70 [1] the following set of Horn clauses is unsatisfiable: % 2.55/2.70 % 2.55/2.70 divide(A, divide(divide(A, B), divide(C, B))) = C % 2.55/2.70 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 2.55/2.70 inverse(A) = divide(divide(B, B), A) % 2.55/2.70 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom % 2.55/2.70 % 2.55/2.70 This holds because % 2.55/2.70 % 2.55/2.70 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 2.55/2.70 % 2.55/2.70 E: % 2.55/2.70 divide(A, divide(divide(A, B), divide(C, B))) = C % 2.55/2.70 f1(a2) = false__ % 2.55/2.70 f1(multiply(multiply(inverse(b2), b2), a2)) = true__ % 2.55/2.70 inverse(A) = divide(divide(B, B), A) % 2.55/2.70 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 2.55/2.70 G: % 2.55/2.70 true__ = false__ % 2.55/2.70 % 2.55/2.70 This holds because % 2.55/2.70 % 2.55/2.70 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 2.55/2.70 % 2.55/2.70 % 2.55/2.70 divide(A, divide(divide(A, B), divide(C, B))) -> C % 2.55/2.70 divide(X1, X1) -> g1 % 2.55/2.70 divide(Y0, divide(X2, divide(Y2, divide(divide(Y0, X1), divide(X2, X1))))) -> Y2 % 2.55/2.70 divide(Y0, divide(Y0, Y1)) -> Y1 % 2.55/2.70 divide(Y0, divide(Y3, divide(Y2, divide(Y0, Y3)))) -> Y2 % 2.55/2.70 divide(Y0, divide(g1, divide(Y1, Y0))) -> Y1 % 2.55/2.70 divide(Y0, g1) -> Y0 % 2.55/2.70 divide(Y3, divide(Y1, divide(Y2, divide(g1, divide(Y1, Y3))))) -> Y2 % 2.55/2.70 divide(divide(X1, X0), X1) -> divide(g1, X0) % 2.55/2.70 divide(divide(Y0, Y3), divide(Y1, Y3)) -> divide(Y0, Y1) % 2.55/2.70 divide(divide(Y0, divide(X2, X1)), X1) -> divide(Y0, X2) % 2.55/2.70 divide(divide(g1, X1), divide(Y1, X1)) -> divide(g1, Y1) % 2.55/2.70 divide(divide(g1, divide(Y0, Y1)), divide(g1, Y0)) -> Y1 % 2.55/2.70 divide(g1, divide(X0, divide(Y2, divide(g1, X0)))) -> Y2 % 2.55/2.70 divide(g1, divide(g1, Y0)) -> Y0 % 2.55/2.70 f1(a2) -> false__ % 2.55/2.70 f1(divide(g1, divide(g1, a2))) -> true__ % 2.55/2.70 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__ % 2.55/2.70 g2 -> g1 % 2.55/2.70 inverse(Y1) -> divide(g1, Y1) % 2.55/2.70 inverse(divide(inverse(inverse(divide(X1, Y1))), X1)) -> Y1 % 2.55/2.70 multiply(A, B) -> divide(A, divide(g1, B)) % 2.55/2.70 true__ -> false__ % 2.55/2.70 with the LPO induced by % 2.55/2.70 b2 > multiply > g2 > inverse > divide > g1 > a2 > f1 > true__ > false__ % 2.55/2.70 % 2.55/2.70 % SZS output end Proof % 2.55/2.70 %------------------------------------------------------------------------------