%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP448-1 : 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 10:55:31 EDT 2022 % Result : Unsatisfiable 2.72s 2.81s % Output : Proof 2.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GRP448-1 : TPTP v8.1.0. Released v2.6.0. % 0.06/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n015.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Mon Jun 13 10:38:37 EDT 2022 % 0.14/0.34 % CPUTime : % 2.72/2.81 % SZS status Unsatisfiable % 2.72/2.81 % SZS output start Proof % 2.72/2.81 The input problem is unsatisfiable because % 2.72/2.81 % 2.72/2.81 [1] the following set of Horn clauses is unsatisfiable: % 2.72/2.81 % 2.72/2.81 divide(A, divide(divide(divide(divide(B, B), B), C), divide(divide(divide(B, B), A), C))) = B % 2.72/2.81 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 2.72/2.81 inverse(A) = divide(divide(B, B), A) % 2.72/2.81 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom % 2.72/2.81 % 2.72/2.81 This holds because % 2.72/2.81 % 2.72/2.81 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 2.72/2.81 % 2.72/2.81 E: % 2.72/2.81 divide(A, divide(divide(divide(divide(B, B), B), C), divide(divide(divide(B, B), A), C))) = B % 2.72/2.81 f1(multiply(inverse(a1), a1)) = true__ % 2.72/2.81 f1(multiply(inverse(b1), b1)) = false__ % 2.72/2.81 inverse(A) = divide(divide(B, B), A) % 2.72/2.81 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 2.72/2.81 G: % 2.72/2.81 true__ = false__ % 2.72/2.81 % 2.72/2.81 This holds because % 2.72/2.81 % 2.72/2.81 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 2.72/2.81 % 2.72/2.81 % 2.72/2.81 divide(A, divide(divide(divide(divide(B, B), B), C), divide(divide(divide(B, B), A), C))) -> B % 2.72/2.81 divide(X1, X1) -> g1 % 2.72/2.81 divide(Y0, divide(divide(inverse(Y1), Y2), divide(inverse(Y0), Y2))) -> Y1 % 2.72/2.81 divide(Y0, divide(g1, divide(divide(g1, Y0), X0))) -> divide(g1, divide(g1, divide(g1, X0))) % 2.72/2.81 divide(Y0, divide(g1, divide(g1, Y0))) -> g1 % 2.72/2.81 divide(Y0, inverse(divide(inverse(Y0), inverse(Y1)))) -> Y1 % 2.72/2.81 divide(Y1, g1) -> Y1 % 2.72/2.81 divide(divide(divide(g1, X0), X1), divide(g1, X1)) -> divide(g1, divide(g1, divide(g1, X0))) % 2.72/2.81 divide(divide(g1, Y0), divide(g1, divide(Y0, divide(g1, Y1)))) -> Y1 % 2.72/2.81 divide(divide(g1, Y0), divide(g1, divide(Y0, g1))) -> g1 % 2.72/2.81 divide(divide(g1, divide(g1, Y0)), g1) -> divide(Y0, g1) % 2.72/2.81 divide(g1, divide(divide(X0, Y1), divide(g1, Y1))) -> divide(g1, divide(g1, divide(g1, X0))) % 2.72/2.81 divide(g1, divide(g1, divide(g1, divide(g1, Y0)))) -> Y0 % 2.72/2.81 divide(g1, inverse(divide(g1, inverse(Y1)))) -> Y1 % 2.72/2.81 divide(inverse(X0), inverse(divide(X0, inverse(Y1)))) -> Y1 % 2.72/2.81 divide(inverse(Y0), inverse(divide(Y0, g1))) -> g1 % 2.72/2.81 divide(inverse(inverse(Y0)), g1) -> divide(Y0, g1) % 2.72/2.81 divide(inverse(inverse(Y0)), inverse(X1)) -> divide(Y0, divide(g1, X1)) % 2.72/2.81 f1(divide(inverse(a1), inverse(a1))) -> true__ % 2.72/2.81 f1(g1) -> false__ % 2.72/2.81 f1(g1) -> true__ % 2.72/2.81 f1(inverse(divide(X1, X1))) -> false__ % 2.72/2.81 f1(inverse(divide(X1, X1))) -> true__ % 2.72/2.81 f1(multiply(inverse(a1), a1)) -> true__ % 2.72/2.81 f1(multiply(inverse(b1), b1)) -> false__ % 2.72/2.81 g2 -> g1 % 2.72/2.81 inverse(Y1) -> divide(g1, Y1) % 2.72/2.81 inverse(divide(divide(inverse(Y0), inverse(inverse(inverse(X0)))), X0)) -> Y0 % 2.72/2.81 inverse(divide(divide(inverse(Y1), Y2), divide(inverse(divide(X0, X0)), Y2))) -> Y1 % 2.72/2.81 inverse(divide(divide(inverse(Y1), Y2), divide(inverse(inverse(divide(X0, X0))), Y2))) -> Y1 % 2.72/2.81 inverse(divide(divide(inverse(Y1), Y2), inverse(Y2))) -> Y1 % 2.72/2.81 inverse(inverse(divide(inverse(inverse(divide(X0, X0))), inverse(Y1)))) -> Y1 % 2.72/2.81 inverse(inverse(inverse(inverse(Y1)))) -> Y1 % 2.72/2.81 multiply(A, B) -> divide(A, divide(g1, B)) % 2.72/2.81 true__ -> false__ % 2.72/2.81 with the LPO induced by % 2.72/2.81 a1 > b1 > multiply > g2 > inverse > divide > g1 > f1 > true__ > false__ % 2.72/2.81 % 2.72/2.81 % SZS output end Proof % 2.72/2.81 %------------------------------------------------------------------------------