%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP445-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n017.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 10:55:30 EDT 2022 % Result : Unsatisfiable 2.92s 3.05s % Output : Proof 2.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP445-1 : TPTP v8.1.0. Released v2.6.0. % 0.03/0.12 % Command : moca.sh %s % 0.13/0.33 % Computer : n017.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jun 13 13:13:08 EDT 2022 % 0.13/0.34 % CPUTime : % 2.92/3.05 % SZS status Unsatisfiable % 2.92/3.05 % SZS output start Proof % 2.92/3.05 The input problem is unsatisfiable because % 2.92/3.05 % 2.92/3.05 [1] the following set of Horn clauses is unsatisfiable: % 2.92/3.05 % 2.92/3.05 divide(A, divide(divide(divide(divide(A, A), B), C), divide(divide(divide(A, A), A), C))) = B % 2.92/3.05 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 2.92/3.05 inverse(A) = divide(divide(B, B), A) % 2.92/3.05 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom % 2.92/3.05 % 2.92/3.05 This holds because % 2.92/3.05 % 2.92/3.05 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 2.92/3.05 % 2.92/3.05 E: % 2.92/3.05 divide(A, divide(divide(divide(divide(A, A), B), C), divide(divide(divide(A, A), A), C))) = B % 2.92/3.05 f1(multiply(inverse(a1), a1)) = true__ % 2.92/3.05 f1(multiply(inverse(b1), b1)) = false__ % 2.92/3.05 inverse(A) = divide(divide(B, B), A) % 2.92/3.05 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 2.92/3.05 G: % 2.92/3.05 true__ = false__ % 2.92/3.05 % 2.92/3.05 This holds because % 2.92/3.05 % 2.92/3.05 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 2.92/3.05 % 2.92/3.05 % 2.92/3.05 divide(A, divide(divide(C, C), B)) -> multiply(A, B) % 2.92/3.05 divide(Y0, divide(X0, divide(inverse(Y0), inverse(inverse(inverse(X0)))))) -> g1 % 2.92/3.05 divide(Y0, divide(divide(X0, Y2), divide(inverse(Y0), Y2))) -> inverse(inverse(inverse(X0))) % 2.92/3.05 divide(Y0, divide(inverse(Y2), divide(inverse(Y0), Y2))) -> g1 % 2.92/3.05 divide(Y0, divide(inverse(inverse(Y0)), g1)) -> g1 % 2.92/3.05 divide(Y0, inverse(Y2)) -> multiply(Y0, Y2) % 2.92/3.05 divide(Y0, inverse(divide(inverse(Y0), X0))) -> inverse(inverse(inverse(X0))) % 2.92/3.05 divide(Y0, inverse(inverse(Y0))) -> g1 % 2.92/3.05 divide(Y1, Y1) -> g1 % 2.92/3.05 divide(Y1, g1) -> Y1 % 2.92/3.05 divide(g1, Y1) -> inverse(Y1) % 2.92/3.05 divide(inverse(inverse(Y0)), Y0) -> g1 % 2.92/3.05 divide(inverse(inverse(Y1)), divide(Y1, g1)) -> g1 % 2.92/3.05 divide(inverse(inverse(inverse(X0))), divide(divide(inverse(Y1), Y2), divide(X0, Y2))) -> Y1 % 2.92/3.05 divide(inverse(inverse(inverse(X0))), inverse(divide(X0, inverse(Y1)))) -> Y1 % 2.92/3.05 divide(inverse(inverse(inverse(Y0))), inverse(Y0)) -> g1 % 2.92/3.05 divide(inverse(inverse(inverse(Y0))), inverse(divide(Y0, g1))) -> g1 % 2.92/3.05 f1(divide(inverse(a1), inverse(a1))) -> true__ % 2.92/3.05 f1(g1) -> false__ % 2.92/3.05 f1(g1) -> true__ % 2.92/3.05 f1(multiply(inverse(a1), a1)) -> true__ % 2.92/3.05 f1(multiply(inverse(b1), b1)) -> false__ % 2.92/3.05 inverse(divide(divide(Y1, Y2), inverse(Y2))) -> inverse(inverse(inverse(Y1))) % 2.92/3.05 inverse(g1) -> g1 % 2.92/3.05 inverse(inverse(inverse(Y0))) -> inverse(Y0) % 2.92/3.05 inverse(inverse(inverse(inverse(Y1)))) -> Y1 % 2.92/3.05 multiply(Y0, g1) -> Y0 % 2.92/3.05 true__ -> false__ % 2.92/3.05 with the LPO induced by % 2.92/3.05 a1 > f1 > b1 > divide > inverse > g1 > multiply > true__ > false__ % 2.92/3.05 % 2.92/3.05 % SZS output end Proof % 2.92/3.05 %------------------------------------------------------------------------------