%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP530-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n012.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 10:56:04 EDT 2022 % Result : Unsatisfiable 0.48s 0.70s % Output : Proof 0.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GRP530-1 : TPTP v8.1.0. Released v2.6.0. % 0.04/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n012.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 03:36:55 EDT 2022 % 0.13/0.34 % CPUTime : % 0.48/0.70 % SZS status Unsatisfiable % 0.48/0.70 % SZS output start Proof % 0.48/0.70 The input problem is unsatisfiable because % 0.48/0.70 % 0.48/0.70 [1] the following set of Horn clauses is unsatisfiable: % 0.48/0.70 % 0.48/0.70 divide(divide(A, divide(B, C)), divide(A, B)) = C % 0.48/0.70 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 0.48/0.70 inverse(A) = divide(divide(B, B), A) % 0.48/0.70 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom % 0.48/0.70 % 0.48/0.70 This holds because % 0.48/0.70 % 0.48/0.70 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.48/0.70 % 0.48/0.70 E: % 0.48/0.70 divide(divide(A, divide(B, C)), divide(A, B)) = C % 0.48/0.70 f1(a2) = false__ % 0.48/0.70 f1(multiply(multiply(inverse(b2), b2), a2)) = true__ % 0.48/0.70 inverse(A) = divide(divide(B, B), A) % 0.48/0.70 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 0.48/0.70 G: % 0.48/0.70 true__ = false__ % 0.48/0.70 % 0.48/0.70 This holds because % 0.48/0.70 % 0.48/0.70 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.48/0.70 % 0.48/0.70 divide(Y0, Y0) = divide(X0, X0) % 0.48/0.70 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 0.48/0.70 divide(X1, inverse(divide(Y1, X1))) -> Y1 % 0.48/0.70 divide(X2, divide(divide(Y1, divide(Y2, X2)), Y1)) -> Y2 % 0.48/0.70 divide(Y1, divide(X0, X0)) -> Y1 % 0.48/0.70 divide(divide(A, divide(B, C)), divide(A, B)) -> C % 0.48/0.70 divide(divide(B, B), A) -> inverse(A) % 0.48/0.70 divide(divide(X0, X1), X0) -> inverse(X1) % 0.48/0.70 divide(divide(Y0, X2), divide(Y0, divide(X0, divide(X1, X2)))) -> divide(X0, X1) % 0.48/0.70 divide(divide(Y0, inverse(Y2)), divide(Y0, divide(X0, X0))) -> Y2 % 0.48/0.70 divide(inverse(X0), divide(X1, X1)) -> inverse(X0) % 0.48/0.70 divide(inverse(divide(X0, X0)), Y1) -> inverse(Y1) % 0.48/0.70 divide(inverse(divide(Y1, Y2)), inverse(Y1)) -> Y2 % 0.48/0.70 divide(inverse(divide(divide(divide(X0, X1), X0), Y1)), X1) -> Y1 % 0.48/0.70 divide(inverse(divide(inverse(X0), Y1)), X0) -> Y1 % 0.48/0.70 divide(inverse(inverse(Y1)), inverse(divide(X0, X0))) -> Y1 % 0.48/0.70 divide(inverse(inverse(divide(X0, X0))), Y1) -> inverse(Y1) % 0.48/0.70 f1(a2) -> false__ % 0.48/0.70 f1(inverse(inverse(a2))) -> true__ % 0.48/0.70 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__ % 0.48/0.70 inverse(divide(X0, divide(Y1, Y1))) -> inverse(X0) % 0.48/0.70 inverse(divide(divide(Y1, Y2), Y1)) -> Y2 % 0.48/0.70 inverse(divide(inverse(Y1), divide(X0, X0))) -> Y1 % 0.48/0.70 inverse(divide(inverse(Y1), inverse(divide(X0, X0)))) -> Y1 % 0.48/0.70 inverse(inverse(Y1)) -> Y1 % 0.48/0.70 true__ -> false__ % 0.48/0.70 with the LPO induced by % 0.48/0.70 b2 > a2 > f1 > multiply > divide > inverse > true__ > false__ % 0.48/0.70 % 0.48/0.70 % SZS output end Proof % 0.48/0.70 %------------------------------------------------------------------------------