%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP522-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n003.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 10:56:00 EDT 2022 % Result : Unsatisfiable 2.23s 2.38s % Output : Proof 2.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : GRP522-1 : TPTP v8.1.0. Released v2.6.0. % 0.04/0.14 % Command : moca.sh %s % 0.14/0.35 % Computer : n003.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Tue Jun 14 07:54:40 EDT 2022 % 0.14/0.36 % CPUTime : % 2.23/2.38 % SZS status Unsatisfiable % 2.23/2.38 % SZS output start Proof % 2.23/2.38 The input problem is unsatisfiable because % 2.23/2.38 % 2.23/2.38 [1] the following set of Horn clauses is unsatisfiable: % 2.23/2.38 % 2.23/2.38 divide(A, divide(B, divide(C, divide(A, B)))) = C % 2.23/2.38 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 2.23/2.38 inverse(A) = divide(divide(B, B), A) % 2.23/2.38 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom % 2.23/2.38 % 2.23/2.38 This holds because % 2.23/2.38 % 2.23/2.38 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 2.23/2.38 % 2.23/2.38 E: % 2.23/2.38 divide(A, divide(B, divide(C, divide(A, B)))) = C % 2.23/2.38 f1(a2) = false__ % 2.23/2.38 f1(multiply(multiply(inverse(b2), b2), a2)) = true__ % 2.23/2.38 inverse(A) = divide(divide(B, B), A) % 2.23/2.38 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 2.23/2.38 G: % 2.23/2.38 true__ = false__ % 2.23/2.38 % 2.23/2.38 This holds because % 2.23/2.38 % 2.23/2.38 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 2.23/2.38 % 2.23/2.38 divide(X1, X1) = divide(Y0, Y0) % 2.23/2.38 divide(X1, X1) = inverse(divide(Y0, Y0)) % 2.23/2.38 divide(A, divide(B, divide(C, divide(A, B)))) -> C % 2.23/2.38 divide(X0, divide(X1, inverse(X0))) -> inverse(X1) % 2.23/2.38 divide(Y0, divide(X1, X1)) -> Y0 % 2.23/2.38 divide(Y0, divide(divide(X1, divide(X2, divide(Y0, X1))), divide(Y2, X2))) -> Y2 % 2.23/2.38 divide(Y0, divide(divide(X2, divide(Y2, Y0)), X2)) -> Y2 % 2.23/2.38 divide(Y0, inverse(divide(X1, X1))) -> Y0 % 2.23/2.38 divide(Y0, inverse(divide(Y2, Y0))) -> Y2 % 2.23/2.38 divide(Y1, divide(Y1, Y2)) -> Y2 % 2.23/2.38 divide(divide(B, B), A) -> inverse(A) % 2.23/2.38 divide(divide(X0, X1), X0) -> inverse(X1) % 2.23/2.38 divide(inverse(divide(X0, X0)), Y1) -> inverse(Y1) % 2.23/2.38 divide(inverse(divide(X1, Y1)), inverse(X1)) -> Y1 % 2.23/2.38 divide(inverse(divide(inverse(X0), Y1)), X0) -> Y1 % 2.23/2.38 f1(a2) -> false__ % 2.23/2.38 f1(inverse(inverse(a2))) -> true__ % 2.23/2.38 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__ % 2.23/2.38 inverse(divide(Y1, divide(Y2, inverse(Y1)))) -> Y2 % 2.23/2.38 inverse(divide(divide(Y1, Y2), Y1)) -> Y2 % 2.23/2.38 inverse(divide(divide(Y1, divide(Y2, divide(X0, X0))), Y1)) -> Y2 % 2.23/2.38 inverse(divide(inverse(X0), divide(Y1, X0))) -> Y1 % 2.23/2.38 inverse(inverse(Y1)) -> Y1 % 2.23/2.38 multiply(A, B) -> divide(A, inverse(B)) % 2.23/2.38 true__ -> false__ % 2.23/2.38 with the LPO induced by % 2.23/2.38 b2 > multiply > divide > inverse > a2 > f1 > true__ > false__ % 2.23/2.38 % 2.23/2.38 % SZS output end Proof % 2.23/2.38 %------------------------------------------------------------------------------