%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP446-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n028.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 3.81s 3.88s % Output : Proof 3.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRP446-1 : TPTP v8.1.0. Released v2.6.0. % 0.12/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n028.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Tue Jun 14 03:53:08 EDT 2022 % 0.12/0.33 % CPUTime : % 3.81/3.88 % SZS status Unsatisfiable % 3.81/3.88 % SZS output start Proof % 3.81/3.88 The input problem is unsatisfiable because % 3.81/3.88 % 3.81/3.88 [1] the following set of Horn clauses is unsatisfiable: % 3.81/3.88 % 3.81/3.88 divide(A, divide(divide(divide(divide(A, A), B), C), divide(divide(divide(A, A), A), C))) = B % 3.81/3.88 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 3.81/3.88 inverse(A) = divide(divide(B, B), A) % 3.81/3.88 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom % 3.81/3.88 % 3.81/3.88 This holds because % 3.81/3.88 % 3.81/3.88 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 3.81/3.88 % 3.81/3.88 E: % 3.81/3.88 divide(A, divide(divide(divide(divide(A, A), B), C), divide(divide(divide(A, A), A), C))) = B % 3.81/3.88 f1(a2) = false__ % 3.81/3.88 f1(multiply(multiply(inverse(b2), b2), a2)) = true__ % 3.81/3.88 inverse(A) = divide(divide(B, B), A) % 3.81/3.88 multiply(A, B) = divide(A, divide(divide(C, C), B)) % 3.81/3.88 G: % 3.81/3.88 true__ = false__ % 3.81/3.88 % 3.81/3.88 This holds because % 3.81/3.88 % 3.81/3.88 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 3.81/3.88 % 3.81/3.88 divide(Y0, divide(X0, divide(g1, Y0))) = divide(g1, X0) % 3.81/3.88 divide(A, divide(divide(divide(divide(A, A), B), C), divide(divide(divide(A, A), A), C))) -> B % 3.81/3.88 divide(X0, X0) -> g2 % 3.81/3.88 divide(Y0, divide(divide(X0, Y2), divide(divide(g1, Y0), Y2))) -> divide(g1, X0) % 3.81/3.88 divide(Y0, divide(divide(g1, Y1), divide(g1, Y0))) -> Y1 % 3.81/3.88 divide(Y0, divide(divide(inverse(Y1), Y2), divide(inverse(Y0), Y2))) -> Y1 % 3.81/3.88 divide(Y0, divide(g1, divide(divide(g1, Y0), X0))) -> divide(g1, X0) % 3.81/3.88 divide(Y0, divide(g1, divide(g1, Y0))) -> g1 % 3.81/3.88 divide(Y0, divide(inverse(Y2), divide(inverse(Y0), Y2))) -> g2 % 3.81/3.88 divide(Y0, inverse(divide(inverse(Y0), inverse(Y1)))) -> Y1 % 3.81/3.88 divide(Y1, g1) -> Y1 % 3.81/3.88 divide(divide(g1, X0), divide(divide(g1, Y1), X0)) -> Y1 % 3.81/3.88 divide(divide(g1, X0), divide(g1, divide(X0, Y1))) -> divide(g1, Y1) % 3.81/3.88 divide(divide(g1, Y0), divide(divide(g1, Y2), divide(Y0, Y2))) -> g1 % 3.81/3.88 divide(divide(g1, Y0), divide(g1, divide(Y0, divide(g1, Y1)))) -> Y1 % 3.81/3.88 divide(divide(g1, divide(g1, Y1)), Y1) -> g1 % 3.81/3.88 divide(divide(g1, divide(g1, divide(g1, Y0))), divide(divide(g1, Y2), divide(Y0, Y2))) -> g1 % 3.81/3.88 divide(divide(g1, divide(g1, divide(g1, Y0))), divide(g1, divide(Y0, divide(g1, Y1)))) -> Y1 % 3.81/3.88 divide(divide(g1, divide(g1, divide(g1, Y0))), divide(g1, divide(Y0, g1))) -> g1 % 3.81/3.88 divide(divide(g1, divide(g1, divide(g1, Y2))), divide(divide(g1, Y1), Y2)) -> Y1 % 3.81/3.88 divide(g1, divide(Y1, divide(g1, divide(g1, divide(g1, divide(g1, Y1)))))) -> g1 % 3.81/3.88 divide(g1, divide(divide(Y1, Y2), divide(g1, Y2))) -> divide(g1, Y1) % 3.81/3.88 divide(g1, divide(divide(divide(g1, Y1), Y2), divide(g1, Y2))) -> Y1 % 3.81/3.88 divide(g1, divide(g1, Y0)) -> Y0 % 3.81/3.88 divide(g2, A) -> divide(g1, A) % 3.81/3.88 divide(inverse(inverse(inverse(X0))), divide(divide(inverse(Y1), Y2), divide(X0, Y2))) -> Y1 % 3.81/3.88 divide(inverse(inverse(inverse(X0))), inverse(divide(X0, inverse(Y1)))) -> Y1 % 3.81/3.88 f1(a2) -> false__ % 3.81/3.88 f1(divide(g1, divide(g1, a2))) -> true__ % 3.81/3.88 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__ % 3.81/3.88 g2 -> g1 % 3.81/3.88 inverse(Y1) -> divide(g1, Y1) % 3.81/3.88 inverse(divide(X0, X0)) -> g1 % 3.81/3.88 inverse(divide(divide(inverse(Y0), Y1), divide(inverse(inverse(divide(X0, X0))), Y1))) -> Y0 % 3.81/3.88 inverse(divide(inverse(Y1), divide(inverse(inverse(divide(X0, X0))), Y1))) -> g2 % 3.81/3.88 inverse(g1) -> g1 % 3.81/3.88 inverse(inverse(divide(inverse(inverse(divide(X0, X0))), inverse(Y1)))) -> Y1 % 3.81/3.88 inverse(inverse(g1)) -> g1 % 3.81/3.88 multiply(A, B) -> divide(A, divide(g2, B)) % 3.81/3.88 true__ -> false__ % 3.81/3.88 with the LPO induced by % 3.81/3.88 b2 > multiply > inverse > divide > g2 > g1 > a2 > f1 > true__ > false__ % 3.81/3.88 % 3.81/3.88 % SZS output end Proof % 3.81/3.88 %------------------------------------------------------------------------------