%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP551-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n019.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 10:56:12 EDT 2022 % Result : Unsatisfiable 15.26s 15.28s % Output : Proof 15.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : GRP551-1 : TPTP v8.1.0. Released v2.6.0. % 0.08/0.14 % Command : moca.sh %s % 0.14/0.36 % Computer : n019.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Mon Jun 13 19:20:09 EDT 2022 % 0.14/0.36 % CPUTime : % 15.26/15.28 % SZS status Unsatisfiable % 15.26/15.28 % SZS output start Proof % 15.26/15.28 The input problem is unsatisfiable because % 15.26/15.28 % 15.26/15.28 [1] the following set of Horn clauses is unsatisfiable: % 15.26/15.28 % 15.26/15.28 divide(divide(identity, A), divide(divide(divide(B, A), C), B)) = C % 15.26/15.28 multiply(A, B) = divide(A, divide(identity, B)) % 15.26/15.28 inverse(A) = divide(identity, A) % 15.26/15.28 identity = divide(A, A) % 15.26/15.28 multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)) ==> \bottom % 15.26/15.28 % 15.26/15.28 This holds because % 15.26/15.28 % 15.26/15.28 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 15.26/15.28 % 15.26/15.28 E: % 15.26/15.28 divide(divide(identity, A), divide(divide(divide(B, A), C), B)) = C % 15.26/15.28 f1(multiply(a3, multiply(b3, c3))) = false__ % 15.26/15.28 f1(multiply(multiply(a3, b3), c3)) = true__ % 15.26/15.28 identity = divide(A, A) % 15.26/15.28 inverse(A) = divide(identity, A) % 15.26/15.28 multiply(A, B) = divide(A, divide(identity, B)) % 15.26/15.28 G: % 15.26/15.28 true__ = false__ % 15.26/15.28 % 15.26/15.28 This holds because % 15.26/15.28 % 15.26/15.28 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 15.26/15.28 % 15.26/15.28 divide(X0, inverse(Y1)) = divide(Y1, inverse(X0)) % 15.26/15.28 divide(X0, inverse(Y1)) = divide(Y1, inverse(inverse(inverse(X0)))) % 15.26/15.28 divide(X1, inverse(Y1)) = divide(Y1, inverse(divide(false__, inverse(divide(X0, divide(false__, inverse(divide(X0, X1)))))))) % 15.26/15.28 divide(Y0, X1) = inverse(divide(X0, inverse(divide(X1, divide(X0, inverse(Y0)))))) % 15.26/15.28 divide(divide(X1, X0), inverse(Y1)) = divide(Y1, divide(X0, X1)) % 15.26/15.28 divide(divide(Y0, Y1), divide(X1, X0)) = divide(divide(X0, X1), divide(Y1, Y0)) % 15.26/15.28 divide(inverse(Y0), X0) = divide(inverse(X0), Y0) % 15.26/15.28 divide(inverse(Y0), X0) = divide(inverse(inverse(inverse(X0))), Y0) % 15.26/15.28 divide(inverse(Y0), inverse(Y1)) = divide(Y1, Y0) % 15.26/15.28 inverse(divide(X0, divide(X1, inverse(Y1)))) = divide(X1, divide(X0, Y1)) % 15.26/15.28 inverse(divide(X0, divide(X1, inverse(Y1)))) = divide(Y1, divide(X0, X1)) % 15.26/15.28 inverse(divide(X1, Y0)) = divide(Y0, X1) % 15.26/15.28 inverse(divide(Y0, inverse(X1))) = divide(X0, divide(X1, inverse(divide(X0, inverse(Y0))))) % 15.26/15.28 inverse(divide(Y0, inverse(X1))) = inverse(divide(X0, inverse(divide(X1, divide(X0, Y0))))) % 15.26/15.28 inverse(divide(Y0, inverse(divide(X1, X0)))) = divide(divide(X0, X1), Y0) % 15.26/15.28 inverse(divide(Y0, inverse(divide(X1, Y1)))) = divide(divide(Y1, Y0), X1) % 15.26/15.28 inverse(divide(Y0, inverse(divide(X1, Y1)))) = inverse(divide(X1, divide(Y1, Y0))) % 15.26/15.28 inverse(divide(divide(X2, X0), X1)) = divide(X0, inverse(divide(X1, X2))) % 15.26/15.28 inverse(divide(divide(X2, X1), X0)) = divide(X0, inverse(divide(X1, X2))) % 15.26/15.28 divide(A, A) -> identity % 15.26/15.28 divide(X0, divide(X0, Y1)) -> Y1 % 15.26/15.28 divide(X0, divide(X1, divide(divide(X1, X0), X2))) -> inverse(X2) % 15.26/15.28 divide(X0, divide(inverse(Y1), inverse(X0))) -> Y1 % 15.26/15.28 divide(X0, divide(inverse(Y1), inverse(divide(divide(Y1, inverse(X0)), Y2)))) -> Y2 % 15.26/15.28 divide(X0, inverse(divide(Y1, divide(divide(Y1, inverse(X0)), Y2)))) -> Y2 % 15.26/15.28 divide(X0, inverse(divide(inverse(X0), Y1))) -> inverse(Y1) % 15.26/15.28 divide(X2, divide(X1, divide(divide(X1, X0), X2))) -> inverse(X0) % 15.26/15.28 divide(Y0, divide(X0, inverse(Y0))) -> inverse(X0) % 15.26/15.28 divide(Y0, inverse(divide(Y1, Y0))) -> Y1 % 15.26/15.28 divide(Y1, identity) -> inverse(inverse(Y1)) % 15.26/15.28 divide(divide(X1, X0), divide(Y1, divide(X0, X1))) -> inverse(Y1) % 15.26/15.28 divide(divide(X1, X0), inverse(divide(Y1, inverse(divide(X0, X1))))) -> Y1 % 15.26/15.28 divide(divide(X1, Y1), divide(divide(X1, Y2), Y1)) -> Y2 % 15.26/15.28 divide(divide(Y1, Y0), X1) -> inverse(divide(Y0, divide(Y1, X1))) % 15.26/15.28 divide(divide(identity, A), divide(divide(divide(B, A), C), B)) -> C % 15.26/15.28 divide(identity, A) -> inverse(A) % 15.26/15.28 divide(inverse(X0), inverse(divide(X0, X1))) -> inverse(X1) % 15.26/15.28 divide(inverse(Y0), X1) -> inverse(divide(Y0, inverse(X1))) % 15.26/15.28 divide(inverse(Y0), divide(X0, Y0)) -> inverse(X0) % 15.26/15.28 divide(inverse(Y0), divide(divide(divide(Y1, Y0), Y2), Y1)) -> Y2 % 15.26/15.28 divide(inverse(Y0), divide(divide(inverse(Y0), Y2), identity)) -> Y2 % 15.26/15.28 divide(inverse(Y0), divide(inverse(Y2), Y0)) -> Y2 % 15.26/15.28 divide(inverse(Y0), identity) -> inverse(Y0) % 15.26/15.28 divide(inverse(Y0), inverse(X1)) -> inverse(divide(Y0, X1)) % 15.26/15.28 divide(inverse(inverse(X1)), inverse(inverse(X0))) -> divide(X1, X0) % 15.26/15.28 divide(inverse(inverse(Y1)), identity) -> Y1 % 15.26/15.28 f1(divide(a3, inverse(divide(b3, inverse(c3))))) -> false__ % 15.26/15.28 f1(divide(b3, inverse(divide(a3, inverse(c3))))) -> true__ % 15.26/15.28 f1(divide(divide(a3, inverse(b3)), inverse(c3))) -> true__ % 15.26/15.28 f1(multiply(a3, multiply(b3, c3))) -> false__ % 15.26/15.28 f1(multiply(multiply(a3, b3), c3)) -> true__ % 15.26/15.28 inverse(divide(X0, divide(X1, divide(Y1, divide(X0, X1))))) -> inverse(Y1) % 15.26/15.28 inverse(divide(X0, divide(X1, inverse(divide(Y1, inverse(divide(X0, X1))))))) -> Y1 % 15.26/15.28 inverse(divide(X0, divide(Y1, divide(divide(Y1, X0), Y2)))) -> Y2 % 15.26/15.28 inverse(divide(X0, inverse(divide(inverse(X0), Y1)))) -> Y1 % 15.26/15.28 inverse(divide(X1, divide(divide(X1, X0), X2))) -> inverse(divide(X0, inverse(X2))) % 15.26/15.28 inverse(divide(Y0, inverse(divide(X0, Y0)))) -> inverse(X0) % 15.26/15.28 inverse(divide(Y0, inverse(divide(divide(X1, X0), Y0)))) -> divide(X0, X1) % 15.26/15.28 inverse(divide(divide(Y1, X1), divide(Y1, divide(X1, Y2)))) -> Y2 % 15.26/15.28 inverse(divide(divide(Y1, X1), inverse(divide(divide(X1, Y2), Y1)))) -> Y2 % 15.26/15.28 inverse(divide(divide(divide(Y1, identity), Y2), Y1)) -> Y2 % 15.26/15.28 inverse(divide(false__, inverse(divide(X0, divide(false__, inverse(divide(X0, X1))))))) -> inverse(X1) % 15.26/15.28 inverse(divide(false__, inverse(divide(X0, divide(false__, inverse(divide(X0, inverse(Y1)))))))) -> Y1 % 15.26/15.28 inverse(divide(false__, inverse(divide(X1, divide(false__, divide(Y1, X1)))))) -> inverse(Y1) % 15.26/15.28 inverse(divide(false__, inverse(divide(X1, divide(false__, inverse(divide(Y1, inverse(X1)))))))) -> Y1 % 15.26/15.28 inverse(divide(inverse(X0), inverse(divide(X0, Y1)))) -> Y1 % 15.26/15.28 inverse(divide(inverse(Y0), inverse(X1))) -> divide(Y0, X1) % 15.26/15.28 inverse(divide(inverse(Y0), inverse(divide(X1, inverse(Y0))))) -> inverse(X1) % 15.26/15.28 inverse(divide(inverse(Y0), inverse(divide(inverse(inverse(Y0)), Y1)))) -> Y1 % 15.26/15.28 inverse(divide(inverse(Y1), identity)) -> Y1 % 15.26/15.28 inverse(identity) -> identity % 15.26/15.28 inverse(inverse(Y0)) -> Y0 % 15.26/15.28 inverse(inverse(inverse(Y0))) -> inverse(Y0) % 15.26/15.28 inverse(inverse(inverse(inverse(Y1)))) -> Y1 % 15.26/15.28 multiply(A, B) -> divide(A, divide(identity, B)) % 15.26/15.28 true__ -> false__ % 15.26/15.28 with the LPO induced by % 15.26/15.28 c3 > b3 > a3 > f1 > multiply > divide > identity > inverse > true__ > false__ % 15.26/15.28 % 15.26/15.28 % SZS output end Proof % 15.26/15.28 %------------------------------------------------------------------------------