%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP457-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n015.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 10:55:35 EDT 2022 % Result : Unsatisfiable 0.12s 0.39s % Output : Proof 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP457-1 : TPTP v8.1.0. Released v2.6.0. % 0.11/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n015.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 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Mon Jun 13 07:25:37 EDT 2022 % 0.12/0.34 % CPUTime : % 0.12/0.39 % SZS status Unsatisfiable % 0.12/0.39 % SZS output start Proof % 0.12/0.39 The input problem is unsatisfiable because % 0.12/0.39 % 0.12/0.39 [1] the following set of Horn clauses is unsatisfiable: % 0.12/0.39 % 0.12/0.39 divide(divide(divide(A, A), divide(A, divide(B, divide(divide(identity, A), C)))), C) = B % 0.12/0.39 multiply(A, B) = divide(A, divide(identity, B)) % 0.12/0.39 inverse(A) = divide(identity, A) % 0.12/0.39 identity = divide(A, A) % 0.12/0.39 multiply(inverse(a1), a1) = identity ==> \bottom % 0.12/0.39 % 0.12/0.39 This holds because % 0.12/0.39 % 0.12/0.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.12/0.39 % 0.12/0.39 E: % 0.12/0.39 divide(divide(divide(A, A), divide(A, divide(B, divide(divide(identity, A), C)))), C) = B % 0.12/0.39 f1(identity) = false__ % 0.12/0.39 f1(multiply(inverse(a1), a1)) = true__ % 0.12/0.39 identity = divide(A, A) % 0.12/0.39 inverse(A) = divide(identity, A) % 0.12/0.39 multiply(A, B) = divide(A, divide(identity, B)) % 0.12/0.39 G: % 0.12/0.39 true__ = false__ % 0.12/0.39 % 0.12/0.39 This holds because % 0.12/0.39 % 0.12/0.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.12/0.39 % 0.12/0.39 % 0.12/0.39 divide(A, A) -> identity % 0.12/0.39 divide(divide(divide(A, A), divide(A, divide(B, divide(divide(identity, A), C)))), C) -> B % 0.12/0.39 divide(divide(inverse(identity), inverse(divide(Y1, divide(inverse(identity), Y2)))), Y2) -> Y1 % 0.12/0.39 divide(divide(inverse(identity), inverse(divide(Y1, inverse(Y2)))), Y2) -> Y1 % 0.12/0.39 divide(identity, A) -> inverse(A) % 0.12/0.39 divide(inverse(Y0), inverse(divide(Y0, identity))) -> identity % 0.12/0.39 divide(inverse(divide(Y0, divide(Y1, divide(inverse(Y0), Y2)))), Y2) -> Y1 % 0.12/0.39 divide(inverse(divide(Y0, divide(Y1, identity))), inverse(Y0)) -> Y1 % 0.12/0.39 divide(inverse(divide(Y0, identity)), Y2) -> divide(inverse(Y0), Y2) % 0.12/0.39 divide(inverse(divide(Y0, inverse(divide(inverse(Y0), Y2)))), Y2) -> identity % 0.12/0.39 divide(inverse(inverse(divide(X0, identity))), Y1) -> divide(inverse(inverse(X0)), Y1) % 0.12/0.39 divide(inverse(inverse(divide(Y0, inverse(Y1)))), Y1) -> Y0 % 0.12/0.39 divide(inverse(inverse(divide(Y1, identity))), identity) -> Y1 % 0.12/0.39 divide(inverse(inverse(inverse(inverse(Y1)))), Y1) -> identity % 0.12/0.39 f1(identity) -> false__ % 0.12/0.39 f1(multiply(inverse(a1), a1)) -> true__ % 0.12/0.39 inverse(identity) -> identity % 0.12/0.39 inverse(inverse(divide(Y1, identity))) -> Y1 % 0.12/0.39 multiply(A, B) -> divide(A, divide(identity, B)) % 0.12/0.39 true__ -> false__ % 0.12/0.39 with the LPO induced by % 0.12/0.39 a1 > f1 > multiply > divide > identity > inverse > true__ > false__ % 0.12/0.39 % 0.12/0.39 % SZS output end Proof % 0.12/0.39 %------------------------------------------------------------------------------