%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP542-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n008.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 10:56:09 EDT 2022 % Result : Unsatisfiable 0.86s 1.00s % Output : Proof 0.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GRP542-1 : TPTP v8.1.0. Released v2.6.0. % 0.06/0.12 % Command : moca.sh %s % 0.13/0.33 % Computer : n008.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Tue Jun 14 08:08:07 EDT 2022 % 0.13/0.34 % CPUTime : % 0.86/1.00 % SZS status Unsatisfiable % 0.86/1.00 % SZS output start Proof % 0.86/1.00 The input problem is unsatisfiable because % 0.86/1.00 % 0.86/1.00 [1] the following set of Horn clauses is unsatisfiable: % 0.86/1.00 % 0.86/1.00 divide(divide(identity, divide(divide(divide(A, B), C), A)), C) = B % 0.86/1.00 multiply(A, B) = divide(A, divide(identity, B)) % 0.86/1.00 inverse(A) = divide(identity, A) % 0.86/1.00 identity = divide(A, A) % 0.86/1.00 multiply(multiply(inverse(b2), b2), a2) = a2 ==> \bottom % 0.86/1.00 % 0.86/1.00 This holds because % 0.86/1.00 % 0.86/1.00 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.86/1.00 % 0.86/1.00 E: % 0.86/1.00 divide(divide(identity, divide(divide(divide(A, B), C), A)), C) = B % 0.86/1.00 f1(a2) = false__ % 0.86/1.00 f1(multiply(multiply(inverse(b2), b2), a2)) = true__ % 0.86/1.00 identity = divide(A, A) % 0.86/1.00 inverse(A) = divide(identity, A) % 0.86/1.00 multiply(A, B) = divide(A, divide(identity, B)) % 0.86/1.00 G: % 0.86/1.00 true__ = false__ % 0.86/1.00 % 0.86/1.00 This holds because % 0.86/1.00 % 0.86/1.00 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.86/1.00 % 0.86/1.00 divide(X0, Y1) = divide(inverse(divide(Y1, identity)), inverse(X0)) % 0.86/1.00 divide(X0, inverse(Y1)) = divide(Y1, inverse(X0)) % 0.86/1.00 divide(inverse(X1), inverse(X0)) = divide(X0, X1) % 0.86/1.00 divide(inverse(Y2), Y1) = divide(inverse(divide(Y1, identity)), Y2) % 0.86/1.00 divide(A, A) -> identity % 0.86/1.00 divide(Y0, divide(Y0, Y1)) -> Y1 % 0.86/1.00 divide(Y1, identity) -> Y1 % 0.86/1.00 divide(divide(divide(X0, X1), Y2), X0) -> divide(inverse(divide(X1, identity)), Y2) % 0.86/1.00 divide(divide(identity, divide(divide(divide(A, B), C), A)), C) -> B % 0.86/1.00 divide(divide(inverse(Y1), Y2), identity) -> divide(inverse(divide(Y1, identity)), Y2) % 0.86/1.00 divide(identity, A) -> inverse(A) % 0.86/1.00 divide(inverse(X0), divide(inverse(X0), Y1)) -> Y1 % 0.86/1.00 divide(inverse(Y0), identity) -> inverse(Y0) % 0.86/1.00 divide(inverse(divide(Y1, identity)), divide(Y0, Y1)) -> inverse(Y0) % 0.86/1.00 divide(inverse(divide(divide(divide(Y0, Y1), Y2), Y0)), Y2) -> Y1 % 0.86/1.00 divide(inverse(divide(divide(inverse(Y1), Y2), identity)), Y2) -> Y1 % 0.86/1.00 divide(inverse(divide(inverse(Y2), Y1)), Y2) -> Y1 % 0.86/1.00 divide(inverse(inverse(Y0)), divide(Y0, Y1)) -> Y1 % 0.86/1.00 divide(inverse(inverse(Y1)), identity) -> Y1 % 0.86/1.00 divide(inverse(inverse(inverse(inverse(X0)))), X1) -> divide(X0, X1) % 0.86/1.00 f1(a2) -> false__ % 0.86/1.00 f1(inverse(inverse(a2))) -> true__ % 0.86/1.00 f1(multiply(multiply(inverse(b2), b2), a2)) -> true__ % 0.86/1.00 inverse(identity) -> identity % 0.86/1.00 inverse(inverse(Y1)) -> Y1 % 0.86/1.00 multiply(A, B) -> divide(A, divide(identity, B)) % 0.86/1.00 true__ -> false__ % 0.86/1.00 with the LPO induced by % 0.86/1.00 b2 > a2 > f1 > multiply > divide > identity > inverse > true__ > false__ % 0.86/1.00 % 0.86/1.00 % SZS output end Proof % 0.86/1.00 %------------------------------------------------------------------------------