%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP581-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n018.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 10:56:25 EDT 2022 % Result : Unsatisfiable 0.93s 1.15s % Output : Proof 0.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP581-1 : TPTP v8.1.0. Released v2.6.0. % 0.03/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n018.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % 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 04:33:42 EDT 2022 % 0.12/0.34 % CPUTime : % 0.93/1.15 % SZS status Unsatisfiable % 0.93/1.15 % SZS output start Proof % 0.93/1.15 The input problem is unsatisfiable because % 0.93/1.15 % 0.93/1.15 [1] the following set of Horn clauses is unsatisfiable: % 0.93/1.15 % 0.93/1.15 double_divide(double_divide(A, double_divide(double_divide(identity, B), double_divide(C, double_divide(B, A)))), double_divide(identity, identity)) = C % 0.93/1.15 multiply(A, B) = double_divide(double_divide(B, A), identity) % 0.93/1.15 inverse(A) = double_divide(A, identity) % 0.93/1.15 identity = double_divide(A, inverse(A)) % 0.93/1.15 multiply(inverse(a1), a1) = identity ==> \bottom % 0.93/1.15 % 0.93/1.15 This holds because % 0.93/1.15 % 0.93/1.15 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.93/1.15 % 0.93/1.15 E: % 0.93/1.15 double_divide(double_divide(A, double_divide(double_divide(identity, B), double_divide(C, double_divide(B, A)))), double_divide(identity, identity)) = C % 0.93/1.15 f1(identity) = false__ % 0.93/1.15 f1(multiply(inverse(a1), a1)) = true__ % 0.93/1.15 identity = double_divide(A, inverse(A)) % 0.93/1.15 inverse(A) = double_divide(A, identity) % 0.93/1.15 multiply(A, B) = double_divide(double_divide(B, A), identity) % 0.93/1.15 G: % 0.93/1.15 true__ = false__ % 0.93/1.15 % 0.93/1.15 This holds because % 0.93/1.15 % 0.93/1.15 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.93/1.15 % 0.93/1.15 double_divide(double_divide(identity, double_divide(inverse(identity), X2)), inverse(identity)) = double_divide(X0, double_divide(double_divide(identity, X1), double_divide(X2, double_divide(X1, X0)))) % 0.93/1.15 double_divide(A, identity) -> inverse(A) % 0.93/1.15 double_divide(A, inverse(A)) -> identity % 0.93/1.15 double_divide(double_divide(A, double_divide(double_divide(identity, B), double_divide(C, double_divide(B, A)))), double_divide(identity, identity)) -> C % 0.93/1.15 double_divide(double_divide(Y0, double_divide(double_divide(identity, Y1), double_divide(Y2, double_divide(Y1, Y0)))), inverse(identity)) -> Y2 % 0.93/1.15 double_divide(double_divide(Y0, double_divide(identity, double_divide(Y2, double_divide(inverse(identity), Y0)))), inverse(identity)) -> Y2 % 0.93/1.15 double_divide(double_divide(Y0, double_divide(inverse(identity), double_divide(Y2, double_divide(identity, Y0)))), inverse(identity)) -> Y2 % 0.93/1.15 double_divide(double_divide(identity, double_divide(double_divide(identity, Y1), double_divide(Y2, inverse(Y1)))), inverse(identity)) -> Y2 % 0.93/1.15 double_divide(double_divide(identity, double_divide(identity, double_divide(Y1, inverse(inverse(identity))))), inverse(identity)) -> Y1 % 0.93/1.15 double_divide(double_divide(identity, inverse(double_divide(identity, Y0))), inverse(identity)) -> Y0 % 0.93/1.15 double_divide(double_divide(identity, inverse(inverse(identity))), inverse(identity)) -> identity % 0.93/1.15 double_divide(double_divide(inverse(Y1), double_divide(double_divide(identity, Y1), inverse(Y2))), inverse(identity)) -> Y2 % 0.93/1.15 double_divide(double_divide(inverse(double_divide(inverse(identity), double_divide(X1, inverse(identity)))), X1), inverse(identity)) -> identity % 0.93/1.15 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(Y1))), inverse(identity)) -> Y1 % 0.93/1.15 double_divide(double_divide(inverse(inverse(double_divide(identity, X0))), X0), inverse(identity)) -> identity % 0.93/1.15 double_divide(double_divide(inverse(inverse(identity)), double_divide(identity, inverse(Y1))), inverse(identity)) -> Y1 % 0.93/1.15 double_divide(false__, double_divide(double_divide(identity, false__), double_divide(X0, double_divide(false__, false__)))) -> double_divide(identity, inverse(double_divide(identity, X0))) % 0.93/1.15 double_divide(false__, double_divide(double_divide(identity, false__), double_divide(double_divide(Y1, inverse(identity)), double_divide(false__, false__)))) -> Y1 % 0.93/1.15 double_divide(false__, double_divide(double_divide(identity, false__), double_divide(double_divide(identity, X0), double_divide(false__, false__)))) -> inverse(inverse(X0)) % 0.93/1.15 double_divide(false__, double_divide(double_divide(identity, false__), double_divide(identity, double_divide(false__, false__)))) -> identity % 0.93/1.15 double_divide(identity, Y0) -> inverse(inverse(inverse(Y0))) % 0.93/1.15 double_divide(identity, inverse(double_divide(identity, inverse(Y0)))) -> Y0 % 0.93/1.15 double_divide(identity, inverse(inverse(identity))) -> identity % 0.93/1.15 double_divide(inverse(inverse(Y0)), inverse(identity)) -> double_divide(identity, Y0) % 0.93/1.15 f1(identity) -> false__ % 0.93/1.15 f1(inverse(identity)) -> true__ % 0.93/1.15 f1(multiply(inverse(a1), a1)) -> true__ % 0.93/1.15 inverse(double_divide(identity, double_divide(identity, inverse(Y0)))) -> Y0 % 0.93/1.15 inverse(double_divide(identity, inverse(double_divide(identity, Y0)))) -> Y0 % 0.93/1.15 inverse(double_divide(inverse(Y0), inverse(double_divide(identity, Y0)))) -> identity % 0.93/1.15 inverse(double_divide(inverse(inverse(double_divide(identity, Y0))), Y0)) -> identity % 0.93/1.15 inverse(identity) -> identity % 0.93/1.15 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 0.93/1.15 true__ -> false__ % 0.93/1.15 with the LPO induced by % 0.93/1.15 a1 > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 0.93/1.15 % 0.93/1.15 % SZS output end Proof % 0.93/1.15 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