%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP578-1 : 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 10:56:24 EDT 2022 % Result : Unsatisfiable 17.85s 17.91s % Output : Proof 17.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : GRP578-1 : TPTP v8.1.0. Released v2.6.0. % 0.12/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n015.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 : Tue Jun 14 00:06:53 EDT 2022 % 0.12/0.34 % CPUTime : % 17.85/17.91 % SZS status Unsatisfiable % 17.85/17.91 % SZS output start Proof % 17.85/17.91 The input problem is unsatisfiable because % 17.85/17.91 % 17.85/17.91 [1] the following set of Horn clauses is unsatisfiable: % 17.85/17.91 % 17.85/17.91 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity))), double_divide(identity, identity)) = C % 17.85/17.91 multiply(A, B) = double_divide(double_divide(B, A), identity) % 17.85/17.91 inverse(A) = double_divide(A, identity) % 17.85/17.91 identity = double_divide(A, inverse(A)) % 17.85/17.91 multiply(identity, a2) = a2 ==> \bottom % 17.85/17.91 % 17.85/17.91 This holds because % 17.85/17.91 % 17.85/17.91 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 17.85/17.91 % 17.85/17.91 E: % 17.85/17.91 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity))), double_divide(identity, identity)) = C % 17.85/17.91 f1(a2) = false__ % 17.85/17.91 f1(multiply(identity, a2)) = true__ % 17.85/17.91 identity = double_divide(A, inverse(A)) % 17.85/17.91 inverse(A) = double_divide(A, identity) % 17.85/17.91 multiply(A, B) = double_divide(double_divide(B, A), identity) % 17.85/17.91 G: % 17.85/17.91 true__ = false__ % 17.85/17.91 % 17.85/17.91 This holds because % 17.85/17.91 % 17.85/17.91 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 17.85/17.92 % 17.85/17.92 double_divide(X0, inverse(identity)) = inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, X0))))) % 17.85/17.92 inverse(double_divide(Y0, inverse(inverse(Y1)))) = inverse(double_divide(Y1, Y0)) % 17.85/17.92 double_divide(A, identity) -> inverse(A) % 17.85/17.92 double_divide(A, inverse(A)) -> identity % 17.85/17.92 double_divide(X0, double_divide(identity, X0)) -> identity % 17.85/17.92 double_divide(X0, double_divide(identity, inverse(double_divide(identity, X0)))) -> inverse(identity) % 17.85/17.92 double_divide(X0, double_divide(identity, inverse(inverse(X0)))) -> identity % 17.85/17.92 double_divide(X0, double_divide(inverse(double_divide(X1, X0)), inverse(X1))) -> identity % 17.85/17.92 double_divide(X0, inverse(inverse(inverse(X0)))) -> identity % 17.85/17.92 double_divide(X1, double_divide(X0, inverse(double_divide(inverse(X0), X1)))) -> identity % 17.85/17.92 double_divide(double_divide(A, double_divide(double_divide(double_divide(B, A), C), double_divide(B, identity))), double_divide(identity, identity)) -> C % 17.85/17.92 double_divide(double_divide(X0, X1), inverse(double_divide(X1, inverse(inverse(X0))))) -> identity % 17.85/17.92 double_divide(double_divide(X0, inverse(double_divide(inverse(X0), X1))), X1) -> identity % 17.85/17.92 double_divide(double_divide(X0, inverse(inverse(X1))), inverse(double_divide(X1, X0))) -> identity % 17.85/17.92 double_divide(double_divide(Y0, double_divide(double_divide(double_divide(Y1, Y0), Y2), inverse(Y1))), inverse(identity)) -> Y2 % 17.85/17.92 double_divide(double_divide(Y0, double_divide(identity, inverse(Y1))), inverse(identity)) -> inverse(double_divide(Y1, Y0)) % 17.85/17.92 double_divide(double_divide(Y0, double_divide(inverse(double_divide(Y1, Y0)), inverse(Y1))), inverse(identity)) -> identity % 17.85/17.92 double_divide(double_divide(Y0, inverse(double_divide(identity, double_divide(identity, Y0)))), inverse(identity)) -> identity % 17.85/17.92 double_divide(double_divide(double_divide(X1, double_divide(identity, Y0)), X2), inverse(X1)) -> double_divide(double_divide(Y0, X2), inverse(identity)) % 17.85/17.92 double_divide(double_divide(double_divide(Y0, inverse(identity)), Y2), inverse(Y0)) -> double_divide(double_divide(identity, Y2), inverse(identity)) % 17.85/17.92 double_divide(double_divide(identity, X0), X0) -> identity % 17.85/17.92 double_divide(double_divide(identity, X0), inverse(inverse(X0))) -> identity % 17.85/17.92 double_divide(double_divide(identity, double_divide(double_divide(inverse(Y1), Y2), inverse(Y1))), inverse(identity)) -> Y2 % 17.85/17.92 double_divide(double_divide(identity, double_divide(identity, X0)), inverse(inverse(inverse(X0)))) -> identity % 17.85/17.92 double_divide(double_divide(identity, double_divide(identity, inverse(double_divide(identity, X0)))), double_divide(X0, inverse(identity))) -> identity % 17.85/17.92 double_divide(double_divide(identity, double_divide(inverse(double_divide(identity, Y0)), inverse(Y0))), inverse(identity)) -> inverse(identity) % 17.85/17.92 double_divide(double_divide(identity, double_divide(inverse(inverse(Y1)), inverse(Y1))), inverse(identity)) -> identity % 17.85/17.92 double_divide(double_divide(identity, inverse(double_divide(identity, X0))), X0) -> identity % 17.85/17.92 double_divide(double_divide(identity, inverse(inverse(Y0))), Y0) -> identity % 17.85/17.92 double_divide(double_divide(identity, inverse(inverse(identity))), inverse(identity)) -> identity % 17.85/17.92 double_divide(double_divide(inverse(Y1), double_divide(double_divide(identity, Y2), inverse(Y1))), inverse(identity)) -> Y2 % 17.85/17.92 double_divide(double_divide(inverse(Y1), double_divide(inverse(identity), inverse(Y1))), inverse(identity)) -> identity % 17.85/17.92 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(double_divide(X0, double_divide(inverse(double_divide(X1, X0)), inverse(X1)))))), inverse(identity)) -> identity % 17.85/17.92 double_divide(double_divide(inverse(identity), double_divide(inverse(inverse(double_divide(identity, X0))), inverse(inverse(X0)))), inverse(identity)) -> identity % 17.85/17.92 double_divide(identity, X0) -> inverse(X0) % 17.85/17.92 double_divide(identity, inverse(inverse(X0))) -> inverse(inverse(inverse(X0))) % 17.85/17.92 double_divide(inverse(X0), X0) -> inverse(identity) % 17.85/17.92 double_divide(inverse(X0), double_divide(identity, inverse(inverse(inverse(X0))))) -> identity % 17.85/17.92 double_divide(inverse(Y0), inverse(identity)) -> inverse(double_divide(identity, Y0)) % 17.85/17.92 double_divide(inverse(double_divide(Y0, double_divide(identity, Y1))), inverse(Y0)) -> double_divide(inverse(Y1), inverse(identity)) % 17.85/17.92 double_divide(inverse(double_divide(Y0, inverse(identity))), inverse(Y0)) -> inverse(inverse(identity)) % 17.85/17.92 double_divide(inverse(inverse(X0)), double_divide(identity, X0)) -> identity % 17.85/17.92 double_divide(inverse(inverse(Y0)), inverse(Y0)) -> inverse(identity) % 17.85/17.92 double_divide(inverse(inverse(double_divide(identity, Y1))), inverse(identity)) -> Y1 % 17.85/17.92 double_divide(inverse(inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, X0))))))))), X0) -> inverse(identity) % 17.85/17.92 double_divide(inverse(inverse(inverse(X0))), X0) -> identity % 17.85/17.92 f1(a2) -> false__ % 17.85/17.92 f1(inverse(inverse(a2))) -> true__ % 17.85/17.92 f1(multiply(identity, a2)) -> true__ % 17.85/17.92 inverse(double_divide(Y0, double_divide(double_divide(double_divide(Y1, Y0), Y2), inverse(Y1)))) -> Y2 % 17.85/17.92 inverse(double_divide(Y0, double_divide(inverse(double_divide(Y1, Y0)), inverse(Y1)))) -> identity % 17.85/17.92 inverse(double_divide(Y0, double_divide(inverse(double_divide(inverse(inverse(inverse(X0))), Y0)), X0))) -> identity % 17.85/17.92 inverse(double_divide(Y0, inverse(double_divide(identity, double_divide(identity, Y0))))) -> identity % 17.85/17.92 inverse(double_divide(Y0, inverse(double_divide(inverse(Y0), Y2)))) -> Y2 % 17.85/17.92 inverse(double_divide(Y0, inverse(inverse(inverse(Y0))))) -> identity % 17.85/17.92 inverse(double_divide(identity, Y0)) -> inverse(inverse(Y0)) % 17.85/17.92 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, X0))))) -> inverse(X0) % 17.85/17.92 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, double_divide(Y0, inverse(double_divide(identity, double_divide(inverse(identity), Y0))))))))) -> identity % 17.85/17.92 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, double_divide(Y0, inverse(inverse(double_divide(identity, Y0))))))))) -> identity % 17.85/17.92 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, inverse(Y0)))))) -> inverse(double_divide(identity, Y0)) % 17.85/17.92 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(identity, inverse(inverse(double_divide(identity, Y1)))))))) -> Y1 % 17.85/17.92 inverse(double_divide(identity, double_divide(identity, inverse(inverse(identity))))) -> identity % 17.85/17.92 inverse(double_divide(identity, inverse(double_divide(identity, Y0)))) -> Y0 % 17.85/17.92 inverse(double_divide(identity, inverse(inverse(identity)))) -> identity % 17.85/17.92 inverse(double_divide(inverse(Y0), double_divide(identity, inverse(Y0)))) -> identity % 17.85/17.92 inverse(double_divide(inverse(Y0), double_divide(inverse(Y1), inverse(Y0)))) -> Y1 % 17.85/17.92 inverse(double_divide(inverse(inverse(inverse(X0))), inverse(double_divide(X0, Y1)))) -> Y1 % 17.85/17.92 inverse(identity) -> identity % 17.85/17.92 inverse(inverse(Y0)) -> Y0 % 17.85/17.92 inverse(inverse(double_divide(double_divide(identity, inverse(inverse(identity))), inverse(identity)))) -> inverse(inverse(identity)) % 17.85/17.92 inverse(inverse(double_divide(double_divide(inverse(Y0), Y1), inverse(Y0)))) -> Y1 % 17.85/17.92 inverse(inverse(identity)) -> inverse(identity) % 17.85/17.92 inverse(inverse(inverse(double_divide(identity, Y0)))) -> Y0 % 17.85/17.92 inverse(inverse(inverse(inverse(Y0)))) -> Y0 % 17.85/17.92 multiply(A, B) -> double_divide(double_divide(B, A), identity) % 17.85/17.92 true__ -> false__ % 17.85/17.92 with the LPO induced by % 17.85/17.92 a2 > f1 > multiply > double_divide > inverse > identity > true__ > false__ % 17.85/17.92 % 17.85/17.92 % SZS output end Proof % 17.85/17.92 %------------------------------------------------------------------------------