%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP487-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n016.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 10:55:46 EDT 2022 % Result : Unsatisfiable 225.98s 226.07s % Output : Proof 225.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP487-1 : TPTP v8.1.0. Released v2.6.0. % 0.07/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n016.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 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Tue Jun 14 02:28:45 EDT 2022 % 0.12/0.34 % CPUTime : % 225.98/226.07 % SZS status Unsatisfiable % 225.98/226.07 % SZS output start Proof % 225.98/226.07 The input problem is unsatisfiable because % 225.98/226.07 % 225.98/226.07 [1] the following set of Horn clauses is unsatisfiable: % 225.98/226.07 % 225.98/226.07 double_divide(A, double_divide(double_divide(double_divide(identity, double_divide(double_divide(A, identity), double_divide(B, C))), B), identity)) = C % 225.98/226.07 multiply(A, B) = double_divide(double_divide(B, A), identity) % 225.98/226.07 inverse(A) = double_divide(A, identity) % 225.98/226.07 identity = double_divide(A, inverse(A)) % 225.98/226.07 multiply(inverse(a1), a1) = identity ==> \bottom % 225.98/226.07 % 225.98/226.07 This holds because % 225.98/226.07 % 225.98/226.07 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 225.98/226.07 % 225.98/226.07 E: % 225.98/226.07 double_divide(A, double_divide(double_divide(double_divide(identity, double_divide(double_divide(A, identity), double_divide(B, C))), B), identity)) = C % 225.98/226.07 f1(identity) = false__ % 225.98/226.07 f1(multiply(inverse(a1), a1)) = true__ % 225.98/226.07 identity = double_divide(A, inverse(A)) % 225.98/226.07 inverse(A) = double_divide(A, identity) % 225.98/226.07 multiply(A, B) = double_divide(double_divide(B, A), identity) % 225.98/226.07 G: % 225.98/226.07 true__ = false__ % 225.98/226.07 % 225.98/226.07 This holds because % 225.98/226.07 % 225.98/226.07 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 225.98/226.07 % 225.98/226.07 % 225.98/226.07 double_divide(A, identity) -> inverse(A) % 225.98/226.07 double_divide(A, inverse(A)) -> identity % 225.98/226.07 double_divide(Y0, double_divide(double_divide(double_divide(identity, identity), double_divide(Y0, identity)), identity)) -> identity % 225.98/226.07 double_divide(Y0, double_divide(double_divide(double_divide(identity, identity), double_divide(double_divide(identity, identity), double_divide(double_divide(Y0, identity), identity))), identity)) -> identity % 225.98/226.07 double_divide(Y0, inverse(double_divide(double_divide(identity, X2), double_divide(double_divide(identity, double_divide(inverse(inverse(Y0)), double_divide(X1, X2))), X1)))) -> identity % 225.98/226.07 double_divide(Y0, inverse(double_divide(double_divide(identity, Y1), inverse(double_divide(identity, double_divide(inverse(inverse(Y0)), double_divide(identity, Y1))))))) -> identity % 225.98/226.07 double_divide(Y0, inverse(double_divide(double_divide(identity, double_divide(inverse(Y0), double_divide(Y1, Y2))), Y1))) -> Y2 % 225.98/226.07 double_divide(Y0, inverse(double_divide(double_divide(identity, double_divide(inverse(Y0), inverse(Y1))), Y1))) -> identity % 225.98/226.07 double_divide(Y0, inverse(double_divide(double_divide(identity, inverse(inverse(Y0))), Y1))) -> inverse(Y1) % 225.98/226.07 double_divide(Y0, inverse(double_divide(identity, inverse(Y0)))) -> identity % 225.98/226.07 double_divide(Y0, inverse(double_divide(inverse(identity), double_divide(double_divide(identity, double_divide(inverse(inverse(Y0)), inverse(Y2))), Y2)))) -> identity % 225.98/226.07 double_divide(Y0, inverse(double_divide(inverse(identity), inverse(Y0)))) -> identity % 225.98/226.07 double_divide(Y0, inverse(inverse(double_divide(identity, double_divide(inverse(Y0), double_divide(identity, Y2)))))) -> Y2 % 225.98/226.07 double_divide(Y0, inverse(inverse(double_divide(identity, inverse(inverse(Y0)))))) -> identity % 225.98/226.07 double_divide(Y0, multiply(double_divide(Y0, identity), double_divide(identity, identity))) -> identity % 225.98/226.07 double_divide(double_divide(double_divide(identity, double_divide(double_divide(Y0, identity), identity)), identity), identity) -> inverse(Y0) % 225.98/226.07 double_divide(double_divide(double_divide(identity, double_divide(double_divide(double_divide(identity, identity), identity), double_divide(X1, X2))), X1), double_divide(X2, identity)) -> identity % 225.98/226.07 double_divide(double_divide(double_divide(identity, double_divide(double_divide(double_divide(identity, identity), identity), identity)), Y0), double_divide(double_divide(Y0, identity), identity)) -> identity % 225.98/226.07 double_divide(double_divide(double_divide(identity, inverse(inverse(inverse(identity)))), X1), inverse(inverse(X1))) -> identity % 225.98/226.07 double_divide(double_divide(identity, inverse(inverse(inverse(identity)))), inverse(double_divide(inverse(identity), Y1))) -> inverse(Y1) % 225.98/226.07 double_divide(identity, inverse(double_divide(identity, Y1))) -> inverse(Y1) % 225.98/226.07 double_divide(inverse(double_divide(identity, inverse(double_divide(identity, inverse(inverse(X0)))))), inverse(X0)) -> identity % 225.98/226.07 double_divide(inverse(double_divide(identity, inverse(inverse(X0)))), double_divide(X0, inverse(identity))) -> identity % 225.98/226.07 double_divide(inverse(double_divide(identity, inverse(inverse(X0)))), inverse(X0)) -> identity % 225.98/226.07 double_divide(inverse(double_divide(identity, inverse(inverse(X0)))), inverse(double_divide(identity, inverse(X0)))) -> identity % 225.98/226.07 double_divide(inverse(double_divide(identity, inverse(inverse(X0)))), inverse(double_divide(inverse(identity), double_divide(X0, inverse(identity))))) -> identity % 225.98/226.07 double_divide(inverse(double_divide(identity, inverse(inverse(inverse(identity))))), inverse(double_divide(identity, Y1))) -> inverse(Y1) % 225.98/226.07 f1(identity) -> false__ % 225.98/226.07 f1(inverse(identity)) -> true__ % 225.98/226.07 false__ -> true__ % 225.98/226.07 inverse(double_divide(identity, inverse(inverse(X0)))) -> inverse(inverse(double_divide(identity, inverse(X0)))) % 225.98/226.07 inverse(identity) -> identity % 225.98/226.07 inverse(inverse(double_divide(double_divide(identity, inverse(inverse(double_divide(identity, inverse(inverse(Y0)))))), X1))) -> double_divide(Y0, inverse(inverse(X1))) % 225.98/226.07 inverse(inverse(double_divide(identity, inverse(double_divide(identity, inverse(inverse(Y0))))))) -> inverse(Y0) % 225.98/226.07 inverse(inverse(double_divide(identity, inverse(inverse(Y0))))) -> inverse(Y0) % 225.98/226.07 multiply(A, B) -> inverse(double_divide(B, A)) % 225.98/226.07 with the LPO induced by % 225.98/226.07 f1 > multiply > double_divide > inverse > identity > a1 > false__ > true__ % 225.98/226.07 % 225.98/226.07 % SZS output end Proof % 225.98/226.07 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