%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : BOO075-1 : TPTP v8.1.0. Released v2.6.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n024.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 : Thu Jul 14 23:46:47 EDT 2022 % Result : Unsatisfiable 21.08s 21.24s % Output : Proof 21.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : BOO075-1 : TPTP v8.1.0. Released v2.6.0. % 0.03/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n024.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 : Wed Jun 1 20:26:21 EDT 2022 % 0.12/0.34 % CPUTime : % 21.08/21.24 % SZS status Unsatisfiable % 21.08/21.24 % SZS output start Proof % 21.08/21.24 The input problem is unsatisfiable because % 21.08/21.24 % 21.08/21.24 [1] the following set of Horn clauses is unsatisfiable: % 21.08/21.24 % 21.08/21.24 nand(nand(A, nand(nand(B, A), A)), nand(B, nand(C, A))) = B % 21.08/21.24 nand(nand(a, a), nand(b, a)) = a ==> \bottom % 21.08/21.24 % 21.08/21.24 This holds because % 21.08/21.24 % 21.08/21.24 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 21.08/21.24 % 21.08/21.24 E: % 21.08/21.24 f1(a) = false__ % 21.08/21.24 f1(nand(nand(a, a), nand(b, a))) = true__ % 21.08/21.24 nand(nand(A, nand(nand(B, A), A)), nand(B, nand(C, A))) = B % 21.08/21.24 G: % 21.08/21.24 true__ = false__ % 21.08/21.24 % 21.08/21.24 This holds because % 21.08/21.24 % 21.08/21.24 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 21.08/21.24 % 21.08/21.24 % 21.08/21.24 f1(a) -> false__ % 21.08/21.24 f1(nand(nand(a, a), nand(b, a))) -> true__ % 21.08/21.24 nand(X0, nand(Y1, nand(nand(nand(X0, X0), Y1), Y1))) -> nand(X0, X0) % 21.08/21.24 nand(X0, nand(nand(X0, X0), nand(Y1, nand(nand(nand(X0, X0), Y1), Y1)))) -> nand(X0, X0) % 21.08/21.24 nand(X0, nand(nand(X1, X0), nand(X0, nand(X1, X0)))) -> nand(X0, X0) % 21.08/21.24 nand(Y0, nand(X1, nand(Y0, Y0))) -> nand(Y0, Y0) % 21.08/21.24 nand(Y1, nand(nand(X0, nand(nand(Y1, X0), X0)), Y1)) -> nand(X0, nand(nand(Y1, X0), X0)) % 21.08/21.24 nand(Y1, nand(nand(nand(nand(Y0, Y1), nand(Y0, Y1)), Y1), Y1)) -> nand(Y0, Y1) % 21.08/21.24 nand(Y2, nand(nand(Y2, Y2), Y2)) -> nand(Y2, Y2) % 21.08/21.24 nand(Y2, nand(nand(Y2, Y2), nand(Y3, nand(Y2, Y2)))) -> nand(Y2, Y2) % 21.08/21.24 nand(nand(A, nand(nand(B, A), A)), nand(B, nand(C, A))) -> B % 21.08/21.24 nand(nand(X0, nand(X1, X0)), nand(X0, nand(X0, nand(X1, X0)))) -> X0 % 21.08/21.24 nand(nand(X0, nand(nand(X1, X0), X0)), nand(X1, nand(X0, nand(nand(X1, X0), X0)))) -> X1 % 21.08/21.24 nand(nand(Y0, Y0), nand(X1, Y0)) -> Y0 % 21.08/21.24 nand(nand(Y0, Y0), nand(X1, nand(nand(Y0, X1), X1))) -> Y0 % 21.08/21.24 nand(nand(Y0, nand(nand(Y1, Y0), Y0)), nand(Y1, Y1)) -> Y1 % 21.08/21.24 nand(nand(Y0, nand(nand(nand(X0, X0), Y0), Y0)), X0) -> nand(X0, X0) % 21.08/21.24 nand(nand(Y1, Y1), nand(Y1, nand(Y2, Y1))) -> Y1 % 21.08/21.24 nand(nand(Y1, Y1), nand(Y1, nand(Y2, nand(nand(Y1, Y2), Y2)))) -> Y1 % 21.08/21.24 nand(nand(Y1, nand(nand(Y3, Y1), Y1)), nand(Y3, nand(X0, nand(nand(Y1, X0), X0)))) -> Y3 % 21.08/21.24 nand(nand(nand(X0, X1), X0), nand(nand(X0, X1), nand(nand(X0, X1), X0))) -> nand(X0, X1) % 21.08/21.24 nand(nand(nand(X0, nand(X1, X0)), nand(X0, nand(X1, X0))), X0) -> nand(X0, nand(X1, X0)) % 21.08/21.24 nand(nand(nand(X1, X0), nand(X0, nand(X1, X0))), X0) -> nand(X0, X0) % 21.08/21.24 nand(nand(nand(X1, X0), nand(X1, X0)), X0) -> nand(X1, X0) % 21.08/21.24 nand(nand(nand(X1, X0), nand(X1, X0)), nand(nand(X1, X0), X0)) -> nand(X1, X0) % 21.08/21.24 nand(nand(nand(X1, nand(X2, X0)), nand(X1, nand(X1, nand(X2, X0)))), nand(nand(X0, nand(nand(X1, X0), X0)), nand(Y2, nand(X1, nand(X2, X0))))) -> nand(X0, nand(nand(X1, X0), X0)) % 21.08/21.24 nand(nand(nand(X2, X0), nand(nand(nand(X0, nand(nand(Y2, X0), X0)), nand(X2, X0)), nand(X2, X0))), Y2) -> nand(X0, nand(nand(Y2, X0), X0)) % 21.08/21.24 nand(nand(nand(Y0, X1), nand(nand(Y3, nand(Y0, X1)), nand(Y0, X1))), nand(Y3, Y0)) -> Y3 % 21.08/21.24 nand(nand(nand(Y0, Y1), nand(Y0, Y1)), nand(nand(Y0, Y1), Y0)) -> nand(Y0, Y1) % 21.08/21.24 true__ -> false__ % 21.08/21.24 with the LPO induced by % 21.08/21.24 b > nand > a > f1 > true__ > false__ % 21.08/21.24 % 21.08/21.24 % SZS output end Proof % 21.08/21.24 %------------------------------------------------------------------------------