%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SWV021-10 : TPTP v8.1.0. Released v7.5.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n026.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 : Wed Jul 20 20:40:59 EDT 2022 % Result : Unknown 3.29s 3.50s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV021-10 : TPTP v8.1.0. Released v7.5.0. % 0.12/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n026.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Wed Jun 15 12:46:52 EDT 2022 % 0.13/0.34 % CPUTime : % 3.29/3.50 % SZS status Satisfiable % 3.29/3.50 % SZS output start Proof % 3.29/3.50 The input problem is satisfiable because % 3.29/3.50 % 3.29/3.50 [1] the following set of Horn clauses is satisfiable: % 3.29/3.50 % 3.29/3.50 ifeq(A, A, B, C) = B % 3.29/3.50 n0 = s(X) ==> \bottom % 3.29/3.50 ifeq(s(X), s(Y), X, Y) = Y % 3.29/3.50 add(n0, Y) = Y % 3.29/3.50 add(s(X), Y) = s(add(X, Y)) % 3.29/3.50 add(X, Y) = add(Y, X) % 3.29/3.50 % 3.29/3.50 This holds because % 3.29/3.50 % 3.29/3.50 [2] the following E does not entail the following G (Claessen-Smallbone's transformation (2018)): % 3.29/3.50 % 3.29/3.50 E: % 3.29/3.50 add(X, Y) = add(Y, X) % 3.29/3.50 add(n0, Y) = Y % 3.29/3.50 add(s(X), Y) = s(add(X, Y)) % 3.29/3.50 f1(n0) = false__ % 3.29/3.50 f1(s(X)) = true__ % 3.29/3.50 ifeq(A, A, B, C) = B % 3.29/3.50 ifeq(s(X), s(Y), X, Y) = Y % 3.29/3.50 G: % 3.29/3.50 true__ = false__ % 3.29/3.50 % 3.29/3.50 This holds because % 3.29/3.50 % 3.29/3.50 [3] the following ground-complete ordered TRS entails E but does not entail G: % 3.29/3.50 % 3.29/3.50 add(X, Y) = add(Y, X) % 3.29/3.50 s(add(Y1, Y0)) = s(add(Y0, Y1)) % 3.29/3.50 add(Y1, n0) -> Y1 % 3.29/3.50 add(Y1, s(Y0)) -> s(add(Y1, Y0)) % 3.29/3.50 add(n0, Y) -> Y % 3.29/3.50 add(s(X), Y) -> s(add(X, Y)) % 3.29/3.50 f1(n0) -> false__ % 3.29/3.50 f1(s(X)) -> true__ % 3.29/3.50 ifeq(A, A, B, C) -> B % 3.29/3.50 ifeq(s(X), s(Y), X, Y) -> Y % 3.29/3.50 with the LPO induced by % 3.29/3.50 ifeq > add > s > n0 > f1 > true__ > false__ % 3.29/3.50 % 3.29/3.50 % SZS output end Proof % 3.29/3.50 %------------------------------------------------------------------------------