%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN033-1 : TPTP v8.1.0. Released v1.0.0. % 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 : Thu Jul 21 09:13:09 EDT 2022 % Result : Unsatisfiable 0.68s 0.91s % Output : Proof 0.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SYN033-1 : TPTP v8.1.0. Released v1.0.0. % 0.04/0.13 % 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 : Mon Jul 11 15:54:42 EDT 2022 % 0.13/0.34 % CPUTime : % 0.68/0.91 % SZS status Unsatisfiable % 0.68/0.91 % SZS output start Proof % 0.68/0.91 The input problem is unsatisfiable because % 0.68/0.91 % 0.68/0.91 [1] the following set of Horn clauses is unsatisfiable: % 0.68/0.91 % 0.68/0.91 p(g(A, B), A, B) % 0.68/0.91 p(A, h(A, B), B) % 0.68/0.91 p(A, B, C) & p(D, E, B) & p(A, D, F) ==> p(F, E, C) % 0.68/0.91 p(k(A), A, k(A)) ==> \bottom % 0.68/0.91 % 0.68/0.91 This holds because % 0.68/0.91 % 0.68/0.91 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.68/0.91 % 0.68/0.91 E: % 0.68/0.91 f1(true__, F, E, C) = p(F, E, C) % 0.68/0.91 f2(true__, A, B, C, F, E) = f1(p(A, B, C), F, E, C) % 0.68/0.91 f3(p(A, D, F), D, E, B, A, C, F) = true__ % 0.68/0.91 f3(true__, D, E, B, A, C, F) = f2(p(D, E, B), A, B, C, F, E) % 0.68/0.91 f4(p(k(A), A, k(A))) = true__ % 0.68/0.91 f4(true__) = false__ % 0.68/0.91 p(A, h(A, B), B) = true__ % 0.68/0.91 p(g(A, B), A, B) = true__ % 0.68/0.91 G: % 0.68/0.91 true__ = false__ % 0.68/0.91 % 0.68/0.91 This holds because % 0.68/0.91 % 0.68/0.91 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.68/0.91 % 0.68/0.91 % 0.68/0.91 f1(f1(true__, Y0, Y3, Y4), Y1, h(h(Y0, Y1), Y3), Y4) -> true__ % 0.68/0.91 f1(f1(true__, Y0, h(Y0, Y1), Y4), Y1, h(X1, X1), Y4) -> true__ % 0.68/0.91 f1(f1(true__, g(Y0, Y3), Y2, Y4), Y3, h(Y0, Y2), Y4) -> true__ % 0.68/0.91 f1(f1(true__, g(Y2, Y3), Y2, Y4), Y3, h(X1, X1), Y4) -> true__ % 0.68/0.91 f1(f1(true__, g(g(Y1, Y2), Y3), Y2, Y4), Y3, Y1, Y4) -> true__ % 0.68/0.91 f1(true__, Y0, h(Y0, Y2), Y2) -> true__ % 0.68/0.91 f1(true__, Y1, h(Y0, h(X1, X1)), g(Y0, Y1)) -> true__ % 0.68/0.91 f1(true__, Y1, h(Y0, h(g(Y0, Y1), Y3)), Y3) -> true__ % 0.68/0.91 f1(true__, Y2, Y0, g(g(Y0, h(X1, X1)), Y2)) -> true__ % 0.68/0.91 f1(true__, Y3, h(Y2, Y2), Y3) -> true__ % 0.68/0.91 f1(true__, Y3, h(h(Y0, Y3), h(Y0, Y2)), Y2) -> true__ % 0.68/0.91 f1(true__, Y3, h(h(g(Y1, Y2), Y3), Y1), Y2) -> true__ % 0.68/0.91 f1(true__, g(Y1, Y2), Y1, Y2) -> true__ % 0.68/0.91 f2(f1(true__, Y1, Y3, Y4), g(Y1, Y2), Y4, Y5, Y2, Y3) -> true__ % 0.68/0.91 f2(f1(true__, h(X1, X1), Y3, Y4), Y2, Y4, Y5, Y2, Y3) -> true__ % 0.68/0.91 f2(f1(true__, h(Y0, Y2), Y3, Y4), Y0, Y4, Y5, Y2, Y3) -> true__ % 0.68/0.91 f2(f1(true__, h(h(g(X1, Y2), Y0), X1), Y3, Y4), Y0, Y4, Y5, Y2, Y3) -> true__ % 0.68/0.91 f2(true__, A, B, C, F, E) -> f1(p(A, B, C), F, E, C) % 0.68/0.91 f3(f1(true__, Y0, Y1, Y2), Y1, Y3, Y4, Y0, Y5, Y2) -> true__ % 0.68/0.91 f3(p(A, D, F), D, E, B, A, C, F) -> true__ % 0.68/0.91 f3(true__, D, E, B, A, C, F) -> f2(p(D, E, B), A, B, C, F, E) % 0.68/0.91 f4(f1(true__, k(Y0), Y0, k(Y0))) -> true__ % 0.68/0.91 f4(p(k(A), A, k(A))) -> true__ % 0.68/0.91 f4(true__) -> false__ % 0.68/0.91 false__ -> true__ % 0.68/0.91 p(A, h(A, B), B) -> true__ % 0.68/0.91 p(F, E, C) -> f1(true__, F, E, C) % 0.68/0.91 p(g(A, B), A, B) -> true__ % 0.68/0.91 with the LPO induced by % 0.68/0.91 k > f4 > f3 > f2 > p > f1 > h > g > false__ > true__ % 0.68/0.91 % 0.68/0.91 % SZS output end Proof % 0.68/0.91 %------------------------------------------------------------------------------