%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN062-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n027.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 09:13:31 EDT 2022 % Result : Unsatisfiable 1.30s 1.45s % Output : Proof 1.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SYN062-1 : TPTP v8.1.0. Released v1.0.0. % 0.06/0.12 % Command : moca.sh %s % 0.13/0.33 % Computer : n027.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Tue Jul 12 03:29:04 EDT 2022 % 0.13/0.33 % CPUTime : % 1.30/1.45 % SZS status Unsatisfiable % 1.30/1.45 % SZS output start Proof % 1.30/1.45 The input problem is unsatisfiable because % 1.30/1.45 % 1.30/1.45 [1] the following set of Horn clauses is unsatisfiable: % 1.30/1.45 % 1.30/1.45 big_f(X) & big_g(X) ==> big_i(X) % 1.30/1.45 big_f(X) & big_h(X) ==> big_i(X) % 1.30/1.45 big_i(X) & big_h(X) ==> big_j(X) % 1.30/1.45 big_k(X) ==> big_h(X) % 1.30/1.45 big_f(a) % 1.30/1.45 big_k(a) % 1.30/1.45 big_j(a) ==> \bottom % 1.30/1.45 % 1.30/1.45 This holds because % 1.30/1.45 % 1.30/1.45 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.30/1.45 % 1.30/1.45 E: % 1.30/1.45 big_f(a) = true__ % 1.30/1.45 big_k(a) = true__ % 1.30/1.45 f1(true__, X) = big_i(X) % 1.30/1.45 f2(big_g(X), X) = true__ % 1.30/1.45 f2(true__, X) = f1(big_f(X), X) % 1.30/1.45 f3(true__, X) = big_i(X) % 1.30/1.45 f4(big_h(X), X) = true__ % 1.30/1.45 f4(true__, X) = f3(big_f(X), X) % 1.30/1.45 f5(true__, X) = big_j(X) % 1.30/1.45 f6(big_h(X), X) = true__ % 1.30/1.45 f6(true__, X) = f5(big_i(X), X) % 1.30/1.45 f7(big_k(X), X) = true__ % 1.30/1.45 f7(true__, X) = big_h(X) % 1.30/1.45 f8(big_j(a)) = true__ % 1.30/1.45 f8(true__) = false__ % 1.30/1.45 G: % 1.30/1.45 true__ = false__ % 1.30/1.45 % 1.30/1.45 This holds because % 1.30/1.45 % 1.30/1.45 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.30/1.45 % 1.30/1.45 % 1.30/1.45 big_f(a) -> true__ % 1.30/1.45 big_h(X) -> f7(true__, X) % 1.30/1.45 big_i(X) -> f1(true__, X) % 1.30/1.45 big_j(a) -> true__ % 1.30/1.45 big_k(a) -> true__ % 1.30/1.45 f1(big_f(X), X) -> f2(true__, X) % 1.30/1.45 f1(true__, a) -> f2(true__, a) % 1.30/1.45 f1(true__, a) -> f4(true__, a) % 1.30/1.45 f2(big_g(X), X) -> true__ % 1.30/1.45 f2(true__, a) -> f4(true__, a) % 1.30/1.45 f3(big_f(X), X) -> f4(true__, X) % 1.30/1.45 f3(true__, X) -> big_i(X) % 1.30/1.45 f4(big_h(X), X) -> true__ % 1.30/1.45 f4(f7(true__, Y0), Y0) -> true__ % 1.30/1.45 f4(true__, a) -> true__ % 1.30/1.45 f5(f4(true__, a), a) -> true__ % 1.30/1.45 f5(true__, X) -> big_j(X) % 1.30/1.45 f6(big_h(X), X) -> true__ % 1.30/1.45 f6(f7(true__, Y0), Y0) -> true__ % 1.30/1.45 f6(true__, X) -> f5(big_i(X), X) % 1.30/1.45 f7(big_k(X), X) -> true__ % 1.30/1.45 f7(true__, a) -> true__ % 1.30/1.45 f8(big_j(a)) -> true__ % 1.30/1.45 f8(true__) -> false__ % 1.30/1.45 false__ -> true__ % 1.30/1.45 with the LPO induced by % 1.30/1.45 f8 > a > f6 > f5 > f3 > big_i > f1 > f2 > f4 > big_f > big_k > big_j > big_g > big_h > f7 > false__ > true__ % 1.30/1.45 % 1.30/1.45 % SZS output end Proof % 1.30/1.45 %------------------------------------------------------------------------------