%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN035-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n025.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 0.18s 0.38s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SYN035-1 : TPTP v8.1.0. Released v1.0.0. % 0.06/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n025.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 : Mon Jul 11 21:41:47 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.38 % SZS status Unsatisfiable % 0.18/0.38 % SZS output start Proof % 0.18/0.38 The input problem is unsatisfiable because % 0.18/0.38 % 0.18/0.38 [1] the following set of Horn clauses is unsatisfiable: % 0.18/0.38 % 0.18/0.38 p(A, B) % 0.18/0.38 p(f(A, B), f(A, B)) & p(B, f(A, B)) ==> q(A, B) % 0.18/0.38 q(f(A, B), f(A, B)) & q(A, f(A, B)) & p(f(A, B), f(A, B)) & p(B, f(A, B)) ==> \bottom % 0.18/0.38 % 0.18/0.38 This holds because % 0.18/0.38 % 0.18/0.38 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.18/0.38 % 0.18/0.38 E: % 0.18/0.38 f1(true__, A, B) = q(A, B) % 0.18/0.38 f2(p(B, f(A, B)), A, B) = true__ % 0.18/0.38 f2(true__, A, B) = f1(p(f(A, B), f(A, B)), A, B) % 0.18/0.38 f3(true__) = false__ % 0.18/0.38 f4(true__, A, B) = f3(q(f(A, B), f(A, B))) % 0.18/0.38 f5(true__, A, B) = f4(q(A, f(A, B)), A, B) % 0.18/0.38 f6(p(B, f(A, B)), A, B) = true__ % 0.18/0.38 f6(true__, A, B) = f5(p(f(A, B), f(A, B)), A, B) % 0.18/0.38 p(A, B) = true__ % 0.18/0.38 G: % 0.18/0.38 true__ = false__ % 0.18/0.38 % 0.18/0.38 This holds because % 0.18/0.38 % 0.18/0.38 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.18/0.38 % 0.18/0.38 % 0.18/0.38 f1(true__, Y1, Y0) -> true__ % 0.18/0.38 f2(p(B, f(A, B)), A, B) -> true__ % 0.18/0.38 f2(true__, A, B) -> f1(p(f(A, B), f(A, B)), A, B) % 0.18/0.38 f3(true__) -> false__ % 0.18/0.38 f4(f1(true__, Y1, f(Y1, Y0)), Y1, Y0) -> true__ % 0.18/0.38 f4(true__, A, B) -> f3(q(f(A, B), f(A, B))) % 0.18/0.38 f5(true__, A, B) -> f4(q(A, f(A, B)), A, B) % 0.18/0.38 f6(p(B, f(A, B)), A, B) -> true__ % 0.18/0.38 f6(true__, A, B) -> f5(p(f(A, B), f(A, B)), A, B) % 0.18/0.38 false__ -> true__ % 0.18/0.38 p(A, B) -> true__ % 0.18/0.38 q(A, B) -> f1(true__, A, B) % 0.18/0.38 with the LPO induced by % 0.18/0.38 f6 > f5 > f4 > q > f3 > f2 > f > p > f1 > false__ > true__ % 0.18/0.38 % 0.18/0.38 % SZS output end Proof % 0.18/0.38 %------------------------------------------------------------------------------