%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : CAT017-4 : TPTP v8.1.0. Released v1.0.0. % 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 : Fri Jul 15 00:05:01 EDT 2022 % Result : Unsatisfiable 8.16s 8.22s % Output : Proof 8.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : CAT017-4 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n024.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 : Sun May 29 16:51:36 EDT 2022 % 0.13/0.35 % CPUTime : % 8.16/8.22 % SZS status Unsatisfiable % 8.16/8.22 % SZS output start Proof % 8.16/8.22 The input problem is unsatisfiable because % 8.16/8.22 % 8.16/8.22 [1] the following set of Horn clauses is unsatisfiable: % 8.16/8.22 % 8.16/8.22 equivalent(X, Y) ==> there_exists(X) % 8.16/8.22 equivalent(X, Y) ==> X = Y % 8.16/8.22 there_exists(X) & X = Y ==> equivalent(X, Y) % 8.16/8.22 there_exists(domain(X)) ==> there_exists(X) % 8.16/8.22 there_exists(codomain(X)) ==> there_exists(X) % 8.16/8.22 there_exists(compose(X, Y)) ==> there_exists(domain(X)) % 8.16/8.22 there_exists(compose(X, Y)) ==> domain(X) = codomain(Y) % 8.16/8.22 there_exists(domain(X)) & domain(X) = codomain(Y) ==> there_exists(compose(X, Y)) % 8.16/8.22 compose(X, compose(Y, Z)) = compose(compose(X, Y), Z) % 8.16/8.22 compose(X, domain(X)) = X % 8.16/8.22 compose(codomain(X), X) = X % 8.16/8.22 there_exists(a) % 8.16/8.22 there_exists(codomain(a)) ==> \bottom % 8.16/8.22 % 8.16/8.22 This holds because % 8.16/8.22 % 8.16/8.22 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 8.16/8.22 % 8.16/8.22 E: % 8.16/8.22 compose(X, compose(Y, Z)) = compose(compose(X, Y), Z) % 8.16/8.22 compose(X, domain(X)) = X % 8.16/8.22 compose(codomain(X), X) = X % 8.16/8.22 f1(equivalent(X, Y), X) = true__ % 8.16/8.22 f1(true__, X) = there_exists(X) % 8.16/8.22 f10(codomain(Y), Y, X) = f9(there_exists(domain(X)), X, Y) % 8.16/8.22 f10(domain(X), Y, X) = true__ % 8.16/8.22 f11(there_exists(codomain(a))) = true__ % 8.16/8.22 f11(true__) = false__ % 8.16/8.22 f2(equivalent(X, Y), X, Y) = Y % 8.16/8.22 f2(true__, X, Y) = X % 8.16/8.22 f3(true__, X, Y) = equivalent(X, Y) % 8.16/8.22 f4(X, Y, X) = true__ % 8.16/8.22 f4(Y, Y, X) = f3(there_exists(X), X, Y) % 8.16/8.22 f5(there_exists(domain(X)), X) = true__ % 8.16/8.22 f5(true__, X) = there_exists(X) % 8.16/8.22 f6(there_exists(codomain(X)), X) = true__ % 8.16/8.22 f6(true__, X) = there_exists(X) % 8.16/8.22 f7(there_exists(compose(X, Y)), X) = true__ % 8.16/8.22 f7(true__, X) = there_exists(domain(X)) % 8.16/8.22 f8(there_exists(compose(X, Y)), X, Y) = codomain(Y) % 8.16/8.22 f8(true__, X, Y) = domain(X) % 8.16/8.22 f9(true__, X, Y) = there_exists(compose(X, Y)) % 8.16/8.22 there_exists(a) = true__ % 8.16/8.22 G: % 8.16/8.22 true__ = false__ % 8.16/8.22 % 8.16/8.22 This holds because % 8.16/8.22 % 8.16/8.22 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 8.16/8.22 % 8.16/8.22 % 8.16/8.22 codomain(domain(a)) -> domain(a) % 8.16/8.22 compose(X, domain(X)) -> X % 8.16/8.22 compose(Y0, compose(Y1, domain(compose(Y0, Y1)))) -> compose(Y0, Y1) % 8.16/8.22 compose(Y0, compose(domain(Y0), Y2)) -> compose(Y0, Y2) % 8.16/8.22 compose(Y0, domain(domain(Y0))) -> Y0 % 8.16/8.22 compose(codomain(X), X) -> X % 8.16/8.22 compose(codomain(Y1), compose(Y1, Y2)) -> compose(Y1, Y2) % 8.16/8.22 compose(codomain(a), codomain(a)) -> codomain(a) % 8.16/8.22 compose(codomain(codomain(Y1)), Y1) -> Y1 % 8.16/8.22 compose(compose(X, Y), Z) -> compose(X, compose(Y, Z)) % 8.16/8.22 compose(domain(a), domain(a)) -> domain(a) % 8.16/8.22 domain(codomain(a)) -> codomain(a) % 8.16/8.22 domain(domain(a)) -> domain(a) % 8.16/8.22 equivalent(a, a) -> true__ % 8.16/8.22 equivalent(codomain(a), codomain(a)) -> true__ % 8.16/8.22 equivalent(domain(a), domain(a)) -> true__ % 8.16/8.22 f1(equivalent(X, Y), X) -> true__ % 8.16/8.22 f1(true__, a) -> true__ % 8.16/8.22 f1(true__, codomain(a)) -> true__ % 8.16/8.22 f1(true__, domain(a)) -> true__ % 8.16/8.22 f1(true__, domain(codomain(a))) -> true__ % 8.16/8.22 f1(true__, domain(codomain(codomain(a)))) -> true__ % 8.16/8.22 f1(true__, domain(codomain(domain(codomain(a))))) -> true__ % 8.16/8.22 f1(true__, domain(domain(a))) -> true__ % 8.16/8.22 f1(true__, domain(domain(codomain(a)))) -> true__ % 8.16/8.22 f1(true__, domain(domain(domain(a)))) -> true__ % 8.16/8.22 f10(codomain(Y), Y, X) -> f9(there_exists(domain(X)), X, Y) % 8.16/8.22 f10(codomain(a), Y1, codomain(a)) -> true__ % 8.16/8.22 f10(domain(X), Y, X) -> true__ % 8.16/8.22 f10(domain(a), Y1, domain(a)) -> true__ % 8.16/8.22 f11(f1(true__, codomain(a))) -> true__ % 8.16/8.22 f11(there_exists(codomain(a))) -> true__ % 8.16/8.22 f11(true__) -> false__ % 8.16/8.22 f2(equivalent(X, Y), X, Y) -> Y % 8.16/8.22 f2(true__, X, Y) -> X % 8.16/8.22 f3(f1(true__, Y1), Y1, Y1) -> true__ % 8.16/8.22 f3(true__, X, Y) -> equivalent(X, Y) % 8.16/8.22 f4(X, Y, X) -> true__ % 8.16/8.22 f4(Y, Y, X) -> f3(there_exists(X), X, Y) % 8.16/8.22 f5(f1(true__, domain(Y0)), Y0) -> true__ % 8.16/8.22 f5(there_exists(domain(X)), X) -> true__ % 8.16/8.22 f5(true__, X) -> there_exists(X) % 8.16/8.22 f6(f1(true__, codomain(Y0)), Y0) -> true__ % 8.16/8.22 f6(there_exists(codomain(X)), X) -> true__ % 8.16/8.22 f6(true__, X) -> there_exists(X) % 8.16/8.22 f7(f1(true__, Y0), Y0) -> true__ % 8.16/8.22 f7(f1(true__, Y1), codomain(Y1)) -> true__ % 8.16/8.22 f7(f1(true__, compose(Y0, Y1)), Y0) -> true__ % 8.16/8.22 f7(there_exists(compose(X, Y)), X) -> true__ % 8.16/8.22 f7(true__, X) -> there_exists(domain(X)) % 8.16/8.22 f8(f1(true__, Y0), Y0, domain(Y0)) -> codomain(domain(Y0)) % 8.16/8.22 f8(f1(true__, Y1), codomain(Y1), Y1) -> codomain(Y1) % 8.16/8.22 f8(f1(true__, compose(Y0, Y1)), Y0, Y1) -> codomain(Y1) % 8.16/8.22 f8(there_exists(compose(X, Y)), X, Y) -> codomain(Y) % 8.16/8.22 f8(true__, X, Y) -> domain(X) % 8.16/8.22 f9(true__, X, Y) -> there_exists(compose(X, Y)) % 8.16/8.22 false__ -> true__ % 8.16/8.22 there_exists(X) -> f1(true__, X) % 8.16/8.22 there_exists(a) -> true__ % 8.16/8.22 with the LPO induced by % 8.16/8.22 f11 > f7 > f10 > f9 > a > f2 > f8 > domain > f6 > f5 > f4 > f3 > there_exists > f1 > compose > codomain > equivalent > false__ > true__ % 8.16/8.22 % 8.16/8.22 % SZS output end Proof % 8.16/8.22 %------------------------------------------------------------------------------