%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : CAT006-4 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n019.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 00:04:50 EDT 2022 % Result : Unsatisfiable 12.05s 11.96s % Output : Proof 12.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : CAT006-4 : TPTP v8.1.0. Released v1.0.0. % 0.12/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n019.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 17:54:41 EDT 2022 % 0.13/0.35 % CPUTime : % 12.05/11.96 % SZS status Unsatisfiable % 12.05/11.96 % SZS output start Proof % 12.05/11.96 The input problem is unsatisfiable because % 12.05/11.96 % 12.05/11.96 [1] the following set of Horn clauses is unsatisfiable: % 12.05/11.96 % 12.05/11.96 equivalent(X, Y) ==> there_exists(X) % 12.05/11.96 equivalent(X, Y) ==> X = Y % 12.05/11.96 there_exists(X) & X = Y ==> equivalent(X, Y) % 12.05/11.96 there_exists(domain(X)) ==> there_exists(X) % 12.05/11.96 there_exists(codomain(X)) ==> there_exists(X) % 12.05/11.96 there_exists(compose(X, Y)) ==> there_exists(domain(X)) % 12.05/11.96 there_exists(compose(X, Y)) ==> domain(X) = codomain(Y) % 12.05/11.96 there_exists(domain(X)) & domain(X) = codomain(Y) ==> there_exists(compose(X, Y)) % 12.05/11.96 compose(X, compose(Y, Z)) = compose(compose(X, Y), Z) % 12.05/11.96 compose(X, domain(X)) = X % 12.05/11.96 compose(codomain(X), X) = X % 12.05/11.96 there_exists(compose(d, a)) % 12.05/11.96 there_exists(compose(X, d)) ==> compose(X, d) = X % 12.05/11.96 there_exists(compose(d, X)) ==> compose(d, X) = X % 12.05/11.96 codomain(a) = d ==> \bottom % 12.05/11.96 % 12.05/11.96 This holds because % 12.05/11.96 % 12.05/11.96 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 12.05/11.96 % 12.05/11.96 E: % 12.05/11.96 compose(X, compose(Y, Z)) = compose(compose(X, Y), Z) % 12.05/11.96 compose(X, domain(X)) = X % 12.05/11.96 compose(codomain(X), X) = X % 12.05/11.96 f1(equivalent(X, Y), X) = true__ % 12.05/11.96 f1(true__, X) = there_exists(X) % 12.05/11.96 f10(codomain(Y), Y, X) = f9(there_exists(domain(X)), X, Y) % 12.05/11.96 f10(domain(X), Y, X) = true__ % 12.05/11.96 f11(there_exists(compose(X, d)), X) = X % 12.05/11.96 f11(true__, X) = compose(X, d) % 12.05/11.96 f12(there_exists(compose(d, X)), X) = X % 12.05/11.96 f12(true__, X) = compose(d, X) % 12.05/11.96 f13(codomain(a)) = true__ % 12.05/11.96 f13(d) = false__ % 12.05/11.96 f2(equivalent(X, Y), X, Y) = Y % 12.05/11.96 f2(true__, X, Y) = X % 12.05/11.96 f3(true__, X, Y) = equivalent(X, Y) % 12.05/11.96 f4(X, Y, X) = true__ % 12.05/11.96 f4(Y, Y, X) = f3(there_exists(X), X, Y) % 12.05/11.96 f5(there_exists(domain(X)), X) = true__ % 12.05/11.96 f5(true__, X) = there_exists(X) % 12.05/11.96 f6(there_exists(codomain(X)), X) = true__ % 12.05/11.96 f6(true__, X) = there_exists(X) % 12.05/11.96 f7(there_exists(compose(X, Y)), X) = true__ % 12.05/11.96 f7(true__, X) = there_exists(domain(X)) % 12.05/11.96 f8(there_exists(compose(X, Y)), X, Y) = codomain(Y) % 12.05/11.96 f8(true__, X, Y) = domain(X) % 12.05/11.96 f9(true__, X, Y) = there_exists(compose(X, Y)) % 12.05/11.96 there_exists(compose(d, a)) = true__ % 12.05/11.96 G: % 12.05/11.96 true__ = false__ % 12.05/11.96 % 12.05/11.96 This holds because % 12.05/11.96 % 12.05/11.96 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 12.05/11.96 % 12.05/11.96 f8(f1(true__, compose(Y0, Y1)), Y0, Y1) = f8(f1(true__, compose(true__, Y1)), true__, Y1) % 12.05/11.96 f8(there_exists(compose(X, Y)), X, Y) = codomain(Y) % 12.05/11.96 compose(X, d) -> f11(true__, X) % 12.05/11.96 compose(X, domain(X)) -> X % 12.05/11.96 compose(Y0, compose(Y1, domain(compose(Y0, Y1)))) -> compose(Y0, Y1) % 12.05/11.96 compose(Y0, compose(domain(Y0), Y2)) -> compose(Y0, Y2) % 12.05/11.96 compose(Y0, domain(domain(Y0))) -> Y0 % 12.05/11.96 compose(Y0, f11(true__, Y1)) -> f11(true__, compose(Y0, Y1)) % 12.05/11.96 compose(Y0, f11(true__, domain(Y0))) -> f11(true__, Y0) % 12.05/11.96 compose(codomain(X), X) -> X % 12.05/11.96 compose(compose(X, Y), Z) -> compose(X, compose(Y, Z)) % 12.05/11.96 compose(d, X) -> f12(true__, X) % 12.05/11.96 compose(domain(a), domain(a)) -> domain(a) % 12.05/11.96 compose(domain(domain(a)), domain(domain(a))) -> domain(domain(a)) % 12.05/11.96 compose(f11(true__, Y0), Y2) -> compose(Y0, f12(true__, Y2)) % 12.05/11.96 compose(f12(true__, Y1), Y2) -> f12(true__, compose(Y1, Y2)) % 12.05/11.96 compose(f8(f1(true__, Y0), Y0, domain(Y0)), domain(Y0)) -> domain(Y0) % 12.05/11.96 compose(f8(f1(true__, compose(X1, Y0)), X1, Y0), Y0) -> Y0 % 12.05/11.96 compose(f8(f1(true__, compose(true__, Y1)), true__, Y1), compose(Y1, Y2)) -> compose(Y1, Y2) % 12.05/11.96 compose(f8(f1(true__, true__), true__, domain(true__)), compose(domain(true__), Y1)) -> compose(domain(true__), Y1) % 12.05/11.96 domain(d) -> d % 12.05/11.96 domain(f8(f1(true__, compose(true__, a)), true__, a)) -> f8(f1(true__, compose(true__, a)), true__, a) % 12.05/11.96 equivalent(X, Y) -> f3(true__, X, Y) % 12.05/11.96 f1(equivalent(X, Y), X) -> true__ % 12.05/11.96 f1(f3(true__, Y0, Y1), Y0) -> true__ % 12.05/11.96 f1(true__, a) -> true__ % 12.05/11.96 f1(true__, d) -> true__ % 12.05/11.96 f1(true__, domain(a)) -> true__ % 12.05/11.96 f1(true__, domain(d)) -> true__ % 12.05/11.96 f1(true__, domain(domain(a))) -> true__ % 12.05/11.96 f1(true__, domain(domain(d))) -> true__ % 12.05/11.96 f1(true__, domain(domain(domain(a)))) -> true__ % 12.05/11.96 f1(true__, domain(domain(domain(d)))) -> true__ % 12.05/11.96 f1(true__, domain(domain(domain(domain(a))))) -> true__ % 12.05/11.96 f1(true__, domain(domain(domain(domain(domain(a)))))) -> true__ % 12.05/11.96 f1(true__, domain(domain(domain(domain(domain(domain(a))))))) -> true__ % 12.05/11.96 f1(true__, domain(f12(true__, a))) -> true__ % 12.05/11.96 f1(true__, domain(f8(f1(true__, compose(true__, a)), true__, a))) -> true__ % 12.05/11.96 f1(true__, domain(f8(f1(true__, compose(true__, domain(a))), true__, domain(a)))) -> true__ % 12.05/11.96 f1(true__, f12(true__, a)) -> true__ % 12.05/11.96 f10(codomain(Y), Y, X) -> f9(there_exists(domain(X)), X, Y) % 12.05/11.96 f10(d, Y1, d) -> true__ % 12.05/11.96 f10(domain(X), Y, X) -> true__ % 12.05/11.96 f11(f1(true__, d), f8(f1(true__, f11(true__, true__)), true__, d)) -> f8(f1(true__, f11(true__, true__)), true__, d) % 12.05/11.96 f11(f1(true__, f11(true__, Y0)), Y0) -> Y0 % 12.05/11.96 f11(f1(true__, f12(true__, d)), d) -> d % 12.05/11.96 f11(there_exists(compose(X, d)), X) -> X % 12.05/11.96 f11(true__, d) -> f12(true__, d) % 12.05/11.96 f11(true__, f8(f1(true__, f11(true__, true__)), true__, d)) -> d % 12.05/11.96 f12(f1(true__, a), a) -> a % 12.05/11.96 f12(f1(true__, d), domain(d)) -> domain(d) % 12.05/11.96 f12(f1(true__, f12(true__, Y0)), Y0) -> Y0 % 12.05/11.96 f12(there_exists(compose(d, X)), X) -> X % 12.05/11.96 f12(true__, a) -> a % 12.05/11.96 f12(true__, d) -> d % 12.05/11.96 f12(true__, domain(d)) -> d % 12.05/11.96 f12(true__, f12(true__, Y1)) -> f12(true__, Y1) % 12.05/11.96 f13(codomain(a)) -> true__ % 12.05/11.96 f13(d) -> false__ % 12.05/11.96 f13(domain(f8(f1(true__, compose(true__, a)), true__, a))) -> true__ % 12.05/11.96 f13(f8(f1(true__, compose(X1, a)), X1, a)) -> true__ % 12.05/11.96 f2(equivalent(X, Y), X, Y) -> Y % 12.05/11.96 f2(f3(true__, Y0, Y1), Y0, Y1) -> Y1 % 12.05/11.96 f2(true__, X, Y) -> X % 12.05/11.96 f3(f1(true__, Y1), Y1, Y1) -> true__ % 12.05/11.96 f3(true__, a, a) -> true__ % 12.05/11.96 f3(true__, d, d) -> true__ % 12.05/11.96 f3(true__, domain(a), domain(a)) -> true__ % 12.05/11.96 f3(true__, domain(d), domain(d)) -> true__ % 12.05/11.96 f3(true__, domain(domain(a)), domain(domain(a))) -> true__ % 12.05/11.96 f3(true__, domain(domain(domain(a))), domain(domain(domain(a)))) -> true__ % 12.05/11.96 f4(X, Y, X) -> true__ % 12.05/11.96 f4(Y, Y, X) -> f3(there_exists(X), X, Y) % 12.05/11.96 f5(f1(true__, domain(Y0)), Y0) -> true__ % 12.05/11.96 f5(there_exists(domain(X)), X) -> true__ % 12.05/11.96 f5(true__, X) -> there_exists(X) % 12.05/11.96 f6(f1(true__, f8(f1(true__, Y0), Y0, domain(Y0))), domain(Y0)) -> true__ % 12.05/11.96 f6(f1(true__, f8(f1(true__, compose(X1, Y0)), X1, Y0)), Y0) -> true__ % 12.05/11.96 f6(f1(true__, f8(f1(true__, compose(true__, Y0)), true__, Y0)), Y0) -> true__ % 12.05/11.96 f6(f1(true__, f8(f1(true__, true__), true__, domain(true__))), domain(true__)) -> true__ % 12.05/11.96 f6(there_exists(codomain(X)), X) -> true__ % 12.05/11.96 f6(true__, X) -> there_exists(X) % 12.05/11.96 f7(f1(true__, Y0), Y0) -> true__ % 12.05/11.96 f7(f1(true__, Y1), f8(f1(true__, compose(true__, Y1)), true__, Y1)) -> true__ % 12.05/11.96 f7(f1(true__, compose(Y0, Y1)), Y0) -> true__ % 12.05/11.96 f7(f1(true__, domain(true__)), f8(f1(true__, true__), true__, domain(true__))) -> true__ % 12.05/11.96 f7(f1(true__, f11(true__, Y0)), Y0) -> true__ % 12.05/11.96 f7(f1(true__, f12(true__, Y1)), d) -> true__ % 12.05/11.96 f7(there_exists(compose(X, Y)), X) -> true__ % 12.05/11.96 f7(true__, X) -> there_exists(domain(X)) % 12.05/11.96 f8(f1(true__, Y1), f8(f1(true__, compose(true__, Y1)), true__, Y1), Y1) -> f8(f1(true__, compose(true__, Y1)), true__, Y1) % 12.05/11.96 f8(f1(true__, f11(true__, Y0)), Y0, d) -> d % 12.05/11.96 f8(f1(true__, f11(true__, true__)), true__, d) -> d % 12.05/11.96 f8(true__, X, Y) -> domain(X) % 12.05/11.96 f9(true__, X, Y) -> there_exists(compose(X, Y)) % 12.05/11.96 false__ -> true__ % 12.05/11.96 there_exists(X) -> f1(true__, X) % 12.05/11.96 there_exists(compose(d, a)) -> true__ % 12.05/11.96 with the LPO induced by % 12.05/11.96 f2 > f13 > codomain > f7 > f10 > f4 > d > f9 > f6 > f5 > there_exists > f1 > compose > f11 > f12 > a > f8 > domain > equivalent > f3 > false__ > true__ % 12.05/11.96 % 12.05/11.96 % SZS output end Proof % 12.05/11.96 %------------------------------------------------------------------------------