%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : CAT013-4 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n022.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 00:04:57 EDT 2022 % Result : Unsatisfiable 9.77s 9.78s % Output : Proof 9.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : CAT013-4 : TPTP v8.1.0. Released v1.0.0. % 0.04/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n022.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Sun May 29 19:49:38 EDT 2022 % 0.14/0.34 % CPUTime : % 9.77/9.78 % SZS status Unsatisfiable % 9.77/9.78 % SZS output start Proof % 9.77/9.78 The input problem is unsatisfiable because % 9.77/9.78 % 9.77/9.78 [1] the following set of Horn clauses is unsatisfiable: % 9.77/9.78 % 9.77/9.78 equivalent(X, Y) ==> there_exists(X) % 9.77/9.78 equivalent(X, Y) ==> X = Y % 9.77/9.78 there_exists(X) & X = Y ==> equivalent(X, Y) % 9.77/9.78 there_exists(domain(X)) ==> there_exists(X) % 9.77/9.78 there_exists(codomain(X)) ==> there_exists(X) % 9.77/9.78 there_exists(compose(X, Y)) ==> there_exists(domain(X)) % 9.77/9.78 there_exists(compose(X, Y)) ==> domain(X) = codomain(Y) % 9.77/9.78 there_exists(domain(X)) & domain(X) = codomain(Y) ==> there_exists(compose(X, Y)) % 9.77/9.78 compose(X, compose(Y, Z)) = compose(compose(X, Y), Z) % 9.77/9.78 compose(X, domain(X)) = X % 9.77/9.78 compose(codomain(X), X) = X % 9.77/9.78 there_exists(codomain(a)) % 9.77/9.78 domain(codomain(a)) = codomain(a) ==> \bottom % 9.77/9.78 % 9.77/9.78 This holds because % 9.77/9.78 % 9.77/9.78 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 9.77/9.78 % 9.77/9.78 E: % 9.77/9.78 compose(X, compose(Y, Z)) = compose(compose(X, Y), Z) % 9.77/9.78 compose(X, domain(X)) = X % 9.77/9.78 compose(codomain(X), X) = X % 9.77/9.78 f1(equivalent(X, Y), X) = true__ % 9.77/9.78 f1(true__, X) = there_exists(X) % 9.77/9.78 f10(codomain(Y), Y, X) = f9(there_exists(domain(X)), X, Y) % 9.77/9.78 f10(domain(X), Y, X) = true__ % 9.77/9.78 f11(codomain(a)) = false__ % 9.77/9.78 f11(domain(codomain(a))) = true__ % 9.77/9.78 f2(equivalent(X, Y), X, Y) = Y % 9.77/9.78 f2(true__, X, Y) = X % 9.77/9.78 f3(true__, X, Y) = equivalent(X, Y) % 9.77/9.78 f4(X, Y, X) = true__ % 9.77/9.78 f4(Y, Y, X) = f3(there_exists(X), X, Y) % 9.77/9.78 f5(there_exists(domain(X)), X) = true__ % 9.77/9.78 f5(true__, X) = there_exists(X) % 9.77/9.78 f6(there_exists(codomain(X)), X) = true__ % 9.77/9.78 f6(true__, X) = there_exists(X) % 9.77/9.78 f7(there_exists(compose(X, Y)), X) = true__ % 9.77/9.78 f7(true__, X) = there_exists(domain(X)) % 9.77/9.78 f8(there_exists(compose(X, Y)), X, Y) = codomain(Y) % 9.77/9.78 f8(true__, X, Y) = domain(X) % 9.77/9.78 f9(true__, X, Y) = there_exists(compose(X, Y)) % 9.77/9.78 there_exists(codomain(a)) = true__ % 9.77/9.78 G: % 9.77/9.78 true__ = false__ % 9.77/9.78 % 9.77/9.78 This holds because % 9.77/9.78 % 9.77/9.78 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 9.77/9.78 % 9.77/9.78 f8(f5(true__, compose(X, Y)), X, Y) = codomain(Y) % 9.77/9.78 codomain(domain(Y0)) -> f8(f5(true__, Y0), Y0, domain(Y0)) % 9.77/9.78 compose(X, domain(X)) -> X % 9.77/9.78 compose(Y0, compose(Y1, domain(compose(Y0, Y1)))) -> compose(Y0, Y1) % 9.77/9.78 compose(Y0, compose(domain(Y0), Y2)) -> compose(Y0, Y2) % 9.77/9.78 compose(codomain(X), X) -> X % 9.77/9.78 compose(compose(X, Y), Z) -> compose(X, compose(Y, Z)) % 9.77/9.78 compose(f8(f5(true__, compose(X1, Y0)), X1, Y0), Y0) -> Y0 % 9.77/9.78 compose(f8(f5(true__, compose(true__, Y1)), true__, Y1), compose(Y1, Y2)) -> compose(Y1, Y2) % 9.77/9.78 domain(f8(f6(true__, compose(false__, a)), false__, a)) -> f8(f5(true__, compose(false__, a)), false__, a) % 9.77/9.78 equivalent(X, Y) -> f3(true__, X, Y) % 9.77/9.78 f1(equivalent(X, Y), X) -> true__ % 9.77/9.78 f1(true__, X) -> f5(true__, X) % 9.77/9.78 f1(true__, codomain(a)) -> true__ % 9.77/9.78 f10(codomain(Y), Y, X) -> f9(f5(true__, domain(X)), X, Y) % 9.77/9.78 f10(domain(X), Y, X) -> true__ % 9.77/9.78 f11(codomain(a)) -> false__ % 9.77/9.78 f11(domain(codomain(a))) -> true__ % 9.77/9.78 f11(domain(f8(f5(true__, compose(X1, a)), X1, a))) -> true__ % 9.77/9.78 f11(f8(f5(true__, compose(X1, a)), X1, a)) -> false__ % 9.77/9.78 f2(equivalent(X, Y), X, Y) -> Y % 9.77/9.78 f2(true__, X, Y) -> X % 9.77/9.78 f3(f5(true__, Y1), Y1, Y1) -> true__ % 9.77/9.78 f3(true__, a, a) -> true__ % 9.77/9.78 f3(true__, domain(a), domain(a)) -> true__ % 9.77/9.78 f3(true__, f8(f6(true__, compose(false__, a)), false__, a), f8(f6(true__, compose(false__, a)), false__, a)) -> true__ % 9.77/9.78 f4(X, Y, X) -> true__ % 9.77/9.78 f4(Y, Y, X) -> f3(f5(true__, X), X, Y) % 9.77/9.78 f5(f5(true__, domain(Y0)), Y0) -> true__ % 9.77/9.78 f5(true__, a) -> true__ % 9.77/9.78 f5(true__, domain(a)) -> true__ % 9.77/9.78 f5(true__, domain(domain(a))) -> true__ % 9.77/9.78 f5(true__, domain(domain(domain(a)))) -> true__ % 9.77/9.78 f5(true__, domain(f8(f5(true__, compose(true__, a)), true__, a))) -> true__ % 9.77/9.78 f5(true__, f8(f5(true__, compose(X1, a)), X1, a)) -> true__ % 9.77/9.78 f6(f1(true__, codomain(Y0)), Y0) -> true__ % 9.77/9.78 f6(f5(true__, f8(f5(true__, compose(true__, Y0)), true__, Y0)), Y0) -> true__ % 9.77/9.78 f6(f6(true__, codomain(Y0)), Y0) -> true__ % 9.77/9.78 f6(there_exists(codomain(X)), X) -> true__ % 9.77/9.78 f6(true__, X) -> f5(true__, X) % 9.77/9.78 f6(true__, codomain(a)) -> true__ % 9.77/9.78 f6(true__, domain(domain(domain(a)))) -> true__ % 9.77/9.78 f7(f1(true__, Y1), codomain(Y1)) -> true__ % 9.77/9.78 f7(f5(true__, Y0), Y0) -> true__ % 9.77/9.78 f7(f5(true__, Y1), f8(f5(true__, compose(true__, Y1)), true__, Y1)) -> true__ % 9.77/9.78 f7(f5(true__, compose(Y0, Y1)), Y0) -> true__ % 9.77/9.78 f7(f6(true__, Y1), codomain(Y1)) -> true__ % 9.77/9.78 f7(true__, X) -> f5(true__, domain(X)) % 9.77/9.78 f8(f6(true__, Y1), codomain(Y1), Y1) -> codomain(Y1) % 9.77/9.78 f8(true__, X, Y) -> domain(X) % 9.77/9.78 f9(true__, X, Y) -> f5(true__, compose(X, Y)) % 9.77/9.78 false__ -> true__ % 9.77/9.78 there_exists(X) -> f5(true__, X) % 9.77/9.78 there_exists(codomain(a)) -> true__ % 9.77/9.78 with the LPO induced by % 9.77/9.78 f7 > f10 > f4 > f9 > codomain > f8 > domain > f6 > f1 > there_exists > f5 > f2 > f11 > equivalent > f3 > compose > a > false__ > true__ % 9.77/9.78 % 9.77/9.78 % SZS output end Proof % 9.77/9.78 %------------------------------------------------------------------------------