TSTP Solution File: CAT010-4 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : CAT010-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n032.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 00:04:53 EDT 2022
% Result : Unsatisfiable 14.84s 14.67s
% Output : Proof 14.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : CAT010-4 : TPTP v8.1.0. Released v1.0.0.
% 0.02/0.09 % Command : moca.sh %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Sun May 29 17:48:11 EDT 2022
% 0.08/0.28 % CPUTime :
% 14.84/14.67 % SZS status Unsatisfiable
% 14.84/14.67 % SZS output start Proof
% 14.84/14.67 The input problem is unsatisfiable because
% 14.84/14.67
% 14.84/14.67 [1] the following set of Horn clauses is unsatisfiable:
% 14.84/14.67
% 14.84/14.67 equivalent(X, Y) ==> there_exists(X)
% 14.84/14.67 equivalent(X, Y) ==> X = Y
% 14.84/14.67 there_exists(X) & X = Y ==> equivalent(X, Y)
% 14.84/14.67 there_exists(domain(X)) ==> there_exists(X)
% 14.84/14.67 there_exists(codomain(X)) ==> there_exists(X)
% 14.84/14.67 there_exists(compose(X, Y)) ==> there_exists(domain(X))
% 14.84/14.67 there_exists(compose(X, Y)) ==> domain(X) = codomain(Y)
% 14.84/14.67 there_exists(domain(X)) & domain(X) = codomain(Y) ==> there_exists(compose(X, Y))
% 14.84/14.67 compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)
% 14.84/14.67 compose(X, domain(X)) = X
% 14.84/14.67 compose(codomain(X), X) = X
% 14.84/14.67 there_exists(compose(a, b))
% 14.84/14.67 codomain(compose(a, b)) = codomain(a) ==> \bottom
% 14.84/14.67
% 14.84/14.67 This holds because
% 14.84/14.67
% 14.84/14.67 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 14.84/14.67
% 14.84/14.67 E:
% 14.84/14.67 compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)
% 14.84/14.67 compose(X, domain(X)) = X
% 14.84/14.67 compose(codomain(X), X) = X
% 14.84/14.67 f1(equivalent(X, Y), X) = true__
% 14.84/14.67 f1(true__, X) = there_exists(X)
% 14.84/14.67 f10(codomain(Y), Y, X) = f9(there_exists(domain(X)), X, Y)
% 14.84/14.67 f10(domain(X), Y, X) = true__
% 14.84/14.67 f11(codomain(a)) = false__
% 14.84/14.67 f11(codomain(compose(a, b))) = true__
% 14.84/14.67 f2(equivalent(X, Y), X, Y) = Y
% 14.84/14.67 f2(true__, X, Y) = X
% 14.84/14.67 f3(true__, X, Y) = equivalent(X, Y)
% 14.84/14.67 f4(X, Y, X) = true__
% 14.84/14.67 f4(Y, Y, X) = f3(there_exists(X), X, Y)
% 14.84/14.67 f5(there_exists(domain(X)), X) = true__
% 14.84/14.67 f5(true__, X) = there_exists(X)
% 14.84/14.67 f6(there_exists(codomain(X)), X) = true__
% 14.84/14.67 f6(true__, X) = there_exists(X)
% 14.84/14.67 f7(there_exists(compose(X, Y)), X) = true__
% 14.84/14.67 f7(true__, X) = there_exists(domain(X))
% 14.84/14.67 f8(there_exists(compose(X, Y)), X, Y) = codomain(Y)
% 14.84/14.67 f8(true__, X, Y) = domain(X)
% 14.84/14.67 f9(true__, X, Y) = there_exists(compose(X, Y))
% 14.84/14.67 there_exists(compose(a, b)) = true__
% 14.84/14.67 G:
% 14.84/14.67 true__ = false__
% 14.84/14.67
% 14.84/14.67 This holds because
% 14.84/14.67
% 14.84/14.67 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 14.84/14.67
% 14.84/14.67
% 14.84/14.67 codomain(b) -> domain(a)
% 14.84/14.67 codomain(codomain(a)) -> codomain(a)
% 14.84/14.67 codomain(codomain(domain(a))) -> codomain(domain(a))
% 14.84/14.67 codomain(compose(a, b)) -> domain(codomain(a))
% 14.84/14.67 codomain(compose(domain(a), domain(a))) -> domain(a)
% 14.84/14.67 codomain(compose(domain(b), domain(b))) -> domain(b)
% 14.84/14.67 codomain(compose(domain(domain(a)), b)) -> domain(domain(a))
% 14.84/14.67 codomain(domain(a)) -> domain(a)
% 14.84/14.67 codomain(domain(b)) -> domain(b)
% 14.84/14.67 codomain(domain(b)) -> domain(compose(a, b))
% 14.84/14.67 codomain(domain(compose(a, b))) -> domain(compose(a, b))
% 14.84/14.67 codomain(domain(domain(a))) -> domain(domain(a))
% 14.84/14.67 codomain(domain(domain(b))) -> domain(b)
% 14.84/14.67 codomain(domain(domain(b))) -> domain(domain(b))
% 14.84/14.67 codomain(domain(domain(domain(a)))) -> domain(domain(domain(a)))
% 14.84/14.67 codomain(domain(domain(domain(b)))) -> domain(domain(b))
% 14.84/14.67 compose(X, domain(X)) -> X
% 14.84/14.67 compose(X0, compose(X1, compose(Y1, domain(compose(X0, compose(X1, Y1)))))) -> compose(X0, compose(X1, Y1))
% 14.84/14.67 compose(Y0, compose(X1, compose(domain(compose(Y0, X1)), domain(compose(Y0, X1))))) -> compose(Y0, X1)
% 14.84/14.67 compose(Y0, compose(X1, domain(compose(domain(Y0), X1)))) -> compose(Y0, X1)
% 14.84/14.67 compose(Y0, compose(Y1, compose(domain(compose(Y0, Y1)), X1))) -> compose(Y0, compose(Y1, X1))
% 14.84/14.67 compose(Y0, compose(Y1, domain(compose(Y0, Y1)))) -> compose(Y0, Y1)
% 14.84/14.67 compose(Y0, compose(Y1, domain(domain(compose(Y0, Y1))))) -> compose(Y0, Y1)
% 14.84/14.67 compose(Y0, compose(Y1, domain(domain(domain(compose(Y0, Y1)))))) -> compose(Y0, Y1)
% 14.84/14.67 compose(Y0, compose(Y1, domain(domain(domain(domain(compose(Y0, Y1))))))) -> compose(Y0, Y1)
% 14.84/14.67 compose(Y0, compose(domain(Y0), Y2)) -> compose(Y0, Y2)
% 14.84/14.67 compose(Y0, compose(domain(domain(Y0)), X1)) -> compose(Y0, X1)
% 14.84/14.67 compose(Y0, compose(domain(domain(domain(Y0))), Y2)) -> compose(Y0, Y2)
% 14.84/14.67 compose(Y0, compose(domain(domain(domain(Y0))), domain(Y0))) -> Y0
% 14.84/14.67 compose(Y0, compose(domain(domain(domain(Y0))), domain(domain(Y0)))) -> compose(Y0, domain(domain(domain(Y0))))
% 14.84/14.67 compose(Y0, compose(domain(domain(domain(domain(Y0)))), Y2)) -> compose(Y0, Y2)
% 14.84/14.67 compose(Y0, domain(domain(Y0))) -> Y0
% 14.84/14.67 compose(Y0, domain(domain(domain(Y0)))) -> Y0
% 14.84/14.67 compose(Y0, domain(domain(domain(domain(Y0))))) -> Y0
% 14.84/14.67 compose(Y0, domain(domain(domain(domain(domain(Y0)))))) -> Y0
% 14.84/14.67 compose(codomain(X), X) -> X
% 14.84/14.67 compose(codomain(Y1), compose(Y1, Y2)) -> compose(Y1, Y2)
% 14.84/14.67 compose(codomain(a), codomain(a)) -> codomain(a)
% 14.84/14.67 compose(codomain(a), compose(codomain(a), Y1)) -> compose(codomain(a), Y1)
% 14.84/14.67 compose(codomain(codomain(X0)), compose(X0, X1)) -> compose(X0, X1)
% 14.84/14.67 compose(codomain(codomain(Y1)), Y1) -> Y1
% 14.84/14.67 compose(codomain(codomain(a)), codomain(codomain(a))) -> codomain(codomain(a))
% 14.84/14.67 compose(codomain(codomain(codomain(Y1))), Y1) -> Y1
% 14.84/14.67 compose(codomain(codomain(codomain(Y1))), compose(Y1, Y2)) -> compose(Y1, Y2)
% 14.84/14.67 compose(codomain(codomain(codomain(a))), compose(a, b)) -> compose(a, b)
% 14.84/14.67 compose(codomain(codomain(codomain(codomain(Y1)))), Y1) -> Y1
% 14.84/14.67 compose(codomain(codomain(codomain(codomain(Y1)))), compose(Y1, Y2)) -> compose(Y1, Y2)
% 14.84/14.67 compose(codomain(codomain(codomain(codomain(a)))), compose(a, b)) -> compose(a, b)
% 14.84/14.67 compose(codomain(codomain(codomain(codomain(codomain(Y1))))), Y1) -> Y1
% 14.84/14.67 compose(codomain(codomain(domain(a))), b) -> b
% 14.84/14.67 compose(codomain(compose(X0, X1)), compose(X0, compose(X1, Y1))) -> compose(X0, compose(X1, Y1))
% 14.84/14.67 compose(codomain(compose(Y0, codomain(Y2))), compose(Y0, Y2)) -> compose(Y0, Y2)
% 14.84/14.67 compose(codomain(compose(Y0, codomain(domain(Y0)))), Y0) -> Y0
% 14.84/14.67 compose(codomain(compose(Y0, codomain(domain(domain(Y0))))), Y0) -> Y0
% 14.84/14.67 compose(codomain(compose(Y0, domain(a))), compose(Y0, b)) -> compose(Y0, b)
% 14.84/14.67 compose(codomain(compose(a, b)), codomain(compose(a, b))) -> codomain(compose(a, b))
% 14.84/14.67 compose(codomain(compose(codomain(Y1), codomain(Y1))), Y1) -> Y1
% 14.84/14.67 compose(codomain(compose(codomain(compose(Y1, Y2)), Y1)), compose(Y1, Y2)) -> compose(Y1, Y2)
% 14.84/14.67 compose(codomain(compose(domain(a), domain(a))), b) -> b
% 14.84/14.67 compose(codomain(domain(a)), b) -> b
% 14.84/14.67 compose(codomain(domain(a)), codomain(domain(a))) -> codomain(domain(a))
% 14.84/14.67 compose(codomain(domain(a)), compose(b, Y1)) -> compose(b, Y1)
% 14.84/14.67 compose(codomain(domain(a)), compose(codomain(domain(a)), Y1)) -> compose(codomain(domain(a)), Y1)
% 14.84/14.67 compose(compose(X, Y), Z) -> compose(X, compose(Y, Z))
% 14.84/14.67 compose(domain(a), b) -> b
% 14.84/14.67 compose(domain(a), compose(b, Y1)) -> compose(b, Y1)
% 14.84/14.67 compose(domain(a), compose(domain(a), Y1)) -> compose(domain(a), Y1)
% 14.84/14.67 compose(domain(a), compose(domain(a), compose(domain(a), Y1))) -> compose(domain(a), compose(domain(a), Y1))
% 14.84/14.67 compose(domain(a), compose(domain(a), domain(a))) -> compose(domain(a), domain(a))
% 14.84/14.67 compose(domain(a), domain(a)) -> domain(a)
% 14.84/14.67 compose(domain(b), compose(domain(b), Y1)) -> compose(domain(b), Y1)
% 14.84/14.67 compose(domain(b), domain(b)) -> domain(b)
% 14.84/14.67 compose(domain(compose(a, b)), compose(domain(b), Y1)) -> compose(domain(b), Y1)
% 14.84/14.67 compose(domain(compose(a, b)), compose(domain(compose(a, b)), Y1)) -> compose(domain(compose(a, b)), Y1)
% 14.84/14.67 compose(domain(compose(a, b)), domain(b)) -> domain(b)
% 14.84/14.67 compose(domain(compose(a, b)), domain(compose(a, b))) -> domain(compose(a, b))
% 14.84/14.67 compose(domain(domain(a)), compose(domain(domain(a)), Y1)) -> compose(domain(domain(a)), Y1)
% 14.84/14.67 compose(domain(domain(a)), domain(domain(a))) -> domain(domain(a))
% 14.84/14.67 domain(codomain(a)) -> codomain(a)
% 14.84/14.67 domain(codomain(codomain(a))) -> codomain(a)
% 14.84/14.67 domain(codomain(codomain(a))) -> codomain(codomain(a))
% 14.84/14.67 domain(codomain(codomain(codomain(a)))) -> codomain(codomain(a))
% 14.84/14.67 domain(codomain(codomain(codomain(a)))) -> codomain(codomain(codomain(a)))
% 14.84/14.67 domain(codomain(codomain(compose(a, b)))) -> codomain(codomain(compose(a, b)))
% 14.84/14.67 domain(codomain(codomain(domain(a)))) -> codomain(codomain(domain(a)))
% 14.84/14.67 domain(codomain(compose(a, b))) -> codomain(compose(a, b))
% 14.84/14.67 domain(codomain(domain(a))) -> codomain(domain(a))
% 14.84/14.67 domain(compose(a, b)) -> domain(b)
% 14.84/14.67 domain(compose(b, domain(compose(a, b)))) -> domain(compose(a, b))
% 14.84/14.67 domain(compose(codomain(a), codomain(a))) -> codomain(a)
% 14.84/14.67 domain(compose(codomain(codomain(a)), codomain(codomain(a)))) -> codomain(codomain(a))
% 14.84/14.67 domain(compose(codomain(compose(a, b)), a)) -> domain(a)
% 14.84/14.67 domain(compose(domain(a), domain(a))) -> domain(a)
% 14.84/14.67 domain(compose(domain(b), codomain(domain(domain(b))))) -> codomain(domain(domain(b)))
% 14.84/14.67 domain(compose(domain(b), domain(compose(a, b)))) -> domain(compose(a, b))
% 14.84/14.67 domain(domain(a)) -> domain(a)
% 14.84/14.67 domain(domain(b)) -> domain(compose(a, b))
% 14.84/14.67 domain(domain(compose(a, b))) -> domain(compose(a, b))
% 14.84/14.67 domain(domain(domain(a))) -> domain(domain(a))
% 14.84/14.67 equivalent(X, Y) -> f3(true__, X, Y)
% 14.84/14.67 f1(equivalent(X, Y), X) -> true__
% 14.84/14.67 f1(f3(true__, Y0, Y1), Y0) -> true__
% 14.84/14.67 f1(true__, a) -> true__
% 14.84/14.67 f1(true__, b) -> true__
% 14.84/14.67 f1(true__, codomain(a)) -> true__
% 14.84/14.67 f1(true__, codomain(codomain(a))) -> true__
% 14.84/14.67 f1(true__, codomain(compose(a, b))) -> true__
% 14.84/14.67 f1(true__, codomain(domain(a))) -> true__
% 14.84/14.67 f1(true__, compose(a, b)) -> true__
% 14.84/14.67 f1(true__, compose(domain(a), domain(a))) -> true__
% 14.84/14.67 f1(true__, domain(a)) -> true__
% 14.84/14.67 f1(true__, domain(b)) -> true__
% 14.84/14.67 f1(true__, domain(codomain(a))) -> true__
% 14.84/14.67 f1(true__, domain(codomain(codomain(a)))) -> true__
% 14.84/14.67 f1(true__, domain(codomain(codomain(codomain(a))))) -> true__
% 14.84/14.67 f1(true__, domain(codomain(codomain(codomain(codomain(a)))))) -> true__
% 14.84/14.67 f1(true__, domain(codomain(codomain(compose(a, b))))) -> true__
% 14.84/14.67 f1(true__, domain(codomain(codomain(domain(a))))) -> true__
% 14.84/14.67 f1(true__, domain(codomain(compose(a, b)))) -> true__
% 14.84/14.67 f1(true__, domain(codomain(domain(a)))) -> true__
% 14.84/14.67 f1(true__, domain(compose(a, b))) -> true__
% 14.84/14.67 f1(true__, domain(compose(b, codomain(domain(domain(b)))))) -> true__
% 14.84/14.67 f1(true__, domain(compose(b, domain(compose(a, b))))) -> true__
% 14.84/14.67 f1(true__, domain(compose(codomain(a), codomain(a)))) -> true__
% 14.84/14.67 f1(true__, domain(compose(codomain(a), codomain(codomain(a))))) -> true__
% 14.84/14.67 f1(true__, domain(compose(codomain(codomain(a)), codomain(codomain(a))))) -> true__
% 14.84/14.67 f1(true__, domain(compose(codomain(codomain(a)), codomain(codomain(codomain(a)))))) -> true__
% 14.84/14.67 f1(true__, domain(compose(codomain(compose(a, b)), a))) -> true__
% 14.84/14.67 f1(true__, domain(compose(domain(a), domain(a)))) -> true__
% 14.84/14.67 f1(true__, domain(compose(domain(b), codomain(domain(domain(b)))))) -> true__
% 14.84/14.67 f1(true__, domain(compose(domain(b), codomain(domain(domain(domain(b))))))) -> true__
% 14.84/14.67 f1(true__, domain(compose(domain(b), domain(compose(a, b))))) -> true__
% 14.84/14.67 f1(true__, domain(domain(a))) -> true__
% 14.84/14.67 f1(true__, domain(domain(b))) -> true__
% 14.84/14.67 f1(true__, domain(domain(compose(a, b)))) -> true__
% 14.84/14.67 f1(true__, domain(domain(domain(a)))) -> true__
% 14.84/14.67 f10(codomain(Y), Y, X) -> f9(there_exists(domain(X)), X, Y)
% 14.84/14.67 f10(codomain(a), Y1, codomain(a)) -> true__
% 14.84/14.67 f10(codomain(codomain(a)), Y1, codomain(codomain(a))) -> true__
% 14.84/14.67 f10(codomain(compose(a, b)), Y1, codomain(compose(a, b))) -> true__
% 14.84/14.67 f10(codomain(domain(a)), Y1, codomain(domain(a))) -> true__
% 14.84/14.67 f10(domain(X), Y, X) -> true__
% 14.84/14.67 f10(domain(a), Y1, compose(domain(a), domain(a))) -> true__
% 14.84/14.67 f10(domain(a), Y1, domain(a)) -> true__
% 14.84/14.67 f10(domain(a), b, Y1) -> f9(f1(true__, domain(Y1)), Y1, b)
% 14.84/14.67 f10(domain(a), domain(a), Y1) -> f9(f1(true__, domain(Y1)), Y1, domain(a))
% 14.84/14.67 f10(domain(b), domain(b), Y1) -> f9(f1(true__, domain(Y1)), Y1, domain(b))
% 14.84/14.67 f10(domain(compose(a, b)), Y1, domain(compose(a, b))) -> true__
% 14.84/14.67 f11(codomain(a)) -> false__
% 14.84/14.67 f11(codomain(compose(a, b))) -> true__
% 14.84/14.67 f2(equivalent(X, Y), X, Y) -> Y
% 14.84/14.67 f2(f3(true__, Y0, Y1), Y0, Y1) -> Y1
% 14.84/14.67 f2(true__, X, Y) -> X
% 14.84/14.67 f3(f1(true__, Y1), Y1, Y1) -> true__
% 14.84/14.67 f3(true__, a, a) -> true__
% 14.84/14.67 f3(true__, b, b) -> true__
% 14.84/14.67 f3(true__, codomain(a), codomain(a)) -> true__
% 14.84/14.67 f3(true__, codomain(codomain(a)), codomain(codomain(a))) -> true__
% 14.84/14.67 f3(true__, codomain(compose(a, b)), codomain(compose(a, b))) -> true__
% 14.84/14.67 f3(true__, codomain(domain(a)), codomain(domain(a))) -> true__
% 14.84/14.67 f3(true__, compose(a, b), compose(a, b)) -> true__
% 14.84/14.67 f3(true__, domain(a), domain(a)) -> true__
% 14.84/14.67 f3(true__, domain(b), domain(b)) -> true__
% 14.84/14.67 f3(true__, domain(compose(a, b)), domain(compose(a, b))) -> true__
% 14.84/14.67 f3(true__, domain(domain(a)), domain(domain(a))) -> true__
% 14.84/14.67 f4(X, Y, X) -> true__
% 14.84/14.67 f4(Y, Y, X) -> f3(there_exists(X), X, Y)
% 14.84/14.67 f5(f1(true__, codomain(a)), codomain(a)) -> true__
% 14.84/14.67 f5(f1(true__, codomain(codomain(a))), codomain(codomain(a))) -> true__
% 14.84/14.67 f5(f1(true__, codomain(compose(a, b))), codomain(compose(a, b))) -> true__
% 14.84/14.67 f5(f1(true__, codomain(domain(a))), codomain(domain(a))) -> true__
% 14.84/14.67 f5(f1(true__, domain(Y0)), Y0) -> true__
% 14.84/14.67 f5(there_exists(domain(X)), X) -> true__
% 14.84/14.67 f5(true__, X) -> there_exists(X)
% 14.84/14.67 f6(f1(true__, codomain(Y0)), Y0) -> true__
% 14.84/14.67 f6(there_exists(codomain(X)), X) -> true__
% 14.84/14.67 f6(true__, X) -> there_exists(X)
% 14.84/14.67 f7(f1(true__, Y0), Y0) -> true__
% 14.84/14.67 f7(f1(true__, Y0), compose(Y0, codomain(codomain(codomain(domain(Y0)))))) -> true__
% 14.84/14.67 f7(f1(true__, Y0), compose(Y0, codomain(codomain(domain(Y0))))) -> true__
% 14.84/14.67 f7(f1(true__, Y0), compose(Y0, codomain(codomain(domain(domain(Y0)))))) -> true__
% 14.84/14.67 f7(f1(true__, Y0), compose(Y0, codomain(domain(Y0)))) -> true__
% 14.84/14.67 f7(f1(true__, Y0), compose(Y0, codomain(domain(domain(Y0))))) -> true__
% 14.84/14.67 f7(f1(true__, Y0), compose(Y0, codomain(domain(domain(domain(Y0)))))) -> true__
% 14.84/14.67 f7(f1(true__, Y1), codomain(Y1)) -> true__
% 14.84/14.67 f7(f1(true__, Y1), codomain(codomain(Y1))) -> true__
% 14.84/14.67 f7(f1(true__, Y1), codomain(codomain(codomain(Y1)))) -> true__
% 14.84/14.67 f7(f1(true__, Y1), codomain(codomain(codomain(codomain(Y1))))) -> true__
% 14.84/14.67 f7(f1(true__, Y1), codomain(codomain(codomain(codomain(codomain(Y1)))))) -> true__
% 14.84/14.67 f7(f1(true__, Y1), compose(codomain(Y1), codomain(Y1))) -> true__
% 14.84/14.67 f7(f1(true__, Y1), compose(codomain(Y1), codomain(codomain(Y1)))) -> true__
% 14.84/14.67 f7(f1(true__, Y1), compose(codomain(Y1), codomain(codomain(codomain(Y1))))) -> true__
% 14.84/14.67 f7(f1(true__, Y1), compose(codomain(codomain(Y1)), codomain(codomain(Y1)))) -> true__
% 14.84/14.67 f7(f1(true__, b), domain(a)) -> true__
% 14.84/14.67 f7(f1(true__, codomain(a)), compose(codomain(a), codomain(codomain(a)))) -> true__
% 14.84/14.67 f7(f1(true__, compose(X0, X1)), codomain(X0)) -> true__
% 14.84/14.67 f7(f1(true__, compose(X0, X1)), codomain(codomain(X0))) -> true__
% 14.84/14.67 f7(f1(true__, compose(X0, compose(X1, Y1))), compose(X0, X1)) -> true__
% 14.84/14.67 f7(f1(true__, compose(X0, compose(X1, compose(Y1, Y2)))), compose(X0, compose(X1, Y1))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y0, Y1)), Y0) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y0, Y1)), compose(Y0, compose(Y1, codomain(domain(Y1))))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y0, Y2)), compose(Y0, codomain(Y2))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y0, Y2)), compose(Y0, codomain(codomain(Y2)))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y0, Y2)), compose(Y0, codomain(codomain(codomain(Y2))))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y0, Y2)), compose(Y0, compose(codomain(Y2), codomain(Y2)))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y0, b)), compose(Y0, codomain(domain(a)))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y0, b)), compose(Y0, domain(a))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y0, compose(X0, X1))), compose(Y0, codomain(X0))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y0, compose(Y1, Y3))), compose(Y0, compose(Y1, codomain(Y3)))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y0, compose(Y1, b))), compose(Y0, compose(Y1, domain(a)))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y0, compose(Y2, Y3))), compose(Y0, compose(codomain(compose(Y2, Y3)), Y2))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y0, compose(b, Y2))), compose(Y0, domain(a))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y1, Y2)), compose(codomain(codomain(compose(Y1, Y2))), Y1)) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y1, Y2)), compose(codomain(codomain(compose(Y1, Y2))), codomain(Y1))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y1, Y2)), compose(codomain(compose(Y1, Y2)), Y1)) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y1, Y2)), compose(codomain(compose(Y1, Y2)), codomain(Y1))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y1, Y2)), compose(codomain(compose(Y1, Y2)), compose(Y1, codomain(Y2)))) -> true__
% 14.84/14.67 f7(f1(true__, compose(Y1, compose(Y2, Y3))), compose(codomain(compose(Y1, compose(Y2, Y3))), compose(Y1, Y2))) -> true__
% 14.84/14.67 f7(f1(true__, compose(b, Y1)), compose(codomain(codomain(compose(b, Y1))), domain(a))) -> true__
% 14.84/14.67 f7(f1(true__, compose(b, Y1)), compose(codomain(compose(b, Y1)), domain(a))) -> true__
% 14.84/14.67 f7(f1(true__, compose(b, Y1)), domain(a)) -> true__
% 14.84/14.67 f7(f1(true__, compose(codomain(codomain(codomain(Y1))), Y1)), codomain(Y1)) -> true__
% 14.84/14.67 f7(f1(true__, compose(domain(b), Y1)), domain(compose(a, b))) -> true__
% 14.84/14.67 f7(there_exists(compose(X, Y)), X) -> true__
% 14.84/14.67 f7(true__, X) -> there_exists(domain(X))
% 14.84/14.67 f8(f1(true__, Y0), Y0, compose(domain(Y0), domain(Y0))) -> codomain(compose(domain(Y0), domain(Y0)))
% 14.84/14.67 f8(f1(true__, Y0), Y0, domain(Y0)) -> codomain(domain(Y0))
% 14.84/14.67 f8(f1(true__, Y0), Y0, domain(domain(Y0))) -> codomain(domain(domain(Y0)))
% 14.84/14.67 f8(f1(true__, Y0), Y0, domain(domain(domain(Y0)))) -> codomain(domain(domain(domain(Y0))))
% 14.84/14.67 f8(f1(true__, Y0), Y0, domain(domain(domain(domain(Y0))))) -> codomain(domain(domain(domain(domain(Y0)))))
% 14.84/14.67 f8(f1(true__, Y0), compose(Y0, codomain(codomain(domain(Y0)))), domain(Y0)) -> codomain(domain(Y0))
% 14.84/14.67 f8(f1(true__, Y0), compose(Y0, codomain(domain(Y0))), domain(Y0)) -> codomain(domain(Y0))
% 14.84/14.67 f8(f1(true__, Y0), compose(Y0, codomain(domain(domain(Y0)))), domain(domain(Y0))) -> codomain(domain(domain(Y0)))
% 14.84/14.67 f8(f1(true__, Y1), codomain(Y1), Y1) -> codomain(Y1)
% 14.84/14.67 f8(f1(true__, Y1), codomain(Y1), compose(domain(codomain(Y1)), Y1)) -> codomain(compose(domain(codomain(Y1)), Y1))
% 14.84/14.67 f8(f1(true__, Y1), codomain(codomain(Y1)), Y1) -> codomain(Y1)
% 14.84/14.67 f8(f1(true__, Y1), codomain(codomain(codomain(Y1))), Y1) -> codomain(Y1)
% 14.84/14.67 f8(f1(true__, Y1), codomain(codomain(codomain(codomain(Y1)))), Y1) -> codomain(Y1)
% 14.84/14.67 f8(f1(true__, Y1), compose(codomain(Y1), codomain(Y1)), Y1) -> codomain(Y1)
% 14.84/14.67 f8(f1(true__, Y1), compose(codomain(Y1), codomain(codomain(Y1))), Y1) -> codomain(Y1)
% 14.84/14.67 f8(f1(true__, b), domain(a), b) -> domain(a)
% 14.84/14.67 f8(f1(true__, codomain(a)), codomain(a), codomain(a)) -> codomain(codomain(a))
% 14.84/14.67 f8(f1(true__, codomain(a)), compose(codomain(a), codomain(codomain(a))), codomain(a)) -> codomain(codomain(a))
% 14.84/14.67 f8(f1(true__, compose(X0, X1)), codomain(X0), compose(X0, X1)) -> codomain(compose(X0, X1))
% 14.84/14.67 f8(f1(true__, compose(X0, compose(X1, Y1))), compose(X0, X1), Y1) -> codomain(Y1)
% 14.84/14.67 f8(f1(true__, compose(X0, compose(X1, compose(Y1, Y2)))), compose(X0, compose(X1, Y1)), Y2) -> codomain(Y2)
% 14.84/14.67 f8(f1(true__, compose(Y0, X1)), Y0, compose(X1, domain(compose(Y0, X1)))) -> codomain(compose(X1, domain(compose(Y0, X1))))
% 14.84/14.67 f8(f1(true__, compose(Y0, X1)), Y0, compose(domain(Y0), X1)) -> codomain(compose(domain(Y0), X1))
% 14.84/14.67 f8(f1(true__, compose(Y0, Y1)), Y0, Y1) -> codomain(Y1)
% 14.84/14.67 f8(f1(true__, compose(Y0, Y1)), compose(Y0, Y1), compose(domain(Y1), domain(Y1))) -> codomain(compose(domain(Y1), domain(Y1)))
% 14.84/14.67 f8(f1(true__, compose(Y0, Y1)), compose(Y0, Y1), domain(Y1)) -> codomain(domain(Y1))
% 14.84/14.67 f8(f1(true__, compose(Y0, Y1)), compose(Y0, Y1), domain(domain(Y1))) -> codomain(domain(domain(Y1)))
% 14.84/14.67 f8(f1(true__, compose(Y0, Y1)), compose(Y0, Y1), domain(domain(compose(Y0, Y1)))) -> codomain(domain(domain(compose(Y0, Y1))))
% 14.84/14.67 f8(f1(true__, compose(Y0, Y2)), Y0, compose(Y2, domain(compose(domain(Y0), Y2)))) -> codomain(compose(Y2, domain(compose(domain(Y0), Y2))))
% 14.84/14.67 f8(f1(true__, compose(Y0, Y2)), Y0, compose(domain(domain(Y0)), Y2)) -> codomain(compose(domain(domain(Y0)), Y2))
% 14.84/14.67 f8(f1(true__, compose(Y0, Y2)), compose(Y0, codomain(Y2)), Y2) -> codomain(Y2)
% 14.84/14.67 f8(f1(true__, compose(Y0, Y2)), compose(Y0, codomain(Y2)), compose(domain(codomain(Y2)), Y2)) -> codomain(compose(domain(codomain(Y2)), Y2))
% 14.84/14.67 f8(f1(true__, compose(Y0, Y2)), compose(Y0, codomain(codomain(Y2))), Y2) -> codomain(Y2)
% 14.84/14.67 f8(f1(true__, compose(Y0, b)), compose(Y0, codomain(domain(a))), b) -> domain(a)
% 14.84/14.67 f8(f1(true__, compose(Y0, b)), compose(Y0, domain(a)), b) -> domain(a)
% 14.84/14.67 f8(f1(true__, compose(Y0, codomain(a))), compose(Y0, codomain(a)), codomain(a)) -> codomain(codomain(a))
% 14.84/14.67 f8(f1(true__, compose(Y0, compose(X0, X1))), compose(Y0, codomain(X0)), compose(X0, X1)) -> codomain(compose(X0, X1))
% 14.84/14.67 f8(f1(true__, compose(Y0, compose(X1, compose(domain(compose(Y0, X1)), Y2)))), compose(Y0, X1), Y2) -> codomain(Y2)
% 14.84/14.67 f8(f1(true__, compose(Y0, compose(Y1, X1))), compose(Y0, Y1), compose(X1, domain(compose(Y1, X1)))) -> codomain(compose(X1, domain(compose(Y1, X1))))
% 14.84/14.67 f8(f1(true__, compose(Y0, compose(Y1, X1))), compose(Y0, Y1), compose(domain(Y1), X1)) -> codomain(compose(domain(Y1), X1))
% 14.84/14.67 f8(f1(true__, compose(Y0, compose(Y1, Y2))), compose(Y0, compose(Y1, Y2)), domain(Y2)) -> codomain(domain(Y2))
% 14.84/14.67 f8(f1(true__, compose(Y0, compose(Y1, Y3))), compose(Y0, compose(Y1, codomain(Y3))), Y3) -> codomain(Y3)
% 14.84/14.67 f8(f1(true__, compose(Y0, compose(Y1, b))), compose(Y0, compose(Y1, domain(a))), b) -> domain(a)
% 14.84/14.67 f8(f1(true__, compose(Y0, compose(Y2, Y3))), compose(Y0, compose(codomain(compose(Y2, Y3)), Y2)), Y3) -> codomain(Y3)
% 14.84/14.67 f8(f1(true__, compose(Y0, compose(b, Y2))), compose(Y0, domain(a)), compose(b, Y2)) -> codomain(compose(b, Y2))
% 14.84/14.67 f8(f1(true__, compose(Y0, domain(a))), compose(Y0, domain(a)), domain(a)) -> domain(a)
% 14.84/14.67 f8(f1(true__, compose(Y0, domain(b))), compose(Y0, domain(b)), domain(b)) -> domain(compose(a, b))
% 14.84/14.67 f8(f1(true__, compose(Y1, Y2)), compose(codomain(compose(Y1, Y2)), Y1), Y2) -> codomain(Y2)
% 14.84/14.67 f8(f1(true__, compose(Y1, Y2)), compose(codomain(compose(Y1, Y2)), Y1), compose(domain(Y1), Y2)) -> codomain(compose(domain(Y1), Y2))
% 14.84/14.67 f8(f1(true__, compose(Y1, Y2)), compose(codomain(compose(Y1, Y2)), codomain(Y1)), compose(Y1, Y2)) -> codomain(compose(Y1, Y2))
% 14.84/14.67 f8(f1(true__, compose(Y1, compose(Y2, Y3))), compose(codomain(compose(Y1, compose(Y2, Y3))), compose(Y1, Y2)), Y3) -> codomain(Y3)
% 14.84/14.67 f8(f1(true__, compose(b, Y1)), domain(a), compose(b, Y1)) -> codomain(compose(b, Y1))
% 14.84/14.67 f8(f1(true__, compose(codomain(codomain(codomain(Y1))), Y1)), codomain(Y1), Y1) -> codomain(Y1)
% 14.84/14.67 f8(f1(true__, compose(domain(a), domain(a))), compose(domain(a), domain(a)), domain(a)) -> domain(a)
% 14.84/14.67 f8(there_exists(compose(X, Y)), X, Y) -> codomain(Y)
% 14.84/14.67 f8(true__, X, Y) -> domain(X)
% 14.84/14.67 f9(true__, X, Y) -> there_exists(compose(X, Y))
% 14.84/14.67 false__ -> true__
% 14.84/14.67 there_exists(X) -> f1(true__, X)
% 14.84/14.67 there_exists(compose(a, b)) -> true__
% 14.84/14.67 with the LPO induced by
% 14.84/14.67 f11 > b > equivalent > f4 > f3 > f2 > a > f10 > f8 > codomain > f7 > domain > f9 > compose > f5 > f6 > there_exists > f1 > false__ > true__
% 14.84/14.67
% 14.84/14.67 % SZS output end Proof
% 14.84/14.67
%------------------------------------------------------------------------------