TSTP Solution File: CAT001-4 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : CAT001-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n021.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 00:04:43 EDT 2022
% Result : Unsatisfiable 19.58s 19.30s
% Output : Proof 19.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : CAT001-4 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n021.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 17:34:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 19.58/19.30 % SZS status Unsatisfiable
% 19.58/19.30 % SZS output start Proof
% 19.58/19.30 The input problem is unsatisfiable because
% 19.58/19.30
% 19.58/19.30 [1] the following set of Horn clauses is unsatisfiable:
% 19.58/19.30
% 19.58/19.30 equivalent(X, Y) ==> there_exists(X)
% 19.58/19.30 equivalent(X, Y) ==> X = Y
% 19.58/19.30 there_exists(X) & X = Y ==> equivalent(X, Y)
% 19.58/19.30 there_exists(domain(X)) ==> there_exists(X)
% 19.58/19.30 there_exists(codomain(X)) ==> there_exists(X)
% 19.58/19.30 there_exists(compose(X, Y)) ==> there_exists(domain(X))
% 19.58/19.30 there_exists(compose(X, Y)) ==> domain(X) = codomain(Y)
% 19.58/19.30 there_exists(domain(X)) & domain(X) = codomain(Y) ==> there_exists(compose(X, Y))
% 19.58/19.30 compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)
% 19.58/19.30 compose(X, domain(X)) = X
% 19.58/19.30 compose(codomain(X), X) = X
% 19.58/19.30 there_exists(compose(a, b))
% 19.58/19.30 compose(compose(a, b), X) = Y & compose(compose(a, b), Z) = Y ==> X = Z
% 19.58/19.30 there_exists(compose(b, h))
% 19.58/19.30 compose(b, h) = compose(b, g)
% 19.58/19.30 h = g ==> \bottom
% 19.58/19.30
% 19.58/19.30 This holds because
% 19.58/19.30
% 19.58/19.30 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 19.58/19.30
% 19.58/19.30 E:
% 19.58/19.30 compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)
% 19.58/19.30 compose(X, domain(X)) = X
% 19.58/19.30 compose(b, h) = compose(b, g)
% 19.58/19.30 compose(codomain(X), X) = X
% 19.58/19.30 f1(equivalent(X, Y), X) = true__
% 19.58/19.30 f1(true__, X) = there_exists(X)
% 19.58/19.30 f10(codomain(Y), Y, X) = f9(there_exists(domain(X)), X, Y)
% 19.58/19.30 f10(domain(X), Y, X) = true__
% 19.58/19.30 f11(Y, Y, X, Z) = X
% 19.58/19.30 f12(Y, Y, X, Z) = f11(compose(compose(a, b), X), Y, X, Z)
% 19.58/19.30 f12(compose(compose(a, b), Z), Y, X, Z) = Z
% 19.58/19.30 f13(g) = false__
% 19.58/19.30 f13(h) = true__
% 19.58/19.30 f2(equivalent(X, Y), X, Y) = Y
% 19.58/19.30 f2(true__, X, Y) = X
% 19.58/19.30 f3(true__, X, Y) = equivalent(X, Y)
% 19.58/19.30 f4(X, Y, X) = true__
% 19.58/19.30 f4(Y, Y, X) = f3(there_exists(X), X, Y)
% 19.58/19.30 f5(there_exists(domain(X)), X) = true__
% 19.58/19.30 f5(true__, X) = there_exists(X)
% 19.58/19.30 f6(there_exists(codomain(X)), X) = true__
% 19.58/19.30 f6(true__, X) = there_exists(X)
% 19.58/19.30 f7(there_exists(compose(X, Y)), X) = true__
% 19.58/19.30 f7(true__, X) = there_exists(domain(X))
% 19.58/19.30 f8(there_exists(compose(X, Y)), X, Y) = codomain(Y)
% 19.58/19.30 f8(true__, X, Y) = domain(X)
% 19.58/19.30 f9(true__, X, Y) = there_exists(compose(X, Y))
% 19.58/19.30 there_exists(compose(a, b)) = true__
% 19.58/19.30 there_exists(compose(b, h)) = true__
% 19.58/19.30 G:
% 19.58/19.30 true__ = false__
% 19.58/19.30
% 19.58/19.30 This holds because
% 19.58/19.30
% 19.58/19.30 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 19.58/19.30
% 19.58/19.30 domain(domain(f8(f6(true__, compose(X0, a)), X0, a))) = f8(f6(true__, compose(true__, a)), true__, a)
% 19.58/19.30 f8(f6(true__, Y1), f8(f6(true__, compose(X0, Y1)), X0, Y1), Y1) = f8(f6(true__, compose(true__, Y1)), true__, Y1)
% 19.58/19.30 f8(f6(true__, compose(X0, compose(X1, Y1))), compose(X0, X1), Y1) = f8(f6(true__, compose(Y2, Y1)), Y2, Y1)
% 19.58/19.30 f8(f6(true__, compose(X0, compose(X1, Y1))), compose(X0, X1), Y1) = f8(f6(true__, compose(true__, Y1)), true__, Y1)
% 19.58/19.30 f8(f6(true__, compose(X1, Y0)), X1, Y0) = f8(f6(true__, compose(Y1, Y0)), Y1, Y0)
% 19.58/19.30 f8(f6(true__, compose(Y0, Y1)), compose(Y0, Y1), domain(Y1)) = f8(f6(true__, compose(true__, domain(Y1))), true__, domain(Y1))
% 19.58/19.30 f8(f6(true__, compose(Y0, compose(Y1, X1))), compose(Y0, Y1), compose(domain(Y1), X1)) = f8(f6(true__, compose(true__, compose(domain(Y1), X1))), true__, compose(domain(Y1), X1))
% 19.58/19.30 f8(there_exists(compose(X, Y)), X, Y) = codomain(Y)
% 19.58/19.30 compose(X, domain(X)) -> X
% 19.58/19.30 compose(X0, compose(X1, compose(Y1, domain(compose(X0, compose(X1, Y1)))))) -> compose(X0, compose(X1, Y1))
% 19.58/19.30 compose(X0, compose(X1, compose(Y1, domain(compose(domain(compose(X0, X1)), Y1))))) -> compose(X0, compose(X1, Y1))
% 19.58/19.30 compose(X0, compose(X1, compose(Y1, domain(domain(compose(X0, compose(X1, Y1))))))) -> compose(X0, compose(X1, Y1))
% 19.58/19.30 compose(X0, compose(X1, compose(domain(domain(compose(X0, X1))), Y1))) -> compose(X0, compose(X1, Y1))
% 19.58/19.30 compose(X0, compose(X1, compose(domain(domain(domain(compose(X0, X1)))), Y1))) -> compose(X0, compose(X1, Y1))
% 19.58/19.30 compose(Y0, compose(X0, compose(X1, domain(compose(domain(Y0), compose(X0, X1)))))) -> compose(Y0, compose(X0, X1))
% 19.58/19.30 compose(Y0, compose(X1, compose(domain(compose(Y0, X1)), domain(compose(Y0, X1))))) -> compose(Y0, X1)
% 19.58/19.30 compose(Y0, compose(X1, compose(domain(compose(domain(Y0), X1)), Y2))) -> compose(Y0, compose(X1, Y2))
% 19.58/19.30 compose(Y0, compose(X1, domain(compose(domain(Y0), X1)))) -> compose(Y0, X1)
% 19.58/19.30 compose(Y0, compose(X1, domain(compose(domain(domain(Y0)), X1)))) -> compose(Y0, X1)
% 19.58/19.30 compose(Y0, compose(X1, domain(compose(domain(domain(domain(Y0))), X1)))) -> compose(Y0, X1)
% 19.58/19.30 compose(Y0, compose(X1, domain(domain(compose(domain(Y0), X1))))) -> compose(Y0, X1)
% 19.58/19.30 compose(Y0, compose(Y1, compose(domain(compose(Y0, Y1)), X1))) -> compose(Y0, compose(Y1, X1))
% 19.58/19.30 compose(Y0, compose(Y1, domain(compose(Y0, Y1)))) -> compose(Y0, Y1)
% 19.58/19.30 compose(Y0, compose(Y1, domain(domain(compose(Y0, Y1))))) -> compose(Y0, Y1)
% 19.58/19.30 compose(Y0, compose(Y1, domain(domain(domain(compose(Y0, Y1)))))) -> compose(Y0, Y1)
% 19.58/19.30 compose(Y0, compose(Y1, domain(domain(domain(domain(compose(Y0, Y1))))))) -> compose(Y0, Y1)
% 19.58/19.30 compose(Y0, compose(domain(Y0), Y2)) -> compose(Y0, Y2)
% 19.58/19.30 compose(Y0, compose(domain(domain(Y0)), X1)) -> compose(Y0, X1)
% 19.58/19.30 compose(Y0, compose(domain(domain(domain(Y0))), X1)) -> compose(Y0, X1)
% 19.58/19.30 compose(Y0, compose(domain(domain(domain(Y0))), domain(domain(Y0)))) -> compose(Y0, domain(domain(domain(Y0))))
% 19.58/19.30 compose(Y0, compose(domain(domain(domain(domain(Y0)))), Y2)) -> compose(Y0, Y2)
% 19.58/19.30 compose(Y0, compose(domain(domain(domain(domain(Y0)))), domain(Y0))) -> Y0
% 19.58/19.30 compose(Y0, compose(domain(domain(domain(domain(Y0)))), domain(domain(Y0)))) -> Y0
% 19.58/19.30 compose(Y0, compose(domain(domain(domain(domain(domain(Y0))))), X1)) -> compose(Y0, X1)
% 19.58/19.30 compose(Y0, compose(domain(domain(domain(domain(domain(Y0))))), domain(domain(Y0)))) -> compose(Y0, domain(domain(domain(domain(domain(Y0))))))
% 19.58/19.30 compose(Y0, domain(compose(domain(Y0), domain(Y0)))) -> Y0
% 19.58/19.30 compose(Y0, domain(domain(Y0))) -> Y0
% 19.58/19.30 compose(Y0, domain(domain(domain(Y0)))) -> Y0
% 19.58/19.30 compose(Y0, domain(domain(domain(domain(Y0))))) -> Y0
% 19.58/19.30 compose(Y0, domain(domain(domain(domain(domain(Y0)))))) -> Y0
% 19.58/19.30 compose(Y0, domain(domain(domain(domain(domain(domain(Y0))))))) -> Y0
% 19.58/19.30 compose(Y0, domain(domain(domain(domain(domain(domain(domain(Y0)))))))) -> Y0
% 19.58/19.30 compose(b, compose(g, Y2)) -> compose(b, compose(h, Y2))
% 19.58/19.30 compose(b, compose(h, compose(X0, domain(compose(b, compose(h, X0)))))) -> compose(b, compose(h, X0))
% 19.58/19.30 compose(b, compose(h, compose(X0, domain(domain(compose(b, compose(h, X0))))))) -> compose(b, compose(h, X0))
% 19.58/19.30 compose(b, compose(h, compose(X1, domain(compose(g, X1))))) -> compose(b, compose(h, X1))
% 19.58/19.30 compose(b, compose(h, compose(domain(domain(g)), X1))) -> compose(b, compose(h, X1))
% 19.58/19.30 compose(b, compose(h, compose(domain(g), X1))) -> compose(b, compose(h, X1))
% 19.58/19.30 compose(b, compose(h, domain(domain(domain(domain(domain(h))))))) -> compose(b, h)
% 19.58/19.30 compose(b, compose(h, domain(domain(domain(g))))) -> compose(b, h)
% 19.58/19.30 compose(b, compose(h, domain(domain(g)))) -> compose(b, h)
% 19.58/19.30 compose(b, compose(h, domain(g))) -> compose(b, h)
% 19.58/19.30 compose(b, g) -> compose(b, h)
% 19.58/19.30 compose(codomain(X), X) -> X
% 19.58/19.30 compose(compose(X, Y), Z) -> compose(X, compose(Y, Z))
% 19.58/19.30 compose(domain(a), b) -> b
% 19.58/19.30 compose(domain(a), compose(b, Y2)) -> compose(b, Y2)
% 19.58/19.30 compose(domain(a), compose(domain(a), Y1)) -> compose(domain(a), Y1)
% 19.58/19.30 compose(domain(a), domain(a)) -> domain(a)
% 19.58/19.30 compose(domain(b), compose(domain(b), Y1)) -> compose(domain(b), Y1)
% 19.58/19.30 compose(domain(b), compose(g, Y2)) -> compose(g, Y2)
% 19.58/19.30 compose(domain(b), compose(h, Y2)) -> compose(h, Y2)
% 19.58/19.30 compose(domain(b), compose(h, domain(g))) -> compose(h, domain(g))
% 19.58/19.30 compose(domain(b), domain(b)) -> domain(b)
% 19.58/19.30 compose(domain(b), g) -> g
% 19.58/19.30 compose(domain(b), h) -> h
% 19.58/19.30 compose(domain(compose(a, b)), domain(compose(a, b))) -> domain(compose(a, b))
% 19.58/19.30 compose(domain(compose(b, h)), domain(compose(b, h))) -> domain(compose(b, h))
% 19.58/19.30 compose(domain(domain(a)), b) -> b
% 19.58/19.30 compose(domain(domain(a)), compose(b, Y2)) -> compose(b, Y2)
% 19.58/19.30 compose(domain(domain(a)), domain(domain(a))) -> domain(domain(a))
% 19.58/19.30 compose(domain(domain(b)), compose(g, Y2)) -> compose(g, Y2)
% 19.58/19.30 compose(domain(domain(b)), compose(h, Y2)) -> compose(h, Y2)
% 19.58/19.30 compose(domain(domain(b)), domain(domain(b))) -> domain(domain(b))
% 19.58/19.30 compose(domain(domain(b)), g) -> g
% 19.58/19.30 compose(domain(domain(b)), h) -> h
% 19.58/19.30 compose(domain(domain(compose(a, b))), domain(domain(compose(a, b)))) -> domain(domain(compose(a, b)))
% 19.58/19.30 compose(domain(domain(compose(b, h))), domain(domain(compose(b, h)))) -> domain(domain(compose(b, h)))
% 19.58/19.30 compose(domain(domain(domain(a))), domain(domain(domain(a)))) -> domain(domain(domain(a)))
% 19.58/19.30 compose(domain(domain(domain(b))), domain(domain(domain(b)))) -> domain(domain(domain(b)))
% 19.58/19.30 compose(domain(domain(domain(compose(a, b)))), domain(domain(domain(compose(a, b))))) -> domain(domain(domain(compose(a, b))))
% 19.58/19.30 compose(domain(domain(domain(compose(b, h)))), domain(domain(domain(compose(b, h))))) -> domain(domain(domain(compose(b, h))))
% 19.58/19.30 compose(domain(domain(f8(f6(true__, compose(true__, a)), true__, a))), a) -> a
% 19.58/19.30 compose(domain(domain(h)), compose(domain(domain(h)), Y1)) -> compose(domain(domain(h)), Y1)
% 19.58/19.30 compose(domain(domain(h)), domain(domain(h))) -> domain(domain(h))
% 19.58/19.30 compose(domain(domain(h)), domain(h)) -> domain(h)
% 19.58/19.30 compose(domain(f8(f6(true__, compose(X0, a)), X0, a)), compose(a, Y2)) -> compose(a, Y2)
% 19.58/19.30 compose(domain(f8(f6(true__, compose(X0, compose(X1, a))), compose(X0, X1), a)), a) -> a
% 19.58/19.30 compose(domain(f8(f6(true__, compose(Y1, a)), Y1, a)), a) -> a
% 19.58/19.30 compose(domain(g), domain(g)) -> domain(g)
% 19.58/19.30 compose(domain(h), compose(domain(h), Y2)) -> compose(domain(h), Y2)
% 19.58/19.30 compose(domain(h), domain(h)) -> domain(h)
% 19.58/19.30 compose(f8(f6(true__, Y0), Y0, domain(Y0)), compose(domain(Y0), Y2)) -> compose(domain(Y0), Y2)
% 19.58/19.30 compose(f8(f6(true__, Y0), Y0, domain(Y0)), domain(Y0)) -> domain(Y0)
% 19.58/19.30 compose(f8(f6(true__, Y0), Y0, domain(domain(Y0))), compose(domain(domain(Y0)), Y2)) -> compose(domain(domain(Y0)), Y2)
% 19.58/19.30 compose(f8(f6(true__, Y0), Y0, domain(domain(Y0))), domain(domain(Y0))) -> domain(domain(Y0))
% 19.58/19.30 compose(f8(f6(true__, Y0), Y0, domain(domain(domain(Y0)))), domain(domain(domain(Y0)))) -> domain(domain(domain(Y0)))
% 19.58/19.30 compose(f8(f6(true__, Y0), Y0, domain(domain(domain(domain(Y0))))), domain(domain(domain(domain(Y0))))) -> domain(domain(domain(domain(Y0))))
% 19.58/19.30 compose(f8(f6(true__, Y1), f8(f6(true__, compose(X0, Y1)), X0, Y1), Y1), Y1) -> Y1
% 19.58/19.30 compose(f8(f6(true__, compose(X0, Y1)), X0, Y1), compose(Y1, Y2)) -> compose(Y1, Y2)
% 19.58/19.30 compose(f8(f6(true__, compose(X0, compose(X1, Y1))), compose(X0, X1), Y1), Y1) -> Y1
% 19.58/19.30 compose(f8(f6(true__, compose(X1, Y0)), X1, Y0), Y0) -> Y0
% 19.58/19.30 compose(f8(f6(true__, compose(Y0, X1)), Y0, compose(X1, domain(compose(Y0, X1)))), compose(X1, domain(compose(Y0, X1)))) -> compose(X1, domain(compose(Y0, X1)))
% 19.58/19.30 compose(f8(f6(true__, compose(Y0, X1)), Y0, compose(domain(Y0), X1)), compose(domain(Y0), X1)) -> compose(domain(Y0), X1)
% 19.58/19.30 compose(f8(f6(true__, compose(Y0, X1)), Y0, compose(domain(domain(Y0)), X1)), compose(domain(domain(Y0)), X1)) -> compose(domain(domain(Y0)), X1)
% 19.58/19.30 compose(f8(f6(true__, compose(Y0, Y1)), compose(Y0, Y1), domain(Y1)), domain(Y1)) -> domain(Y1)
% 19.58/19.30 compose(f8(f6(true__, compose(Y0, Y1)), compose(Y0, Y1), domain(domain(Y1))), domain(domain(Y1))) -> domain(domain(Y1))
% 19.58/19.30 compose(f8(f6(true__, compose(Y0, b)), compose(Y0, domain(a)), b), b) -> b
% 19.58/19.30 compose(f8(f6(true__, compose(Y0, f8(f6(true__, compose(true__, Y2)), true__, Y2))), Y0, f8(f6(true__, compose(true__, Y2)), true__, Y2)), Y2) -> Y2
% 19.58/19.30 compose(f8(f6(true__, compose(Y0, g)), compose(Y0, domain(b)), g), g) -> g
% 19.58/19.30 compose(f8(f6(true__, compose(Y0, h)), compose(Y0, domain(b)), h), h) -> h
% 19.58/19.30 compose(f8(f6(true__, compose(b, X0)), domain(a), compose(b, X0)), compose(b, X0)) -> compose(b, X0)
% 19.58/19.30 compose(f8(f6(true__, compose(b, compose(h, X0))), b, compose(g, X0)), compose(g, X0)) -> compose(g, X0)
% 19.58/19.30 compose(f8(f6(true__, compose(domain(a), compose(b, Y2))), b, Y2), Y2) -> Y2
% 19.58/19.30 compose(f8(f6(true__, compose(domain(b), compose(g, Y2))), g, Y2), Y2) -> Y2
% 19.58/19.30 compose(f8(f6(true__, compose(domain(b), compose(h, Y2))), h, Y2), Y2) -> Y2
% 19.58/19.30 compose(f8(f6(true__, compose(h, X0)), domain(b), compose(h, X0)), compose(h, X0)) -> compose(h, X0)
% 19.58/19.30 compose(f8(f6(true__, compose(true__, X1)), true__, compose(domain(true__), X1)), compose(domain(true__), compose(X1, Y1))) -> compose(domain(true__), compose(X1, Y1))
% 19.58/19.30 compose(f8(f6(true__, compose(true__, Y1)), true__, Y1), compose(Y1, Y2)) -> compose(Y1, Y2)
% 19.58/19.30 compose(f8(f6(true__, compose(true__, compose(X0, X1))), true__, compose(X0, X1)), compose(X0, compose(X1, Y1))) -> compose(X0, compose(X1, Y1))
% 19.58/19.30 compose(f8(f6(true__, compose(true__, f8(f6(true__, compose(true__, Y1)), true__, Y1))), true__, f8(f6(true__, compose(true__, Y1)), true__, Y1)), Y1) -> Y1
% 19.58/19.30 compose(f8(f6(true__, domain(Y1)), f8(f6(true__, Y1), Y1, domain(Y1)), domain(Y1)), domain(Y1)) -> domain(Y1)
% 19.58/19.30 compose(f8(f6(true__, true__), true__, domain(domain(true__))), compose(domain(domain(true__)), Y1)) -> compose(domain(domain(true__)), Y1)
% 19.58/19.30 compose(f8(f6(true__, true__), true__, domain(true__)), compose(domain(true__), Y1)) -> compose(domain(true__), Y1)
% 19.58/19.30 domain(domain(a)) -> domain(a)
% 19.58/19.30 domain(domain(b)) -> domain(b)
% 19.58/19.30 domain(domain(compose(a, b))) -> domain(compose(a, b))
% 19.58/19.30 domain(domain(compose(b, h))) -> domain(compose(b, h))
% 19.58/19.30 domain(domain(domain(h))) -> domain(domain(h))
% 19.58/19.30 domain(domain(h)) -> domain(h)
% 19.58/19.30 domain(f8(f6(true__, compose(true__, compose(a, b))), true__, compose(a, b))) -> f8(f6(true__, compose(true__, compose(a, b))), true__, compose(a, b))
% 19.58/19.30 domain(f8(f6(true__, compose(true__, compose(b, h))), true__, compose(b, h))) -> f8(f6(true__, compose(true__, compose(b, h))), true__, compose(b, h))
% 19.58/19.30 domain(f8(f6(true__, compose(true__, domain(a))), true__, domain(a))) -> f8(f6(true__, compose(true__, domain(a))), true__, domain(a))
% 19.58/19.30 domain(f8(f6(true__, compose(true__, domain(b))), true__, domain(b))) -> f8(f6(true__, compose(true__, domain(b))), true__, domain(b))
% 19.58/19.30 equivalent(X, Y) -> f3(true__, X, Y)
% 19.58/19.30 f1(equivalent(X, Y), X) -> true__
% 19.58/19.30 f1(f3(true__, Y0, Y1), Y0) -> true__
% 19.58/19.30 f1(true__, X) -> there_exists(X)
% 19.58/19.30 f10(codomain(Y), Y, X) -> f9(there_exists(domain(X)), X, Y)
% 19.58/19.30 f10(domain(X), Y, X) -> true__
% 19.58/19.30 f10(domain(a), Y1, domain(a)) -> true__
% 19.58/19.30 f10(domain(a), b, Y2) -> f9(f6(true__, domain(Y2)), Y2, b)
% 19.58/19.30 f10(domain(b), Y1, domain(b)) -> true__
% 19.58/19.30 f10(domain(b), g, Y2) -> f9(f6(true__, domain(Y2)), Y2, g)
% 19.58/19.30 f10(domain(b), h, Y2) -> f9(f6(true__, domain(Y2)), Y2, h)
% 19.58/19.30 f10(f8(f6(true__, Y0), Y0, domain(Y0)), domain(Y0), Y2) -> f9(f6(true__, domain(Y2)), Y2, domain(Y0))
% 19.58/19.30 f10(f8(f6(true__, compose(X0, compose(X1, Y1))), compose(X0, X1), Y1), Y1, Y2) -> f9(f6(true__, domain(Y2)), Y2, Y1)
% 19.58/19.30 f10(f8(f6(true__, compose(X1, Y0)), X1, Y0), Y0, Y1) -> f9(f6(true__, domain(Y1)), Y1, Y0)
% 19.58/19.30 f10(f8(f6(true__, compose(Y0, X1)), Y0, compose(domain(Y0), X1)), compose(domain(Y0), X1), Y2) -> f9(f6(true__, domain(Y2)), Y2, compose(domain(Y0), X1))
% 19.58/19.30 f11(Y, Y, X, Z) -> X
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% 19.58/19.30 f11(compose(a, b), compose(a, compose(b, Y1)), domain(b), Y1) -> Y1
% 19.58/19.30 f11(compose(a, b), compose(a, compose(b, Y1)), domain(domain(b)), Y1) -> Y1
% 19.58/19.30 f11(compose(a, b), compose(a, compose(b, h)), domain(b), g) -> g
% 19.58/19.30 f11(compose(a, compose(b, X1)), compose(a, compose(b, Y1)), compose(domain(b), X1), Y1) -> Y1
% 19.58/19.30 f11(compose(a, compose(b, Y0)), compose(a, b), Y0, domain(b)) -> domain(b)
% 19.58/19.30 f11(compose(a, compose(b, Y0)), compose(a, b), Y0, domain(domain(b))) -> domain(domain(b))
% 19.58/19.30 f11(compose(a, compose(b, Y0)), compose(a, compose(b, X1)), Y0, compose(domain(b), X1)) -> compose(domain(b), X1)
% 19.58/19.30 f11(compose(a, compose(b, Y0)), compose(a, compose(b, compose(h, X0))), Y0, compose(g, X0)) -> compose(g, X0)
% 19.58/19.30 f11(compose(a, compose(b, Y0)), compose(a, compose(b, h)), Y0, g) -> g
% 19.58/19.30 f11(compose(a, compose(b, Y1)), compose(a, compose(b, Y2)), Y1, Y2) -> Y2
% 19.58/19.30 f11(compose(a, compose(b, compose(h, X0))), compose(a, compose(b, Y1)), compose(g, X0), Y1) -> Y1
% 19.58/19.30 f11(compose(a, compose(b, h)), compose(a, b), g, domain(b)) -> domain(b)
% 19.58/19.30 f11(compose(a, compose(b, h)), compose(a, compose(b, Y1)), g, Y1) -> Y1
% 19.58/19.30 f12(Y, Y, X, Z) -> f11(compose(compose(a, b), X), Y, X, Z)
% 19.58/19.30 f12(compose(a, b), Y1, Y2, compose(domain(b), domain(b))) -> compose(domain(b), domain(b))
% 19.58/19.30 f12(compose(a, b), Y1, Y2, domain(b)) -> domain(b)
% 19.58/19.30 f12(compose(a, b), Y1, Y2, domain(compose(a, b))) -> domain(compose(a, b))
% 19.58/19.30 f12(compose(a, b), Y1, Y2, domain(domain(b))) -> domain(domain(b))
% 19.58/19.30 f12(compose(a, b), Y1, Y2, domain(domain(compose(a, b)))) -> domain(domain(compose(a, b)))
% 19.58/19.30 f12(compose(a, b), Y1, Y2, domain(domain(domain(compose(a, b))))) -> domain(domain(domain(compose(a, b))))
% 19.58/19.30 f12(compose(a, b), Y1, Y2, domain(domain(domain(domain(compose(a, b)))))) -> domain(domain(domain(domain(compose(a, b)))))
% 19.58/19.30 f12(compose(a, compose(b, X1)), Y1, Y2, compose(X1, domain(compose(a, compose(b, X1))))) -> compose(X1, domain(compose(a, compose(b, X1))))
% 19.58/19.30 f12(compose(a, compose(b, X1)), Y1, Y2, compose(X1, domain(compose(b, X1)))) -> compose(X1, domain(compose(b, X1)))
% 19.58/19.30 f12(compose(a, compose(b, X1)), Y1, Y2, compose(X1, domain(compose(domain(b), X1)))) -> compose(X1, domain(compose(domain(b), X1)))
% 19.58/19.30 f12(compose(a, compose(b, X1)), Y1, Y2, compose(X1, domain(compose(domain(compose(a, b)), X1)))) -> compose(X1, domain(compose(domain(compose(a, b)), X1)))
% 19.58/19.30 f12(compose(a, compose(b, X1)), Y1, Y2, compose(X1, domain(domain(compose(a, compose(b, X1)))))) -> compose(X1, domain(domain(compose(a, compose(b, X1)))))
% 19.58/19.30 f12(compose(a, compose(b, X1)), Y1, Y2, compose(X1, domain(domain(compose(b, X1))))) -> compose(X1, domain(domain(compose(b, X1))))
% 19.58/19.30 f12(compose(a, compose(b, X1)), Y1, Y2, compose(domain(b), X1)) -> compose(domain(b), X1)
% 19.58/19.30 f12(compose(a, compose(b, X1)), Y1, Y2, compose(domain(compose(a, b)), X1)) -> compose(domain(compose(a, b)), X1)
% 19.58/19.30 f12(compose(a, compose(b, X1)), Y1, Y2, compose(domain(domain(compose(a, b))), X1)) -> compose(domain(domain(compose(a, b))), X1)
% 19.58/19.30 f12(compose(a, compose(b, X1)), Y1, Y2, compose(domain(domain(domain(compose(a, b)))), X1)) -> compose(domain(domain(domain(compose(a, b)))), X1)
% 19.58/19.30 f12(compose(a, compose(b, Y0)), Y1, Y2, Y0) -> Y0
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% 19.58/19.30 f12(compose(a, compose(b, h)), Y1, Y2, compose(g, domain(h))) -> compose(g, domain(h))
% 19.58/19.30 f12(compose(a, compose(b, h)), Y1, Y2, compose(h, domain(g))) -> compose(h, domain(g))
% 19.58/19.30 f12(compose(a, compose(b, h)), Y1, Y2, g) -> g
% 19.58/19.30 f12(compose(compose(a, b), Z), Y, X, Z) -> Z
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% 19.58/19.30 f2(equivalent(X, Y), X, Y) -> Y
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% 19.58/19.30 f2(true__, X, Y) -> X
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% 19.58/19.30 f3(true__, compose(b, h), compose(b, h)) -> true__
% 19.58/19.30 f3(true__, domain(a), domain(a)) -> true__
% 19.58/19.30 f3(true__, domain(b), domain(b)) -> true__
% 19.58/19.30 f3(true__, domain(compose(a, b)), domain(compose(a, b))) -> true__
% 19.58/19.30 f3(true__, domain(compose(b, h)), domain(compose(b, h))) -> true__
% 19.58/19.30 f3(true__, domain(domain(a)), domain(domain(a))) -> true__
% 19.58/19.30 f3(true__, domain(domain(b)), domain(domain(b))) -> true__
% 19.58/19.30 f3(true__, domain(domain(compose(a, b))), domain(domain(compose(a, b)))) -> true__
% 19.58/19.30 f3(true__, domain(domain(compose(b, h))), domain(domain(compose(b, h)))) -> true__
% 19.58/19.30 f3(true__, domain(f8(f6(true__, compose(X0, a)), X0, a)), domain(f8(f6(true__, compose(X0, a)), X0, a))) -> true__
% 19.58/19.30 f3(true__, domain(f8(f6(true__, compose(true__, a)), true__, a)), domain(f8(f6(true__, compose(true__, a)), true__, a))) -> true__
% 19.58/19.30 f3(true__, domain(h), domain(h)) -> true__
% 19.58/19.30 f3(true__, g, g) -> true__
% 19.58/19.30 f3(true__, h, h) -> true__
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% 19.58/19.30 f6(f6(true__, domain(domain(domain(compose(a, b))))), domain(domain(domain(compose(a, b))))) -> true__
% 19.58/19.30 f6(f6(true__, domain(domain(domain(compose(b, h))))), domain(domain(domain(compose(b, h))))) -> true__
% 19.58/19.30 f6(f6(true__, domain(domain(h))), domain(domain(domain(h)))) -> true__
% 19.58/19.30 f6(f6(true__, domain(domain(h))), domain(domain(h))) -> true__
% 19.58/19.30 f6(f6(true__, domain(domain(h))), domain(h)) -> true__
% 19.58/19.30 f6(f6(true__, domain(g)), domain(g)) -> true__
% 19.58/19.30 f6(f6(true__, domain(h)), domain(h)) -> true__
% 19.58/19.30 f6(f6(true__, f8(f6(true__, Y0), Y0, domain(Y0))), domain(Y0)) -> true__
% 19.58/19.30 f6(f6(true__, f8(f6(true__, Y0), Y0, domain(domain(Y0)))), domain(domain(Y0))) -> true__
% 19.58/19.30 f6(f6(true__, f8(f6(true__, Y0), Y0, domain(domain(domain(Y0))))), domain(domain(domain(Y0)))) -> true__
% 19.58/19.30 f6(f6(true__, f8(f6(true__, Y0), Y0, domain(domain(domain(domain(Y0)))))), domain(domain(domain(domain(Y0))))) -> true__
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% 19.58/19.30 f6(f6(true__, f8(f6(true__, compose(X0, compose(X1, Y1))), compose(X0, X1), Y1)), Y1) -> true__
% 19.58/19.30 f6(f6(true__, f8(f6(true__, compose(X1, Y0)), X1, Y0)), Y0) -> true__
% 19.58/19.30 f6(f6(true__, f8(f6(true__, compose(Y0, X1)), Y0, compose(X1, domain(compose(Y0, X1))))), compose(X1, domain(compose(Y0, X1)))) -> true__
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% 19.58/19.30 f6(f6(true__, f8(f6(true__, compose(h, X0)), domain(b), compose(h, X0))), compose(h, X0)) -> true__
% 19.58/19.30 f6(f6(true__, f8(f6(true__, compose(true__, X1)), true__, compose(X1, domain(compose(true__, X1))))), compose(X1, domain(compose(true__, X1)))) -> true__
% 19.58/19.30 f6(f6(true__, f8(f6(true__, compose(true__, X1)), true__, compose(domain(true__), X1))), compose(domain(true__), X1)) -> true__
% 19.58/19.30 f6(f6(true__, f8(f6(true__, compose(true__, Y0)), true__, Y0)), Y0) -> true__
% 19.58/19.30 f6(f6(true__, f8(f6(true__, true__), true__, domain(domain(domain(domain(true__)))))), domain(domain(domain(domain(true__))))) -> true__
% 19.58/19.30 f6(f6(true__, f8(f6(true__, true__), true__, domain(domain(domain(true__))))), domain(domain(domain(true__)))) -> true__
% 19.58/19.30 f6(f6(true__, f8(f6(true__, true__), true__, domain(domain(true__)))), domain(domain(true__))) -> true__
% 19.58/19.30 f6(f6(true__, f8(f6(true__, true__), true__, domain(true__))), domain(true__)) -> true__
% 19.58/19.30 f6(there_exists(codomain(X)), X) -> true__
% 19.58/19.30 f6(true__, a) -> true__
% 19.58/19.30 f6(true__, b) -> true__
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% 19.58/19.30 f6(true__, compose(b, h)) -> true__
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% 19.58/19.30 f6(true__, domain(b)) -> true__
% 19.58/19.30 f6(true__, domain(compose(a, b))) -> true__
% 19.58/19.30 f6(true__, domain(compose(b, h))) -> true__
% 19.58/19.30 f6(true__, domain(domain(a))) -> true__
% 19.58/19.30 f6(true__, domain(domain(b))) -> true__
% 19.58/19.30 f6(true__, domain(domain(compose(a, b)))) -> true__
% 19.58/19.30 f6(true__, domain(domain(compose(b, h)))) -> true__
% 19.58/19.30 f6(true__, domain(domain(domain(a)))) -> true__
% 19.58/19.30 f6(true__, domain(domain(domain(b)))) -> true__
% 19.58/19.30 f6(true__, domain(domain(domain(compose(a, b))))) -> true__
% 19.58/19.30 f6(true__, domain(domain(domain(compose(b, h))))) -> true__
% 19.58/19.30 f6(true__, domain(domain(domain(h)))) -> true__
% 19.58/19.30 f6(true__, domain(domain(f8(f6(true__, compose(X0, a)), X0, a)))) -> true__
% 19.58/19.30 f6(true__, domain(domain(f8(f6(true__, compose(true__, a)), true__, a)))) -> true__
% 19.58/19.30 f6(true__, domain(domain(h))) -> true__
% 19.58/19.30 f6(true__, domain(f8(f6(true__, compose(X0, b)), compose(X0, domain(a)), b))) -> true__
% 19.58/19.30 f6(true__, domain(f8(f6(true__, compose(X0, compose(X1, a))), compose(X0, X1), a))) -> true__
% 19.58/19.30 f6(true__, domain(f8(f6(true__, compose(X0, h)), compose(X0, domain(b)), h))) -> true__
% 19.58/19.30 f6(true__, domain(f8(f6(true__, compose(Y1, a)), Y1, a))) -> true__
% 19.58/19.30 f6(true__, domain(f8(f6(true__, compose(Y1, compose(a, b))), Y1, compose(a, b)))) -> true__
% 19.58/19.30 f6(true__, domain(f8(f6(true__, compose(Y1, compose(b, h))), Y1, compose(b, h)))) -> true__
% 19.58/19.30 f6(true__, domain(f8(f6(true__, compose(true__, a)), true__, a))) -> true__
% 19.58/19.30 f6(true__, domain(f8(f6(true__, compose(true__, compose(a, b))), true__, compose(a, b)))) -> true__
% 19.58/19.30 f6(true__, domain(f8(f6(true__, compose(true__, compose(b, h))), true__, compose(b, h)))) -> true__
% 19.58/19.30 f6(true__, domain(f8(f6(true__, compose(true__, domain(a))), true__, domain(a)))) -> true__
% 19.58/19.30 f6(true__, domain(f8(f6(true__, compose(true__, domain(b))), true__, domain(b)))) -> true__
% 19.58/19.30 f6(true__, domain(g)) -> true__
% 19.58/19.30 f6(true__, domain(h)) -> true__
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% 19.58/19.30 f6(true__, f8(f6(true__, compose(true__, a)), true__, a)) -> true__
% 19.58/19.30 f6(true__, g) -> true__
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% 19.58/19.30 f7(f6(true__, compose(Y0, Y1)), Y0) -> true__
% 19.58/19.30 f7(f6(true__, compose(Y0, Y2)), compose(Y0, f8(f6(true__, compose(X0, Y2)), X0, Y2))) -> true__
% 19.58/19.30 f7(f6(true__, compose(Y0, Y2)), compose(Y0, f8(f6(true__, compose(true__, Y2)), true__, Y2))) -> true__
% 19.58/19.30 f7(f6(true__, compose(Y0, b)), compose(Y0, domain(a))) -> true__
% 19.58/19.30 f7(f6(true__, compose(Y0, compose(Y1, Y3))), compose(Y0, compose(Y1, f8(f6(true__, compose(true__, Y3)), true__, Y3)))) -> true__
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% 19.58/19.30 f7(f6(true__, compose(Y0, g)), compose(Y0, domain(b))) -> true__
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% 19.58/19.30 f7(f6(true__, compose(Y1, Y2)), compose(f8(f6(true__, compose(X0, compose(Y1, Y2))), X0, compose(Y1, Y2)), Y1)) -> true__
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% 19.58/19.30 f7(f6(true__, compose(b, compose(h, b))), compose(b, compose(h, domain(a)))) -> true__
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% 19.58/19.30 f7(f6(true__, compose(b, compose(h, h))), compose(b, compose(h, domain(b)))) -> true__
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% 19.58/19.30 f7(f6(true__, compose(domain(a), compose(b, Y2))), b) -> true__
% 19.58/19.30 f7(f6(true__, compose(domain(b), compose(g, Y2))), g) -> true__
% 19.58/19.30 f7(f6(true__, compose(domain(b), compose(h, Y2))), h) -> true__
% 19.58/19.30 f7(f6(true__, compose(domain(domain(true__)), Y1)), f8(f6(true__, true__), true__, domain(domain(true__)))) -> true__
% 19.58/19.30 f7(f6(true__, compose(domain(true__), X1)), f8(f6(true__, compose(true__, X1)), true__, compose(domain(true__), X1))) -> true__
% 19.58/19.30 f7(f6(true__, compose(domain(true__), Y1)), f8(f6(true__, true__), true__, domain(true__))) -> true__
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% 19.58/19.30 f7(f6(true__, domain(domain(domain(domain(true__))))), f8(f6(true__, true__), true__, domain(domain(domain(domain(true__)))))) -> true__
% 19.58/19.30 f7(f6(true__, domain(domain(domain(h)))), domain(domain(h))) -> true__
% 19.58/19.30 f7(f6(true__, domain(domain(domain(true__)))), f8(f6(true__, true__), true__, domain(domain(domain(true__))))) -> true__
% 19.58/19.30 f7(f6(true__, domain(domain(h))), domain(h)) -> true__
% 19.58/19.30 f7(f6(true__, domain(domain(true__))), f8(f6(true__, true__), true__, domain(domain(true__)))) -> true__
% 19.58/19.30 f7(f6(true__, domain(true__)), f8(f6(true__, true__), true__, domain(true__))) -> true__
% 19.58/19.30 f7(there_exists(compose(X, Y)), X) -> true__
% 19.58/19.30 f7(true__, X) -> there_exists(domain(X))
% 19.58/19.30 f8(f6(true__, Y1), f8(f6(true__, compose(true__, Y1)), true__, Y1), Y1) -> f8(f6(true__, compose(true__, Y1)), true__, Y1)
% 19.58/19.30 f8(f6(true__, compose(X0, compose(X1, b))), compose(X0, X1), b) -> domain(a)
% 19.58/19.30 f8(f6(true__, compose(X0, compose(X1, g))), compose(X0, X1), g) -> domain(b)
% 19.58/19.30 f8(f6(true__, compose(X0, compose(X1, h))), compose(X0, X1), h) -> domain(b)
% 19.58/19.30 f8(f6(true__, compose(Y0, Y2)), compose(Y0, f8(f6(true__, compose(true__, Y2)), true__, Y2)), Y2) -> f8(f6(true__, compose(true__, Y2)), true__, Y2)
% 19.58/19.30 f8(f6(true__, compose(Y0, b)), compose(Y0, domain(a)), b) -> domain(a)
% 19.58/19.30 f8(f6(true__, compose(Y0, compose(b, h))), compose(Y0, b), g) -> f8(f6(true__, compose(true__, g)), true__, g)
% 19.58/19.30 f8(f6(true__, compose(Y0, h)), compose(Y0, domain(b)), h) -> domain(b)
% 19.58/19.30 f8(f6(true__, compose(Y1, Y2)), compose(f8(f6(true__, compose(true__, compose(Y1, Y2))), true__, compose(Y1, Y2)), Y1), Y2) -> f8(f6(true__, compose(true__, Y2)), true__, Y2)
% 19.58/19.30 f8(f6(true__, compose(Y1, compose(Y2, domain(true__)))), compose(Y1, Y2), domain(true__)) -> f8(f6(true__, true__), true__, domain(true__))
% 19.58/19.30 f8(f6(true__, compose(Y2, b)), Y2, b) -> domain(a)
% 19.58/19.30 f8(f6(true__, compose(Y2, compose(domain(Y0), X1))), Y2, compose(domain(Y0), X1)) -> f8(f6(true__, compose(Y0, X1)), Y0, compose(domain(Y0), X1))
% 19.58/19.30 f8(f6(true__, compose(Y2, domain(Y0))), Y2, domain(Y0)) -> f8(f6(true__, Y0), Y0, domain(Y0))
% 19.58/19.30 f8(f6(true__, compose(Y2, g)), Y2, g) -> domain(b)
% 19.58/19.30 f8(f6(true__, compose(Y2, h)), Y2, h) -> domain(b)
% 19.58/19.30 f8(f6(true__, domain(true__)), f8(f6(true__, true__), true__, domain(true__)), domain(true__)) -> f8(f6(true__, true__), true__, domain(true__))
% 19.58/19.30 f8(true__, X, Y) -> domain(X)
% 19.58/19.30 f9(true__, X, Y) -> there_exists(compose(X, Y))
% 19.58/19.30 false__ -> true__
% 19.58/19.30 g -> h
% 19.58/19.30 there_exists(X) -> f6(true__, X)
% 19.58/19.30 there_exists(compose(a, b)) -> true__
% 19.58/19.30 there_exists(compose(b, h)) -> true__
% 19.58/19.30 with the LPO induced by
% 19.58/19.30 codomain > f10 > f9 > f2 > f12 > compose > f5 > f1 > f13 > g > h > a > f11 > b > f4 > equivalent > f7 > there_exists > f6 > f3 > f8 > domain > false__ > true__
% 19.58/19.30
% 19.58/19.30 % SZS output end Proof
% 19.58/19.30
%------------------------------------------------------------------------------