TSTP Solution File: CAT012-4 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : CAT012-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n018.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 00:04:56 EDT 2022
% Result : Unsatisfiable 1.59s 1.73s
% Output : Proof 1.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT012-4 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun May 29 20:35:11 EDT 2022
% 0.19/0.34 % CPUTime :
% 1.59/1.73 % SZS status Unsatisfiable
% 1.59/1.73 % SZS output start Proof
% 1.59/1.73 The input problem is unsatisfiable because
% 1.59/1.73
% 1.59/1.73 [1] the following set of Horn clauses is unsatisfiable:
% 1.59/1.73
% 1.59/1.73 equivalent(X, Y) ==> there_exists(X)
% 1.59/1.73 equivalent(X, Y) ==> X = Y
% 1.59/1.73 there_exists(X) & X = Y ==> equivalent(X, Y)
% 1.59/1.73 there_exists(domain(X)) ==> there_exists(X)
% 1.59/1.73 there_exists(codomain(X)) ==> there_exists(X)
% 1.59/1.73 there_exists(compose(X, Y)) ==> there_exists(domain(X))
% 1.59/1.73 there_exists(compose(X, Y)) ==> domain(X) = codomain(Y)
% 1.59/1.73 there_exists(domain(X)) & domain(X) = codomain(Y) ==> there_exists(compose(X, Y))
% 1.59/1.73 compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)
% 1.59/1.73 compose(X, domain(X)) = X
% 1.59/1.73 compose(codomain(X), X) = X
% 1.59/1.73 there_exists(domain(a))
% 1.59/1.73 codomain(domain(a)) = domain(a) ==> \bottom
% 1.59/1.73
% 1.59/1.73 This holds because
% 1.59/1.73
% 1.59/1.73 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.59/1.73
% 1.59/1.73 E:
% 1.59/1.73 compose(X, compose(Y, Z)) = compose(compose(X, Y), Z)
% 1.59/1.73 compose(X, domain(X)) = X
% 1.59/1.73 compose(codomain(X), X) = X
% 1.59/1.73 f1(equivalent(X, Y), X) = true__
% 1.59/1.73 f1(true__, X) = there_exists(X)
% 1.59/1.73 f10(codomain(Y), Y, X) = f9(there_exists(domain(X)), X, Y)
% 1.59/1.73 f10(domain(X), Y, X) = true__
% 1.59/1.73 f11(codomain(domain(a))) = true__
% 1.59/1.73 f11(domain(a)) = false__
% 1.59/1.73 f2(equivalent(X, Y), X, Y) = Y
% 1.59/1.73 f2(true__, X, Y) = X
% 1.59/1.73 f3(true__, X, Y) = equivalent(X, Y)
% 1.59/1.73 f4(X, Y, X) = true__
% 1.59/1.73 f4(Y, Y, X) = f3(there_exists(X), X, Y)
% 1.59/1.73 f5(there_exists(domain(X)), X) = true__
% 1.59/1.73 f5(true__, X) = there_exists(X)
% 1.59/1.73 f6(there_exists(codomain(X)), X) = true__
% 1.59/1.73 f6(true__, X) = there_exists(X)
% 1.59/1.73 f7(there_exists(compose(X, Y)), X) = true__
% 1.59/1.73 f7(true__, X) = there_exists(domain(X))
% 1.59/1.73 f8(there_exists(compose(X, Y)), X, Y) = codomain(Y)
% 1.59/1.73 f8(true__, X, Y) = domain(X)
% 1.59/1.73 f9(true__, X, Y) = there_exists(compose(X, Y))
% 1.59/1.73 there_exists(domain(a)) = true__
% 1.59/1.73 G:
% 1.59/1.73 true__ = false__
% 1.59/1.73
% 1.59/1.73 This holds because
% 1.59/1.73
% 1.59/1.73 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.59/1.73
% 1.59/1.73
% 1.59/1.73 codomain(domain(a)) -> domain(a)
% 1.59/1.73 compose(X, domain(X)) -> X
% 1.59/1.73 compose(Y0, compose(Y1, domain(compose(Y0, Y1)))) -> compose(Y0, Y1)
% 1.59/1.73 compose(codomain(X), X) -> X
% 1.59/1.73 compose(compose(X, Y), Z) -> compose(X, compose(Y, Z))
% 1.59/1.73 compose(domain(a), domain(a)) -> domain(a)
% 1.59/1.73 equivalent(a, a) -> true__
% 1.59/1.73 equivalent(domain(a), domain(a)) -> true__
% 1.59/1.73 f1(equivalent(X, Y), X) -> true__
% 1.59/1.73 f1(true__, a) -> true__
% 1.59/1.73 f1(true__, domain(a)) -> true__
% 1.59/1.73 f1(true__, domain(codomain(a))) -> true__
% 1.59/1.73 f1(true__, domain(codomain(domain(a)))) -> true__
% 1.59/1.73 f1(true__, domain(domain(a))) -> true__
% 1.59/1.73 f1(true__, domain(domain(codomain(a)))) -> true__
% 1.59/1.73 f1(true__, domain(domain(domain(a)))) -> true__
% 1.59/1.73 f10(codomain(Y), Y, X) -> f9(there_exists(domain(X)), X, Y)
% 1.59/1.73 f10(domain(X), Y, X) -> true__
% 1.59/1.73 f11(codomain(domain(a))) -> true__
% 1.59/1.73 f11(domain(a)) -> false__
% 1.59/1.73 f2(equivalent(X, Y), X, Y) -> Y
% 1.59/1.73 f2(true__, X, Y) -> X
% 1.59/1.73 f3(f1(true__, Y1), Y1, Y1) -> true__
% 1.59/1.73 f3(true__, X, Y) -> equivalent(X, Y)
% 1.59/1.73 f4(X, Y, X) -> true__
% 1.59/1.73 f4(Y, Y, X) -> f3(there_exists(X), X, Y)
% 1.59/1.73 f5(f1(true__, domain(Y0)), Y0) -> true__
% 1.59/1.73 f5(there_exists(domain(X)), X) -> true__
% 1.59/1.73 f5(true__, X) -> there_exists(X)
% 1.59/1.73 f6(f1(true__, codomain(Y0)), Y0) -> true__
% 1.59/1.73 f6(there_exists(codomain(X)), X) -> true__
% 1.59/1.74 f6(true__, X) -> there_exists(X)
% 1.59/1.74 f7(f1(true__, Y0), Y0) -> true__
% 1.59/1.74 f7(f1(true__, Y1), codomain(Y1)) -> true__
% 1.59/1.74 f7(f1(true__, compose(Y0, Y1)), Y0) -> true__
% 1.59/1.74 f7(there_exists(compose(X, Y)), X) -> true__
% 1.59/1.74 f7(true__, X) -> there_exists(domain(X))
% 1.59/1.74 f8(f1(true__, Y0), Y0, domain(Y0)) -> codomain(domain(Y0))
% 1.59/1.74 f8(f1(true__, compose(Y0, Y1)), Y0, Y1) -> codomain(Y1)
% 1.59/1.74 f8(there_exists(compose(X, Y)), X, Y) -> codomain(Y)
% 1.59/1.74 f8(true__, X, Y) -> domain(X)
% 1.59/1.74 f9(true__, X, Y) -> there_exists(compose(X, Y))
% 1.59/1.74 false__ -> true__
% 1.59/1.74 there_exists(X) -> f1(true__, X)
% 1.59/1.74 there_exists(domain(a)) -> true__
% 1.59/1.74 with the LPO induced by
% 1.59/1.74 f11 > f7 > f10 > f9 > a > f2 > f8 > domain > f6 > f5 > f4 > f3 > there_exists > f1 > compose > codomain > equivalent > false__ > true__
% 1.59/1.74
% 1.59/1.74 % SZS output end Proof
% 1.59/1.74
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