TSTP Solution File: CAT019-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : CAT019-1 : 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 00:05:03 EDT 2022
% Result : Unsatisfiable 0.45s 0.65s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT019-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n021.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 23:25:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.45/0.65 % SZS status Unsatisfiable
% 0.45/0.65 % SZS output start Proof
% 0.45/0.65 The input problem is unsatisfiable because
% 0.45/0.65
% 0.45/0.65 [1] the following set of Horn clauses is unsatisfiable:
% 0.45/0.65
% 0.45/0.65 defined(X, Y) ==> product(X, Y, compose(X, Y))
% 0.45/0.65 product(X, Y, Z) ==> defined(X, Y)
% 0.45/0.65 product(X, Y, Xy) & defined(Xy, Z) ==> defined(Y, Z)
% 0.45/0.65 product(X, Y, Xy) & product(Y, Z, Yz) & defined(Xy, Z) ==> defined(X, Yz)
% 0.45/0.65 product(X, Y, Xy) & product(Xy, Z, Xyz) & product(Y, Z, Yz) ==> product(X, Yz, Xyz)
% 0.45/0.65 product(Y, Z, Yz) & defined(X, Yz) ==> defined(X, Y)
% 0.45/0.65 product(Y, Z, Yz) & product(X, Y, Xy) & defined(X, Yz) ==> defined(Xy, Z)
% 0.45/0.65 product(Y, Z, Yz) & product(X, Yz, Xyz) & product(X, Y, Xy) ==> product(Xy, Z, Xyz)
% 0.45/0.65 defined(X, Y) & defined(Y, Z) & identity_map(Y) ==> defined(X, Z)
% 0.45/0.65 identity_map(domain(X))
% 0.45/0.65 identity_map(codomain(X))
% 0.45/0.65 defined(X, domain(X))
% 0.45/0.65 defined(codomain(X), X)
% 0.45/0.65 product(X, domain(X), X)
% 0.45/0.65 product(codomain(X), X, X)
% 0.45/0.65 defined(X, Y) & identity_map(X) ==> product(X, Y, Y)
% 0.45/0.65 defined(X, Y) & identity_map(Y) ==> product(X, Y, X)
% 0.45/0.65 product(X, Y, Z) & product(X, Y, W) ==> Z = W
% 0.45/0.65 c2 = Z ==> c1 = Z
% 0.45/0.65 c1 = Z ==> c2 = Z
% 0.45/0.65 c2 = c1 ==> \bottom
% 0.45/0.65
% 0.45/0.65 This holds because
% 0.45/0.65
% 0.45/0.65 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.45/0.65
% 0.45/0.65 E:
% 0.45/0.65 defined(X, domain(X)) = true__
% 0.45/0.65 defined(codomain(X), X) = true__
% 0.45/0.65 f1(defined(X, Y), X, Y) = true__
% 0.45/0.65 f1(true__, X, Y) = product(X, Y, compose(X, Y))
% 0.45/0.65 f10(product(Y, Z, Yz), Xy, Z, Xyz, X, Y, Yz) = true__
% 0.45/0.65 f10(true__, Xy, Z, Xyz, X, Y, Yz) = f9(product(Xy, Z, Xyz), X, Y, Xy, Yz, Xyz)
% 0.45/0.65 f11(true__, X, Y) = defined(X, Y)
% 0.45/0.65 f12(defined(X, Yz), Y, Z, Yz, X) = true__
% 0.45/0.65 f12(true__, Y, Z, Yz, X) = f11(product(Y, Z, Yz), X, Y)
% 0.45/0.65 f13(true__, Xy, Z) = defined(Xy, Z)
% 0.45/0.65 f14(true__, Y, Z, Yz, Xy) = f13(product(Y, Z, Yz), Xy, Z)
% 0.45/0.65 f15(defined(X, Yz), X, Y, Xy, Z, Yz) = true__
% 0.45/0.65 f15(true__, X, Y, Xy, Z, Yz) = f14(product(X, Y, Xy), Y, Z, Yz, Xy)
% 0.45/0.65 f16(true__, Xy, Z, Xyz) = product(Xy, Z, Xyz)
% 0.45/0.65 f17(true__, Y, Z, Yz, Xy, Xyz) = f16(product(Y, Z, Yz), Xy, Z, Xyz)
% 0.45/0.65 f18(product(X, Y, Xy), X, Yz, Xyz, Y, Z, Xy) = true__
% 0.45/0.65 f18(true__, X, Yz, Xyz, Y, Z, Xy) = f17(product(X, Yz, Xyz), Y, Z, Yz, Xy, Xyz)
% 0.45/0.65 f19(true__, X, Z) = defined(X, Z)
% 0.45/0.65 f2(product(X, Y, Z), X, Y) = true__
% 0.45/0.65 f2(true__, X, Y) = defined(X, Y)
% 0.45/0.65 f20(true__, X, Y, Z) = f19(defined(X, Y), X, Z)
% 0.45/0.65 f21(identity_map(Y), Y, Z, X) = true__
% 0.45/0.65 f21(true__, Y, Z, X) = f20(defined(Y, Z), X, Y, Z)
% 0.45/0.65 f22(true__, X, Y) = product(X, Y, Y)
% 0.45/0.65 f23(identity_map(X), X, Y) = true__
% 0.45/0.65 f23(true__, X, Y) = f22(defined(X, Y), X, Y)
% 0.45/0.65 f24(true__, X, Y) = product(X, Y, X)
% 0.45/0.65 f25(identity_map(Y), X, Y) = true__
% 0.45/0.65 f25(true__, X, Y) = f24(defined(X, Y), X, Y)
% 0.45/0.65 f26(true__, Z, W) = Z
% 0.45/0.65 f27(product(X, Y, W), X, Y, Z, W) = W
% 0.45/0.65 f27(true__, X, Y, Z, W) = f26(product(X, Y, Z), Z, W)
% 0.45/0.65 f28(Z, Z) = Z
% 0.45/0.65 f28(c2, Z) = c1
% 0.45/0.65 f29(Z, Z) = Z
% 0.45/0.65 f29(c1, Z) = c2
% 0.45/0.65 f3(true__, Y, Z) = defined(Y, Z)
% 0.45/0.65 f30(c1) = false__
% 0.45/0.65 f30(c2) = true__
% 0.45/0.65 f4(defined(Xy, Z), X, Y, Xy, Z) = true__
% 0.45/0.65 f4(true__, X, Y, Xy, Z) = f3(product(X, Y, Xy), Y, Z)
% 0.45/0.65 f5(true__, X, Yz) = defined(X, Yz)
% 0.45/0.65 f6(true__, X, Y, Xy, Yz) = f5(product(X, Y, Xy), X, Yz)
% 0.45/0.65 f7(defined(Xy, Z), Y, Z, Yz, X, Xy) = true__
% 0.45/0.65 f7(true__, Y, Z, Yz, X, Xy) = f6(product(Y, Z, Yz), X, Y, Xy, Yz)
% 0.45/0.65 f8(true__, X, Yz, Xyz) = product(X, Yz, Xyz)
% 0.45/0.65 f9(true__, X, Y, Xy, Yz, Xyz) = f8(product(X, Y, Xy), X, Yz, Xyz)
% 0.45/0.65 identity_map(codomain(X)) = true__
% 0.45/0.65 identity_map(domain(X)) = true__
% 0.45/0.65 product(X, domain(X), X) = true__
% 0.45/0.65 product(codomain(X), X, X) = true__
% 0.45/0.65 G:
% 0.45/0.65 true__ = false__
% 0.45/0.65
% 0.45/0.65 This holds because
% 0.45/0.65
% 0.45/0.65 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.45/0.65
% 0.45/0.65
% 0.45/0.65 c1 -> c2
% 0.45/0.65 defined(X, Y) -> f2(true__, X, Y)
% 0.45/0.65 defined(X, domain(X)) -> true__
% 0.45/0.65 defined(codomain(X), X) -> true__
% 0.45/0.65 f1(defined(X, Y), X, Y) -> true__
% 0.45/0.65 f1(f2(true__, Y0, Y1), Y0, Y1) -> true__
% 0.45/0.65 f1(true__, X, Y) -> product(X, Y, compose(X, Y))
% 0.45/0.65 f10(product(Y, Z, Yz), Xy, Z, Xyz, X, Y, Yz) -> true__
% 0.45/0.65 f10(true__, Xy, Z, Xyz, X, Y, Yz) -> f9(product(Xy, Z, Xyz), X, Y, Xy, Yz, Xyz)
% 0.45/0.65 f11(true__, X, Y) -> defined(X, Y)
% 0.45/0.65 f12(defined(X, Yz), Y, Z, Yz, X) -> true__
% 0.45/0.65 f12(true__, Y, Z, Yz, X) -> f11(product(Y, Z, Yz), X, Y)
% 0.45/0.65 f13(true__, Xy, Z) -> defined(Xy, Z)
% 0.45/0.65 f14(true__, Y, Z, Yz, Xy) -> f13(product(Y, Z, Yz), Xy, Z)
% 0.45/0.65 f15(defined(X, Yz), X, Y, Xy, Z, Yz) -> true__
% 0.45/0.65 f15(true__, X, Y, Xy, Z, Yz) -> f14(product(X, Y, Xy), Y, Z, Yz, Xy)
% 0.45/0.65 f16(true__, Xy, Z, Xyz) -> product(Xy, Z, Xyz)
% 0.45/0.65 f17(true__, Y, Z, Yz, Xy, Xyz) -> f16(product(Y, Z, Yz), Xy, Z, Xyz)
% 0.45/0.65 f18(product(X, Y, Xy), X, Yz, Xyz, Y, Z, Xy) -> true__
% 0.45/0.65 f18(true__, X, Yz, Xyz, Y, Z, Xy) -> f17(product(X, Yz, Xyz), Y, Z, Yz, Xy, Xyz)
% 0.45/0.65 f19(true__, X, Z) -> defined(X, Z)
% 0.45/0.65 f2(product(X, Y, Z), X, Y) -> true__
% 0.45/0.65 f2(true__, Y0, domain(Y0)) -> true__
% 0.45/0.65 f2(true__, codomain(Y1), Y1) -> true__
% 0.45/0.65 f20(f2(true__, codomain(X0), Y1), Y2, codomain(X0), Y1) -> true__
% 0.45/0.65 f20(f2(true__, domain(X0), Y1), Y2, domain(X0), Y1) -> true__
% 0.45/0.65 f20(true__, X, Y, Z) -> f19(defined(X, Y), X, Z)
% 0.45/0.65 f21(identity_map(Y), Y, Z, X) -> true__
% 0.45/0.65 f21(true__, Y, Z, X) -> f20(defined(Y, Z), X, Y, Z)
% 0.45/0.65 f22(f2(true__, codomain(X0), Y1), codomain(X0), Y1) -> true__
% 0.45/0.65 f22(f2(true__, domain(X0), Y1), domain(X0), Y1) -> true__
% 0.45/0.65 f22(true__, X, Y) -> product(X, Y, Y)
% 0.45/0.65 f23(identity_map(X), X, Y) -> true__
% 0.45/0.65 f23(true__, X, Y) -> f22(defined(X, Y), X, Y)
% 0.45/0.65 f24(f2(true__, Y1, codomain(X0)), Y1, codomain(X0)) -> true__
% 0.45/0.65 f24(f2(true__, Y1, domain(X0)), Y1, domain(X0)) -> true__
% 0.45/0.65 f24(true__, X, Y) -> product(X, Y, X)
% 0.45/0.65 f25(identity_map(Y), X, Y) -> true__
% 0.45/0.65 f25(true__, X, Y) -> f24(defined(X, Y), X, Y)
% 0.45/0.65 f26(true__, Z, W) -> Z
% 0.45/0.65 f27(product(X, Y, W), X, Y, Z, W) -> W
% 0.45/0.65 f27(true__, X, Y, Z, W) -> f26(product(X, Y, Z), Z, W)
% 0.45/0.65 f28(Z, Z) -> Z
% 0.45/0.65 f28(c2, Z) -> c1
% 0.45/0.65 f29(Z, Z) -> Z
% 0.45/0.65 f29(c1, Z) -> c2
% 0.45/0.65 f29(c2, Y0) -> c2
% 0.45/0.65 f3(true__, Y, Z) -> defined(Y, Z)
% 0.45/0.65 f30(c1) -> false__
% 0.45/0.65 f30(c2) -> true__
% 0.45/0.65 f4(defined(Xy, Z), X, Y, Xy, Z) -> true__
% 0.45/0.65 f4(true__, X, Y, Xy, Z) -> f3(product(X, Y, Xy), Y, Z)
% 0.45/0.65 f5(true__, X, Yz) -> defined(X, Yz)
% 0.45/0.65 f6(true__, X, Y, Xy, Yz) -> f5(product(X, Y, Xy), X, Yz)
% 0.45/0.65 f7(defined(Xy, Z), Y, Z, Yz, X, Xy) -> true__
% 0.45/0.65 f7(true__, Y, Z, Yz, X, Xy) -> f6(product(Y, Z, Yz), X, Y, Xy, Yz)
% 0.45/0.65 f8(true__, Y0, domain(Y0), compose(Y0, domain(Y0))) -> true__
% 0.45/0.65 f8(true__, codomain(Y1), Y1, compose(codomain(Y1), Y1)) -> true__
% 0.45/0.65 f9(true__, X, Y, Xy, Yz, Xyz) -> f8(product(X, Y, Xy), X, Yz, Xyz)
% 0.45/0.65 false__ -> true__
% 0.45/0.65 identity_map(codomain(X)) -> true__
% 0.45/0.65 identity_map(domain(X)) -> true__
% 0.45/0.65 product(X, Yz, Xyz) -> f8(true__, X, Yz, Xyz)
% 0.45/0.65 product(X, domain(X), X) -> true__
% 0.45/0.65 product(codomain(X), X, X) -> true__
% 0.45/0.65 with the LPO induced by
% 0.45/0.65 f30 > f1 > f7 > f28 > c1 > c2 > f29 > f27 > f26 > f25 > f24 > f18 > f23 > f22 > codomain > f21 > f20 > f12 > f10 > f9 > f17 > f16 > f15 > f14 > f19 > f13 > f4 > f6 > product > f8 > f11 > f5 > f3 > defined > f2 > domain > identity_map > compose > false__ > true__
% 0.45/0.65
% 0.45/0.65 % SZS output end Proof
% 0.45/0.65
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