TSTP Solution File: HEN002-3 by Moca---0.1
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% File : Moca---0.1
% Problem : HEN002-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n007.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 : Sat Jul 16 12:58:53 EDT 2022
% Result : Unsatisfiable 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN002-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : moca.sh %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 : Fri Jul 1 14:02:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.40 % SZS status Unsatisfiable
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 The input problem is unsatisfiable because
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% 0.18/0.40 [1] the following set of Horn clauses is unsatisfiable:
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% 0.18/0.40 less_equal(X, Y) ==> divide(X, Y) = zero
% 0.18/0.40 divide(X, Y) = zero ==> less_equal(X, Y)
% 0.18/0.40 less_equal(divide(X, Y), X)
% 0.18/0.40 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))
% 0.18/0.40 less_equal(zero, X)
% 0.18/0.40 less_equal(X, Y) & less_equal(Y, X) ==> X = Y
% 0.18/0.40 less_equal(X, identity)
% 0.18/0.40 divide(zero, a) = zero ==> \bottom
% 0.18/0.40
% 0.18/0.40 This holds because
% 0.18/0.40
% 0.18/0.40 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
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% 0.18/0.40 E:
% 0.18/0.40 f1(less_equal(X, Y), X, Y) = zero
% 0.18/0.40 f1(true__, X, Y) = divide(X, Y)
% 0.18/0.40 f2(divide(X, Y), X, Y) = true__
% 0.18/0.40 f2(zero, X, Y) = less_equal(X, Y)
% 0.18/0.40 f3(true__, X, Y) = X
% 0.18/0.40 f4(less_equal(Y, X), X, Y) = Y
% 0.18/0.40 f4(true__, X, Y) = f3(less_equal(X, Y), X, Y)
% 0.18/0.40 f5(divide(zero, a)) = true__
% 0.18/0.40 f5(zero) = false__
% 0.18/0.40 less_equal(X, identity) = true__
% 0.18/0.40 less_equal(divide(X, Y), X) = true__
% 0.18/0.40 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) = true__
% 0.18/0.40 less_equal(zero, X) = true__
% 0.18/0.40 G:
% 0.18/0.40 true__ = false__
% 0.18/0.40
% 0.18/0.40 This holds because
% 0.18/0.40
% 0.18/0.40 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.18/0.40
% 0.18/0.40
% 0.18/0.40 divide(X, Y) -> f1(true__, X, Y)
% 0.18/0.40 f1(f2(zero, Y0, Y1), Y0, Y1) -> zero
% 0.18/0.40 f1(less_equal(X, Y), X, Y) -> zero
% 0.18/0.40 f1(true__, Y0, identity) -> zero
% 0.18/0.40 f1(true__, f1(true__, Y1, X1), Y1) -> zero
% 0.18/0.40 f1(true__, zero, Y1) -> zero
% 0.18/0.40 f2(divide(X, Y), X, Y) -> true__
% 0.18/0.40 f2(f1(true__, Y0, Y1), Y0, Y1) -> true__
% 0.18/0.40 f2(zero, Y0, identity) -> true__
% 0.18/0.40 f2(zero, f1(true__, Y0, Y1), Y0) -> true__
% 0.18/0.40 f2(zero, f1(true__, f1(true__, Y0, Y1), f1(true__, Y2, Y1)), f1(true__, f1(true__, Y0, Y2), Y1)) -> true__
% 0.18/0.40 f2(zero, zero, Y1) -> true__
% 0.18/0.40 f3(f2(zero, Y1, f1(true__, Y1, X1)), Y1, f1(true__, Y1, X1)) -> f1(true__, Y1, X1)
% 0.18/0.40 f3(f2(zero, Y1, zero), Y1, zero) -> zero
% 0.18/0.40 f3(f2(zero, identity, Y0), identity, Y0) -> Y0
% 0.18/0.40 f3(true__, X, Y) -> X
% 0.18/0.40 f4(f2(zero, Y0, Y1), Y1, Y0) -> Y0
% 0.18/0.40 f4(less_equal(Y, X), X, Y) -> Y
% 0.18/0.40 f4(true__, X, Y) -> f3(less_equal(X, Y), X, Y)
% 0.18/0.40 f5(divide(zero, a)) -> true__
% 0.18/0.40 f5(zero) -> false__
% 0.18/0.40 false__ -> true__
% 0.18/0.40 less_equal(X, Y) -> f2(zero, X, Y)
% 0.18/0.40 less_equal(X, identity) -> true__
% 0.18/0.40 less_equal(divide(X, Y), X) -> true__
% 0.18/0.40 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) -> true__
% 0.18/0.40 less_equal(zero, X) -> true__
% 0.18/0.40 with the LPO induced by
% 0.18/0.40 a > divide > f1 > f4 > f3 > less_equal > f5 > identity > f2 > zero > false__ > true__
% 0.18/0.40
% 0.18/0.40 % SZS output end Proof
% 0.18/0.40
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