TSTP Solution File: HEN002-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : HEN002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n019.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 12:58:52 EDT 2022
% Result : Unsatisfiable 0.18s 0.44s
% 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
% 0.06/0.11 % Problem : HEN002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : moca.sh %s
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Fri Jul 1 14:03:08 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.44 % SZS status Unsatisfiable
% 0.18/0.44 % SZS output start Proof
% 0.18/0.44 The input problem is unsatisfiable because
% 0.18/0.44
% 0.18/0.44 [1] the following set of Horn clauses is unsatisfiable:
% 0.18/0.44
% 0.18/0.44 less_equal(X, Y) ==> quotient(X, Y, zero)
% 0.18/0.44 quotient(X, Y, zero) ==> less_equal(X, Y)
% 0.18/0.44 quotient(X, Y, Z) ==> less_equal(Z, X)
% 0.18/0.44 quotient(X, Y, V1) & quotient(Y, Z, V2) & quotient(X, Z, V3) & quotient(V3, V2, V4) & quotient(V1, Z, V5) ==> less_equal(V4, V5)
% 0.18/0.44 less_equal(zero, X)
% 0.18/0.44 less_equal(X, Y) & less_equal(Y, X) ==> X = Y
% 0.18/0.44 less_equal(X, identity)
% 0.18/0.44 quotient(X, Y, divide(X, Y))
% 0.18/0.44 quotient(X, Y, Z) & quotient(X, Y, W) ==> Z = W
% 0.18/0.44 quotient(zero, x, zero) ==> \bottom
% 0.18/0.44
% 0.18/0.44 This holds because
% 0.18/0.44
% 0.18/0.44 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.18/0.44
% 0.18/0.44 E:
% 0.18/0.44 f1(less_equal(X, Y), X, Y) = true__
% 0.18/0.44 f1(true__, X, Y) = quotient(X, Y, zero)
% 0.18/0.44 f10(less_equal(Y, X), X, Y) = Y
% 0.18/0.44 f10(true__, X, Y) = f9(less_equal(X, Y), X, Y)
% 0.18/0.44 f11(true__, Z, W) = Z
% 0.18/0.44 f12(quotient(X, Y, W), X, Y, Z, W) = W
% 0.18/0.44 f12(true__, X, Y, Z, W) = f11(quotient(X, Y, Z), Z, W)
% 0.18/0.44 f13(quotient(zero, x, zero)) = true__
% 0.18/0.44 f13(true__) = false__
% 0.18/0.44 f2(quotient(X, Y, zero), X, Y) = true__
% 0.18/0.44 f2(true__, X, Y) = less_equal(X, Y)
% 0.18/0.44 f3(quotient(X, Y, Z), Z, X) = true__
% 0.18/0.44 f3(true__, Z, X) = less_equal(Z, X)
% 0.18/0.44 f4(true__, V4, V5) = less_equal(V4, V5)
% 0.18/0.44 f5(true__, X, Y, V1, V4, V5) = f4(quotient(X, Y, V1), V4, V5)
% 0.18/0.44 f6(true__, Y, Z, V2, X, V1, V4, V5) = f5(quotient(Y, Z, V2), X, Y, V1, V4, V5)
% 0.18/0.44 f7(true__, X, Z, V3, Y, V2, V1, V4, V5) = f6(quotient(X, Z, V3), Y, Z, V2, X, V1, V4, V5)
% 0.18/0.44 f8(quotient(V1, Z, V5), V3, V2, V4, X, Z, Y, V1, V5) = true__
% 0.18/0.44 f8(true__, V3, V2, V4, X, Z, Y, V1, V5) = f7(quotient(V3, V2, V4), X, Z, V3, Y, V2, V1, V4, V5)
% 0.18/0.44 f9(true__, X, Y) = X
% 0.18/0.44 less_equal(X, identity) = true__
% 0.18/0.44 less_equal(zero, X) = true__
% 0.18/0.44 quotient(X, Y, divide(X, Y)) = true__
% 0.18/0.44 G:
% 0.18/0.44 true__ = false__
% 0.18/0.44
% 0.18/0.44 This holds because
% 0.18/0.44
% 0.18/0.44 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.18/0.44
% 0.18/0.44
% 0.18/0.44 f1(f2(true__, Y0, Y1), Y0, Y1) -> true__
% 0.18/0.44 f1(less_equal(X, Y), X, Y) -> true__
% 0.18/0.44 f1(true__, Y0, identity) -> true__
% 0.18/0.44 f1(true__, zero, Y1) -> true__
% 0.18/0.44 f10(f2(true__, Y0, Y1), Y1, Y0) -> Y0
% 0.18/0.44 f10(less_equal(Y, X), X, Y) -> Y
% 0.18/0.44 f10(true__, X, Y) -> f9(less_equal(X, Y), X, Y)
% 0.18/0.44 f11(quotient(X, Y, Z), Z, W) -> f12(true__, X, Y, Z, W)
% 0.18/0.44 f11(true__, Z, W) -> Z
% 0.18/0.44 f12(quotient(X, Y, W), X, Y, Z, W) -> W
% 0.18/0.44 f12(true__, Y0, Y1, Y3, divide(Y0, Y1)) -> divide(Y0, Y1)
% 0.18/0.44 f12(true__, Y0, Y1, divide(Y0, Y1), Y3) -> divide(Y0, Y1)
% 0.18/0.44 f13(quotient(zero, x, zero)) -> true__
% 0.18/0.44 f13(true__) -> false__
% 0.18/0.44 f2(f1(true__, Y0, Y1), Y0, Y1) -> true__
% 0.18/0.44 f2(quotient(X, Y, zero), X, Y) -> true__
% 0.18/0.44 f2(true__, Y0, identity) -> true__
% 0.18/0.44 f2(true__, divide(Y0, Y1), Y0) -> true__
% 0.18/0.44 f2(true__, zero, Y1) -> true__
% 0.18/0.44 f3(f1(true__, Y0, Y1), zero, Y0) -> true__
% 0.18/0.44 f3(quotient(X, Y, Z), Z, X) -> true__
% 0.18/0.44 f3(true__, Z, X) -> less_equal(Z, X)
% 0.18/0.44 f4(quotient(X, Y, V1), V4, V5) -> f5(true__, X, Y, V1, V4, V5)
% 0.18/0.44 f4(true__, V4, V5) -> less_equal(V4, V5)
% 0.18/0.44 f5(quotient(Y, Z, V2), X, Y, V1, V4, V5) -> f6(true__, Y, Z, V2, X, V1, V4, V5)
% 0.18/0.44 f6(quotient(X, Z, V3), Y, Z, V2, X, V1, V4, V5) -> f7(true__, X, Z, V3, Y, V2, V1, V4, V5)
% 0.18/0.44 f7(quotient(V3, V2, V4), X, Z, V3, Y, V2, V1, V4, V5) -> f8(true__, V3, V2, V4, X, Z, Y, V1, V5)
% 0.18/0.44 f8(quotient(V1, Z, V5), V3, V2, V4, X, Z, Y, V1, V5) -> true__
% 0.18/0.44 f9(f2(true__, Y1, zero), Y1, zero) -> zero
% 0.18/0.44 f9(f2(true__, identity, Y0), identity, Y0) -> Y0
% 0.18/0.44 f9(true__, X, Y) -> X
% 0.18/0.44 false__ -> true__
% 0.18/0.44 less_equal(X, Y) -> f2(true__, X, Y)
% 0.18/0.44 less_equal(X, identity) -> true__
% 0.18/0.44 less_equal(zero, X) -> true__
% 0.18/0.44 quotient(X, Y, divide(X, Y)) -> true__
% 0.18/0.44 quotient(X, Y, zero) -> f1(true__, X, Y)
% 0.18/0.44 with the LPO induced by
% 0.18/0.44 x > f13 > f11 > f12 > divide > f10 > f9 > f4 > f3 > less_equal > f2 > identity > f5 > f6 > f7 > f8 > quotient > f1 > zero > false__ > true__
% 0.18/0.44
% 0.18/0.44 % SZS output end Proof
% 0.18/0.44
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