TSTP Solution File: HEN005-4 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : HEN005-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n005.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 12:58:59 EDT 2022
% Result : Unsatisfiable 7.27s 7.27s
% Output : Proof 7.27s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : HEN005-4 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n005.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 1 13:30:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 7.27/7.27 % SZS status Unsatisfiable
% 7.27/7.27 % SZS output start Proof
% 7.27/7.27 The input problem is unsatisfiable because
% 7.27/7.27
% 7.27/7.27 [1] the following set of Horn clauses is unsatisfiable:
% 7.27/7.27
% 7.27/7.27 less_equal(X, Y) ==> divide(X, Y) = zero
% 7.27/7.27 divide(X, Y) = zero ==> less_equal(X, Y)
% 7.27/7.27 less_equal(divide(X, Y), X)
% 7.27/7.27 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))
% 7.27/7.27 less_equal(zero, X)
% 7.27/7.27 less_equal(X, Y) & less_equal(Y, X) ==> X = Y
% 7.27/7.27 less_equal(X, identity)
% 7.27/7.27 divide(X, identity) = zero
% 7.27/7.27 divide(zero, X) = zero
% 7.27/7.27 divide(X, X) = zero
% 7.27/7.27 divide(X, zero) = X
% 7.27/7.27 less_equal(a, b)
% 7.27/7.27 less_equal(b, c)
% 7.27/7.27 less_equal(a, c) ==> \bottom
% 7.27/7.27
% 7.27/7.27 This holds because
% 7.27/7.27
% 7.27/7.27 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 7.27/7.27
% 7.27/7.27 E:
% 7.27/7.27 divide(X, X) = zero
% 7.27/7.27 divide(X, identity) = zero
% 7.27/7.27 divide(X, zero) = X
% 7.27/7.27 divide(zero, X) = zero
% 7.27/7.27 f1(less_equal(X, Y), X, Y) = zero
% 7.27/7.27 f1(true__, X, Y) = divide(X, Y)
% 7.27/7.27 f2(divide(X, Y), X, Y) = true__
% 7.27/7.27 f2(zero, X, Y) = less_equal(X, Y)
% 7.27/7.27 f3(true__, X, Y) = X
% 7.27/7.27 f4(less_equal(Y, X), X, Y) = Y
% 7.27/7.27 f4(true__, X, Y) = f3(less_equal(X, Y), X, Y)
% 7.27/7.27 f5(less_equal(a, c)) = true__
% 7.27/7.27 f5(true__) = false__
% 7.27/7.27 less_equal(X, identity) = true__
% 7.27/7.27 less_equal(a, b) = true__
% 7.27/7.27 less_equal(b, c) = true__
% 7.27/7.27 less_equal(divide(X, Y), X) = true__
% 7.27/7.27 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) = true__
% 7.27/7.27 less_equal(zero, X) = true__
% 7.27/7.27 G:
% 7.27/7.27 true__ = false__
% 7.27/7.27
% 7.27/7.27 This holds because
% 7.27/7.27
% 7.27/7.27 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 7.27/7.27
% 7.27/7.27
% 7.27/7.27 divide(X, X) -> zero
% 7.27/7.27 divide(X, Y) -> f1(true__, X, Y)
% 7.27/7.27 divide(X, identity) -> zero
% 7.27/7.27 divide(X, zero) -> X
% 7.27/7.27 divide(zero, X) -> zero
% 7.27/7.27 f1(f2(zero, Y0, Y1), Y0, Y1) -> zero
% 7.27/7.27 f1(less_equal(X, Y), X, Y) -> zero
% 7.27/7.27 f1(true__, Y0, identity) -> zero
% 7.27/7.27 f1(true__, Y0, zero) -> Y0
% 7.27/7.27 f1(true__, Y1, Y1) -> zero
% 7.27/7.27 f1(true__, a, b) -> zero
% 7.27/7.27 f1(true__, a, c) -> zero
% 7.27/7.27 f1(true__, b, c) -> zero
% 7.27/7.27 f1(true__, f1(true__, X0, X1), f1(true__, identity, X1)) -> zero
% 7.27/7.27 f1(true__, f1(true__, Y0, Y1), f1(true__, f1(true__, Y0, Y1), Y1)) -> zero
% 7.27/7.27 f1(true__, f1(true__, Y0, Y2), Y2) -> f1(true__, Y0, Y2)
% 7.27/7.27 f1(true__, f1(true__, Y0, b), f1(true__, f1(true__, Y0, a), b)) -> zero
% 7.27/7.27 f1(true__, f1(true__, Y0, c), f1(true__, f1(true__, Y0, a), c)) -> zero
% 7.27/7.27 f1(true__, f1(true__, Y0, c), f1(true__, f1(true__, Y0, b), c)) -> zero
% 7.27/7.27 f1(true__, f1(true__, Y0, f1(true__, Y0, Y2)), f1(true__, Y2, f1(true__, Y0, Y2))) -> zero
% 7.27/7.27 f1(true__, f1(true__, Y1, X1), Y1) -> zero
% 7.27/7.27 f1(true__, f1(true__, a, Y1), f1(true__, b, Y1)) -> zero
% 7.27/7.27 f1(true__, f1(true__, a, Y1), f1(true__, c, Y1)) -> zero
% 7.27/7.27 f1(true__, f1(true__, b, Y1), f1(true__, c, Y1)) -> zero
% 7.27/7.27 f1(true__, f1(true__, f1(true__, X0, X1), f1(true__, X2, X1)), f1(true__, f1(true__, X0, X2), X1)) -> zero
% 7.27/7.27 f1(true__, zero, Y1) -> zero
% 7.27/7.27 f2(Y0, Y0, zero) -> true__
% 7.27/7.27 f2(divide(X, Y), X, Y) -> true__
% 7.27/7.27 f2(f1(true__, X0, Y1), f1(true__, X0, Y1), Y1) -> true__
% 7.27/7.27 f2(f1(true__, Y0, Y1), Y0, Y1) -> true__
% 7.27/7.27 f2(zero, Y0, Y0) -> true__
% 7.27/7.27 f2(zero, Y0, identity) -> true__
% 7.27/7.27 f2(zero, a, b) -> true__
% 7.27/7.27 f2(zero, a, c) -> true__
% 7.27/7.27 f2(zero, b, c) -> true__
% 7.27/7.27 f2(zero, f1(true__, X0, X1), f1(true__, identity, X1)) -> true__
% 7.27/7.27 f2(zero, f1(true__, Y0, Y1), Y0) -> true__
% 7.27/7.27 f2(zero, f1(true__, Y0, Y1), f1(true__, f1(true__, Y0, Y1), Y1)) -> true__
% 7.27/7.27 f2(zero, f1(true__, Y0, b), f1(true__, f1(true__, Y0, a), b)) -> true__
% 7.27/7.27 f2(zero, f1(true__, Y0, c), f1(true__, f1(true__, Y0, a), c)) -> true__
% 7.27/7.27 f2(zero, f1(true__, Y0, c), f1(true__, f1(true__, Y0, b), c)) -> true__
% 7.27/7.27 f2(zero, f1(true__, a, X0), f1(true__, b, X0)) -> true__
% 7.27/7.27 f2(zero, f1(true__, a, X0), f1(true__, c, X0)) -> true__
% 7.27/7.27 f2(zero, f1(true__, a, c), zero) -> true__
% 7.27/7.27 f2(zero, f1(true__, b, X0), f1(true__, c, X0)) -> true__
% 7.27/7.27 f2(zero, f1(true__, f1(true__, Y0, Y1), f1(true__, Y2, Y1)), f1(true__, f1(true__, Y0, Y2), Y1)) -> true__
% 7.27/7.27 f2(zero, f1(true__, f1(true__, Y0, Y1), f1(true__, identity, Y1)), zero) -> true__
% 7.27/7.27 f2(zero, f1(true__, f1(true__, Y0, f1(true__, Y0, Y2)), f1(true__, Y2, f1(true__, Y0, Y2))), zero) -> true__
% 7.27/7.27 f2(zero, f1(true__, f1(true__, a, X1), b), zero) -> true__
% 7.27/7.27 f2(zero, f1(true__, f1(true__, a, Y1), f1(true__, b, Y1)), zero) -> true__
% 7.27/7.27 f2(zero, f1(true__, f1(true__, a, Y1), f1(true__, c, Y1)), zero) -> true__
% 7.27/7.27 f2(zero, f1(true__, f1(true__, b, X1), c), zero) -> true__
% 7.27/7.27 f2(zero, f1(true__, f1(true__, b, Y1), f1(true__, c, Y1)), zero) -> true__
% 7.27/7.27 f2(zero, zero, Y0) -> true__
% 7.27/7.27 f2(zero, zero, zero) -> true__
% 7.27/7.27 f3(f2(zero, Y1, f1(true__, Y1, X1)), Y1, f1(true__, Y1, X1)) -> f1(true__, Y1, X1)
% 7.27/7.27 f3(f2(zero, Y1, zero), Y1, zero) -> zero
% 7.27/7.27 f3(f2(zero, b, a), b, a) -> a
% 7.27/7.27 f3(f2(zero, c, a), c, a) -> a
% 7.27/7.27 f3(f2(zero, c, b), c, b) -> b
% 7.27/7.27 f3(f2(zero, f1(true__, b, X0), f1(true__, a, X0)), f1(true__, b, X0), f1(true__, a, X0)) -> f1(true__, a, X0)
% 7.27/7.27 f3(f2(zero, f1(true__, c, X0), f1(true__, b, X0)), f1(true__, c, X0), f1(true__, b, X0)) -> f1(true__, b, X0)
% 7.27/7.27 f3(f2(zero, f1(true__, f1(true__, X0, X2), X1), f1(true__, f1(true__, X0, X1), f1(true__, X2, X1))), f1(true__, f1(true__, X0, X2), X1), f1(true__, f1(true__, X0, X1), f1(true__, X2, X1))) -> f1(true__, f1(true__, X0, X1), f1(true__, X2, X1))
% 7.27/7.27 f3(f2(zero, f1(true__, f1(true__, Y0, a), b), f1(true__, Y0, b)), f1(true__, f1(true__, Y0, a), b), f1(true__, Y0, b)) -> f1(true__, Y0, b)
% 7.27/7.27 f3(f2(zero, f1(true__, f1(true__, Y0, b), c), f1(true__, Y0, c)), f1(true__, f1(true__, Y0, b), c), f1(true__, Y0, c)) -> f1(true__, Y0, c)
% 7.27/7.27 f3(f2(zero, f1(true__, identity, X1), f1(true__, X0, X1)), f1(true__, identity, X1), f1(true__, X0, X1)) -> f1(true__, X0, X1)
% 7.27/7.27 f3(f2(zero, identity, Y0), identity, Y0) -> Y0
% 7.27/7.27 f3(true__, X, Y) -> X
% 7.27/7.27 f4(f2(zero, Y0, Y1), Y1, Y0) -> Y0
% 7.27/7.27 f4(less_equal(Y, X), X, Y) -> Y
% 7.27/7.27 f4(true__, X, Y) -> f3(less_equal(X, Y), X, Y)
% 7.27/7.27 f5(f2(zero, a, c)) -> true__
% 7.27/7.27 f5(less_equal(a, c)) -> true__
% 7.27/7.27 f5(true__) -> false__
% 7.27/7.27 false__ -> true__
% 7.27/7.27 less_equal(X, Y) -> f2(zero, X, Y)
% 7.27/7.27 less_equal(X, identity) -> true__
% 7.27/7.27 less_equal(a, b) -> true__
% 7.27/7.27 less_equal(b, c) -> true__
% 7.27/7.27 less_equal(divide(X, Y), X) -> true__
% 7.27/7.27 less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) -> true__
% 7.27/7.27 less_equal(zero, X) -> true__
% 7.27/7.27 with the LPO induced by
% 7.27/7.27 f5 > c > b > a > f4 > less_equal > divide > f1 > zero > identity > f3 > f2 > false__ > true__
% 7.27/7.27
% 7.27/7.27 % SZS output end Proof
% 7.27/7.27
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