TSTP Solution File: HEN005-3 by Moca---0.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Moca---0.1
% Problem  : HEN005-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : moca.sh %s

% Computer : n011.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 5.98s 5.99s
% Output   : Proof 5.98s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : HEN005-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : moca.sh %s
% 0.13/0.33  % Computer : n011.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Fri Jul  1 13:48:19 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 5.98/5.99  % SZS status Unsatisfiable
% 5.98/5.99  % SZS output start Proof
% 5.98/5.99  The input problem is unsatisfiable because
% 5.98/5.99  
% 5.98/5.99  [1] the following set of Horn clauses is unsatisfiable:
% 5.98/5.99  
% 5.98/5.99  	less_equal(X, Y) ==> divide(X, Y) = zero
% 5.98/5.99  	divide(X, Y) = zero ==> less_equal(X, Y)
% 5.98/5.99  	less_equal(divide(X, Y), X)
% 5.98/5.99  	less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z))
% 5.98/5.99  	less_equal(zero, X)
% 5.98/5.99  	less_equal(X, Y) & less_equal(Y, X) ==> X = Y
% 5.98/5.99  	less_equal(X, identity)
% 5.98/5.99  	less_equal(a, b)
% 5.98/5.99  	less_equal(b, c)
% 5.98/5.99  	less_equal(a, c) ==> \bottom
% 5.98/5.99  
% 5.98/5.99  This holds because
% 5.98/5.99  
% 5.98/5.99  [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 5.98/5.99  
% 5.98/5.99  E:
% 5.98/5.99  	f1(less_equal(X, Y), X, Y) = zero
% 5.98/5.99  	f1(true__, X, Y) = divide(X, Y)
% 5.98/5.99  	f2(divide(X, Y), X, Y) = true__
% 5.98/5.99  	f2(zero, X, Y) = less_equal(X, Y)
% 5.98/5.99  	f3(true__, X, Y) = X
% 5.98/5.99  	f4(less_equal(Y, X), X, Y) = Y
% 5.98/5.99  	f4(true__, X, Y) = f3(less_equal(X, Y), X, Y)
% 5.98/5.99  	f5(less_equal(a, c)) = true__
% 5.98/5.99  	f5(true__) = false__
% 5.98/5.99  	less_equal(X, identity) = true__
% 5.98/5.99  	less_equal(a, b) = true__
% 5.98/5.99  	less_equal(b, c) = true__
% 5.98/5.99  	less_equal(divide(X, Y), X) = true__
% 5.98/5.99  	less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) = true__
% 5.98/5.99  	less_equal(zero, X) = true__
% 5.98/5.99  G:
% 5.98/5.99  	true__ = false__
% 5.98/5.99  
% 5.98/5.99  This holds because
% 5.98/5.99  
% 5.98/5.99  [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 5.98/5.99  
% 5.98/5.99  
% 5.98/5.99  	divide(X, Y) -> f1(true__, X, Y)
% 5.98/5.99  	f1(f2(zero, Y0, Y1), Y0, Y1) -> zero
% 5.98/5.99  	f1(less_equal(X, Y), X, Y) -> zero
% 5.98/5.99  	f1(true__, X0, X0) -> zero
% 5.98/5.99  	f1(true__, Y0, identity) -> zero
% 5.98/5.99  	f1(true__, a, b) -> zero
% 5.98/5.99  	f1(true__, a, c) -> zero
% 5.98/5.99  	f1(true__, b, b) -> zero
% 5.98/5.99  	f1(true__, b, c) -> zero
% 5.98/5.99  	f1(true__, c, c) -> zero
% 5.98/5.99  	f1(true__, f1(true__, X0, X0), zero) -> zero
% 5.98/5.99  	f1(true__, f1(true__, X0, X1), f1(true__, identity, X1)) -> zero
% 5.98/5.99  	f1(true__, f1(true__, Y1, X1), Y1) -> zero
% 5.98/5.99  	f1(true__, f1(true__, a, X0), f1(true__, c, X0)) -> zero
% 5.98/5.99  	f1(true__, f1(true__, a, Y2), f1(true__, b, Y2)) -> zero
% 5.98/5.99  	f1(true__, f1(true__, a, c), zero) -> zero
% 5.98/5.99  	f1(true__, f1(true__, b, Y2), f1(true__, c, Y2)) -> zero
% 5.98/5.99  	f1(true__, f1(true__, f1(true__, X0, X1), f1(true__, X2, X1)), f1(true__, f1(true__, X0, X2), X1)) -> zero
% 5.98/5.99  	f1(true__, f1(true__, f1(true__, Y0, Y1), f1(true__, identity, Y1)), zero) -> zero
% 5.98/5.99  	f1(true__, f1(true__, f1(true__, Y0, Y1), zero), f1(true__, f1(true__, Y0, zero), Y1)) -> zero
% 5.98/5.99  	f1(true__, f1(true__, f1(true__, Y0, b), zero), f1(true__, f1(true__, Y0, a), b)) -> zero
% 5.98/5.99  	f1(true__, f1(true__, f1(true__, Y0, c), zero), f1(true__, f1(true__, Y0, a), c)) -> zero
% 5.98/5.99  	f1(true__, f1(true__, f1(true__, Y0, c), zero), f1(true__, f1(true__, Y0, b), c)) -> zero
% 5.98/5.99  	f1(true__, f1(true__, f1(true__, Y1, Y1), zero), zero) -> zero
% 5.98/5.99  	f1(true__, f1(true__, f1(true__, a, X0), b), zero) -> zero
% 5.98/5.99  	f1(true__, f1(true__, f1(true__, a, Y1), f1(true__, b, Y1)), zero) -> zero
% 5.98/5.99  	f1(true__, f1(true__, f1(true__, a, Y1), f1(true__, c, Y1)), zero) -> zero
% 5.98/5.99  	f1(true__, f1(true__, f1(true__, a, c), zero), zero) -> zero
% 5.98/5.99  	f1(true__, f1(true__, f1(true__, b, Y1), f1(true__, c, Y1)), zero) -> zero
% 5.98/5.99  	f1(true__, f1(true__, f1(true__, f1(true__, a, X1), b), zero), zero) -> zero
% 5.98/5.99  	f1(true__, zero, Y1) -> zero
% 5.98/5.99  	f2(divide(X, Y), X, Y) -> true__
% 5.98/5.99  	f2(f1(true__, Y0, Y1), Y0, Y1) -> true__
% 5.98/5.99  	f2(zero, Y0, identity) -> true__
% 5.98/5.99  	f2(zero, a, b) -> true__
% 5.98/5.99  	f2(zero, a, c) -> true__
% 5.98/5.99  	f2(zero, b, c) -> true__
% 5.98/5.99  	f2(zero, f1(true__, X0, X0), zero) -> true__
% 5.98/5.99  	f2(zero, f1(true__, X0, X1), f1(true__, identity, X1)) -> true__
% 5.98/5.99  	f2(zero, f1(true__, Y0, Y1), Y0) -> true__
% 5.98/5.99  	f2(zero, f1(true__, a, X0), f1(true__, b, X0)) -> true__
% 5.98/5.99  	f2(zero, f1(true__, a, c), zero) -> true__
% 5.98/5.99  	f2(zero, f1(true__, b, X0), f1(true__, c, X0)) -> true__
% 5.98/5.99  	f2(zero, f1(true__, f1(true__, Y0, Y1), f1(true__, Y2, Y1)), f1(true__, f1(true__, Y0, Y2), Y1)) -> true__
% 5.98/5.99  	f2(zero, f1(true__, f1(true__, Y0, Y1), f1(true__, identity, Y1)), zero) -> true__
% 5.98/5.99  	f2(zero, f1(true__, f1(true__, Y0, Y1), zero), f1(true__, f1(true__, Y0, zero), Y1)) -> true__
% 5.98/5.99  	f2(zero, f1(true__, f1(true__, Y0, b), zero), f1(true__, f1(true__, Y0, a), b)) -> true__
% 5.98/5.99  	f2(zero, f1(true__, f1(true__, Y0, c), zero), f1(true__, f1(true__, Y0, a), c)) -> true__
% 5.98/5.99  	f2(zero, f1(true__, f1(true__, Y0, c), zero), f1(true__, f1(true__, Y0, b), c)) -> true__
% 5.98/5.99  	f2(zero, f1(true__, f1(true__, Y1, Y1), zero), zero) -> true__
% 5.98/5.99  	f2(zero, f1(true__, f1(true__, a, X0), b), zero) -> true__
% 5.98/5.99  	f2(zero, f1(true__, f1(true__, a, Y1), f1(true__, b, Y1)), zero) -> true__
% 5.98/5.99  	f2(zero, f1(true__, f1(true__, a, Y1), f1(true__, c, Y1)), zero) -> true__
% 5.98/5.99  	f2(zero, f1(true__, f1(true__, a, c), zero), zero) -> true__
% 5.98/5.99  	f2(zero, f1(true__, f1(true__, b, Y1), f1(true__, c, Y1)), zero) -> true__
% 5.98/5.99  	f2(zero, f1(true__, f1(true__, f1(true__, a, X1), b), zero), zero) -> true__
% 5.98/5.99  	f2(zero, zero, Y1) -> true__
% 5.98/5.99  	f3(f2(zero, Y1, f1(true__, Y1, X1)), Y1, f1(true__, Y1, X1)) -> f1(true__, Y1, X1)
% 5.98/5.99  	f3(f2(zero, Y1, zero), Y1, zero) -> zero
% 5.98/5.99  	f3(f2(zero, b, a), b, a) -> a
% 5.98/5.99  	f3(f2(zero, c, a), c, a) -> a
% 5.98/5.99  	f3(f2(zero, c, b), c, b) -> b
% 5.98/5.99  	f3(f2(zero, f1(true__, b, X0), f1(true__, a, X0)), f1(true__, b, X0), f1(true__, a, X0)) -> f1(true__, a, X0)
% 5.98/5.99  	f3(f2(zero, f1(true__, c, X0), f1(true__, b, X0)), f1(true__, c, X0), f1(true__, b, X0)) -> f1(true__, b, X0)
% 5.98/5.99  	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))
% 5.98/5.99  	f3(f2(zero, f1(true__, f1(true__, Y0, a), b), f1(true__, f1(true__, Y0, b), zero)), f1(true__, f1(true__, Y0, a), b), f1(true__, f1(true__, Y0, b), zero)) -> f1(true__, f1(true__, Y0, b), zero)
% 5.98/5.99  	f3(f2(zero, f1(true__, f1(true__, Y0, b), c), f1(true__, f1(true__, Y0, c), zero)), f1(true__, f1(true__, Y0, b), c), f1(true__, f1(true__, Y0, c), zero)) -> f1(true__, f1(true__, Y0, c), zero)
% 5.98/5.99  	f3(f2(zero, f1(true__, f1(true__, Y0, zero), Y2), f1(true__, f1(true__, Y0, Y2), zero)), f1(true__, f1(true__, Y0, zero), Y2), f1(true__, f1(true__, Y0, Y2), zero)) -> f1(true__, f1(true__, Y0, Y2), zero)
% 5.98/5.99  	f3(f2(zero, f1(true__, identity, X1), f1(true__, X0, X1)), f1(true__, identity, X1), f1(true__, X0, X1)) -> f1(true__, X0, X1)
% 5.98/5.99  	f3(f2(zero, identity, Y0), identity, Y0) -> Y0
% 5.98/5.99  	f3(true__, X, Y) -> X
% 5.98/5.99  	f4(f2(zero, Y0, Y1), Y1, Y0) -> Y0
% 5.98/5.99  	f4(less_equal(Y, X), X, Y) -> Y
% 5.98/5.99  	f4(true__, X, Y) -> f3(less_equal(X, Y), X, Y)
% 5.98/5.99  	f5(f2(zero, a, c)) -> true__
% 5.98/5.99  	f5(less_equal(a, c)) -> true__
% 5.98/5.99  	f5(true__) -> false__
% 5.98/5.99  	false__ -> true__
% 5.98/5.99  	less_equal(X, Y) -> f2(zero, X, Y)
% 5.98/5.99  	less_equal(X, identity) -> true__
% 5.98/5.99  	less_equal(a, b) -> true__
% 5.98/5.99  	less_equal(b, c) -> true__
% 5.98/5.99  	less_equal(divide(X, Y), X) -> true__
% 5.98/5.99  	less_equal(divide(divide(X, Z), divide(Y, Z)), divide(divide(X, Y), Z)) -> true__
% 5.98/5.99  	less_equal(zero, X) -> true__
% 5.98/5.99  with the LPO induced by
% 5.98/5.99  	f5 > c > b > a > identity > f4 > f3 > divide > f1 > less_equal > f2 > zero > false__ > true__
% 5.98/5.99  
% 5.98/5.99  % SZS output end Proof
% 5.98/5.99  
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