0.03/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.31	% Computer   : n004.cluster.edu
0.12/0.31	% Model      : x86_64 x86_64
0.12/0.31	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.31	% Memory     : 8042.1875MB
0.12/0.31	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.32	% CPULimit   : 180
0.12/0.32	% DateTime   : Thu Aug 29 09:06:38 EDT 2019
0.12/0.32	% CPUTime    : 
5.85/6.04	% SZS status Unsatisfiable
5.85/6.04	
5.85/6.04	% SZS output start Proof
5.85/6.04	Take the following subset of the input axioms:
5.85/6.04	  fof(associativity_of_glb, axiom, ![X, Y, Z]: greatest_lower_bound(X, greatest_lower_bound(Y, Z))=greatest_lower_bound(greatest_lower_bound(X, Y), Z)).
5.85/6.04	  fof(glb_absorbtion, axiom, ![X, Y]: greatest_lower_bound(X, least_upper_bound(X, Y))=X).
5.85/6.04	  fof(lub_absorbtion, axiom, ![X, Y]: X=least_upper_bound(X, greatest_lower_bound(X, Y))).
5.85/6.04	  fof(monotony_glb1, axiom, ![X, Y, Z]: multiply(X, greatest_lower_bound(Y, Z))=greatest_lower_bound(multiply(X, Y), multiply(X, Z))).
5.85/6.04	  fof(monotony_glb2, axiom, ![X, Y, Z]: greatest_lower_bound(multiply(Y, X), multiply(Z, X))=multiply(greatest_lower_bound(Y, Z), X)).
5.85/6.04	  fof(p03d_1, hypothesis, b=least_upper_bound(a, b)).
5.85/6.04	  fof(p03d_2, hypothesis, c=greatest_lower_bound(c, d)).
5.85/6.04	  fof(prove_p03d, negated_conjecture, least_upper_bound(multiply(a, c), multiply(b, d))!=multiply(b, d)).
5.85/6.04	  fof(symmetry_of_glb, axiom, ![X, Y]: greatest_lower_bound(Y, X)=greatest_lower_bound(X, Y)).
5.85/6.04	  fof(symmetry_of_lub, axiom, ![X, Y]: least_upper_bound(X, Y)=least_upper_bound(Y, X)).
5.85/6.04	
5.85/6.04	Now clausify the problem and encode Horn clauses using encoding 3 of
5.85/6.04	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
5.85/6.04	We repeatedly replace C & s=t => u=v by the two clauses:
5.85/6.04	  fresh(y, y, x1...xn) = u
5.85/6.04	  C => fresh(s, t, x1...xn) = v
5.85/6.04	where fresh is a fresh function symbol and x1..xn are the free
5.85/6.04	variables of u and v.
5.85/6.04	A predicate p(X) is encoded as p(X)=true (this is sound, because the
5.85/6.04	input problem has no model of domain size 1).
5.85/6.04	
5.85/6.04	The encoding turns the above axioms into the following unit equations and goals:
5.85/6.04	
5.85/6.04	Axiom 1 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
5.85/6.04	Axiom 2 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
5.85/6.04	Axiom 3 (lub_absorbtion): X = least_upper_bound(X, greatest_lower_bound(X, Y)).
5.85/6.04	Axiom 4 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
5.85/6.04	Axiom 5 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
5.85/6.04	Axiom 6 (monotony_glb2): greatest_lower_bound(multiply(X, Y), multiply(Z, Y)) = multiply(greatest_lower_bound(X, Z), Y).
5.85/6.04	Axiom 7 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
5.85/6.04	Axiom 8 (p03d_1): b = least_upper_bound(a, b).
5.85/6.04	Axiom 9 (p03d_2): c = greatest_lower_bound(c, d).
5.85/6.04	
5.85/6.04	Goal 1 (prove_p03d): least_upper_bound(multiply(a, c), multiply(b, d)) = multiply(b, d).
5.85/6.04	Proof:
5.85/6.04	  least_upper_bound(multiply(a, c), multiply(b, d))
5.85/6.04	= { by axiom 1 (symmetry_of_lub) }
5.85/6.04	  least_upper_bound(multiply(b, d), multiply(a, c))
5.85/6.04	= { by axiom 2 (glb_absorbtion) }
5.85/6.04	  least_upper_bound(multiply(b, d), multiply(greatest_lower_bound(a, least_upper_bound(a, b)), c))
5.85/6.04	= { by axiom 8 (p03d_1) }
5.85/6.04	  least_upper_bound(multiply(b, d), multiply(greatest_lower_bound(a, b), c))
5.85/6.04	= { by axiom 6 (monotony_glb2) }
5.85/6.04	  least_upper_bound(multiply(b, d), greatest_lower_bound(multiply(a, c), multiply(b, c)))
5.85/6.04	= { by axiom 9 (p03d_2) }
5.85/6.04	  least_upper_bound(multiply(b, d), greatest_lower_bound(multiply(a, c), multiply(b, greatest_lower_bound(c, d))))
5.85/6.04	= { by axiom 4 (monotony_glb1) }
5.85/6.04	  least_upper_bound(multiply(b, d), greatest_lower_bound(multiply(a, c), greatest_lower_bound(multiply(b, c), multiply(b, d))))
5.85/6.04	= { by axiom 7 (associativity_of_glb) }
5.85/6.04	  least_upper_bound(multiply(b, d), greatest_lower_bound(greatest_lower_bound(multiply(a, c), multiply(b, c)), multiply(b, d)))
5.85/6.04	= { by axiom 5 (symmetry_of_glb) }
5.85/6.04	  least_upper_bound(multiply(b, d), greatest_lower_bound(multiply(b, d), greatest_lower_bound(multiply(a, c), multiply(b, c))))
5.85/6.04	= { by axiom 6 (monotony_glb2) }
5.85/6.04	  least_upper_bound(multiply(b, d), greatest_lower_bound(multiply(b, d), multiply(greatest_lower_bound(a, b), c)))
5.85/6.04	= { by axiom 3 (lub_absorbtion) }
5.85/6.04	  multiply(b, d)
5.85/6.04	% SZS output end Proof
5.85/6.04	
5.85/6.04	RESULT: Unsatisfiable (the axioms are contradictory).
5.85/6.04	EOF