0.00/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n014.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   : 180
0.12/0.33	% DateTime   : Thu Aug 29 11:16:39 EDT 2019
0.12/0.34	% CPUTime    : 
119.57/119.80	% SZS status Unsatisfiable
119.57/119.80	
119.57/119.80	% SZS output start Proof
119.57/119.80	Take the following subset of the input axioms:
119.57/119.81	  fof(associativity, axiom, ![X, Y, Z]: multiply(multiply(X, Y), Z)=multiply(X, multiply(Y, Z))).
119.57/119.81	  fof(associativity_of_lub, axiom, ![X, Y, Z]: least_upper_bound(X, least_upper_bound(Y, Z))=least_upper_bound(least_upper_bound(X, Y), Z)).
119.57/119.81	  fof(glb_absorbtion, axiom, ![X, Y]: greatest_lower_bound(X, least_upper_bound(X, Y))=X).
119.57/119.81	  fof(idempotence_of_lub, axiom, ![X]: least_upper_bound(X, X)=X).
119.57/119.81	  fof(left_identity, axiom, ![X]: X=multiply(identity, X)).
119.57/119.81	  fof(left_inverse, axiom, ![X]: multiply(inverse(X), X)=identity).
119.57/119.81	  fof(monotony_glb1, axiom, ![X, Y, Z]: multiply(X, greatest_lower_bound(Y, Z))=greatest_lower_bound(multiply(X, Y), multiply(X, Z))).
119.57/119.81	  fof(monotony_lub1, axiom, ![X, Y, Z]: least_upper_bound(multiply(X, Y), multiply(X, Z))=multiply(X, least_upper_bound(Y, Z))).
119.57/119.81	  fof(monotony_lub2, axiom, ![X, Y, Z]: least_upper_bound(multiply(Y, X), multiply(Z, X))=multiply(least_upper_bound(Y, Z), X)).
119.57/119.81	  fof(prove_p22a, negated_conjecture, multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))!=least_upper_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)))).
119.57/119.81	  fof(symmetry_of_glb, axiom, ![X, Y]: greatest_lower_bound(Y, X)=greatest_lower_bound(X, Y)).
119.57/119.81	  fof(symmetry_of_lub, axiom, ![X, Y]: least_upper_bound(X, Y)=least_upper_bound(Y, X)).
119.57/119.81	
119.57/119.81	Now clausify the problem and encode Horn clauses using encoding 3 of
119.57/119.81	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
119.57/119.81	We repeatedly replace C & s=t => u=v by the two clauses:
119.57/119.81	  fresh(y, y, x1...xn) = u
119.57/119.81	  C => fresh(s, t, x1...xn) = v
119.57/119.81	where fresh is a fresh function symbol and x1..xn are the free
119.57/119.81	variables of u and v.
119.57/119.81	A predicate p(X) is encoded as p(X)=true (this is sound, because the
119.57/119.81	input problem has no model of domain size 1).
119.57/119.81	
119.57/119.81	The encoding turns the above axioms into the following unit equations and goals:
119.57/119.81	
119.57/119.82	Axiom 1 (left_inverse): multiply(inverse(X), X) = identity.
119.57/119.82	Axiom 2 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
119.57/119.82	Axiom 3 (left_identity): X = multiply(identity, X).
119.57/119.82	Axiom 4 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
119.57/119.82	Axiom 5 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
119.57/119.82	Axiom 6 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
119.57/119.82	Axiom 7 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
119.57/119.82	Axiom 8 (idempotence_of_lub): least_upper_bound(X, X) = X.
119.57/119.82	Axiom 9 (monotony_lub2): least_upper_bound(multiply(X, Y), multiply(Z, Y)) = multiply(least_upper_bound(X, Z), Y).
119.57/119.82	Axiom 10 (monotony_lub1): least_upper_bound(multiply(X, Y), multiply(X, Z)) = multiply(X, least_upper_bound(Y, Z)).
119.57/119.82	Axiom 11 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
119.57/119.82	
119.57/119.82	Lemma 12: least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(Y, least_upper_bound(X, Z)).
119.57/119.82	Proof:
119.57/119.82	  least_upper_bound(X, least_upper_bound(Y, Z))
119.57/119.82	= { by axiom 11 (associativity_of_lub) }
119.57/119.82	  least_upper_bound(least_upper_bound(X, Y), Z)
119.57/119.82	= { by axiom 4 (symmetry_of_lub) }
119.57/119.82	  least_upper_bound(least_upper_bound(Y, X), Z)
119.57/119.82	= { by axiom 11 (associativity_of_lub) }
119.57/119.82	  least_upper_bound(Y, least_upper_bound(X, Z))
119.57/119.82	
119.57/119.82	Lemma 13: multiply(inverse(X), multiply(X, Y)) = Y.
119.57/119.82	Proof:
119.57/119.82	  multiply(inverse(X), multiply(X, Y))
119.57/119.82	= { by axiom 2 (associativity) }
119.57/119.82	  multiply(multiply(inverse(X), X), Y)
119.57/119.82	= { by axiom 1 (left_inverse) }
119.57/119.82	  multiply(identity, Y)
119.57/119.82	= { by axiom 3 (left_identity) }
119.57/119.82	  Y
119.57/119.82	
119.57/119.82	Lemma 14: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
119.57/119.82	Proof:
119.57/119.82	  multiply(inverse(inverse(X)), Y)
119.57/119.82	= { by lemma 13 }
119.57/119.82	  multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, Y)))
119.57/119.82	= { by lemma 13 }
119.57/119.82	  multiply(X, Y)
119.57/119.82	
119.57/119.82	Lemma 15: multiply(inverse(inverse(X)), identity) = X.
119.57/119.82	Proof:
119.57/119.82	  multiply(inverse(inverse(X)), identity)
119.57/119.82	= { by axiom 1 (left_inverse) }
119.57/119.82	  multiply(inverse(inverse(X)), multiply(inverse(X), X))
119.57/119.82	= { by lemma 13 }
119.57/119.82	  X
119.57/119.82	
119.57/119.82	Lemma 16: multiply(X, identity) = X.
119.57/119.82	Proof:
119.57/119.82	  multiply(X, identity)
119.57/119.82	= { by lemma 14 }
119.57/119.82	  multiply(inverse(inverse(X)), identity)
119.57/119.82	= { by lemma 15 }
119.57/119.82	  X
119.57/119.82	
119.57/119.82	Lemma 17: inverse(inverse(X)) = X.
119.57/119.82	Proof:
119.57/119.82	  inverse(inverse(X))
119.57/119.82	= { by lemma 16 }
119.57/119.82	  multiply(inverse(inverse(X)), identity)
119.57/119.82	= { by lemma 15 }
119.57/119.82	  X
119.57/119.82	
119.57/119.82	Lemma 18: multiply(inverse(X), least_upper_bound(Z, multiply(X, Y))) = least_upper_bound(Y, multiply(inverse(X), Z)).
119.57/119.82	Proof:
119.57/119.82	  multiply(inverse(X), least_upper_bound(Z, multiply(X, Y)))
119.57/119.82	= { by axiom 4 (symmetry_of_lub) }
119.57/119.82	  multiply(inverse(X), least_upper_bound(multiply(X, Y), Z))
119.57/119.82	= { by axiom 10 (monotony_lub1) }
119.57/119.82	  least_upper_bound(multiply(inverse(X), multiply(X, Y)), multiply(inverse(X), Z))
119.57/119.82	= { by lemma 13 }
119.57/119.82	  least_upper_bound(Y, multiply(inverse(X), Z))
119.57/119.82	
119.57/119.82	Lemma 19: least_upper_bound(Y, multiply(X, Y)) = multiply(least_upper_bound(X, identity), Y).
119.57/119.82	Proof:
119.57/119.82	  least_upper_bound(Y, multiply(X, Y))
119.57/119.82	= { by axiom 3 (left_identity) }
119.57/119.82	  least_upper_bound(multiply(identity, Y), multiply(X, Y))
119.57/119.82	= { by axiom 9 (monotony_lub2) }
119.57/119.82	  multiply(least_upper_bound(identity, X), Y)
119.57/119.82	= { by axiom 4 (symmetry_of_lub) }
119.57/119.82	  multiply(least_upper_bound(X, identity), Y)
119.57/119.82	
119.57/119.82	Lemma 20: multiply(inverse(X), least_upper_bound(X, identity)) = least_upper_bound(identity, inverse(X)).
119.57/119.82	Proof:
119.57/119.82	  multiply(inverse(X), least_upper_bound(X, identity))
119.57/119.82	= { by axiom 10 (monotony_lub1) }
119.57/119.82	  least_upper_bound(multiply(inverse(X), X), multiply(inverse(X), identity))
119.57/119.82	= { by axiom 1 (left_inverse) }
119.57/119.82	  least_upper_bound(identity, multiply(inverse(X), identity))
119.57/119.82	= { by lemma 19 }
119.57/119.82	  multiply(least_upper_bound(inverse(X), identity), identity)
119.57/119.82	= { by lemma 16 }
119.57/119.82	  least_upper_bound(inverse(X), identity)
119.57/119.82	= { by axiom 4 (symmetry_of_lub) }
119.57/119.82	  least_upper_bound(identity, inverse(X))
119.57/119.82	
119.57/119.82	Lemma 21: least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(Z, least_upper_bound(X, Y)).
119.57/119.82	Proof:
119.57/119.82	  least_upper_bound(X, least_upper_bound(Y, Z))
119.57/119.82	= { by axiom 11 (associativity_of_lub) }
119.57/119.82	  least_upper_bound(least_upper_bound(X, Y), Z)
119.57/119.82	= { by axiom 4 (symmetry_of_lub) }
119.57/119.82	  least_upper_bound(Z, least_upper_bound(X, Y))
119.57/119.82	
119.57/119.82	Lemma 22: least_upper_bound(Z, multiply(least_upper_bound(X, identity), Y)) = least_upper_bound(Y, least_upper_bound(multiply(X, Y), Z)).
119.57/119.82	Proof:
119.57/119.82	  least_upper_bound(Z, multiply(least_upper_bound(X, identity), Y))
119.57/119.82	= { by lemma 19 }
119.57/119.82	  least_upper_bound(Z, least_upper_bound(Y, multiply(X, Y)))
119.57/119.82	= { by lemma 21 }
119.57/119.82	  least_upper_bound(multiply(X, Y), least_upper_bound(Z, Y))
119.57/119.82	= { by lemma 21 }
119.57/119.82	  least_upper_bound(Y, least_upper_bound(multiply(X, Y), Z))
119.57/119.82	
119.57/119.82	Lemma 23: least_upper_bound(identity, inverse(least_upper_bound(X, identity))) = identity.
119.57/119.82	Proof:
119.57/119.82	  least_upper_bound(identity, inverse(least_upper_bound(X, identity)))
119.57/119.82	= { by axiom 4 (symmetry_of_lub) }
119.57/119.82	  least_upper_bound(identity, inverse(least_upper_bound(identity, X)))
119.57/119.82	= { by lemma 20 }
119.57/119.82	  multiply(inverse(least_upper_bound(identity, X)), least_upper_bound(least_upper_bound(identity, X), identity))
119.57/119.82	= { by axiom 4 (symmetry_of_lub) }
119.57/119.82	  multiply(inverse(least_upper_bound(identity, X)), least_upper_bound(identity, least_upper_bound(identity, X)))
119.57/119.82	= { by lemma 26 }
119.57/119.82	  multiply(inverse(least_upper_bound(identity, X)), least_upper_bound(identity, X))
119.57/119.82	= { by axiom 1 (left_inverse) }
119.57/119.82	  identity
119.57/119.82	
119.57/119.82	Lemma 24: multiply(least_upper_bound(multiply(X, inverse(Z)), Y), Z) = least_upper_bound(X, multiply(Y, Z)).
119.57/119.82	Proof:
119.57/119.82	  multiply(least_upper_bound(multiply(X, inverse(Z)), Y), Z)
119.57/119.82	= { by axiom 4 (symmetry_of_lub) }
119.57/119.82	  multiply(least_upper_bound(Y, multiply(X, inverse(Z))), Z)
119.57/119.82	= { by axiom 4 (symmetry_of_lub) }
119.57/119.82	  multiply(least_upper_bound(multiply(X, inverse(Z)), Y), Z)
119.57/119.82	= { by axiom 9 (monotony_lub2) }
119.57/119.82	  least_upper_bound(multiply(multiply(X, inverse(Z)), Z), multiply(Y, Z))
119.57/119.82	= { by axiom 2 (associativity) }
119.57/119.82	  least_upper_bound(multiply(X, multiply(inverse(Z), Z)), multiply(Y, Z))
119.57/119.82	= { by axiom 1 (left_inverse) }
119.57/119.82	  least_upper_bound(multiply(X, identity), multiply(Y, Z))
119.57/119.82	= { by lemma 16 }
119.57/119.82	  least_upper_bound(X, multiply(Y, Z))
119.57/119.82	
119.57/119.82	Lemma 25: least_upper_bound(Y, least_upper_bound(Z, multiply(X, least_upper_bound(Y, Z)))) = multiply(least_upper_bound(X, identity), least_upper_bound(Y, Z)).
119.57/119.82	Proof:
119.57/119.82	  least_upper_bound(Y, least_upper_bound(Z, multiply(X, least_upper_bound(Y, Z))))
119.57/119.82	= { by axiom 11 (associativity_of_lub) }
119.57/119.82	  least_upper_bound(least_upper_bound(Y, Z), multiply(X, least_upper_bound(Y, Z)))
119.57/119.82	= { by lemma 19 }
119.57/119.83	  multiply(least_upper_bound(X, identity), least_upper_bound(Y, Z))
119.57/119.83	
119.57/119.83	Lemma 26: least_upper_bound(X, least_upper_bound(X, Y)) = least_upper_bound(X, Y).
119.57/119.83	Proof:
119.57/119.83	  least_upper_bound(X, least_upper_bound(X, Y))
119.57/119.83	= { by axiom 3 (left_identity) }
119.57/119.83	  least_upper_bound(X, least_upper_bound(multiply(identity, X), Y))
119.57/119.83	= { by axiom 8 (idempotence_of_lub) }
119.57/119.83	  least_upper_bound(X, least_upper_bound(multiply(least_upper_bound(identity, identity), X), Y))
119.57/119.83	= { by lemma 22 }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(least_upper_bound(identity, identity), identity), X))
119.57/119.83	= { by axiom 4 (symmetry_of_lub) }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(identity, least_upper_bound(identity, identity)), X))
119.57/119.83	= { by lemma 23 }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(identity, least_upper_bound(identity, least_upper_bound(identity, inverse(least_upper_bound(?, identity))))), X))
119.57/119.83	= { by axiom 11 (associativity_of_lub) }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(identity, least_upper_bound(least_upper_bound(identity, identity), inverse(least_upper_bound(?, identity)))), X))
119.57/119.83	= { by axiom 11 (associativity_of_lub) }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(least_upper_bound(identity, least_upper_bound(identity, identity)), inverse(least_upper_bound(?, identity))), X))
119.57/119.83	= { by axiom 4 (symmetry_of_lub) }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(inverse(least_upper_bound(?, identity)), least_upper_bound(identity, least_upper_bound(identity, identity))), X))
119.57/119.83	= { by lemma 12 }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(identity, least_upper_bound(inverse(least_upper_bound(?, identity)), least_upper_bound(identity, identity))), X))
119.57/119.83	= { by axiom 3 (left_identity) }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(identity, least_upper_bound(inverse(least_upper_bound(?, identity)), multiply(identity, least_upper_bound(identity, identity)))), X))
119.57/119.83	= { by lemma 24 }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(identity, multiply(least_upper_bound(multiply(inverse(least_upper_bound(?, identity)), inverse(least_upper_bound(identity, identity))), identity), least_upper_bound(identity, identity))), X))
119.57/119.83	= { by lemma 25 }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(identity, least_upper_bound(identity, least_upper_bound(identity, multiply(multiply(inverse(least_upper_bound(?, identity)), inverse(least_upper_bound(identity, identity))), least_upper_bound(identity, identity))))), X))
119.57/119.83	= { by lemma 26 }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(identity, least_upper_bound(identity, multiply(multiply(inverse(least_upper_bound(?, identity)), inverse(least_upper_bound(identity, identity))), least_upper_bound(identity, identity)))), X))
119.57/119.83	= { by lemma 25 }
119.57/119.83	  least_upper_bound(Y, multiply(multiply(least_upper_bound(multiply(inverse(least_upper_bound(?, identity)), inverse(least_upper_bound(identity, identity))), identity), least_upper_bound(identity, identity)), X))
119.57/119.83	= { by lemma 24 }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(inverse(least_upper_bound(?, identity)), multiply(identity, least_upper_bound(identity, identity))), X))
119.57/119.83	= { by axiom 3 (left_identity) }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(inverse(least_upper_bound(?, identity)), least_upper_bound(identity, identity)), X))
119.57/119.83	= { by lemma 12 }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(identity, least_upper_bound(inverse(least_upper_bound(?, identity)), identity)), X))
119.57/119.83	= { by axiom 11 (associativity_of_lub) }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(least_upper_bound(identity, inverse(least_upper_bound(?, identity))), identity), X))
119.57/119.83	= { by lemma 23 }
119.57/119.83	  least_upper_bound(Y, multiply(least_upper_bound(identity, identity), X))
119.57/119.83	= { by axiom 8 (idempotence_of_lub) }
119.57/119.83	  least_upper_bound(Y, multiply(identity, X))
119.57/119.83	= { by axiom 3 (left_identity) }
119.57/119.83	  least_upper_bound(Y, X)
119.57/119.83	= { by axiom 4 (symmetry_of_lub) }
119.57/119.83	  least_upper_bound(X, Y)
119.57/119.83	
119.57/119.83	Lemma 27: multiply(Y, least_upper_bound(Z, multiply(inverse(Y), X))) = least_upper_bound(X, multiply(Y, Z)).
119.57/119.83	Proof:
119.57/119.83	  multiply(Y, least_upper_bound(Z, multiply(inverse(Y), X)))
119.57/119.83	= { by lemma 14 }
119.57/119.83	  multiply(inverse(inverse(Y)), least_upper_bound(Z, multiply(inverse(Y), X)))
119.57/119.83	= { by lemma 18 }
119.57/119.83	  multiply(inverse(inverse(Y)), multiply(inverse(Y), least_upper_bound(X, multiply(Y, Z))))
119.57/119.83	= { by lemma 13 }
119.57/119.83	  least_upper_bound(X, multiply(Y, Z))
119.57/119.83	
119.57/119.83	Lemma 28: least_upper_bound(multiply(least_upper_bound(Y, identity), X), Z) = least_upper_bound(X, least_upper_bound(Z, multiply(Y, X))).
119.57/119.83	Proof:
119.57/119.83	  least_upper_bound(multiply(least_upper_bound(Y, identity), X), Z)
119.57/119.83	= { by lemma 19 }
119.57/119.83	  least_upper_bound(least_upper_bound(X, multiply(Y, X)), Z)
119.57/119.83	= { by axiom 11 (associativity_of_lub) }
119.57/119.83	  least_upper_bound(X, least_upper_bound(multiply(Y, X), Z))
119.57/119.83	= { by axiom 4 (symmetry_of_lub) }
119.57/119.85	  least_upper_bound(X, least_upper_bound(Z, multiply(Y, X)))
119.57/119.85	
119.57/119.85	Goal 1 (prove_p22a): multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)) = least_upper_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))).
119.57/119.85	Proof:
119.57/119.85	  multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))
119.57/119.85	= { by axiom 4 (symmetry_of_lub) }
119.57/119.85	  multiply(least_upper_bound(identity, a), least_upper_bound(b, identity))
119.57/119.85	= { by lemma 17 }
119.57/119.85	  multiply(inverse(inverse(least_upper_bound(identity, a))), least_upper_bound(b, identity))
119.57/119.85	= { by axiom 5 (glb_absorbtion) }
119.57/119.85	  multiply(inverse(inverse(least_upper_bound(identity, a))), least_upper_bound(b, greatest_lower_bound(identity, least_upper_bound(identity, inverse(least_upper_bound(identity, a))))))
119.57/119.85	= { by axiom 1 (left_inverse) }
119.57/119.85	  multiply(inverse(inverse(least_upper_bound(identity, a))), least_upper_bound(b, greatest_lower_bound(multiply(inverse(least_upper_bound(identity, a)), least_upper_bound(identity, a)), least_upper_bound(identity, inverse(least_upper_bound(identity, a))))))
119.57/119.85	= { by lemma 20 }
119.57/119.85	  multiply(inverse(inverse(least_upper_bound(identity, a))), least_upper_bound(b, greatest_lower_bound(multiply(inverse(least_upper_bound(identity, a)), least_upper_bound(identity, a)), multiply(inverse(least_upper_bound(identity, a)), least_upper_bound(least_upper_bound(identity, a), identity)))))
119.57/119.85	= { by axiom 11 (associativity_of_lub) }
119.57/119.85	  multiply(inverse(inverse(least_upper_bound(identity, a))), least_upper_bound(b, greatest_lower_bound(multiply(inverse(least_upper_bound(identity, a)), least_upper_bound(identity, a)), multiply(inverse(least_upper_bound(identity, a)), least_upper_bound(identity, least_upper_bound(a, identity))))))
119.57/119.85	= { by axiom 6 (monotony_glb1) }
119.57/119.85	  multiply(inverse(inverse(least_upper_bound(identity, a))), least_upper_bound(b, multiply(inverse(least_upper_bound(identity, a)), greatest_lower_bound(least_upper_bound(identity, a), least_upper_bound(identity, least_upper_bound(a, identity))))))
119.57/119.85	= { by axiom 7 (symmetry_of_glb) }
119.57/119.85	  multiply(inverse(inverse(least_upper_bound(identity, a))), least_upper_bound(b, multiply(inverse(least_upper_bound(identity, a)), greatest_lower_bound(least_upper_bound(identity, least_upper_bound(a, identity)), least_upper_bound(identity, a)))))
119.57/119.85	= { by lemma 18 }
119.57/119.85	  least_upper_bound(greatest_lower_bound(least_upper_bound(identity, least_upper_bound(a, identity)), least_upper_bound(identity, a)), multiply(inverse(inverse(least_upper_bound(identity, a))), b))
119.57/119.85	= { by lemma 17 }
119.57/119.85	  least_upper_bound(greatest_lower_bound(least_upper_bound(identity, least_upper_bound(a, identity)), least_upper_bound(identity, a)), multiply(least_upper_bound(identity, a), b))
119.57/119.85	= { by axiom 4 (symmetry_of_lub) }
119.57/119.85	  least_upper_bound(multiply(least_upper_bound(identity, a), b), greatest_lower_bound(least_upper_bound(identity, least_upper_bound(a, identity)), least_upper_bound(identity, a)))
119.57/119.85	= { by axiom 7 (symmetry_of_glb) }
119.57/119.85	  least_upper_bound(multiply(least_upper_bound(identity, a), b), greatest_lower_bound(least_upper_bound(identity, a), least_upper_bound(identity, least_upper_bound(a, identity))))
119.57/119.85	= { by axiom 11 (associativity_of_lub) }
119.57/119.85	  least_upper_bound(multiply(least_upper_bound(identity, a), b), greatest_lower_bound(least_upper_bound(identity, a), least_upper_bound(least_upper_bound(identity, a), identity)))
119.57/119.85	= { by axiom 5 (glb_absorbtion) }
119.57/119.85	  least_upper_bound(multiply(least_upper_bound(identity, a), b), least_upper_bound(identity, a))
119.57/119.85	= { by lemma 12 }
119.57/119.85	  least_upper_bound(identity, least_upper_bound(multiply(least_upper_bound(identity, a), b), a))
119.57/119.85	= { by axiom 4 (symmetry_of_lub) }
119.57/119.85	  least_upper_bound(identity, least_upper_bound(a, multiply(least_upper_bound(identity, a), b)))
119.57/119.85	= { by axiom 8 (idempotence_of_lub) }
119.57/119.85	  least_upper_bound(identity, least_upper_bound(a, multiply(least_upper_bound(identity, least_upper_bound(a, a)), b)))
119.57/119.85	= { by axiom 11 (associativity_of_lub) }
119.57/119.85	  least_upper_bound(identity, least_upper_bound(a, multiply(least_upper_bound(least_upper_bound(identity, a), a), b)))
119.57/119.85	= { by lemma 26 }
119.57/119.85	  least_upper_bound(identity, least_upper_bound(identity, least_upper_bound(a, multiply(least_upper_bound(least_upper_bound(identity, a), a), b))))
119.57/119.85	= { by axiom 11 (associativity_of_lub) }
119.57/119.85	  least_upper_bound(identity, least_upper_bound(least_upper_bound(identity, a), multiply(least_upper_bound(least_upper_bound(identity, a), a), b)))
119.57/119.85	= { by lemma 16 }
119.57/119.85	  least_upper_bound(identity, least_upper_bound(least_upper_bound(identity, a), multiply(least_upper_bound(least_upper_bound(identity, a), multiply(a, identity)), b)))
119.57/119.85	= { by lemma 27 }
119.57/119.85	  least_upper_bound(identity, least_upper_bound(least_upper_bound(identity, a), multiply(multiply(a, least_upper_bound(identity, multiply(inverse(a), least_upper_bound(identity, a)))), b)))
119.57/119.85	= { by axiom 2 (associativity) }
119.57/119.85	  least_upper_bound(identity, least_upper_bound(least_upper_bound(identity, a), multiply(a, multiply(least_upper_bound(identity, multiply(inverse(a), least_upper_bound(identity, a))), b))))
119.57/119.85	= { by lemma 27 }
119.57/119.85	  least_upper_bound(identity, multiply(a, least_upper_bound(multiply(least_upper_bound(identity, multiply(inverse(a), least_upper_bound(identity, a))), b), multiply(inverse(a), least_upper_bound(identity, a)))))
119.57/119.85	= { by axiom 4 (symmetry_of_lub) }
119.57/119.85	  least_upper_bound(identity, multiply(a, least_upper_bound(multiply(least_upper_bound(multiply(inverse(a), least_upper_bound(identity, a)), identity), b), multiply(inverse(a), least_upper_bound(identity, a)))))
119.57/119.85	= { by lemma 28 }
119.57/119.85	  least_upper_bound(identity, multiply(a, least_upper_bound(b, least_upper_bound(multiply(inverse(a), least_upper_bound(identity, a)), multiply(multiply(inverse(a), least_upper_bound(identity, a)), b)))))
119.57/119.85	= { by lemma 16 }
119.57/119.85	  least_upper_bound(identity, multiply(a, least_upper_bound(b, least_upper_bound(multiply(multiply(inverse(a), least_upper_bound(identity, a)), identity), multiply(multiply(inverse(a), least_upper_bound(identity, a)), b)))))
119.57/119.85	= { by axiom 10 (monotony_lub1) }
119.57/119.85	  least_upper_bound(identity, multiply(a, least_upper_bound(b, multiply(multiply(inverse(a), least_upper_bound(identity, a)), least_upper_bound(identity, b)))))
119.57/119.85	= { by axiom 4 (symmetry_of_lub) }
119.57/119.85	  least_upper_bound(identity, multiply(a, least_upper_bound(b, multiply(multiply(inverse(a), least_upper_bound(identity, a)), least_upper_bound(b, identity)))))
119.57/119.85	= { by axiom 2 (associativity) }
119.57/119.85	  least_upper_bound(identity, multiply(a, least_upper_bound(b, multiply(inverse(a), multiply(least_upper_bound(identity, a), least_upper_bound(b, identity))))))
119.57/119.85	= { by lemma 27 }
119.57/119.85	  least_upper_bound(identity, least_upper_bound(multiply(least_upper_bound(identity, a), least_upper_bound(b, identity)), multiply(a, b)))
119.57/119.85	= { by axiom 4 (symmetry_of_lub) }
119.57/119.85	  least_upper_bound(identity, least_upper_bound(multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)), multiply(a, b)))
119.57/119.85	= { by lemma 19 }
119.57/119.85	  least_upper_bound(identity, least_upper_bound(least_upper_bound(least_upper_bound(b, identity), multiply(a, least_upper_bound(b, identity))), multiply(a, b)))
119.57/119.85	= { by axiom 11 (associativity_of_lub) }
119.57/119.85	  least_upper_bound(identity, least_upper_bound(least_upper_bound(b, identity), least_upper_bound(multiply(a, least_upper_bound(b, identity)), multiply(a, b))))
119.57/119.85	= { by lemma 12 }
119.57/119.85	  least_upper_bound(least_upper_bound(b, identity), least_upper_bound(identity, least_upper_bound(multiply(a, least_upper_bound(b, identity)), multiply(a, b))))
119.57/119.85	= { by lemma 12 }
119.57/119.85	  least_upper_bound(least_upper_bound(b, identity), least_upper_bound(multiply(a, least_upper_bound(b, identity)), least_upper_bound(identity, multiply(a, b))))
119.57/119.85	= { by lemma 22 }
119.57/119.85	  least_upper_bound(least_upper_bound(identity, multiply(a, b)), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)))
119.57/119.85	= { by axiom 4 (symmetry_of_lub) }
119.57/119.85	  least_upper_bound(least_upper_bound(identity, multiply(a, b)), multiply(least_upper_bound(identity, a), least_upper_bound(b, identity)))
119.57/119.85	= { by axiom 11 (associativity_of_lub) }
119.57/119.85	  least_upper_bound(identity, least_upper_bound(multiply(a, b), multiply(least_upper_bound(identity, a), least_upper_bound(b, identity))))
119.57/119.85	= { by lemma 12 }
119.57/119.85	  least_upper_bound(multiply(a, b), least_upper_bound(identity, multiply(least_upper_bound(identity, a), least_upper_bound(b, identity))))
119.57/119.85	= { by axiom 4 (symmetry_of_lub) }
119.57/119.85	  least_upper_bound(multiply(a, b), least_upper_bound(identity, multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))))
119.57/119.85	= { by axiom 11 (associativity_of_lub) }
119.57/119.85	  least_upper_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)))
119.57/119.85	% SZS output end Proof
119.57/119.85	
119.57/119.85	RESULT: Unsatisfiable (the axioms are contradictory).
119.57/119.86	EOF