0.04/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.14	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.14/0.35	% Computer   : n004.cluster.edu
0.14/0.35	% Model      : x86_64 x86_64
0.14/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.35	% Memory     : 8042.1875MB
0.14/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.35	% CPULimit   : 180
0.14/0.35	% DateTime   : Thu Aug 29 12:58:53 EDT 2019
0.14/0.35	% CPUTime    : 
6.11/6.25	% SZS status Unsatisfiable
6.11/6.25	
6.11/6.25	% SZS output start Proof
6.11/6.25	Take the following subset of the input axioms:
6.20/6.36	  fof(associativity, axiom, ![X, Y, Z]: multiply(multiply(X, Y), Z)=multiply(X, multiply(Y, Z))).
6.20/6.36	  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)).
6.20/6.36	  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)).
6.20/6.36	  fof(glb_absorbtion, axiom, ![X, Y]: greatest_lower_bound(X, least_upper_bound(X, Y))=X).
6.20/6.36	  fof(left_identity, axiom, ![X]: X=multiply(identity, X)).
6.20/6.36	  fof(left_inverse, axiom, ![X]: multiply(inverse(X), X)=identity).
6.20/6.36	  fof(lub_absorbtion, axiom, ![X, Y]: X=least_upper_bound(X, greatest_lower_bound(X, Y))).
6.20/6.36	  fof(monotony_glb1, axiom, ![X, Y, Z]: multiply(X, greatest_lower_bound(Y, Z))=greatest_lower_bound(multiply(X, Y), multiply(X, Z))).
6.20/6.36	  fof(monotony_glb2, axiom, ![X, Y, Z]: greatest_lower_bound(multiply(Y, X), multiply(Z, X))=multiply(greatest_lower_bound(Y, Z), X)).
6.20/6.36	  fof(monotony_lub1, axiom, ![X, Y, Z]: least_upper_bound(multiply(X, Y), multiply(X, Z))=multiply(X, least_upper_bound(Y, Z))).
6.20/6.36	  fof(monotony_lub2, axiom, ![X, Y, Z]: least_upper_bound(multiply(Y, X), multiply(Z, X))=multiply(least_upper_bound(Y, Z), X)).
6.20/6.36	  fof(p11_1, hypothesis, identity=inverse(identity)).
6.20/6.36	  fof(p11_2, hypothesis, ![X]: X=inverse(inverse(X))).
6.20/6.36	  fof(p11_3, hypothesis, ![X, Y]: inverse(multiply(X, Y))=multiply(inverse(Y), inverse(X))).
6.20/6.36	  fof(prove_p11, negated_conjecture, multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b))!=least_upper_bound(a, b)).
6.20/6.36	  fof(symmetry_of_glb, axiom, ![X, Y]: greatest_lower_bound(Y, X)=greatest_lower_bound(X, Y)).
6.20/6.36	  fof(symmetry_of_lub, axiom, ![X, Y]: least_upper_bound(X, Y)=least_upper_bound(Y, X)).
6.20/6.36	
6.20/6.36	Now clausify the problem and encode Horn clauses using encoding 3 of
6.20/6.36	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
6.20/6.36	We repeatedly replace C & s=t => u=v by the two clauses:
6.20/6.36	  fresh(y, y, x1...xn) = u
6.20/6.36	  C => fresh(s, t, x1...xn) = v
6.20/6.36	where fresh is a fresh function symbol and x1..xn are the free
6.20/6.36	variables of u and v.
6.20/6.36	A predicate p(X) is encoded as p(X)=true (this is sound, because the
6.20/6.36	input problem has no model of domain size 1).
6.20/6.36	
6.20/6.36	The encoding turns the above axioms into the following unit equations and goals:
6.20/6.36	
6.20/6.36	Axiom 1 (left_inverse): multiply(inverse(X), X) = identity.
6.20/6.36	Axiom 2 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
6.20/6.36	Axiom 3 (left_identity): X = multiply(identity, X).
6.20/6.36	Axiom 4 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
6.20/6.36	Axiom 5 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
6.20/6.36	Axiom 6 (lub_absorbtion): X = least_upper_bound(X, greatest_lower_bound(X, Y)).
6.20/6.36	Axiom 7 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
6.20/6.36	Axiom 8 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
6.20/6.36	Axiom 9 (monotony_lub2): least_upper_bound(multiply(X, Y), multiply(Z, Y)) = multiply(least_upper_bound(X, Z), Y).
6.20/6.36	Axiom 10 (monotony_glb2): greatest_lower_bound(multiply(X, Y), multiply(Z, Y)) = multiply(greatest_lower_bound(X, Z), Y).
6.20/6.36	Axiom 11 (monotony_lub1): least_upper_bound(multiply(X, Y), multiply(X, Z)) = multiply(X, least_upper_bound(Y, Z)).
6.20/6.36	Axiom 12 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
6.20/6.36	Axiom 13 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
6.20/6.36	Axiom 14 (p11_2): X = inverse(inverse(X)).
6.20/6.36	Axiom 15 (p11_3): inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)).
6.20/6.36	Axiom 16 (p11_1): identity = inverse(identity).
6.20/6.36	
6.20/6.36	Lemma 17: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
6.20/6.36	Proof:
6.20/6.36	  inverse(multiply(inverse(X), Y))
6.20/6.36	= { by axiom 15 (p11_3) }
6.20/6.36	  multiply(inverse(Y), inverse(inverse(X)))
6.20/6.36	= { by axiom 14 (p11_2) }
6.20/6.36	  multiply(inverse(Y), X)
6.20/6.36	
6.20/6.36	Lemma 18: multiply(X, identity) = X.
6.20/6.36	Proof:
6.20/6.36	  multiply(X, identity)
6.20/6.36	= { by axiom 14 (p11_2) }
6.20/6.36	  inverse(inverse(multiply(X, identity)))
6.20/6.36	= { by axiom 15 (p11_3) }
6.20/6.36	  inverse(multiply(inverse(identity), inverse(X)))
6.20/6.36	= { by axiom 16 (p11_1) }
6.20/6.36	  inverse(multiply(identity, inverse(X)))
6.20/6.36	= { by axiom 3 (left_identity) }
6.20/6.36	  inverse(inverse(X))
6.20/6.36	= { by axiom 14 (p11_2) }
6.20/6.36	  X
6.20/6.36	
6.20/6.36	Lemma 19: multiply(inverse(X), multiply(X, Y)) = Y.
6.20/6.36	Proof:
6.20/6.36	  multiply(inverse(X), multiply(X, Y))
6.20/6.36	= { by axiom 2 (associativity) }
6.20/6.36	  multiply(multiply(inverse(X), X), Y)
6.20/6.36	= { by axiom 1 (left_inverse) }
6.20/6.36	  multiply(identity, Y)
6.20/6.36	= { by axiom 3 (left_identity) }
6.20/6.36	  Y
6.20/6.36	
6.20/6.36	Lemma 20: greatest_lower_bound(Y, multiply(X, Y)) = multiply(greatest_lower_bound(X, identity), Y).
6.20/6.36	Proof:
6.20/6.36	  greatest_lower_bound(Y, multiply(X, Y))
6.20/6.36	= { by axiom 3 (left_identity) }
6.20/6.36	  greatest_lower_bound(multiply(identity, Y), multiply(X, Y))
6.20/6.36	= { by axiom 10 (monotony_glb2) }
6.20/6.36	  multiply(greatest_lower_bound(identity, X), Y)
6.20/6.36	= { by axiom 8 (symmetry_of_glb) }
6.20/6.36	  multiply(greatest_lower_bound(X, identity), Y)
6.20/6.36	
6.20/6.36	Lemma 21: multiply(X, inverse(X)) = identity.
6.20/6.36	Proof:
6.20/6.36	  multiply(X, inverse(X))
6.20/6.36	= { by axiom 14 (p11_2) }
6.20/6.36	  multiply(inverse(inverse(X)), inverse(X))
6.20/6.36	= { by axiom 1 (left_inverse) }
6.20/6.36	  identity
6.20/6.36	
6.20/6.36	Lemma 22: least_upper_bound(identity, multiply(inverse(X), Y)) = multiply(inverse(X), least_upper_bound(X, Y)).
6.20/6.36	Proof:
6.20/6.36	  least_upper_bound(identity, multiply(inverse(X), Y))
6.20/6.36	= { by axiom 1 (left_inverse) }
6.20/6.36	  least_upper_bound(multiply(inverse(X), X), multiply(inverse(X), Y))
6.20/6.36	= { by axiom 11 (monotony_lub1) }
6.20/6.36	  multiply(inverse(X), least_upper_bound(X, Y))
6.20/6.36	
6.20/6.36	Lemma 23: least_upper_bound(Y, multiply(X, Y)) = multiply(least_upper_bound(X, identity), Y).
6.20/6.36	Proof:
6.20/6.36	  least_upper_bound(Y, multiply(X, Y))
6.20/6.36	= { by axiom 3 (left_identity) }
6.20/6.36	  least_upper_bound(multiply(identity, Y), multiply(X, Y))
6.20/6.36	= { by axiom 9 (monotony_lub2) }
6.20/6.36	  multiply(least_upper_bound(identity, X), Y)
6.20/6.36	= { by axiom 4 (symmetry_of_lub) }
6.20/6.36	  multiply(least_upper_bound(X, identity), Y)
6.20/6.36	
6.20/6.36	Lemma 24: multiply(inverse(X), greatest_lower_bound(X, identity)) = greatest_lower_bound(identity, inverse(X)).
6.20/6.36	Proof:
6.20/6.36	  multiply(inverse(X), greatest_lower_bound(X, identity))
6.20/6.36	= { by axiom 7 (monotony_glb1) }
6.20/6.36	  greatest_lower_bound(multiply(inverse(X), X), multiply(inverse(X), identity))
6.20/6.36	= { by axiom 1 (left_inverse) }
6.20/6.36	  greatest_lower_bound(identity, multiply(inverse(X), identity))
6.20/6.36	= { by lemma 20 }
6.20/6.36	  multiply(greatest_lower_bound(inverse(X), identity), identity)
6.20/6.36	= { by lemma 18 }
6.20/6.36	  greatest_lower_bound(inverse(X), identity)
6.20/6.36	= { by axiom 8 (symmetry_of_glb) }
6.20/6.36	  greatest_lower_bound(identity, inverse(X))
6.20/6.36	
6.20/6.36	Lemma 25: multiply(least_upper_bound(identity, inverse(X)), greatest_lower_bound(X, identity)) = multiply(greatest_lower_bound(X, identity), least_upper_bound(identity, inverse(X))).
6.20/6.36	Proof:
6.20/6.36	  multiply(least_upper_bound(identity, inverse(X)), greatest_lower_bound(X, identity))
6.20/6.36	= { by axiom 4 (symmetry_of_lub) }
6.20/6.36	  multiply(least_upper_bound(inverse(X), identity), greatest_lower_bound(X, identity))
6.20/6.36	= { by lemma 23 }
6.20/6.36	  least_upper_bound(greatest_lower_bound(X, identity), multiply(inverse(X), greatest_lower_bound(X, identity)))
6.20/6.36	= { by lemma 18 }
6.20/6.36	  least_upper_bound(multiply(greatest_lower_bound(X, identity), identity), multiply(inverse(X), greatest_lower_bound(X, identity)))
6.20/6.36	= { by lemma 24 }
6.20/6.36	  least_upper_bound(multiply(greatest_lower_bound(X, identity), identity), greatest_lower_bound(identity, inverse(X)))
6.20/6.36	= { by axiom 8 (symmetry_of_glb) }
6.20/6.36	  least_upper_bound(multiply(greatest_lower_bound(X, identity), identity), greatest_lower_bound(inverse(X), identity))
6.20/6.36	= { by lemma 21 }
6.20/6.36	  least_upper_bound(multiply(greatest_lower_bound(X, identity), identity), greatest_lower_bound(inverse(X), multiply(X, inverse(X))))
6.20/6.36	= { by lemma 20 }
6.20/6.36	  least_upper_bound(multiply(greatest_lower_bound(X, identity), identity), multiply(greatest_lower_bound(X, identity), inverse(X)))
6.20/6.36	= { by axiom 11 (monotony_lub1) }
6.20/6.36	  multiply(greatest_lower_bound(X, identity), least_upper_bound(identity, inverse(X)))
6.20/6.36	
6.20/6.36	Lemma 26: least_upper_bound(greatest_lower_bound(X, identity), greatest_lower_bound(identity, inverse(X))) = multiply(least_upper_bound(X, identity), greatest_lower_bound(identity, inverse(X))).
6.20/6.36	Proof:
6.20/6.36	  least_upper_bound(greatest_lower_bound(X, identity), greatest_lower_bound(identity, inverse(X)))
6.20/6.36	= { by lemma 24 }
6.20/6.36	  least_upper_bound(greatest_lower_bound(X, identity), multiply(inverse(X), greatest_lower_bound(X, identity)))
6.20/6.36	= { by axiom 4 (symmetry_of_lub) }
6.20/6.36	  least_upper_bound(multiply(inverse(X), greatest_lower_bound(X, identity)), greatest_lower_bound(X, identity))
6.20/6.36	= { by axiom 3 (left_identity) }
6.20/6.36	  least_upper_bound(multiply(inverse(X), greatest_lower_bound(X, identity)), multiply(identity, greatest_lower_bound(X, identity)))
6.20/6.36	= { by lemma 21 }
6.20/6.36	  least_upper_bound(multiply(inverse(X), greatest_lower_bound(X, identity)), multiply(multiply(X, inverse(X)), greatest_lower_bound(X, identity)))
6.20/6.36	= { by axiom 2 (associativity) }
6.20/6.36	  least_upper_bound(multiply(inverse(X), greatest_lower_bound(X, identity)), multiply(X, multiply(inverse(X), greatest_lower_bound(X, identity))))
6.20/6.36	= { by lemma 23 }
6.20/6.36	  multiply(least_upper_bound(X, identity), multiply(inverse(X), greatest_lower_bound(X, identity)))
6.20/6.36	= { by lemma 24 }
6.30/6.48	  multiply(least_upper_bound(X, identity), greatest_lower_bound(identity, inverse(X)))
6.30/6.48	
6.30/6.48	Goal 1 (prove_p11): multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b)) = least_upper_bound(a, b).
6.30/6.48	Proof:
6.30/6.48	  multiply(a, multiply(inverse(greatest_lower_bound(a, b)), b))
6.30/6.48	= { by axiom 14 (p11_2) }
6.30/6.48	  multiply(inverse(inverse(a)), multiply(inverse(greatest_lower_bound(a, b)), b))
6.30/6.48	= { by lemma 17 }
6.30/6.48	  multiply(inverse(inverse(a)), inverse(multiply(inverse(b), greatest_lower_bound(a, b))))
6.30/6.48	= { by axiom 8 (symmetry_of_glb) }
6.30/6.48	  multiply(inverse(inverse(a)), inverse(multiply(inverse(b), greatest_lower_bound(b, a))))
6.30/6.48	= { by axiom 7 (monotony_glb1) }
6.30/6.48	  multiply(inverse(inverse(a)), inverse(greatest_lower_bound(multiply(inverse(b), b), multiply(inverse(b), a))))
6.30/6.48	= { by axiom 1 (left_inverse) }
6.30/6.48	  multiply(inverse(inverse(a)), inverse(greatest_lower_bound(identity, multiply(inverse(b), a))))
6.30/6.48	= { by axiom 14 (p11_2) }
6.30/6.48	  multiply(inverse(inverse(a)), inverse(greatest_lower_bound(identity, multiply(inverse(b), inverse(inverse(a))))))
6.30/6.48	= { by axiom 15 (p11_3) }
6.30/6.48	  inverse(multiply(greatest_lower_bound(identity, multiply(inverse(b), inverse(inverse(a)))), inverse(a)))
6.30/6.48	= { by axiom 8 (symmetry_of_glb) }
6.30/6.48	  inverse(multiply(greatest_lower_bound(multiply(inverse(b), inverse(inverse(a))), identity), inverse(a)))
6.30/6.48	= { by axiom 10 (monotony_glb2) }
6.30/6.48	  inverse(greatest_lower_bound(multiply(multiply(inverse(b), inverse(inverse(a))), inverse(a)), multiply(identity, inverse(a))))
6.30/6.48	= { by axiom 2 (associativity) }
6.30/6.48	  inverse(greatest_lower_bound(multiply(inverse(b), multiply(inverse(inverse(a)), inverse(a))), multiply(identity, inverse(a))))
6.30/6.48	= { by axiom 1 (left_inverse) }
6.30/6.48	  inverse(greatest_lower_bound(multiply(inverse(b), identity), multiply(identity, inverse(a))))
6.30/6.48	= { by lemma 18 }
6.30/6.48	  inverse(greatest_lower_bound(inverse(b), multiply(identity, inverse(a))))
6.30/6.48	= { by axiom 3 (left_identity) }
6.30/6.48	  inverse(greatest_lower_bound(inverse(b), inverse(a)))
6.30/6.48	= { by axiom 8 (symmetry_of_glb) }
6.30/6.48	  inverse(greatest_lower_bound(inverse(a), inverse(b)))
6.30/6.48	= { by lemma 19 }
6.30/6.48	  inverse(greatest_lower_bound(multiply(inverse(b), multiply(b, inverse(a))), inverse(b)))
6.30/6.48	= { by lemma 18 }
6.30/6.48	  inverse(greatest_lower_bound(multiply(inverse(b), multiply(b, inverse(a))), multiply(inverse(b), identity)))
6.30/6.48	= { by axiom 7 (monotony_glb1) }
6.30/6.48	  inverse(multiply(inverse(b), greatest_lower_bound(multiply(b, inverse(a)), identity)))
6.30/6.48	= { by axiom 8 (symmetry_of_glb) }
6.30/6.48	  inverse(multiply(inverse(b), greatest_lower_bound(identity, multiply(b, inverse(a)))))
6.30/6.48	= { by lemma 17 }
6.30/6.48	  multiply(inverse(greatest_lower_bound(identity, multiply(b, inverse(a)))), b)
6.30/6.48	= { by axiom 8 (symmetry_of_glb) }
6.30/6.48	  multiply(inverse(greatest_lower_bound(multiply(b, inverse(a)), identity)), b)
6.30/6.48	= { by lemma 18 }
6.30/6.48	  multiply(inverse(multiply(greatest_lower_bound(multiply(b, inverse(a)), identity), identity)), b)
6.30/6.48	= { by lemma 20 }
6.30/6.48	  multiply(inverse(greatest_lower_bound(identity, multiply(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by lemma 21 }
6.30/6.48	  multiply(inverse(greatest_lower_bound(multiply(multiply(b, inverse(a)), inverse(multiply(b, inverse(a)))), multiply(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 7 (monotony_glb1) }
6.30/6.48	  multiply(inverse(multiply(multiply(b, inverse(a)), greatest_lower_bound(inverse(multiply(b, inverse(a))), identity))), b)
6.30/6.48	= { by axiom 8 (symmetry_of_glb) }
6.30/6.48	  multiply(inverse(multiply(multiply(b, inverse(a)), greatest_lower_bound(identity, inverse(multiply(b, inverse(a)))))), b)
6.30/6.48	= { by lemma 19 }
6.30/6.48	  multiply(inverse(multiply(inverse(least_upper_bound(multiply(b, inverse(a)), identity)), multiply(least_upper_bound(multiply(b, inverse(a)), identity), multiply(multiply(b, inverse(a)), greatest_lower_bound(identity, inverse(multiply(b, inverse(a)))))))), b)
6.30/6.48	= { by lemma 17 }
6.30/6.48	  multiply(multiply(inverse(multiply(least_upper_bound(multiply(b, inverse(a)), identity), multiply(multiply(b, inverse(a)), greatest_lower_bound(identity, inverse(multiply(b, inverse(a))))))), least_upper_bound(multiply(b, inverse(a)), identity)), b)
6.30/6.48	= { by lemma 23 }
6.30/6.48	  multiply(multiply(inverse(least_upper_bound(multiply(multiply(b, inverse(a)), greatest_lower_bound(identity, inverse(multiply(b, inverse(a))))), multiply(multiply(b, inverse(a)), multiply(multiply(b, inverse(a)), greatest_lower_bound(identity, inverse(multiply(b, inverse(a)))))))), least_upper_bound(multiply(b, inverse(a)), identity)), b)
6.30/6.48	= { by axiom 11 (monotony_lub1) }
6.30/6.48	  multiply(multiply(inverse(multiply(multiply(b, inverse(a)), least_upper_bound(greatest_lower_bound(identity, inverse(multiply(b, inverse(a)))), multiply(multiply(b, inverse(a)), greatest_lower_bound(identity, inverse(multiply(b, inverse(a)))))))), least_upper_bound(multiply(b, inverse(a)), identity)), b)
6.30/6.48	= { by lemma 23 }
6.30/6.48	  multiply(multiply(inverse(multiply(multiply(b, inverse(a)), multiply(least_upper_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(identity, inverse(multiply(b, inverse(a))))))), least_upper_bound(multiply(b, inverse(a)), identity)), b)
6.30/6.48	= { by axiom 15 (p11_3) }
6.30/6.48	  multiply(multiply(multiply(inverse(multiply(least_upper_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(identity, inverse(multiply(b, inverse(a)))))), inverse(multiply(b, inverse(a)))), least_upper_bound(multiply(b, inverse(a)), identity)), b)
6.30/6.48	= { by axiom 2 (associativity) }
6.30/6.48	  multiply(multiply(inverse(multiply(least_upper_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(identity, inverse(multiply(b, inverse(a)))))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by lemma 26 }
6.30/6.48	  multiply(multiply(inverse(least_upper_bound(greatest_lower_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(identity, inverse(multiply(b, inverse(a)))))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 5 (glb_absorbtion) }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(least_upper_bound(greatest_lower_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(identity, inverse(multiply(b, inverse(a))))), least_upper_bound(least_upper_bound(greatest_lower_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(identity, inverse(multiply(b, inverse(a))))), identity))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 4 (symmetry_of_lub) }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(least_upper_bound(greatest_lower_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(identity, inverse(multiply(b, inverse(a))))), least_upper_bound(identity, least_upper_bound(greatest_lower_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(identity, inverse(multiply(b, inverse(a)))))))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 4 (symmetry_of_lub) }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(least_upper_bound(greatest_lower_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(identity, inverse(multiply(b, inverse(a))))), least_upper_bound(identity, least_upper_bound(greatest_lower_bound(identity, inverse(multiply(b, inverse(a)))), greatest_lower_bound(multiply(b, inverse(a)), identity))))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 13 (associativity_of_lub) }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(least_upper_bound(greatest_lower_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(identity, inverse(multiply(b, inverse(a))))), least_upper_bound(least_upper_bound(identity, greatest_lower_bound(identity, inverse(multiply(b, inverse(a))))), greatest_lower_bound(multiply(b, inverse(a)), identity)))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 6 (lub_absorbtion) }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(least_upper_bound(greatest_lower_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(identity, inverse(multiply(b, inverse(a))))), least_upper_bound(identity, greatest_lower_bound(multiply(b, inverse(a)), identity)))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 8 (symmetry_of_glb) }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(least_upper_bound(identity, greatest_lower_bound(multiply(b, inverse(a)), identity)), least_upper_bound(greatest_lower_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(identity, inverse(multiply(b, inverse(a))))))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 8 (symmetry_of_glb) }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(least_upper_bound(identity, greatest_lower_bound(identity, multiply(b, inverse(a)))), least_upper_bound(greatest_lower_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(identity, inverse(multiply(b, inverse(a))))))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 6 (lub_absorbtion) }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(identity, least_upper_bound(greatest_lower_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(identity, inverse(multiply(b, inverse(a))))))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by lemma 26 }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(identity, multiply(least_upper_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(identity, inverse(multiply(b, inverse(a))))))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 8 (symmetry_of_glb) }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(identity, multiply(least_upper_bound(multiply(b, inverse(a)), identity), greatest_lower_bound(inverse(multiply(b, inverse(a))), identity)))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 7 (monotony_glb1) }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(identity, greatest_lower_bound(multiply(least_upper_bound(multiply(b, inverse(a)), identity), inverse(multiply(b, inverse(a)))), multiply(least_upper_bound(multiply(b, inverse(a)), identity), identity)))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by lemma 23 }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(identity, greatest_lower_bound(multiply(least_upper_bound(multiply(b, inverse(a)), identity), inverse(multiply(b, inverse(a)))), least_upper_bound(identity, multiply(multiply(b, inverse(a)), identity))))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 8 (symmetry_of_glb) }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(identity, multiply(multiply(b, inverse(a)), identity)), multiply(least_upper_bound(multiply(b, inverse(a)), identity), inverse(multiply(b, inverse(a))))))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 12 (associativity_of_glb) }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(greatest_lower_bound(identity, least_upper_bound(identity, multiply(multiply(b, inverse(a)), identity))), multiply(least_upper_bound(multiply(b, inverse(a)), identity), inverse(multiply(b, inverse(a)))))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 5 (glb_absorbtion) }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(identity, multiply(least_upper_bound(multiply(b, inverse(a)), identity), inverse(multiply(b, inverse(a)))))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 9 (monotony_lub2) }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(identity, least_upper_bound(multiply(multiply(b, inverse(a)), inverse(multiply(b, inverse(a)))), multiply(identity, inverse(multiply(b, inverse(a))))))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by lemma 21 }
6.30/6.48	  multiply(multiply(inverse(greatest_lower_bound(identity, least_upper_bound(identity, multiply(identity, inverse(multiply(b, inverse(a))))))), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by axiom 5 (glb_absorbtion) }
6.30/6.48	  multiply(multiply(inverse(identity), multiply(inverse(multiply(b, inverse(a))), least_upper_bound(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by lemma 22 }
6.30/6.48	  multiply(multiply(inverse(identity), least_upper_bound(identity, multiply(inverse(multiply(b, inverse(a))), identity))), b)
6.30/6.48	= { by lemma 23 }
6.30/6.48	  multiply(multiply(inverse(identity), multiply(least_upper_bound(inverse(multiply(b, inverse(a))), identity), identity)), b)
6.30/6.48	= { by lemma 18 }
6.30/6.48	  multiply(multiply(inverse(identity), least_upper_bound(inverse(multiply(b, inverse(a))), identity)), b)
6.30/6.48	= { by axiom 4 (symmetry_of_lub) }
6.30/6.48	  multiply(multiply(inverse(identity), least_upper_bound(identity, inverse(multiply(b, inverse(a))))), b)
6.30/6.48	= { by lemma 22 }
6.30/6.48	  multiply(least_upper_bound(identity, multiply(inverse(identity), inverse(multiply(b, inverse(a))))), b)
6.30/6.48	= { by axiom 15 (p11_3) }
6.30/6.48	  multiply(least_upper_bound(identity, inverse(multiply(multiply(b, inverse(a)), identity))), b)
6.30/6.48	= { by lemma 18 }
6.30/6.48	  multiply(least_upper_bound(identity, inverse(multiply(b, inverse(a)))), b)
6.30/6.48	= { by axiom 4 (symmetry_of_lub) }
6.30/6.48	  multiply(least_upper_bound(inverse(multiply(b, inverse(a))), identity), b)
6.30/6.48	= { by axiom 14 (p11_2) }
6.30/6.48	  multiply(least_upper_bound(inverse(multiply(b, inverse(a))), identity), inverse(inverse(b)))
6.30/6.48	= { by axiom 9 (monotony_lub2) }
6.30/6.48	  least_upper_bound(multiply(inverse(multiply(b, inverse(a))), inverse(inverse(b))), multiply(identity, inverse(inverse(b))))
6.30/6.48	= { by axiom 15 (p11_3) }
6.30/6.48	  least_upper_bound(inverse(multiply(inverse(b), multiply(b, inverse(a)))), multiply(identity, inverse(inverse(b))))
6.30/6.48	= { by axiom 4 (symmetry_of_lub) }
6.30/6.48	  least_upper_bound(multiply(identity, inverse(inverse(b))), inverse(multiply(inverse(b), multiply(b, inverse(a)))))
6.30/6.48	= { by axiom 14 (p11_2) }
6.30/6.48	  least_upper_bound(multiply(identity, b), inverse(multiply(inverse(b), multiply(b, inverse(a)))))
6.30/6.48	= { by lemma 19 }
6.30/6.48	  least_upper_bound(multiply(identity, b), inverse(inverse(a)))
6.30/6.48	= { by axiom 4 (symmetry_of_lub) }
6.30/6.48	  least_upper_bound(inverse(inverse(a)), multiply(identity, b))
6.30/6.48	= { by axiom 3 (left_identity) }
6.30/6.48	  least_upper_bound(inverse(inverse(a)), b)
6.30/6.48	= { by axiom 4 (symmetry_of_lub) }
6.30/6.48	  least_upper_bound(b, inverse(inverse(a)))
6.30/6.48	= { by axiom 14 (p11_2) }
6.30/6.48	  least_upper_bound(b, a)
6.30/6.48	= { by axiom 4 (symmetry_of_lub) }
6.30/6.48	  least_upper_bound(a, b)
6.30/6.48	% SZS output end Proof
6.30/6.48	
6.30/6.48	RESULT: Unsatisfiable (the axioms are contradictory).
6.30/6.48	EOF