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
0.13/0.34	% Computer   : n005.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 180
0.13/0.34	% DateTime   : Thu Aug 29 12:54:03 EDT 2019
0.13/0.34	% CPUTime    : 
5.85/6.03	% SZS status Unsatisfiable
5.85/6.03	
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, axiom, ![X, Y, Z]: multiply(multiply(X, Y), Z)=multiply(X, multiply(Y, Z))).
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(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)).
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(left_identity, axiom, ![X]: X=multiply(identity, X)).
5.85/6.04	  fof(left_inverse, axiom, ![X]: multiply(inverse(X), X)=identity).
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(monotony_lub1, axiom, ![X, Y, Z]: least_upper_bound(multiply(X, Y), multiply(X, Z))=multiply(X, least_upper_bound(Y, Z))).
5.85/6.04	  fof(monotony_lub2, axiom, ![X, Y, Z]: least_upper_bound(multiply(Y, X), multiply(Z, X))=multiply(least_upper_bound(Y, Z), X)).
5.85/6.04	  fof(p20x_1, hypothesis, identity=inverse(identity)).
5.85/6.04	  fof(p20x_2, hypothesis, ![X]: inverse(inverse(X))=X).
5.85/6.04	  fof(p20x_3, hypothesis, ![X, Y]: multiply(inverse(Y), inverse(X))=inverse(multiply(X, Y))).
5.85/6.04	  fof(prove_20x, negated_conjecture, greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity))!=identity).
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 (left_inverse): multiply(inverse(X), X) = identity.
5.85/6.04	Axiom 2 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
5.85/6.04	Axiom 3 (left_identity): X = multiply(identity, X).
5.85/6.04	Axiom 4 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
5.85/6.04	Axiom 5 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
5.85/6.04	Axiom 6 (lub_absorbtion): X = least_upper_bound(X, greatest_lower_bound(X, Y)).
5.85/6.04	Axiom 7 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
5.85/6.04	Axiom 8 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
5.85/6.04	Axiom 9 (monotony_lub2): least_upper_bound(multiply(X, Y), multiply(Z, Y)) = multiply(least_upper_bound(X, Z), Y).
5.85/6.04	Axiom 10 (monotony_glb2): greatest_lower_bound(multiply(X, Y), multiply(Z, Y)) = multiply(greatest_lower_bound(X, Z), Y).
5.85/6.04	Axiom 11 (monotony_lub1): least_upper_bound(multiply(X, Y), multiply(X, Z)) = multiply(X, least_upper_bound(Y, Z)).
5.85/6.04	Axiom 12 (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 13 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
5.85/6.04	Axiom 14 (p20x_3): multiply(inverse(X), inverse(Y)) = inverse(multiply(Y, X)).
5.85/6.04	Axiom 15 (p20x_1): identity = inverse(identity).
5.85/6.04	Axiom 16 (p20x_2): inverse(inverse(X)) = X.
5.85/6.04	
5.85/6.04	Lemma 17: least_upper_bound(Y, multiply(X, Y)) = multiply(least_upper_bound(X, identity), Y).
5.85/6.04	Proof:
5.85/6.04	  least_upper_bound(Y, multiply(X, Y))
5.85/6.04	= { by axiom 3 (left_identity) }
5.85/6.04	  least_upper_bound(multiply(identity, Y), multiply(X, Y))
5.85/6.04	= { by axiom 9 (monotony_lub2) }
5.85/6.04	  multiply(least_upper_bound(identity, X), Y)
5.85/6.04	= { by axiom 4 (symmetry_of_lub) }
5.85/6.04	  multiply(least_upper_bound(X, identity), Y)
5.85/6.04	
5.85/6.04	Lemma 18: multiply(X, identity) = X.
5.85/6.04	Proof:
5.85/6.04	  multiply(X, identity)
5.85/6.04	= { by axiom 16 (p20x_2) }
5.85/6.04	  inverse(inverse(multiply(X, identity)))
5.85/6.04	= { by axiom 14 (p20x_3) }
5.85/6.04	  inverse(multiply(inverse(identity), inverse(X)))
5.85/6.04	= { by axiom 15 (p20x_1) }
5.85/6.04	  inverse(multiply(identity, inverse(X)))
5.85/6.04	= { by axiom 3 (left_identity) }
5.85/6.04	  inverse(inverse(X))
5.85/6.04	= { by axiom 16 (p20x_2) }
5.85/6.04	  X
5.85/6.04	
5.85/6.04	Lemma 19: multiply(inverse(X), least_upper_bound(X, identity)) = least_upper_bound(identity, inverse(X)).
5.85/6.04	Proof:
5.85/6.04	  multiply(inverse(X), least_upper_bound(X, identity))
5.85/6.04	= { by axiom 11 (monotony_lub1) }
5.85/6.04	  least_upper_bound(multiply(inverse(X), X), multiply(inverse(X), identity))
5.85/6.04	= { by axiom 1 (left_inverse) }
5.85/6.04	  least_upper_bound(identity, multiply(inverse(X), identity))
5.85/6.04	= { by lemma 17 }
5.85/6.04	  multiply(least_upper_bound(inverse(X), identity), identity)
5.85/6.04	= { by lemma 18 }
5.85/6.04	  least_upper_bound(inverse(X), identity)
5.85/6.04	= { by axiom 4 (symmetry_of_lub) }
5.85/6.04	  least_upper_bound(identity, inverse(X))
5.85/6.04	
5.85/6.04	Lemma 20: greatest_lower_bound(Y, multiply(X, Y)) = multiply(greatest_lower_bound(X, identity), Y).
5.85/6.04	Proof:
5.85/6.04	  greatest_lower_bound(Y, multiply(X, Y))
5.85/6.04	= { by axiom 3 (left_identity) }
5.85/6.04	  greatest_lower_bound(multiply(identity, Y), multiply(X, Y))
5.85/6.04	= { by axiom 10 (monotony_glb2) }
5.85/6.04	  multiply(greatest_lower_bound(identity, X), Y)
5.85/6.04	= { by axiom 8 (symmetry_of_glb) }
5.85/6.04	  multiply(greatest_lower_bound(X, identity), Y)
5.85/6.04	
5.85/6.04	Lemma 21: multiply(X, inverse(X)) = identity.
5.85/6.04	Proof:
5.85/6.04	  multiply(X, inverse(X))
5.85/6.04	= { by axiom 16 (p20x_2) }
5.85/6.04	  multiply(inverse(inverse(X)), inverse(X))
5.85/6.04	= { by axiom 1 (left_inverse) }
5.85/6.04	  identity
5.85/6.04	
5.85/6.04	Lemma 22: multiply(inverse(X), greatest_lower_bound(X, identity)) = greatest_lower_bound(identity, inverse(X)).
5.85/6.04	Proof:
5.85/6.04	  multiply(inverse(X), greatest_lower_bound(X, identity))
5.85/6.04	= { by axiom 7 (monotony_glb1) }
5.85/6.04	  greatest_lower_bound(multiply(inverse(X), X), multiply(inverse(X), identity))
5.85/6.04	= { by axiom 1 (left_inverse) }
5.85/6.04	  greatest_lower_bound(identity, multiply(inverse(X), identity))
5.85/6.04	= { by lemma 20 }
5.85/6.04	  multiply(greatest_lower_bound(inverse(X), identity), identity)
5.85/6.04	= { by lemma 18 }
5.85/6.04	  greatest_lower_bound(inverse(X), identity)
5.85/6.04	= { by axiom 8 (symmetry_of_glb) }
5.85/6.04	  greatest_lower_bound(identity, inverse(X))
5.85/6.04	
5.85/6.04	Lemma 23: multiply(least_upper_bound(identity, inverse(X)), greatest_lower_bound(X, identity)) = multiply(greatest_lower_bound(X, identity), least_upper_bound(identity, inverse(X))).
5.85/6.04	Proof:
5.85/6.04	  multiply(least_upper_bound(identity, inverse(X)), greatest_lower_bound(X, identity))
5.85/6.04	= { by axiom 4 (symmetry_of_lub) }
5.85/6.04	  multiply(least_upper_bound(inverse(X), identity), greatest_lower_bound(X, identity))
5.85/6.04	= { by lemma 17 }
5.85/6.04	  least_upper_bound(greatest_lower_bound(X, identity), multiply(inverse(X), greatest_lower_bound(X, identity)))
5.85/6.04	= { by lemma 18 }
5.85/6.04	  least_upper_bound(multiply(greatest_lower_bound(X, identity), identity), multiply(inverse(X), greatest_lower_bound(X, identity)))
5.85/6.04	= { by lemma 22 }
5.85/6.04	  least_upper_bound(multiply(greatest_lower_bound(X, identity), identity), greatest_lower_bound(identity, inverse(X)))
5.85/6.04	= { by axiom 8 (symmetry_of_glb) }
5.85/6.04	  least_upper_bound(multiply(greatest_lower_bound(X, identity), identity), greatest_lower_bound(inverse(X), identity))
5.85/6.04	= { by lemma 21 }
5.85/6.04	  least_upper_bound(multiply(greatest_lower_bound(X, identity), identity), greatest_lower_bound(inverse(X), multiply(X, inverse(X))))
5.85/6.04	= { by lemma 20 }
5.85/6.04	  least_upper_bound(multiply(greatest_lower_bound(X, identity), identity), multiply(greatest_lower_bound(X, identity), inverse(X)))
5.85/6.04	= { by axiom 11 (monotony_lub1) }
5.85/6.04	  multiply(greatest_lower_bound(X, identity), least_upper_bound(identity, inverse(X)))
5.85/6.04	
5.85/6.04	Lemma 24: 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))).
5.85/6.04	Proof:
5.85/6.04	  least_upper_bound(greatest_lower_bound(X, identity), greatest_lower_bound(identity, inverse(X)))
5.85/6.04	= { by lemma 22 }
5.85/6.04	  least_upper_bound(greatest_lower_bound(X, identity), multiply(inverse(X), greatest_lower_bound(X, identity)))
5.85/6.04	= { by axiom 4 (symmetry_of_lub) }
5.85/6.04	  least_upper_bound(multiply(inverse(X), greatest_lower_bound(X, identity)), greatest_lower_bound(X, identity))
5.85/6.04	= { by axiom 3 (left_identity) }
5.85/6.04	  least_upper_bound(multiply(inverse(X), greatest_lower_bound(X, identity)), multiply(identity, greatest_lower_bound(X, identity)))
5.85/6.04	= { by lemma 21 }
5.85/6.04	  least_upper_bound(multiply(inverse(X), greatest_lower_bound(X, identity)), multiply(multiply(X, inverse(X)), greatest_lower_bound(X, identity)))
5.85/6.04	= { by axiom 2 (associativity) }
5.85/6.04	  least_upper_bound(multiply(inverse(X), greatest_lower_bound(X, identity)), multiply(X, multiply(inverse(X), greatest_lower_bound(X, identity))))
5.85/6.04	= { by lemma 17 }
5.85/6.04	  multiply(least_upper_bound(X, identity), multiply(inverse(X), greatest_lower_bound(X, identity)))
5.85/6.04	= { by lemma 22 }
5.85/6.04	  multiply(least_upper_bound(X, identity), greatest_lower_bound(identity, inverse(X)))
5.85/6.04	
5.85/6.04	Goal 1 (prove_20x): greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity)) = identity.
5.85/6.04	Proof:
5.85/6.04	  greatest_lower_bound(least_upper_bound(a, identity), least_upper_bound(inverse(a), identity))
5.85/6.04	= { by lemma 18 }
5.85/6.04	  greatest_lower_bound(multiply(least_upper_bound(a, identity), identity), least_upper_bound(inverse(a), identity))
5.85/6.04	= { by lemma 21 }
5.85/6.04	  greatest_lower_bound(multiply(least_upper_bound(a, identity), identity), least_upper_bound(inverse(a), multiply(a, inverse(a))))
5.85/6.04	= { by lemma 17 }
5.85/6.04	  greatest_lower_bound(multiply(least_upper_bound(a, identity), identity), multiply(least_upper_bound(a, identity), inverse(a)))
5.85/6.04	= { by axiom 7 (monotony_glb1) }
5.85/6.04	  multiply(least_upper_bound(a, identity), greatest_lower_bound(identity, inverse(a)))
5.85/6.04	= { by lemma 24 }
5.85/6.04	  least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(identity, inverse(a)))
5.85/6.04	= { by axiom 5 (glb_absorbtion) }
5.85/6.04	  greatest_lower_bound(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(identity, inverse(a))), least_upper_bound(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(identity, inverse(a))), identity))
5.85/6.04	= { by axiom 4 (symmetry_of_lub) }
5.85/6.04	  greatest_lower_bound(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(identity, inverse(a))), least_upper_bound(identity, least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(identity, inverse(a)))))
5.85/6.04	= { by axiom 4 (symmetry_of_lub) }
5.85/6.04	  greatest_lower_bound(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(identity, inverse(a))), least_upper_bound(identity, least_upper_bound(greatest_lower_bound(identity, inverse(a)), greatest_lower_bound(a, identity))))
5.85/6.04	= { by axiom 13 (associativity_of_lub) }
5.85/6.04	  greatest_lower_bound(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(identity, inverse(a))), least_upper_bound(least_upper_bound(identity, greatest_lower_bound(identity, inverse(a))), greatest_lower_bound(a, identity)))
5.85/6.04	= { by axiom 6 (lub_absorbtion) }
5.85/6.04	  greatest_lower_bound(least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(identity, inverse(a))), least_upper_bound(identity, greatest_lower_bound(a, identity)))
5.85/6.04	= { by axiom 8 (symmetry_of_glb) }
5.85/6.04	  greatest_lower_bound(least_upper_bound(identity, greatest_lower_bound(a, identity)), least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(identity, inverse(a))))
5.85/6.04	= { by axiom 8 (symmetry_of_glb) }
5.85/6.04	  greatest_lower_bound(least_upper_bound(identity, greatest_lower_bound(identity, a)), least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(identity, inverse(a))))
5.85/6.04	= { by axiom 6 (lub_absorbtion) }
5.85/6.04	  greatest_lower_bound(identity, least_upper_bound(greatest_lower_bound(a, identity), greatest_lower_bound(identity, inverse(a))))
5.85/6.04	= { by lemma 24 }
5.85/6.04	  greatest_lower_bound(identity, multiply(least_upper_bound(a, identity), greatest_lower_bound(identity, inverse(a))))
5.85/6.04	= { by axiom 8 (symmetry_of_glb) }
5.85/6.04	  greatest_lower_bound(identity, multiply(least_upper_bound(a, identity), greatest_lower_bound(inverse(a), identity)))
5.85/6.04	= { by axiom 7 (monotony_glb1) }
5.85/6.05	  greatest_lower_bound(identity, greatest_lower_bound(multiply(least_upper_bound(a, identity), inverse(a)), multiply(least_upper_bound(a, identity), identity)))
5.85/6.05	= { by lemma 17 }
5.85/6.05	  greatest_lower_bound(identity, greatest_lower_bound(multiply(least_upper_bound(a, identity), inverse(a)), least_upper_bound(identity, multiply(a, identity))))
5.85/6.05	= { by axiom 8 (symmetry_of_glb) }
5.85/6.05	  greatest_lower_bound(identity, greatest_lower_bound(least_upper_bound(identity, multiply(a, identity)), multiply(least_upper_bound(a, identity), inverse(a))))
5.85/6.05	= { by axiom 12 (associativity_of_glb) }
5.85/6.05	  greatest_lower_bound(greatest_lower_bound(identity, least_upper_bound(identity, multiply(a, identity))), multiply(least_upper_bound(a, identity), inverse(a)))
5.85/6.05	= { by axiom 5 (glb_absorbtion) }
5.85/6.05	  greatest_lower_bound(identity, multiply(least_upper_bound(a, identity), inverse(a)))
5.85/6.05	= { by axiom 9 (monotony_lub2) }
5.85/6.05	  greatest_lower_bound(identity, least_upper_bound(multiply(a, inverse(a)), multiply(identity, inverse(a))))
5.85/6.05	= { by lemma 21 }
5.85/6.05	  greatest_lower_bound(identity, least_upper_bound(identity, multiply(identity, inverse(a))))
5.85/6.05	= { by axiom 5 (glb_absorbtion) }
5.85/6.05	  identity
5.85/6.05	% SZS output end Proof
5.85/6.05	
5.85/6.05	RESULT: Unsatisfiable (the axioms are contradictory).
5.85/6.05	EOF