0.08/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.14	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.36	% Computer   : n026.cluster.edu
0.13/0.36	% Model      : x86_64 x86_64
0.13/0.36	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.36	% Memory     : 8042.1875MB
0.13/0.36	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.36	% CPULimit   : 180
0.13/0.36	% DateTime   : Thu Aug 29 10:51:20 EDT 2019
0.13/0.36	% CPUTime    : 
0.13/0.38	% SZS status Unsatisfiable
0.13/0.38	
0.13/0.38	% SZS output start Proof
0.13/0.38	Take the following subset of the input axioms:
0.13/0.38	  fof(multiply, axiom, ![A, B]: inverse(double_divide(B, A))=multiply(A, B)).
0.13/0.38	  fof(prove_these_axioms_2, negated_conjecture, a2!=multiply(multiply(inverse(b2), b2), a2)).
0.13/0.38	  fof(single_axiom, axiom, ![C, A, B]: C=double_divide(inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(C))))), B)).
0.13/0.38	
0.13/0.38	Now clausify the problem and encode Horn clauses using encoding 3 of
0.13/0.38	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.13/0.38	We repeatedly replace C & s=t => u=v by the two clauses:
0.13/0.38	  fresh(y, y, x1...xn) = u
0.13/0.38	  C => fresh(s, t, x1...xn) = v
0.13/0.38	where fresh is a fresh function symbol and x1..xn are the free
0.13/0.38	variables of u and v.
0.13/0.38	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.13/0.38	input problem has no model of domain size 1).
0.13/0.38	
0.13/0.38	The encoding turns the above axioms into the following unit equations and goals:
0.13/0.38	
0.13/0.38	Axiom 1 (multiply): inverse(double_divide(X, Y)) = multiply(Y, X).
0.13/0.38	Axiom 2 (single_axiom): X = double_divide(inverse(double_divide(double_divide(Y, Z), inverse(double_divide(Y, inverse(X))))), Z).
0.13/0.38	
0.13/0.38	Lemma 3: double_divide(multiply(multiply(inverse(X), Y), double_divide(Y, Z)), Z) = X.
0.13/0.38	Proof:
0.13/0.38	  double_divide(multiply(multiply(inverse(X), Y), double_divide(Y, Z)), Z)
0.13/0.38	= { by axiom 1 (multiply) }
0.13/0.38	  double_divide(multiply(inverse(double_divide(Y, inverse(X))), double_divide(Y, Z)), Z)
0.13/0.38	= { by axiom 1 (multiply) }
0.13/0.38	  double_divide(inverse(double_divide(double_divide(Y, Z), inverse(double_divide(Y, inverse(X))))), Z)
0.13/0.38	= { by axiom 2 (single_axiom) }
0.13/0.38	  X
0.13/0.38	
0.13/0.38	Lemma 4: multiply(X, multiply(multiply(inverse(Y), Z), double_divide(Z, X))) = inverse(Y).
0.13/0.38	Proof:
0.13/0.38	  multiply(X, multiply(multiply(inverse(Y), Z), double_divide(Z, X)))
0.13/0.38	= { by axiom 1 (multiply) }
0.13/0.38	  inverse(double_divide(multiply(multiply(inverse(Y), Z), double_divide(Z, X)), X))
0.13/0.38	= { by lemma 3 }
0.13/0.38	  inverse(Y)
0.13/0.38	
0.13/0.38	Lemma 5: double_divide(multiply(inverse(Y), Y), inverse(X)) = X.
0.13/0.38	Proof:
0.13/0.38	  double_divide(multiply(inverse(Y), Y), inverse(X))
0.13/0.38	= { by lemma 4 }
0.13/0.38	  double_divide(multiply(multiply(inverse(X), multiply(multiply(inverse(Y), ?), double_divide(?, inverse(X)))), Y), inverse(X))
0.13/0.38	= { by lemma 3 }
0.13/0.38	  double_divide(multiply(multiply(inverse(X), multiply(multiply(inverse(Y), ?), double_divide(?, inverse(X)))), double_divide(multiply(multiply(inverse(Y), ?), double_divide(?, inverse(X))), inverse(X))), inverse(X))
0.13/0.38	= { by lemma 3 }
0.13/0.38	  X
0.13/0.38	
0.13/0.38	Lemma 6: multiply(inverse(X), multiply(inverse(Y), Y)) = inverse(X).
0.13/0.38	Proof:
0.13/0.38	  multiply(inverse(X), multiply(inverse(Y), Y))
0.13/0.38	= { by axiom 1 (multiply) }
0.13/0.38	  inverse(double_divide(multiply(inverse(Y), Y), inverse(X)))
0.13/0.38	= { by lemma 5 }
0.13/0.38	  inverse(X)
0.13/0.38	
0.13/0.38	Lemma 7: double_divide(multiply(inverse(X), Y), inverse(Y)) = X.
0.13/0.38	Proof:
0.13/0.38	  double_divide(multiply(inverse(X), Y), inverse(Y))
0.13/0.38	= { by lemma 6 }
0.13/0.38	  double_divide(multiply(multiply(inverse(X), multiply(inverse(?), ?)), Y), inverse(Y))
0.13/0.38	= { by lemma 3 }
0.13/0.38	  double_divide(multiply(multiply(inverse(X), multiply(inverse(?), ?)), double_divide(multiply(multiply(inverse(Y), ?), double_divide(?, ?)), ?)), inverse(Y))
0.13/0.38	= { by lemma 5 }
0.13/0.39	  double_divide(multiply(multiply(inverse(X), multiply(inverse(?), ?)), double_divide(multiply(inverse(?), ?), inverse(double_divide(multiply(multiply(inverse(Y), ?), double_divide(?, ?)), ?)))), inverse(Y))
0.13/0.39	= { by axiom 1 (multiply) }
0.13/0.39	  double_divide(multiply(multiply(inverse(X), multiply(inverse(?), ?)), double_divide(multiply(inverse(?), ?), multiply(?, multiply(multiply(inverse(Y), ?), double_divide(?, ?))))), inverse(Y))
0.13/0.39	= { by lemma 4 }
0.13/0.39	  double_divide(multiply(multiply(inverse(X), multiply(inverse(?), ?)), double_divide(multiply(inverse(?), ?), multiply(?, multiply(multiply(inverse(Y), ?), double_divide(?, ?))))), multiply(?, multiply(multiply(inverse(Y), ?), double_divide(?, ?))))
0.13/0.39	= { by lemma 3 }
0.13/0.39	  X
0.13/0.39	
0.13/0.39	Lemma 8: double_divide(inverse(Y), inverse(multiply(inverse(Y), X))) = X.
0.13/0.39	Proof:
0.13/0.39	  double_divide(inverse(Y), inverse(multiply(inverse(Y), X)))
0.13/0.39	= { by lemma 7 }
0.13/0.39	  double_divide(inverse(double_divide(multiply(inverse(Y), X), inverse(X))), inverse(multiply(inverse(Y), X)))
0.13/0.39	= { by axiom 1 (multiply) }
0.13/0.39	  double_divide(multiply(inverse(X), multiply(inverse(Y), X)), inverse(multiply(inverse(Y), X)))
0.13/0.39	= { by lemma 7 }
0.13/0.39	  X
0.13/0.39	
0.13/0.39	Lemma 9: multiply(inverse(X), X) = multiply(inverse(?), ?).
0.13/0.39	Proof:
0.13/0.39	  multiply(inverse(X), X)
0.13/0.39	= { by lemma 8 }
0.13/0.39	  double_divide(inverse(Y), inverse(multiply(inverse(Y), multiply(inverse(X), X))))
0.13/0.39	= { by lemma 6 }
0.13/0.39	  double_divide(inverse(Y), inverse(inverse(Y)))
0.13/0.39	= { by lemma 6 }
0.13/0.39	  double_divide(inverse(Y), inverse(multiply(inverse(Y), multiply(inverse(?), ?))))
0.13/0.39	= { by lemma 8 }
0.13/0.39	  multiply(inverse(?), ?)
0.13/0.39	
0.13/0.39	Lemma 10: inverse(multiply(inverse(?), ?)) = multiply(inverse(?), ?).
0.13/0.39	Proof:
0.13/0.39	  inverse(multiply(inverse(?), ?))
0.13/0.39	= { by lemma 8 }
0.13/0.39	  double_divide(inverse(?), inverse(multiply(inverse(?), inverse(multiply(inverse(?), ?)))))
0.13/0.39	= { by lemma 6 }
0.13/0.39	  double_divide(inverse(?), inverse(multiply(inverse(?), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?)))))
0.13/0.39	= { by lemma 6 }
0.13/0.39	  double_divide(inverse(?), inverse(inverse(?)))
0.13/0.39	= { by lemma 6 }
0.13/0.39	  double_divide(inverse(?), inverse(multiply(inverse(?), multiply(inverse(?), ?))))
0.13/0.39	= { by lemma 8 }
0.13/0.39	  multiply(inverse(?), ?)
0.13/0.39	
0.13/0.39	Lemma 11: multiply(inverse(?), ?) = double_divide(?, inverse(?)).
0.13/0.39	Proof:
0.13/0.39	  multiply(inverse(?), ?)
0.13/0.39	= { by lemma 3 }
0.13/0.39	  double_divide(multiply(multiply(inverse(multiply(inverse(?), ?)), ?), double_divide(?, ?)), ?)
0.13/0.39	= { by lemma 10 }
0.13/0.39	  double_divide(multiply(multiply(multiply(inverse(?), ?), ?), double_divide(?, ?)), ?)
0.13/0.39	= { by axiom 1 (multiply) }
0.13/0.39	  double_divide(multiply(multiply(inverse(double_divide(?, inverse(?))), ?), double_divide(?, ?)), ?)
0.13/0.39	= { by lemma 3 }
0.13/0.39	  double_divide(?, inverse(?))
0.13/0.39	
0.13/0.39	Goal 1 (prove_these_axioms_2): a2 = multiply(multiply(inverse(b2), b2), a2).
0.13/0.39	Proof:
0.13/0.39	  a2
0.13/0.39	= { by lemma 8 }
0.13/0.39	  double_divide(inverse(multiply(inverse(?), ?)), inverse(multiply(inverse(multiply(inverse(?), ?)), a2)))
0.13/0.39	= { by lemma 6 }
0.13/0.39	  double_divide(multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?)), inverse(multiply(inverse(multiply(inverse(?), ?)), a2)))
0.13/0.39	= { by lemma 5 }
0.13/0.39	  multiply(inverse(multiply(inverse(?), ?)), a2)
0.13/0.39	= { by lemma 10 }
0.13/0.39	  multiply(multiply(inverse(?), ?), a2)
0.13/0.39	= { by lemma 9 }
0.13/0.39	  multiply(multiply(inverse(b2), b2), a2)
0.13/0.39	% SZS output end Proof
0.13/0.39	
0.13/0.39	RESULT: Unsatisfiable (the axioms are contradictory).
0.13/0.39	EOF