0.11/0.14	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.15	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.37	% Computer   : n018.cluster.edu
0.12/0.37	% Model      : x86_64 x86_64
0.12/0.37	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.37	% Memory     : 8042.1875MB
0.12/0.37	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.37	% CPULimit   : 180
0.12/0.37	% DateTime   : Thu Aug 29 10:21:51 EDT 2019
0.12/0.37	% CPUTime    : 
0.12/0.39	% SZS status Unsatisfiable
0.12/0.39	
0.12/0.39	% SZS output start Proof
0.12/0.39	Take the following subset of the input axioms:
0.12/0.39	  fof(multiply, axiom, ![B, A]: inverse(double_divide(B, A))=multiply(A, B)).
0.12/0.39	  fof(prove_these_axioms_1, negated_conjecture, multiply(inverse(a1), a1)!=multiply(inverse(b1), b1)).
0.12/0.39	  fof(single_axiom, axiom, ![B, A, C]: B=inverse(double_divide(inverse(double_divide(A, inverse(double_divide(B, double_divide(A, C))))), C))).
0.12/0.39	
0.12/0.39	Now clausify the problem and encode Horn clauses using encoding 3 of
0.12/0.39	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.12/0.39	We repeatedly replace C & s=t => u=v by the two clauses:
0.12/0.39	  fresh(y, y, x1...xn) = u
0.12/0.39	  C => fresh(s, t, x1...xn) = v
0.12/0.39	where fresh is a fresh function symbol and x1..xn are the free
0.12/0.39	variables of u and v.
0.12/0.39	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.12/0.39	input problem has no model of domain size 1).
0.12/0.39	
0.12/0.39	The encoding turns the above axioms into the following unit equations and goals:
0.12/0.39	
0.12/0.39	Axiom 1 (single_axiom): X = inverse(double_divide(inverse(double_divide(Y, inverse(double_divide(X, double_divide(Y, Z))))), Z)).
0.12/0.40	Axiom 2 (multiply): inverse(double_divide(X, Y)) = multiply(Y, X).
0.12/0.40	
0.12/0.40	Lemma 3: multiply(X, multiply(multiply(double_divide(Y, X), Z), Y)) = Z.
0.12/0.40	Proof:
0.12/0.40	  multiply(X, multiply(multiply(double_divide(Y, X), Z), Y))
0.12/0.40	= { by axiom 2 (multiply) }
0.12/0.40	  multiply(X, multiply(inverse(double_divide(Z, double_divide(Y, X))), Y))
0.12/0.40	= { by axiom 2 (multiply) }
0.12/0.40	  multiply(X, inverse(double_divide(Y, inverse(double_divide(Z, double_divide(Y, X))))))
0.12/0.40	= { by axiom 2 (multiply) }
0.12/0.40	  inverse(double_divide(inverse(double_divide(Y, inverse(double_divide(Z, double_divide(Y, X))))), X))
0.12/0.40	= { by axiom 1 (single_axiom) }
0.12/0.40	  Z
0.12/0.40	
0.12/0.40	Lemma 4: multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X) = multiply(Z, multiply(W, Y)).
0.12/0.40	Proof:
0.12/0.40	  multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X)
0.12/0.40	= { by lemma 3 }
0.12/0.40	  multiply(Z, multiply(multiply(double_divide(Y, Z), multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X)), Y))
0.12/0.40	= { by lemma 3 }
0.12/0.40	  multiply(Z, multiply(W, Y))
0.12/0.40	
0.12/0.40	Lemma 5: multiply(double_divide(Y, Z), multiply(Z, multiply(X, Y))) = X.
0.12/0.40	Proof:
0.12/0.40	  multiply(double_divide(Y, Z), multiply(Z, multiply(X, Y)))
0.12/0.40	= { by lemma 4 }
0.12/0.40	  multiply(double_divide(Y, Z), multiply(multiply(double_divide(?, double_divide(Y, Z)), X), ?))
0.12/0.40	= { by lemma 3 }
0.12/0.40	  X
0.12/0.40	
0.12/0.40	Lemma 6: multiply(double_divide(multiply(Y, Z), double_divide(Z, X)), Y) = X.
0.12/0.40	Proof:
0.12/0.40	  multiply(double_divide(multiply(Y, Z), double_divide(Z, X)), Y)
0.12/0.40	= { by lemma 5 }
0.12/0.40	  multiply(double_divide(multiply(Y, Z), double_divide(Z, X)), multiply(double_divide(Z, X), multiply(X, multiply(Y, Z))))
0.12/0.40	= { by lemma 5 }
0.12/0.40	  X
0.12/0.40	
0.12/0.40	Lemma 7: multiply(double_divide(X, W), multiply(W, Z)) = double_divide(multiply(X, ?), double_divide(?, Z)).
0.12/0.40	Proof:
0.12/0.40	  multiply(double_divide(X, W), multiply(W, Z))
0.12/0.40	= { by lemma 6 }
0.12/0.40	  multiply(double_divide(X, W), multiply(W, multiply(double_divide(multiply(X, ?), double_divide(?, Z)), X)))
0.12/0.40	= { by lemma 5 }
0.12/0.40	  double_divide(multiply(X, ?), double_divide(?, Z))
0.12/0.40	
0.12/0.40	Lemma 8: double_divide(multiply(multiply(Y, multiply(Z, X)), ?), double_divide(?, Z)) = double_divide(X, Y).
0.12/0.40	Proof:
0.12/0.40	  double_divide(multiply(multiply(Y, multiply(Z, X)), ?), double_divide(?, Z))
0.12/0.40	= { by lemma 7 }
0.12/0.40	  multiply(double_divide(multiply(Y, multiply(Z, X)), ?), multiply(?, Z))
0.12/0.40	= { by lemma 5 }
0.12/0.40	  multiply(double_divide(multiply(Y, multiply(Z, X)), ?), multiply(?, multiply(double_divide(X, Y), multiply(Y, multiply(Z, X)))))
0.12/0.40	= { by lemma 5 }
0.12/0.40	  double_divide(X, Y)
0.12/0.40	
0.12/0.40	Lemma 9: double_divide(multiply(X, ?), double_divide(?, multiply(Y, X))) = Y.
0.12/0.40	Proof:
0.12/0.40	  double_divide(multiply(X, ?), double_divide(?, multiply(Y, X)))
0.12/0.40	= { by lemma 7 }
0.12/0.40	  multiply(double_divide(X, ?), multiply(?, multiply(Y, X)))
0.12/0.40	= { by lemma 5 }
0.12/0.40	  Y
0.12/0.40	
0.12/0.40	Lemma 10: multiply(multiply(X, Y), multiply(Z, ?)) = multiply(multiply(X, Z), multiply(Y, ?)).
0.12/0.40	Proof:
0.12/0.40	  multiply(multiply(X, Y), multiply(Z, ?))
0.12/0.40	= { by lemma 4 }
0.12/0.40	  multiply(multiply(double_divide(multiply(Y, ?), double_divide(?, multiply(X, Y))), Z), multiply(Y, ?))
0.12/0.40	= { by lemma 9 }
0.12/0.40	  multiply(multiply(X, Z), multiply(Y, ?))
0.12/0.40	
0.12/0.40	Lemma 11: multiply(multiply(X, inverse(X)), multiply(Y, ?)) = multiply(Y, ?).
0.12/0.40	Proof:
0.12/0.40	  multiply(multiply(X, inverse(X)), multiply(Y, ?))
0.12/0.40	= { by lemma 10 }
0.12/0.40	  multiply(multiply(X, Y), multiply(inverse(X), ?))
0.12/0.40	= { by axiom 2 (multiply) }
0.12/0.40	  multiply(multiply(X, Y), inverse(double_divide(?, inverse(X))))
0.12/0.40	= { by axiom 2 (multiply) }
0.12/0.40	  inverse(double_divide(inverse(double_divide(?, inverse(X))), multiply(X, Y)))
0.12/0.40	= { by lemma 9 }
0.12/0.40	  inverse(double_divide(inverse(double_divide(?, inverse(double_divide(multiply(Y, ?), double_divide(?, multiply(X, Y)))))), multiply(X, Y)))
0.12/0.40	= { by axiom 1 (single_axiom) }
0.12/0.40	  multiply(Y, ?)
0.12/0.40	
0.12/0.40	Lemma 12: multiply(X, multiply(Z, multiply(W, Y))) = multiply(Z, multiply(multiply(X, W), Y)).
0.12/0.40	Proof:
0.12/0.40	  multiply(X, multiply(Z, multiply(W, Y)))
0.12/0.40	= { by lemma 4 }
0.12/0.40	  multiply(X, multiply(multiply(double_divide(?, double_divide(Y, Z)), W), ?))
0.12/0.40	= { by axiom 2 (multiply) }
0.12/0.40	  multiply(X, multiply(inverse(double_divide(W, double_divide(?, double_divide(Y, Z)))), ?))
0.12/0.40	= { by axiom 2 (multiply) }
0.12/0.40	  multiply(X, inverse(double_divide(?, inverse(double_divide(W, double_divide(?, double_divide(Y, Z)))))))
0.12/0.40	= { by axiom 2 (multiply) }
0.12/0.40	  inverse(double_divide(inverse(double_divide(?, inverse(double_divide(W, double_divide(?, double_divide(Y, Z)))))), X))
0.12/0.40	= { by lemma 8 }
0.12/0.40	  inverse(double_divide(inverse(double_divide(?, inverse(double_divide(multiply(multiply(double_divide(?, double_divide(Y, Z)), multiply(X, W)), ?), double_divide(?, X))))), X))
0.12/0.40	= { by axiom 1 (single_axiom) }
0.12/0.40	  multiply(multiply(double_divide(?, double_divide(Y, Z)), multiply(X, W)), ?)
0.12/0.40	= { by lemma 4 }
0.12/0.40	  multiply(Z, multiply(multiply(X, W), Y))
0.12/0.40	
0.12/0.40	Lemma 13: multiply(multiply(Y, X), ?) = multiply(Y, multiply(X, ?)).
0.12/0.40	Proof:
0.12/0.40	  multiply(multiply(Y, X), ?)
0.12/0.40	= { by lemma 11 }
0.12/0.40	  multiply(multiply(?, inverse(?)), multiply(multiply(Y, X), ?))
0.12/0.40	= { by lemma 12 }
0.12/0.40	  multiply(Y, multiply(multiply(?, inverse(?)), multiply(X, ?)))
0.12/0.40	= { by lemma 11 }
0.12/0.40	  multiply(Y, multiply(X, ?))
0.12/0.40	
0.12/0.40	Lemma 14: multiply(multiply(X, inverse(X)), Y) = Y.
0.12/0.40	Proof:
0.12/0.40	  multiply(multiply(X, inverse(X)), Y)
0.12/0.40	= { by lemma 6 }
0.12/0.40	  multiply(multiply(X, inverse(X)), multiply(double_divide(multiply(?, ?), double_divide(?, Y)), ?))
0.12/0.40	= { by lemma 11 }
0.12/0.40	  multiply(double_divide(multiply(?, ?), double_divide(?, Y)), ?)
0.12/0.40	= { by lemma 6 }
0.12/0.40	  Y
0.12/0.40	
0.12/0.40	Lemma 15: multiply(Y, ?) = multiply(?, Y).
0.12/0.40	Proof:
0.12/0.40	  multiply(Y, ?)
0.12/0.40	= { by lemma 3 }
0.12/0.40	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(Y, ?)), ?))
0.12/0.40	= { by lemma 13 }
0.12/0.40	  multiply(?, multiply(multiply(multiply(double_divide(?, ?), Y), ?), ?))
0.12/0.40	= { by axiom 2 (multiply) }
0.12/0.40	  multiply(?, multiply(multiply(inverse(double_divide(Y, double_divide(?, ?))), ?), ?))
0.12/0.40	= { by lemma 4 }
0.12/0.40	  multiply(multiply(double_divide(Y, double_divide(?, ?)), multiply(inverse(double_divide(Y, double_divide(?, ?))), ?)), Y)
0.12/0.40	= { by lemma 13 }
0.12/0.40	  multiply(multiply(multiply(double_divide(Y, double_divide(?, ?)), inverse(double_divide(Y, double_divide(?, ?)))), ?), Y)
0.12/0.40	= { by lemma 14 }
0.12/0.40	  multiply(?, Y)
0.12/0.40	
0.12/0.40	Lemma 16: multiply(multiply(Y, Z), W) = multiply(Y, multiply(Z, W)).
0.12/0.40	Proof:
0.12/0.40	  multiply(multiply(Y, Z), W)
0.12/0.40	= { by lemma 14 }
0.12/0.40	  multiply(multiply(?, inverse(?)), multiply(multiply(Y, Z), W))
0.12/0.40	= { by lemma 12 }
0.12/0.40	  multiply(Y, multiply(multiply(?, inverse(?)), multiply(Z, W)))
0.12/0.40	= { by lemma 14 }
0.12/0.40	  multiply(Y, multiply(Z, W))
0.12/0.40	
0.12/0.40	Lemma 17: multiply(X, Y) = multiply(Y, X).
0.12/0.40	Proof:
0.12/0.40	  multiply(X, Y)
0.12/0.40	= { by axiom 2 (multiply) }
0.12/0.40	  inverse(double_divide(Y, X))
0.12/0.40	= { by lemma 8 }
0.12/0.40	  inverse(double_divide(multiply(multiply(X, multiply(?, Y)), ?), double_divide(?, ?)))
0.12/0.40	= { by lemma 15 }
0.12/0.40	  inverse(double_divide(multiply(multiply(X, multiply(Y, ?)), ?), double_divide(?, ?)))
0.12/0.40	= { by lemma 14 }
0.12/0.40	  inverse(double_divide(multiply(multiply(multiply(?, inverse(?)), multiply(X, multiply(Y, ?))), ?), double_divide(?, ?)))
0.12/0.40	= { by lemma 16 }
0.12/0.40	  inverse(double_divide(multiply(multiply(multiply(multiply(?, inverse(?)), X), multiply(Y, ?)), ?), double_divide(?, ?)))
0.12/0.40	= { by lemma 10 }
0.12/0.40	  inverse(double_divide(multiply(multiply(multiply(multiply(?, inverse(?)), Y), multiply(X, ?)), ?), double_divide(?, ?)))
0.12/0.40	= { by lemma 14 }
0.12/0.40	  inverse(double_divide(multiply(multiply(Y, multiply(X, ?)), ?), double_divide(?, ?)))
0.12/0.40	= { by lemma 15 }
0.12/0.40	  inverse(double_divide(multiply(multiply(Y, multiply(?, X)), ?), double_divide(?, ?)))
0.12/0.40	= { by lemma 8 }
0.12/0.40	  inverse(double_divide(X, Y))
0.12/0.40	= { by axiom 2 (multiply) }
0.12/0.41	  multiply(Y, X)
0.12/0.41	
0.12/0.41	Lemma 18: multiply(X, multiply(Y, inverse(X))) = Y.
0.12/0.41	Proof:
0.12/0.41	  multiply(X, multiply(Y, inverse(X)))
0.12/0.41	= { by lemma 17 }
0.12/0.41	  multiply(X, multiply(inverse(X), Y))
0.12/0.41	= { by lemma 16 }
0.12/0.41	  multiply(multiply(X, inverse(X)), Y)
0.12/0.41	= { by lemma 14 }
0.12/0.41	  Y
0.12/0.41	
0.12/0.41	Lemma 19: multiply(X, inverse(X)) = multiply(?, inverse(?)).
0.12/0.41	Proof:
0.12/0.41	  multiply(X, inverse(X))
0.12/0.41	= { by lemma 18 }
0.12/0.41	  multiply(Y, multiply(multiply(X, inverse(X)), inverse(Y)))
0.12/0.41	= { by lemma 14 }
0.12/0.41	  multiply(Y, inverse(Y))
0.12/0.41	= { by lemma 14 }
0.12/0.41	  multiply(Y, multiply(multiply(?, inverse(?)), inverse(Y)))
0.12/0.41	= { by lemma 18 }
0.12/0.41	  multiply(?, inverse(?))
0.12/0.41	
0.12/0.41	Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
0.12/0.41	Proof:
0.12/0.41	  multiply(inverse(a1), a1)
0.12/0.41	= { by lemma 17 }
0.12/0.41	  multiply(a1, inverse(a1))
0.12/0.41	= { by lemma 19 }
0.12/0.41	  multiply(?, inverse(?))
0.12/0.41	= { by lemma 19 }
0.12/0.41	  multiply(b1, inverse(b1))
0.12/0.41	= { by lemma 17 }
0.12/0.41	  multiply(inverse(b1), b1)
0.12/0.41	% SZS output end Proof
0.12/0.41	
0.12/0.41	RESULT: Unsatisfiable (the axioms are contradictory).
0.12/0.41	EOF