0.06/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.33	% Computer   : n004.cluster.edu
0.13/0.33	% Model      : x86_64 x86_64
0.13/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory     : 8042.1875MB
0.13/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit   : 180
0.13/0.33	% DateTime   : Thu Aug 29 12:01:53 EDT 2019
0.13/0.33	% CPUTime    : 
0.19/0.42	% SZS status Unsatisfiable
0.19/0.42	
0.19/0.42	% SZS output start Proof
0.19/0.42	Take the following subset of the input axioms:
0.19/0.42	  fof(multiply, axiom, ![A, B]: divide(A, inverse(B))=multiply(A, B)).
0.19/0.42	  fof(prove_these_axioms_3, negated_conjecture, multiply(a3, multiply(b3, c3))!=multiply(multiply(a3, b3), c3)).
0.19/0.42	  fof(single_axiom, axiom, ![C, A, B, D]: C=divide(inverse(divide(divide(divide(A, A), B), divide(C, divide(B, D)))), D)).
0.19/0.42	
0.19/0.42	Now clausify the problem and encode Horn clauses using encoding 3 of
0.19/0.42	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.19/0.42	We repeatedly replace C & s=t => u=v by the two clauses:
0.19/0.42	  fresh(y, y, x1...xn) = u
0.19/0.42	  C => fresh(s, t, x1...xn) = v
0.19/0.42	where fresh is a fresh function symbol and x1..xn are the free
0.19/0.42	variables of u and v.
0.19/0.42	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.19/0.42	input problem has no model of domain size 1).
0.19/0.42	
0.19/0.42	The encoding turns the above axioms into the following unit equations and goals:
0.19/0.42	
0.19/0.42	Axiom 1 (multiply): divide(X, inverse(Y)) = multiply(X, Y).
0.19/0.43	Axiom 2 (single_axiom): X = divide(inverse(divide(divide(divide(Y, Y), Z), divide(X, divide(Z, W)))), W).
0.19/0.43	
0.19/0.43	Lemma 3: divide(inverse(divide(divide(divide(U, U), W), Z)), V) = divide(inverse(divide(divide(divide(?, ?), W), Z)), V).
0.19/0.43	Proof:
0.19/0.43	  divide(inverse(divide(divide(divide(U, U), W), Z)), V)
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  divide(inverse(divide(divide(divide(U, U), W), divide(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, divide(W, V))))), divide(W, V)))), V)
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, divide(W, V)))))
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  divide(inverse(divide(divide(divide(?, ?), W), divide(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, divide(W, V))))), divide(W, V)))), V)
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  divide(inverse(divide(divide(divide(?, ?), W), Z)), V)
0.19/0.43	
0.19/0.43	Lemma 4: inverse(divide(divide(divide(X, X), Y), Z)) = inverse(divide(divide(divide(?, ?), Y), Z)).
0.19/0.43	Proof:
0.19/0.43	  inverse(divide(divide(divide(X, X), Y), Z))
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  divide(inverse(divide(divide(divide(W, W), V), divide(inverse(divide(divide(divide(X, X), Y), Z)), divide(V, U)))), U)
0.19/0.43	= { by lemma 3 }
0.19/0.43	  divide(inverse(divide(divide(divide(W, W), V), divide(inverse(divide(divide(divide(?, ?), Y), Z)), divide(V, U)))), U)
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  inverse(divide(divide(divide(?, ?), Y), Z))
0.19/0.43	
0.19/0.43	Lemma 5: inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, divide(W, V))))) = divide(inverse(divide(divide(divide(?, ?), W), Z)), V).
0.19/0.43	Proof:
0.19/0.43	  inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, divide(W, V)))))
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  divide(inverse(divide(divide(divide(?, ?), W), divide(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, divide(W, V))))), divide(W, V)))), V)
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  divide(inverse(divide(divide(divide(?, ?), W), Z)), V)
0.19/0.43	
0.19/0.43	Lemma 6: divide(divide(inverse(divide(divide(divide(?, ?), Y), X)), Z), divide(Y, Z)) = X.
0.19/0.43	Proof:
0.19/0.43	  divide(divide(inverse(divide(divide(divide(?, ?), Y), X)), Z), divide(Y, Z))
0.19/0.43	= { by lemma 5 }
0.19/0.43	  divide(inverse(divide(divide(divide(?, ?), ?), divide(X, divide(?, divide(Y, Z))))), divide(Y, Z))
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  X
0.19/0.43	
0.19/0.43	Lemma 7: multiply(X, divide(divide(divide(?, ?), X), divide(divide(?, ?), Y))) = Y.
0.19/0.43	Proof:
0.19/0.43	  multiply(X, divide(divide(divide(?, ?), X), divide(divide(?, ?), Y)))
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  divide(inverse(divide(divide(divide(?, ?), ?), divide(multiply(X, divide(divide(divide(?, ?), X), divide(divide(?, ?), Y))), divide(?, ?)))), ?)
0.19/0.43	= { by lemma 6 }
0.19/0.43	  divide(inverse(divide(divide(inverse(divide(divide(divide(?, ?), Y), divide(divide(divide(?, ?), ?), divide(multiply(X, divide(divide(divide(?, ?), X), divide(divide(?, ?), Y))), divide(?, ?))))), divide(?, ?)), divide(Y, divide(?, ?)))), ?)
0.19/0.43	= { by lemma 6 }
0.19/0.43	  divide(inverse(divide(divide(inverse(divide(divide(divide(inverse(divide(divide(divide(?, ?), X), divide(divide(?, ?), Y))), inverse(divide(divide(divide(?, ?), X), divide(divide(?, ?), Y)))), divide(X, inverse(divide(divide(divide(?, ?), X), divide(divide(?, ?), Y))))), divide(divide(divide(?, ?), ?), divide(multiply(X, divide(divide(divide(?, ?), X), divide(divide(?, ?), Y))), divide(?, ?))))), divide(?, ?)), divide(Y, divide(?, ?)))), ?)
0.19/0.43	= { by axiom 1 (multiply) }
0.19/0.43	  divide(inverse(divide(divide(inverse(divide(divide(divide(inverse(divide(divide(divide(?, ?), X), divide(divide(?, ?), Y))), inverse(divide(divide(divide(?, ?), X), divide(divide(?, ?), Y)))), divide(X, inverse(divide(divide(divide(?, ?), X), divide(divide(?, ?), Y))))), divide(divide(divide(?, ?), ?), divide(divide(X, inverse(divide(divide(divide(?, ?), X), divide(divide(?, ?), Y)))), divide(?, ?))))), divide(?, ?)), divide(Y, divide(?, ?)))), ?)
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  divide(inverse(divide(divide(divide(?, ?), ?), divide(Y, divide(?, ?)))), ?)
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  Y
0.19/0.43	
0.19/0.43	Lemma 8: inverse(divide(divide(divide(?, ?), X), divide(?, ?))) = X.
0.19/0.43	Proof:
0.19/0.43	  inverse(divide(divide(divide(?, ?), X), divide(?, ?)))
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  divide(inverse(divide(divide(divide(?, ?), ?), divide(inverse(divide(divide(divide(?, ?), X), divide(?, ?))), divide(?, ?)))), ?)
0.19/0.43	= { by lemma 5 }
0.19/0.43	  divide(inverse(divide(divide(divide(?, ?), ?), inverse(divide(divide(divide(?, ?), divide(divide(?, ?), ?)), divide(divide(?, ?), divide(divide(divide(?, ?), ?), divide(X, divide(?, ?)))))))), ?)
0.19/0.43	= { by axiom 1 (multiply) }
0.19/0.43	  divide(inverse(multiply(divide(divide(?, ?), ?), divide(divide(divide(?, ?), divide(divide(?, ?), ?)), divide(divide(?, ?), divide(divide(divide(?, ?), ?), divide(X, divide(?, ?))))))), ?)
0.19/0.43	= { by lemma 7 }
0.19/0.43	  divide(inverse(divide(divide(divide(?, ?), ?), divide(X, divide(?, ?)))), ?)
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  X
0.19/0.43	
0.19/0.43	Lemma 9: divide(divide(X, Y), divide(X, Y)) = divide(?, ?).
0.19/0.43	Proof:
0.19/0.43	  divide(divide(X, Y), divide(X, Y))
0.19/0.43	= { by lemma 8 }
0.19/0.43	  divide(divide(inverse(divide(divide(divide(?, ?), X), divide(?, ?))), Y), divide(X, Y))
0.19/0.43	= { by lemma 6 }
0.19/0.43	  divide(?, ?)
0.19/0.43	
0.19/0.43	Lemma 10: inverse(divide(?, ?)) = divide(?, ?).
0.19/0.43	Proof:
0.19/0.43	  inverse(divide(?, ?))
0.19/0.43	= { by lemma 9 }
0.19/0.43	  inverse(divide(divide(?, ?), divide(?, ?)))
0.19/0.43	= { by lemma 9 }
0.19/0.43	  inverse(divide(divide(divide(?, ?), divide(?, ?)), divide(?, ?)))
0.19/0.43	= { by lemma 8 }
0.19/0.43	  divide(?, ?)
0.19/0.43	
0.19/0.43	Lemma 11: divide(X, divide(?, ?)) = X.
0.19/0.43	Proof:
0.19/0.43	  divide(X, divide(?, ?))
0.19/0.43	= { by lemma 10 }
0.19/0.43	  divide(X, inverse(divide(?, ?)))
0.19/0.43	= { by axiom 1 (multiply) }
0.19/0.43	  multiply(X, divide(?, ?))
0.19/0.43	= { by lemma 9 }
0.19/0.43	  multiply(X, divide(divide(divide(?, ?), X), divide(divide(?, ?), X)))
0.19/0.43	= { by lemma 7 }
0.19/0.43	  X
0.19/0.43	
0.19/0.43	Lemma 12: inverse(divide(divide(?, ?), X)) = X.
0.19/0.43	Proof:
0.19/0.43	  inverse(divide(divide(?, ?), X))
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  inverse(divide(divide(divide(inverse(divide(divide(divide(?, ?), ?), divide(?, divide(?, ?)))), ?), ?), X))
0.19/0.43	= { by axiom 2 (single_axiom) }
0.19/0.43	  inverse(divide(divide(divide(inverse(divide(divide(divide(?, ?), ?), divide(?, divide(?, ?)))), ?), divide(inverse(divide(divide(divide(?, ?), ?), divide(?, divide(?, ?)))), ?)), X))
0.19/0.43	= { by lemma 9 }
0.19/0.43	  inverse(divide(divide(?, ?), X))
0.19/0.43	= { by lemma 11 }
0.19/0.43	  inverse(divide(divide(divide(?, ?), X), divide(?, ?)))
0.19/0.43	= { by lemma 8 }
0.19/0.43	  X
0.19/0.43	
0.19/0.43	Lemma 13: inverse(multiply(divide(?, ?), X)) = inverse(X).
0.19/0.43	Proof:
0.19/0.43	  inverse(multiply(divide(?, ?), X))
0.19/0.43	= { by lemma 11 }
0.19/0.43	  inverse(divide(multiply(divide(?, ?), X), divide(?, ?)))
0.19/0.43	= { by axiom 1 (multiply) }
0.19/0.43	  inverse(divide(divide(divide(?, ?), inverse(X)), divide(?, ?)))
0.19/0.43	= { by lemma 8 }
0.19/0.44	  inverse(X)
0.19/0.44	
0.19/0.44	Lemma 14: divide(divide(?, ?), X) = inverse(X).
0.19/0.44	Proof:
0.19/0.44	  divide(divide(?, ?), X)
0.19/0.44	= { by lemma 12 }
0.19/0.44	  inverse(divide(divide(?, ?), divide(divide(?, ?), X)))
0.19/0.44	= { by lemma 9 }
0.19/0.44	  inverse(divide(divide(divide(?, ?), divide(?, ?)), divide(divide(?, ?), X)))
0.19/0.44	= { by lemma 13 }
0.19/0.44	  inverse(multiply(divide(?, ?), divide(divide(divide(?, ?), divide(?, ?)), divide(divide(?, ?), X))))
0.19/0.44	= { by lemma 7 }
0.19/0.44	  inverse(X)
0.19/0.44	
0.19/0.44	Lemma 15: multiply(divide(?, ?), X) = X.
0.19/0.44	Proof:
0.19/0.44	  multiply(divide(?, ?), X)
0.19/0.44	= { by lemma 12 }
0.19/0.44	  inverse(divide(divide(?, ?), multiply(divide(?, ?), X)))
0.19/0.44	= { by lemma 10 }
0.19/0.44	  inverse(divide(inverse(divide(?, ?)), multiply(divide(?, ?), X)))
0.19/0.44	= { by lemma 14 }
0.19/0.44	  inverse(divide(divide(divide(?, ?), divide(?, ?)), multiply(divide(?, ?), X)))
0.19/0.44	= { by lemma 13 }
0.19/0.44	  inverse(multiply(divide(?, ?), divide(divide(divide(?, ?), divide(?, ?)), multiply(divide(?, ?), X))))
0.19/0.44	= { by axiom 1 (multiply) }
0.19/0.44	  inverse(multiply(divide(?, ?), divide(divide(divide(?, ?), divide(?, ?)), divide(divide(?, ?), inverse(X)))))
0.19/0.44	= { by lemma 7 }
0.19/0.44	  inverse(inverse(X))
0.19/0.44	= { by lemma 11 }
0.19/0.44	  inverse(divide(inverse(X), divide(?, ?)))
0.19/0.44	= { by lemma 14 }
0.19/0.44	  inverse(divide(divide(divide(?, ?), X), divide(?, ?)))
0.19/0.44	= { by lemma 8 }
0.19/0.44	  X
0.19/0.44	
0.19/0.44	Lemma 16: multiply(divide(X, Y), Y) = X.
0.19/0.44	Proof:
0.19/0.44	  multiply(divide(X, Y), Y)
0.19/0.44	= { by lemma 12 }
0.19/0.44	  multiply(divide(inverse(divide(divide(?, ?), X)), Y), Y)
0.19/0.44	= { by lemma 10 }
0.19/0.44	  multiply(divide(inverse(divide(inverse(divide(?, ?)), X)), Y), Y)
0.19/0.44	= { by lemma 14 }
0.19/0.44	  multiply(divide(inverse(divide(divide(divide(?, ?), divide(?, ?)), X)), Y), Y)
0.19/0.44	= { by axiom 1 (multiply) }
0.19/0.44	  divide(divide(inverse(divide(divide(divide(?, ?), divide(?, ?)), X)), Y), inverse(Y))
0.19/0.44	= { by lemma 14 }
0.19/0.44	  divide(divide(inverse(divide(divide(divide(?, ?), divide(?, ?)), X)), Y), divide(divide(?, ?), Y))
0.19/0.44	= { by lemma 6 }
0.19/0.44	  X
0.19/0.44	
0.19/0.44	Lemma 17: inverse(divide(X, Y)) = divide(Y, X).
0.19/0.44	Proof:
0.19/0.44	  inverse(divide(X, Y))
0.19/0.44	= { by axiom 2 (single_axiom) }
0.19/0.44	  divide(inverse(divide(divide(divide(?, ?), divide(?, ?)), divide(inverse(divide(X, Y)), divide(divide(?, ?), multiply(divide(X, Y), Y))))), multiply(divide(X, Y), Y))
0.19/0.44	= { by lemma 14 }
0.19/0.44	  divide(inverse(divide(inverse(divide(?, ?)), divide(inverse(divide(X, Y)), divide(divide(?, ?), multiply(divide(X, Y), Y))))), multiply(divide(X, Y), Y))
0.19/0.44	= { by lemma 10 }
0.19/0.44	  divide(inverse(divide(divide(?, ?), divide(inverse(divide(X, Y)), divide(divide(?, ?), multiply(divide(X, Y), Y))))), multiply(divide(X, Y), Y))
0.19/0.44	= { by lemma 14 }
0.19/0.44	  divide(inverse(divide(divide(?, ?), divide(inverse(divide(X, Y)), inverse(multiply(divide(X, Y), Y))))), multiply(divide(X, Y), Y))
0.19/0.44	= { by axiom 1 (multiply) }
0.19/0.44	  divide(inverse(divide(divide(?, ?), multiply(inverse(divide(X, Y)), multiply(divide(X, Y), Y)))), multiply(divide(X, Y), Y))
0.19/0.44	= { by lemma 12 }
0.19/0.44	  divide(multiply(inverse(divide(X, Y)), multiply(divide(X, Y), Y)), multiply(divide(X, Y), Y))
0.19/0.44	= { by axiom 1 (multiply) }
0.19/0.44	  divide(multiply(inverse(divide(X, Y)), divide(divide(X, Y), inverse(Y))), multiply(divide(X, Y), Y))
0.19/0.44	= { by lemma 15 }
0.19/0.44	  divide(multiply(inverse(divide(X, Y)), divide(multiply(divide(?, ?), divide(X, Y)), inverse(Y))), multiply(divide(X, Y), Y))
0.19/0.44	= { by axiom 1 (multiply) }
0.19/0.44	  divide(multiply(inverse(divide(X, Y)), divide(divide(divide(?, ?), inverse(divide(X, Y))), inverse(Y))), multiply(divide(X, Y), Y))
0.19/0.44	= { by lemma 14 }
0.19/0.44	  divide(multiply(inverse(divide(X, Y)), divide(divide(divide(?, ?), inverse(divide(X, Y))), divide(divide(?, ?), Y))), multiply(divide(X, Y), Y))
0.19/0.44	= { by lemma 7 }
0.19/0.44	  divide(Y, multiply(divide(X, Y), Y))
0.19/0.44	= { by lemma 16 }
0.19/0.44	  divide(Y, X)
0.19/0.44	
0.19/0.44	Lemma 18: divide(divide(inverse(multiply(divide(divide(?, ?), Y), X)), Z), divide(Y, Z)) = inverse(X).
0.19/0.44	Proof:
0.19/0.44	  divide(divide(inverse(multiply(divide(divide(?, ?), Y), X)), Z), divide(Y, Z))
0.19/0.44	= { by axiom 1 (multiply) }
0.19/0.44	  divide(divide(inverse(divide(divide(divide(?, ?), Y), inverse(X))), Z), divide(Y, Z))
0.19/0.44	= { by lemma 6 }
0.19/0.44	  inverse(X)
0.19/0.44	
0.19/0.44	Goal 1 (prove_these_axioms_3): multiply(a3, multiply(b3, c3)) = multiply(multiply(a3, b3), c3).
0.19/0.44	Proof:
0.19/0.44	  multiply(a3, multiply(b3, c3))
0.19/0.44	= { by lemma 15 }
0.19/0.44	  multiply(a3, multiply(multiply(divide(?, ?), b3), c3))
0.19/0.44	= { by axiom 1 (multiply) }
0.19/0.44	  divide(a3, inverse(multiply(multiply(divide(?, ?), b3), c3)))
0.19/0.44	= { by lemma 17 }
0.19/0.44	  inverse(divide(inverse(multiply(multiply(divide(?, ?), b3), c3)), a3))
0.19/0.44	= { by lemma 18 }
0.19/0.44	  divide(divide(inverse(multiply(divide(divide(?, ?), divide(inverse(multiply(multiply(divide(?, ?), b3), c3)), a3)), divide(inverse(multiply(multiply(divide(?, ?), b3), c3)), a3))), divide(inverse(b3), a3)), divide(divide(inverse(multiply(multiply(divide(?, ?), b3), c3)), a3), divide(inverse(b3), a3)))
0.19/0.44	= { by lemma 16 }
0.19/0.44	  divide(divide(inverse(divide(?, ?)), divide(inverse(b3), a3)), divide(divide(inverse(multiply(multiply(divide(?, ?), b3), c3)), a3), divide(inverse(b3), a3)))
0.19/0.44	= { by lemma 10 }
0.19/0.44	  divide(divide(divide(?, ?), divide(inverse(b3), a3)), divide(divide(inverse(multiply(multiply(divide(?, ?), b3), c3)), a3), divide(inverse(b3), a3)))
0.19/0.44	= { by lemma 14 }
0.19/0.44	  divide(inverse(divide(inverse(b3), a3)), divide(divide(inverse(multiply(multiply(divide(?, ?), b3), c3)), a3), divide(inverse(b3), a3)))
0.19/0.44	= { by axiom 1 (multiply) }
0.19/0.44	  divide(inverse(divide(inverse(b3), a3)), divide(divide(inverse(multiply(divide(divide(?, ?), inverse(b3)), c3)), a3), divide(inverse(b3), a3)))
0.19/0.44	= { by lemma 18 }
0.19/0.44	  divide(inverse(divide(inverse(b3), a3)), inverse(c3))
0.19/0.44	= { by axiom 1 (multiply) }
0.19/0.44	  multiply(inverse(divide(inverse(b3), a3)), c3)
0.19/0.44	= { by lemma 17 }
0.19/0.44	  multiply(divide(a3, inverse(b3)), c3)
0.19/0.44	= { by axiom 1 (multiply) }
0.19/0.44	  multiply(multiply(a3, b3), c3)
0.19/0.44	% SZS output end Proof
0.19/0.44	
0.19/0.44	RESULT: Unsatisfiable (the axioms are contradictory).
0.19/0.44	EOF