0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.34	% Computer   : n008.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 12:01:23 EDT 2019
0.13/0.34	% CPUTime    : 
0.56/0.72	% SZS status Unsatisfiable
0.56/0.72	
0.56/0.72	% SZS output start Proof
0.56/0.72	Take the following subset of the input axioms:
0.56/0.72	  fof(multiply, axiom, ![A, B]: divide(A, inverse(B))=multiply(A, B)).
0.56/0.72	  fof(prove_these_axioms_1, negated_conjecture, multiply(inverse(b1), b1)!=multiply(inverse(a1), a1)).
0.56/0.72	  fof(single_axiom, axiom, ![A, B, C, D]: divide(inverse(divide(A, divide(B, divide(C, D)))), divide(divide(D, C), A))=B).
0.56/0.72	
0.56/0.72	Now clausify the problem and encode Horn clauses using encoding 3 of
0.56/0.72	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.56/0.72	We repeatedly replace C & s=t => u=v by the two clauses:
0.56/0.72	  fresh(y, y, x1...xn) = u
0.56/0.72	  C => fresh(s, t, x1...xn) = v
0.56/0.72	where fresh is a fresh function symbol and x1..xn are the free
0.56/0.72	variables of u and v.
0.56/0.72	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.56/0.72	input problem has no model of domain size 1).
0.56/0.72	
0.56/0.72	The encoding turns the above axioms into the following unit equations and goals:
0.56/0.72	
0.56/0.72	Axiom 1 (single_axiom): divide(inverse(divide(X, divide(Y, divide(Z, W)))), divide(divide(W, Z), X)) = Y.
0.56/0.73	Axiom 2 (multiply): divide(X, inverse(Y)) = multiply(X, Y).
0.56/0.73	
0.56/0.73	Lemma 3: divide(inverse(divide(V, Y)), divide(divide(X, divide(W, Z)), V)) = inverse(divide(X, divide(Y, divide(Z, W)))).
0.56/0.73	Proof:
0.56/0.73	  divide(inverse(divide(V, Y)), divide(divide(X, divide(W, Z)), V))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  divide(inverse(divide(V, divide(inverse(divide(X, divide(Y, divide(Z, W)))), divide(divide(W, Z), X)))), divide(divide(X, divide(W, Z)), V))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  inverse(divide(X, divide(Y, divide(Z, W))))
0.56/0.73	
0.56/0.73	Lemma 4: divide(inverse(divide(U, V)), divide(Y, U)) = divide(inverse(divide(?, V)), divide(Y, ?)).
0.56/0.73	Proof:
0.56/0.73	  divide(inverse(divide(U, V)), divide(Y, U))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  divide(inverse(divide(U, V)), divide(divide(inverse(divide(X, divide(Y, divide(Z, W)))), divide(divide(W, Z), X)), U))
0.56/0.73	= { by lemma 3 }
0.56/0.73	  inverse(divide(inverse(divide(X, divide(Y, divide(Z, W)))), divide(V, divide(X, divide(W, Z)))))
0.56/0.73	= { by lemma 3 }
0.56/0.73	  divide(inverse(divide(?, V)), divide(divide(inverse(divide(X, divide(Y, divide(Z, W)))), divide(divide(W, Z), X)), ?))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  divide(inverse(divide(?, V)), divide(Y, ?))
0.56/0.73	
0.56/0.73	Lemma 5: divide(inverse(V), multiply(W, divide(Z, divide(V, divide(Y, X))))) = divide(inverse(?), multiply(W, divide(Z, divide(?, divide(Y, X))))).
0.56/0.73	Proof:
0.56/0.73	  divide(inverse(V), multiply(W, divide(Z, divide(V, divide(Y, X)))))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  divide(inverse(divide(inverse(divide(Z, divide(V, divide(Y, X)))), divide(divide(X, Y), Z))), multiply(W, divide(Z, divide(V, divide(Y, X)))))
0.56/0.73	= { by axiom 2 (multiply) }
0.56/0.73	  divide(inverse(divide(inverse(divide(Z, divide(V, divide(Y, X)))), divide(divide(X, Y), Z))), divide(W, inverse(divide(Z, divide(V, divide(Y, X))))))
0.56/0.73	= { by lemma 4 }
0.56/0.73	  divide(inverse(divide(?, divide(divide(X, Y), Z))), divide(W, ?))
0.56/0.73	= { by lemma 4 }
0.56/0.73	  divide(inverse(divide(inverse(divide(Z, divide(?, divide(Y, X)))), divide(divide(X, Y), Z))), divide(W, inverse(divide(Z, divide(?, divide(Y, X))))))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  divide(inverse(?), divide(W, inverse(divide(Z, divide(?, divide(Y, X))))))
0.56/0.73	= { by axiom 2 (multiply) }
0.56/0.73	  divide(inverse(?), multiply(W, divide(Z, divide(?, divide(Y, X)))))
0.56/0.73	
0.56/0.73	Lemma 6: divide(inverse(T), multiply(X, divide(Y, divide(T, W)))) = divide(inverse(?), multiply(X, divide(Y, divide(?, W)))).
0.56/0.73	Proof:
0.56/0.73	  divide(inverse(T), multiply(X, divide(Y, divide(T, W))))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  divide(inverse(T), multiply(X, divide(Y, divide(T, divide(inverse(divide(Z, divide(W, divide(V, U)))), divide(divide(U, V), Z))))))
0.56/0.73	= { by lemma 5 }
0.56/0.73	  divide(inverse(?), multiply(X, divide(Y, divide(?, divide(inverse(divide(Z, divide(W, divide(V, U)))), divide(divide(U, V), Z))))))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  divide(inverse(?), multiply(X, divide(Y, divide(?, W))))
0.56/0.73	
0.56/0.73	Lemma 7: divide(inverse(divide(Y, divide(X, multiply(Z, W)))), divide(divide(inverse(W), Z), Y)) = X.
0.56/0.73	Proof:
0.56/0.73	  divide(inverse(divide(Y, divide(X, multiply(Z, W)))), divide(divide(inverse(W), Z), Y))
0.56/0.73	= { by axiom 2 (multiply) }
0.56/0.73	  divide(inverse(divide(Y, divide(X, divide(Z, inverse(W))))), divide(divide(inverse(W), Z), Y))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  X
0.56/0.73	
0.56/0.73	Lemma 8: divide(inverse(divide(inverse(Y), divide(X, divide(Z, W)))), multiply(divide(W, Z), Y)) = X.
0.56/0.73	Proof:
0.56/0.73	  divide(inverse(divide(inverse(Y), divide(X, divide(Z, W)))), multiply(divide(W, Z), Y))
0.56/0.73	= { by axiom 2 (multiply) }
0.56/0.73	  divide(inverse(divide(inverse(Y), divide(X, divide(Z, W)))), divide(divide(W, Z), inverse(Y)))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  X
0.56/0.73	
0.56/0.73	Lemma 9: divide(inverse(Z), multiply(divide(W, V), divide(divide(V, W), divide(Z, divide(Y, X))))) = divide(X, Y).
0.56/0.73	Proof:
0.56/0.73	  divide(inverse(Z), multiply(divide(W, V), divide(divide(V, W), divide(Z, divide(Y, X)))))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  divide(inverse(divide(inverse(divide(divide(V, W), divide(Z, divide(Y, X)))), divide(divide(X, Y), divide(V, W)))), multiply(divide(W, V), divide(divide(V, W), divide(Z, divide(Y, X)))))
0.56/0.73	= { by lemma 8 }
0.56/0.73	  divide(X, Y)
0.56/0.73	
0.56/0.73	Lemma 10: divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, W)))) = multiply(divide(divide(?, ?), ?), divide(?, divide(W, divide(?, ?)))).
0.56/0.73	Proof:
0.56/0.73	  divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, W))))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(inverse(divide(?, divide(W, divide(?, ?)))), divide(divide(?, ?), ?))))))
0.56/0.73	= { by lemma 9 }
0.56/0.73	  divide(divide(divide(?, ?), ?), inverse(divide(?, divide(W, divide(?, ?)))))
0.56/0.73	= { by axiom 2 (multiply) }
0.56/0.73	  multiply(divide(divide(?, ?), ?), divide(?, divide(W, divide(?, ?))))
0.56/0.73	
0.56/0.73	Lemma 11: multiply(divide(divide(inverse(X), Y), Z), divide(Z, divide(W, multiply(Y, X)))) = multiply(divide(divide(?, ?), ?), divide(?, divide(W, divide(?, ?)))).
0.56/0.73	Proof:
0.56/0.73	  multiply(divide(divide(inverse(X), Y), Z), divide(Z, divide(W, multiply(Y, X))))
0.56/0.73	= { by axiom 2 (multiply) }
0.56/0.73	  divide(divide(divide(inverse(X), Y), Z), inverse(divide(Z, divide(W, multiply(Y, X)))))
0.56/0.73	= { by lemma 9 }
0.56/0.73	  divide(inverse(?), multiply(divide(?, ?), divide(divide(?, ?), divide(?, divide(inverse(divide(Z, divide(W, multiply(Y, X)))), divide(divide(inverse(X), Y), Z))))))
0.56/0.73	= { by lemma 7 }
0.56/0.73	  divide(inverse(?), multiply(divide(?, ?), divide(divide(?, ?), divide(?, W))))
0.56/0.73	= { by lemma 10 }
0.56/0.73	  multiply(divide(divide(?, ?), ?), divide(?, divide(W, divide(?, ?))))
0.56/0.73	
0.56/0.73	Lemma 12: divide(inverse(Z), multiply(divide(W, V), divide(divide(V, W), divide(Z, multiply(Y, X))))) = divide(inverse(X), Y).
0.56/0.73	Proof:
0.56/0.73	  divide(inverse(Z), multiply(divide(W, V), divide(divide(V, W), divide(Z, multiply(Y, X)))))
0.56/0.73	= { by lemma 7 }
0.56/0.73	  divide(inverse(divide(inverse(divide(divide(V, W), divide(Z, multiply(Y, X)))), divide(divide(inverse(X), Y), divide(V, W)))), multiply(divide(W, V), divide(divide(V, W), divide(Z, multiply(Y, X)))))
0.56/0.73	= { by axiom 2 (multiply) }
0.56/0.73	  divide(inverse(divide(inverse(divide(divide(V, W), divide(Z, multiply(Y, X)))), divide(divide(inverse(X), Y), divide(V, W)))), divide(divide(W, V), inverse(divide(divide(V, W), divide(Z, multiply(Y, X))))))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  divide(inverse(X), Y)
0.56/0.73	
0.56/0.73	Lemma 13: multiply(multiply(divide(V, U), divide(divide(U, V), divide(T, Y))), T) = Y.
0.56/0.73	Proof:
0.56/0.73	  multiply(multiply(divide(V, U), divide(divide(U, V), divide(T, Y))), T)
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  multiply(multiply(divide(V, U), divide(divide(U, V), divide(T, divide(inverse(divide(?, divide(Y, divide(?, ?)))), divide(divide(?, ?), ?))))), T)
0.56/0.73	= { by axiom 2 (multiply) }
0.56/0.73	  divide(multiply(divide(V, U), divide(divide(U, V), divide(T, divide(inverse(divide(?, divide(Y, divide(?, ?)))), divide(divide(?, ?), ?))))), inverse(T))
0.56/0.73	= { by lemma 9 }
0.56/0.73	  divide(inverse(?), multiply(divide(?, ?), divide(divide(?, ?), divide(?, divide(inverse(T), multiply(divide(V, U), divide(divide(U, V), divide(T, divide(inverse(divide(?, divide(Y, divide(?, ?)))), divide(divide(?, ?), ?))))))))))
0.56/0.73	= { by lemma 9 }
0.56/0.73	  divide(inverse(?), multiply(divide(?, ?), divide(divide(?, ?), divide(?, divide(divide(divide(?, ?), ?), inverse(divide(?, divide(Y, divide(?, ?)))))))))
0.56/0.73	= { by lemma 9 }
0.56/0.73	  divide(inverse(divide(?, divide(Y, divide(?, ?)))), divide(divide(?, ?), ?))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  Y
0.56/0.73	
0.56/0.73	Lemma 14: multiply(multiply(X, divide(W, divide(?, divide(Z, Y)))), ?) = multiply(divide(X, ?), divide(?, divide(divide(Y, Z), W))).
0.56/0.73	Proof:
0.56/0.73	  multiply(multiply(X, divide(W, divide(?, divide(Z, Y)))), ?)
0.56/0.73	= { by axiom 2 (multiply) }
0.56/0.73	  divide(multiply(X, divide(W, divide(?, divide(Z, Y)))), inverse(?))
0.56/0.73	= { by lemma 9 }
0.56/0.73	  divide(inverse(?), multiply(divide(?, ?), divide(divide(?, ?), divide(?, divide(inverse(?), multiply(X, divide(W, divide(?, divide(Z, Y)))))))))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  divide(inverse(?), multiply(divide(?, ?), divide(divide(?, ?), divide(?, divide(inverse(divide(inverse(divide(W, divide(?, divide(Z, Y)))), divide(divide(Y, Z), W))), multiply(X, divide(W, divide(?, divide(Z, Y)))))))))
0.56/0.73	= { by axiom 2 (multiply) }
0.56/0.73	  divide(inverse(?), multiply(divide(?, ?), divide(divide(?, ?), divide(?, divide(inverse(divide(inverse(divide(W, divide(?, divide(Z, Y)))), divide(divide(Y, Z), W))), divide(X, inverse(divide(W, divide(?, divide(Z, Y))))))))))
0.56/0.73	= { by lemma 4 }
0.56/0.73	  divide(inverse(?), multiply(divide(?, ?), divide(divide(?, ?), divide(?, divide(inverse(divide(?, divide(divide(Y, Z), W))), divide(X, ?))))))
0.56/0.73	= { by lemma 9 }
0.56/0.73	  divide(divide(X, ?), inverse(divide(?, divide(divide(Y, Z), W))))
0.56/0.73	= { by axiom 2 (multiply) }
0.56/0.73	  multiply(divide(X, ?), divide(?, divide(divide(Y, Z), W)))
0.56/0.73	
0.56/0.73	Lemma 15: multiply(divide(multiply(divide(X, Y), Z), ?), divide(?, multiply(divide(X, Y), Z))) = multiply(divide(divide(divide(?, ?), ?), ?), divide(?, divide(divide(?, ?), ?))).
0.56/0.73	Proof:
0.56/0.73	  multiply(divide(multiply(divide(X, Y), Z), ?), divide(?, multiply(divide(X, Y), Z)))
0.56/0.73	= { by axiom 2 (multiply) }
0.56/0.73	  multiply(divide(multiply(divide(X, Y), Z), ?), divide(?, divide(divide(X, Y), inverse(Z))))
0.56/0.73	= { by lemma 14 }
0.56/0.73	  multiply(multiply(multiply(divide(X, Y), Z), divide(inverse(Z), divide(?, divide(Y, X)))), ?)
0.56/0.73	= { by axiom 2 (multiply) }
0.56/0.73	  multiply(divide(multiply(divide(X, Y), Z), inverse(divide(inverse(Z), divide(?, divide(Y, X))))), ?)
0.56/0.73	= { by lemma 9 }
0.56/0.73	  multiply(divide(inverse(?), multiply(divide(?, ?), divide(divide(?, ?), divide(?, divide(inverse(divide(inverse(Z), divide(?, divide(Y, X)))), multiply(divide(X, Y), Z)))))), ?)
0.56/0.73	= { by lemma 8 }
0.56/0.73	  multiply(divide(inverse(?), multiply(divide(?, ?), divide(divide(?, ?), divide(?, ?)))), ?)
0.56/0.73	= { by lemma 10 }
0.56/0.73	  multiply(multiply(divide(divide(?, ?), ?), divide(?, divide(?, divide(?, ?)))), ?)
0.56/0.73	= { by lemma 14 }
0.56/0.73	  multiply(divide(divide(divide(?, ?), ?), ?), divide(?, divide(divide(?, ?), ?)))
0.56/0.73	
0.56/0.73	Lemma 16: multiply(divide(multiply(X, Y), ?), divide(?, multiply(X, Y))) = multiply(divide(multiply(?, ?), ?), divide(?, multiply(?, ?))).
0.56/0.73	Proof:
0.56/0.73	  multiply(divide(multiply(X, Y), ?), divide(?, multiply(X, Y)))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  multiply(divide(multiply(divide(inverse(divide(Z, divide(X, divide(W, V)))), divide(divide(V, W), Z)), Y), ?), divide(?, multiply(X, Y)))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  multiply(divide(multiply(divide(inverse(divide(Z, divide(X, divide(W, V)))), divide(divide(V, W), Z)), Y), ?), divide(?, multiply(divide(inverse(divide(Z, divide(X, divide(W, V)))), divide(divide(V, W), Z)), Y)))
0.56/0.73	= { by lemma 15 }
0.56/0.73	  multiply(divide(divide(divide(?, ?), ?), ?), divide(?, divide(divide(?, ?), ?)))
0.56/0.73	= { by lemma 15 }
0.56/0.73	  multiply(divide(multiply(divide(inverse(divide(Z, divide(?, divide(W, V)))), divide(divide(V, W), Z)), ?), ?), divide(?, multiply(divide(inverse(divide(Z, divide(?, divide(W, V)))), divide(divide(V, W), Z)), ?)))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  multiply(divide(multiply(?, ?), ?), divide(?, multiply(divide(inverse(divide(Z, divide(?, divide(W, V)))), divide(divide(V, W), Z)), ?)))
0.56/0.73	= { by axiom 1 (single_axiom) }
0.56/0.73	  multiply(divide(multiply(?, ?), ?), divide(?, multiply(?, ?)))
0.56/0.73	
0.56/0.73	Lemma 17: multiply(divide(X, ?), divide(?, X)) = multiply(divide(?, ?), divide(?, ?)).
0.56/0.73	Proof:
0.56/0.73	  multiply(divide(X, ?), divide(?, X))
0.56/0.73	= { by lemma 13 }
0.56/0.73	  multiply(divide(multiply(multiply(divide(Y, Z), divide(divide(Z, Y), divide(W, X))), W), ?), divide(?, X))
0.56/0.73	= { by lemma 13 }
0.56/0.73	  multiply(divide(multiply(multiply(divide(Y, Z), divide(divide(Z, Y), divide(W, X))), W), ?), divide(?, multiply(multiply(divide(Y, Z), divide(divide(Z, Y), divide(W, X))), W)))
0.56/0.73	= { by lemma 16 }
0.56/0.73	  multiply(divide(multiply(?, ?), ?), divide(?, multiply(?, ?)))
0.56/0.73	= { by lemma 16 }
0.56/0.73	  multiply(divide(multiply(multiply(divide(Y, Z), divide(divide(Z, Y), divide(W, ?))), W), ?), divide(?, multiply(multiply(divide(Y, Z), divide(divide(Z, Y), divide(W, ?))), W)))
0.56/0.73	= { by lemma 13 }
0.56/0.73	  multiply(divide(?, ?), divide(?, multiply(multiply(divide(Y, Z), divide(divide(Z, Y), divide(W, ?))), W)))
0.56/0.73	= { by lemma 13 }
0.56/0.74	  multiply(divide(?, ?), divide(?, ?))
0.56/0.74	
0.56/0.74	Lemma 18: inverse(divide(divide(inverse(X), Y), divide(divide(divide(inverse(X), Y), divide(Z, W)), divide(W, Z)))) = divide(inverse(divide(?, ?)), divide(?, ?)).
0.56/0.74	Proof:
0.56/0.74	  inverse(divide(divide(inverse(X), Y), divide(divide(divide(inverse(X), Y), divide(Z, W)), divide(W, Z))))
0.56/0.74	= { by lemma 3 }
0.56/0.74	  divide(inverse(divide(inverse(divide(divide(Z, W), divide(?, multiply(Y, X)))), divide(divide(inverse(X), Y), divide(Z, W)))), divide(divide(divide(inverse(X), Y), divide(Z, W)), inverse(divide(divide(Z, W), divide(?, multiply(Y, X))))))
0.56/0.74	= { by lemma 7 }
0.56/0.74	  divide(inverse(?), divide(divide(divide(inverse(X), Y), divide(Z, W)), inverse(divide(divide(Z, W), divide(?, multiply(Y, X))))))
0.56/0.74	= { by lemma 7 }
0.56/0.74	  divide(inverse(divide(inverse(divide(inverse(?), divide(?, multiply(inverse(?), ?)))), divide(divide(inverse(?), inverse(?)), inverse(?)))), divide(divide(divide(inverse(X), Y), divide(Z, W)), inverse(divide(divide(Z, W), divide(?, multiply(Y, X))))))
0.56/0.74	= { by axiom 2 (multiply) }
0.56/0.74	  divide(inverse(divide(inverse(divide(inverse(?), divide(?, multiply(inverse(?), ?)))), multiply(divide(inverse(?), inverse(?)), ?))), divide(divide(divide(inverse(X), Y), divide(Z, W)), inverse(divide(divide(Z, W), divide(?, multiply(Y, X))))))
0.56/0.74	= { by axiom 2 (multiply) }
0.56/0.74	  divide(inverse(divide(inverse(divide(inverse(?), divide(?, multiply(inverse(?), ?)))), multiply(multiply(inverse(?), ?), ?))), divide(divide(divide(inverse(X), Y), divide(Z, W)), inverse(divide(divide(Z, W), divide(?, multiply(Y, X))))))
0.56/0.74	= { by axiom 2 (multiply) }
0.56/0.74	  divide(inverse(divide(inverse(divide(inverse(?), divide(?, multiply(inverse(?), ?)))), multiply(multiply(inverse(?), ?), ?))), multiply(divide(divide(inverse(X), Y), divide(Z, W)), divide(divide(Z, W), divide(?, multiply(Y, X)))))
0.56/0.74	= { by lemma 11 }
0.56/0.74	  divide(inverse(divide(inverse(divide(inverse(?), divide(?, multiply(inverse(?), ?)))), multiply(multiply(inverse(?), ?), ?))), multiply(divide(divide(?, ?), ?), divide(?, divide(?, divide(?, ?)))))
0.56/0.74	= { by lemma 11 }
0.56/0.74	  divide(inverse(divide(inverse(divide(inverse(?), divide(?, multiply(inverse(?), ?)))), multiply(multiply(inverse(?), ?), ?))), multiply(divide(divide(inverse(?), inverse(?)), inverse(?)), divide(inverse(?), divide(?, multiply(inverse(?), ?)))))
0.56/0.74	= { by axiom 2 (multiply) }
0.56/0.74	  divide(inverse(divide(inverse(divide(inverse(?), divide(?, multiply(inverse(?), ?)))), multiply(multiply(inverse(?), ?), ?))), divide(divide(divide(inverse(?), inverse(?)), inverse(?)), inverse(divide(inverse(?), divide(?, multiply(inverse(?), ?))))))
0.56/0.74	= { by lemma 4 }
0.56/0.74	  divide(inverse(divide(?, multiply(multiply(inverse(?), ?), ?))), divide(divide(divide(inverse(?), inverse(?)), inverse(?)), ?))
0.56/0.74	= { by axiom 2 (multiply) }
0.56/0.74	  divide(inverse(divide(?, multiply(multiply(inverse(?), ?), ?))), divide(multiply(divide(inverse(?), inverse(?)), ?), ?))
0.56/0.74	= { by axiom 2 (multiply) }
0.56/0.74	  divide(inverse(divide(?, multiply(multiply(inverse(?), ?), ?))), divide(multiply(multiply(inverse(?), ?), ?), ?))
0.56/0.74	= { by lemma 12 }
0.56/0.74	  divide(inverse(?), multiply(divide(?, ?), divide(divide(?, ?), divide(?, multiply(divide(multiply(multiply(inverse(?), ?), ?), ?), divide(?, multiply(multiply(inverse(?), ?), ?)))))))
0.56/0.74	= { by lemma 17 }
0.56/0.74	  divide(inverse(?), multiply(divide(?, ?), divide(divide(?, ?), divide(?, multiply(divide(?, ?), divide(?, ?))))))
0.56/0.74	= { by lemma 12 }
0.56/0.74	  divide(inverse(divide(?, ?)), divide(?, ?))
0.56/0.74	
0.56/0.74	Lemma 19: divide(divide(inverse(divide(?, ?)), divide(?, ?)), divide(divide(Y, Z), X)) = divide(X, divide(Y, Z)).
0.56/0.74	Proof:
0.56/0.74	  divide(divide(inverse(divide(?, ?)), divide(?, ?)), divide(divide(Y, Z), X))
0.56/0.74	= { by lemma 18 }
0.56/0.74	  divide(inverse(divide(divide(inverse(divide(?, divide(X, divide(?, ?)))), divide(divide(?, ?), ?)), divide(divide(divide(inverse(divide(?, divide(X, divide(?, ?)))), divide(divide(?, ?), ?)), divide(Y, Z)), divide(Z, Y)))), divide(divide(Y, Z), X))
0.56/0.74	= { by axiom 1 (single_axiom) }
0.56/0.74	  divide(inverse(divide(X, divide(divide(divide(inverse(divide(?, divide(X, divide(?, ?)))), divide(divide(?, ?), ?)), divide(Y, Z)), divide(Z, Y)))), divide(divide(Y, Z), X))
0.56/0.74	= { by axiom 1 (single_axiom) }
0.56/0.74	  divide(inverse(divide(X, divide(divide(X, divide(Y, Z)), divide(Z, Y)))), divide(divide(Y, Z), X))
0.56/0.74	= { by axiom 1 (single_axiom) }
0.56/0.74	  divide(X, divide(Y, Z))
0.56/0.74	
0.56/0.74	Lemma 20: inverse(divide(divide(X, divide(Y, Z)), divide(X, divide(Y, Z)))) = divide(inverse(divide(?, ?)), divide(?, ?)).
0.56/0.74	Proof:
0.56/0.74	  inverse(divide(divide(X, divide(Y, Z)), divide(X, divide(Y, Z))))
0.56/0.74	= { by lemma 19 }
0.56/0.74	  inverse(divide(divide(inverse(divide(?, ?)), divide(?, ?)), divide(divide(X, divide(Y, Z)), divide(X, divide(Y, Z)))))
0.56/0.74	= { by lemma 19 }
0.56/0.74	  inverse(divide(divide(inverse(divide(?, ?)), divide(?, ?)), divide(divide(divide(inverse(divide(?, ?)), divide(?, ?)), divide(divide(Y, Z), X)), divide(X, divide(Y, Z)))))
0.56/0.74	= { by lemma 18 }
0.56/0.74	  divide(inverse(divide(?, ?)), divide(?, ?))
0.56/0.74	
0.56/0.74	Lemma 21: divide(divide(X, divide(Y, Z)), divide(X, divide(Y, Z))) = inverse(divide(?, ?)).
0.56/0.74	Proof:
0.56/0.74	  divide(divide(X, divide(Y, Z)), divide(X, divide(Y, Z)))
0.56/0.74	= { by lemma 19 }
0.56/0.74	  divide(divide(divide(inverse(divide(?, ?)), divide(?, ?)), divide(divide(Y, Z), X)), divide(X, divide(Y, Z)))
0.56/0.74	= { by lemma 19 }
0.56/0.74	  divide(divide(inverse(divide(?, ?)), divide(?, ?)), divide(divide(X, divide(Y, Z)), divide(divide(inverse(divide(?, ?)), divide(?, ?)), divide(divide(Y, Z), X))))
0.56/0.74	= { by lemma 20 }
0.56/0.74	  divide(inverse(divide(divide(divide(inverse(divide(?, ?)), divide(?, ?)), divide(divide(Y, Z), X)), divide(divide(inverse(divide(?, ?)), divide(?, ?)), divide(divide(Y, Z), X)))), divide(divide(X, divide(Y, Z)), divide(divide(inverse(divide(?, ?)), divide(?, ?)), divide(divide(Y, Z), X))))
0.56/0.74	= { by axiom 1 (single_axiom) }
0.56/0.74	  divide(inverse(divide(?, ?)), divide(?, ?))
0.56/0.74	= { by lemma 20 }
0.56/0.74	  inverse(divide(divide(inverse(divide(?, divide(?, divide(?, ?)))), divide(divide(?, ?), ?)), divide(inverse(divide(?, divide(?, divide(?, ?)))), divide(divide(?, ?), ?))))
0.56/0.74	= { by axiom 1 (single_axiom) }
0.56/0.74	  inverse(divide(?, divide(inverse(divide(?, divide(?, divide(?, ?)))), divide(divide(?, ?), ?))))
0.56/0.74	= { by axiom 1 (single_axiom) }
0.56/0.74	  inverse(divide(?, ?))
0.56/0.74	
0.56/0.74	Lemma 22: multiply(inverse(X), X) = divide(?, ?).
0.56/0.74	Proof:
0.56/0.74	  multiply(inverse(X), X)
0.56/0.74	= { by axiom 2 (multiply) }
0.56/0.74	  divide(inverse(X), inverse(X))
0.56/0.74	= { by axiom 1 (single_axiom) }
0.56/0.74	  divide(divide(inverse(divide(?, divide(inverse(X), divide(?, ?)))), divide(divide(?, ?), ?)), inverse(X))
0.56/0.74	= { by axiom 1 (single_axiom) }
0.56/0.74	  divide(divide(inverse(divide(?, divide(inverse(X), divide(?, ?)))), divide(divide(?, ?), ?)), divide(inverse(divide(?, divide(inverse(X), divide(?, ?)))), divide(divide(?, ?), ?)))
0.56/0.74	= { by lemma 21 }
0.56/0.74	  inverse(divide(?, ?))
0.56/0.74	= { by lemma 21 }
0.56/0.74	  divide(divide(inverse(divide(?, divide(?, divide(?, ?)))), divide(divide(?, ?), ?)), divide(inverse(divide(?, divide(?, divide(?, ?)))), divide(divide(?, ?), ?)))
0.56/0.74	= { by axiom 1 (single_axiom) }
0.56/0.74	  divide(?, divide(inverse(divide(?, divide(?, divide(?, ?)))), divide(divide(?, ?), ?)))
0.56/0.74	= { by axiom 1 (single_axiom) }
0.56/0.74	  divide(?, ?)
0.56/0.74	
0.56/0.74	Goal 1 (prove_these_axioms_1): multiply(inverse(b1), b1) = multiply(inverse(a1), a1).
0.56/0.74	Proof:
0.56/0.74	  multiply(inverse(b1), b1)
0.56/0.74	= { by lemma 22 }
0.56/0.74	  divide(?, ?)
0.56/0.74	= { by lemma 22 }
0.56/0.74	  multiply(inverse(a1), a1)
0.56/0.74	% SZS output end Proof
0.56/0.74	
0.56/0.74	RESULT: Unsatisfiable (the axioms are contradictory).
0.56/0.74	EOF