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
0.13/0.34	% Computer   : n020.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 10:29:55 EDT 2019
0.13/0.34	% CPUTime    : 
1.58/1.80	% SZS status Unsatisfiable
1.58/1.80	
1.58/1.80	% SZS output start Proof
1.58/1.80	Take the following subset of the input axioms:
1.64/1.82	  fof(prove_tba_axioms_2, negated_conjecture, a!=multiply(b, a, a)).
1.64/1.82	  fof(single_axiom, axiom, ![A, B, C, D, E, F, G]: multiply(multiply(A, inverse(A), B), inverse(multiply(multiply(C, D, E), F, multiply(C, D, G))), multiply(D, multiply(G, F, E), C))=B).
1.64/1.82	
1.64/1.82	Now clausify the problem and encode Horn clauses using encoding 3 of
1.64/1.82	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
1.64/1.82	We repeatedly replace C & s=t => u=v by the two clauses:
1.64/1.82	  fresh(y, y, x1...xn) = u
1.64/1.82	  C => fresh(s, t, x1...xn) = v
1.64/1.82	where fresh is a fresh function symbol and x1..xn are the free
1.64/1.82	variables of u and v.
1.64/1.82	A predicate p(X) is encoded as p(X)=true (this is sound, because the
1.64/1.82	input problem has no model of domain size 1).
1.64/1.82	
1.64/1.82	The encoding turns the above axioms into the following unit equations and goals:
1.64/1.82	
1.64/1.82	Axiom 1 (single_axiom): multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, W, V), U, multiply(Z, W, T))), multiply(W, multiply(T, U, V), Z)) = Y.
1.64/1.82	
1.64/1.82	Lemma 2: multiply(multiply(Z, X, Y), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)) = multiply(X, multiply(Y, inverse(multiply(Z, X, ?)), ?), Z).
1.64/1.82	Proof:
1.64/1.82	  multiply(multiply(Z, X, Y), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  multiply(multiply(multiply(multiply(Z, X, ?), inverse(multiply(Z, X, ?)), multiply(Z, X, Y)), inverse(multiply(multiply(Z, X, ?), inverse(multiply(Z, X, ?)), multiply(Z, X, Y))), multiply(X, multiply(Y, inverse(multiply(Z, X, ?)), ?), Z)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  multiply(X, multiply(Y, inverse(multiply(Z, X, ?)), ?), Z)
1.64/1.82	
1.64/1.82	Lemma 3: multiply(inverse(X), multiply(Y, inverse(multiply(X, inverse(X), ?)), ?), X) = Y.
1.64/1.82	Proof:
1.64/1.82	  multiply(inverse(X), multiply(Y, inverse(multiply(X, inverse(X), ?)), ?), X)
1.64/1.82	= { by lemma 2 }
1.64/1.82	  multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  Y
1.64/1.82	
1.64/1.82	Lemma 4: multiply(multiply(Y, inverse(Y), X), inverse(multiply(multiply(Z, inverse(Z), ?), inverse(multiply(Z, inverse(Z), ?)), multiply(Z, inverse(Z), W))), W) = X.
1.64/1.82	Proof:
1.64/1.82	  multiply(multiply(Y, inverse(Y), X), inverse(multiply(multiply(Z, inverse(Z), ?), inverse(multiply(Z, inverse(Z), ?)), multiply(Z, inverse(Z), W))), W)
1.64/1.82	= { by lemma 3 }
1.64/1.82	  multiply(multiply(Y, inverse(Y), X), inverse(multiply(multiply(Z, inverse(Z), ?), inverse(multiply(Z, inverse(Z), ?)), multiply(Z, inverse(Z), W))), multiply(inverse(Z), multiply(W, inverse(multiply(Z, inverse(Z), ?)), ?), Z))
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  X
1.64/1.82	
1.64/1.82	Lemma 5: multiply(multiply(Z, X, Y), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V)) = multiply(multiply(Z, X, Y), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)).
1.64/1.82	Proof:
1.64/1.82	  multiply(multiply(Z, X, Y), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V))
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  multiply(multiply(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y)), inverse(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y))), multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z)), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V))
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z)
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  multiply(multiply(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y)), inverse(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y))), multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  multiply(multiply(Z, X, Y), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	
1.64/1.82	Lemma 6: multiply(multiply(multiply(multiply(V, X, W), Z, multiply(V, X, Y)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)) = multiply(X, multiply(Y, Z, W), V).
1.64/1.82	Proof:
1.64/1.82	  multiply(multiply(multiply(multiply(V, X, W), Z, multiply(V, X, Y)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by lemma 5 }
1.64/1.82	  multiply(multiply(multiply(multiply(V, X, W), Z, multiply(V, X, Y)), inverse(multiply(multiply(V, X, W), Z, multiply(V, X, Y))), multiply(X, multiply(Y, Z, W), V)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  multiply(X, multiply(Y, Z, W), V)
1.64/1.82	
1.64/1.82	Lemma 7: multiply(multiply(W, inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)) = multiply(inverse(?), multiply(?, inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(?, inverse(?), ?)))), W), ?).
1.64/1.82	Proof:
1.64/1.82	  multiply(multiply(W, inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by lemma 4 }
1.64/1.82	  multiply(multiply(multiply(multiply(?, inverse(?), W), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(?, inverse(?), ?)))), multiply(?, inverse(?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by lemma 6 }
1.64/1.82	  multiply(inverse(?), multiply(?, inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(?, inverse(?), ?)))), W), ?)
1.64/1.82	
1.64/1.82	Lemma 8: multiply(inverse(?), multiply(?, inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(?, inverse(?), ?)))), multiply(X, inverse(X), Y)), ?) = multiply(Y, inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)).
1.64/1.82	Proof:
1.64/1.82	  multiply(inverse(?), multiply(?, inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(?, inverse(?), ?)))), multiply(X, inverse(X), Y)), ?)
1.64/1.82	= { by lemma 7 }
1.64/1.82	  multiply(multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  multiply(Y, inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	
1.64/1.82	Lemma 9: multiply(inverse(Z), X, Z) = X.
1.64/1.82	Proof:
1.64/1.82	  multiply(inverse(Z), X, Z)
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  multiply(inverse(Z), multiply(multiply(?, inverse(?), X), inverse(multiply(multiply(?, inverse(?), multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(Z, inverse(Z), multiply(?, inverse(?), X))))), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(?, inverse(?), ?)))), multiply(?, inverse(?), ?))), multiply(inverse(?), multiply(?, inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(?, inverse(?), ?)))), multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(Z, inverse(Z), multiply(?, inverse(?), X))))), ?)), Z)
1.64/1.82	= { by lemma 4 }
1.64/1.82	  multiply(inverse(Z), multiply(multiply(?, inverse(?), X), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(Z, inverse(Z), multiply(?, inverse(?), X))))), multiply(inverse(?), multiply(?, inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(?, inverse(?), ?)))), multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(Z, inverse(Z), multiply(?, inverse(?), X))))), ?)), Z)
1.64/1.82	= { by lemma 8 }
1.64/1.82	  multiply(inverse(Z), multiply(multiply(?, inverse(?), X), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(Z, inverse(Z), multiply(?, inverse(?), X))))), multiply(multiply(?, inverse(?), multiply(Z, inverse(Z), multiply(?, inverse(?), X))), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))), Z)
1.64/1.82	= { by lemma 6 }
1.64/1.82	  multiply(multiply(multiply(multiply(Z, inverse(Z), multiply(multiply(?, inverse(?), multiply(Z, inverse(Z), multiply(?, inverse(?), X))), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(Z, inverse(Z), multiply(?, inverse(?), X))))), multiply(Z, inverse(Z), multiply(?, inverse(?), X))), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by lemma 4 }
1.64/1.82	  multiply(multiply(multiply(multiply(?, inverse(?), multiply(Z, inverse(Z), multiply(?, inverse(?), X))), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by lemma 4 }
1.64/1.82	  multiply(multiply(multiply(multiply(?, inverse(?), multiply(multiply(?, inverse(?), multiply(Z, inverse(Z), multiply(?, inverse(?), X))), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(?, inverse(?), ?)))), multiply(?, inverse(?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by lemma 6 }
1.64/1.82	  multiply(inverse(?), multiply(?, inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(?, inverse(?), ?)))), multiply(multiply(?, inverse(?), multiply(Z, inverse(Z), multiply(?, inverse(?), X))), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))), ?)
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  multiply(inverse(?), multiply(?, inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(?, inverse(?), ?)))), multiply(Z, inverse(Z), multiply(?, inverse(?), X))), ?)
1.64/1.82	= { by lemma 8 }
1.64/1.82	  multiply(multiply(?, inverse(?), X), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  X
1.64/1.82	
1.64/1.82	Lemma 10: inverse(multiply(X, inverse(X), ?)) = inverse(?).
1.64/1.82	Proof:
1.64/1.82	  inverse(multiply(X, inverse(X), ?))
1.64/1.82	= { by lemma 9 }
1.64/1.82	  multiply(inverse(X), inverse(multiply(X, inverse(X), ?)), X)
1.64/1.82	= { by lemma 9 }
1.64/1.82	  multiply(inverse(X), multiply(inverse(?), inverse(multiply(X, inverse(X), ?)), ?), X)
1.64/1.82	= { by lemma 3 }
1.64/1.82	  inverse(?)
1.64/1.82	
1.64/1.82	Lemma 11: multiply(X, inverse(?), ?) = X.
1.64/1.82	Proof:
1.64/1.82	  multiply(X, inverse(?), ?)
1.64/1.82	= { by lemma 9 }
1.64/1.82	  multiply(inverse(?), multiply(X, inverse(?), ?), ?)
1.64/1.82	= { by lemma 10 }
1.64/1.82	  multiply(inverse(?), multiply(X, inverse(multiply(?, inverse(?), ?)), ?), ?)
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  multiply(multiply(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), X)), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), X))), multiply(inverse(?), multiply(X, inverse(multiply(?, inverse(?), ?)), ?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  multiply(multiply(?, inverse(?), X), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by axiom 1 (single_axiom) }
1.64/1.82	  X
1.64/1.82	
1.64/1.82	Lemma 12: multiply(Y, inverse(Y), X) = X.
1.64/1.82	Proof:
1.64/1.82	  multiply(Y, inverse(Y), X)
1.64/1.82	= { by lemma 11 }
1.64/1.82	  multiply(multiply(Y, inverse(Y), X), inverse(?), ?)
1.64/1.82	= { by lemma 10 }
1.64/1.82	  multiply(multiply(Y, inverse(Y), X), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), ?)), ?)
1.64/1.82	= { by lemma 11 }
1.64/1.82	  multiply(multiply(Y, inverse(Y), X), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), ?))), ?)
1.64/1.82	= { by lemma 4 }
1.64/1.82	  X
1.64/1.82	
1.64/1.82	Lemma 13: multiply(Y, Z, W) = multiply(W, Z, Y).
1.64/1.82	Proof:
1.64/1.82	  multiply(Y, Z, W)
1.64/1.82	= { by lemma 9 }
1.64/1.82	  multiply(inverse(?), multiply(Y, Z, W), ?)
1.64/1.82	= { by lemma 6 }
1.64/1.82	  multiply(multiply(multiply(multiply(?, inverse(?), W), Z, multiply(?, inverse(?), Y)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by lemma 12 }
1.64/1.82	  multiply(multiply(multiply(W, Z, multiply(?, inverse(?), Y)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.82	= { by lemma 7 }
1.64/1.82	  multiply(inverse(?), multiply(?, inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(?, inverse(?), ?)))), multiply(W, Z, multiply(?, inverse(?), Y))), ?)
1.64/1.82	= { by lemma 9 }
1.64/1.82	  multiply(?, inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), multiply(?, inverse(?), ?)))), multiply(W, Z, multiply(?, inverse(?), Y)))
1.64/1.82	= { by lemma 12 }
1.64/1.82	  multiply(?, inverse(multiply(?, inverse(?), multiply(?, inverse(?), ?))), multiply(W, Z, multiply(?, inverse(?), Y)))
1.64/1.82	= { by lemma 12 }
1.64/1.82	  multiply(?, inverse(multiply(?, inverse(?), ?)), multiply(W, Z, multiply(?, inverse(?), Y)))
1.64/1.82	= { by lemma 10 }
1.64/1.82	  multiply(?, inverse(?), multiply(W, Z, multiply(?, inverse(?), Y)))
1.64/1.82	= { by lemma 12 }
1.64/1.82	  multiply(?, inverse(?), multiply(W, Z, Y))
1.64/1.82	= { by lemma 12 }
1.64/1.82	  multiply(W, Z, Y)
1.64/1.82	
1.64/1.82	Lemma 14: multiply(Y, inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)) = Y.
1.64/1.82	Proof:
1.64/1.83	  multiply(Y, inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.83	= { by lemma 12 }
1.64/1.83	  multiply(multiply(?, inverse(?), Y), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.83	= { by axiom 1 (single_axiom) }
1.64/1.83	  Y
1.64/1.83	
1.64/1.83	Lemma 15: multiply(X, multiply(?, inverse(multiply(?, X, Z)), Y), Z) = multiply(Y, X, Z).
1.64/1.83	Proof:
1.64/1.83	  multiply(X, multiply(?, inverse(multiply(?, X, Z)), Y), Z)
1.64/1.83	= { by lemma 13 }
1.64/1.83	  multiply(X, multiply(?, inverse(multiply(Z, X, ?)), Y), Z)
1.64/1.83	= { by lemma 13 }
1.64/1.83	  multiply(X, multiply(Y, inverse(multiply(Z, X, ?)), ?), Z)
1.64/1.83	= { by axiom 1 (single_axiom) }
1.64/1.83	  multiply(multiply(multiply(multiply(Z, X, ?), inverse(multiply(Z, X, ?)), multiply(Z, X, Y)), inverse(multiply(multiply(Z, X, ?), inverse(multiply(Z, X, ?)), multiply(Z, X, Y))), multiply(X, multiply(Y, inverse(multiply(Z, X, ?)), ?), Z)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.83	= { by axiom 1 (single_axiom) }
1.64/1.83	  multiply(multiply(Z, X, Y), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.83	= { by lemma 14 }
1.64/1.83	  multiply(Z, X, Y)
1.64/1.83	= { by lemma 13 }
1.64/1.83	  multiply(Y, X, Z)
1.64/1.83	
1.64/1.83	Lemma 16: inverse(inverse(X)) = X.
1.64/1.83	Proof:
1.64/1.83	  inverse(inverse(X))
1.64/1.83	= { by lemma 9 }
1.64/1.83	  multiply(inverse(X), inverse(inverse(X)), X)
1.64/1.83	= { by lemma 12 }
1.64/1.83	  X
1.64/1.83	
1.64/1.83	Lemma 17: multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z) = multiply(X, multiply(Y, inverse(multiply(Z, X, ?)), ?), Z).
1.64/1.83	Proof:
1.64/1.83	  multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z)
1.64/1.83	= { by axiom 1 (single_axiom) }
1.64/1.83	  multiply(multiply(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y)), inverse(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y))), multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z)), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V))
1.64/1.83	= { by axiom 1 (single_axiom) }
1.64/1.83	  multiply(multiply(Z, X, Y), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V))
1.64/1.83	= { by axiom 1 (single_axiom) }
1.64/1.83	  multiply(multiply(multiply(multiply(Z, X, ?), inverse(multiply(Z, X, ?)), multiply(Z, X, Y)), inverse(multiply(multiply(Z, X, ?), inverse(multiply(Z, X, ?)), multiply(Z, X, Y))), multiply(X, multiply(Y, inverse(multiply(Z, X, ?)), ?), Z)), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V))
1.64/1.83	= { by axiom 1 (single_axiom) }
1.64/1.83	  multiply(X, multiply(Y, inverse(multiply(Z, X, ?)), ?), Z)
1.64/1.83	
1.64/1.83	Lemma 18: multiply(Z, multiply(X, inverse(Z), Y), inverse(Y)) = multiply(X, Z, inverse(Y)).
1.64/1.83	Proof:
1.64/1.83	  multiply(Z, multiply(X, inverse(Z), Y), inverse(Y))
1.64/1.83	= { by lemma 11 }
1.64/1.83	  multiply(multiply(Z, inverse(?), ?), multiply(X, inverse(Z), Y), inverse(Y))
1.64/1.83	= { by lemma 10 }
1.64/1.83	  multiply(multiply(Z, inverse(multiply(Y, inverse(Y), ?)), ?), multiply(X, inverse(Z), Y), inverse(Y))
1.64/1.83	= { by lemma 3 }
1.64/1.83	  multiply(multiply(Z, inverse(multiply(Y, inverse(Y), ?)), ?), multiply(X, inverse(multiply(inverse(Y), multiply(Z, inverse(multiply(Y, inverse(Y), ?)), ?), Y)), Y), inverse(Y))
1.64/1.83	= { by lemma 17 }
1.64/1.83	  multiply(multiply(Z, inverse(multiply(Y, inverse(Y), ?)), ?), multiply(X, inverse(multiply(inverse(Y), multiply(Z, inverse(multiply(Y, inverse(Y), ?)), ?), ?)), ?), inverse(Y))
1.64/1.83	= { by lemma 13 }
1.64/1.83	  multiply(multiply(Z, inverse(multiply(Y, inverse(Y), ?)), ?), multiply(?, inverse(multiply(inverse(Y), multiply(Z, inverse(multiply(Y, inverse(Y), ?)), ?), ?)), X), inverse(Y))
1.64/1.83	= { by lemma 13 }
1.64/1.83	  multiply(multiply(Z, inverse(multiply(Y, inverse(Y), ?)), ?), multiply(?, inverse(multiply(?, multiply(Z, inverse(multiply(Y, inverse(Y), ?)), ?), inverse(Y))), X), inverse(Y))
1.64/1.83	= { by lemma 15 }
1.64/1.83	  multiply(X, multiply(Z, inverse(multiply(Y, inverse(Y), ?)), ?), inverse(Y))
1.64/1.83	= { by lemma 10 }
1.64/1.83	  multiply(X, multiply(Z, inverse(?), ?), inverse(Y))
1.64/1.83	= { by lemma 11 }
1.64/1.83	  multiply(X, Z, inverse(Y))
1.64/1.83	
1.64/1.83	Lemma 19: multiply(multiply(X, inverse(multiply(Y, inverse(Y), ?)), ?), multiply(Z, inverse(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), ?)), ?), ?)), ?), inverse(Y)) = multiply(multiply(X, inverse(multiply(Y, inverse(Y), ?)), ?), multiply(Z, inverse(X), Y), inverse(Y)).
1.64/1.83	Proof:
1.64/1.83	  multiply(multiply(X, inverse(multiply(Y, inverse(Y), ?)), ?), multiply(Z, inverse(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), ?)), ?), ?)), ?), inverse(Y))
1.64/1.83	= { by lemma 17 }
1.64/1.83	  multiply(multiply(X, inverse(multiply(Y, inverse(Y), ?)), ?), multiply(Z, inverse(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), ?)), ?), Y)), Y), inverse(Y))
1.64/1.83	= { by lemma 3 }
1.64/1.83	  multiply(multiply(X, inverse(multiply(Y, inverse(Y), ?)), ?), multiply(Z, inverse(X), Y), inverse(Y))
1.64/1.83	
1.64/1.83	Lemma 20: multiply(multiply(X, inverse(multiply(Y, inverse(Y), ?)), ?), multiply(Y, inverse(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), ?)), ?), ?)), ?), inverse(Y)) = multiply(X, inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)).
1.64/1.83	Proof:
1.64/1.83	  multiply(multiply(X, inverse(multiply(Y, inverse(Y), ?)), ?), multiply(Y, inverse(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), ?)), ?), ?)), ?), inverse(Y))
1.64/1.83	= { by lemma 2 }
1.64/1.83	  multiply(multiply(inverse(Y), multiply(X, inverse(multiply(Y, inverse(Y), ?)), ?), Y), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.83	= { by lemma 3 }
1.64/1.83	  multiply(X, inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.83	
1.64/1.83	Lemma 21: multiply(X, inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)) = multiply(multiply(X, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(X), ?), inverse(?)).
1.64/1.83	Proof:
1.64/1.83	  multiply(X, inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.83	= { by lemma 20 }
1.64/1.83	  multiply(multiply(X, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(multiply(inverse(?), multiply(X, inverse(multiply(?, inverse(?), ?)), ?), ?)), ?), inverse(?))
1.64/1.83	= { by lemma 3 }
1.64/1.83	  multiply(multiply(X, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(X), ?), inverse(?))
1.64/1.83	
1.64/1.83	Lemma 22: multiply(multiply(Y, inverse(Y), X), inverse(multiply(Z, inverse(Z), Z)), multiply(multiply(Z, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(Z), ?), inverse(?))) = X.
1.64/1.83	Proof:
1.64/1.83	  multiply(multiply(Y, inverse(Y), X), inverse(multiply(Z, inverse(Z), Z)), multiply(multiply(Z, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(Z), ?), inverse(?)))
1.64/1.83	= { by lemma 3 }
1.64/1.83	  multiply(multiply(Y, inverse(Y), X), inverse(multiply(multiply(inverse(?), multiply(Z, inverse(multiply(?, inverse(?), ?)), ?), ?), inverse(Z), Z)), multiply(multiply(Z, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(Z), ?), inverse(?)))
1.64/1.83	= { by lemma 3 }
1.64/1.83	  multiply(multiply(Y, inverse(Y), X), inverse(multiply(multiply(inverse(?), multiply(Z, inverse(multiply(?, inverse(?), ?)), ?), ?), inverse(Z), multiply(inverse(?), multiply(Z, inverse(multiply(?, inverse(?), ?)), ?), ?))), multiply(multiply(Z, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(Z), ?), inverse(?)))
1.64/1.83	= { by axiom 1 (single_axiom) }
1.64/1.83	  X
1.64/1.83	
1.64/1.83	Lemma 23: multiply(multiply(Y, inverse(Y), X), inverse(multiply(multiply(Z, W, V), inverse(multiply(Z, W, V)), multiply(Z, W, U))), multiply(W, multiply(U, inverse(multiply(Z, W, ?)), ?), Z)) = X.
1.64/1.83	Proof:
1.64/1.83	  multiply(multiply(Y, inverse(Y), X), inverse(multiply(multiply(Z, W, V), inverse(multiply(Z, W, V)), multiply(Z, W, U))), multiply(W, multiply(U, inverse(multiply(Z, W, ?)), ?), Z))
1.64/1.83	= { by lemma 17 }
1.64/1.83	  multiply(multiply(Y, inverse(Y), X), inverse(multiply(multiply(Z, W, V), inverse(multiply(Z, W, V)), multiply(Z, W, U))), multiply(W, multiply(U, inverse(multiply(Z, W, V)), V), Z))
1.64/1.83	= { by axiom 1 (single_axiom) }
1.64/1.83	  X
1.64/1.83	
1.64/1.83	Lemma 24: multiply(multiply(Y, inverse(Y), X), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), V))), V) = X.
1.64/1.83	Proof:
1.64/1.83	  multiply(multiply(Y, inverse(Y), X), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), V))), V)
1.64/1.83	= { by lemma 3 }
1.64/1.83	  multiply(multiply(Y, inverse(Y), X), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), V))), multiply(inverse(Z), multiply(V, inverse(multiply(Z, inverse(Z), ?)), ?), Z))
1.64/1.83	= { by lemma 23 }
1.64/1.83	  X
1.64/1.83	
1.64/1.83	Lemma 25: multiply(multiply(Y, inverse(Y), X), inverse(multiply(Z, inverse(Z), multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), V))), V) = X.
1.64/1.83	Proof:
1.64/1.83	  multiply(multiply(Y, inverse(Y), X), inverse(multiply(Z, inverse(Z), multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), V))), V)
1.64/1.83	= { by lemma 24 }
1.64/1.83	  multiply(multiply(Y, inverse(Y), X), inverse(multiply(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), V))), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), V)))), multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), V))), V)
1.64/1.83	= { by lemma 3 }
1.64/1.83	  multiply(multiply(Y, inverse(Y), X), inverse(multiply(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), V))), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), V)))), multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), V))), multiply(inverse(multiply(Z, inverse(Z), W)), multiply(V, inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), ?)), ?), multiply(Z, inverse(Z), W)))
1.64/1.83	= { by lemma 23 }
1.64/1.83	  X
1.64/1.83	
1.64/1.83	Lemma 26: multiply(multiply(Z, X, Y), inverse(multiply(multiply(V, inverse(V), ?), inverse(multiply(V, inverse(V), ?)), multiply(V, inverse(V), U))), U) = multiply(multiply(Z, X, Y), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), ?))), ?).
1.64/1.83	Proof:
1.64/1.83	  multiply(multiply(Z, X, Y), inverse(multiply(multiply(V, inverse(V), ?), inverse(multiply(V, inverse(V), ?)), multiply(V, inverse(V), U))), U)
1.64/1.83	= { by axiom 1 (single_axiom) }
1.64/1.83	  multiply(multiply(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y)), inverse(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y))), multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z)), inverse(multiply(multiply(V, inverse(V), ?), inverse(multiply(V, inverse(V), ?)), multiply(V, inverse(V), U))), U)
1.64/1.83	= { by lemma 4 }
1.64/1.83	  multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z)
1.64/1.83	= { by lemma 4 }
1.64/1.83	  multiply(multiply(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y)), inverse(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y))), multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z)), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), ?))), ?)
1.64/1.83	= { by axiom 1 (single_axiom) }
1.64/1.84	  multiply(multiply(Z, X, Y), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), ?))), ?)
1.64/1.84	
1.64/1.84	Goal 1 (prove_tba_axioms_2): a = multiply(b, a, a).
1.64/1.84	Proof:
1.64/1.84	  a
1.64/1.84	= { by lemma 14 }
1.64/1.84	  multiply(a, inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.84	= { by axiom 1 (single_axiom) }
1.64/1.84	  multiply(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.84	= { by axiom 1 (single_axiom) }
1.64/1.84	  multiply(multiply(multiply(?, inverse(?), multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))
1.64/1.84	= { by lemma 5 }
1.64/1.84	  multiply(multiply(multiply(?, inverse(?), multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), ?))), multiply(inverse(?), multiply(?, inverse(multiply(?, inverse(?), ?)), ?), ?))
1.64/1.84	= { by axiom 1 (single_axiom) }
1.64/1.84	  multiply(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), ?))), multiply(inverse(?), multiply(?, inverse(multiply(?, inverse(?), ?)), ?), ?))
1.64/1.84	= { by axiom 1 (single_axiom) }
1.64/1.84	  multiply(multiply(multiply(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?), inverse(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?)), multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))), inverse(multiply(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?), inverse(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?)), multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)))), multiply(inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(multiply(?, multiply(?, ?, ?), ?), inverse(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?)), ?), multiply(?, inverse(?), a))), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), ?))), multiply(inverse(?), multiply(?, inverse(multiply(?, inverse(?), ?)), ?), ?))
1.64/1.84	= { by lemma 3 }
1.64/1.84	  multiply(multiply(multiply(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?), inverse(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?)), multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))), inverse(multiply(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?), inverse(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?)), multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)))), multiply(inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(multiply(?, multiply(?, ?, ?), ?), inverse(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?)), ?), multiply(?, inverse(?), a))), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(?), ?))), ?)
1.64/1.84	= { by lemma 24 }
1.64/1.84	  multiply(inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(multiply(?, multiply(?, ?, ?), ?), inverse(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?)), ?), multiply(?, inverse(?), a))
1.64/1.84	= { by lemma 24 }
1.64/1.84	  multiply(multiply(multiply(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?), inverse(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?)), multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?))), inverse(multiply(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?), inverse(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?)), multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)))), multiply(inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(multiply(?, multiply(?, ?, ?), ?), inverse(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), ?)), ?), multiply(?, inverse(?), a))), inverse(multiply(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(multiply(?, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(?), ?), inverse(?))), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(multiply(?, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(?), ?), inverse(?)))), multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), ?))), ?)
1.64/1.84	= { by axiom 1 (single_axiom) }
1.64/1.84	  multiply(multiply(multiply(?, inverse(?), a), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), inverse(multiply(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(multiply(?, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(?), ?), inverse(?))), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(multiply(?, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(?), ?), inverse(?)))), multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), ?))), ?)
1.64/1.84	= { by axiom 1 (single_axiom) }
1.64/1.84	  multiply(a, inverse(multiply(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(multiply(?, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(?), ?), inverse(?))), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(multiply(?, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(?), ?), inverse(?)))), multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), ?))), ?)
1.64/1.84	= { by lemma 22 }
1.64/1.84	  multiply(multiply(multiply(a, inverse(a), a), inverse(multiply(a, inverse(a), a)), multiply(multiply(a, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(a), ?), inverse(?))), inverse(multiply(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(multiply(?, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(?), ?), inverse(?))), inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(multiply(?, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(?), ?), inverse(?)))), multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), ?))), ?)
1.64/1.84	= { by lemma 22 }
1.64/1.84	  multiply(multiply(multiply(a, inverse(a), a), inverse(multiply(a, inverse(a), a)), multiply(multiply(a, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(a), ?), inverse(?))), inverse(multiply(?, inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(multiply(?, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(?), ?), inverse(?)))), multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), ?))), ?)
1.64/1.84	= { by lemma 22 }
1.64/1.84	  multiply(multiply(multiply(a, inverse(a), a), inverse(multiply(a, inverse(a), a)), multiply(multiply(a, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(a), ?), inverse(?))), inverse(multiply(?, inverse(?), multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), ?))), ?)
1.64/1.84	= { by lemma 25 }
1.64/1.84	  multiply(multiply(a, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(a), ?), inverse(?))
1.64/1.84	= { by lemma 25 }
1.64/1.84	  multiply(multiply(multiply(a, inverse(a), a), inverse(multiply(a, inverse(a), a)), multiply(multiply(a, inverse(multiply(?, inverse(?), ?)), ?), multiply(?, inverse(a), ?), inverse(?))), inverse(multiply(?, inverse(?), multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(multiply(?, a, a)), b)))), multiply(?, inverse(multiply(?, a, a)), b))
1.64/1.84	= { by lemma 22 }
1.64/1.85	  multiply(a, inverse(multiply(?, inverse(?), multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(multiply(?, a, a)), b)))), multiply(?, inverse(multiply(?, a, a)), b))
1.64/1.85	= { by lemma 12 }
1.64/1.85	  multiply(a, inverse(multiply(multiply(?, inverse(?), ?), inverse(multiply(?, inverse(?), ?)), multiply(?, inverse(multiply(?, a, a)), b))), multiply(?, inverse(multiply(?, a, a)), b))
1.64/1.85	= { by lemma 12 }
1.64/1.85	  multiply(a, inverse(multiply(?, inverse(multiply(?, a, a)), b)), multiply(?, inverse(multiply(?, a, a)), b))
1.64/1.85	= { by lemma 13 }
1.64/1.85	  multiply(multiply(?, inverse(multiply(?, a, a)), b), inverse(multiply(?, inverse(multiply(?, a, a)), b)), a)
1.64/1.85	= { by lemma 14 }
1.64/1.85	  multiply(multiply(?, inverse(multiply(?, a, a)), b), multiply(inverse(multiply(?, inverse(multiply(?, a, a)), b)), inverse(multiply(multiply(?, ?, ?), ?, multiply(?, ?, ?))), multiply(?, multiply(?, ?, ?), ?)), a)
1.64/1.85	= { by lemma 20 }
1.64/1.85	  multiply(multiply(?, inverse(multiply(?, a, a)), b), multiply(multiply(inverse(multiply(?, inverse(multiply(?, a, a)), b)), inverse(multiply(a, inverse(a), ?)), ?), multiply(a, inverse(multiply(inverse(a), multiply(inverse(multiply(?, inverse(multiply(?, a, a)), b)), inverse(multiply(a, inverse(a), ?)), ?), ?)), ?), inverse(a)), a)
1.64/1.85	= { by lemma 19 }
1.64/1.85	  multiply(multiply(?, inverse(multiply(?, a, a)), b), multiply(multiply(inverse(multiply(?, inverse(multiply(?, a, a)), b)), inverse(multiply(a, inverse(a), ?)), ?), multiply(a, inverse(inverse(multiply(?, inverse(multiply(?, a, a)), b))), a), inverse(a)), a)
1.64/1.85	= { by lemma 10 }
1.64/1.85	  multiply(multiply(?, inverse(multiply(?, a, a)), b), multiply(multiply(inverse(multiply(?, inverse(multiply(?, a, a)), b)), inverse(?), ?), multiply(a, inverse(inverse(multiply(?, inverse(multiply(?, a, a)), b))), a), inverse(a)), a)
1.64/1.85	= { by lemma 11 }
1.64/1.85	  multiply(multiply(?, inverse(multiply(?, a, a)), b), multiply(inverse(multiply(?, inverse(multiply(?, a, a)), b)), multiply(a, inverse(inverse(multiply(?, inverse(multiply(?, a, a)), b))), a), inverse(a)), a)
1.64/1.85	= { by lemma 18 }
1.64/1.85	  multiply(multiply(?, inverse(multiply(?, a, a)), b), multiply(a, inverse(multiply(?, inverse(multiply(?, a, a)), b)), inverse(a)), a)
1.64/1.85	= { by lemma 16 }
1.64/1.85	  multiply(multiply(?, inverse(multiply(?, a, a)), b), multiply(a, inverse(multiply(?, inverse(multiply(?, a, a)), b)), inverse(a)), inverse(inverse(a)))
1.64/1.85	= { by lemma 18 }
1.64/1.85	  multiply(a, multiply(?, inverse(multiply(?, a, a)), b), inverse(inverse(a)))
1.64/1.85	= { by lemma 16 }
1.64/1.85	  multiply(a, multiply(?, inverse(multiply(?, a, a)), b), a)
1.64/1.85	= { by lemma 15 }
1.64/1.85	  multiply(b, a, a)
1.64/1.85	% SZS output end Proof
1.64/1.85	
1.64/1.85	RESULT: Unsatisfiable (the axioms are contradictory).
1.64/1.85	EOF