0.07/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.14	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.14/0.35	% Computer   : n010.cluster.edu
0.14/0.35	% Model      : x86_64 x86_64
0.14/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.35	% Memory     : 8042.1875MB
0.14/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.35	% CPULimit   : 1200
0.14/0.35	% WCLimit    : 120
0.14/0.35	% DateTime   : Tue Jul 13 14:42:21 EDT 2021
0.14/0.35	% CPUTime    : 
7.78/1.41	% SZS status Theorem
7.78/1.41	
8.41/1.45	% SZS output start Proof
8.41/1.45	Take the following subset of the input axioms:
8.41/1.45	  fof(f01, axiom, ![B, A]: mult(A, ld(A, B))=B).
8.41/1.45	  fof(f02, axiom, ![B, A]: B=ld(A, mult(A, B))).
8.41/1.45	  fof(f03, axiom, ![B, A]: mult(rd(A, B), B)=A).
8.41/1.45	  fof(f04, axiom, ![B, A]: rd(mult(A, B), B)=A).
8.41/1.45	  fof(f05, axiom, ![C, B, A]: mult(mult(mult(A, B), C), B)=mult(A, mult(B, mult(C, B)))).
8.41/1.45	  fof(goals, conjecture, ![X0, X1]: (mult(ld(X1, X1), X0)=X0 & X0=mult(X0, ld(X1, X1)))).
8.41/1.45	
8.41/1.45	Now clausify the problem and encode Horn clauses using encoding 3 of
8.41/1.45	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
8.41/1.45	We repeatedly replace C & s=t => u=v by the two clauses:
8.41/1.45	  fresh(y, y, x1...xn) = u
8.41/1.45	  C => fresh(s, t, x1...xn) = v
8.41/1.45	where fresh is a fresh function symbol and x1..xn are the free
8.41/1.45	variables of u and v.
8.41/1.45	A predicate p(X) is encoded as p(X)=true (this is sound, because the
8.41/1.45	input problem has no model of domain size 1).
8.41/1.45	
8.41/1.45	The encoding turns the above axioms into the following unit equations and goals:
8.41/1.45	
8.41/1.45	Axiom 1 (f01): mult(X, ld(X, Y)) = Y.
8.41/1.45	Axiom 2 (f03): mult(rd(X, Y), Y) = X.
8.41/1.45	Axiom 3 (f02): X = ld(Y, mult(Y, X)).
8.41/1.45	Axiom 4 (f04): rd(mult(X, Y), Y) = X.
8.41/1.45	Axiom 5 (f05): mult(mult(mult(X, Y), Z), Y) = mult(X, mult(Y, mult(Z, Y))).
8.41/1.45	
8.41/1.45	Lemma 6: rd(mult(X, mult(Y, mult(Z, Y))), Y) = mult(mult(X, Y), Z).
8.41/1.45	Proof:
8.41/1.45	  rd(mult(X, mult(Y, mult(Z, Y))), Y)
8.41/1.45	= { by axiom 5 (f05) R->L }
8.41/1.45	  rd(mult(mult(mult(X, Y), Z), Y), Y)
8.41/1.45	= { by axiom 4 (f04) }
8.41/1.45	  mult(mult(X, Y), Z)
8.41/1.45	
8.41/1.45	Lemma 7: rd(mult(X, mult(Y, Z)), Y) = mult(mult(X, Y), rd(Z, Y)).
8.41/1.45	Proof:
8.41/1.45	  rd(mult(X, mult(Y, Z)), Y)
8.41/1.45	= { by axiom 2 (f03) R->L }
8.41/1.45	  rd(mult(X, mult(Y, mult(rd(Z, Y), Y))), Y)
8.41/1.45	= { by lemma 6 }
8.41/1.45	  mult(mult(X, Y), rd(Z, Y))
8.41/1.45	
8.41/1.45	Lemma 8: mult(mult(X, Y), rd(ld(Y, Z), Y)) = rd(mult(X, Z), Y).
8.41/1.45	Proof:
8.41/1.45	  mult(mult(X, Y), rd(ld(Y, Z), Y))
8.41/1.45	= { by lemma 7 R->L }
8.41/1.45	  rd(mult(X, mult(Y, ld(Y, Z))), Y)
8.41/1.45	= { by axiom 1 (f01) }
8.41/1.45	  rd(mult(X, Z), Y)
8.41/1.45	
8.41/1.45	Lemma 9: ld(rd(X, Y), X) = Y.
8.41/1.45	Proof:
8.41/1.45	  ld(rd(X, Y), X)
8.41/1.45	= { by axiom 2 (f03) R->L }
8.41/1.45	  ld(rd(X, Y), mult(rd(X, Y), Y))
8.41/1.45	= { by axiom 3 (f02) R->L }
8.41/1.45	  Y
8.41/1.45	
8.41/1.45	Lemma 10: mult(rd(X, Y), mult(Y, mult(Z, Y))) = mult(mult(X, Z), Y).
8.41/1.45	Proof:
8.41/1.45	  mult(rd(X, Y), mult(Y, mult(Z, Y)))
8.41/1.45	= { by axiom 5 (f05) R->L }
8.41/1.45	  mult(mult(mult(rd(X, Y), Y), Z), Y)
8.41/1.45	= { by axiom 2 (f03) }
8.41/1.45	  mult(mult(X, Z), Y)
8.41/1.45	
8.41/1.45	Lemma 11: ld(rd(X, Y), mult(mult(X, Z), Y)) = mult(Y, mult(Z, Y)).
8.41/1.45	Proof:
8.41/1.46	  ld(rd(X, Y), mult(mult(X, Z), Y))
8.41/1.46	= { by lemma 10 R->L }
8.41/1.46	  ld(rd(X, Y), mult(rd(X, Y), mult(Y, mult(Z, Y))))
8.41/1.46	= { by axiom 3 (f02) R->L }
8.41/1.46	  mult(Y, mult(Z, Y))
8.41/1.46	
8.41/1.46	Lemma 12: mult(X, mult(ld(Y, rd(Y, X)), X)) = X.
8.41/1.46	Proof:
8.41/1.46	  mult(X, mult(ld(Y, rd(Y, X)), X))
8.41/1.46	= { by lemma 11 R->L }
8.41/1.46	  ld(rd(Y, X), mult(mult(Y, ld(Y, rd(Y, X))), X))
8.41/1.46	= { by axiom 1 (f01) }
8.41/1.46	  ld(rd(Y, X), mult(rd(Y, X), X))
8.41/1.46	= { by axiom 3 (f02) R->L }
8.41/1.46	  X
8.41/1.46	
8.41/1.46	Lemma 13: mult(ld(X, rd(X, Y)), Y) = ld(Y, Y).
8.41/1.46	Proof:
8.41/1.46	  mult(ld(X, rd(X, Y)), Y)
8.41/1.46	= { by axiom 3 (f02) }
8.41/1.46	  ld(Y, mult(Y, mult(ld(X, rd(X, Y)), Y)))
8.41/1.46	= { by lemma 12 }
8.41/1.46	  ld(Y, Y)
8.41/1.46	
8.41/1.46	Lemma 14: ld(Z, rd(Z, Y)) = ld(X, rd(X, Y)).
8.41/1.46	Proof:
8.41/1.46	  ld(Z, rd(Z, Y))
8.41/1.46	= { by axiom 4 (f04) R->L }
8.41/1.46	  rd(mult(ld(Z, rd(Z, Y)), Y), Y)
8.41/1.46	= { by lemma 13 }
8.41/1.46	  rd(ld(Y, Y), Y)
8.41/1.46	= { by lemma 13 R->L }
8.41/1.46	  rd(mult(ld(X, rd(X, Y)), Y), Y)
8.41/1.46	= { by axiom 4 (f04) }
8.41/1.46	  ld(X, rd(X, Y))
8.41/1.46	
8.41/1.46	Lemma 15: mult(X, ld(Y, rd(Y, Z))) = rd(X, Z).
8.41/1.46	Proof:
8.41/1.46	  mult(X, ld(Y, rd(Y, Z)))
8.41/1.46	= { by lemma 14 }
8.41/1.46	  mult(X, ld(X, rd(X, Z)))
8.41/1.46	= { by axiom 1 (f01) }
8.41/1.46	  rd(X, Z)
8.41/1.46	
8.41/1.46	Lemma 16: rd(X, ld(Y, X)) = Y.
8.41/1.46	Proof:
8.41/1.46	  rd(X, ld(Y, X))
8.41/1.46	= { by axiom 1 (f01) R->L }
8.41/1.46	  rd(mult(Y, ld(Y, X)), ld(Y, X))
8.41/1.46	= { by axiom 4 (f04) }
8.41/1.46	  Y
8.41/1.46	
8.41/1.46	Lemma 17: rd(X, ld(Y, Z)) = mult(X, ld(Z, Y)).
8.41/1.46	Proof:
8.41/1.46	  rd(X, ld(Y, Z))
8.41/1.46	= { by lemma 15 R->L }
8.41/1.46	  mult(X, ld(Z, rd(Z, ld(Y, Z))))
8.41/1.46	= { by lemma 16 }
8.41/1.46	  mult(X, ld(Z, Y))
8.41/1.46	
8.41/1.46	Lemma 18: rd(ld(X, X), X) = ld(Y, rd(Y, X)).
8.41/1.46	Proof:
8.41/1.46	  rd(ld(X, X), X)
8.41/1.46	= { by lemma 13 R->L }
8.41/1.46	  rd(mult(ld(Y, rd(Y, X)), X), X)
8.41/1.46	= { by axiom 4 (f04) }
8.41/1.46	  ld(Y, rd(Y, X))
8.41/1.46	
8.41/1.46	Lemma 19: mult(mult(X, ld(Y, Y)), Y) = mult(rd(X, Y), mult(Y, Y)).
8.41/1.46	Proof:
8.41/1.46	  mult(mult(X, ld(Y, Y)), Y)
8.41/1.46	= { by lemma 9 R->L }
8.41/1.46	  mult(mult(X, ld(Y, Y)), ld(rd(Z, Y), Z))
8.41/1.46	= { by lemma 17 R->L }
8.41/1.46	  rd(mult(X, ld(Y, Y)), ld(Z, rd(Z, Y)))
8.41/1.46	= { by lemma 18 R->L }
8.41/1.46	  rd(mult(X, ld(Y, Y)), rd(ld(Y, Y), Y))
8.41/1.46	= { by axiom 2 (f03) R->L }
8.41/1.46	  rd(mult(X, mult(rd(ld(Y, Y), Y), Y)), rd(ld(Y, Y), Y))
8.41/1.46	= { by lemma 7 }
8.41/1.46	  mult(mult(X, rd(ld(Y, Y), Y)), rd(Y, rd(ld(Y, Y), Y)))
8.41/1.46	= { by lemma 18 }
8.41/1.46	  mult(mult(X, ld(W, rd(W, Y))), rd(Y, rd(ld(Y, Y), Y)))
8.41/1.46	= { by lemma 15 }
8.41/1.46	  mult(rd(X, Y), rd(Y, rd(ld(Y, Y), Y)))
8.41/1.46	= { by lemma 18 }
8.41/1.46	  mult(rd(X, Y), rd(Y, ld(V, rd(V, Y))))
8.41/1.46	= { by lemma 17 }
8.41/1.46	  mult(rd(X, Y), mult(Y, ld(rd(V, Y), V)))
8.41/1.46	= { by lemma 9 }
8.41/1.46	  mult(rd(X, Y), mult(Y, Y))
8.41/1.46	
8.41/1.46	Lemma 20: mult(X, rd(Y, Y)) = mult(X, ld(Y, Y)).
8.41/1.46	Proof:
8.41/1.46	  mult(X, rd(Y, Y))
8.41/1.46	= { by axiom 3 (f02) }
8.41/1.46	  mult(X, rd(ld(Y, mult(Y, Y)), Y))
8.41/1.46	= { by axiom 2 (f03) R->L }
8.41/1.46	  mult(mult(rd(X, Y), Y), rd(ld(Y, mult(Y, Y)), Y))
8.41/1.46	= { by lemma 8 }
8.41/1.46	  rd(mult(rd(X, Y), mult(Y, Y)), Y)
8.41/1.46	= { by lemma 19 R->L }
8.41/1.46	  rd(mult(mult(X, ld(Y, Y)), Y), Y)
8.41/1.46	= { by axiom 4 (f04) }
8.41/1.46	  mult(X, ld(Y, Y))
8.41/1.46	
8.41/1.46	Lemma 21: rd(X, X) = ld(X, X).
8.41/1.46	Proof:
8.41/1.46	  rd(X, X)
8.41/1.46	= { by axiom 3 (f02) }
8.41/1.46	  ld(Y, mult(Y, rd(X, X)))
8.41/1.46	= { by lemma 20 }
8.41/1.46	  ld(Y, mult(Y, ld(X, X)))
8.41/1.46	= { by axiom 3 (f02) R->L }
8.41/1.46	  ld(X, X)
8.41/1.46	
8.41/1.46	Lemma 22: mult(ld(X, X), X) = X.
8.41/1.46	Proof:
8.41/1.46	  mult(ld(X, X), X)
8.41/1.46	= { by lemma 21 R->L }
8.41/1.46	  mult(rd(X, X), X)
8.41/1.46	= { by axiom 2 (f03) }
8.41/1.46	  X
8.41/1.46	
8.41/1.46	Lemma 23: ld(X, rd(X, Y)) = ld(Y, ld(Y, Y)).
8.41/1.46	Proof:
8.41/1.46	  ld(X, rd(X, Y))
8.41/1.46	= { by lemma 14 }
8.41/1.46	  ld(Y, rd(Y, Y))
8.41/1.46	= { by lemma 21 }
8.41/1.46	  ld(Y, ld(Y, Y))
8.41/1.46	
8.41/1.46	Lemma 24: ld(mult(X, Y), X) = ld(Z, rd(Z, Y)).
8.41/1.46	Proof:
8.41/1.46	  ld(mult(X, Y), X)
8.41/1.46	= { by axiom 4 (f04) R->L }
8.41/1.46	  ld(mult(X, Y), rd(mult(X, Y), Y))
8.41/1.46	= { by lemma 14 R->L }
8.41/1.46	  ld(Z, rd(Z, Y))
8.41/1.46	
8.41/1.46	Lemma 25: ld(mult(X, Y), rd(mult(X, Z), Y)) = rd(ld(Y, Z), Y).
8.41/1.46	Proof:
8.41/1.46	  ld(mult(X, Y), rd(mult(X, Z), Y))
8.41/1.46	= { by lemma 8 R->L }
8.41/1.46	  ld(mult(X, Y), mult(mult(X, Y), rd(ld(Y, Z), Y)))
8.41/1.46	= { by axiom 3 (f02) R->L }
8.41/1.46	  rd(ld(Y, Z), Y)
8.41/1.46	
8.41/1.46	Lemma 26: mult(X, mult(ld(X, Y), mult(Z, ld(X, Y)))) = mult(mult(Y, Z), ld(X, Y)).
8.41/1.46	Proof:
8.41/1.46	  mult(X, mult(ld(X, Y), mult(Z, ld(X, Y))))
8.41/1.46	= { by axiom 5 (f05) R->L }
8.41/1.46	  mult(mult(mult(X, ld(X, Y)), Z), ld(X, Y))
8.41/1.46	= { by axiom 1 (f01) }
8.41/1.46	  mult(mult(Y, Z), ld(X, Y))
8.41/1.46	
8.41/1.46	Lemma 27: ld(X, mult(mult(Y, Z), ld(X, Y))) = mult(ld(X, Y), mult(Z, ld(X, Y))).
8.41/1.46	Proof:
8.41/1.46	  ld(X, mult(mult(Y, Z), ld(X, Y)))
8.41/1.46	= { by lemma 26 R->L }
8.41/1.46	  ld(X, mult(X, mult(ld(X, Y), mult(Z, ld(X, Y)))))
8.41/1.46	= { by axiom 3 (f02) R->L }
8.41/1.46	  mult(ld(X, Y), mult(Z, ld(X, Y)))
8.41/1.46	
8.41/1.46	Lemma 28: mult(ld(ld(X, X), Y), ld(X, X)) = mult(ld(X, X), mult(Y, ld(X, X))).
8.41/1.46	Proof:
8.41/1.46	  mult(ld(ld(X, X), Y), ld(X, X))
8.41/1.46	= { by lemma 17 R->L }
8.41/1.46	  rd(ld(ld(X, X), Y), ld(X, X))
8.41/1.46	= { by lemma 13 R->L }
8.41/1.46	  rd(ld(mult(ld(Z, rd(Z, X)), X), Y), ld(X, X))
8.41/1.46	= { by lemma 13 R->L }
8.41/1.46	  rd(ld(mult(ld(Z, rd(Z, X)), X), Y), mult(ld(Z, rd(Z, X)), X))
8.41/1.46	= { by lemma 25 R->L }
8.41/1.46	  ld(mult(X, mult(ld(Z, rd(Z, X)), X)), rd(mult(X, Y), mult(ld(Z, rd(Z, X)), X)))
8.41/1.46	= { by lemma 12 }
8.41/1.46	  ld(X, rd(mult(X, Y), mult(ld(Z, rd(Z, X)), X)))
8.41/1.46	= { by lemma 13 }
8.41/1.46	  ld(X, rd(mult(X, Y), ld(X, X)))
8.41/1.46	= { by lemma 17 }
8.41/1.46	  ld(X, mult(mult(X, Y), ld(X, X)))
8.41/1.46	= { by lemma 27 }
8.41/1.46	  mult(ld(X, X), mult(Y, ld(X, X)))
8.41/1.46	
8.41/1.46	Lemma 29: mult(mult(X, ld(Y, Y)), ld(Y, Y)) = X.
8.41/1.46	Proof:
8.41/1.46	  mult(mult(X, ld(Y, Y)), ld(Y, Y))
8.41/1.46	= { by lemma 10 R->L }
8.41/1.46	  mult(rd(X, ld(Y, Y)), mult(ld(Y, Y), mult(ld(Y, Y), ld(Y, Y))))
8.41/1.46	= { by axiom 2 (f03) R->L }
8.41/1.46	  mult(rd(X, ld(Y, Y)), mult(ld(Y, Y), mult(ld(Y, Y), mult(rd(ld(Y, Y), ld(Y, Y)), ld(Y, Y)))))
8.41/1.46	= { by lemma 28 R->L }
8.41/1.46	  mult(rd(X, ld(Y, Y)), mult(ld(Y, Y), mult(ld(ld(Y, Y), rd(ld(Y, Y), ld(Y, Y))), ld(Y, Y))))
8.41/1.46	= { by lemma 12 }
8.41/1.46	  mult(rd(X, ld(Y, Y)), ld(Y, Y))
8.41/1.46	= { by axiom 2 (f03) }
8.41/1.46	  X
8.41/1.46	
8.41/1.46	Lemma 30: mult(ld(X, X), mult(mult(ld(X, X), Y), ld(X, X))) = mult(Y, ld(X, X)).
8.41/1.46	Proof:
8.41/1.46	  mult(ld(X, X), mult(mult(ld(X, X), Y), ld(X, X)))
8.41/1.46	= { by lemma 28 R->L }
8.41/1.46	  mult(ld(ld(X, X), mult(ld(X, X), Y)), ld(X, X))
8.41/1.46	= { by axiom 3 (f02) R->L }
8.41/1.46	  mult(Y, ld(X, X))
8.41/1.46	
8.41/1.46	Lemma 31: rd(ld(X, ld(Y, Z)), X) = ld(mult(Y, X), rd(Z, X)).
8.41/1.46	Proof:
8.41/1.46	  rd(ld(X, ld(Y, Z)), X)
8.41/1.46	= { by lemma 25 R->L }
8.41/1.46	  ld(mult(Y, X), rd(mult(Y, ld(Y, Z)), X))
8.41/1.46	= { by axiom 1 (f01) }
8.41/1.46	  ld(mult(Y, X), rd(Z, X))
8.41/1.46	
8.41/1.46	Lemma 32: mult(ld(X, X), ld(Y, Y)) = ld(Y, Y).
8.41/1.46	Proof:
8.41/1.46	  mult(ld(X, X), ld(Y, Y))
8.41/1.46	= { by lemma 29 R->L }
8.41/1.46	  mult(ld(X, X), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 21 R->L }
8.41/1.46	  mult(rd(X, X), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 15 R->L }
8.41/1.46	  mult(mult(X, ld(Z, rd(Z, X))), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 18 R->L }
8.41/1.46	  mult(mult(X, rd(ld(X, X), X)), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 15 R->L }
8.41/1.46	  mult(mult(X, mult(ld(X, X), ld(W, rd(W, X)))), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 24 R->L }
8.41/1.46	  mult(mult(X, mult(ld(X, X), ld(mult(V, X), V))), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by axiom 1 (f01) R->L }
8.41/1.46	  mult(mult(X, mult(ld(X, X), ld(mult(V, X), mult(mult(V, X), ld(mult(V, X), V))))), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 27 }
8.41/1.46	  mult(mult(X, mult(ld(X, X), mult(ld(mult(V, X), V), mult(X, ld(mult(V, X), V))))), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 24 }
8.41/1.46	  mult(mult(X, mult(ld(X, X), mult(ld(mult(V, X), V), mult(X, ld(U, rd(U, X)))))), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 24 }
8.41/1.46	  mult(mult(X, mult(ld(X, X), mult(ld(T, rd(T, X)), mult(X, ld(U, rd(U, X)))))), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 15 }
8.41/1.46	  mult(mult(X, mult(ld(X, X), mult(ld(T, rd(T, X)), rd(X, X)))), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 23 }
8.41/1.46	  mult(mult(X, mult(ld(X, X), mult(ld(X, ld(X, X)), rd(X, X)))), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 20 }
8.41/1.46	  mult(mult(X, mult(ld(X, X), mult(ld(X, ld(X, X)), ld(X, X)))), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 23 R->L }
8.41/1.46	  mult(mult(X, mult(ld(X, X), mult(ld(S, rd(S, X)), ld(X, X)))), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 26 }
8.41/1.46	  mult(mult(mult(X, ld(S, rd(S, X))), ld(X, X)), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 15 }
8.41/1.46	  mult(mult(rd(X, X), ld(X, X)), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 21 }
8.41/1.46	  mult(mult(ld(X, X), ld(X, X)), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 17 R->L }
8.41/1.46	  mult(rd(ld(X, X), ld(X, X)), mult(mult(ld(Y, Y), ld(X, X)), ld(X, X)))
8.41/1.46	= { by lemma 30 R->L }
8.41/1.46	  mult(rd(ld(X, X), ld(X, X)), mult(ld(X, X), mult(mult(ld(X, X), mult(ld(Y, Y), ld(X, X))), ld(X, X))))
8.41/1.46	= { by lemma 10 }
8.41/1.46	  mult(mult(ld(X, X), mult(ld(X, X), mult(ld(Y, Y), ld(X, X)))), ld(X, X))
8.41/1.46	= { by lemma 22 R->L }
8.41/1.46	  mult(mult(ld(X, X), mult(ld(mult(ld(X, X), mult(ld(Y, Y), ld(X, X))), mult(ld(X, X), mult(ld(Y, Y), ld(X, X)))), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.46	= { by lemma 29 R->L }
8.41/1.46	  mult(mult(ld(X, X), mult(ld(mult(ld(X, X), mult(ld(Y, Y), ld(X, X))), mult(ld(X, X), mult(ld(Y, Y), mult(mult(ld(X, X), ld(Y, Y)), ld(Y, Y))))), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by axiom 5 (f05) R->L }
8.41/1.47	  mult(mult(ld(X, X), mult(ld(mult(ld(X, X), mult(ld(Y, Y), ld(X, X))), mult(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by lemma 17 R->L }
8.41/1.47	  mult(mult(ld(X, X), mult(ld(mult(ld(X, X), mult(ld(Y, Y), ld(X, X))), rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by lemma 29 R->L }
8.41/1.47	  mult(mult(ld(X, X), mult(ld(mult(mult(mult(ld(X, X), ld(Y, Y)), ld(Y, Y)), mult(ld(Y, Y), ld(X, X))), rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by lemma 6 R->L }
8.41/1.47	  mult(mult(ld(X, X), mult(ld(rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), mult(mult(ld(Y, Y), ld(X, X)), ld(Y, Y)))), ld(Y, Y)), rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by lemma 30 }
8.41/1.47	  mult(mult(ld(X, X), mult(ld(rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y)), rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by lemma 17 }
8.41/1.47	  mult(mult(ld(X, X), mult(ld(mult(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y)), rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by lemma 31 R->L }
8.41/1.47	  mult(mult(ld(X, X), mult(rd(ld(ld(Y, Y), ld(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y)), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by lemma 21 R->L }
8.41/1.47	  mult(mult(ld(X, X), mult(rd(ld(ld(Y, Y), rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y)), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by axiom 1 (f01) R->L }
8.41/1.47	  mult(mult(ld(X, X), mult(rd(ld(ld(Y, Y), rd(mult(mult(mult(ld(X, X), ld(Y, Y)), ld(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y)))), mult(ld(X, X), ld(Y, Y))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y)), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by lemma 19 }
8.41/1.47	  mult(mult(ld(X, X), mult(rd(ld(ld(Y, Y), rd(mult(rd(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y)))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y)), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by lemma 21 }
8.41/1.47	  mult(mult(ld(X, X), mult(rd(ld(ld(Y, Y), rd(mult(ld(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y)))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y)), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by axiom 4 (f04) }
8.41/1.47	  mult(mult(ld(X, X), mult(rd(ld(ld(Y, Y), ld(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y)))), ld(Y, Y)), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by lemma 31 }
8.41/1.47	  mult(mult(ld(X, X), mult(ld(mult(mult(ld(X, X), ld(Y, Y)), ld(Y, Y)), rd(mult(ld(X, X), ld(Y, Y)), ld(Y, Y))), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by lemma 29 }
8.41/1.47	  mult(mult(ld(X, X), mult(ld(ld(X, X), rd(mult(ld(X, X), ld(Y, Y)), ld(Y, Y))), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by axiom 4 (f04) }
8.41/1.47	  mult(mult(ld(X, X), mult(ld(ld(X, X), ld(X, X)), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by lemma 21 R->L }
8.41/1.47	  mult(mult(ld(X, X), mult(rd(ld(X, X), ld(X, X)), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))), ld(X, X))
8.41/1.47	= { by lemma 10 }
8.41/1.47	  mult(mult(ld(X, X), mult(mult(ld(X, X), ld(Y, Y)), ld(X, X))), ld(X, X))
8.41/1.47	= { by lemma 17 R->L }
8.41/1.47	  rd(mult(ld(X, X), mult(mult(ld(X, X), ld(Y, Y)), ld(X, X))), ld(X, X))
8.41/1.47	= { by lemma 28 R->L }
8.41/1.47	  rd(mult(ld(ld(X, X), mult(ld(X, X), ld(Y, Y))), ld(X, X)), ld(X, X))
8.41/1.47	= { by axiom 4 (f04) }
8.41/1.47	  ld(ld(X, X), mult(ld(X, X), ld(Y, Y)))
8.41/1.47	= { by axiom 3 (f02) R->L }
8.41/1.47	  ld(Y, Y)
8.41/1.47	
8.41/1.47	Goal 1 (goals): tuple(mult(ld(x1_2, x1_2), x0_2), x0) = tuple(x0_2, mult(x0, ld(x1, x1))).
8.41/1.47	Proof:
8.41/1.47	  tuple(mult(ld(x1_2, x1_2), x0_2), x0)
8.41/1.47	= { by axiom 4 (f04) R->L }
8.41/1.47	  tuple(mult(rd(mult(ld(x1_2, x1_2), ld(X, X)), ld(X, X)), x0_2), x0)
8.41/1.47	= { by lemma 32 }
8.41/1.47	  tuple(mult(rd(ld(X, X), ld(X, X)), x0_2), x0)
8.41/1.47	= { by lemma 32 R->L }
8.41/1.47	  tuple(mult(rd(mult(ld(x0_2, x0_2), ld(X, X)), ld(X, X)), x0_2), x0)
8.41/1.47	= { by axiom 4 (f04) }
8.41/1.47	  tuple(mult(ld(x0_2, x0_2), x0_2), x0)
8.41/1.47	= { by lemma 22 }
8.41/1.47	  tuple(x0_2, x0)
8.41/1.47	= { by axiom 2 (f03) R->L }
8.41/1.47	  tuple(x0_2, mult(rd(x0, ld(x0, x0)), ld(x0, x0)))
8.41/1.47	= { by lemma 32 R->L }
8.41/1.47	  tuple(x0_2, mult(rd(x0, mult(ld(x1, x1), ld(x0, x0))), ld(x0, x0)))
8.41/1.47	= { by lemma 17 R->L }
8.41/1.47	  tuple(x0_2, mult(rd(x0, rd(ld(x1, x1), ld(x0, x0))), ld(x0, x0)))
8.41/1.47	= { by lemma 16 R->L }
8.41/1.47	  tuple(x0_2, rd(x0, ld(mult(rd(x0, rd(ld(x1, x1), ld(x0, x0))), ld(x0, x0)), x0)))
8.41/1.47	= { by axiom 2 (f03) R->L }
8.41/1.47	  tuple(x0_2, rd(x0, ld(mult(rd(x0, rd(ld(x1, x1), ld(x0, x0))), ld(x0, mult(rd(x0, rd(ld(x1, x1), ld(x0, x0))), rd(ld(x1, x1), ld(x0, x0))))), x0)))
8.41/1.47	= { by lemma 17 R->L }
8.41/1.47	  tuple(x0_2, rd(x0, ld(rd(rd(x0, rd(ld(x1, x1), ld(x0, x0))), ld(mult(rd(x0, rd(ld(x1, x1), ld(x0, x0))), rd(ld(x1, x1), ld(x0, x0))), x0)), x0)))
8.41/1.47	= { by axiom 1 (f01) R->L }
8.41/1.47	  tuple(x0_2, rd(x0, ld(rd(rd(x0, rd(ld(x1, x1), ld(x0, x0))), ld(mult(rd(x0, rd(ld(x1, x1), ld(x0, x0))), rd(ld(x1, x1), ld(x0, x0))), x0)), mult(mult(rd(x0, rd(ld(x1, x1), ld(x0, x0))), rd(ld(x1, x1), ld(x0, x0))), ld(mult(rd(x0, rd(ld(x1, x1), ld(x0, x0))), rd(ld(x1, x1), ld(x0, x0))), x0)))))
8.41/1.47	= { by lemma 11 }
8.41/1.47	  tuple(x0_2, rd(x0, mult(ld(mult(rd(x0, rd(ld(x1, x1), ld(x0, x0))), rd(ld(x1, x1), ld(x0, x0))), x0), mult(rd(ld(x1, x1), ld(x0, x0)), ld(mult(rd(x0, rd(ld(x1, x1), ld(x0, x0))), rd(ld(x1, x1), ld(x0, x0))), x0)))))
8.41/1.47	= { by axiom 2 (f03) }
8.41/1.47	  tuple(x0_2, rd(x0, mult(ld(x0, x0), mult(rd(ld(x1, x1), ld(x0, x0)), ld(mult(rd(x0, rd(ld(x1, x1), ld(x0, x0))), rd(ld(x1, x1), ld(x0, x0))), x0)))))
8.41/1.47	= { by axiom 2 (f03) }
8.41/1.47	  tuple(x0_2, rd(x0, mult(ld(x0, x0), mult(rd(ld(x1, x1), ld(x0, x0)), ld(x0, x0)))))
8.41/1.47	= { by axiom 2 (f03) }
8.41/1.47	  tuple(x0_2, rd(x0, mult(ld(x0, x0), ld(x1, x1))))
8.41/1.47	= { by lemma 32 }
8.41/1.47	  tuple(x0_2, rd(x0, ld(x1, x1)))
8.41/1.47	= { by lemma 17 }
8.41/1.47	  tuple(x0_2, mult(x0, ld(x1, x1)))
8.41/1.47	% SZS output end Proof
8.41/1.47	
8.41/1.47	RESULT: Theorem (the conjecture is true).
8.41/1.48	EOF