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
0.12/0.34	% Computer   : n008.cluster.edu
0.12/0.34	% Model      : x86_64 x86_64
0.12/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory     : 8042.1875MB
0.12/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 180
0.12/0.34	% DateTime   : Thu Aug 29 12:20:08 EDT 2019
0.12/0.34	% CPUTime    : 
71.08/71.32	% SZS status Theorem
71.08/71.32	
71.08/71.32	% SZS output start Proof
71.08/71.32	Take the following subset of the input axioms:
71.10/71.33	  fof(modus_ponens_for_nand, axiom, ![Q, P, R]: ((p(P) & p(nand(P, nand(Q, R)))) => p(R))).
71.10/71.33	  fof(tautology, conjecture, ![A, B]: p(nand(nand(A, nand(B, B)), nand(nand(nand(B, B), nand(nand(A, A), nand(A, A))), nand(nand(B, B), nand(nand(A, A), nand(A, A))))))).
71.10/71.33	  fof(wajsbergs_axiom, axiom, ![A, B, C, D]: p(nand(nand(A, nand(B, C)), nand(nand(nand(D, C), nand(nand(A, D), nand(A, D))), nand(A, nand(A, B)))))).
71.10/71.33	
71.10/71.33	Now clausify the problem and encode Horn clauses using encoding 3 of
71.10/71.33	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
71.10/71.33	We repeatedly replace C & s=t => u=v by the two clauses:
71.10/71.33	  fresh(y, y, x1...xn) = u
71.10/71.33	  C => fresh(s, t, x1...xn) = v
71.10/71.33	where fresh is a fresh function symbol and x1..xn are the free
71.10/71.33	variables of u and v.
71.10/71.33	A predicate p(X) is encoded as p(X)=true (this is sound, because the
71.10/71.33	input problem has no model of domain size 1).
71.10/71.33	
71.10/71.33	The encoding turns the above axioms into the following unit equations and goals:
71.10/71.33	
71.10/71.33	Axiom 1 (modus_ponens_for_nand): fresh(X, X, Y, Z) = p(Z).
71.10/71.33	Axiom 2 (modus_ponens_for_nand): fresh2(X, X, Y) = true.
71.10/71.33	Axiom 3 (wajsbergs_axiom): p(nand(nand(X, nand(Y, Z)), nand(nand(nand(W, Z), nand(nand(X, W), nand(X, W))), nand(X, nand(X, Y))))) = true.
71.10/71.35	Axiom 4 (modus_ponens_for_nand): fresh(p(nand(X, nand(Y, Z))), true, X, Z) = fresh2(p(X), true, Z).
71.10/71.35	
71.10/71.35	Lemma 5: fresh2(p(nand(X, nand(Y, Z))), true, nand(X, nand(X, Y))) = p(nand(X, nand(X, Y))).
71.10/71.35	Proof:
71.10/71.35	  fresh2(p(nand(X, nand(Y, Z))), true, nand(X, nand(X, Y)))
71.10/71.35	= { by axiom 4 (modus_ponens_for_nand) }
71.10/71.35	  fresh(p(nand(nand(X, nand(Y, Z)), nand(nand(nand(?, Z), nand(nand(X, ?), nand(X, ?))), nand(X, nand(X, Y))))), true, nand(X, nand(Y, Z)), nand(X, nand(X, Y)))
71.10/71.35	= { by axiom 3 (wajsbergs_axiom) }
71.10/71.35	  fresh(true, true, nand(X, nand(Y, Z)), nand(X, nand(X, Y)))
71.10/71.35	= { by axiom 1 (modus_ponens_for_nand) }
71.10/71.35	  p(nand(X, nand(X, Y)))
71.10/71.35	
71.10/71.35	Lemma 6: p(nand(nand(X, nand(Y, Z)), nand(nand(X, nand(Y, Z)), nand(nand(W, Z), nand(nand(X, W), nand(X, W)))))) = true.
71.10/71.35	Proof:
71.10/71.35	  p(nand(nand(X, nand(Y, Z)), nand(nand(X, nand(Y, Z)), nand(nand(W, Z), nand(nand(X, W), nand(X, W))))))
71.10/71.35	= { by lemma 5 }
71.10/71.35	  fresh2(p(nand(nand(X, nand(Y, Z)), nand(nand(nand(W, Z), nand(nand(X, W), nand(X, W))), nand(X, nand(X, Y))))), true, nand(nand(X, nand(Y, Z)), nand(nand(X, nand(Y, Z)), nand(nand(W, Z), nand(nand(X, W), nand(X, W))))))
71.10/71.35	= { by axiom 3 (wajsbergs_axiom) }
71.10/71.35	  fresh2(true, true, nand(nand(X, nand(Y, Z)), nand(nand(X, nand(Y, Z)), nand(nand(W, Z), nand(nand(X, W), nand(X, W))))))
71.10/71.35	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.35	  true
71.10/71.35	
71.10/71.35	Lemma 7: fresh2(p(nand(X, nand(Y, Z))), true, nand(nand(W, Z), nand(nand(X, W), nand(X, W)))) = p(nand(nand(W, Z), nand(nand(X, W), nand(X, W)))).
71.10/71.35	Proof:
71.10/71.35	  fresh2(p(nand(X, nand(Y, Z))), true, nand(nand(W, Z), nand(nand(X, W), nand(X, W))))
71.10/71.35	= { by axiom 4 (modus_ponens_for_nand) }
71.10/71.35	  fresh(p(nand(nand(X, nand(Y, Z)), nand(nand(X, nand(Y, Z)), nand(nand(W, Z), nand(nand(X, W), nand(X, W)))))), true, nand(X, nand(Y, Z)), nand(nand(W, Z), nand(nand(X, W), nand(X, W))))
71.10/71.35	= { by lemma 6 }
71.10/71.35	  fresh(true, true, nand(X, nand(Y, Z)), nand(nand(W, Z), nand(nand(X, W), nand(X, W))))
71.10/71.35	= { by axiom 1 (modus_ponens_for_nand) }
71.10/71.35	  p(nand(nand(W, Z), nand(nand(X, W), nand(X, W))))
71.10/71.35	
71.10/71.35	Lemma 8: fresh2(p(nand(X, nand(Y, nand(Y, Z)))), true, nand(nand(Y, nand(Z, W)), X)) = p(nand(nand(Y, nand(Z, W)), X)).
71.10/71.35	Proof:
71.10/71.35	  fresh2(p(nand(X, nand(Y, nand(Y, Z)))), true, nand(nand(Y, nand(Z, W)), X))
71.10/71.35	= { by axiom 4 (modus_ponens_for_nand) }
71.10/71.35	  fresh(p(nand(nand(X, nand(Y, nand(Y, Z))), nand(nand(nand(Y, nand(Z, W)), X), nand(nand(Y, nand(Z, W)), X)))), true, nand(X, nand(Y, nand(Y, Z))), nand(nand(Y, nand(Z, W)), X))
71.10/71.35	= { by lemma 7 }
71.10/71.35	  fresh(fresh2(p(nand(nand(Y, nand(Z, W)), nand(nand(nand(?, W), nand(nand(Y, ?), nand(Y, ?))), nand(Y, nand(Y, Z))))), true, nand(nand(X, nand(Y, nand(Y, Z))), nand(nand(nand(Y, nand(Z, W)), X), nand(nand(Y, nand(Z, W)), X)))), true, nand(X, nand(Y, nand(Y, Z))), nand(nand(Y, nand(Z, W)), X))
71.10/71.35	= { by axiom 3 (wajsbergs_axiom) }
71.10/71.35	  fresh(fresh2(true, true, nand(nand(X, nand(Y, nand(Y, Z))), nand(nand(nand(Y, nand(Z, W)), X), nand(nand(Y, nand(Z, W)), X)))), true, nand(X, nand(Y, nand(Y, Z))), nand(nand(Y, nand(Z, W)), X))
71.10/71.35	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.35	  fresh(true, true, nand(X, nand(Y, nand(Y, Z))), nand(nand(Y, nand(Z, W)), X))
71.10/71.35	= { by axiom 1 (modus_ponens_for_nand) }
71.10/71.35	  p(nand(nand(Y, nand(Z, W)), X))
71.10/71.35	
71.10/71.35	Lemma 9: p(nand(nand(X, nand(Y, Z)), nand(nand(X, nand(Y, Z)), nand(X, nand(Y, Z))))) = true.
71.10/71.35	Proof:
71.10/71.35	  p(nand(nand(X, nand(Y, Z)), nand(nand(X, nand(Y, Z)), nand(X, nand(Y, Z)))))
71.10/71.35	= { by lemma 5 }
71.10/71.35	  fresh2(p(nand(nand(X, nand(Y, Z)), nand(nand(X, nand(Y, Z)), nand(nand(?, Z), nand(nand(X, ?), nand(X, ?)))))), true, nand(nand(X, nand(Y, Z)), nand(nand(X, nand(Y, Z)), nand(X, nand(Y, Z)))))
71.10/71.35	= { by lemma 6 }
71.10/71.35	  fresh2(true, true, nand(nand(X, nand(Y, Z)), nand(nand(X, nand(Y, Z)), nand(X, nand(Y, Z)))))
71.10/71.35	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.35	  true
71.10/71.35	
71.10/71.35	Lemma 10: fresh2(p(nand(X, nand(Y, nand(Z, W)))), true, nand(nand(Y, nand(Z, W)), X)) = p(nand(nand(Y, nand(Z, W)), X)).
71.10/71.35	Proof:
71.10/71.35	  fresh2(p(nand(X, nand(Y, nand(Z, W)))), true, nand(nand(Y, nand(Z, W)), X))
71.10/71.35	= { by axiom 4 (modus_ponens_for_nand) }
71.10/71.35	  fresh(p(nand(nand(X, nand(Y, nand(Z, W))), nand(nand(nand(Y, nand(Z, W)), X), nand(nand(Y, nand(Z, W)), X)))), true, nand(X, nand(Y, nand(Z, W))), nand(nand(Y, nand(Z, W)), X))
71.10/71.35	= { by lemma 7 }
71.10/71.35	  fresh(fresh2(p(nand(nand(Y, nand(Z, W)), nand(nand(Y, nand(Z, W)), nand(Y, nand(Z, W))))), true, nand(nand(X, nand(Y, nand(Z, W))), nand(nand(nand(Y, nand(Z, W)), X), nand(nand(Y, nand(Z, W)), X)))), true, nand(X, nand(Y, nand(Z, W))), nand(nand(Y, nand(Z, W)), X))
71.10/71.35	= { by lemma 9 }
71.10/71.35	  fresh(fresh2(true, true, nand(nand(X, nand(Y, nand(Z, W))), nand(nand(nand(Y, nand(Z, W)), X), nand(nand(Y, nand(Z, W)), X)))), true, nand(X, nand(Y, nand(Z, W))), nand(nand(Y, nand(Z, W)), X))
71.10/71.35	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.35	  fresh(true, true, nand(X, nand(Y, nand(Z, W))), nand(nand(Y, nand(Z, W)), X))
71.10/71.35	= { by axiom 1 (modus_ponens_for_nand) }
71.10/71.35	  p(nand(nand(Y, nand(Z, W)), X))
71.10/71.35	
71.10/71.35	Lemma 11: p(nand(nand(nand(X, nand(Y, Z)), nand(X, nand(Y, Z))), nand(X, nand(Y, Z)))) = true.
71.10/71.35	Proof:
71.10/71.35	  p(nand(nand(nand(X, nand(Y, Z)), nand(X, nand(Y, Z))), nand(X, nand(Y, Z))))
71.10/71.35	= { by lemma 10 }
71.10/71.35	  fresh2(p(nand(nand(X, nand(Y, Z)), nand(nand(X, nand(Y, Z)), nand(X, nand(Y, Z))))), true, nand(nand(nand(X, nand(Y, Z)), nand(X, nand(Y, Z))), nand(X, nand(Y, Z))))
71.10/71.35	= { by lemma 9 }
71.10/71.35	  fresh2(true, true, nand(nand(nand(X, nand(Y, Z)), nand(X, nand(Y, Z))), nand(X, nand(Y, Z))))
71.10/71.35	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.35	  true
71.10/71.35	
71.10/71.35	Lemma 12: fresh2(p(nand(X, nand(Y, Z))), true, nand(X, nand(X, X))) = p(nand(X, nand(X, X))).
71.10/71.35	Proof:
71.10/71.35	  fresh2(p(nand(X, nand(Y, Z))), true, nand(X, nand(X, X)))
71.10/71.35	= { by axiom 4 (modus_ponens_for_nand) }
71.10/71.35	  fresh(p(nand(nand(X, nand(Y, Z)), nand(nand(X, nand(X, X)), nand(X, nand(X, X))))), true, nand(X, nand(Y, Z)), nand(X, nand(X, X)))
71.10/71.35	= { by lemma 8 }
71.10/71.35	  fresh(fresh2(p(nand(nand(nand(X, nand(X, X)), nand(X, nand(X, X))), nand(X, nand(X, Y)))), true, nand(nand(X, nand(Y, Z)), nand(nand(X, nand(X, X)), nand(X, nand(X, X))))), true, nand(X, nand(Y, Z)), nand(X, nand(X, X)))
71.10/71.35	= { by lemma 10 }
71.10/71.35	  fresh(fresh2(fresh2(p(nand(nand(X, nand(X, Y)), nand(nand(X, nand(X, X)), nand(X, nand(X, X))))), true, nand(nand(nand(X, nand(X, X)), nand(X, nand(X, X))), nand(X, nand(X, Y)))), true, nand(nand(X, nand(Y, Z)), nand(nand(X, nand(X, X)), nand(X, nand(X, X))))), true, nand(X, nand(Y, Z)), nand(X, nand(X, X)))
71.10/71.35	= { by lemma 8 }
71.10/71.35	  fresh(fresh2(fresh2(fresh2(p(nand(nand(nand(X, nand(X, X)), nand(X, nand(X, X))), nand(X, nand(X, X)))), true, nand(nand(X, nand(X, Y)), nand(nand(X, nand(X, X)), nand(X, nand(X, X))))), true, nand(nand(nand(X, nand(X, X)), nand(X, nand(X, X))), nand(X, nand(X, Y)))), true, nand(nand(X, nand(Y, Z)), nand(nand(X, nand(X, X)), nand(X, nand(X, X))))), true, nand(X, nand(Y, Z)), nand(X, nand(X, X)))
71.10/71.35	= { by lemma 11 }
71.10/71.35	  fresh(fresh2(fresh2(fresh2(true, true, nand(nand(X, nand(X, Y)), nand(nand(X, nand(X, X)), nand(X, nand(X, X))))), true, nand(nand(nand(X, nand(X, X)), nand(X, nand(X, X))), nand(X, nand(X, Y)))), true, nand(nand(X, nand(Y, Z)), nand(nand(X, nand(X, X)), nand(X, nand(X, X))))), true, nand(X, nand(Y, Z)), nand(X, nand(X, X)))
71.10/71.35	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.35	  fresh(fresh2(fresh2(true, true, nand(nand(nand(X, nand(X, X)), nand(X, nand(X, X))), nand(X, nand(X, Y)))), true, nand(nand(X, nand(Y, Z)), nand(nand(X, nand(X, X)), nand(X, nand(X, X))))), true, nand(X, nand(Y, Z)), nand(X, nand(X, X)))
71.10/71.35	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.35	  fresh(fresh2(true, true, nand(nand(X, nand(Y, Z)), nand(nand(X, nand(X, X)), nand(X, nand(X, X))))), true, nand(X, nand(Y, Z)), nand(X, nand(X, X)))
71.10/71.35	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.35	  fresh(true, true, nand(X, nand(Y, Z)), nand(X, nand(X, X)))
71.10/71.35	= { by axiom 1 (modus_ponens_for_nand) }
71.10/71.35	  p(nand(X, nand(X, X)))
71.10/71.35	
71.10/71.35	Lemma 13: p(nand(nand(X, Y), nand(nand(X, Y), nand(X, Y)))) = true.
71.10/71.35	Proof:
71.10/71.35	  p(nand(nand(X, Y), nand(nand(X, Y), nand(X, Y))))
71.10/71.35	= { by lemma 12 }
71.10/71.35	  fresh2(p(nand(nand(X, Y), nand(nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), X), nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), X)))), true, nand(nand(X, Y), nand(nand(X, Y), nand(X, Y))))
71.10/71.35	= { by lemma 7 }
71.10/71.35	  fresh2(fresh2(p(nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), Y))), true, nand(nand(X, Y), nand(nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), X), nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), X)))), true, nand(nand(X, Y), nand(nand(X, Y), nand(X, Y))))
71.10/71.35	= { by lemma 5 }
71.10/71.35	  fresh2(fresh2(fresh2(p(nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), nand(Y, nand(?, ?)))), true, nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), Y))), true, nand(nand(X, Y), nand(nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), X), nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), X)))), true, nand(nand(X, Y), nand(nand(X, Y), nand(X, Y))))
71.10/71.35	= { by lemma 11 }
71.10/71.35	  fresh2(fresh2(fresh2(true, true, nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), Y))), true, nand(nand(X, Y), nand(nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), X), nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), X)))), true, nand(nand(X, Y), nand(nand(X, Y), nand(X, Y))))
71.10/71.35	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.35	  fresh2(fresh2(true, true, nand(nand(X, Y), nand(nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), X), nand(nand(nand(Y, nand(?, ?)), nand(Y, nand(?, ?))), X)))), true, nand(nand(X, Y), nand(nand(X, Y), nand(X, Y))))
71.10/71.35	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.35	  fresh2(true, true, nand(nand(X, Y), nand(nand(X, Y), nand(X, Y))))
71.10/71.35	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.36	  true
71.10/71.36	
71.10/71.36	Lemma 14: p(nand(nand(X, Y), nand(nand(Y, X), nand(Y, X)))) = true.
71.10/71.36	Proof:
71.10/71.36	  p(nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.36	= { by lemma 7 }
71.10/71.36	  fresh2(p(nand(Y, nand(Y, Y))), true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.36	= { by lemma 12 }
71.10/71.36	  fresh2(fresh2(p(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), true, nand(Y, nand(Y, Y))), true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.36	= { by axiom 1 (modus_ponens_for_nand) }
71.10/71.36	  fresh2(fresh2(fresh(true, true, nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), true, nand(Y, nand(Y, Y))), true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.36	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.36	  fresh2(fresh2(fresh(fresh2(true, true, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))))), true, nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), true, nand(Y, nand(Y, Y))), true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.36	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.36	  fresh2(fresh2(fresh(fresh2(fresh2(true, true, nand(nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), true, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))))), true, nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), true, nand(Y, nand(Y, Y))), true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.36	= { by lemma 9 }
71.10/71.36	  fresh2(fresh2(fresh(fresh2(fresh2(p(nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), true, nand(nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), true, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))))), true, nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), true, nand(Y, nand(Y, Y))), true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.36	= { by axiom 4 (modus_ponens_for_nand) }
71.10/71.37	  fresh2(fresh2(fresh(fresh2(fresh(p(nand(nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(nand(nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))), nand(nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))))), true, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), true, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))))), true, nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), true, nand(Y, nand(Y, Y))), true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.37	= { by lemma 7 }
71.10/71.37	  fresh2(fresh2(fresh(fresh2(fresh(fresh2(p(nand(nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))))), true, nand(nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(nand(nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))), nand(nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))))), true, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), true, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))))), true, nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), true, nand(Y, nand(Y, Y))), true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.37	= { by lemma 11 }
71.10/71.37	  fresh2(fresh2(fresh(fresh2(fresh(fresh2(true, true, nand(nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(nand(nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))), nand(nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))))), true, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), true, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))))), true, nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), true, nand(Y, nand(Y, Y))), true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.37	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.37	  fresh2(fresh2(fresh(fresh2(fresh(true, true, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), true, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))))), true, nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), true, nand(Y, nand(Y, Y))), true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.37	= { by axiom 1 (modus_ponens_for_nand) }
71.10/71.37	  fresh2(fresh2(fresh(fresh2(p(nand(nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), true, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))))), true, nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), true, nand(Y, nand(Y, Y))), true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.37	= { by lemma 10 }
71.10/71.37	  fresh2(fresh2(fresh(p(nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))))), true, nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), true, nand(Y, nand(Y, Y))), true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.37	= { by axiom 4 (modus_ponens_for_nand) }
71.10/71.37	  fresh2(fresh2(fresh2(p(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))), true, nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), true, nand(Y, nand(Y, Y))), true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.37	= { by lemma 13 }
71.10/71.37	  fresh2(fresh2(fresh2(true, true, nand(Y, nand(nand(nand(?, ?), nand(nand(?, ?), nand(?, ?))), nand(nand(?, ?), nand(nand(?, ?), nand(?, ?)))))), true, nand(Y, nand(Y, Y))), true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.37	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.37	  fresh2(fresh2(true, true, nand(Y, nand(Y, Y))), true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.37	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.37	  fresh2(true, true, nand(nand(X, Y), nand(nand(Y, X), nand(Y, X))))
71.10/71.37	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.39	  true
71.10/71.39	
71.10/71.39	Goal 1 (tautology): p(nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))) = true.
71.10/71.39	Proof:
71.10/71.39	  p(nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by axiom 1 (modus_ponens_for_nand) }
71.10/71.39	  fresh(true, true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A)), nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.39	  fresh(fresh2(true, true, nand(nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A)), nand(nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))), nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A)), nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by lemma 14 }
71.10/71.39	  fresh(fresh2(p(nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A)))), true, nand(nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A)), nand(nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))), nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A)), nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by lemma 7 }
71.10/71.39	  fresh(p(nand(nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A)), nand(nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))), nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A)), nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by axiom 4 (modus_ponens_for_nand) }
71.10/71.39	  fresh2(p(nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by axiom 1 (modus_ponens_for_nand) }
71.10/71.39	  fresh2(fresh(true, true, nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))), nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by lemma 14 }
71.10/71.39	  fresh2(fresh(p(nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))), nand(nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A)), nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))))), true, nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))), nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by axiom 4 (modus_ponens_for_nand) }
71.10/71.39	  fresh2(fresh2(p(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by axiom 1 (modus_ponens_for_nand) }
71.10/71.39	  fresh2(fresh2(fresh(true, true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.39	  fresh2(fresh2(fresh(fresh2(true, true, nand(nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))), nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.39	  fresh2(fresh2(fresh(fresh2(fresh2(true, true, nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))))), true, nand(nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))), nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.39	  fresh2(fresh2(fresh(fresh2(fresh2(fresh2(true, true, nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK2_tautology_A, sK2_tautology_A))), true, nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))))), true, nand(nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))), nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by lemma 13 }
71.10/71.39	  fresh2(fresh2(fresh(fresh2(fresh2(fresh2(p(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), true, nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK2_tautology_A, sK2_tautology_A))), true, nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))))), true, nand(nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))), nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by lemma 10 }
71.10/71.39	  fresh2(fresh2(fresh(fresh2(fresh2(p(nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK2_tautology_A, sK2_tautology_A))), true, nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))))), true, nand(nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))), nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by lemma 7 }
71.10/71.39	  fresh2(fresh2(fresh(fresh2(p(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))))), true, nand(nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))), nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by lemma 7 }
71.10/71.39	  fresh2(fresh2(fresh(p(nand(nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))), nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B))), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by axiom 4 (modus_ponens_for_nand) }
71.10/71.39	  fresh2(fresh2(fresh2(p(nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B)))), true, nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by lemma 10 }
71.10/71.39	  fresh2(fresh2(fresh2(fresh2(p(nand(nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B)))), true, nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by lemma 14 }
71.10/71.39	  fresh2(fresh2(fresh2(fresh2(true, true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)), nand(sK1_tautology_B, sK1_tautology_B)))), true, nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.39	  fresh2(fresh2(fresh2(true, true, nand(nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))))), true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.39	  fresh2(fresh2(true, true, nand(nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A)))), nand(nand(sK1_tautology_B, sK1_tautology_B), sK2_tautology_A))), true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.39	  fresh2(true, true, nand(nand(sK2_tautology_A, nand(sK1_tautology_B, sK1_tautology_B)), nand(nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))), nand(nand(sK1_tautology_B, sK1_tautology_B), nand(nand(sK2_tautology_A, sK2_tautology_A), nand(sK2_tautology_A, sK2_tautology_A))))))
71.10/71.39	= { by axiom 2 (modus_ponens_for_nand) }
71.10/71.39	  true
71.10/71.39	% SZS output end Proof
71.10/71.39	
71.10/71.39	RESULT: Theorem (the conjecture is true).
71.10/71.40	EOF