TSTP Solution File: BOO039-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : BOO039-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 18:11:32 EDT 2023
% Result : Unsatisfiable 82.36s 10.93s
% Output : Proof 86.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO039-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 08:30:10 EDT 2023
% 0.14/0.34 % CPUTime :
% 82.36/10.93 Command-line arguments: --ground-connectedness --complete-subsets
% 82.36/10.93
% 82.36/10.93 % SZS status Unsatisfiable
% 82.36/10.93
% 84.97/11.34 % SZS output start Proof
% 84.97/11.34 Take the following subset of the input axioms:
% 84.97/11.34 fof(prove_meredith_2_basis, negated_conjecture, nand(nand(a, a), nand(b, a))!=a | nand(a, nand(b, nand(a, c)))!=nand(nand(nand(c, b), b), a)).
% 84.97/11.34 fof(sh_1, axiom, ![A, B, C]: nand(nand(A, nand(nand(B, A), A)), nand(B, nand(C, A)))=B).
% 84.97/11.34
% 84.97/11.34 Now clausify the problem and encode Horn clauses using encoding 3 of
% 84.97/11.34 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 84.97/11.34 We repeatedly replace C & s=t => u=v by the two clauses:
% 84.97/11.34 fresh(y, y, x1...xn) = u
% 84.97/11.34 C => fresh(s, t, x1...xn) = v
% 84.97/11.34 where fresh is a fresh function symbol and x1..xn are the free
% 84.97/11.34 variables of u and v.
% 84.97/11.34 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 84.97/11.34 input problem has no model of domain size 1).
% 84.97/11.34
% 84.97/11.34 The encoding turns the above axioms into the following unit equations and goals:
% 84.97/11.34
% 84.97/11.34 Axiom 1 (sh_1): nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(Z, X))) = Y.
% 84.97/11.34
% 84.97/11.34 Lemma 2: nand(nand(nand(X, nand(Y, Z)), nand(nand(W, nand(X, nand(Y, Z))), nand(X, nand(Y, Z)))), nand(W, X)) = W.
% 84.97/11.34 Proof:
% 84.97/11.34 nand(nand(nand(X, nand(Y, Z)), nand(nand(W, nand(X, nand(Y, Z))), nand(X, nand(Y, Z)))), nand(W, X))
% 84.97/11.34 = { by axiom 1 (sh_1) R->L }
% 84.97/11.34 nand(nand(nand(X, nand(Y, Z)), nand(nand(W, nand(X, nand(Y, Z))), nand(X, nand(Y, Z)))), nand(W, nand(nand(Z, nand(nand(X, Z), Z)), nand(X, nand(Y, Z)))))
% 84.97/11.34 = { by axiom 1 (sh_1) }
% 84.97/11.34 W
% 84.97/11.34
% 84.97/11.34 Lemma 3: nand(nand(nand(X, Y), nand(nand(Z, nand(X, Y)), nand(X, Y))), nand(Z, X)) = Z.
% 84.97/11.34 Proof:
% 84.97/11.34 nand(nand(nand(X, Y), nand(nand(Z, nand(X, Y)), nand(X, Y))), nand(Z, X))
% 84.97/11.34 = { by lemma 2 R->L }
% 84.97/11.34 nand(nand(nand(X, Y), nand(nand(Z, nand(X, Y)), nand(X, Y))), nand(Z, nand(nand(nand(Y, nand(W, V)), nand(nand(X, nand(Y, nand(W, V))), nand(Y, nand(W, V)))), nand(X, Y))))
% 84.97/11.34 = { by axiom 1 (sh_1) }
% 84.97/11.34 Z
% 84.97/11.34
% 84.97/11.34 Lemma 4: nand(nand(nand(X, Y), nand(nand(nand(Y, nand(nand(Z, Y), Y)), nand(X, Y)), nand(X, Y))), Z) = nand(Y, nand(nand(Z, Y), Y)).
% 84.97/11.34 Proof:
% 84.97/11.34 nand(nand(nand(X, Y), nand(nand(nand(Y, nand(nand(Z, Y), Y)), nand(X, Y)), nand(X, Y))), Z)
% 84.97/11.34 = { by axiom 1 (sh_1) R->L }
% 84.97/11.34 nand(nand(nand(X, Y), nand(nand(nand(Y, nand(nand(Z, Y), Y)), nand(X, Y)), nand(X, Y))), nand(nand(Y, nand(nand(Z, Y), Y)), nand(Z, nand(X, Y))))
% 84.97/11.34 = { by axiom 1 (sh_1) }
% 84.97/11.34 nand(Y, nand(nand(Z, Y), Y))
% 84.97/11.34
% 84.97/11.34 Lemma 5: nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(Z, nand(nand(X, Z), Z)))) = Y.
% 84.97/11.34 Proof:
% 84.97/11.34 nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(Z, nand(nand(X, Z), Z))))
% 84.97/11.34 = { by lemma 4 R->L }
% 84.97/11.34 nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(nand(nand(W, Z), nand(nand(nand(Z, nand(nand(X, Z), Z)), nand(W, Z)), nand(W, Z))), X)))
% 84.97/11.34 = { by axiom 1 (sh_1) }
% 84.97/11.34 Y
% 84.97/11.34
% 84.97/11.34 Lemma 6: nand(nand(X, nand(nand(nand(Y, nand(nand(Y, Y), Y)), X), X)), Y) = nand(Y, nand(nand(Y, Y), Y)).
% 84.97/11.34 Proof:
% 84.97/11.34 nand(nand(X, nand(nand(nand(Y, nand(nand(Y, Y), Y)), X), X)), Y)
% 84.97/11.34 = { by axiom 1 (sh_1) R->L }
% 84.97/11.34 nand(nand(X, nand(nand(nand(Y, nand(nand(Y, Y), Y)), X), X)), nand(nand(Y, nand(nand(Y, Y), Y)), nand(Y, nand(nand(X, Y), Y))))
% 84.97/11.34 = { by lemma 5 }
% 84.97/11.34 nand(Y, nand(nand(Y, Y), Y))
% 84.97/11.34
% 84.97/11.34 Lemma 7: nand(X, nand(nand(X, X), X)) = nand(X, X).
% 84.97/11.34 Proof:
% 84.97/11.34 nand(X, nand(nand(X, X), X))
% 84.97/11.34 = { by lemma 6 R->L }
% 84.97/11.34 nand(nand(nand(X, nand(nand(X, X), X)), nand(nand(nand(X, nand(nand(X, X), X)), nand(X, nand(nand(X, X), X))), nand(X, nand(nand(X, X), X)))), X)
% 84.97/11.34 = { by axiom 1 (sh_1) }
% 84.97/11.34 nand(nand(nand(X, nand(nand(X, X), X)), nand(X, nand(X, nand(nand(X, X), X)))), X)
% 84.97/11.34 = { by lemma 5 }
% 84.97/11.34 nand(X, X)
% 84.97/11.34
% 84.97/11.34 Lemma 8: nand(nand(X, nand(nand(nand(Y, Y), X), X)), Y) = nand(Y, Y).
% 84.97/11.34 Proof:
% 84.97/11.34 nand(nand(X, nand(nand(nand(Y, Y), X), X)), Y)
% 84.97/11.34 = { by lemma 7 R->L }
% 84.97/11.34 nand(nand(X, nand(nand(nand(Y, nand(nand(Y, Y), Y)), X), X)), Y)
% 84.97/11.34 = { by lemma 6 }
% 84.97/11.34 nand(Y, nand(nand(Y, Y), Y))
% 84.97/11.34 = { by lemma 7 }
% 84.97/11.34 nand(Y, Y)
% 84.97/11.34
% 84.97/11.34 Lemma 9: nand(nand(X, nand(nand(Y, X), X)), nand(Y, Y)) = Y.
% 84.97/11.34 Proof:
% 84.97/11.34 nand(nand(X, nand(nand(Y, X), X)), nand(Y, Y))
% 84.97/11.34 = { by lemma 7 R->L }
% 84.97/11.34 nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(nand(Y, Y), Y)))
% 84.97/11.34 = { by axiom 1 (sh_1) R->L }
% 84.97/11.34 nand(nand(X, nand(nand(nand(nand(Y, nand(nand(Y, Y), Y)), nand(Y, nand(nand(Y, Y), Y))), X), X)), nand(Y, nand(nand(Y, Y), Y)))
% 84.97/11.34 = { by lemma 8 }
% 84.97/11.34 nand(nand(Y, nand(nand(Y, Y), Y)), nand(Y, nand(nand(Y, Y), Y)))
% 84.97/11.34 = { by axiom 1 (sh_1) }
% 84.97/11.34 Y
% 84.97/11.34
% 84.97/11.34 Lemma 10: nand(X, nand(nand(nand(nand(Y, X), nand(Y, X)), X), X)) = nand(Y, X).
% 84.97/11.34 Proof:
% 84.97/11.34 nand(X, nand(nand(nand(nand(Y, X), nand(Y, X)), X), X))
% 84.97/11.34 = { by lemma 4 R->L }
% 84.97/11.34 nand(nand(nand(Y, X), nand(nand(nand(X, nand(nand(nand(nand(Y, X), nand(Y, X)), X), X)), nand(Y, X)), nand(Y, X))), nand(nand(Y, X), nand(Y, X)))
% 84.97/11.34 = { by lemma 8 }
% 84.97/11.34 nand(nand(nand(Y, X), nand(nand(nand(Y, X), nand(Y, X)), nand(Y, X))), nand(nand(Y, X), nand(Y, X)))
% 84.97/11.34 = { by lemma 9 }
% 84.97/11.34 nand(Y, X)
% 84.97/11.34
% 84.97/11.34 Lemma 11: nand(nand(X, X), nand(Y, X)) = X.
% 84.97/11.34 Proof:
% 84.97/11.34 nand(nand(X, X), nand(Y, X))
% 84.97/11.34 = { by lemma 7 R->L }
% 84.97/11.34 nand(nand(X, nand(nand(X, X), X)), nand(Y, X))
% 84.97/11.34 = { by lemma 10 R->L }
% 84.97/11.34 nand(nand(X, nand(nand(X, X), X)), nand(X, nand(nand(nand(nand(Y, X), nand(Y, X)), X), X)))
% 84.97/11.34 = { by axiom 1 (sh_1) }
% 84.97/11.34 X
% 84.97/11.34
% 84.97/11.34 Lemma 12: nand(nand(nand(X, Y), nand(X, Y)), X) = nand(X, Y).
% 84.97/11.34 Proof:
% 84.97/11.34 nand(nand(nand(X, Y), nand(X, Y)), X)
% 84.97/11.34 = { by lemma 3 R->L }
% 84.97/11.34 nand(nand(nand(X, Y), nand(X, Y)), nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(X, Y)))
% 84.97/11.34 = { by lemma 11 }
% 84.97/11.34 nand(X, Y)
% 84.97/11.34
% 84.97/11.34 Lemma 13: nand(nand(X, Y), nand(Y, nand(X, Y))) = Y.
% 84.97/11.34 Proof:
% 84.97/11.34 nand(nand(X, Y), nand(Y, nand(X, Y)))
% 84.97/11.34 = { by lemma 11 R->L }
% 84.97/11.34 nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y)))
% 84.97/11.34 = { by lemma 11 R->L }
% 84.97/11.34 nand(nand(X, Y), nand(nand(nand(Y, nand(nand(Y, Y), nand(X, Y))), nand(X, Y)), nand(X, Y)))
% 84.97/11.34 = { by lemma 11 R->L }
% 84.97/11.34 nand(nand(X, Y), nand(nand(nand(nand(nand(Y, Y), nand(X, Y)), nand(nand(Y, Y), nand(X, Y))), nand(X, Y)), nand(X, Y)))
% 84.97/11.34 = { by lemma 10 }
% 84.97/11.34 nand(nand(Y, Y), nand(X, Y))
% 84.97/11.34 = { by lemma 11 }
% 84.97/11.34 Y
% 84.97/11.34
% 84.97/11.34 Lemma 14: nand(nand(X, Y), nand(X, nand(X, Y))) = X.
% 84.97/11.34 Proof:
% 84.97/11.34 nand(nand(X, Y), nand(X, nand(X, Y)))
% 84.97/11.34 = { by lemma 12 R->L }
% 84.97/11.34 nand(nand(X, Y), nand(X, nand(nand(nand(X, Y), nand(X, Y)), X)))
% 84.97/11.34 = { by lemma 12 R->L }
% 84.97/11.34 nand(nand(nand(nand(X, Y), nand(X, Y)), X), nand(X, nand(nand(nand(X, Y), nand(X, Y)), X)))
% 84.97/11.34 = { by lemma 13 }
% 84.97/11.34 X
% 84.97/11.34
% 84.97/11.34 Lemma 15: nand(nand(X, X), nand(nand(Y, nand(nand(nand(X, X), Y), Y)), nand(Z, X))) = nand(Y, nand(nand(nand(X, X), Y), Y)).
% 84.97/11.34 Proof:
% 84.97/11.34 nand(nand(X, X), nand(nand(Y, nand(nand(nand(X, X), Y), Y)), nand(Z, X)))
% 84.97/11.34 = { by lemma 7 R->L }
% 84.97/11.34 nand(nand(X, nand(nand(X, X), X)), nand(nand(Y, nand(nand(nand(X, X), Y), Y)), nand(Z, X)))
% 84.97/11.34 = { by lemma 8 R->L }
% 84.97/11.34 nand(nand(X, nand(nand(nand(Y, nand(nand(nand(X, X), Y), Y)), X), X)), nand(nand(Y, nand(nand(nand(X, X), Y), Y)), nand(Z, X)))
% 84.97/11.34 = { by axiom 1 (sh_1) }
% 84.97/11.34 nand(Y, nand(nand(nand(X, X), Y), Y))
% 84.97/11.34
% 84.97/11.34 Lemma 16: nand(nand(X, Y), nand(nand(nand(X, X), nand(X, Y)), nand(X, Y))) = X.
% 84.97/11.34 Proof:
% 84.97/11.34 nand(nand(X, Y), nand(nand(nand(X, X), nand(X, Y)), nand(X, Y)))
% 84.97/11.34 = { by lemma 15 R->L }
% 84.97/11.34 nand(nand(X, X), nand(nand(nand(X, Y), nand(nand(nand(X, X), nand(X, Y)), nand(X, Y))), nand(nand(X, X), X)))
% 84.97/11.34 = { by lemma 3 }
% 84.97/11.34 nand(nand(X, X), nand(X, X))
% 84.97/11.34 = { by lemma 11 }
% 84.97/11.34 X
% 84.97/11.34
% 84.97/11.34 Lemma 17: nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(X, Z))) = Y.
% 84.97/11.34 Proof:
% 84.97/11.34 nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(X, Z)))
% 84.97/11.35 = { by lemma 16 R->L }
% 84.97/11.35 nand(nand(X, nand(nand(Y, nand(nand(X, Z), nand(nand(nand(X, X), nand(X, Z)), nand(X, Z)))), X)), nand(Y, nand(X, Z)))
% 84.97/11.35 = { by lemma 16 R->L }
% 84.97/11.35 nand(nand(X, nand(nand(Y, nand(nand(X, Z), nand(nand(nand(X, X), nand(X, Z)), nand(X, Z)))), nand(nand(X, Z), nand(nand(nand(X, X), nand(X, Z)), nand(X, Z))))), nand(Y, nand(X, Z)))
% 84.97/11.35 = { by lemma 16 R->L }
% 84.97/11.35 nand(nand(nand(nand(X, Z), nand(nand(nand(X, X), nand(X, Z)), nand(X, Z))), nand(nand(Y, nand(nand(X, Z), nand(nand(nand(X, X), nand(X, Z)), nand(X, Z)))), nand(nand(X, Z), nand(nand(nand(X, X), nand(X, Z)), nand(X, Z))))), nand(Y, nand(X, Z)))
% 84.97/11.35 = { by lemma 3 }
% 84.97/11.35 Y
% 84.97/11.35
% 84.97/11.35 Lemma 18: nand(X, nand(nand(Y, X), X)) = nand(X, Y).
% 84.97/11.35 Proof:
% 84.97/11.35 nand(X, nand(nand(Y, X), X))
% 84.97/11.35 = { by axiom 1 (sh_1) R->L }
% 84.97/11.35 nand(nand(nand(X, nand(X, nand(nand(Y, X), X))), nand(nand(nand(X, nand(nand(Y, X), X)), nand(X, nand(X, nand(nand(Y, X), X)))), nand(X, nand(X, nand(nand(Y, X), X))))), nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(X, nand(X, nand(nand(Y, X), X))))))
% 84.97/11.35 = { by lemma 14 }
% 84.97/11.35 nand(nand(nand(X, nand(X, nand(nand(Y, X), X))), nand(X, nand(X, nand(X, nand(nand(Y, X), X))))), nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(X, nand(X, nand(nand(Y, X), X))))))
% 84.97/11.35 = { by lemma 14 }
% 84.97/11.35 nand(X, nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(X, nand(X, nand(nand(Y, X), X))))))
% 84.97/11.35 = { by lemma 17 }
% 84.97/11.35 nand(X, Y)
% 84.97/11.35
% 84.97/11.35 Lemma 19: nand(nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))), nand(nand(Z, Y), nand(nand(nand(Y, Y), nand(Z, Y)), nand(Z, Y)))) = nand(Y, Y).
% 84.97/11.35 Proof:
% 84.97/11.35 nand(nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))), nand(nand(Z, Y), nand(nand(nand(Y, Y), nand(Z, Y)), nand(Z, Y))))
% 84.97/11.35 = { by lemma 7 R->L }
% 84.97/11.35 nand(nand(nand(X, Y), nand(nand(nand(Y, nand(nand(Y, Y), Y)), nand(X, Y)), nand(X, Y))), nand(nand(Z, Y), nand(nand(nand(Y, Y), nand(Z, Y)), nand(Z, Y))))
% 84.97/11.35 = { by lemma 7 R->L }
% 84.97/11.35 nand(nand(nand(X, Y), nand(nand(nand(Y, nand(nand(Y, nand(nand(Y, Y), Y)), Y)), nand(X, Y)), nand(X, Y))), nand(nand(Z, Y), nand(nand(nand(Y, Y), nand(Z, Y)), nand(Z, Y))))
% 84.97/11.35 = { by lemma 7 R->L }
% 84.97/11.35 nand(nand(nand(X, Y), nand(nand(nand(Y, nand(nand(Y, nand(nand(Y, Y), Y)), Y)), nand(X, Y)), nand(X, Y))), nand(nand(Z, Y), nand(nand(nand(Y, nand(nand(Y, Y), Y)), nand(Z, Y)), nand(Z, Y))))
% 84.97/11.35 = { by lemma 4 R->L }
% 84.97/11.35 nand(nand(nand(X, Y), nand(nand(nand(Y, nand(nand(nand(nand(Z, Y), nand(nand(nand(Y, nand(nand(Y, Y), Y)), nand(Z, Y)), nand(Z, Y))), Y), Y)), nand(X, Y)), nand(X, Y))), nand(nand(Z, Y), nand(nand(nand(Y, nand(nand(Y, Y), Y)), nand(Z, Y)), nand(Z, Y))))
% 84.97/11.35 = { by lemma 4 }
% 84.97/11.35 nand(Y, nand(nand(nand(nand(Z, Y), nand(nand(nand(Y, nand(nand(Y, Y), Y)), nand(Z, Y)), nand(Z, Y))), Y), Y))
% 84.97/11.35 = { by lemma 4 }
% 84.97/11.35 nand(Y, nand(nand(Y, nand(nand(Y, Y), Y)), Y))
% 84.97/11.35 = { by lemma 7 }
% 84.97/11.35 nand(Y, nand(nand(Y, Y), Y))
% 84.97/11.35 = { by lemma 7 }
% 84.97/11.35 nand(Y, Y)
% 84.97/11.35
% 84.97/11.35 Lemma 20: nand(nand(X, X), nand(X, nand(Y, X))) = X.
% 84.97/11.35 Proof:
% 84.97/11.35 nand(nand(X, X), nand(X, nand(Y, X)))
% 84.97/11.35 = { by lemma 7 R->L }
% 84.97/11.35 nand(nand(X, nand(nand(X, X), X)), nand(X, nand(Y, X)))
% 84.97/11.35 = { by axiom 1 (sh_1) }
% 84.97/11.35 X
% 84.97/11.35
% 84.97/11.35 Lemma 21: nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(nand(Y, Y), nand(X, nand(nand(nand(Y, Y), X), X)))), nand(Y, Y)) = Y.
% 84.97/11.35 Proof:
% 84.97/11.35 nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(nand(Y, Y), nand(X, nand(nand(nand(Y, Y), X), X)))), nand(Y, Y))
% 84.97/11.35 = { by axiom 1 (sh_1) R->L }
% 84.97/11.35 nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(nand(nand(nand(Y, Y), nand(nand(nand(Y, Y), nand(Y, Y)), nand(Y, Y))), nand(nand(Y, Y), nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(Y, Y)))), nand(X, nand(nand(nand(Y, Y), X), X)))), nand(Y, Y))
% 84.97/11.35 = { by lemma 7 R->L }
% 84.97/11.35 nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(nand(nand(nand(Y, Y), nand(nand(nand(Y, Y), nand(Y, Y)), nand(Y, Y))), nand(nand(Y, nand(nand(Y, Y), Y)), nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(Y, Y)))), nand(X, nand(nand(nand(Y, Y), X), X)))), nand(Y, Y))
% 84.97/11.35 = { by lemma 8 R->L }
% 84.97/11.35 nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(nand(nand(nand(Y, Y), nand(nand(nand(Y, Y), nand(Y, Y)), nand(Y, Y))), nand(nand(Y, nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), Y), Y)), nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(Y, Y)))), nand(X, nand(nand(nand(Y, Y), X), X)))), nand(Y, Y))
% 84.97/11.35 = { by axiom 1 (sh_1) }
% 84.97/11.35 nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(nand(nand(nand(Y, Y), nand(nand(nand(Y, Y), nand(Y, Y)), nand(Y, Y))), nand(X, nand(nand(nand(Y, Y), X), X))), nand(X, nand(nand(nand(Y, Y), X), X)))), nand(Y, Y))
% 84.97/11.35 = { by lemma 11 }
% 84.97/11.35 nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(nand(nand(nand(Y, Y), nand(Y, nand(Y, Y))), nand(X, nand(nand(nand(Y, Y), X), X))), nand(X, nand(nand(nand(Y, Y), X), X)))), nand(Y, Y))
% 84.97/11.35 = { by lemma 20 }
% 84.97/11.35 nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(nand(Y, nand(X, nand(nand(nand(Y, Y), X), X))), nand(X, nand(nand(nand(Y, Y), X), X)))), nand(Y, Y))
% 84.97/11.35 = { by lemma 4 R->L }
% 84.97/11.35 nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(nand(Y, nand(nand(nand(Z, X), nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(Z, X)), nand(Z, X))), nand(Y, Y))), nand(X, nand(nand(nand(Y, Y), X), X)))), nand(Y, Y))
% 84.97/11.35 = { by lemma 4 R->L }
% 84.97/11.35 nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(nand(Y, nand(nand(nand(Z, X), nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(Z, X)), nand(Z, X))), nand(Y, Y))), nand(nand(nand(Z, X), nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(Z, X)), nand(Z, X))), nand(Y, Y)))), nand(Y, Y))
% 84.97/11.35 = { by lemma 4 R->L }
% 84.97/11.35 nand(nand(nand(nand(nand(Z, X), nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(Z, X)), nand(Z, X))), nand(Y, Y)), nand(nand(Y, nand(nand(nand(Z, X), nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(Z, X)), nand(Z, X))), nand(Y, Y))), nand(nand(nand(Z, X), nand(nand(nand(X, nand(nand(nand(Y, Y), X), X)), nand(Z, X)), nand(Z, X))), nand(Y, Y)))), nand(Y, Y))
% 84.97/11.35 = { by lemma 9 }
% 84.97/11.35 Y
% 84.97/11.35
% 84.97/11.35 Lemma 22: nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))) = Y.
% 84.97/11.35 Proof:
% 84.97/11.35 nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y)))
% 84.97/11.35 = { by axiom 1 (sh_1) R->L }
% 84.97/11.35 nand(nand(nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))), nand(nand(nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))), nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y)))), nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))))), nand(nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))), nand(nand(Y, Y), nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))))))
% 84.97/11.35 = { by lemma 17 }
% 84.97/11.35 nand(nand(nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))), nand(nand(nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))), nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y)))), nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))))), nand(Y, Y))
% 84.97/11.35 = { by lemma 19 }
% 84.97/11.35 nand(nand(nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))), nand(nand(Y, Y), nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))))), nand(Y, Y))
% 84.97/11.35 = { by lemma 21 }
% 84.97/11.35 Y
% 84.97/11.35
% 84.97/11.35 Lemma 23: nand(nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)), nand(nand(nand(X, X), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)))) = X.
% 84.97/11.35 Proof:
% 84.97/11.35 nand(nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)), nand(nand(nand(X, X), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))))
% 84.97/11.35 = { by lemma 15 R->L }
% 84.97/11.35 nand(nand(X, X), nand(nand(nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)), nand(nand(nand(X, X), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)))), nand(nand(X, X), X)))
% 84.97/11.35 = { by lemma 22 R->L }
% 84.97/11.35 nand(nand(X, X), nand(nand(nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)), nand(nand(nand(X, X), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)))), nand(nand(X, X), nand(nand(Y, X), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))))))
% 84.97/11.35 = { by axiom 1 (sh_1) }
% 84.97/11.35 nand(nand(X, X), nand(X, X))
% 84.97/11.35 = { by lemma 11 }
% 84.97/11.35 X
% 84.97/11.35
% 84.97/11.35 Lemma 24: nand(nand(X, nand(Y, X)), X) = nand(Y, X).
% 84.97/11.35 Proof:
% 84.97/11.35 nand(nand(X, nand(Y, X)), X)
% 84.97/11.35 = { by lemma 18 R->L }
% 84.97/11.35 nand(nand(X, nand(nand(nand(Y, X), X), X)), X)
% 84.97/11.35 = { by lemma 23 R->L }
% 84.97/11.35 nand(nand(X, nand(nand(nand(Y, X), nand(nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)), nand(nand(nand(X, X), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))))), X)), X)
% 84.97/11.35 = { by lemma 23 R->L }
% 84.97/11.35 nand(nand(X, nand(nand(nand(Y, X), nand(nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)), nand(nand(nand(X, X), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))))), nand(nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)), nand(nand(nand(X, X), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)))))), X)
% 84.97/11.35 = { by lemma 23 R->L }
% 84.97/11.35 nand(nand(nand(nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)), nand(nand(nand(X, X), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)))), nand(nand(nand(Y, X), nand(nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)), nand(nand(nand(X, X), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))))), nand(nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)), nand(nand(nand(X, X), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)))))), X)
% 84.97/11.35 = { by lemma 22 R->L }
% 84.97/11.35 nand(nand(nand(nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)), nand(nand(nand(X, X), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)))), nand(nand(nand(Y, X), nand(nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)), nand(nand(nand(X, X), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))))), nand(nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)), nand(nand(nand(X, X), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X)))))), nand(nand(Y, X), nand(nand(nand(X, X), nand(Y, X)), nand(Y, X))))
% 84.97/11.35 = { by lemma 3 }
% 84.97/11.36 nand(Y, X)
% 84.97/11.36
% 84.97/11.36 Lemma 25: nand(X, nand(nand(X, Y), X)) = nand(X, Y).
% 84.97/11.36 Proof:
% 84.97/11.36 nand(X, nand(nand(X, Y), X))
% 84.97/11.36 = { by lemma 3 R->L }
% 84.97/11.36 nand(X, nand(nand(X, Y), nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(X, Y))))
% 84.97/11.36 = { by lemma 3 R->L }
% 84.97/11.36 nand(nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(X, Y)), nand(nand(X, Y), nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(X, Y))))
% 84.97/11.36 = { by lemma 13 }
% 84.97/11.36 nand(X, Y)
% 84.97/11.36
% 84.97/11.36 Lemma 26: nand(nand(X, nand(nand(Y, X), X)), X) = nand(X, nand(Y, X)).
% 84.97/11.36 Proof:
% 84.97/11.36 nand(nand(X, nand(nand(Y, X), X)), X)
% 84.97/11.36 = { by lemma 24 R->L }
% 84.97/11.36 nand(nand(X, nand(nand(nand(X, nand(Y, X)), X), X)), X)
% 84.97/11.36 = { by lemma 14 R->L }
% 84.97/11.36 nand(nand(X, nand(nand(nand(X, nand(Y, X)), X), X)), nand(nand(X, nand(Y, X)), nand(X, nand(X, nand(Y, X)))))
% 84.97/11.36 = { by lemma 17 }
% 84.97/11.36 nand(X, nand(Y, X))
% 84.97/11.36
% 84.97/11.36 Lemma 27: nand(X, nand(Y, X)) = nand(X, nand(X, Y)).
% 84.97/11.36 Proof:
% 84.97/11.36 nand(X, nand(Y, X))
% 84.97/11.36 = { by lemma 25 R->L }
% 84.97/11.36 nand(X, nand(nand(X, nand(Y, X)), X))
% 84.97/11.36 = { by lemma 26 R->L }
% 84.97/11.36 nand(X, nand(nand(nand(X, nand(nand(Y, X), X)), X), X))
% 84.97/11.36 = { by lemma 18 }
% 84.97/11.36 nand(X, nand(X, nand(nand(Y, X), X)))
% 84.97/11.36 = { by lemma 18 }
% 84.97/11.36 nand(X, nand(X, Y))
% 84.97/11.36
% 84.97/11.36 Lemma 28: nand(nand(X, Y), nand(X, nand(Y, X))) = X.
% 84.97/11.36 Proof:
% 84.97/11.36 nand(nand(X, Y), nand(X, nand(Y, X)))
% 84.97/11.36 = { by lemma 27 }
% 84.97/11.36 nand(nand(X, Y), nand(X, nand(X, Y)))
% 84.97/11.36 = { by lemma 14 }
% 84.97/11.36 X
% 84.97/11.36
% 84.97/11.36 Lemma 29: nand(Y, X) = nand(X, Y).
% 84.97/11.36 Proof:
% 84.97/11.36 nand(Y, X)
% 84.97/11.36 = { by lemma 24 R->L }
% 84.97/11.36 nand(nand(X, nand(Y, X)), X)
% 84.97/11.36 = { by lemma 27 }
% 84.97/11.36 nand(nand(X, nand(X, Y)), X)
% 84.97/11.36 = { by lemma 18 R->L }
% 84.97/11.36 nand(nand(X, nand(nand(nand(X, Y), X), X)), X)
% 84.97/11.36 = { by lemma 28 R->L }
% 84.97/11.36 nand(nand(X, nand(nand(nand(X, Y), X), X)), nand(nand(X, Y), nand(X, nand(Y, X))))
% 84.97/11.36 = { by lemma 17 }
% 84.97/11.36 nand(X, Y)
% 84.97/11.36
% 84.97/11.36 Lemma 30: nand(X, nand(nand(Y, X), X)) = nand(Y, X).
% 84.97/11.36 Proof:
% 84.97/11.36 nand(X, nand(nand(Y, X), X))
% 84.97/11.36 = { by axiom 1 (sh_1) R->L }
% 84.97/11.36 nand(X, nand(nand(nand(nand(Y, X), nand(nand(nand(Y, X), nand(Y, X)), nand(Y, X))), nand(nand(Y, X), nand(X, nand(Y, X)))), X))
% 84.97/11.36 = { by lemma 13 }
% 84.97/11.36 nand(X, nand(nand(nand(nand(Y, X), nand(nand(nand(Y, X), nand(Y, X)), nand(Y, X))), X), X))
% 84.97/11.36 = { by lemma 7 }
% 84.97/11.36 nand(X, nand(nand(nand(nand(Y, X), nand(Y, X)), X), X))
% 84.97/11.36 = { by lemma 10 }
% 84.97/11.36 nand(Y, X)
% 84.97/11.36
% 84.97/11.36 Lemma 31: nand(X, nand(Y, nand(X, nand(Z, Y)))) = nand(X, nand(Z, Y)).
% 84.97/11.36 Proof:
% 84.97/11.36 nand(X, nand(Y, nand(X, nand(Z, Y))))
% 84.97/11.36 = { by lemma 29 }
% 84.97/11.36 nand(X, nand(Y, nand(X, nand(Y, Z))))
% 84.97/11.36 = { by lemma 29 }
% 84.97/11.36 nand(X, nand(nand(X, nand(Y, Z)), Y))
% 84.97/11.36 = { by lemma 29 }
% 84.97/11.36 nand(nand(nand(X, nand(Y, Z)), Y), X)
% 84.97/11.36 = { by lemma 30 R->L }
% 84.97/11.36 nand(nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), Y), X)
% 84.97/11.36 = { by lemma 3 R->L }
% 84.97/11.36 nand(nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), Y), nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(X, Y)))
% 84.97/11.36 = { by lemma 29 }
% 84.97/11.36 nand(nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(X, Y)), nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), Y))
% 84.97/11.36 = { by lemma 30 R->L }
% 84.97/11.36 nand(nand(nand(X, Y), nand(nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(X, Y)), nand(X, Y))), nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), Y))
% 84.97/11.36 = { by lemma 30 R->L }
% 84.97/11.36 nand(nand(nand(X, Y), nand(nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(Y, nand(nand(X, Y), Y))), nand(X, Y))), nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), Y))
% 84.97/11.36 = { by lemma 30 R->L }
% 84.97/11.36 nand(nand(nand(X, Y), nand(nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(Y, nand(nand(X, Y), Y))), nand(Y, nand(nand(X, Y), Y)))), nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), Y))
% 84.97/11.36 = { by lemma 30 R->L }
% 84.97/11.36 nand(nand(nand(Y, nand(nand(X, Y), Y)), nand(nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(Y, nand(nand(X, Y), Y))), nand(Y, nand(nand(X, Y), Y)))), nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), Y))
% 84.97/11.36 = { by lemma 3 }
% 84.97/11.36 nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z)))
% 84.97/11.36 = { by lemma 30 }
% 84.97/11.36 nand(X, nand(Y, Z))
% 84.97/11.36 = { by lemma 29 R->L }
% 84.97/11.36 nand(X, nand(Z, Y))
% 84.97/11.36
% 84.97/11.36 Lemma 32: nand(nand(X, Y), nand(X, nand(Y, Z))) = X.
% 84.97/11.36 Proof:
% 84.97/11.36 nand(nand(X, Y), nand(X, nand(Y, Z)))
% 84.97/11.36 = { by lemma 29 }
% 84.97/11.36 nand(nand(X, Y), nand(X, nand(Z, Y)))
% 84.97/11.36 = { by lemma 30 R->L }
% 84.97/11.36 nand(nand(Y, nand(nand(X, Y), Y)), nand(X, nand(Z, Y)))
% 84.97/11.36 = { by axiom 1 (sh_1) }
% 84.97/11.36 X
% 84.97/11.36
% 84.97/11.36 Lemma 33: nand(X, nand(Y, nand(X, Y))) = nand(X, X).
% 84.97/11.36 Proof:
% 84.97/11.36 nand(X, nand(Y, nand(X, Y)))
% 84.97/11.36 = { by lemma 31 R->L }
% 84.97/11.36 nand(X, nand(nand(X, Y), nand(X, nand(Y, nand(X, Y)))))
% 84.97/11.36 = { by lemma 32 }
% 84.97/11.36 nand(X, X)
% 84.97/11.36
% 84.97/11.36 Lemma 34: nand(nand(X, Y), nand(X, nand(Z, Y))) = X.
% 84.97/11.36 Proof:
% 84.97/11.36 nand(nand(X, Y), nand(X, nand(Z, Y)))
% 84.97/11.36 = { by lemma 30 R->L }
% 84.97/11.36 nand(nand(Y, nand(nand(X, Y), Y)), nand(X, nand(Z, Y)))
% 84.97/11.36 = { by axiom 1 (sh_1) }
% 84.97/11.36 X
% 84.97/11.36
% 84.97/11.36 Lemma 35: nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))) = nand(Y, Y).
% 84.97/11.36 Proof:
% 84.97/11.36 nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y))))
% 84.97/11.36 = { by lemma 2 R->L }
% 84.97/11.36 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(Y, Y), Y)))
% 84.97/11.36 = { by lemma 16 R->L }
% 84.97/11.36 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(Y, Y), nand(nand(Y, nand(nand(nand(Y, Y), Y), Y)), nand(nand(nand(Y, Y), nand(Y, nand(nand(nand(Y, Y), Y), Y))), nand(Y, nand(nand(nand(Y, Y), Y), Y)))))))
% 84.97/11.36 = { by lemma 30 }
% 84.97/11.36 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(Y, Y), nand(nand(nand(Y, Y), Y), nand(nand(nand(Y, Y), nand(Y, nand(nand(nand(Y, Y), Y), Y))), nand(Y, nand(nand(nand(Y, Y), Y), Y)))))))
% 84.97/11.36 = { by lemma 20 }
% 84.97/11.36 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(Y, Y), nand(nand(nand(Y, Y), Y), nand(Y, nand(Y, nand(nand(nand(Y, Y), Y), Y)))))))
% 84.97/11.36 = { by lemma 22 R->L }
% 84.97/11.36 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(Y, Y), nand(nand(nand(Y, Y), Y), nand(nand(nand(W, Y), nand(nand(nand(Y, Y), nand(W, Y)), nand(W, Y))), nand(Y, nand(nand(nand(Y, Y), Y), Y)))))))
% 84.97/11.36 = { by lemma 7 R->L }
% 84.97/11.36 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(Y, Y), nand(nand(nand(Y, Y), Y), nand(nand(nand(W, Y), nand(nand(nand(Y, nand(nand(Y, Y), Y)), nand(W, Y)), nand(W, Y))), nand(Y, nand(nand(nand(Y, Y), Y), Y)))))))
% 84.97/11.36 = { by lemma 8 R->L }
% 84.97/11.36 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(Y, Y), nand(nand(nand(Y, Y), Y), nand(nand(nand(W, Y), nand(nand(nand(Y, nand(nand(nand(Y, nand(nand(nand(Y, Y), Y), Y)), Y), Y)), nand(W, Y)), nand(W, Y))), nand(Y, nand(nand(nand(Y, Y), Y), Y)))))))
% 84.97/11.36 = { by lemma 4 }
% 84.97/11.36 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(Y, Y), nand(nand(nand(Y, Y), Y), nand(Y, nand(nand(nand(Y, nand(nand(nand(Y, Y), Y), Y)), Y), Y))))))
% 84.97/11.36 = { by lemma 8 }
% 84.97/11.36 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(Y, Y), nand(nand(nand(Y, Y), Y), nand(Y, nand(nand(Y, Y), Y))))))
% 84.97/11.36 = { by lemma 7 }
% 84.97/11.36 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(Y, Y), nand(nand(nand(Y, Y), Y), nand(Y, Y)))))
% 84.97/11.37 = { by lemma 29 }
% 84.97/11.37 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(Y, Y), nand(nand(Y, nand(Y, Y)), nand(Y, Y)))))
% 84.97/11.37 = { by lemma 20 R->L }
% 84.97/11.37 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), nand(nand(nand(X, nand(Y, Y)), nand(nand(nand(nand(Y, Y), nand(Y, nand(Y, Y))), nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(Y, Y), nand(nand(Y, nand(Y, Y)), nand(Y, Y)))))
% 84.97/11.37 = { by lemma 3 R->L }
% 84.97/11.37 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), nand(nand(nand(X, nand(Y, Y)), nand(nand(nand(nand(Y, Y), nand(nand(nand(nand(Y, Y), nand(nand(Y, nand(Y, Y)), nand(Y, Y))), nand(Y, Y)), nand(Y, Y))), nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(Y, Y), nand(nand(Y, nand(Y, Y)), nand(Y, Y)))))
% 84.97/11.37 = { by lemma 4 }
% 84.97/11.37 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), nand(nand(Y, Y), nand(nand(nand(nand(Y, Y), nand(nand(Y, nand(Y, Y)), nand(Y, Y))), nand(Y, Y)), nand(Y, Y))))
% 84.97/11.37 = { by lemma 3 }
% 84.97/11.37 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), nand(nand(Y, Y), nand(Y, nand(Y, Y))))
% 84.97/11.37 = { by lemma 20 }
% 84.97/11.37 nand(nand(nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), Y)
% 84.97/11.37 = { by lemma 34 }
% 84.97/11.37 nand(nand(nand(Y, Y), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y)))), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), Y)
% 84.97/11.37 = { by lemma 34 }
% 84.97/11.37 nand(nand(nand(Y, Y), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(Y, Y)), nand(nand(nand(Y, Y), Y), nand(nand(Y, Y), nand(Z, Y))))), Y)
% 84.97/11.37 = { by lemma 34 }
% 84.97/11.37 nand(nand(nand(Y, Y), nand(nand(nand(nand(X, nand(Y, Y)), nand(nand(Y, nand(X, nand(Y, Y))), nand(X, nand(Y, Y)))), nand(Y, Y)), nand(Y, Y))), Y)
% 84.97/11.37 = { by lemma 9 }
% 84.97/11.37 nand(nand(nand(Y, Y), nand(Y, nand(Y, Y))), Y)
% 84.97/11.37 = { by lemma 20 }
% 84.97/11.37 nand(Y, Y)
% 84.97/11.37
% 84.97/11.37 Lemma 36: nand(nand(X, X), nand(X, Y)) = X.
% 84.97/11.37 Proof:
% 84.97/11.37 nand(nand(X, X), nand(X, Y))
% 84.97/11.37 = { by lemma 35 R->L }
% 84.97/11.37 nand(nand(nand(Y, nand(X, X)), nand(nand(X, nand(Y, nand(X, X))), nand(Y, nand(X, X)))), nand(X, Y))
% 84.97/11.37 = { by lemma 2 }
% 84.97/11.37 X
% 84.97/11.37
% 84.97/11.37 Lemma 37: nand(nand(nand(X, X), nand(Y, X)), nand(nand(Z, X), nand(nand(nand(Z, X), nand(Z, X)), nand(Z, X)))) = nand(nand(nand(X, X), nand(W, X)), Z).
% 84.97/11.37 Proof:
% 84.97/11.37 nand(nand(nand(X, X), nand(Y, X)), nand(nand(Z, X), nand(nand(nand(Z, X), nand(Z, X)), nand(Z, X))))
% 84.97/11.37 = { by lemma 11 }
% 84.97/11.37 nand(X, nand(nand(Z, X), nand(nand(nand(Z, X), nand(Z, X)), nand(Z, X))))
% 84.97/11.37 = { by lemma 18 R->L }
% 84.97/11.37 nand(X, nand(nand(nand(nand(Z, X), nand(nand(nand(Z, X), nand(Z, X)), nand(Z, X))), X), X))
% 84.97/11.37 = { by lemma 22 R->L }
% 84.97/11.37 nand(X, nand(nand(nand(nand(Z, X), nand(nand(nand(Z, X), nand(Z, X)), nand(Z, X))), nand(nand(Z, X), nand(nand(nand(X, X), nand(Z, X)), nand(Z, X)))), X))
% 84.97/11.37 = { by axiom 1 (sh_1) }
% 84.97/11.37 nand(X, nand(nand(Z, X), X))
% 84.97/11.37 = { by lemma 18 }
% 84.97/11.37 nand(X, Z)
% 84.97/11.37 = { by lemma 11 R->L }
% 84.97/11.37 nand(nand(nand(X, X), nand(W, X)), Z)
% 84.97/11.37
% 84.97/11.37 Lemma 38: nand(nand(nand(X, X), nand(Y, X)), Z) = nand(Z, X).
% 84.97/11.37 Proof:
% 84.97/11.37 nand(nand(nand(X, X), nand(Y, X)), Z)
% 84.97/11.37 = { by lemma 37 R->L }
% 84.97/11.37 nand(nand(nand(X, X), nand(W, X)), nand(nand(Z, X), nand(nand(nand(Z, X), nand(Z, X)), nand(Z, X))))
% 84.97/11.37 = { by lemma 7 }
% 84.97/11.37 nand(nand(nand(X, X), nand(W, X)), nand(nand(Z, X), nand(Z, X)))
% 84.97/11.37 = { by lemma 11 }
% 84.97/11.37 nand(X, nand(nand(Z, X), nand(Z, X)))
% 84.97/11.37 = { by lemma 18 R->L }
% 84.97/11.37 nand(X, nand(nand(nand(nand(Z, X), nand(Z, X)), X), X))
% 84.97/11.37 = { by lemma 4 R->L }
% 84.97/11.37 nand(nand(nand(Z, X), nand(nand(nand(X, nand(nand(nand(nand(Z, X), nand(Z, X)), X), X)), nand(Z, X)), nand(Z, X))), nand(nand(Z, X), nand(Z, X)))
% 84.97/11.37 = { by lemma 8 }
% 84.97/11.37 nand(nand(nand(Z, X), nand(nand(nand(Z, X), nand(Z, X)), nand(Z, X))), nand(nand(Z, X), nand(Z, X)))
% 84.97/11.37 = { by lemma 7 }
% 84.97/11.37 nand(nand(nand(Z, X), nand(Z, X)), nand(nand(Z, X), nand(Z, X)))
% 84.97/11.37 = { by lemma 11 }
% 84.97/11.37 nand(Z, X)
% 84.97/11.37
% 84.97/11.37 Lemma 39: nand(nand(nand(X, X), nand(Y, X)), nand(nand(Z, X), nand(Z, X))) = nand(Z, X).
% 84.97/11.37 Proof:
% 84.97/11.37 nand(nand(nand(X, X), nand(Y, X)), nand(nand(Z, X), nand(Z, X)))
% 84.97/11.37 = { by lemma 7 R->L }
% 84.97/11.37 nand(nand(nand(X, X), nand(Y, X)), nand(nand(Z, X), nand(nand(nand(Z, X), nand(Z, X)), nand(Z, X))))
% 84.97/11.37 = { by lemma 37 }
% 84.97/11.37 nand(nand(nand(X, X), nand(W, X)), Z)
% 84.97/11.37 = { by lemma 38 }
% 84.97/11.37 nand(Z, X)
% 84.97/11.37
% 84.97/11.37 Lemma 40: nand(nand(X, X), nand(Z, X)) = nand(nand(X, X), nand(Y, X)).
% 84.97/11.37 Proof:
% 84.97/11.37 nand(nand(X, X), nand(Z, X))
% 84.97/11.37 = { by lemma 11 }
% 84.97/11.37 X
% 84.97/11.37 = { by lemma 36 R->L }
% 84.97/11.37 nand(nand(X, X), nand(X, nand(X, X)))
% 84.97/11.37 = { by lemma 9 R->L }
% 84.97/11.37 nand(nand(X, X), nand(nand(nand(nand(nand(Y, X), nand(Y, X)), nand(nand(X, nand(nand(Y, X), nand(Y, X))), nand(nand(Y, X), nand(Y, X)))), nand(X, X)), nand(X, X)))
% 84.97/11.37 = { by lemma 4 R->L }
% 84.97/11.37 nand(nand(nand(V, nand(X, X)), nand(nand(nand(nand(X, X), nand(nand(nand(nand(nand(Y, X), nand(Y, X)), nand(nand(X, nand(nand(Y, X), nand(Y, X))), nand(nand(Y, X), nand(Y, X)))), nand(X, X)), nand(X, X))), nand(V, nand(X, X))), nand(V, nand(X, X)))), nand(nand(nand(Y, X), nand(Y, X)), nand(nand(X, nand(nand(Y, X), nand(Y, X))), nand(nand(Y, X), nand(Y, X)))))
% 84.97/11.37 = { by lemma 9 }
% 84.97/11.37 nand(nand(nand(V, nand(X, X)), nand(nand(nand(nand(X, X), nand(X, nand(X, X))), nand(V, nand(X, X))), nand(V, nand(X, X)))), nand(nand(nand(Y, X), nand(Y, X)), nand(nand(X, nand(nand(Y, X), nand(Y, X))), nand(nand(Y, X), nand(Y, X)))))
% 84.97/11.37 = { by lemma 36 }
% 84.97/11.37 nand(nand(nand(V, nand(X, X)), nand(nand(X, nand(V, nand(X, X))), nand(V, nand(X, X)))), nand(nand(nand(Y, X), nand(Y, X)), nand(nand(X, nand(nand(Y, X), nand(Y, X))), nand(nand(Y, X), nand(Y, X)))))
% 84.97/11.37 = { by lemma 35 }
% 84.97/11.37 nand(nand(X, X), nand(nand(nand(Y, X), nand(Y, X)), nand(nand(X, nand(nand(Y, X), nand(Y, X))), nand(nand(Y, X), nand(Y, X)))))
% 84.97/11.37 = { by lemma 11 R->L }
% 84.97/11.37 nand(nand(X, X), nand(nand(nand(Y, X), nand(Y, X)), nand(nand(nand(nand(X, X), nand(W, X)), nand(nand(Y, X), nand(Y, X))), nand(nand(Y, X), nand(Y, X)))))
% 84.97/11.37 = { by lemma 39 }
% 84.97/11.37 nand(nand(X, X), nand(nand(nand(Y, X), nand(Y, X)), nand(nand(Y, X), nand(nand(Y, X), nand(Y, X)))))
% 84.97/11.37 = { by lemma 20 }
% 84.97/11.37 nand(nand(X, X), nand(Y, X))
% 84.97/11.37
% 84.97/11.37 Lemma 41: nand(nand(X, Y), nand(Y, nand(X, Z))) = Y.
% 84.97/11.37 Proof:
% 84.97/11.37 nand(nand(X, Y), nand(Y, nand(X, Z)))
% 84.97/11.37 = { by lemma 18 R->L }
% 84.97/11.37 nand(nand(X, nand(nand(Y, X), X)), nand(Y, nand(X, Z)))
% 84.97/11.37 = { by lemma 17 }
% 84.97/11.37 Y
% 84.97/11.37
% 84.97/11.37 Lemma 42: nand(nand(X, nand(Y, Z)), nand(X, Z)) = X.
% 84.97/11.37 Proof:
% 84.97/11.37 nand(nand(X, nand(Y, Z)), nand(X, Z))
% 84.97/11.37 = { by lemma 30 R->L }
% 84.97/11.37 nand(nand(nand(Y, Z), nand(nand(X, nand(Y, Z)), nand(Y, Z))), nand(X, Z))
% 84.97/11.37 = { by lemma 38 R->L }
% 84.97/11.37 nand(nand(nand(Y, Z), nand(nand(X, nand(nand(nand(Z, Z), nand(W, Z)), Y)), nand(Y, Z))), nand(X, Z))
% 84.97/11.37 = { by lemma 38 R->L }
% 84.97/11.37 nand(nand(nand(Y, Z), nand(nand(X, nand(nand(nand(Z, Z), nand(W, Z)), Y)), nand(nand(nand(Z, Z), nand(V, Z)), Y))), nand(X, Z))
% 84.97/11.37 = { by lemma 38 R->L }
% 84.97/11.37 nand(nand(nand(nand(nand(Z, Z), nand(U, Z)), Y), nand(nand(X, nand(nand(nand(Z, Z), nand(W, Z)), Y)), nand(nand(nand(Z, Z), nand(V, Z)), Y))), nand(X, Z))
% 84.97/11.37 = { by lemma 11 }
% 84.97/11.37 nand(nand(nand(Z, Y), nand(nand(X, nand(nand(nand(Z, Z), nand(W, Z)), Y)), nand(nand(nand(Z, Z), nand(V, Z)), Y))), nand(X, Z))
% 84.97/11.37 = { by lemma 11 }
% 84.97/11.37 nand(nand(nand(Z, Y), nand(nand(X, nand(Z, Y)), nand(nand(nand(Z, Z), nand(V, Z)), Y))), nand(X, Z))
% 84.97/11.37 = { by lemma 11 }
% 84.97/11.37 nand(nand(nand(Z, Y), nand(nand(X, nand(Z, Y)), nand(Z, Y))), nand(X, Z))
% 84.97/11.37 = { by lemma 3 }
% 84.97/11.37 X
% 84.97/11.37
% 84.97/11.37 Lemma 43: nand(nand(nand(X, Y), nand(X, Y)), nand(nand(X, X), nand(Z, X))) = nand(X, Y).
% 84.97/11.37 Proof:
% 84.97/11.37 nand(nand(nand(X, Y), nand(X, Y)), nand(nand(X, X), nand(Z, X)))
% 84.97/11.37 = { by lemma 11 }
% 84.97/11.37 nand(nand(nand(X, Y), nand(X, Y)), X)
% 84.97/11.37 = { by lemma 12 }
% 84.97/11.37 nand(X, Y)
% 84.97/11.37
% 84.97/11.37 Lemma 44: nand(nand(nand(X, Y), nand(Y, Z)), X) = nand(X, Y).
% 84.97/11.37 Proof:
% 84.97/11.37 nand(nand(nand(X, Y), nand(Y, Z)), X)
% 84.97/11.37 = { by lemma 30 R->L }
% 84.97/11.37 nand(nand(nand(Y, Z), nand(nand(nand(X, Y), nand(Y, Z)), nand(Y, Z))), X)
% 84.97/11.37 = { by lemma 43 R->L }
% 84.97/11.37 nand(nand(nand(Y, Z), nand(nand(nand(X, Y), nand(nand(nand(Y, Z), nand(Y, Z)), nand(nand(Y, Y), nand(W, Y)))), nand(Y, Z))), X)
% 84.97/11.37 = { by lemma 43 R->L }
% 84.97/11.37 nand(nand(nand(Y, Z), nand(nand(nand(X, Y), nand(nand(nand(Y, Z), nand(Y, Z)), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(Y, Z)), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.37 = { by lemma 7 R->L }
% 84.97/11.37 nand(nand(nand(Y, Z), nand(nand(nand(X, Y), nand(nand(nand(Y, Z), nand(nand(nand(Y, Z), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(Y, Z)), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.37 = { by lemma 7 R->L }
% 84.97/11.37 nand(nand(nand(Y, Z), nand(nand(nand(X, Y), nand(nand(nand(Y, Z), nand(nand(nand(Y, Z), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Y, Z), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.37 = { by lemma 30 R->L }
% 84.97/11.37 nand(nand(nand(Z, nand(nand(Y, Z), Z)), nand(nand(nand(X, Y), nand(nand(nand(Y, Z), nand(nand(nand(Y, Z), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Y, Z), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.37 = { by lemma 30 R->L }
% 84.97/11.37 nand(nand(nand(Z, nand(nand(Y, Z), Z)), nand(nand(nand(X, Y), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(Y, Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Y, Z), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.38 = { by lemma 30 R->L }
% 84.97/11.38 nand(nand(nand(Z, nand(nand(Y, Z), Z)), nand(nand(nand(X, Y), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(Y, Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(Y, Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.38 = { by lemma 11 R->L }
% 84.97/11.38 nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(nand(nand(X, Y), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(Y, Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(Y, Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.38 = { by lemma 11 R->L }
% 84.97/11.38 nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(nand(nand(X, Y), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(Y, Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.38 = { by lemma 11 R->L }
% 84.97/11.38 nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(nand(nand(X, Y), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.38 = { by lemma 4 R->L }
% 84.97/11.38 nand(nand(nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(U, Y))), nand(nand(nand(X, Y), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.38 = { by lemma 38 R->L }
% 84.97/11.38 nand(nand(nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(U, Y))), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), X), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.38 = { by lemma 11 }
% 84.97/11.38 nand(nand(nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(U, Y))), nand(nand(nand(Y, X), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.38 = { by lemma 18 R->L }
% 84.97/11.38 nand(nand(nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(U, Y))), nand(nand(nand(Y, nand(nand(X, Y), Y)), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.38 = { by lemma 11 R->L }
% 84.97/11.38 nand(nand(nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(U, Y))), nand(nand(nand(nand(nand(Y, Y), nand(S, Y)), nand(nand(X, Y), Y)), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.38 = { by lemma 11 R->L }
% 84.97/11.38 nand(nand(nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(U, Y))), nand(nand(nand(nand(nand(Y, Y), nand(S, Y)), nand(nand(X, Y), nand(nand(Y, Y), nand(X2, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.38 = { by lemma 11 }
% 84.97/11.38 nand(nand(nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), Y), nand(nand(nand(nand(nand(Y, Y), nand(S, Y)), nand(nand(X, Y), nand(nand(Y, Y), nand(X2, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.38 = { by lemma 11 }
% 84.97/11.38 nand(nand(nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), Y), nand(nand(nand(Y, nand(nand(X, Y), nand(nand(Y, Y), nand(X2, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.38 = { by lemma 11 }
% 84.97/11.38 nand(nand(nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), Y), nand(nand(nand(Y, nand(nand(X, Y), Y)), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(W, Y)))), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.38 = { by lemma 11 }
% 84.97/11.38 nand(nand(nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), Y), nand(nand(nand(Y, nand(nand(X, Y), Y)), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), Y)), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), nand(nand(Y, Y), nand(V, Y))))), X)
% 84.97/11.38 = { by lemma 11 }
% 84.97/11.38 nand(nand(nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), Y), nand(nand(nand(Y, nand(nand(X, Y), Y)), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), Y)), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), Y))), X)
% 84.97/11.38 = { by axiom 1 (sh_1) R->L }
% 84.97/11.38 nand(nand(nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), Y), nand(nand(nand(Y, nand(nand(X, Y), Y)), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), Y)), nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), Y))), nand(nand(Y, nand(nand(X, Y), Y)), nand(X, nand(nand(nand(Y, Z), nand(nand(nand(Z, nand(nand(nand(nand(Y, Y), nand(U, Y)), Z), Z)), nand(Y, Z)), nand(Y, Z))), Y))))
% 84.97/11.38 = { by axiom 1 (sh_1) }
% 84.97/11.38 nand(Y, nand(nand(X, Y), Y))
% 84.97/11.38 = { by lemma 18 }
% 84.97/11.38 nand(Y, X)
% 84.97/11.38 = { by lemma 11 R->L }
% 84.97/11.38 nand(nand(nand(Y, Y), nand(Y2, Y)), X)
% 84.97/11.38 = { by lemma 38 }
% 84.97/11.38 nand(X, Y)
% 84.97/11.38
% 84.97/11.38 Lemma 45: nand(nand(nand(X, X), nand(Y, X)), nand(nand(Z, nand(nand(X, X), nand(W, X))), nand(nand(X, X), nand(V, X)))) = nand(nand(nand(X, X), nand(U, X)), Z).
% 84.97/11.38 Proof:
% 84.97/11.38 nand(nand(nand(X, X), nand(Y, X)), nand(nand(Z, nand(nand(X, X), nand(W, X))), nand(nand(X, X), nand(V, X))))
% 84.97/11.38 = { by lemma 11 }
% 84.97/11.38 nand(nand(nand(X, X), nand(Y, X)), nand(nand(Z, X), nand(nand(X, X), nand(V, X))))
% 84.97/11.38 = { by lemma 11 }
% 84.97/11.38 nand(nand(nand(X, X), nand(Y, X)), nand(nand(Z, X), X))
% 84.97/11.38 = { by lemma 11 }
% 84.97/11.38 nand(X, nand(nand(Z, X), X))
% 84.97/11.38 = { by lemma 18 }
% 84.97/11.38 nand(X, Z)
% 84.97/11.38 = { by lemma 11 R->L }
% 84.97/11.38 nand(nand(nand(X, X), nand(U, X)), Z)
% 84.97/11.38
% 84.97/11.38 Lemma 46: nand(nand(nand(Y, Y), nand(W, Y)), X) = nand(X, nand(nand(Y, Y), nand(Z, Y))).
% 84.97/11.38 Proof:
% 84.97/11.38 nand(nand(nand(Y, Y), nand(W, Y)), X)
% 84.97/11.38 = { by lemma 45 R->L }
% 84.97/11.38 nand(nand(nand(Y, Y), nand(U, Y)), nand(nand(X, nand(nand(Y, Y), nand(T, Y))), nand(nand(Y, Y), nand(V, Y))))
% 84.97/11.38 = { by lemma 40 }
% 84.97/11.38 nand(nand(nand(Y, Y), nand(U, Y)), nand(nand(X, nand(nand(Y, Y), nand(Y, Y))), nand(nand(Y, Y), nand(V, Y))))
% 84.97/11.38 = { by lemma 40 }
% 84.97/11.38 nand(nand(nand(Y, Y), nand(Y, Y)), nand(nand(X, nand(nand(Y, Y), nand(Y, Y))), nand(nand(Y, Y), nand(V, Y))))
% 84.97/11.38 = { by axiom 1 (sh_1) R->L }
% 84.97/11.38 nand(nand(nand(nand(nand(Y, Y), nand(Y, Y)), nand(nand(nand(nand(Y, Y), nand(Y, Y)), nand(nand(Y, Y), nand(Y, Y))), nand(nand(Y, Y), nand(Y, Y)))), nand(nand(nand(Y, Y), nand(Y, Y)), nand(nand(nand(nand(X, nand(nand(Y, Y), nand(Y, Y))), nand(X, nand(nand(Y, Y), nand(Y, Y)))), nand(nand(Y, Y), nand(Y, Y))), nand(nand(Y, Y), nand(Y, Y))))), nand(nand(X, nand(nand(Y, Y), nand(Y, Y))), nand(nand(Y, Y), nand(V, Y))))
% 84.97/11.38 = { by lemma 11 }
% 84.97/11.38 nand(nand(nand(nand(nand(Y, Y), nand(Y, Y)), nand(nand(Y, Y), nand(nand(Y, Y), nand(Y, Y)))), nand(nand(nand(Y, Y), nand(Y, Y)), nand(nand(nand(nand(X, nand(nand(Y, Y), nand(Y, Y))), nand(X, nand(nand(Y, Y), nand(Y, Y)))), nand(nand(Y, Y), nand(Y, Y))), nand(nand(Y, Y), nand(Y, Y))))), nand(nand(X, nand(nand(Y, Y), nand(Y, Y))), nand(nand(Y, Y), nand(V, Y))))
% 84.97/11.38 = { by lemma 20 }
% 84.97/11.38 nand(nand(nand(Y, Y), nand(nand(nand(Y, Y), nand(Y, Y)), nand(nand(nand(nand(X, nand(nand(Y, Y), nand(Y, Y))), nand(X, nand(nand(Y, Y), nand(Y, Y)))), nand(nand(Y, Y), nand(Y, Y))), nand(nand(Y, Y), nand(Y, Y))))), nand(nand(X, nand(nand(Y, Y), nand(Y, Y))), nand(nand(Y, Y), nand(V, Y))))
% 84.97/11.38 = { by lemma 10 }
% 84.97/11.38 nand(nand(nand(Y, Y), nand(X, nand(nand(Y, Y), nand(Y, Y)))), nand(nand(X, nand(nand(Y, Y), nand(Y, Y))), nand(nand(Y, Y), nand(V, Y))))
% 84.97/11.38 = { by lemma 41 }
% 84.97/11.38 nand(X, nand(nand(Y, Y), nand(Y, Y)))
% 84.97/11.38 = { by lemma 40 R->L }
% 84.97/11.38 nand(X, nand(nand(Y, Y), nand(Z, Y)))
% 84.97/11.38
% 84.97/11.38 Lemma 47: nand(nand(nand(Y, Y), nand(W, Y)), nand(X, Y)) = nand(nand(X, Y), nand(nand(Y, Y), nand(Z, Y))).
% 84.97/11.38 Proof:
% 84.97/11.38 nand(nand(nand(Y, Y), nand(W, Y)), nand(X, Y))
% 84.97/11.38 = { by lemma 11 }
% 84.97/11.38 nand(Y, nand(X, Y))
% 84.97/11.38 = { by lemma 26 R->L }
% 84.97/11.38 nand(nand(Y, nand(nand(X, Y), Y)), Y)
% 84.97/11.38 = { by lemma 18 }
% 84.97/11.38 nand(nand(Y, X), Y)
% 84.97/11.38 = { by lemma 29 R->L }
% 84.97/11.38 nand(nand(X, Y), Y)
% 84.97/11.38 = { by lemma 11 R->L }
% 84.97/11.38 nand(nand(X, Y), nand(nand(Y, Y), nand(Z, Y)))
% 84.97/11.38
% 84.97/11.38 Lemma 48: nand(nand(X, nand(nand(nand(X, Y), X), X)), X) = nand(X, Y).
% 84.97/11.38 Proof:
% 84.97/11.38 nand(nand(X, nand(nand(nand(X, Y), X), X)), X)
% 84.97/11.38 = { by lemma 14 R->L }
% 84.97/11.38 nand(nand(X, nand(nand(nand(X, Y), X), X)), nand(nand(X, Y), nand(X, nand(X, Y))))
% 84.97/11.38 = { by lemma 17 }
% 84.97/11.38 nand(X, Y)
% 84.97/11.38
% 84.97/11.39 Lemma 49: nand(nand(X, Y), nand(nand(nand(Y, Y), nand(Z, Y)), nand(W, X))) = nand(nand(Y, Y), nand(V, Y)).
% 84.97/11.39 Proof:
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(Y, Y), nand(Z, Y)), nand(W, X)))
% 84.97/11.39 = { by lemma 40 }
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(Y, Y), nand(V, Y)), nand(W, X)))
% 84.97/11.39 = { by lemma 25 R->L }
% 84.97/11.39 nand(nand(X, nand(nand(X, Y), X)), nand(nand(nand(Y, Y), nand(V, Y)), nand(W, X)))
% 84.97/11.39 = { by lemma 38 R->L }
% 84.97/11.39 nand(nand(X, nand(nand(nand(nand(Y, Y), nand(V, Y)), X), X)), nand(nand(nand(Y, Y), nand(V, Y)), nand(W, X)))
% 84.97/11.39 = { by axiom 1 (sh_1) }
% 84.97/11.39 nand(nand(Y, Y), nand(V, Y))
% 84.97/11.39
% 84.97/11.39 Lemma 50: nand(nand(nand(nand(X, X), nand(Y, X)), nand(Z, X)), nand(Z, X)) = nand(nand(X, X), nand(W, X)).
% 84.97/11.39 Proof:
% 84.97/11.39 nand(nand(nand(nand(X, X), nand(Y, X)), nand(Z, X)), nand(Z, X))
% 84.97/11.39 = { by lemma 11 }
% 84.97/11.39 nand(nand(X, nand(Z, X)), nand(Z, X))
% 84.97/11.39 = { by lemma 29 }
% 84.97/11.39 nand(nand(X, nand(Z, X)), nand(X, Z))
% 84.97/11.39 = { by lemma 18 R->L }
% 84.97/11.39 nand(nand(X, nand(Z, X)), nand(X, nand(nand(Z, X), X)))
% 84.97/11.39 = { by lemma 28 }
% 84.97/11.39 X
% 84.97/11.39 = { by lemma 11 R->L }
% 84.97/11.39 nand(nand(X, X), nand(W, X))
% 84.97/11.39
% 84.97/11.39 Lemma 51: nand(nand(nand(X, Y), nand(nand(nand(nand(nand(Y, Y), nand(Z, Y)), W), nand(X, Y)), nand(X, Y))), W) = nand(nand(nand(Y, Y), nand(V, Y)), W).
% 84.97/11.39 Proof:
% 84.97/11.39 nand(nand(nand(X, Y), nand(nand(nand(nand(nand(Y, Y), nand(Z, Y)), W), nand(X, Y)), nand(X, Y))), W)
% 84.97/11.39 = { by lemma 11 }
% 84.97/11.39 nand(nand(nand(X, Y), nand(nand(nand(Y, W), nand(X, Y)), nand(X, Y))), W)
% 84.97/11.39 = { by lemma 18 R->L }
% 84.97/11.39 nand(nand(nand(X, Y), nand(nand(nand(Y, nand(nand(W, Y), Y)), nand(X, Y)), nand(X, Y))), W)
% 84.97/11.39 = { by axiom 1 (sh_1) R->L }
% 84.97/11.39 nand(nand(nand(X, Y), nand(nand(nand(Y, nand(nand(W, Y), Y)), nand(X, Y)), nand(X, Y))), nand(nand(Y, nand(nand(W, Y), Y)), nand(W, nand(X, Y))))
% 84.97/11.39 = { by axiom 1 (sh_1) }
% 84.97/11.39 nand(Y, nand(nand(W, Y), Y))
% 84.97/11.39 = { by lemma 18 }
% 84.97/11.39 nand(Y, W)
% 84.97/11.39 = { by lemma 11 R->L }
% 84.97/11.39 nand(nand(nand(Y, Y), nand(V, Y)), W)
% 84.97/11.39
% 84.97/11.39 Lemma 52: nand(nand(X, Y), nand(nand(nand(Z, X), Y), nand(nand(Z, X), Y))) = nand(nand(nand(Y, Y), nand(W, Y)), nand(X, Y)).
% 84.97/11.39 Proof:
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(Z, X), Y), nand(nand(Z, X), Y)))
% 84.97/11.39 = { by axiom 1 (sh_1) R->L }
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(Z, X), Y), nand(nand(nand(X, Y), nand(nand(nand(nand(Z, X), Y), nand(X, Y)), nand(X, Y))), nand(nand(nand(Z, X), Y), nand(nand(nand(Y, Y), nand(V, Y)), nand(X, Y))))))
% 84.97/11.39 = { by lemma 38 R->L }
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(Z, X), Y), nand(nand(nand(X, Y), nand(nand(nand(nand(Z, X), Y), nand(nand(nand(Y, Y), nand(U, Y)), X)), nand(X, Y))), nand(nand(nand(Z, X), Y), nand(nand(nand(Y, Y), nand(V, Y)), nand(X, Y))))))
% 84.97/11.39 = { by lemma 11 R->L }
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(Z, X), Y), nand(nand(nand(X, Y), nand(nand(nand(nand(Z, X), Y), nand(nand(nand(Y, Y), nand(U, Y)), nand(nand(X, X), nand(Z, X)))), nand(X, Y))), nand(nand(nand(Z, X), Y), nand(nand(nand(Y, Y), nand(V, Y)), nand(X, Y))))))
% 84.97/11.39 = { by lemma 49 }
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(Z, X), Y), nand(nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))), nand(nand(nand(Z, X), Y), nand(nand(nand(Y, Y), nand(V, Y)), nand(X, Y))))))
% 84.97/11.39 = { by axiom 1 (sh_1) R->L }
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))), nand(nand(nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))), nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y)))), nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))))), nand(nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))), nand(nand(Y, Y), nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y)))))), nand(nand(nand(Z, X), Y), nand(nand(nand(Y, Y), nand(V, Y)), nand(X, Y))))))
% 84.97/11.39 = { by lemma 17 }
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))), nand(nand(nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))), nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y)))), nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))))), nand(Y, Y)), nand(nand(nand(Z, X), Y), nand(nand(nand(Y, Y), nand(V, Y)), nand(X, Y))))))
% 84.97/11.39 = { by lemma 19 }
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))), nand(nand(Y, Y), nand(nand(X, Y), nand(nand(nand(Y, Y), nand(X, Y)), nand(X, Y))))), nand(Y, Y)), nand(nand(nand(Z, X), Y), nand(nand(nand(Y, Y), nand(V, Y)), nand(X, Y))))))
% 84.97/11.39 = { by lemma 21 }
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(Z, X), Y), nand(Y, nand(nand(nand(Z, X), Y), nand(nand(nand(Y, Y), nand(V, Y)), nand(X, Y))))))
% 84.97/11.39 = { by lemma 11 R->L }
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(Z, X), Y), nand(nand(nand(Y, Y), nand(V, Y)), nand(nand(nand(Z, X), Y), nand(nand(nand(Y, Y), nand(V, Y)), nand(X, Y))))))
% 84.97/11.39 = { by lemma 29 R->L }
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(Z, X), Y), nand(nand(nand(Y, Y), nand(V, Y)), nand(nand(nand(Z, X), Y), nand(nand(X, Y), nand(nand(Y, Y), nand(V, Y)))))))
% 84.97/11.39 = { by lemma 31 }
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(Z, X), Y), nand(nand(X, Y), nand(nand(Y, Y), nand(V, Y)))))
% 84.97/11.39 = { by lemma 47 R->L }
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(Z, X), Y), nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y))))
% 84.97/11.39 = { by lemma 29 }
% 84.97/11.39 nand(nand(X, Y), nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)))
% 84.97/11.39 = { by lemma 30 R->L }
% 86.00/11.39 nand(nand(X, Y), nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))))
% 86.00/11.39 = { by lemma 29 }
% 86.00/11.39 nand(nand(Y, X), nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))))
% 86.00/11.39 = { by lemma 18 R->L }
% 86.00/11.39 nand(nand(Y, nand(nand(X, Y), Y)), nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))))
% 86.00/11.39 = { by lemma 27 }
% 86.00/11.39 nand(nand(Y, nand(Y, nand(X, Y))), nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))))
% 86.00/11.39 = { by lemma 11 R->L }
% 86.00/11.39 nand(nand(nand(nand(Y, Y), nand(S, Y)), nand(Y, nand(X, Y))), nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))))
% 86.00/11.39 = { by lemma 11 R->L }
% 86.00/11.39 nand(nand(nand(nand(Y, Y), nand(S, Y)), nand(nand(nand(Y, Y), nand(X2, Y)), nand(X, Y))), nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))))
% 86.00/11.39 = { by lemma 47 }
% 86.00/11.39 nand(nand(nand(nand(Y, Y), nand(S, Y)), nand(nand(X, Y), nand(nand(Y, Y), nand(Y2, Y)))), nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))))
% 86.00/11.39 = { by lemma 50 R->L }
% 86.00/11.39 nand(nand(nand(nand(Y, Y), nand(S, Y)), nand(nand(X, Y), nand(nand(nand(nand(Y, Y), nand(Z2, Y)), nand(X, Y)), nand(X, Y)))), nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))))
% 86.00/11.39 = { by lemma 51 R->L }
% 86.00/11.39 nand(nand(nand(nand(Y, Y), nand(S, Y)), nand(nand(X, Y), nand(nand(nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))), nand(X, Y)), nand(X, Y)))), nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))))
% 86.00/11.39 = { by lemma 45 R->L }
% 86.00/11.39 nand(nand(nand(nand(Y, Y), nand(X, Y)), nand(nand(nand(nand(X, Y), nand(nand(nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))), nand(X, Y)), nand(X, Y))), nand(nand(Y, Y), nand(X, Y))), nand(nand(Y, Y), nand(X, Y)))), nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))))
% 86.00/11.39 = { by axiom 1 (sh_1) R->L }
% 86.00/11.39 nand(nand(nand(nand(Y, Y), nand(X, Y)), nand(nand(nand(nand(X, Y), nand(nand(nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))), nand(X, Y)), nand(X, Y))), nand(nand(Y, Y), nand(X, Y))), nand(nand(Y, Y), nand(X, Y)))), nand(nand(nand(X, Y), nand(nand(nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))), nand(X, Y)), nand(X, Y))), nand(nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))), nand(nand(Y, Y), nand(X, Y)))))
% 86.00/11.39 = { by axiom 1 (sh_1) }
% 86.00/11.39 nand(nand(X, Y), nand(nand(nand(nand(nand(Z, X), Y), nand(nand(nand(nand(nand(Y, Y), nand(T, Y)), nand(X, Y)), nand(nand(Z, X), Y)), nand(nand(Z, X), Y))), nand(X, Y)), nand(X, Y)))
% 86.00/11.39 = { by lemma 51 }
% 86.00/11.39 nand(nand(X, Y), nand(nand(nand(nand(Y, Y), nand(W2, Y)), nand(X, Y)), nand(X, Y)))
% 86.00/11.39 = { by lemma 50 }
% 86.00/11.39 nand(nand(X, Y), nand(nand(Y, Y), nand(V2, Y)))
% 86.00/11.39 = { by lemma 47 R->L }
% 86.00/11.39 nand(nand(nand(Y, Y), nand(W, Y)), nand(X, Y))
% 86.00/11.39
% 86.00/11.39 Lemma 53: nand(nand(X, Y), nand(nand(nand(X, X), nand(Z, X)), nand(X, Y))) = nand(nand(X, X), nand(W, X)).
% 86.00/11.39 Proof:
% 86.00/11.39 nand(nand(X, Y), nand(nand(nand(X, X), nand(Z, X)), nand(X, Y)))
% 86.00/11.39 = { by lemma 11 }
% 86.00/11.39 nand(nand(X, Y), nand(X, nand(X, Y)))
% 86.00/11.39 = { by lemma 14 }
% 86.00/11.39 X
% 86.00/11.39 = { by lemma 11 R->L }
% 86.04/11.40 nand(nand(X, X), nand(W, X))
% 86.04/11.40
% 86.04/11.40 Lemma 54: nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(X, Y), Y), Z)) = nand(nand(nand(nand(X, Y), Y), Z), nand(Z, nand(Y, nand(W, X)))).
% 86.04/11.40 Proof:
% 86.04/11.40 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(X, Y), Y), Z))
% 86.04/11.40 = { by lemma 33 R->L }
% 86.04/11.40 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))))))
% 86.04/11.40 = { by lemma 5 R->L }
% 86.04/11.40 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(nand(Z, nand(Y, nand(W, X))), nand(nand(Y, nand(W, X)), nand(Y, nand(W, X)))), nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))))), nand(nand(Z, nand(Y, nand(W, X))), nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), Z), Z))))))))
% 86.07/11.40 = { by lemma 11 R->L }
% 86.07/11.40 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(nand(nand(nand(Z, Z), nand(S2, Z)), nand(Y, nand(W, X))), nand(nand(Y, nand(W, X)), nand(Y, nand(W, X)))), nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))))), nand(nand(Z, nand(Y, nand(W, X))), nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), Z), Z))))))))
% 86.07/11.40 = { by lemma 45 R->L }
% 86.07/11.40 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(U2, Z))), nand(nand(Z, Z), nand(U2, Z)))), nand(nand(Y, nand(W, X)), nand(Y, nand(W, X)))), nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))))), nand(nand(Z, nand(Y, nand(W, X))), nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), Z), Z))))))))
% 86.07/11.40 = { by lemma 5 R->L }
% 86.07/11.40 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(U2, Z))), nand(nand(Z, Z), nand(U2, Z)))), nand(nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(Y, nand(W, X)), nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))), nand(Y, nand(W, X))))), nand(nand(Y, nand(W, X)), nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))), nand(Y, nand(W, X)))))), nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(T2, nand(Y, nand(W, X)))), nand(nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(Z, Z), nand(U2, Z)), nand(T2, nand(Y, nand(W, X))))), nand(nand(nand(Z, Z), nand(U2, Z)), nand(T2, nand(Y, nand(W, X))))))))), nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))))), nand(nand(Z, nand(Y, nand(W, X))), nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), Z), Z))))))))
% 86.07/11.41 = { by axiom 1 (sh_1) }
% 86.07/11.41 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(U2, Z))), nand(nand(Z, Z), nand(U2, Z)))), nand(nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(Y, nand(W, X)), nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))), nand(Y, nand(W, X))))), nand(nand(Y, nand(W, X)), nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))), nand(Y, nand(W, X)))))), nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(T2, nand(Y, nand(W, X)))), nand(nand(nand(Z, Z), nand(U2, Z)), nand(nand(nand(Z, Z), nand(U2, Z)), nand(T2, nand(Y, nand(W, X))))))))), nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))))), nand(nand(Z, nand(Y, nand(W, X))), nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), Z), Z))))))))
% 86.07/11.41 = { by lemma 14 }
% 86.07/11.41 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(U2, Z))), nand(nand(Z, Z), nand(U2, Z)))), nand(nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(Y, nand(W, X)), nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))), nand(Y, nand(W, X))))), nand(nand(Y, nand(W, X)), nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))), nand(Y, nand(W, X)))))), nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(Z, Z), nand(U2, Z))))), nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))))), nand(nand(Z, nand(Y, nand(W, X))), nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), Z), Z))))))))
% 86.07/11.41 = { by lemma 20 }
% 86.07/11.41 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(U2, Z))), nand(nand(Z, Z), nand(U2, Z)))), nand(nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(Y, nand(W, X)), nand(nand(Y, nand(W, X)), nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))), nand(Y, nand(W, X)))))), nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(Z, Z), nand(U2, Z))))), nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))))), nand(nand(Z, nand(Y, nand(W, X))), nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), Z), Z))))))))
% 86.07/11.41 = { by lemma 30 }
% 86.07/11.41 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(U2, Z))), nand(nand(Z, Z), nand(U2, Z)))), nand(nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(Y, nand(W, X)), nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))))), nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(Z, Z), nand(U2, Z))))), nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))))), nand(nand(Z, nand(Y, nand(W, X))), nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), Z), Z))))))))
% 86.07/11.41 = { by lemma 30 }
% 86.07/11.41 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(U2, Z))), nand(nand(Z, Z), nand(U2, Z)))), nand(nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))), nand(nand(Y, nand(W, X)), nand(nand(nand(Z, Z), nand(U2, Z)), nand(Y, nand(W, X))))), nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(Z, Z), nand(U2, Z))))), nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))))), nand(nand(Z, nand(Y, nand(W, X))), nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), Z), Z))))))))
% 86.07/11.41 = { by lemma 41 }
% 86.07/11.41 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(nand(nand(nand(Z, Z), nand(U2, Z)), nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(U2, Z))), nand(nand(Z, Z), nand(U2, Z)))), nand(nand(Y, nand(W, X)), nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(Z, Z), nand(U2, Z))))), nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))))), nand(nand(Z, nand(Y, nand(W, X))), nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), Z), Z))))))))
% 86.07/11.41 = { by axiom 1 (sh_1) }
% 86.07/11.41 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), nand(nand(Y, nand(W, X)), nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))))), nand(nand(Z, nand(Y, nand(W, X))), nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), Z), Z))))))))
% 86.07/11.41 = { by lemma 36 }
% 86.07/11.41 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, nand(Y, nand(W, X))), nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))), Z), Z))))))))
% 86.07/11.41 = { by lemma 18 }
% 86.07/11.41 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, nand(Y, nand(W, X))), nand(Z, nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))))))))))
% 86.07/11.41 = { by lemma 30 R->L }
% 86.07/11.41 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(Y, nand(W, X)), nand(nand(nand(Y, nand(W, X)), nand(nand(Z, nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(Z, nand(nand(Y, nand(W, X)), nand(Y, nand(W, X))))))))))
% 86.07/11.41 = { by axiom 1 (sh_1) }
% 86.07/11.41 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(Y, nand(W, X)), Z)))))
% 86.07/11.41 = { by lemma 11 R->L }
% 86.07/11.41 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))))))
% 86.07/11.41 = { by lemma 46 }
% 86.07/11.41 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))))))
% 86.07/11.42 = { by lemma 5 R->L }
% 86.07/11.42 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(S, Z)))))))))
% 86.07/11.42 = { by lemma 29 }
% 86.07/11.42 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))))))))
% 86.07/11.42 = { by lemma 46 R->L }
% 86.07/11.42 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(Z, Z), nand(V2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))))))))
% 86.07/11.42 = { by lemma 46 }
% 86.07/11.42 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(Z, Z), nand(V2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.42 = { by lemma 11 }
% 86.07/11.42 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.42 = { by axiom 1 (sh_1) R->L }
% 86.07/11.42 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))))), nand(nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(Z, Z), nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.42 = { by lemma 16 }
% 86.07/11.42 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))))), Z), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.42 = { by lemma 7 }
% 86.07/11.42 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), Z), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.42 = { by lemma 11 R->L }
% 86.07/11.42 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(Z, Z), nand(Y2, Z))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.42 = { by lemma 11 R->L }
% 86.07/11.42 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(Z, Z), nand(Y2, Z))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.42 = { by lemma 11 R->L }
% 86.07/11.42 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(Z, Z), nand(Y2, Z))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.42 = { by lemma 7 R->L }
% 86.07/11.42 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))))), nand(nand(Z, Z), nand(Y2, Z))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.43 = { by lemma 8 R->L }
% 86.07/11.43 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(nand(nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))))), nand(nand(Z, Z), nand(Y2, Z))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.43 = { by lemma 11 }
% 86.07/11.43 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(nand(nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))))), nand(nand(Z, Z), nand(Y2, Z))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.43 = { by lemma 11 }
% 86.07/11.43 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(nand(nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))))), nand(nand(Z, Z), nand(Y2, Z))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.43 = { by lemma 18 R->L }
% 86.07/11.43 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(nand(nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), Z), Z)), nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))))), nand(nand(Z, Z), nand(Y2, Z))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.43 = { by lemma 18 R->L }
% 86.07/11.43 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(nand(nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), Z), Z)), nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), Z), Z))), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))))), nand(nand(Z, Z), nand(Y2, Z))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.43 = { by lemma 17 R->L }
% 86.07/11.43 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(nand(nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), Z), Z)), nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), Z), Z))), nand(nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), Z), Z)), nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), Z), Z))))), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))))), nand(nand(Z, Z), nand(Y2, Z))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.43 = { by lemma 20 }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), Z), Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))))), nand(nand(Z, Z), nand(Y2, Z))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.44 = { by lemma 18 }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))))), nand(nand(Z, Z), nand(Y2, Z))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.44 = { by lemma 11 R->L }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(nand(nand(Z, Z), nand(Y2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(W2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))))), nand(nand(Z, Z), nand(Y2, Z))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.44 = { by lemma 4 }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(nand(nand(Z, Z), nand(Y2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Z, Z), nand(Z2, Z))))))))
% 86.07/11.44 = { by lemma 46 R->L }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(nand(nand(Z, Z), nand(Y2, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))), nand(nand(nand(Z, Z), nand(Y2, Z)), nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))))))))))
% 86.07/11.44 = { by axiom 1 (sh_1) }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Y, nand(W, X)), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(Y, nand(W, X)))), nand(nand(Z, Z), nand(Y2, Z))))))
% 86.07/11.44 = { by lemma 30 }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X))), nand(nand(Z, Z), nand(Y2, Z))))))
% 86.07/11.44 = { by lemma 46 R->L }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(T, Z)), nand(nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))), nand(Y, nand(W, X)))))))
% 86.07/11.44 = { by lemma 29 R->L }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(T, Z)), nand(nand(Y, nand(W, X)), nand(nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z))), nand(nand(Z, Z), nand(X2, Z))))))))
% 86.07/11.44 = { by lemma 46 R->L }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(T, Z)), nand(nand(Y, nand(W, X)), nand(nand(nand(Z, Z), nand(S, Z)), nand(nand(Y, nand(W, X)), nand(nand(Z, Z), nand(S, Z)))))))))
% 86.07/11.44 = { by lemma 33 }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(T, Z)), nand(nand(Y, nand(W, X)), nand(Y, nand(W, X)))))))
% 86.07/11.44 = { by lemma 5 R->L }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(T, Z)), nand(nand(Y, nand(W, X)), nand(nand(nand(X, Y), nand(nand(nand(Y, nand(W, X)), nand(X, Y)), nand(X, Y))), nand(nand(Y, nand(W, X)), nand(Y, nand(nand(nand(X, Y), Y), Y)))))))))
% 86.07/11.44 = { by lemma 29 }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(T, Z)), nand(nand(Y, nand(W, X)), nand(nand(nand(X, Y), nand(nand(nand(Y, nand(W, X)), nand(Y, X)), nand(X, Y))), nand(nand(Y, nand(W, X)), nand(Y, nand(nand(nand(X, Y), Y), Y)))))))))
% 86.07/11.44 = { by lemma 42 }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(T, Z)), nand(nand(Y, nand(W, X)), nand(nand(nand(X, Y), nand(Y, nand(X, Y))), nand(nand(Y, nand(W, X)), nand(Y, nand(nand(nand(X, Y), Y), Y)))))))))
% 86.07/11.44 = { by lemma 13 }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(T, Z)), nand(nand(Y, nand(W, X)), nand(Y, nand(nand(Y, nand(W, X)), nand(Y, nand(nand(nand(X, Y), Y), Y)))))))))
% 86.07/11.44 = { by lemma 30 }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(T, Z)), nand(nand(Y, nand(W, X)), nand(Y, nand(nand(Y, nand(W, X)), nand(nand(X, Y), Y))))))))
% 86.07/11.44 = { by lemma 31 }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(T, Z)), nand(nand(Y, nand(W, X)), nand(nand(X, Y), Y))))))
% 86.07/11.44 = { by lemma 29 R->L }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(T, Z)), nand(nand(nand(X, Y), Y), nand(Y, nand(W, X)))))))
% 86.07/11.44 = { by lemma 12 R->L }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(Z, Z), nand(T, Z)), nand(nand(nand(nand(nand(X, Y), Y), nand(Y, nand(W, X))), nand(nand(nand(X, Y), Y), nand(Y, nand(W, X)))), nand(nand(X, Y), Y))))))
% 86.07/11.44 = { by lemma 49 }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), nand(nand(Z, Z), nand(U, Z))))
% 86.07/11.44 = { by lemma 11 }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(Z, nand(Y, nand(W, X)))), Z))
% 86.07/11.44 = { by lemma 48 R->L }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(Z, nand(nand(nand(Z, nand(Y, nand(W, X))), Z), Z)), Z)), Z))
% 86.07/11.44 = { by lemma 18 }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(Z, nand(Z, nand(Y, nand(W, X)))), Z)), Z))
% 86.07/11.44 = { by lemma 29 R->L }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(nand(nand(Z, Z), nand(V, Z)), nand(nand(nand(Z, nand(Y, nand(W, X))), Z), Z)), Z))
% 86.07/11.44 = { by lemma 11 }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(nand(Z, nand(nand(nand(Z, nand(Y, nand(W, X))), Z), Z)), Z))
% 86.07/11.44 = { by lemma 48 }
% 86.07/11.44 nand(nand(nand(nand(X, Y), Y), Z), nand(Z, nand(Y, nand(W, X))))
% 86.07/11.44
% 86.07/11.44 Lemma 55: nand(nand(nand(X, Y), nand(nand(nand(nand(Z, Z), nand(W, Z)), nand(X, Y)), nand(X, Y))), nand(Z, X)) = nand(nand(Z, Z), nand(V, Z)).
% 86.07/11.44 Proof:
% 86.07/11.44 nand(nand(nand(X, Y), nand(nand(nand(nand(Z, Z), nand(W, Z)), nand(X, Y)), nand(X, Y))), nand(Z, X))
% 86.07/11.44 = { by lemma 11 }
% 86.07/11.44 nand(nand(nand(X, Y), nand(nand(Z, nand(X, Y)), nand(X, Y))), nand(Z, X))
% 86.07/11.44 = { by lemma 3 }
% 86.07/11.44 Z
% 86.07/11.44 = { by lemma 11 R->L }
% 86.07/11.44 nand(nand(Z, Z), nand(V, Z))
% 86.07/11.44
% 86.07/11.44 Lemma 56: nand(nand(nand(X, X), nand(Y, X)), nand(nand(X, nand(Z, nand(X, W))), nand(W, V))) = nand(X, nand(Z, nand(X, W))).
% 86.07/11.44 Proof:
% 86.07/11.44 nand(nand(nand(X, X), nand(Y, X)), nand(nand(X, nand(Z, nand(X, W))), nand(W, V)))
% 86.07/11.44 = { by lemma 46 }
% 86.07/11.44 nand(nand(nand(X, nand(Z, nand(X, W))), nand(W, V)), nand(nand(X, X), nand(U, X)))
% 86.07/11.44 = { by lemma 53 R->L }
% 86.07/11.44 nand(nand(nand(X, nand(Z, nand(X, W))), nand(W, V)), nand(nand(X, W), nand(nand(nand(X, X), nand(T, X)), nand(X, W))))
% 86.07/11.44 = { by lemma 55 R->L }
% 86.07/11.44 nand(nand(nand(X, nand(Z, nand(X, W))), nand(W, V)), nand(nand(X, W), nand(nand(nand(nand(W, V), nand(nand(nand(nand(X, X), nand(S, X)), nand(W, V)), nand(W, V))), nand(X, W)), nand(X, W))))
% 86.07/11.44 = { by lemma 4 R->L }
% 86.07/11.44 nand(nand(nand(X, nand(Z, nand(X, W))), nand(W, V)), nand(nand(nand(Z, nand(X, W)), nand(nand(nand(nand(X, W), nand(nand(nand(nand(W, V), nand(nand(nand(nand(X, X), nand(S, X)), nand(W, V)), nand(W, V))), nand(X, W)), nand(X, W))), nand(Z, nand(X, W))), nand(Z, nand(X, W)))), nand(nand(W, V), nand(nand(nand(nand(X, X), nand(S, X)), nand(W, V)), nand(W, V)))))
% 86.07/11.44 = { by lemma 55 }
% 86.07/11.45 nand(nand(nand(X, nand(Z, nand(X, W))), nand(W, V)), nand(nand(nand(Z, nand(X, W)), nand(nand(nand(nand(X, W), nand(nand(nand(X, X), nand(X2, X)), nand(X, W))), nand(Z, nand(X, W))), nand(Z, nand(X, W)))), nand(nand(W, V), nand(nand(nand(nand(X, X), nand(S, X)), nand(W, V)), nand(W, V)))))
% 86.07/11.45 = { by lemma 53 }
% 86.07/11.45 nand(nand(nand(X, nand(Z, nand(X, W))), nand(W, V)), nand(nand(nand(Z, nand(X, W)), nand(nand(nand(nand(X, X), nand(Y2, X)), nand(Z, nand(X, W))), nand(Z, nand(X, W)))), nand(nand(W, V), nand(nand(nand(nand(X, X), nand(S, X)), nand(W, V)), nand(W, V)))))
% 86.07/11.45 = { by lemma 11 }
% 86.07/11.45 nand(nand(nand(X, nand(Z, nand(X, W))), nand(W, V)), nand(nand(nand(Z, nand(X, W)), nand(nand(X, nand(Z, nand(X, W))), nand(Z, nand(X, W)))), nand(nand(W, V), nand(nand(nand(nand(X, X), nand(S, X)), nand(W, V)), nand(W, V)))))
% 86.07/11.45 = { by lemma 30 }
% 86.07/11.45 nand(nand(nand(X, nand(Z, nand(X, W))), nand(W, V)), nand(nand(X, nand(Z, nand(X, W))), nand(nand(W, V), nand(nand(nand(nand(X, X), nand(S, X)), nand(W, V)), nand(W, V)))))
% 86.07/11.45 = { by lemma 32 }
% 86.07/11.45 nand(X, nand(Z, nand(X, W)))
% 86.07/11.45
% 86.07/11.45 Goal 1 (prove_meredith_2_basis): tuple(nand(a, nand(b, nand(a, c))), nand(nand(a, a), nand(b, a))) = tuple(nand(nand(nand(c, b), b), a), a).
% 86.07/11.45 Proof:
% 86.07/11.45 tuple(nand(a, nand(b, nand(a, c))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by axiom 1 (sh_1) R->L }
% 86.07/11.45 tuple(nand(nand(nand(b, a), nand(nand(nand(a, nand(b, nand(a, c))), nand(b, a)), nand(b, a))), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(a, a), nand(X, a)), nand(b, a)))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 30 R->L }
% 86.07/11.45 tuple(nand(nand(nand(b, a), nand(nand(nand(nand(b, nand(a, c)), nand(nand(a, nand(b, nand(a, c))), nand(b, nand(a, c)))), nand(b, a)), nand(b, a))), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(a, a), nand(X, a)), nand(b, a)))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 29 }
% 86.07/11.45 tuple(nand(nand(nand(b, a), nand(nand(nand(nand(b, nand(a, c)), nand(nand(a, nand(b, nand(a, c))), nand(b, nand(a, c)))), nand(a, b)), nand(b, a))), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(a, a), nand(X, a)), nand(b, a)))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 2 }
% 86.07/11.45 tuple(nand(nand(nand(b, a), nand(a, nand(b, a))), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(a, a), nand(X, a)), nand(b, a)))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 11 R->L }
% 86.07/11.45 tuple(nand(nand(nand(b, a), nand(nand(nand(a, a), nand(b, a)), nand(b, a))), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(a, a), nand(X, a)), nand(b, a)))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 22 }
% 86.07/11.45 tuple(nand(a, nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(a, a), nand(X, a)), nand(b, a)))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 11 R->L }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(a, a), nand(X, a)), nand(b, a)))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 52 R->L }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(b, a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 29 }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, a)))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 30 R->L }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(b, a), nand(nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, a)), nand(b, a))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 4 R->L }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(b, nand(Z, a)), nand(b, a)), nand(nand(nand(nand(b, a), nand(nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, a)), nand(b, a))), nand(nand(b, nand(Z, a)), nand(b, a))), nand(nand(b, nand(Z, a)), nand(b, a)))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 42 }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(b, nand(nand(nand(nand(b, a), nand(nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, a)), nand(b, a))), nand(nand(b, nand(Z, a)), nand(b, a))), nand(nand(b, nand(Z, a)), nand(b, a)))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 30 }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(b, nand(nand(nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, a)), nand(nand(b, nand(Z, a)), nand(b, a))), nand(nand(b, nand(Z, a)), nand(b, a)))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 42 }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(b, nand(nand(nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, a)), nand(nand(b, nand(Z, a)), nand(b, a))), b)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 42 }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(b, nand(nand(nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, a)), b), b)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 30 }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, a)), b), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 29 R->L }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, a)), b)))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 29 R->L }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, a)))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 29 R->L }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(b, a), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 52 }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(a, a), nand(W, a)), nand(b, a)))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 31 R->L }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(b, a), nand(b, nand(nand(nand(a, a), nand(W, a)), nand(b, a)))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 11 }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(b, a), nand(b, nand(a, nand(b, a)))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 29 }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(a, b), nand(b, nand(a, nand(b, a)))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 18 R->L }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(a, nand(nand(b, a), a)), nand(b, nand(a, nand(b, a)))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 17 }
% 86.07/11.45 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, b)))), nand(nand(a, a), nand(b, a)))
% 86.07/11.45 = { by lemma 33 R->L }
% 86.07/11.46 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(b, nand(nand(nand(nand(c, b), b), a), nand(c, b)))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.46 = { by axiom 1 (sh_1) R->L }
% 86.07/11.46 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(nand(nand(c, nand(nand(b, c), c)), nand(b, nand(V, c))), nand(nand(nand(nand(c, b), b), a), nand(c, b)))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.46 = { by lemma 29 R->L }
% 86.07/11.46 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(nand(nand(c, nand(nand(c, b), c)), nand(b, nand(V, c))), nand(nand(nand(nand(c, b), b), a), nand(c, b)))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.46 = { by lemma 25 }
% 86.07/11.46 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(nand(nand(nand(c, b), b), a), nand(c, b)))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.46 = { by lemma 30 R->L }
% 86.07/11.46 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))), nand(nand(nand(nand(c, b), b), a), nand(c, b)))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.46 = { by lemma 2 R->L }
% 86.07/11.46 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))), nand(nand(c, b), b))))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.46 = { by lemma 29 }
% 86.07/11.46 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))), nand(nand(nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))), nand(nand(c, b), b)), nand(nand(nand(c, b), b), a)))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.46 = { by lemma 29 }
% 86.07/11.46 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(nand(nand(nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))), nand(nand(c, b), b)), nand(nand(nand(c, b), b), a)), nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.46 = { by lemma 30 R->L }
% 86.07/11.46 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))), nand(nand(c, b), b)), nand(nand(nand(c, b), b), a)), nand(nand(nand(c, b), b), a))), nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.46 = { by lemma 44 R->L }
% 86.07/11.46 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))), nand(nand(c, b), b)), nand(nand(nand(nand(nand(c, b), b), a), nand(a, U)), nand(nand(c, b), b))), nand(nand(nand(c, b), b), a))), nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.46 = { by lemma 44 R->L }
% 86.07/11.46 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))), nand(nand(c, b), b)), nand(nand(nand(nand(nand(c, b), b), a), nand(a, U)), nand(nand(c, b), b))), nand(nand(nand(nand(nand(c, b), b), a), nand(a, U)), nand(nand(c, b), b)))), nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.46 = { by lemma 30 R->L }
% 86.07/11.46 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(c, b), b), nand(nand(nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))), nand(nand(c, b), b)), nand(nand(c, b), b))), nand(nand(nand(nand(nand(c, b), b), a), nand(a, U)), nand(nand(c, b), b))), nand(nand(nand(nand(nand(c, b), b), a), nand(a, U)), nand(nand(c, b), b)))), nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.46 = { by lemma 44 R->L }
% 86.07/11.46 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(nand(nand(nand(nand(nand(nand(c, b), b), a), nand(a, U)), nand(nand(c, b), b)), nand(nand(nand(nand(nand(c, b), b), nand(nand(nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))), nand(nand(c, b), b)), nand(nand(c, b), b))), nand(nand(nand(nand(nand(c, b), b), a), nand(a, U)), nand(nand(c, b), b))), nand(nand(nand(nand(nand(c, b), b), a), nand(a, U)), nand(nand(c, b), b)))), nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.46 = { by lemma 4 }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(nand(nand(c, b), b), nand(nand(nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))), nand(nand(c, b), b)), nand(nand(c, b), b)))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 30 }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(nand(nand(b, nand(V, c)), nand(nand(nand(c, b), nand(b, nand(V, c))), nand(b, nand(V, c)))), nand(nand(c, b), b))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 2 }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(c, b)))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 29 R->L }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(c, b), nand(nand(nand(nand(c, b), b), a), nand(c, b))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 5 R->L }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), nand(nand(nand(nand(c, b), b), a), nand(c, b))), nand(nand(nand(c, b), b), a)), nand(nand(nand(c, b), b), a))), nand(nand(nand(c, b), nand(nand(nand(nand(c, b), b), a), nand(c, b))), nand(nand(c, b), nand(nand(nand(nand(nand(c, b), b), a), nand(c, b)), nand(c, b))))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 32 }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(c, b), nand(nand(nand(nand(c, b), b), a), nand(c, b))), nand(nand(nand(c, b), b), a)), nand(nand(nand(c, b), b), a))), nand(c, b)))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 30 }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(c, b), nand(nand(nand(nand(c, b), b), a), nand(c, b))), nand(nand(nand(c, b), b), a)), nand(c, b)))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 29 R->L }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(c, b), nand(nand(nand(c, b), nand(nand(nand(nand(c, b), b), a), nand(c, b))), nand(nand(nand(c, b), b), a))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 29 R->L }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(c, b), nand(nand(nand(nand(c, b), b), a), nand(nand(c, b), nand(nand(nand(nand(c, b), b), a), nand(c, b))))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 33 }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(c, b), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 29 }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(b, nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(c, b)))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 31 }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a)), nand(c, b)))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 29 R->L }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(c, b), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 54 }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(c, b), nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c))))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 29 }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(c, b)))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 29 }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(c, b)), nand(a, nand(b, nand(a, c))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 30 R->L }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(nand(c, b), nand(nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(c, b)), nand(c, b))), nand(a, nand(b, nand(a, c))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 56 R->L }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(nand(c, b), nand(nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(c, b)), nand(c, b))), nand(nand(nand(a, a), nand(T, a)), nand(nand(a, nand(b, nand(a, c))), nand(c, b))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 51 R->L }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(nand(c, b), nand(nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(c, b)), nand(c, b))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(nand(nand(a, a), nand(S, a)), nand(nand(a, nand(b, nand(a, c))), nand(c, b))), nand(nand(nand(c, b), b), a)), nand(nand(nand(c, b), b), a))), nand(nand(a, nand(b, nand(a, c))), nand(c, b))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 56 }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(nand(c, b), nand(nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(c, b)), nand(c, b))), nand(nand(nand(nand(nand(c, b), b), a), nand(nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(c, b), b), a)), nand(nand(nand(c, b), b), a))), nand(nand(a, nand(b, nand(a, c))), nand(c, b))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 30 }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(nand(c, b), nand(nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(c, b)), nand(c, b))), nand(nand(nand(a, nand(b, nand(a, c))), nand(nand(nand(c, b), b), a)), nand(nand(a, nand(b, nand(a, c))), nand(c, b))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 29 R->L }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(nand(c, b), nand(nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(c, b)), nand(c, b))), nand(nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c)))), nand(nand(a, nand(b, nand(a, c))), nand(c, b))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by axiom 1 (sh_1) }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(nand(nand(c, b), b), a), nand(a, nand(b, nand(a, c))))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 54 R->L }
% 86.07/11.47 tuple(nand(nand(nand(a, a), nand(Y, a)), nand(nand(nand(nand(c, b), b), a), nand(nand(nand(c, b), b), a))), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 39 }
% 86.07/11.47 tuple(nand(nand(nand(c, b), b), a), nand(nand(a, a), nand(b, a)))
% 86.07/11.47 = { by lemma 11 }
% 86.07/11.47 tuple(nand(nand(nand(c, b), b), a), a)
% 86.07/11.47 % SZS output end Proof
% 86.07/11.47
% 86.07/11.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------