TSTP Solution File: HWV002-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : HWV002-1 : TPTP v8.1.2. Released v1.1.0.
% 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 : n026.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 : Thu Aug 31 02:31:29 EDT 2023
% Result : Unsatisfiable 267.02s 34.76s
% Output : Proof 285.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HWV002-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.35 % Computer : n026.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Aug 29 16:01:50 EDT 2023
% 0.17/0.35 % CPUTime :
% 267.02/34.76 Command-line arguments: --flatten
% 267.02/34.76
% 267.02/34.76 % SZS status Unsatisfiable
% 267.02/34.76
% 283.61/36.90 % SZS output start Proof
% 283.61/36.90 Take the following subset of the input axioms:
% 283.64/36.90 fof(and_commutativity, negated_conjecture, ![X, Y, Z]: and(Y, and(X, Z))=and(X, and(Y, Z))).
% 283.64/36.90 fof(and_definition2, axiom, ![X2]: and(X2, n0)=n0).
% 283.64/36.90 fof(and_definition4, axiom, ![X2]: and(X2, n1)=X2).
% 283.64/36.90 fof(and_simplification1, axiom, ![X2]: and(X2, X2)=X2).
% 283.64/36.90 fof(and_simplification2, axiom, ![X2, Y2]: and(X2, and(X2, Y2))=and(X2, Y2)).
% 283.64/36.90 fof(and_symmetry, negated_conjecture, ![X2, Y2]: and(X2, Y2)=and(Y2, X2)).
% 283.64/36.90 fof(and_xor_simplification, axiom, ![X2, Y2, Z2]: and(X2, xor(Y2, Z2))=xor(and(X2, Y2), and(X2, Z2))).
% 283.64/36.90 fof(constructor1, negated_conjecture, o1=n13).
% 283.64/36.90 fof(constructor10, negated_conjecture, n7=and(n6, i3)).
% 283.64/36.90 fof(constructor11, negated_conjecture, n8=or(a1, n10)).
% 283.64/36.90 fof(constructor12, negated_conjecture, n9=or(n8, n2)).
% 283.64/36.90 fof(constructor13, negated_conjecture, n10=or(n24, n7)).
% 283.64/36.90 fof(constructor14, negated_conjecture, n11=or(a1, n2)).
% 283.64/36.90 fof(constructor15, negated_conjecture, n12=or(n11, n16)).
% 283.64/36.90 fof(constructor16, negated_conjecture, n13=or(n12, n21)).
% 283.64/36.90 fof(constructor17, negated_conjecture, n14=and(i2, i3)).
% 283.64/36.90 fof(constructor18, negated_conjecture, n15=and(inv2, n6)).
% 283.64/36.90 fof(constructor19, negated_conjecture, n16=and(n14, inv2)).
% 283.64/36.90 fof(constructor2, negated_conjecture, o2=n17).
% 283.64/36.90 fof(constructor20, negated_conjecture, n17=or(n18, n21)).
% 283.64/36.90 fof(constructor21, negated_conjecture, n18=or(n19, n25)).
% 283.64/36.90 fof(constructor22, negated_conjecture, n19=and(n23, inv2)).
% 283.64/36.90 fof(constructor23, negated_conjecture, n20=or(n22, n14)).
% 283.64/36.90 fof(constructor24, negated_conjecture, n21=and(inv1, inv2)).
% 283.64/36.90 fof(constructor25, negated_conjecture, n22=or(n23, n6)).
% 283.64/36.90 fof(constructor26, negated_conjecture, n23=and(i1, i3)).
% 283.64/36.90 fof(constructor27, negated_conjecture, n24=and(i1, inv1)).
% 283.64/36.90 fof(constructor28, negated_conjecture, n25=or(n2, n24)).
% 283.64/36.90 fof(constructor29, negated_conjecture, inv1=not(n20)).
% 283.64/36.90 fof(constructor3, negated_conjecture, o3=n5).
% 283.64/36.90 fof(constructor30, negated_conjecture, inv2=not(n9)).
% 283.64/36.90 fof(constructor4, negated_conjecture, a1=and(inv1, i2)).
% 283.64/36.90 fof(constructor5, negated_conjecture, n2=and(inv1, i3)).
% 283.64/36.90 fof(constructor6, negated_conjecture, n3=or(a1, n24)).
% 283.64/36.90 fof(constructor7, negated_conjecture, n4=or(n15, n3)).
% 283.64/36.90 fof(constructor8, negated_conjecture, n5=or(n4, n21)).
% 283.64/36.90 fof(constructor9, negated_conjecture, n6=and(i1, i2)).
% 283.64/36.90 fof(not_to_xor, axiom, ![X2]: not(X2)=xor(n1, X2)).
% 283.64/36.90 fof(or_to_xor, axiom, ![X2, Y2]: or(X2, Y2)=xor(and(X2, Y2), xor(X2, Y2))).
% 283.64/36.90 fof(output1, negated_conjecture, circuit(o1)).
% 283.64/36.90 fof(output2, negated_conjecture, circuit(o2)).
% 283.64/36.90 fof(output3, negated_conjecture, circuit(o3)).
% 283.64/36.90 fof(prove_inversion, negated_conjecture, ~circuit(not(i1)) | (~circuit(not(i2)) | ~circuit(not(i3)))).
% 283.64/36.90 fof(xor_commutativity, negated_conjecture, ![X2, Y2, Z2]: xor(Y2, xor(X2, Z2))=xor(X2, xor(Y2, Z2))).
% 283.64/36.90 fof(xor_definition1, axiom, ![X2]: xor(n0, X2)=X2).
% 283.64/36.91 fof(xor_definition2, axiom, ![X2]: xor(X2, n0)=X2).
% 283.64/36.91 fof(xor_definition3, axiom, ![X2]: xor(X2, X2)=n0).
% 283.64/36.91 fof(xor_simplification1, axiom, ![X2, Y2]: xor(X2, xor(X2, Y2))=Y2).
% 283.64/36.91 fof(xor_symmetry, negated_conjecture, ![X2, Y2]: xor(X2, Y2)=xor(Y2, X2)).
% 283.64/36.91
% 283.64/36.91 Now clausify the problem and encode Horn clauses using encoding 3 of
% 283.64/36.91 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 283.64/36.91 We repeatedly replace C & s=t => u=v by the two clauses:
% 283.64/36.91 fresh(y, y, x1...xn) = u
% 283.64/36.91 C => fresh(s, t, x1...xn) = v
% 283.64/36.91 where fresh is a fresh function symbol and x1..xn are the free
% 283.64/36.91 variables of u and v.
% 283.64/36.91 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 283.64/36.91 input problem has no model of domain size 1).
% 283.64/36.91
% 283.64/36.91 The encoding turns the above axioms into the following unit equations and goals:
% 283.64/36.91
% 283.64/36.91 Axiom 1 (constructor1): o1 = n13.
% 283.64/36.91 Axiom 2 (constructor2): o2 = n17.
% 283.64/36.91 Axiom 3 (constructor3): o3 = n5.
% 283.64/36.91 Axiom 4 (output1): circuit(o1) = true.
% 283.64/36.91 Axiom 5 (output2): circuit(o2) = true.
% 283.64/36.91 Axiom 6 (output3): circuit(o3) = true.
% 283.64/36.91 Axiom 7 (constructor30): inv2 = not(n9).
% 283.64/36.91 Axiom 8 (constructor29): inv1 = not(n20).
% 283.64/36.91 Axiom 9 (xor_definition3): xor(X, X) = n0.
% 283.64/36.91 Axiom 10 (xor_symmetry): xor(X, Y) = xor(Y, X).
% 283.64/36.91 Axiom 11 (xor_definition2): xor(X, n0) = X.
% 283.64/36.91 Axiom 12 (not_to_xor): not(X) = xor(n1, X).
% 283.64/36.91 Axiom 13 (xor_definition1): xor(n0, X) = X.
% 283.64/36.91 Axiom 14 (constructor8): n5 = or(n4, n21).
% 283.64/36.91 Axiom 15 (constructor7): n4 = or(n15, n3).
% 283.64/36.91 Axiom 16 (constructor12): n9 = or(n8, n2).
% 283.64/36.91 Axiom 17 (constructor15): n12 = or(n11, n16).
% 283.64/36.91 Axiom 18 (constructor16): n13 = or(n12, n21).
% 283.64/36.91 Axiom 19 (constructor20): n17 = or(n18, n21).
% 283.64/36.91 Axiom 20 (constructor21): n18 = or(n19, n25).
% 283.64/36.91 Axiom 21 (constructor23): n20 = or(n22, n14).
% 283.64/36.91 Axiom 22 (constructor25): n22 = or(n23, n6).
% 283.64/36.91 Axiom 23 (constructor11): n8 = or(a1, n10).
% 283.64/36.91 Axiom 24 (constructor14): n11 = or(a1, n2).
% 283.64/36.91 Axiom 25 (constructor6): n3 = or(a1, n24).
% 283.64/36.91 Axiom 26 (constructor28): n25 = or(n2, n24).
% 283.64/36.91 Axiom 27 (constructor13): n10 = or(n24, n7).
% 283.64/36.91 Axiom 28 (and_simplification1): and(X, X) = X.
% 283.64/36.91 Axiom 29 (and_symmetry): and(X, Y) = and(Y, X).
% 283.64/36.91 Axiom 30 (and_definition4): and(X, n1) = X.
% 283.64/36.91 Axiom 31 (and_definition2): and(X, n0) = n0.
% 283.64/36.91 Axiom 32 (constructor19): n16 = and(n14, inv2).
% 283.64/36.91 Axiom 33 (constructor22): n19 = and(n23, inv2).
% 283.64/36.91 Axiom 34 (constructor10): n7 = and(n6, i3).
% 283.64/36.91 Axiom 35 (constructor24): n21 = and(inv1, inv2).
% 283.64/36.91 Axiom 36 (constructor4): a1 = and(inv1, i2).
% 283.64/36.91 Axiom 37 (constructor5): n2 = and(inv1, i3).
% 283.64/36.91 Axiom 38 (constructor18): n15 = and(inv2, n6).
% 283.64/36.91 Axiom 39 (constructor17): n14 = and(i2, i3).
% 283.64/36.91 Axiom 40 (constructor27): n24 = and(i1, inv1).
% 283.64/36.91 Axiom 41 (constructor9): n6 = and(i1, i2).
% 283.64/36.91 Axiom 42 (constructor26): n23 = and(i1, i3).
% 283.64/36.91 Axiom 43 (xor_simplification1): xor(X, xor(X, Y)) = Y.
% 283.64/36.91 Axiom 44 (xor_commutativity): xor(X, xor(Y, Z)) = xor(Y, xor(X, Z)).
% 283.64/36.91 Axiom 45 (and_simplification2): and(X, and(X, Y)) = and(X, Y).
% 283.64/36.91 Axiom 46 (and_commutativity): and(X, and(Y, Z)) = and(Y, and(X, Z)).
% 283.64/36.91 Axiom 47 (or_to_xor): or(X, Y) = xor(and(X, Y), xor(X, Y)).
% 283.64/36.91 Axiom 48 (and_xor_simplification): and(X, xor(Y, Z)) = xor(and(X, Y), and(X, Z)).
% 283.64/36.91
% 283.64/36.91 Lemma 49: not(n0) = n1.
% 283.64/36.91 Proof:
% 283.64/36.91 not(n0)
% 283.64/36.91 = { by axiom 12 (not_to_xor) }
% 283.64/36.91 xor(n1, n0)
% 283.64/36.91 = { by axiom 11 (xor_definition2) }
% 283.64/36.91 n1
% 283.64/36.91
% 283.64/36.91 Lemma 50: xor(X, n1) = not(X).
% 283.64/36.91 Proof:
% 283.64/36.91 xor(X, n1)
% 283.64/36.91 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.91 xor(n1, X)
% 283.64/36.91 = { by axiom 12 (not_to_xor) R->L }
% 283.64/36.91 not(X)
% 283.64/36.91
% 283.64/36.91 Lemma 51: not(not(X)) = X.
% 283.64/36.91 Proof:
% 283.64/36.91 not(not(X))
% 283.64/36.91 = { by axiom 12 (not_to_xor) }
% 283.64/36.91 not(xor(n1, X))
% 283.64/36.91 = { by axiom 12 (not_to_xor) }
% 283.64/36.91 xor(n1, xor(n1, X))
% 283.64/36.91 = { by axiom 43 (xor_simplification1) }
% 283.64/36.91 X
% 283.64/36.91
% 283.64/36.91 Lemma 52: xor(Y, not(X)) = xor(X, not(Y)).
% 283.64/36.91 Proof:
% 283.64/36.91 xor(Y, not(X))
% 283.64/36.91 = { by lemma 50 R->L }
% 283.64/36.91 xor(Y, xor(X, n1))
% 283.64/36.91 = { by axiom 44 (xor_commutativity) }
% 283.64/36.91 xor(X, xor(Y, n1))
% 283.64/36.91 = { by lemma 50 }
% 283.64/36.91 xor(X, not(Y))
% 283.64/36.91
% 283.64/36.91 Lemma 53: xor(not(X), Y) = xor(X, not(Y)).
% 283.64/36.91 Proof:
% 283.64/36.91 xor(not(X), Y)
% 283.64/36.91 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.91 xor(Y, not(X))
% 283.64/36.91 = { by lemma 52 R->L }
% 283.64/36.91 xor(X, not(Y))
% 283.64/36.91
% 283.64/36.91 Lemma 54: xor(X, xor(Y, and(X, Y))) = or(X, Y).
% 283.64/36.91 Proof:
% 283.64/36.91 xor(X, xor(Y, and(X, Y)))
% 283.64/36.91 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.91 xor(X, xor(and(X, Y), Y))
% 283.64/36.91 = { by axiom 44 (xor_commutativity) R->L }
% 283.64/36.91 xor(and(X, Y), xor(X, Y))
% 283.64/36.91 = { by axiom 47 (or_to_xor) R->L }
% 283.64/36.91 or(X, Y)
% 283.64/36.91
% 283.64/36.91 Lemma 55: xor(X, and(X, Y)) = and(X, not(Y)).
% 283.64/36.91 Proof:
% 283.64/36.91 xor(X, and(X, Y))
% 283.64/36.91 = { by axiom 30 (and_definition4) R->L }
% 283.64/36.91 xor(and(X, n1), and(X, Y))
% 283.64/36.91 = { by axiom 48 (and_xor_simplification) R->L }
% 283.64/36.91 and(X, xor(n1, Y))
% 283.64/36.91 = { by axiom 12 (not_to_xor) R->L }
% 283.64/36.91 and(X, not(Y))
% 283.64/36.91
% 283.64/36.91 Lemma 56: xor(X, or(X, Y)) = and(Y, not(X)).
% 283.64/36.91 Proof:
% 283.64/36.91 xor(X, or(X, Y))
% 283.64/36.91 = { by lemma 54 R->L }
% 283.64/36.91 xor(X, xor(X, xor(Y, and(X, Y))))
% 283.64/36.91 = { by axiom 43 (xor_simplification1) }
% 283.64/36.91 xor(Y, and(X, Y))
% 283.64/36.91 = { by axiom 29 (and_symmetry) }
% 283.64/36.91 xor(Y, and(Y, X))
% 283.64/36.91 = { by lemma 55 }
% 283.64/36.91 and(Y, not(X))
% 283.64/36.91
% 283.64/36.91 Lemma 57: xor(X, and(Y, not(X))) = or(X, Y).
% 283.64/36.91 Proof:
% 283.64/36.91 xor(X, and(Y, not(X)))
% 283.64/36.91 = { by lemma 56 R->L }
% 283.64/36.91 xor(X, xor(X, or(X, Y)))
% 283.64/36.91 = { by axiom 43 (xor_simplification1) }
% 283.64/36.91 or(X, Y)
% 283.64/36.91
% 283.64/36.91 Lemma 58: xor(X, not(and(X, Y))) = or(not(X), Y).
% 283.64/36.91 Proof:
% 283.64/36.91 xor(X, not(and(X, Y)))
% 283.64/36.91 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.91 xor(X, not(and(Y, X)))
% 283.64/36.91 = { by lemma 53 R->L }
% 283.64/36.91 xor(not(X), and(Y, X))
% 283.64/36.91 = { by lemma 51 R->L }
% 283.64/36.91 xor(not(X), and(Y, not(not(X))))
% 283.64/36.91 = { by lemma 57 }
% 283.64/36.91 or(not(X), Y)
% 283.64/36.91
% 283.64/36.91 Lemma 59: not(xor(X, Y)) = xor(X, not(Y)).
% 283.64/36.91 Proof:
% 283.64/36.91 not(xor(X, Y))
% 283.64/36.91 = { by axiom 12 (not_to_xor) }
% 283.64/36.91 xor(n1, xor(X, Y))
% 283.64/36.91 = { by axiom 44 (xor_commutativity) }
% 283.64/36.91 xor(X, xor(n1, Y))
% 283.64/36.91 = { by axiom 12 (not_to_xor) R->L }
% 283.64/36.91 xor(X, not(Y))
% 283.64/36.91
% 283.64/36.91 Lemma 60: not(or(not(X), Y)) = xor(X, and(X, Y)).
% 283.64/36.91 Proof:
% 283.64/36.91 not(or(not(X), Y))
% 283.64/36.91 = { by lemma 58 R->L }
% 283.64/36.91 not(xor(X, not(and(X, Y))))
% 283.64/36.91 = { by lemma 59 }
% 283.64/36.91 xor(X, not(not(and(X, Y))))
% 283.64/36.91 = { by lemma 51 }
% 283.64/36.91 xor(X, and(X, Y))
% 283.64/36.91
% 283.64/36.91 Lemma 61: not(or(not(X), Y)) = and(X, not(Y)).
% 283.64/36.91 Proof:
% 283.64/36.91 not(or(not(X), Y))
% 283.64/36.91 = { by lemma 60 }
% 283.64/36.91 xor(X, and(X, Y))
% 283.64/36.91 = { by lemma 55 }
% 283.64/36.91 and(X, not(Y))
% 283.64/36.91
% 283.64/36.91 Lemma 62: xor(X, and(Y, X)) = and(X, not(Y)).
% 283.64/36.91 Proof:
% 283.64/36.91 xor(X, and(Y, X))
% 283.64/36.91 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.91 xor(X, and(X, Y))
% 283.64/36.91 = { by lemma 55 }
% 283.64/36.91 and(X, not(Y))
% 283.64/36.91
% 283.64/36.91 Lemma 63: and(not(X), not(Y)) = not(or(X, Y)).
% 283.64/36.91 Proof:
% 283.64/36.91 and(not(X), not(Y))
% 283.64/36.91 = { by lemma 62 R->L }
% 283.64/36.91 xor(not(X), and(Y, not(X)))
% 283.64/36.91 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.91 xor(and(Y, not(X)), not(X))
% 283.64/36.91 = { by lemma 52 R->L }
% 283.64/36.91 xor(X, not(and(Y, not(X))))
% 283.64/36.91 = { by lemma 59 R->L }
% 283.64/36.91 not(xor(X, and(Y, not(X))))
% 283.64/36.91 = { by lemma 57 }
% 283.64/36.91 not(or(X, Y))
% 283.64/36.91
% 283.64/36.91 Lemma 64: or(Y, X) = or(X, Y).
% 283.64/36.91 Proof:
% 283.64/36.91 or(Y, X)
% 283.64/36.91 = { by lemma 51 R->L }
% 283.64/36.91 not(not(or(Y, X)))
% 283.64/36.91 = { by lemma 51 R->L }
% 283.64/36.91 not(not(or(not(not(Y)), X)))
% 283.64/36.91 = { by lemma 61 }
% 283.64/36.91 not(and(not(Y), not(X)))
% 283.64/36.91 = { by axiom 29 (and_symmetry) }
% 283.64/36.91 not(and(not(X), not(Y)))
% 283.64/36.91 = { by lemma 63 }
% 283.64/36.91 not(not(or(X, Y)))
% 283.64/36.91 = { by lemma 51 }
% 283.64/36.91 or(X, Y)
% 283.64/36.91
% 283.64/36.91 Lemma 65: or(n8, n2) = not(not(n9)).
% 283.64/36.91 Proof:
% 283.64/36.91 or(n8, n2)
% 283.64/36.91 = { by axiom 16 (constructor12) R->L }
% 283.64/36.91 n9
% 283.64/36.91 = { by lemma 51 R->L }
% 283.64/36.91 not(not(n9))
% 283.64/36.91
% 283.64/36.91 Lemma 66: or(n22, n14) = not(not(n20)).
% 283.64/36.91 Proof:
% 283.64/36.91 or(n22, n14)
% 283.64/36.91 = { by axiom 21 (constructor23) R->L }
% 283.64/36.91 n20
% 283.64/36.91 = { by lemma 51 R->L }
% 283.64/36.91 not(not(n20))
% 283.64/36.91
% 283.64/36.91 Lemma 67: and(not(n9), not(n20)) = and(inv1, inv2).
% 283.64/36.91 Proof:
% 283.64/36.91 and(not(n9), not(n20))
% 283.64/36.91 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.91 and(not(n20), not(n9))
% 283.64/36.91 = { by axiom 7 (constructor30) R->L }
% 283.64/36.91 and(not(n20), inv2)
% 283.64/36.91 = { by axiom 8 (constructor29) R->L }
% 283.64/36.91 and(inv1, inv2)
% 283.64/36.91
% 283.64/36.91 Lemma 68: and(not(n9), and(X, not(n20))) = and(X, and(inv1, inv2)).
% 283.64/36.91 Proof:
% 283.64/36.91 and(not(n9), and(X, not(n20)))
% 283.64/36.91 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.91 and(X, and(not(n9), not(n20)))
% 283.64/36.91 = { by lemma 67 }
% 283.64/36.91 and(X, and(inv1, inv2))
% 283.64/36.91
% 283.64/36.91 Lemma 69: and(and(inv1, X), not(n20)) = and(inv1, X).
% 283.64/36.91 Proof:
% 283.64/36.91 and(and(inv1, X), not(n20))
% 283.64/36.91 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.91 and(not(n20), and(inv1, X))
% 283.64/36.91 = { by axiom 8 (constructor29) }
% 283.64/36.91 and(not(n20), and(not(n20), X))
% 283.64/36.91 = { by axiom 45 (and_simplification2) }
% 283.64/36.91 and(not(n20), X)
% 283.64/36.91 = { by axiom 8 (constructor29) R->L }
% 283.64/36.91 and(inv1, X)
% 283.64/36.91
% 283.64/36.91 Lemma 70: and(and(inv1, X), and(inv1, inv2)) = and(and(inv1, X), not(n9)).
% 283.64/36.91 Proof:
% 283.64/36.91 and(and(inv1, X), and(inv1, inv2))
% 283.64/36.91 = { by lemma 68 R->L }
% 283.64/36.91 and(not(n9), and(and(inv1, X), not(n20)))
% 283.64/36.91 = { by lemma 69 }
% 283.64/36.91 and(not(n9), and(inv1, X))
% 283.64/36.91 = { by axiom 29 (and_symmetry) }
% 283.64/36.91 and(and(inv1, X), not(n9))
% 283.64/36.91
% 283.64/36.91 Lemma 71: and(and(inv1, i3), not(or(a1, n10))) = xor(or(a1, n10), or(n8, n2)).
% 283.64/36.91 Proof:
% 283.64/36.91 and(and(inv1, i3), not(or(a1, n10)))
% 283.64/36.91 = { by axiom 23 (constructor11) R->L }
% 283.64/36.91 and(and(inv1, i3), not(n8))
% 283.64/36.91 = { by axiom 37 (constructor5) R->L }
% 283.64/36.91 and(n2, not(n8))
% 283.64/36.91 = { by lemma 56 R->L }
% 283.64/36.91 xor(n8, or(n8, n2))
% 283.64/36.91 = { by axiom 23 (constructor11) }
% 283.64/36.91 xor(or(a1, n10), or(n8, n2))
% 283.64/36.91
% 283.64/36.91 Lemma 72: and(not(and(inv1, i3)), not(or(a1, n10))) = not(n9).
% 283.64/36.91 Proof:
% 283.64/36.91 and(not(and(inv1, i3)), not(or(a1, n10)))
% 283.64/36.91 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.91 and(not(or(a1, n10)), not(and(inv1, i3)))
% 283.64/36.91 = { by lemma 62 R->L }
% 283.64/36.91 xor(not(or(a1, n10)), and(and(inv1, i3), not(or(a1, n10))))
% 283.64/36.91 = { by lemma 71 }
% 283.64/36.91 xor(not(or(a1, n10)), xor(or(a1, n10), or(n8, n2)))
% 283.64/36.91 = { by lemma 53 }
% 283.64/36.91 xor(or(a1, n10), not(xor(or(a1, n10), or(n8, n2))))
% 283.64/36.91 = { by lemma 59 }
% 283.64/36.91 xor(or(a1, n10), xor(or(a1, n10), not(or(n8, n2))))
% 283.64/36.91 = { by axiom 43 (xor_simplification1) }
% 283.64/36.91 not(or(n8, n2))
% 283.64/36.91 = { by axiom 16 (constructor12) R->L }
% 283.64/36.91 not(n9)
% 283.64/36.91
% 283.64/36.91 Lemma 73: and(and(inv1, i3), and(inv1, inv2)) = n0.
% 283.64/36.91 Proof:
% 283.64/36.91 and(and(inv1, i3), and(inv1, inv2))
% 283.64/36.91 = { by lemma 70 }
% 283.64/36.91 and(and(inv1, i3), not(n9))
% 283.64/36.91 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.91 and(not(n9), and(inv1, i3))
% 283.64/36.91 = { by lemma 51 R->L }
% 283.64/36.91 and(not(n9), not(not(and(inv1, i3))))
% 283.64/36.91 = { by lemma 55 R->L }
% 283.64/36.91 xor(not(n9), and(not(n9), not(and(inv1, i3))))
% 283.64/36.91 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.91 xor(not(n9), and(not(and(inv1, i3)), not(n9)))
% 283.64/36.91 = { by lemma 72 R->L }
% 283.64/36.91 xor(not(n9), and(not(and(inv1, i3)), and(not(and(inv1, i3)), not(or(a1, n10)))))
% 283.64/36.91 = { by axiom 45 (and_simplification2) }
% 283.64/36.91 xor(not(n9), and(not(and(inv1, i3)), not(or(a1, n10))))
% 283.64/36.91 = { by lemma 72 }
% 283.64/36.91 xor(not(n9), not(n9))
% 283.64/36.91 = { by axiom 9 (xor_definition3) }
% 283.64/36.91 n0
% 283.64/36.91
% 283.64/36.91 Lemma 74: and(not(n9), and(not(n20), X)) = and(X, and(inv1, inv2)).
% 283.64/36.91 Proof:
% 283.64/36.91 and(not(n9), and(not(n20), X))
% 283.64/36.91 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.91 and(not(n9), and(X, not(n20)))
% 283.64/36.91 = { by lemma 68 }
% 283.64/36.91 and(X, and(inv1, inv2))
% 283.64/36.91
% 283.64/36.91 Lemma 75: xor(X, and(not(X), Y)) = or(X, Y).
% 283.64/36.91 Proof:
% 283.64/36.91 xor(X, and(not(X), Y))
% 283.64/36.91 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.91 xor(X, and(Y, not(X)))
% 283.64/36.91 = { by lemma 57 }
% 283.64/36.91 or(X, Y)
% 283.64/36.91
% 283.64/36.91 Lemma 76: and(X, xor(X, Y)) = and(X, not(Y)).
% 283.64/36.91 Proof:
% 283.64/36.91 and(X, xor(X, Y))
% 283.64/36.91 = { by axiom 48 (and_xor_simplification) }
% 283.64/36.91 xor(and(X, X), and(X, Y))
% 283.64/36.91 = { by axiom 28 (and_simplification1) }
% 283.64/36.91 xor(X, and(X, Y))
% 283.64/36.91 = { by lemma 55 }
% 283.64/36.91 and(X, not(Y))
% 283.64/36.91
% 283.64/36.91 Lemma 77: or(X, xor(X, not(Y))) = or(X, not(Y)).
% 283.64/36.91 Proof:
% 283.64/36.91 or(X, xor(X, not(Y)))
% 283.64/36.91 = { by lemma 53 R->L }
% 283.64/36.91 or(X, xor(not(X), Y))
% 283.64/36.91 = { by lemma 75 R->L }
% 283.64/36.91 xor(X, and(not(X), xor(not(X), Y)))
% 283.64/36.91 = { by lemma 76 }
% 283.64/36.91 xor(X, and(not(X), not(Y)))
% 283.64/36.91 = { by lemma 75 }
% 283.64/36.91 or(X, not(Y))
% 283.64/36.91
% 283.64/36.91 Lemma 78: xor(X, xor(Y, X)) = Y.
% 283.64/36.91 Proof:
% 283.64/36.91 xor(X, xor(Y, X))
% 283.64/36.91 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.91 xor(X, xor(X, Y))
% 283.64/36.91 = { by axiom 43 (xor_simplification1) }
% 283.64/36.91 Y
% 283.64/36.91
% 283.64/36.91 Lemma 79: and(and(inv2, X), not(n9)) = and(inv2, X).
% 283.64/36.91 Proof:
% 283.64/36.91 and(and(inv2, X), not(n9))
% 283.64/36.91 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.91 and(not(n9), and(inv2, X))
% 283.64/36.91 = { by axiom 7 (constructor30) }
% 283.64/36.91 and(not(n9), and(not(n9), X))
% 283.64/36.91 = { by axiom 45 (and_simplification2) }
% 283.64/36.91 and(not(n9), X)
% 283.64/36.91 = { by axiom 7 (constructor30) R->L }
% 283.64/36.91 and(inv2, X)
% 283.64/36.91
% 283.64/36.91 Lemma 80: xor(and(inv1, inv2), and(X, not(n9))) = and(not(n9), xor(X, not(n20))).
% 283.64/36.91 Proof:
% 283.64/36.91 xor(and(inv1, inv2), and(X, not(n9)))
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 xor(and(inv1, inv2), and(not(n9), X))
% 283.64/36.92 = { by lemma 67 R->L }
% 283.64/36.92 xor(and(not(n9), not(n20)), and(not(n9), X))
% 283.64/36.92 = { by axiom 48 (and_xor_simplification) R->L }
% 283.64/36.92 and(not(n9), xor(not(n20), X))
% 283.64/36.92 = { by axiom 10 (xor_symmetry) }
% 283.64/36.92 and(not(n9), xor(X, not(n20)))
% 283.64/36.92
% 283.64/36.92 Lemma 81: xor(and(X, Y), and(Y, Z)) = and(Y, xor(X, Z)).
% 283.64/36.92 Proof:
% 283.64/36.92 xor(and(X, Y), and(Y, Z))
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 xor(and(Y, X), and(Y, Z))
% 283.64/36.92 = { by axiom 48 (and_xor_simplification) R->L }
% 283.64/36.92 and(Y, xor(X, Z))
% 283.64/36.92
% 283.64/36.92 Lemma 82: and(and(X, Y), Y) = and(X, Y).
% 283.64/36.92 Proof:
% 283.64/36.92 and(and(X, Y), Y)
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 and(Y, and(X, Y))
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 and(Y, and(Y, X))
% 283.64/36.92 = { by axiom 45 (and_simplification2) }
% 283.64/36.92 and(Y, X)
% 283.64/36.92 = { by axiom 29 (and_symmetry) }
% 283.64/36.92 and(X, Y)
% 283.64/36.92
% 283.64/36.92 Lemma 83: and(not(X), xor(Y, and(Z, X))) = and(Y, not(X)).
% 283.64/36.92 Proof:
% 283.64/36.92 and(not(X), xor(Y, and(Z, X)))
% 283.64/36.92 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.92 and(not(X), xor(and(Z, X), Y))
% 283.64/36.92 = { by lemma 81 R->L }
% 283.64/36.92 xor(and(and(Z, X), not(X)), and(not(X), Y))
% 283.64/36.92 = { by lemma 55 R->L }
% 283.64/36.92 xor(xor(and(Z, X), and(and(Z, X), X)), and(not(X), Y))
% 283.64/36.92 = { by lemma 82 }
% 283.64/36.92 xor(xor(and(Z, X), and(Z, X)), and(not(X), Y))
% 283.64/36.92 = { by axiom 9 (xor_definition3) }
% 283.64/36.92 xor(n0, and(not(X), Y))
% 283.64/36.92 = { by axiom 13 (xor_definition1) }
% 283.64/36.92 and(not(X), Y)
% 283.64/36.92 = { by axiom 29 (and_symmetry) }
% 283.64/36.92 and(Y, not(X))
% 283.64/36.92
% 283.64/36.92 Lemma 84: or(X, and(X, Y)) = X.
% 283.64/36.92 Proof:
% 283.64/36.92 or(X, and(X, Y))
% 283.64/36.92 = { by lemma 54 R->L }
% 283.64/36.92 xor(X, xor(and(X, Y), and(X, and(X, Y))))
% 283.64/36.92 = { by axiom 45 (and_simplification2) }
% 283.64/36.92 xor(X, xor(and(X, Y), and(X, Y)))
% 283.64/36.92 = { by axiom 48 (and_xor_simplification) R->L }
% 283.64/36.92 xor(X, and(X, xor(Y, Y)))
% 283.64/36.92 = { by axiom 9 (xor_definition3) }
% 283.64/36.92 xor(X, and(X, n0))
% 283.64/36.92 = { by axiom 31 (and_definition2) }
% 283.64/36.92 xor(X, n0)
% 283.64/36.92 = { by axiom 11 (xor_definition2) }
% 283.64/36.92 X
% 283.64/36.92
% 283.64/36.92 Lemma 85: or(X, and(Y, X)) = X.
% 283.64/36.92 Proof:
% 283.64/36.92 or(X, and(Y, X))
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 or(X, and(X, Y))
% 283.64/36.92 = { by lemma 84 }
% 283.64/36.92 X
% 283.64/36.92
% 283.64/36.92 Lemma 86: and(and(X, Y), Z) = and(and(Z, Y), X).
% 283.64/36.92 Proof:
% 283.64/36.92 and(and(X, Y), Z)
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 and(Z, and(X, Y))
% 283.64/36.92 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.92 and(X, and(Z, Y))
% 283.64/36.92 = { by axiom 29 (and_symmetry) }
% 283.64/36.92 and(and(Z, Y), X)
% 283.64/36.92
% 283.64/36.92 Lemma 87: and(and(X, Y), and(Z, Y)) = and(and(X, Y), Z).
% 283.64/36.92 Proof:
% 283.64/36.92 and(and(X, Y), and(Z, Y))
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 and(and(Z, Y), and(X, Y))
% 283.64/36.92 = { by axiom 46 (and_commutativity) }
% 283.64/36.92 and(X, and(and(Z, Y), Y))
% 283.64/36.92 = { by lemma 82 }
% 283.64/36.92 and(X, and(Z, Y))
% 283.64/36.92 = { by axiom 29 (and_symmetry) }
% 283.64/36.92 and(and(Z, Y), X)
% 283.64/36.92 = { by lemma 86 }
% 283.64/36.92 and(and(X, Y), Z)
% 283.64/36.92
% 283.64/36.92 Lemma 88: and(X, and(Y, Z)) = and(Y, and(Z, X)).
% 283.64/36.92 Proof:
% 283.64/36.92 and(X, and(Y, Z))
% 283.64/36.92 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.92 and(Y, and(X, Z))
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 and(Y, and(Z, X))
% 283.64/36.92
% 283.64/36.92 Lemma 89: and(and(i1, i2), X) = and(n6, X).
% 283.64/36.92 Proof:
% 283.64/36.92 and(and(i1, i2), X)
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 and(X, and(i1, i2))
% 283.64/36.92 = { by axiom 41 (constructor9) R->L }
% 283.64/36.92 and(X, n6)
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 and(n6, X)
% 283.64/36.92
% 283.64/36.92 Lemma 90: and(and(i2, X), and(i1, X)) = and(n6, X).
% 283.64/36.92 Proof:
% 283.64/36.92 and(and(i2, X), and(i1, X))
% 283.64/36.92 = { by lemma 87 }
% 283.64/36.92 and(and(i2, X), i1)
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 and(i1, and(i2, X))
% 283.64/36.92 = { by lemma 88 }
% 283.64/36.92 and(i2, and(X, i1))
% 283.64/36.92 = { by lemma 88 }
% 283.64/36.92 and(X, and(i1, i2))
% 283.64/36.92 = { by axiom 29 (and_symmetry) }
% 283.64/36.92 and(and(i1, i2), X)
% 283.64/36.92 = { by lemma 89 }
% 283.64/36.92 and(n6, X)
% 283.64/36.92
% 283.64/36.92 Lemma 91: and(and(i1, i2), not(and(i1, i3))) = xor(and(i1, i3), or(n23, n6)).
% 283.64/36.92 Proof:
% 283.64/36.92 and(and(i1, i2), not(and(i1, i3)))
% 283.64/36.92 = { by axiom 42 (constructor26) R->L }
% 283.64/36.92 and(and(i1, i2), not(n23))
% 283.64/36.92 = { by axiom 41 (constructor9) R->L }
% 283.64/36.92 and(n6, not(n23))
% 283.64/36.92 = { by lemma 56 R->L }
% 283.64/36.92 xor(n23, or(n23, n6))
% 283.64/36.92 = { by axiom 42 (constructor26) }
% 283.64/36.92 xor(and(i1, i3), or(n23, n6))
% 283.64/36.92
% 283.64/36.92 Lemma 92: and(and(X, Y), X) = and(X, Y).
% 283.64/36.92 Proof:
% 283.64/36.92 and(and(X, Y), X)
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 and(X, and(X, Y))
% 283.64/36.92 = { by axiom 45 (and_simplification2) }
% 283.64/36.92 and(X, Y)
% 283.64/36.92
% 283.64/36.92 Lemma 93: and(and(Y, Z), and(X, Z)) = and(and(X, Y), and(X, Z)).
% 283.64/36.92 Proof:
% 283.64/36.92 and(and(Y, Z), and(X, Z))
% 283.64/36.92 = { by lemma 87 }
% 283.64/36.92 and(and(Y, Z), X)
% 283.64/36.92 = { by lemma 86 R->L }
% 283.64/36.92 and(and(X, Z), Y)
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 and(Y, and(X, Z))
% 283.64/36.92 = { by lemma 92 R->L }
% 283.64/36.92 and(Y, and(and(X, Z), X))
% 283.64/36.92 = { by lemma 88 }
% 283.64/36.92 and(and(X, Z), and(X, Y))
% 283.64/36.92 = { by axiom 29 (and_symmetry) }
% 283.64/36.92 and(and(X, Y), and(X, Z))
% 283.64/36.92
% 283.64/36.92 Lemma 94: xor(and(i1, i2), or(n23, n6)) = xor(and(n6, i3), and(i1, i3)).
% 283.64/36.92 Proof:
% 283.64/36.92 xor(and(i1, i2), or(n23, n6))
% 283.64/36.92 = { by lemma 51 R->L }
% 283.64/36.92 xor(and(i1, i2), not(not(or(n23, n6))))
% 283.64/36.92 = { by lemma 53 R->L }
% 283.64/36.92 xor(not(and(i1, i2)), not(or(n23, n6)))
% 283.64/36.92 = { by axiom 43 (xor_simplification1) R->L }
% 283.64/36.92 xor(not(and(i1, i2)), xor(and(i1, i3), xor(and(i1, i3), not(or(n23, n6)))))
% 283.64/36.92 = { by lemma 59 R->L }
% 283.64/36.92 xor(not(and(i1, i2)), xor(and(i1, i3), not(xor(and(i1, i3), or(n23, n6)))))
% 283.64/36.92 = { by lemma 53 R->L }
% 283.64/36.92 xor(not(and(i1, i2)), xor(not(and(i1, i3)), xor(and(i1, i3), or(n23, n6))))
% 283.64/36.92 = { by lemma 91 R->L }
% 283.64/36.92 xor(not(and(i1, i2)), xor(not(and(i1, i3)), and(and(i1, i2), not(and(i1, i3)))))
% 283.64/36.92 = { by lemma 62 }
% 283.64/36.92 xor(not(and(i1, i2)), and(not(and(i1, i3)), not(and(i1, i2))))
% 283.64/36.92 = { by axiom 29 (and_symmetry) }
% 283.64/36.92 xor(not(and(i1, i2)), and(not(and(i1, i2)), not(and(i1, i3))))
% 283.64/36.92 = { by lemma 55 }
% 283.64/36.92 and(not(and(i1, i2)), not(not(and(i1, i3))))
% 283.64/36.92 = { by lemma 51 }
% 283.64/36.92 and(not(and(i1, i2)), and(i1, i3))
% 283.64/36.92 = { by axiom 29 (and_symmetry) }
% 283.64/36.92 and(and(i1, i3), not(and(i1, i2)))
% 283.64/36.92 = { by lemma 62 R->L }
% 283.64/36.92 xor(and(i1, i3), and(and(i1, i2), and(i1, i3)))
% 283.64/36.92 = { by lemma 93 R->L }
% 283.64/36.92 xor(and(i1, i3), and(and(i2, i3), and(i1, i3)))
% 283.64/36.92 = { by lemma 90 }
% 283.64/36.92 xor(and(i1, i3), and(n6, i3))
% 283.64/36.92 = { by axiom 10 (xor_symmetry) }
% 283.64/36.92 xor(and(n6, i3), and(i1, i3))
% 283.64/36.92
% 283.64/36.92 Lemma 95: and(and(n6, X), and(i1, i2)) = and(n6, X).
% 283.64/36.92 Proof:
% 283.64/36.92 and(and(n6, X), and(i1, i2))
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 and(and(i1, i2), and(n6, X))
% 283.64/36.92 = { by axiom 41 (constructor9) R->L }
% 283.64/36.92 and(n6, and(n6, X))
% 283.64/36.92 = { by axiom 45 (and_simplification2) }
% 283.64/36.92 and(n6, X)
% 283.64/36.92
% 283.64/36.92 Lemma 96: and(and(i2, X), i1) = and(n6, X).
% 283.64/36.92 Proof:
% 283.64/36.92 and(and(i2, X), i1)
% 283.64/36.92 = { by lemma 86 R->L }
% 283.64/36.92 and(and(i1, X), i2)
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 and(i2, and(i1, X))
% 283.64/36.92 = { by lemma 82 R->L }
% 283.64/36.92 and(i2, and(and(i1, X), X))
% 283.64/36.92 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.92 and(and(i1, X), and(i2, X))
% 283.64/36.92 = { by axiom 29 (and_symmetry) }
% 283.64/36.92 and(and(i2, X), and(i1, X))
% 283.64/36.92 = { by lemma 90 }
% 283.64/36.92 and(n6, X)
% 283.64/36.92
% 283.64/36.92 Lemma 97: and(not(X), xor(Y, and(X, Z))) = and(Y, not(X)).
% 283.64/36.92 Proof:
% 283.64/36.92 and(not(X), xor(Y, and(X, Z)))
% 283.64/36.92 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.92 and(not(X), xor(and(X, Z), Y))
% 283.64/36.92 = { by lemma 81 R->L }
% 283.64/36.92 xor(and(and(X, Z), not(X)), and(not(X), Y))
% 283.64/36.92 = { by lemma 55 R->L }
% 283.64/36.92 xor(xor(and(X, Z), and(and(X, Z), X)), and(not(X), Y))
% 283.64/36.92 = { by lemma 92 }
% 283.64/36.92 xor(xor(and(X, Z), and(X, Z)), and(not(X), Y))
% 283.64/36.92 = { by axiom 9 (xor_definition3) }
% 283.64/36.92 xor(n0, and(not(X), Y))
% 283.64/36.92 = { by axiom 13 (xor_definition1) }
% 283.64/36.92 and(not(X), Y)
% 283.64/36.92 = { by axiom 29 (and_symmetry) }
% 283.64/36.92 and(Y, not(X))
% 283.64/36.92
% 283.64/36.92 Lemma 98: and(not(X), xor(and(X, Y), Z)) = and(Z, not(X)).
% 283.64/36.92 Proof:
% 283.64/36.92 and(not(X), xor(and(X, Y), Z))
% 283.64/36.92 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.92 and(not(X), xor(Z, and(X, Y)))
% 283.64/36.92 = { by lemma 97 }
% 283.64/36.92 and(Z, not(X))
% 283.64/36.92
% 283.64/36.92 Lemma 99: xor(and(Z, X), and(Y, X)) = and(X, xor(Y, Z)).
% 283.64/36.92 Proof:
% 283.64/36.92 xor(and(Z, X), and(Y, X))
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 xor(and(Z, X), and(X, Y))
% 283.64/36.92 = { by axiom 29 (and_symmetry) }
% 283.64/36.92 xor(and(X, Z), and(X, Y))
% 283.64/36.92 = { by axiom 48 (and_xor_simplification) R->L }
% 283.64/36.92 and(X, xor(Z, Y))
% 283.64/36.92 = { by axiom 10 (xor_symmetry) }
% 283.64/36.92 and(X, xor(Y, Z))
% 283.64/36.92
% 283.64/36.92 Lemma 100: xor(and(i1, i3), or(n23, n6)) = xor(and(n6, i3), and(i1, i2)).
% 283.64/36.92 Proof:
% 283.64/36.92 xor(and(i1, i3), or(n23, n6))
% 283.64/36.92 = { by lemma 91 R->L }
% 283.64/36.92 and(and(i1, i2), not(and(i1, i3)))
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 and(not(and(i1, i3)), and(i1, i2))
% 283.64/36.92 = { by lemma 88 R->L }
% 283.64/36.92 and(i2, and(not(and(i1, i3)), i1))
% 283.64/36.92 = { by axiom 29 (and_symmetry) }
% 283.64/36.92 and(i2, and(i1, not(and(i1, i3))))
% 283.64/36.92 = { by lemma 62 R->L }
% 283.64/36.92 and(i2, xor(i1, and(and(i1, i3), i1)))
% 283.64/36.92 = { by lemma 92 }
% 283.64/36.92 and(i2, xor(i1, and(i1, i3)))
% 283.64/36.92 = { by axiom 10 (xor_symmetry) }
% 283.64/36.92 and(i2, xor(and(i1, i3), i1))
% 283.64/36.92 = { by lemma 99 R->L }
% 283.64/36.92 xor(and(i1, i2), and(and(i1, i3), i2))
% 283.64/36.92 = { by lemma 86 }
% 283.64/36.92 xor(and(i1, i2), and(and(i2, i3), i1))
% 283.64/36.92 = { by lemma 87 R->L }
% 283.64/36.92 xor(and(i1, i2), and(and(i2, i3), and(i1, i3)))
% 283.64/36.92 = { by lemma 90 }
% 283.64/36.92 xor(and(i1, i2), and(n6, i3))
% 283.64/36.92 = { by axiom 10 (xor_symmetry) }
% 283.64/36.92 xor(and(n6, i3), and(i1, i2))
% 283.64/36.92
% 283.64/36.92 Lemma 101: or(X, and(Y, and(X, Z))) = X.
% 283.64/36.92 Proof:
% 283.64/36.92 or(X, and(Y, and(X, Z)))
% 283.64/36.92 = { by axiom 46 (and_commutativity) }
% 283.64/36.92 or(X, and(X, and(Y, Z)))
% 283.64/36.92 = { by lemma 84 }
% 283.64/36.92 X
% 283.64/36.92
% 283.64/36.92 Lemma 102: and(or(n23, n6), i1) = or(n23, n6).
% 283.64/36.92 Proof:
% 283.64/36.92 and(or(n23, n6), i1)
% 283.64/36.92 = { by lemma 51 R->L }
% 283.64/36.92 and(or(n23, n6), not(not(i1)))
% 283.64/36.92 = { by lemma 62 R->L }
% 283.64/36.92 xor(or(n23, n6), and(not(i1), or(n23, n6)))
% 283.64/36.92 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.92 xor(or(n23, n6), and(or(n23, n6), not(i1)))
% 283.64/36.92 = { by lemma 98 R->L }
% 283.64/36.92 xor(or(n23, n6), and(not(i1), xor(and(i1, i3), or(n23, n6))))
% 283.64/36.92 = { by lemma 100 }
% 283.64/36.92 xor(or(n23, n6), and(not(i1), xor(and(n6, i3), and(i1, i2))))
% 283.64/36.92 = { by lemma 97 }
% 283.64/36.92 xor(or(n23, n6), and(and(n6, i3), not(i1)))
% 283.64/36.92 = { by lemma 56 R->L }
% 283.64/36.92 xor(or(n23, n6), xor(i1, or(i1, and(n6, i3))))
% 283.64/36.92 = { by lemma 90 R->L }
% 283.64/36.92 xor(or(n23, n6), xor(i1, or(i1, and(and(i2, i3), and(i1, i3)))))
% 283.64/36.92 = { by lemma 101 }
% 283.64/36.92 xor(or(n23, n6), xor(i1, i1))
% 283.64/36.92 = { by axiom 9 (xor_definition3) }
% 283.64/36.92 xor(or(n23, n6), n0)
% 283.64/36.92 = { by axiom 11 (xor_definition2) }
% 283.64/36.92 or(n23, n6)
% 283.64/36.92
% 283.64/36.92 Lemma 103: and(and(i2, i3), not(or(n23, n6))) = xor(or(n23, n6), or(n22, n14)).
% 283.64/36.92 Proof:
% 283.64/36.92 and(and(i2, i3), not(or(n23, n6)))
% 283.64/36.92 = { by axiom 22 (constructor25) R->L }
% 283.64/36.92 and(and(i2, i3), not(n22))
% 283.64/36.92 = { by axiom 39 (constructor17) R->L }
% 283.64/36.92 and(n14, not(n22))
% 283.64/36.92 = { by lemma 56 R->L }
% 283.64/36.92 xor(n22, or(n22, n14))
% 283.64/36.92 = { by axiom 22 (constructor25) }
% 283.64/36.92 xor(or(n23, n6), or(n22, n14))
% 283.64/36.92
% 283.64/36.92 Lemma 104: xor(and(i2, i3), and(n6, i3)) = xor(or(n23, n6), or(n22, n14)).
% 283.64/36.92 Proof:
% 283.64/36.92 xor(and(i2, i3), and(n6, i3))
% 283.64/36.92 = { by axiom 11 (xor_definition2) R->L }
% 283.64/36.92 xor(and(i2, i3), xor(and(n6, i3), n0))
% 283.64/36.92 = { by axiom 9 (xor_definition3) R->L }
% 283.64/36.92 xor(and(i2, i3), xor(and(n6, i3), xor(and(i1, i3), and(i1, i3))))
% 283.64/36.92 = { by lemma 85 R->L }
% 283.64/36.92 xor(and(i2, i3), xor(and(n6, i3), xor(and(i1, i3), or(and(i1, i3), and(and(i2, i3), and(i1, i3))))))
% 283.64/36.92 = { by lemma 90 }
% 283.64/36.92 xor(and(i2, i3), xor(and(n6, i3), xor(and(i1, i3), or(and(i1, i3), and(n6, i3)))))
% 283.64/36.92 = { by lemma 56 }
% 283.64/36.92 xor(and(i2, i3), xor(and(n6, i3), and(and(n6, i3), not(and(i1, i3)))))
% 283.64/36.92 = { by lemma 76 R->L }
% 283.64/36.92 xor(and(i2, i3), xor(and(n6, i3), and(and(n6, i3), xor(and(n6, i3), and(i1, i3)))))
% 283.64/36.92 = { by lemma 94 R->L }
% 283.64/36.92 xor(and(i2, i3), xor(and(n6, i3), and(and(n6, i3), xor(and(i1, i2), or(n23, n6)))))
% 283.64/36.92 = { by axiom 48 (and_xor_simplification) }
% 283.64/36.92 xor(and(i2, i3), xor(and(n6, i3), xor(and(and(n6, i3), and(i1, i2)), and(and(n6, i3), or(n23, n6)))))
% 283.64/36.92 = { by lemma 95 }
% 283.64/36.92 xor(and(i2, i3), xor(and(n6, i3), xor(and(n6, i3), and(and(n6, i3), or(n23, n6)))))
% 283.64/36.92 = { by lemma 55 }
% 283.64/36.92 xor(and(i2, i3), xor(and(n6, i3), and(and(n6, i3), not(or(n23, n6)))))
% 283.64/36.92 = { by lemma 55 }
% 283.64/36.93 xor(and(i2, i3), and(and(n6, i3), not(not(or(n23, n6)))))
% 283.64/36.93 = { by lemma 51 }
% 283.64/36.93 xor(and(i2, i3), and(and(n6, i3), or(n23, n6)))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 xor(and(i2, i3), and(or(n23, n6), and(n6, i3)))
% 283.64/36.93 = { by lemma 96 R->L }
% 283.64/36.93 xor(and(i2, i3), and(or(n23, n6), and(and(i2, i3), i1)))
% 283.64/36.93 = { by axiom 46 (and_commutativity) }
% 283.64/36.93 xor(and(i2, i3), and(and(i2, i3), and(or(n23, n6), i1)))
% 283.64/36.93 = { by lemma 102 }
% 283.64/36.93 xor(and(i2, i3), and(and(i2, i3), or(n23, n6)))
% 283.64/36.93 = { by lemma 51 R->L }
% 283.64/36.93 xor(and(i2, i3), and(and(i2, i3), not(not(or(n23, n6)))))
% 283.64/36.93 = { by lemma 55 R->L }
% 283.64/36.93 xor(and(i2, i3), xor(and(i2, i3), and(and(i2, i3), not(or(n23, n6)))))
% 283.64/36.93 = { by lemma 103 }
% 283.64/36.93 xor(and(i2, i3), xor(and(i2, i3), xor(or(n23, n6), or(n22, n14))))
% 283.64/36.93 = { by axiom 43 (xor_simplification1) }
% 283.64/36.93 xor(or(n23, n6), or(n22, n14))
% 283.64/36.93
% 283.64/36.93 Lemma 105: xor(and(n6, X), and(i1, i2)) = and(and(i1, i2), not(X)).
% 283.64/36.93 Proof:
% 283.64/36.93 xor(and(n6, X), and(i1, i2))
% 283.64/36.93 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.93 xor(and(i1, i2), and(n6, X))
% 283.64/36.93 = { by axiom 41 (constructor9) R->L }
% 283.64/36.93 xor(n6, and(n6, X))
% 283.64/36.93 = { by lemma 55 }
% 283.64/36.93 and(n6, not(X))
% 283.64/36.93 = { by axiom 41 (constructor9) }
% 283.64/36.93 and(and(i1, i2), not(X))
% 283.64/36.93
% 283.64/36.93 Lemma 106: xor(not(n9), not(X)) = xor(X, or(n8, n2)).
% 283.64/36.93 Proof:
% 283.64/36.93 xor(not(n9), not(X))
% 283.64/36.93 = { by lemma 52 }
% 283.64/36.93 xor(X, not(not(n9)))
% 283.64/36.93 = { by lemma 65 R->L }
% 283.64/36.93 xor(X, or(n8, n2))
% 283.64/36.93
% 283.64/36.93 Lemma 107: xor(or(n8, n2), not(X)) = xor(X, not(n9)).
% 283.64/36.93 Proof:
% 283.64/36.93 xor(or(n8, n2), not(X))
% 283.64/36.93 = { by lemma 52 }
% 283.64/36.93 xor(X, not(or(n8, n2)))
% 283.64/36.93 = { by axiom 16 (constructor12) R->L }
% 283.64/36.93 xor(X, not(n9))
% 283.64/36.93
% 283.64/36.93 Lemma 108: and(not(n9), or(n22, n14)) = xor(and(inv1, inv2), not(n9)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(not(n9), or(n22, n14))
% 283.64/36.93 = { by lemma 66 }
% 283.64/36.93 and(not(n9), not(not(n20)))
% 283.64/36.93 = { by lemma 55 R->L }
% 283.64/36.93 xor(not(n9), and(not(n9), not(n20)))
% 283.64/36.93 = { by lemma 67 }
% 283.64/36.93 xor(not(n9), and(inv1, inv2))
% 283.64/36.93 = { by axiom 10 (xor_symmetry) }
% 283.64/36.93 xor(and(inv1, inv2), not(n9))
% 283.64/36.93
% 283.64/36.93 Lemma 109: and(and(inv1, X), or(n22, n14)) = n0.
% 283.64/36.93 Proof:
% 283.64/36.93 and(and(inv1, X), or(n22, n14))
% 283.64/36.93 = { by lemma 66 }
% 283.64/36.93 and(and(inv1, X), not(not(n20)))
% 283.64/36.93 = { by lemma 55 R->L }
% 283.64/36.93 xor(and(inv1, X), and(and(inv1, X), not(n20)))
% 283.64/36.93 = { by lemma 69 }
% 283.64/36.93 xor(and(inv1, X), and(inv1, X))
% 283.64/36.93 = { by axiom 9 (xor_definition3) }
% 283.64/36.93 n0
% 283.64/36.93
% 283.64/36.93 Lemma 110: and(or(n22, n14), xor(X, and(inv1, Y))) = and(X, or(n22, n14)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(or(n22, n14), xor(X, and(inv1, Y)))
% 283.64/36.93 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.93 and(or(n22, n14), xor(and(inv1, Y), X))
% 283.64/36.93 = { by lemma 81 R->L }
% 283.64/36.93 xor(and(and(inv1, Y), or(n22, n14)), and(or(n22, n14), X))
% 283.64/36.93 = { by lemma 109 }
% 283.64/36.93 xor(n0, and(or(n22, n14), X))
% 283.64/36.93 = { by axiom 13 (xor_definition1) }
% 283.64/36.93 and(or(n22, n14), X)
% 283.64/36.93 = { by axiom 29 (and_symmetry) }
% 283.64/36.93 and(X, or(n22, n14))
% 283.64/36.93
% 283.64/36.93 Lemma 111: and(or(n22, n14), xor(and(inv1, X), Y)) = and(Y, or(n22, n14)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(or(n22, n14), xor(and(inv1, X), Y))
% 283.64/36.93 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.93 and(or(n22, n14), xor(Y, and(inv1, X)))
% 283.64/36.93 = { by lemma 110 }
% 283.64/36.93 and(Y, or(n22, n14))
% 283.64/36.93
% 283.64/36.93 Lemma 112: and(and(X, Y), and(Z, Y)) = and(Z, and(X, Y)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(and(X, Y), and(Z, Y))
% 283.64/36.93 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.93 and(Z, and(and(X, Y), Y))
% 283.64/36.93 = { by lemma 82 }
% 283.64/36.93 and(Z, and(X, Y))
% 283.64/36.93
% 283.64/36.93 Lemma 113: and(not(n20), and(X, Y)) = and(X, and(inv1, Y)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(not(n20), and(X, Y))
% 283.64/36.93 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.93 and(X, and(not(n20), Y))
% 283.64/36.93 = { by axiom 8 (constructor29) R->L }
% 283.64/36.93 and(X, and(inv1, Y))
% 283.64/36.93
% 283.64/36.93 Lemma 114: and(and(inv1, X), and(X, Y)) = and(and(X, Y), not(n20)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(and(inv1, X), and(X, Y))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(and(X, Y), and(inv1, X))
% 283.64/36.93 = { by lemma 113 R->L }
% 283.64/36.93 and(not(n20), and(and(X, Y), X))
% 283.64/36.93 = { by lemma 92 }
% 283.64/36.93 and(not(n20), and(X, Y))
% 283.64/36.93 = { by axiom 29 (and_symmetry) }
% 283.64/36.93 and(and(X, Y), not(n20))
% 283.64/36.93
% 283.64/36.93 Lemma 115: and(not(and(i2, i3)), not(or(n23, n6))) = not(n20).
% 283.64/36.93 Proof:
% 283.64/36.93 and(not(and(i2, i3)), not(or(n23, n6)))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(not(or(n23, n6)), not(and(i2, i3)))
% 283.64/36.93 = { by lemma 62 R->L }
% 283.64/36.93 xor(not(or(n23, n6)), and(and(i2, i3), not(or(n23, n6))))
% 283.64/36.93 = { by lemma 103 }
% 283.64/36.93 xor(not(or(n23, n6)), xor(or(n23, n6), or(n22, n14)))
% 283.64/36.93 = { by lemma 53 }
% 283.64/36.93 xor(or(n23, n6), not(xor(or(n23, n6), or(n22, n14))))
% 283.64/36.93 = { by lemma 59 }
% 283.64/36.93 xor(or(n23, n6), xor(or(n23, n6), not(or(n22, n14))))
% 283.64/36.93 = { by axiom 43 (xor_simplification1) }
% 283.64/36.93 not(or(n22, n14))
% 283.64/36.93 = { by axiom 21 (constructor23) R->L }
% 283.64/36.93 not(n20)
% 283.64/36.93
% 283.64/36.93 Lemma 116: and(not(n20), not(and(i2, i3))) = not(n20).
% 283.64/36.93 Proof:
% 283.64/36.93 and(not(n20), not(and(i2, i3)))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(not(and(i2, i3)), not(n20))
% 283.64/36.93 = { by lemma 115 R->L }
% 283.64/36.93 and(not(and(i2, i3)), and(not(and(i2, i3)), not(or(n23, n6))))
% 283.64/36.93 = { by axiom 45 (and_simplification2) }
% 283.64/36.93 and(not(and(i2, i3)), not(or(n23, n6)))
% 283.64/36.93 = { by lemma 115 }
% 283.64/36.93 not(n20)
% 283.64/36.93
% 283.64/36.93 Lemma 117: and(and(inv1, i2), and(i2, i3)) = n0.
% 283.64/36.93 Proof:
% 283.64/36.93 and(and(inv1, i2), and(i2, i3))
% 283.64/36.93 = { by lemma 114 }
% 283.64/36.93 and(and(i2, i3), not(n20))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(not(n20), and(i2, i3))
% 283.64/36.93 = { by lemma 51 R->L }
% 283.64/36.93 and(not(n20), not(not(and(i2, i3))))
% 283.64/36.93 = { by lemma 55 R->L }
% 283.64/36.93 xor(not(n20), and(not(n20), not(and(i2, i3))))
% 283.64/36.93 = { by lemma 116 }
% 283.64/36.93 xor(not(n20), not(n20))
% 283.64/36.93 = { by axiom 9 (xor_definition3) }
% 283.64/36.93 n0
% 283.64/36.93
% 283.64/36.93 Lemma 118: and(and(inv1, i2), and(inv1, i3)) = n0.
% 283.64/36.93 Proof:
% 283.64/36.93 and(and(inv1, i2), and(inv1, i3))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(and(inv1, i3), and(inv1, i2))
% 283.64/36.93 = { by lemma 112 R->L }
% 283.64/36.93 and(and(inv1, i2), and(and(inv1, i3), i2))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(and(inv1, i2), and(i2, and(inv1, i3)))
% 283.64/36.93 = { by lemma 113 R->L }
% 283.64/36.93 and(and(inv1, i2), and(not(n20), and(i2, i3)))
% 283.64/36.93 = { by axiom 29 (and_symmetry) }
% 283.64/36.93 and(and(inv1, i2), and(and(i2, i3), not(n20)))
% 283.64/36.93 = { by lemma 114 R->L }
% 283.64/36.93 and(and(inv1, i2), and(and(inv1, i2), and(i2, i3)))
% 283.64/36.93 = { by axiom 45 (and_simplification2) }
% 283.64/36.93 and(and(inv1, i2), and(i2, i3))
% 283.64/36.93 = { by lemma 117 }
% 283.64/36.93 n0
% 283.64/36.93
% 283.64/36.93 Lemma 119: and(and(inv1, i3), not(and(inv1, i2))) = and(inv1, i3).
% 283.64/36.93 Proof:
% 283.64/36.93 and(and(inv1, i3), not(and(inv1, i2)))
% 283.64/36.93 = { by lemma 62 R->L }
% 283.64/36.93 xor(and(inv1, i3), and(and(inv1, i2), and(inv1, i3)))
% 283.64/36.93 = { by lemma 118 }
% 283.64/36.93 xor(and(inv1, i3), n0)
% 283.64/36.93 = { by axiom 11 (xor_definition2) }
% 283.64/36.93 and(inv1, i3)
% 283.64/36.93
% 283.64/36.93 Lemma 120: and(or(n24, n7), not(and(inv1, i2))) = xor(and(inv1, i2), or(a1, n10)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(or(n24, n7), not(and(inv1, i2)))
% 283.64/36.93 = { by axiom 36 (constructor4) R->L }
% 283.64/36.93 and(or(n24, n7), not(a1))
% 283.64/36.93 = { by axiom 27 (constructor13) R->L }
% 283.64/36.93 and(n10, not(a1))
% 283.64/36.93 = { by lemma 56 R->L }
% 283.64/36.93 xor(a1, or(a1, n10))
% 283.64/36.93 = { by axiom 36 (constructor4) }
% 283.64/36.93 xor(and(inv1, i2), or(a1, n10))
% 283.64/36.93
% 283.64/36.93 Lemma 121: and(not(and(inv1, i2)), not(or(n24, n7))) = not(or(a1, n10)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(not(and(inv1, i2)), not(or(n24, n7)))
% 283.64/36.93 = { by lemma 62 R->L }
% 283.64/36.93 xor(not(and(inv1, i2)), and(or(n24, n7), not(and(inv1, i2))))
% 283.64/36.93 = { by lemma 120 }
% 283.64/36.93 xor(not(and(inv1, i2)), xor(and(inv1, i2), or(a1, n10)))
% 283.64/36.93 = { by lemma 53 }
% 283.64/36.93 xor(and(inv1, i2), not(xor(and(inv1, i2), or(a1, n10))))
% 283.64/36.93 = { by lemma 59 }
% 283.64/36.93 xor(and(inv1, i2), xor(and(inv1, i2), not(or(a1, n10))))
% 283.64/36.93 = { by axiom 43 (xor_simplification1) }
% 283.64/36.93 not(or(a1, n10))
% 283.64/36.93
% 283.64/36.93 Lemma 122: and(X, xor(Y, and(X, Z))) = and(X, xor(Z, Y)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(X, xor(Y, and(X, Z)))
% 283.64/36.93 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.93 and(X, xor(and(X, Z), Y))
% 283.64/36.93 = { by axiom 48 (and_xor_simplification) }
% 283.64/36.93 xor(and(X, and(X, Z)), and(X, Y))
% 283.64/36.93 = { by axiom 45 (and_simplification2) }
% 283.64/36.93 xor(and(X, Z), and(X, Y))
% 283.64/36.93 = { by axiom 48 (and_xor_simplification) R->L }
% 283.64/36.93 and(X, xor(Z, Y))
% 283.64/36.93
% 283.64/36.93 Lemma 123: and(X, not(and(X, Y))) = and(X, not(Y)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(X, not(and(X, Y)))
% 283.64/36.93 = { by axiom 12 (not_to_xor) }
% 283.64/36.93 and(X, xor(n1, and(X, Y)))
% 283.64/36.93 = { by lemma 122 }
% 283.64/36.93 and(X, xor(Y, n1))
% 283.64/36.93 = { by lemma 50 }
% 283.64/36.93 and(X, not(Y))
% 283.64/36.93
% 283.64/36.93 Lemma 124: and(or(a1, n10), not(and(inv1, i2))) = xor(and(inv1, i2), or(a1, n10)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(or(a1, n10), not(and(inv1, i2)))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(not(and(inv1, i2)), or(a1, n10))
% 283.64/36.93 = { by lemma 51 R->L }
% 283.64/36.93 and(not(and(inv1, i2)), not(not(or(a1, n10))))
% 283.64/36.93 = { by lemma 121 R->L }
% 283.64/36.93 and(not(and(inv1, i2)), not(and(not(and(inv1, i2)), not(or(n24, n7)))))
% 283.64/36.93 = { by lemma 123 }
% 283.64/36.93 and(not(and(inv1, i2)), not(not(or(n24, n7))))
% 283.64/36.93 = { by lemma 51 }
% 283.64/36.93 and(not(and(inv1, i2)), or(n24, n7))
% 283.64/36.93 = { by axiom 29 (and_symmetry) }
% 283.64/36.93 and(or(n24, n7), not(and(inv1, i2)))
% 283.64/36.93 = { by lemma 120 }
% 283.64/36.93 xor(and(inv1, i2), or(a1, n10))
% 283.64/36.93
% 283.64/36.93 Lemma 125: and(X, not(and(Y, X))) = and(X, not(Y)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(X, not(and(Y, X)))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(X, not(and(X, Y)))
% 283.64/36.93 = { by lemma 123 }
% 283.64/36.93 and(X, not(Y))
% 283.64/36.93
% 283.64/36.93 Lemma 126: and(and(i1, inv1), not(and(inv1, i2))) = xor(and(inv1, i2), or(a1, n24)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(and(i1, inv1), not(and(inv1, i2)))
% 283.64/36.93 = { by axiom 36 (constructor4) R->L }
% 283.64/36.93 and(and(i1, inv1), not(a1))
% 283.64/36.93 = { by axiom 40 (constructor27) R->L }
% 283.64/36.93 and(n24, not(a1))
% 283.64/36.93 = { by lemma 56 R->L }
% 283.64/36.93 xor(a1, or(a1, n24))
% 283.64/36.93 = { by axiom 36 (constructor4) }
% 283.64/36.93 xor(and(inv1, i2), or(a1, n24))
% 283.64/36.93
% 283.64/36.93 Lemma 127: and(not(and(inv1, i2)), not(and(i1, inv1))) = not(or(a1, n24)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(not(and(inv1, i2)), not(and(i1, inv1)))
% 283.64/36.93 = { by lemma 62 R->L }
% 283.64/36.93 xor(not(and(inv1, i2)), and(and(i1, inv1), not(and(inv1, i2))))
% 283.64/36.93 = { by lemma 126 }
% 283.64/36.93 xor(not(and(inv1, i2)), xor(and(inv1, i2), or(a1, n24)))
% 283.64/36.93 = { by lemma 53 }
% 283.64/36.93 xor(and(inv1, i2), not(xor(and(inv1, i2), or(a1, n24))))
% 283.64/36.93 = { by lemma 59 }
% 283.64/36.93 xor(and(inv1, i2), xor(and(inv1, i2), not(or(a1, n24))))
% 283.64/36.93 = { by axiom 43 (xor_simplification1) }
% 283.64/36.93 not(or(a1, n24))
% 283.64/36.93
% 283.64/36.93 Lemma 128: xor(and(inv1, i2), and(and(inv1, i2), and(i1, inv1))) = xor(and(i1, inv1), or(a1, n24)).
% 283.64/36.93 Proof:
% 283.64/36.93 xor(and(inv1, i2), and(and(inv1, i2), and(i1, inv1)))
% 283.64/36.93 = { by lemma 55 }
% 283.64/36.93 and(and(inv1, i2), not(and(i1, inv1)))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(not(and(i1, inv1)), and(inv1, i2))
% 283.64/36.93 = { by lemma 51 R->L }
% 283.64/36.93 and(not(and(i1, inv1)), not(not(and(inv1, i2))))
% 283.64/36.93 = { by lemma 62 R->L }
% 283.64/36.93 xor(not(and(i1, inv1)), and(not(and(inv1, i2)), not(and(i1, inv1))))
% 283.64/36.93 = { by lemma 127 }
% 283.64/36.93 xor(not(and(i1, inv1)), not(or(a1, n24)))
% 283.64/36.93 = { by lemma 53 }
% 283.64/36.93 xor(and(i1, inv1), not(not(or(a1, n24))))
% 283.64/36.93 = { by lemma 51 }
% 283.64/36.93 xor(and(i1, inv1), or(a1, n24))
% 283.64/36.93
% 283.64/36.93 Lemma 129: and(and(inv1, X), and(i1, i2)) = and(and(n6, X), not(n20)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(and(inv1, X), and(i1, i2))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(and(i1, i2), and(inv1, X))
% 283.64/36.93 = { by axiom 41 (constructor9) R->L }
% 283.64/36.93 and(n6, and(inv1, X))
% 283.64/36.93 = { by lemma 113 R->L }
% 283.64/36.93 and(not(n20), and(n6, X))
% 283.64/36.93 = { by axiom 29 (and_symmetry) }
% 283.64/36.93 and(and(n6, X), not(n20))
% 283.64/36.93
% 283.64/36.93 Lemma 130: and(and(inv1, X), and(i1, i2)) = and(and(inv1, X), and(n6, X)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(and(inv1, X), and(i1, i2))
% 283.64/36.93 = { by lemma 129 }
% 283.64/36.93 and(and(n6, X), not(n20))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(not(n20), and(n6, X))
% 283.64/36.93 = { by lemma 82 R->L }
% 283.64/36.93 and(not(n20), and(and(n6, X), X))
% 283.64/36.93 = { by lemma 113 }
% 283.64/36.93 and(and(n6, X), and(inv1, X))
% 283.64/36.93 = { by axiom 29 (and_symmetry) }
% 283.64/36.93 and(and(inv1, X), and(n6, X))
% 283.64/36.93
% 283.64/36.93 Lemma 131: and(and(n6, X), and(Y, and(i1, i2))) = and(Y, and(n6, X)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(and(n6, X), and(Y, and(i1, i2)))
% 283.64/36.93 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.93 and(Y, and(and(n6, X), and(i1, i2)))
% 283.64/36.93 = { by lemma 95 }
% 283.64/36.93 and(Y, and(n6, X))
% 283.64/36.93
% 283.64/36.93 Lemma 132: and(and(inv1, Y), and(X, Y)) = and(and(X, Y), not(n20)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(and(inv1, Y), and(X, Y))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(and(X, Y), and(inv1, Y))
% 283.64/36.93 = { by lemma 113 R->L }
% 283.64/36.93 and(not(n20), and(and(X, Y), Y))
% 283.64/36.93 = { by lemma 82 }
% 283.64/36.93 and(not(n20), and(X, Y))
% 283.64/36.93 = { by axiom 29 (and_symmetry) }
% 283.64/36.93 and(and(X, Y), not(n20))
% 283.64/36.93
% 283.64/36.93 Lemma 133: and(not(n20), and(X, Y)) = and(Y, and(inv1, X)).
% 283.64/36.93 Proof:
% 283.64/36.93 and(not(n20), and(X, Y))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(not(n20), and(Y, X))
% 283.64/36.93 = { by lemma 113 }
% 283.64/36.93 and(Y, and(inv1, X))
% 283.64/36.93
% 283.64/36.93 Lemma 134: and(and(inv1, i2), and(X, i3)) = n0.
% 283.64/36.93 Proof:
% 283.64/36.93 and(and(inv1, i2), and(X, i3))
% 283.64/36.93 = { by lemma 82 R->L }
% 283.64/36.93 and(and(inv1, i2), and(and(X, i3), i3))
% 283.64/36.93 = { by axiom 46 (and_commutativity) }
% 283.64/36.93 and(and(X, i3), and(and(inv1, i2), i3))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(and(X, i3), and(i3, and(inv1, i2)))
% 283.64/36.93 = { by lemma 133 R->L }
% 283.64/36.93 and(and(X, i3), and(not(n20), and(i2, i3)))
% 283.64/36.93 = { by axiom 29 (and_symmetry) }
% 283.64/36.93 and(and(X, i3), and(and(i2, i3), not(n20)))
% 283.64/36.93 = { by lemma 114 R->L }
% 283.64/36.93 and(and(X, i3), and(and(inv1, i2), and(i2, i3)))
% 283.64/36.93 = { by lemma 117 }
% 283.64/36.93 and(and(X, i3), n0)
% 283.64/36.93 = { by axiom 31 (and_definition2) }
% 283.64/36.93 n0
% 283.64/36.93
% 283.64/36.93 Lemma 135: and(and(inv1, i3), and(n6, i3)) = n0.
% 283.64/36.93 Proof:
% 283.64/36.93 and(and(inv1, i3), and(n6, i3))
% 283.64/36.93 = { by lemma 130 R->L }
% 283.64/36.93 and(and(inv1, i3), and(i1, i2))
% 283.64/36.93 = { by lemma 129 }
% 283.64/36.93 and(and(n6, i3), not(n20))
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(not(n20), and(n6, i3))
% 283.64/36.93 = { by lemma 131 R->L }
% 283.64/36.93 and(and(n6, i3), and(not(n20), and(i1, i2)))
% 283.64/36.93 = { by axiom 29 (and_symmetry) }
% 283.64/36.93 and(and(n6, i3), and(and(i1, i2), not(n20)))
% 283.64/36.93 = { by lemma 132 R->L }
% 283.64/36.93 and(and(n6, i3), and(and(inv1, i2), and(i1, i2)))
% 283.64/36.93 = { by lemma 131 }
% 283.64/36.93 and(and(inv1, i2), and(n6, i3))
% 283.64/36.93 = { by lemma 134 }
% 283.64/36.93 n0
% 283.64/36.93
% 283.64/36.93 Lemma 136: and(not(n20), X) = and(X, inv1).
% 283.64/36.93 Proof:
% 283.64/36.93 and(not(n20), X)
% 283.64/36.93 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.93 and(X, not(n20))
% 283.64/36.94 = { by axiom 8 (constructor29) R->L }
% 283.64/36.94 and(X, inv1)
% 283.64/36.94
% 283.64/36.94 Lemma 137: and(and(X, inv1), not(n20)) = and(X, inv1).
% 283.64/36.94 Proof:
% 283.64/36.94 and(and(X, inv1), not(n20))
% 283.64/36.94 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.94 and(not(n20), and(X, inv1))
% 283.64/36.94 = { by lemma 136 R->L }
% 283.64/36.94 and(not(n20), and(not(n20), X))
% 283.64/36.94 = { by axiom 45 (and_simplification2) }
% 283.64/36.94 and(not(n20), X)
% 283.64/36.94 = { by lemma 136 }
% 283.64/36.94 and(X, inv1)
% 283.64/36.94
% 283.64/36.94 Lemma 138: and(not(n20), xor(X, and(Y, inv1))) = xor(and(Y, inv1), and(X, not(n20))).
% 283.64/36.94 Proof:
% 283.64/36.94 and(not(n20), xor(X, and(Y, inv1)))
% 283.64/36.94 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.94 and(not(n20), xor(and(Y, inv1), X))
% 283.64/36.94 = { by lemma 81 R->L }
% 283.64/36.94 xor(and(and(Y, inv1), not(n20)), and(not(n20), X))
% 283.64/36.94 = { by lemma 137 }
% 283.64/36.94 xor(and(Y, inv1), and(not(n20), X))
% 283.64/36.94 = { by axiom 29 (and_symmetry) }
% 283.64/36.94 xor(and(Y, inv1), and(X, not(n20)))
% 283.64/36.94
% 283.64/36.94 Lemma 139: xor(and(i1, inv1), or(n24, n7)) = and(n6, i3).
% 283.64/36.94 Proof:
% 283.64/36.94 xor(and(i1, inv1), or(n24, n7))
% 283.64/36.94 = { by axiom 43 (xor_simplification1) R->L }
% 283.64/36.94 xor(and(n6, i3), xor(and(n6, i3), xor(and(i1, inv1), or(n24, n7))))
% 283.64/36.94 = { by axiom 40 (constructor27) R->L }
% 283.64/36.94 xor(and(n6, i3), xor(and(n6, i3), xor(n24, or(n24, n7))))
% 283.64/36.94 = { by lemma 56 }
% 283.64/36.94 xor(and(n6, i3), xor(and(n6, i3), and(n7, not(n24))))
% 283.64/36.94 = { by axiom 34 (constructor10) }
% 283.64/36.94 xor(and(n6, i3), xor(and(n6, i3), and(and(n6, i3), not(n24))))
% 283.64/36.94 = { by axiom 40 (constructor27) }
% 283.64/36.94 xor(and(n6, i3), xor(and(n6, i3), and(and(n6, i3), not(and(i1, inv1)))))
% 283.64/36.94 = { by lemma 55 }
% 283.64/36.94 xor(and(n6, i3), and(and(n6, i3), not(not(and(i1, inv1)))))
% 283.64/36.94 = { by lemma 51 }
% 283.64/36.94 xor(and(n6, i3), and(and(n6, i3), and(i1, inv1)))
% 283.64/36.94 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.94 xor(and(n6, i3), and(and(i1, inv1), and(n6, i3)))
% 283.64/36.94 = { by lemma 131 R->L }
% 283.64/36.94 xor(and(n6, i3), and(and(n6, i3), and(and(i1, inv1), and(i1, i2))))
% 283.64/36.94 = { by lemma 93 R->L }
% 283.64/36.94 xor(and(n6, i3), and(and(n6, i3), and(and(inv1, i2), and(i1, i2))))
% 283.64/36.94 = { by lemma 131 }
% 283.64/36.94 xor(and(n6, i3), and(and(inv1, i2), and(n6, i3)))
% 283.64/36.94 = { by lemma 134 }
% 283.64/36.94 xor(and(n6, i3), n0)
% 283.64/36.94 = { by axiom 11 (xor_definition2) }
% 283.64/36.94 and(n6, i3)
% 283.64/36.94
% 283.64/36.94 Lemma 140: xor(and(n6, i3), and(i1, inv1)) = or(n24, n7).
% 283.64/36.94 Proof:
% 283.64/36.94 xor(and(n6, i3), and(i1, inv1))
% 283.64/36.94 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.94 xor(and(i1, inv1), and(n6, i3))
% 283.64/36.94 = { by lemma 139 R->L }
% 283.64/36.94 xor(and(i1, inv1), xor(and(i1, inv1), or(n24, n7)))
% 283.64/36.94 = { by axiom 43 (xor_simplification1) }
% 283.64/36.94 or(n24, n7)
% 283.64/36.94
% 283.64/36.94 Lemma 141: and(and(inv1, X), and(i1, inv1)) = and(and(inv1, X), or(n24, n7)).
% 283.64/36.94 Proof:
% 283.64/36.94 and(and(inv1, X), and(i1, inv1))
% 283.64/36.94 = { by axiom 11 (xor_definition2) R->L }
% 283.64/36.94 and(and(inv1, X), xor(and(i1, inv1), n0))
% 283.64/36.94 = { by lemma 135 R->L }
% 283.64/36.94 and(and(inv1, X), xor(and(i1, inv1), and(and(inv1, i3), and(n6, i3))))
% 283.64/36.94 = { by lemma 130 R->L }
% 283.64/36.94 and(and(inv1, X), xor(and(i1, inv1), and(and(inv1, i3), and(i1, i2))))
% 283.64/36.94 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.94 and(and(inv1, X), xor(and(i1, inv1), and(and(i1, i2), and(inv1, i3))))
% 283.64/36.94 = { by axiom 41 (constructor9) R->L }
% 283.64/36.94 and(and(inv1, X), xor(and(i1, inv1), and(n6, and(inv1, i3))))
% 283.64/36.94 = { by lemma 113 R->L }
% 283.64/36.94 and(and(inv1, X), xor(and(i1, inv1), and(not(n20), and(n6, i3))))
% 283.64/36.94 = { by axiom 29 (and_symmetry) }
% 283.64/36.94 and(and(inv1, X), xor(and(i1, inv1), and(and(n6, i3), not(n20))))
% 283.64/36.94 = { by lemma 138 R->L }
% 283.64/36.94 and(and(inv1, X), and(not(n20), xor(and(n6, i3), and(i1, inv1))))
% 283.64/36.94 = { by lemma 140 }
% 283.64/36.94 and(and(inv1, X), and(not(n20), or(n24, n7)))
% 283.64/36.94 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.94 and(and(inv1, X), and(or(n24, n7), not(n20)))
% 283.64/36.94 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.94 and(or(n24, n7), and(and(inv1, X), not(n20)))
% 283.64/36.94 = { by lemma 69 }
% 283.64/36.94 and(or(n24, n7), and(inv1, X))
% 283.64/36.94 = { by axiom 29 (and_symmetry) }
% 283.64/36.94 and(and(inv1, X), or(n24, n7))
% 283.64/36.94
% 283.64/36.94 Lemma 142: xor(and(i1, inv1), or(a1, n24)) = xor(or(a1, n10), or(n24, n7)).
% 283.64/36.94 Proof:
% 283.64/36.94 xor(and(i1, inv1), or(a1, n24))
% 283.64/36.94 = { by lemma 128 R->L }
% 283.64/36.94 xor(and(inv1, i2), and(and(inv1, i2), and(i1, inv1)))
% 283.64/36.94 = { by lemma 141 }
% 283.64/36.94 xor(and(inv1, i2), and(and(inv1, i2), or(n24, n7)))
% 283.64/36.94 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.94 xor(and(inv1, i2), and(or(n24, n7), and(inv1, i2)))
% 283.64/36.94 = { by lemma 51 R->L }
% 283.64/36.94 xor(and(inv1, i2), and(or(n24, n7), not(not(and(inv1, i2)))))
% 283.64/36.94 = { by lemma 55 R->L }
% 283.64/36.94 xor(and(inv1, i2), xor(or(n24, n7), and(or(n24, n7), not(and(inv1, i2)))))
% 283.64/36.94 = { by lemma 120 }
% 283.64/36.94 xor(and(inv1, i2), xor(or(n24, n7), xor(and(inv1, i2), or(a1, n10))))
% 283.64/36.94 = { by axiom 44 (xor_commutativity) }
% 283.64/36.94 xor(and(inv1, i2), xor(and(inv1, i2), xor(or(n24, n7), or(a1, n10))))
% 283.64/36.94 = { by axiom 10 (xor_symmetry) }
% 283.64/36.94 xor(and(inv1, i2), xor(and(inv1, i2), xor(or(a1, n10), or(n24, n7))))
% 283.64/36.94 = { by axiom 43 (xor_simplification1) }
% 283.64/36.94 xor(or(a1, n10), or(n24, n7))
% 283.64/36.94
% 283.64/36.94 Lemma 143: and(not(n20), and(X, Y)) = and(X, and(Y, inv1)).
% 283.64/36.94 Proof:
% 283.64/36.94 and(not(n20), and(X, Y))
% 283.64/36.94 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.94 and(X, and(not(n20), Y))
% 283.64/36.94 = { by lemma 136 }
% 283.64/36.94 and(X, and(Y, inv1))
% 283.64/36.94
% 283.64/36.94 Lemma 144: and(and(X, Y), not(n20)) = and(and(inv1, Y), X).
% 283.64/36.94 Proof:
% 283.64/36.94 and(and(X, Y), not(n20))
% 283.64/36.94 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.94 and(not(n20), and(X, Y))
% 283.64/36.94 = { by lemma 113 }
% 283.64/36.94 and(X, and(inv1, Y))
% 283.64/36.94 = { by axiom 29 (and_symmetry) }
% 283.64/36.94 and(and(inv1, Y), X)
% 283.64/36.94
% 283.64/36.94 Lemma 145: and(and(inv1, X), and(Y, X)) = and(and(inv1, X), Y).
% 283.64/36.94 Proof:
% 283.64/36.94 and(and(inv1, X), and(Y, X))
% 283.64/36.94 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.94 and(and(Y, X), and(inv1, X))
% 283.64/36.94 = { by lemma 113 R->L }
% 283.64/36.94 and(not(n20), and(and(Y, X), X))
% 283.64/36.94 = { by lemma 82 }
% 283.64/36.94 and(not(n20), and(Y, X))
% 283.64/36.94 = { by axiom 29 (and_symmetry) }
% 283.64/36.94 and(and(Y, X), not(n20))
% 283.64/36.94 = { by lemma 144 }
% 283.64/36.94 and(and(inv1, X), Y)
% 283.64/36.94
% 283.64/36.94 Lemma 146: and(and(inv1, X), and(Y, inv1)) = and(and(inv1, X), and(Y, X)).
% 283.64/36.94 Proof:
% 283.64/36.94 and(and(inv1, X), and(Y, inv1))
% 283.64/36.94 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.94 and(and(Y, inv1), and(inv1, X))
% 283.64/36.94 = { by lemma 112 R->L }
% 283.64/36.94 and(and(inv1, X), and(and(Y, inv1), X))
% 283.64/36.94 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.94 and(and(inv1, X), and(X, and(Y, inv1)))
% 283.64/36.94 = { by lemma 143 R->L }
% 283.64/36.94 and(and(inv1, X), and(not(n20), and(X, Y)))
% 283.64/36.94 = { by lemma 133 }
% 283.64/36.94 and(and(inv1, X), and(Y, and(inv1, X)))
% 283.64/36.94 = { by axiom 29 (and_symmetry) }
% 283.64/36.94 and(and(inv1, X), and(and(inv1, X), Y))
% 283.64/36.94 = { by lemma 145 R->L }
% 283.64/36.94 and(and(inv1, X), and(and(inv1, X), and(Y, X)))
% 283.64/36.94 = { by axiom 45 (and_simplification2) }
% 283.64/36.94 and(and(inv1, X), and(Y, X))
% 283.64/36.94
% 283.64/36.94 Lemma 147: and(and(inv1, Y), and(X, inv1)) = and(and(X, inv1), Y).
% 283.64/36.94 Proof:
% 283.64/36.94 and(and(inv1, Y), and(X, inv1))
% 283.64/36.94 = { by lemma 146 }
% 283.64/36.94 and(and(inv1, Y), and(X, Y))
% 283.64/36.94 = { by lemma 132 }
% 283.64/36.94 and(and(X, Y), not(n20))
% 283.64/36.94 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.94 and(not(n20), and(X, Y))
% 283.64/36.94 = { by axiom 29 (and_symmetry) }
% 283.64/36.94 and(not(n20), and(Y, X))
% 283.64/36.94 = { by lemma 143 }
% 283.64/36.94 and(Y, and(X, inv1))
% 283.64/36.94 = { by axiom 29 (and_symmetry) }
% 283.64/36.94 and(and(X, inv1), Y)
% 283.64/36.94
% 283.64/36.94 Lemma 148: xor(and(X, inv1), and(Y, X)) = and(X, xor(Y, not(n20))).
% 283.64/36.94 Proof:
% 283.64/36.94 xor(and(X, inv1), and(Y, X))
% 283.64/36.94 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.94 xor(and(X, inv1), and(X, Y))
% 283.64/36.94 = { by lemma 136 R->L }
% 283.64/36.94 xor(and(not(n20), X), and(X, Y))
% 283.64/36.94 = { by lemma 81 }
% 283.64/36.94 and(X, xor(not(n20), Y))
% 283.64/36.94 = { by axiom 10 (xor_symmetry) }
% 283.64/36.94 and(X, xor(Y, not(n20)))
% 283.64/36.94
% 283.64/36.94 Lemma 149: xor(X, not(X)) = n1.
% 283.64/36.94 Proof:
% 283.64/36.94 xor(X, not(X))
% 283.64/36.94 = { by lemma 50 R->L }
% 283.64/36.94 xor(X, xor(X, n1))
% 283.64/36.94 = { by axiom 43 (xor_simplification1) }
% 283.64/36.94 n1
% 283.64/36.94
% 283.64/36.94 Lemma 150: and(X, or(Y, X)) = X.
% 283.64/36.94 Proof:
% 283.64/36.94 and(X, or(Y, X))
% 283.64/36.94 = { by lemma 57 R->L }
% 283.64/36.94 and(X, xor(Y, and(X, not(Y))))
% 283.64/36.94 = { by lemma 122 }
% 283.64/36.94 and(X, xor(not(Y), Y))
% 283.64/36.94 = { by lemma 53 }
% 283.64/36.94 and(X, xor(Y, not(Y)))
% 283.64/36.94 = { by lemma 149 }
% 283.64/36.94 and(X, n1)
% 283.64/36.94 = { by axiom 30 (and_definition4) }
% 283.64/36.94 X
% 283.64/36.94
% 283.64/36.94 Lemma 151: xor(and(i1, inv1), or(n23, n6)) = i1.
% 283.64/36.94 Proof:
% 283.64/36.94 xor(and(i1, inv1), or(n23, n6))
% 283.64/36.94 = { by lemma 102 R->L }
% 283.64/36.94 xor(and(i1, inv1), and(or(n23, n6), i1))
% 283.64/36.94 = { by lemma 148 }
% 283.64/36.94 and(i1, xor(or(n23, n6), not(n20)))
% 283.64/36.94 = { by axiom 21 (constructor23) }
% 283.64/36.94 and(i1, xor(or(n23, n6), not(or(n22, n14))))
% 283.64/36.94 = { by lemma 59 R->L }
% 283.64/36.94 and(i1, not(xor(or(n23, n6), or(n22, n14))))
% 283.64/36.94 = { by lemma 104 R->L }
% 283.64/36.94 and(i1, not(xor(and(i2, i3), and(n6, i3))))
% 283.64/36.94 = { by lemma 59 }
% 283.64/36.94 and(i1, xor(and(i2, i3), not(and(n6, i3))))
% 283.64/36.94 = { by lemma 96 R->L }
% 283.64/36.94 and(i1, xor(and(i2, i3), not(and(and(i2, i3), i1))))
% 283.64/36.94 = { by lemma 58 }
% 283.64/36.94 and(i1, or(not(and(i2, i3)), i1))
% 283.64/36.94 = { by lemma 150 }
% 283.64/36.94 i1
% 283.64/36.94
% 283.64/36.94 Lemma 152: xor(or(n23, n6), i1) = and(i1, inv1).
% 283.64/36.94 Proof:
% 283.64/36.94 xor(or(n23, n6), i1)
% 283.64/36.94 = { by lemma 151 R->L }
% 283.64/36.94 xor(or(n23, n6), xor(and(i1, inv1), or(n23, n6)))
% 283.64/36.94 = { by lemma 78 }
% 283.64/36.94 and(i1, inv1)
% 283.64/36.94
% 283.64/36.94 Lemma 153: and(X, xor(and(Y, X), Z)) = xor(and(Y, X), and(Z, X)).
% 283.64/36.94 Proof:
% 283.64/36.94 and(X, xor(and(Y, X), Z))
% 283.64/36.94 = { by lemma 81 R->L }
% 283.64/36.94 xor(and(and(Y, X), X), and(X, Z))
% 283.64/36.94 = { by lemma 82 }
% 283.64/36.94 xor(and(Y, X), and(X, Z))
% 283.64/36.94 = { by axiom 29 (and_symmetry) }
% 283.64/36.94 xor(and(Y, X), and(Z, X))
% 283.64/36.94
% 283.64/36.94 Lemma 154: and(and(n6, X), not(i2)) = n0.
% 283.64/36.94 Proof:
% 283.64/36.94 and(and(n6, X), not(i2))
% 283.64/36.94 = { by lemma 56 R->L }
% 283.64/36.94 xor(i2, or(i2, and(n6, X)))
% 283.64/36.94 = { by lemma 95 R->L }
% 283.64/36.94 xor(i2, or(i2, and(and(n6, X), and(i1, i2))))
% 283.64/36.94 = { by lemma 88 R->L }
% 283.64/36.94 xor(i2, or(i2, and(i2, and(and(n6, X), i1))))
% 283.64/36.94 = { by lemma 84 }
% 283.64/36.94 xor(i2, i2)
% 283.64/36.94 = { by axiom 9 (xor_definition3) }
% 283.64/36.94 n0
% 283.64/36.94
% 283.64/36.94 Lemma 155: and(or(n23, n6), i2) = and(i1, i2).
% 283.64/36.94 Proof:
% 283.64/36.94 and(or(n23, n6), i2)
% 283.64/36.94 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.94 and(i2, or(n23, n6))
% 283.64/36.94 = { by lemma 102 R->L }
% 283.64/36.94 and(i2, and(or(n23, n6), i1))
% 283.64/36.94 = { by lemma 88 }
% 283.64/36.94 and(or(n23, n6), and(i1, i2))
% 283.64/36.94 = { by axiom 29 (and_symmetry) }
% 283.64/36.94 and(and(i1, i2), or(n23, n6))
% 283.64/36.94 = { by axiom 43 (xor_simplification1) R->L }
% 283.64/36.94 xor(and(i1, i2), xor(and(i1, i2), and(and(i1, i2), or(n23, n6))))
% 283.64/36.94 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.94 xor(and(i1, i2), xor(and(i1, i2), and(or(n23, n6), and(i1, i2))))
% 283.64/36.94 = { by lemma 88 R->L }
% 283.64/36.94 xor(and(i1, i2), xor(and(i1, i2), and(i2, and(or(n23, n6), i1))))
% 283.64/36.94 = { by lemma 102 }
% 283.64/36.94 xor(and(i1, i2), xor(and(i1, i2), and(i2, or(n23, n6))))
% 283.64/36.94 = { by axiom 29 (and_symmetry) }
% 283.64/36.94 xor(and(i1, i2), xor(and(i1, i2), and(or(n23, n6), i2)))
% 283.64/36.94 = { by lemma 153 R->L }
% 283.64/36.94 xor(and(i1, i2), and(i2, xor(and(i1, i2), or(n23, n6))))
% 283.64/36.94 = { by lemma 94 }
% 283.64/36.94 xor(and(i1, i2), and(i2, xor(and(n6, i3), and(i1, i3))))
% 283.64/36.94 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.94 xor(and(i1, i2), and(i2, xor(and(i1, i3), and(n6, i3))))
% 283.64/36.94 = { by lemma 81 R->L }
% 283.64/36.94 xor(and(i1, i2), xor(and(and(i1, i3), i2), and(i2, and(n6, i3))))
% 283.64/36.94 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.94 xor(and(i1, i2), xor(and(i2, and(i1, i3)), and(i2, and(n6, i3))))
% 283.64/36.94 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.94 xor(and(i1, i2), xor(and(i1, and(i2, i3)), and(i2, and(n6, i3))))
% 283.64/36.94 = { by axiom 29 (and_symmetry) }
% 283.64/36.94 xor(and(i1, i2), xor(and(and(i2, i3), i1), and(i2, and(n6, i3))))
% 283.64/36.94 = { by lemma 87 R->L }
% 283.64/36.94 xor(and(i1, i2), xor(and(and(i2, i3), and(i1, i3)), and(i2, and(n6, i3))))
% 283.64/36.94 = { by lemma 90 }
% 283.64/36.94 xor(and(i1, i2), xor(and(n6, i3), and(i2, and(n6, i3))))
% 283.64/36.94 = { by axiom 29 (and_symmetry) }
% 283.64/36.94 xor(and(i1, i2), xor(and(n6, i3), and(and(n6, i3), i2)))
% 283.64/36.94 = { by lemma 55 }
% 283.64/36.94 xor(and(i1, i2), and(and(n6, i3), not(i2)))
% 283.64/36.94 = { by lemma 154 }
% 283.64/36.94 xor(and(i1, i2), n0)
% 283.64/36.94 = { by axiom 11 (xor_definition2) }
% 283.64/36.94 and(i1, i2)
% 283.64/36.94
% 283.64/36.94 Lemma 156: and(and(inv1, i2), and(i1, inv1)) = n0.
% 283.64/36.94 Proof:
% 283.64/36.94 and(and(inv1, i2), and(i1, inv1))
% 283.64/36.94 = { by lemma 147 }
% 283.64/36.94 and(and(i1, inv1), i2)
% 283.64/36.94 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.94 and(i2, and(i1, inv1))
% 283.64/36.94 = { by lemma 152 R->L }
% 283.64/36.94 and(i2, xor(or(n23, n6), i1))
% 283.64/36.94 = { by lemma 99 R->L }
% 283.64/36.94 xor(and(i1, i2), and(or(n23, n6), i2))
% 283.64/36.94 = { by lemma 155 }
% 283.64/36.94 xor(and(i1, i2), and(i1, i2))
% 283.64/36.94 = { by axiom 9 (xor_definition3) }
% 283.64/36.94 n0
% 283.64/36.95
% 283.64/36.95 Lemma 157: and(or(a1, n10), not(or(n24, n7))) = and(inv1, i2).
% 283.64/36.95 Proof:
% 283.64/36.95 and(or(a1, n10), not(or(n24, n7)))
% 283.64/36.95 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.95 and(not(or(n24, n7)), or(a1, n10))
% 283.64/36.95 = { by lemma 51 R->L }
% 283.64/36.95 and(not(or(n24, n7)), not(not(or(a1, n10))))
% 283.64/36.95 = { by lemma 121 R->L }
% 283.64/36.95 and(not(or(n24, n7)), not(and(not(and(inv1, i2)), not(or(n24, n7)))))
% 283.64/36.95 = { by lemma 125 }
% 283.64/36.95 and(not(or(n24, n7)), not(not(and(inv1, i2))))
% 283.64/36.95 = { by lemma 62 R->L }
% 283.64/36.95 xor(not(or(n24, n7)), and(not(and(inv1, i2)), not(or(n24, n7))))
% 283.64/36.95 = { by lemma 121 }
% 283.64/36.95 xor(not(or(n24, n7)), not(or(a1, n10)))
% 283.64/36.95 = { by lemma 53 }
% 283.64/36.95 xor(or(n24, n7), not(not(or(a1, n10))))
% 283.64/36.95 = { by lemma 51 }
% 283.64/36.95 xor(or(n24, n7), or(a1, n10))
% 283.64/36.95 = { by axiom 10 (xor_symmetry) }
% 283.64/36.95 xor(or(a1, n10), or(n24, n7))
% 283.64/36.95 = { by lemma 142 R->L }
% 283.64/36.95 xor(and(i1, inv1), or(a1, n24))
% 283.64/36.95 = { by lemma 128 R->L }
% 283.64/36.95 xor(and(inv1, i2), and(and(inv1, i2), and(i1, inv1)))
% 283.64/36.95 = { by lemma 156 }
% 283.64/36.95 xor(and(inv1, i2), n0)
% 283.64/36.95 = { by axiom 11 (xor_definition2) }
% 283.64/36.95 and(inv1, i2)
% 283.64/36.95
% 283.64/36.95 Lemma 158: and(X, not(X)) = n0.
% 283.64/36.95 Proof:
% 283.64/36.95 and(X, not(X))
% 283.64/36.95 = { by lemma 55 R->L }
% 283.64/36.95 xor(X, and(X, X))
% 283.64/36.95 = { by axiom 28 (and_simplification1) }
% 283.64/36.95 xor(X, X)
% 283.64/36.95 = { by axiom 9 (xor_definition3) }
% 283.64/36.95 n0
% 283.64/36.95
% 283.64/36.95 Lemma 159: and(X, and(Y, not(X))) = n0.
% 283.64/36.95 Proof:
% 283.64/36.95 and(X, and(Y, not(X)))
% 283.64/36.95 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.95 and(Y, and(X, not(X)))
% 283.64/36.95 = { by lemma 158 }
% 283.64/36.95 and(Y, n0)
% 283.64/36.95 = { by axiom 31 (and_definition2) }
% 283.64/36.95 n0
% 283.64/36.95
% 283.64/36.95 Lemma 160: and(or(a1, n10), or(n24, n7)) = or(n24, n7).
% 283.64/36.95 Proof:
% 283.64/36.95 and(or(a1, n10), or(n24, n7))
% 283.64/36.95 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.95 and(or(n24, n7), or(a1, n10))
% 283.64/36.95 = { by lemma 51 R->L }
% 283.64/36.95 and(or(n24, n7), not(not(or(a1, n10))))
% 283.64/36.95 = { by lemma 55 R->L }
% 283.64/36.95 xor(or(n24, n7), and(or(n24, n7), not(or(a1, n10))))
% 283.64/36.95 = { by lemma 121 R->L }
% 283.64/36.95 xor(or(n24, n7), and(or(n24, n7), and(not(and(inv1, i2)), not(or(n24, n7)))))
% 283.64/36.95 = { by lemma 159 }
% 283.64/36.95 xor(or(n24, n7), n0)
% 283.64/36.95 = { by axiom 11 (xor_definition2) }
% 283.64/36.95 or(n24, n7)
% 283.64/36.95
% 283.64/36.95 Lemma 161: xor(and(inv1, i2), or(a1, n10)) = or(n24, n7).
% 283.64/36.95 Proof:
% 283.64/36.95 xor(and(inv1, i2), or(a1, n10))
% 283.64/36.95 = { by lemma 124 R->L }
% 283.64/36.95 and(or(a1, n10), not(and(inv1, i2)))
% 283.64/36.95 = { by lemma 157 R->L }
% 283.64/36.95 and(or(a1, n10), not(and(or(a1, n10), not(or(n24, n7)))))
% 283.64/36.95 = { by lemma 123 }
% 283.64/36.95 and(or(a1, n10), not(not(or(n24, n7))))
% 283.64/36.95 = { by lemma 51 }
% 283.64/36.95 and(or(a1, n10), or(n24, n7))
% 283.64/36.95 = { by lemma 160 }
% 283.64/36.95 or(n24, n7)
% 283.64/36.95
% 283.64/36.95 Lemma 162: and(and(i1, i3), not(or(n23, n6))) = n0.
% 283.64/36.95 Proof:
% 283.64/36.95 and(and(i1, i3), not(or(n23, n6)))
% 283.64/36.95 = { by lemma 76 R->L }
% 283.64/36.95 and(and(i1, i3), xor(and(i1, i3), or(n23, n6)))
% 283.64/36.95 = { by lemma 91 R->L }
% 283.64/36.95 and(and(i1, i3), and(and(i1, i2), not(and(i1, i3))))
% 283.64/36.95 = { by lemma 159 }
% 283.64/36.95 n0
% 283.64/36.95
% 283.64/36.95 Lemma 163: and(and(inv1, i3), and(i1, inv1)) = n0.
% 283.64/36.95 Proof:
% 283.64/36.95 and(and(inv1, i3), and(i1, inv1))
% 283.64/36.95 = { by lemma 146 }
% 283.64/36.95 and(and(inv1, i3), and(i1, i3))
% 283.64/36.95 = { by lemma 145 }
% 283.64/36.95 and(and(inv1, i3), i1)
% 283.64/36.95 = { by lemma 144 R->L }
% 283.64/36.95 and(and(i1, i3), not(n20))
% 283.64/36.95 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.95 and(not(n20), and(i1, i3))
% 283.64/36.95 = { by lemma 92 R->L }
% 283.64/36.95 and(not(n20), and(and(i1, i3), i1))
% 283.64/36.95 = { by lemma 143 }
% 283.64/36.95 and(and(i1, i3), and(i1, inv1))
% 283.64/36.95 = { by lemma 152 R->L }
% 283.64/36.95 and(and(i1, i3), xor(or(n23, n6), i1))
% 283.64/36.95 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.95 and(and(i1, i3), xor(i1, or(n23, n6)))
% 283.64/36.95 = { by axiom 48 (and_xor_simplification) }
% 283.64/36.95 xor(and(and(i1, i3), i1), and(and(i1, i3), or(n23, n6)))
% 283.64/36.95 = { by lemma 92 }
% 283.64/36.95 xor(and(i1, i3), and(and(i1, i3), or(n23, n6)))
% 283.64/36.95 = { by lemma 55 }
% 283.64/36.95 and(and(i1, i3), not(or(n23, n6)))
% 283.64/36.95 = { by lemma 162 }
% 283.64/36.95 n0
% 283.64/36.95
% 283.64/36.95 Lemma 164: and(and(inv1, i3), or(a1, n10)) = n0.
% 283.64/36.95 Proof:
% 283.64/36.95 and(and(inv1, i3), or(a1, n10))
% 283.64/36.95 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.95 and(or(a1, n10), and(inv1, i3))
% 283.64/36.95 = { by lemma 119 R->L }
% 283.64/36.95 and(or(a1, n10), and(and(inv1, i3), not(and(inv1, i2))))
% 283.64/36.95 = { by axiom 46 (and_commutativity) }
% 283.64/36.95 and(and(inv1, i3), and(or(a1, n10), not(and(inv1, i2))))
% 283.64/36.95 = { by lemma 124 }
% 283.64/36.95 and(and(inv1, i3), xor(and(inv1, i2), or(a1, n10)))
% 283.64/36.95 = { by lemma 161 }
% 283.64/36.95 and(and(inv1, i3), or(n24, n7))
% 283.64/36.95 = { by lemma 141 R->L }
% 283.64/36.95 and(and(inv1, i3), and(i1, inv1))
% 283.64/36.95 = { by lemma 163 }
% 283.64/36.95 n0
% 283.64/36.95
% 283.64/36.95 Lemma 165: xor(and(inv1, i3), or(n8, n2)) = or(a1, n10).
% 283.64/36.95 Proof:
% 283.64/36.95 xor(and(inv1, i3), or(n8, n2))
% 283.64/36.95 = { by lemma 65 }
% 283.64/36.95 xor(and(inv1, i3), not(not(n9)))
% 283.64/36.95 = { by lemma 53 R->L }
% 283.64/36.95 xor(not(and(inv1, i3)), not(n9))
% 283.64/36.95 = { by lemma 72 R->L }
% 283.64/36.95 xor(not(and(inv1, i3)), and(not(and(inv1, i3)), not(or(a1, n10))))
% 283.64/36.95 = { by lemma 55 }
% 283.64/36.95 and(not(and(inv1, i3)), not(not(or(a1, n10))))
% 283.64/36.95 = { by lemma 51 }
% 283.64/36.95 and(not(and(inv1, i3)), or(a1, n10))
% 283.64/36.95 = { by axiom 29 (and_symmetry) }
% 283.64/36.95 and(or(a1, n10), not(and(inv1, i3)))
% 283.64/36.95 = { by lemma 62 R->L }
% 283.64/36.95 xor(or(a1, n10), and(and(inv1, i3), or(a1, n10)))
% 283.64/36.95 = { by lemma 164 }
% 283.64/36.95 xor(or(a1, n10), n0)
% 283.64/36.95 = { by axiom 11 (xor_definition2) }
% 283.64/36.95 or(a1, n10)
% 283.64/36.95
% 283.64/36.95 Lemma 166: xor(and(inv1, i2), or(n24, n7)) = or(a1, n10).
% 283.64/36.95 Proof:
% 283.64/36.95 xor(and(inv1, i2), or(n24, n7))
% 283.64/36.95 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.95 xor(or(n24, n7), and(inv1, i2))
% 283.64/36.95 = { by lemma 157 R->L }
% 283.64/36.95 xor(or(n24, n7), and(or(a1, n10), not(or(n24, n7))))
% 283.64/36.95 = { by lemma 57 }
% 283.64/36.95 or(or(n24, n7), or(a1, n10))
% 283.64/36.95 = { by lemma 160 R->L }
% 283.64/36.95 or(and(or(a1, n10), or(n24, n7)), or(a1, n10))
% 283.64/36.95 = { by lemma 57 R->L }
% 283.64/36.95 xor(and(or(a1, n10), or(n24, n7)), and(or(a1, n10), not(and(or(a1, n10), or(n24, n7)))))
% 283.64/36.95 = { by lemma 123 }
% 283.64/36.95 xor(and(or(a1, n10), or(n24, n7)), and(or(a1, n10), not(or(n24, n7))))
% 283.64/36.95 = { by axiom 48 (and_xor_simplification) R->L }
% 283.64/36.95 and(or(a1, n10), xor(or(n24, n7), not(or(n24, n7))))
% 283.64/36.95 = { by lemma 149 }
% 283.64/36.95 and(or(a1, n10), n1)
% 283.64/36.95 = { by axiom 30 (and_definition4) }
% 283.64/36.95 or(a1, n10)
% 283.64/36.95
% 283.64/36.95 Lemma 167: and(and(i1, i2), and(X, Y)) = and(X, and(n6, Y)).
% 283.64/36.95 Proof:
% 283.64/36.95 and(and(i1, i2), and(X, Y))
% 283.64/36.95 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.95 and(X, and(and(i1, i2), Y))
% 283.64/36.95 = { by lemma 89 }
% 283.64/36.95 and(X, and(n6, Y))
% 283.64/36.95
% 283.64/36.95 Lemma 168: and(or(n8, n2), or(n22, n14)) = and(n6, i3).
% 283.64/36.95 Proof:
% 283.64/36.95 and(or(n8, n2), or(n22, n14))
% 283.64/36.95 = { by lemma 111 R->L }
% 283.64/36.95 and(or(n22, n14), xor(and(inv1, i3), or(n8, n2)))
% 283.64/36.95 = { by lemma 165 }
% 283.64/36.95 and(or(n22, n14), or(a1, n10))
% 283.64/36.95 = { by lemma 166 R->L }
% 283.64/36.95 and(or(n22, n14), xor(and(inv1, i2), or(n24, n7)))
% 283.64/36.95 = { by lemma 111 }
% 283.64/36.95 and(or(n24, n7), or(n22, n14))
% 283.64/36.95 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.95 and(or(n22, n14), or(n24, n7))
% 283.64/36.95 = { by lemma 140 R->L }
% 283.64/36.95 and(or(n22, n14), xor(and(n6, i3), and(i1, inv1)))
% 283.64/36.95 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.95 and(or(n22, n14), xor(and(i1, inv1), and(n6, i3)))
% 283.64/36.95 = { by lemma 81 R->L }
% 283.64/36.95 xor(and(and(i1, inv1), or(n22, n14)), and(or(n22, n14), and(n6, i3)))
% 283.64/36.95 = { by lemma 66 }
% 283.64/36.95 xor(and(and(i1, inv1), not(not(n20))), and(or(n22, n14), and(n6, i3)))
% 283.64/36.95 = { by lemma 55 R->L }
% 283.64/36.95 xor(xor(and(i1, inv1), and(and(i1, inv1), not(n20))), and(or(n22, n14), and(n6, i3)))
% 283.64/36.95 = { by lemma 137 }
% 283.64/36.95 xor(xor(and(i1, inv1), and(i1, inv1)), and(or(n22, n14), and(n6, i3)))
% 283.64/36.95 = { by axiom 9 (xor_definition3) }
% 283.64/36.95 xor(n0, and(or(n22, n14), and(n6, i3)))
% 283.64/36.95 = { by axiom 13 (xor_definition1) }
% 283.64/36.95 and(or(n22, n14), and(n6, i3))
% 283.64/36.95 = { by lemma 167 R->L }
% 283.64/36.95 and(and(i1, i2), and(or(n22, n14), i3))
% 283.64/36.95 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.95 and(and(i1, i2), and(i3, or(n22, n14)))
% 283.64/36.95 = { by lemma 66 }
% 283.64/36.95 and(and(i1, i2), and(i3, not(not(n20))))
% 283.64/36.95 = { by lemma 62 R->L }
% 283.64/36.95 and(and(i1, i2), xor(i3, and(not(n20), i3)))
% 283.64/36.95 = { by axiom 8 (constructor29) R->L }
% 283.64/36.95 and(and(i1, i2), xor(i3, and(inv1, i3)))
% 283.64/36.95 = { by axiom 41 (constructor9) R->L }
% 283.64/36.95 and(n6, xor(i3, and(inv1, i3)))
% 283.64/36.95 = { by axiom 48 (and_xor_simplification) }
% 283.64/36.95 xor(and(n6, i3), and(n6, and(inv1, i3)))
% 283.64/36.95 = { by axiom 41 (constructor9) }
% 283.64/36.95 xor(and(n6, i3), and(and(i1, i2), and(inv1, i3)))
% 283.64/36.95 = { by axiom 29 (and_symmetry) }
% 283.64/36.95 xor(and(n6, i3), and(and(inv1, i3), and(i1, i2)))
% 283.64/36.95 = { by lemma 130 }
% 283.64/36.95 xor(and(n6, i3), and(and(inv1, i3), and(n6, i3)))
% 283.64/36.95 = { by lemma 135 }
% 283.64/36.95 xor(and(n6, i3), n0)
% 283.64/36.95 = { by axiom 11 (xor_definition2) }
% 283.64/36.95 and(n6, i3)
% 283.64/36.95
% 283.64/36.95 Lemma 169: or(not(n9), not(n20)) = not(and(n6, i3)).
% 283.64/36.95 Proof:
% 283.64/36.95 or(not(n9), not(n20))
% 283.64/36.95 = { by lemma 51 R->L }
% 283.64/36.95 not(not(or(not(n9), not(n20))))
% 283.64/36.95 = { by lemma 54 R->L }
% 283.64/36.95 not(not(xor(not(n9), xor(not(n20), and(not(n9), not(n20))))))
% 283.64/36.95 = { by lemma 67 }
% 283.64/36.95 not(not(xor(not(n9), xor(not(n20), and(inv1, inv2)))))
% 283.64/36.95 = { by axiom 10 (xor_symmetry) }
% 283.64/36.95 not(not(xor(not(n9), xor(and(inv1, inv2), not(n20)))))
% 283.64/36.95 = { by axiom 44 (xor_commutativity) }
% 283.64/36.95 not(not(xor(and(inv1, inv2), xor(not(n9), not(n20)))))
% 283.64/36.95 = { by lemma 59 }
% 283.64/36.95 not(xor(and(inv1, inv2), not(xor(not(n9), not(n20)))))
% 283.64/36.95 = { by lemma 59 }
% 283.64/36.95 not(xor(and(inv1, inv2), xor(not(n9), not(not(n20)))))
% 283.64/36.95 = { by lemma 106 }
% 283.64/36.95 not(xor(and(inv1, inv2), xor(not(n20), or(n8, n2))))
% 283.64/36.95 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.95 not(xor(and(inv1, inv2), xor(or(n8, n2), not(n20))))
% 283.64/36.95 = { by lemma 107 }
% 283.64/36.95 not(xor(and(inv1, inv2), xor(n20, not(n9))))
% 283.64/36.95 = { by axiom 21 (constructor23) }
% 283.64/36.95 not(xor(and(inv1, inv2), xor(or(n22, n14), not(n9))))
% 283.64/36.95 = { by axiom 44 (xor_commutativity) R->L }
% 283.64/36.95 not(xor(or(n22, n14), xor(and(inv1, inv2), not(n9))))
% 283.64/36.95 = { by lemma 108 R->L }
% 283.64/36.95 not(xor(or(n22, n14), and(not(n9), or(n22, n14))))
% 283.64/36.95 = { by lemma 62 }
% 283.64/36.95 not(and(or(n22, n14), not(not(n9))))
% 283.64/36.95 = { by lemma 65 R->L }
% 283.64/36.95 not(and(or(n22, n14), or(n8, n2)))
% 283.64/36.95 = { by axiom 29 (and_symmetry) }
% 283.64/36.95 not(and(or(n8, n2), or(n22, n14)))
% 283.64/36.95 = { by lemma 168 }
% 283.64/36.95 not(and(n6, i3))
% 283.64/36.95
% 283.64/36.95 Lemma 170: and(not(n20), or(n8, n2)) = xor(and(inv1, inv2), not(n20)).
% 283.64/36.95 Proof:
% 283.64/36.95 and(not(n20), or(n8, n2))
% 283.64/36.95 = { by lemma 65 }
% 283.64/36.95 and(not(n20), not(not(n9)))
% 283.64/36.95 = { by lemma 62 R->L }
% 283.64/36.95 xor(not(n20), and(not(n9), not(n20)))
% 283.64/36.95 = { by lemma 67 }
% 283.64/36.95 xor(not(n20), and(inv1, inv2))
% 283.64/36.95 = { by axiom 10 (xor_symmetry) }
% 283.64/36.95 xor(and(inv1, inv2), not(n20))
% 283.64/36.95
% 283.64/36.95 Lemma 171: and(and(X, Y), Z) = and(X, and(Z, Y)).
% 283.64/36.95 Proof:
% 283.64/36.95 and(and(X, Y), Z)
% 283.64/36.95 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.95 and(Z, and(X, Y))
% 283.64/36.95 = { by axiom 46 (and_commutativity) }
% 283.64/36.95 and(X, and(Z, Y))
% 283.64/36.95
% 283.64/36.95 Lemma 172: xor(not(n9), and(X, or(n8, n2))) = or(not(n9), X).
% 283.64/36.95 Proof:
% 283.64/36.95 xor(not(n9), and(X, or(n8, n2)))
% 283.64/36.95 = { by lemma 65 }
% 283.64/36.95 xor(not(n9), and(X, not(not(n9))))
% 283.64/36.95 = { by lemma 57 }
% 283.64/36.95 or(not(n9), X)
% 283.64/36.95
% 283.64/36.95 Lemma 173: or(not(n9), xor(and(inv1, inv2), not(n20))) = not(and(n6, i3)).
% 283.64/36.95 Proof:
% 283.64/36.95 or(not(n9), xor(and(inv1, inv2), not(n20)))
% 283.64/36.95 = { by lemma 172 R->L }
% 283.64/36.95 xor(not(n9), and(xor(and(inv1, inv2), not(n20)), or(n8, n2)))
% 283.64/36.95 = { by axiom 29 (and_symmetry) }
% 283.64/36.95 xor(not(n9), and(or(n8, n2), xor(and(inv1, inv2), not(n20))))
% 283.64/36.95 = { by lemma 170 R->L }
% 283.64/36.95 xor(not(n9), and(or(n8, n2), and(not(n20), or(n8, n2))))
% 283.64/36.95 = { by axiom 46 (and_commutativity) }
% 283.64/36.95 xor(not(n9), and(not(n20), and(or(n8, n2), or(n8, n2))))
% 283.64/36.95 = { by axiom 28 (and_simplification1) }
% 283.64/36.95 xor(not(n9), and(not(n20), or(n8, n2)))
% 283.64/36.95 = { by lemma 172 }
% 283.64/36.95 or(not(n9), not(n20))
% 283.64/36.95 = { by lemma 169 }
% 283.64/36.95 not(and(n6, i3))
% 283.64/36.95
% 283.64/36.95 Lemma 174: and(or(n8, n2), not(X)) = not(or(not(n9), X)).
% 283.64/36.95 Proof:
% 283.64/36.95 and(or(n8, n2), not(X))
% 283.64/36.95 = { by lemma 62 R->L }
% 283.64/36.95 xor(or(n8, n2), and(X, or(n8, n2)))
% 283.64/36.95 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.95 xor(and(X, or(n8, n2)), or(n8, n2))
% 283.64/36.95 = { by lemma 106 R->L }
% 283.64/36.95 xor(not(n9), not(and(X, or(n8, n2))))
% 283.64/36.95 = { by lemma 59 R->L }
% 283.64/36.95 not(xor(not(n9), and(X, or(n8, n2))))
% 283.64/36.95 = { by lemma 172 }
% 283.64/36.95 not(or(not(n9), X))
% 283.64/36.95
% 283.64/36.95 Lemma 175: and(and(Y, X), and(i1, i2)) = and(and(n6, X), Y).
% 283.64/36.95 Proof:
% 283.64/36.95 and(and(Y, X), and(i1, i2))
% 283.64/36.95 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.95 and(and(i1, i2), and(Y, X))
% 283.64/36.95 = { by axiom 41 (constructor9) R->L }
% 283.64/36.95 and(n6, and(Y, X))
% 283.64/36.95 = { by axiom 46 (and_commutativity) }
% 283.64/36.95 and(Y, and(n6, X))
% 283.64/36.95 = { by axiom 29 (and_symmetry) }
% 283.64/36.95 and(and(n6, X), Y)
% 283.64/36.95
% 283.64/36.95 Lemma 176: and(and(X, Y), and(i1, i2)) = and(and(X, Y), and(n6, Y)).
% 283.64/36.95 Proof:
% 283.64/36.95 and(and(X, Y), and(i1, i2))
% 283.64/36.95 = { by lemma 175 }
% 283.64/36.95 and(and(n6, Y), X)
% 283.64/36.95 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.95 and(X, and(n6, Y))
% 283.64/36.95 = { by lemma 82 R->L }
% 283.64/36.95 and(X, and(and(n6, Y), Y))
% 283.64/36.95 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.95 and(and(n6, Y), and(X, Y))
% 283.64/36.95 = { by axiom 29 (and_symmetry) }
% 283.64/36.95 and(and(X, Y), and(n6, Y))
% 283.64/36.95
% 283.64/36.95 Lemma 177: and(and(i2, X), and(n6, X)) = and(n6, X).
% 283.64/36.95 Proof:
% 283.64/36.95 and(and(i2, X), and(n6, X))
% 283.64/36.95 = { by lemma 176 R->L }
% 283.64/36.95 and(and(i2, X), and(i1, i2))
% 283.64/36.95 = { by lemma 175 }
% 283.64/36.95 and(and(n6, X), i2)
% 283.64/36.95 = { by lemma 51 R->L }
% 283.64/36.95 and(and(n6, X), not(not(i2)))
% 283.64/36.95 = { by lemma 55 R->L }
% 283.64/36.95 xor(and(n6, X), and(and(n6, X), not(i2)))
% 283.64/36.95 = { by lemma 154 }
% 283.64/36.95 xor(and(n6, X), n0)
% 283.64/36.95 = { by axiom 11 (xor_definition2) }
% 283.64/36.95 and(n6, X)
% 283.64/36.95
% 283.64/36.95 Lemma 178: and(and(n6, X), i1) = and(n6, X).
% 283.64/36.95 Proof:
% 283.64/36.95 and(and(n6, X), i1)
% 283.64/36.95 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.95 and(i1, and(n6, X))
% 283.64/36.95 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.95 and(n6, and(i1, X))
% 283.64/36.95 = { by axiom 41 (constructor9) }
% 283.64/36.95 and(and(i1, i2), and(i1, X))
% 283.64/36.95 = { by lemma 93 R->L }
% 283.64/36.95 and(and(i2, X), and(i1, X))
% 283.64/36.95 = { by lemma 90 }
% 283.64/36.95 and(n6, X)
% 283.64/36.95
% 283.64/36.96 Lemma 179: xor(and(i1, inv1), xor(X, or(n24, n7))) = xor(X, and(n6, i3)).
% 283.64/36.96 Proof:
% 283.64/36.96 xor(and(i1, inv1), xor(X, or(n24, n7)))
% 283.64/36.96 = { by axiom 44 (xor_commutativity) R->L }
% 283.64/36.96 xor(X, xor(and(i1, inv1), or(n24, n7)))
% 283.64/36.96 = { by lemma 139 }
% 283.64/36.96 xor(X, and(n6, i3))
% 283.64/36.96
% 283.64/36.96 Lemma 180: xor(xor(X, Y), Z) = xor(X, xor(Z, Y)).
% 283.64/36.96 Proof:
% 283.64/36.96 xor(xor(X, Y), Z)
% 283.64/36.96 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.96 xor(Z, xor(X, Y))
% 283.64/36.96 = { by axiom 44 (xor_commutativity) }
% 283.64/36.96 xor(X, xor(Z, Y))
% 283.64/36.96
% 283.64/36.96 Lemma 181: and(not(i1), xor(X, and(n6, Y))) = and(X, not(i1)).
% 283.64/36.96 Proof:
% 283.64/36.96 and(not(i1), xor(X, and(n6, Y)))
% 283.64/36.96 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.96 and(xor(X, and(n6, Y)), not(i1))
% 283.64/36.96 = { by lemma 62 R->L }
% 283.64/36.96 xor(xor(X, and(n6, Y)), and(i1, xor(X, and(n6, Y))))
% 283.64/36.96 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.96 xor(xor(X, and(n6, Y)), and(i1, xor(and(n6, Y), X)))
% 283.64/36.96 = { by lemma 81 R->L }
% 283.64/36.96 xor(xor(X, and(n6, Y)), xor(and(and(n6, Y), i1), and(i1, X)))
% 283.64/36.96 = { by lemma 178 }
% 283.64/36.96 xor(xor(X, and(n6, Y)), xor(and(n6, Y), and(i1, X)))
% 283.64/36.96 = { by axiom 29 (and_symmetry) }
% 283.64/36.96 xor(xor(X, and(n6, Y)), xor(and(n6, Y), and(X, i1)))
% 283.64/36.96 = { by lemma 180 }
% 283.64/36.96 xor(X, xor(xor(and(n6, Y), and(X, i1)), and(n6, Y)))
% 283.64/36.96 = { by lemma 180 }
% 283.64/36.96 xor(X, xor(and(n6, Y), xor(and(n6, Y), and(X, i1))))
% 283.64/36.96 = { by axiom 43 (xor_simplification1) }
% 283.64/36.96 xor(X, and(X, i1))
% 283.64/36.96 = { by lemma 55 }
% 283.64/36.96 and(X, not(i1))
% 283.64/36.96
% 283.64/36.96 Lemma 182: xor(not(X), and(Y, X)) = or(not(X), Y).
% 283.64/36.96 Proof:
% 283.64/36.96 xor(not(X), and(Y, X))
% 283.64/36.96 = { by lemma 51 R->L }
% 283.64/36.96 xor(not(X), and(Y, not(not(X))))
% 283.64/36.96 = { by lemma 57 }
% 283.64/36.96 or(not(X), Y)
% 283.64/36.96
% 283.64/36.96 Lemma 183: and(or(a1, n10), i1) = or(n24, n7).
% 283.64/36.96 Proof:
% 283.64/36.96 and(or(a1, n10), i1)
% 283.64/36.96 = { by lemma 51 R->L }
% 283.64/36.96 and(or(a1, n10), not(not(i1)))
% 283.64/36.96 = { by lemma 125 R->L }
% 283.64/36.96 and(or(a1, n10), not(and(not(i1), or(a1, n10))))
% 283.64/36.96 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.96 and(or(a1, n10), not(and(or(a1, n10), not(i1))))
% 283.64/36.96 = { by lemma 98 R->L }
% 283.64/36.96 and(or(a1, n10), not(and(not(i1), xor(and(i1, inv1), or(a1, n10)))))
% 283.64/36.96 = { by lemma 166 R->L }
% 283.64/36.96 and(or(a1, n10), not(and(not(i1), xor(and(i1, inv1), xor(and(inv1, i2), or(n24, n7))))))
% 283.64/36.96 = { by lemma 179 }
% 283.64/36.96 and(or(a1, n10), not(and(not(i1), xor(and(inv1, i2), and(n6, i3)))))
% 283.64/36.96 = { by lemma 181 }
% 283.64/36.96 and(or(a1, n10), not(and(and(inv1, i2), not(i1))))
% 283.64/36.96 = { by axiom 11 (xor_definition2) R->L }
% 283.64/36.96 and(or(a1, n10), not(and(and(inv1, i2), xor(not(i1), n0))))
% 283.64/36.96 = { by lemma 156 R->L }
% 283.64/36.96 and(or(a1, n10), not(and(and(inv1, i2), xor(not(i1), and(and(inv1, i2), and(i1, inv1))))))
% 283.64/36.96 = { by lemma 146 }
% 283.64/36.96 and(or(a1, n10), not(and(and(inv1, i2), xor(not(i1), and(and(inv1, i2), and(i1, i2))))))
% 283.64/36.96 = { by lemma 132 }
% 283.64/36.96 and(or(a1, n10), not(and(and(inv1, i2), xor(not(i1), and(and(i1, i2), not(n20))))))
% 283.64/36.96 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.96 and(or(a1, n10), not(and(and(inv1, i2), xor(not(i1), and(not(n20), and(i1, i2))))))
% 283.64/36.96 = { by axiom 29 (and_symmetry) }
% 283.64/36.96 and(or(a1, n10), not(and(and(inv1, i2), xor(not(i1), and(not(n20), and(i2, i1))))))
% 283.64/36.96 = { by lemma 133 }
% 283.64/36.96 and(or(a1, n10), not(and(and(inv1, i2), xor(not(i1), and(i1, and(inv1, i2))))))
% 283.64/36.96 = { by axiom 29 (and_symmetry) }
% 283.64/36.96 and(or(a1, n10), not(and(and(inv1, i2), xor(not(i1), and(and(inv1, i2), i1)))))
% 283.64/36.96 = { by lemma 182 }
% 283.64/36.96 and(or(a1, n10), not(and(and(inv1, i2), or(not(i1), and(inv1, i2)))))
% 283.64/36.96 = { by lemma 150 }
% 283.64/36.96 and(or(a1, n10), not(and(inv1, i2)))
% 283.64/36.96 = { by lemma 124 }
% 283.64/36.96 xor(and(inv1, i2), or(a1, n10))
% 283.64/36.96 = { by lemma 161 }
% 283.64/36.96 or(n24, n7)
% 283.64/36.96
% 283.64/36.96 Lemma 184: and(and(i1, i2), not(n9)) = and(inv2, n6).
% 283.64/36.96 Proof:
% 283.64/36.96 and(and(i1, i2), not(n9))
% 283.64/36.96 = { by axiom 41 (constructor9) R->L }
% 283.64/36.96 and(n6, not(n9))
% 283.64/36.96 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.96 and(not(n9), n6)
% 283.64/36.96 = { by axiom 7 (constructor30) R->L }
% 283.64/36.96 and(inv2, n6)
% 283.64/36.96
% 283.64/36.96 Lemma 185: and(and(i1, i2), or(n8, n2)) = xor(and(i1, i2), and(inv2, n6)).
% 283.64/36.96 Proof:
% 283.64/36.96 and(and(i1, i2), or(n8, n2))
% 283.64/36.96 = { by lemma 65 }
% 283.64/36.96 and(and(i1, i2), not(not(n9)))
% 283.64/36.96 = { by lemma 55 R->L }
% 283.64/36.96 xor(and(i1, i2), and(and(i1, i2), not(n9)))
% 283.64/36.96 = { by lemma 184 }
% 283.64/36.96 xor(and(i1, i2), and(inv2, n6))
% 283.64/36.96
% 283.64/36.96 Lemma 186: xor(X, not(or(X, Y))) = not(and(Y, not(X))).
% 283.64/36.96 Proof:
% 283.64/36.96 xor(X, not(or(X, Y)))
% 283.64/36.96 = { by lemma 59 R->L }
% 283.64/36.96 not(xor(X, or(X, Y)))
% 283.64/36.96 = { by lemma 56 }
% 283.64/36.96 not(and(Y, not(X)))
% 283.64/36.96
% 283.64/36.96 Lemma 187: and(X, xor(X, not(Y))) = and(X, Y).
% 283.64/36.96 Proof:
% 283.64/36.96 and(X, xor(X, not(Y)))
% 283.64/36.96 = { by lemma 53 R->L }
% 283.64/36.96 and(X, xor(not(X), Y))
% 283.64/36.96 = { by axiom 48 (and_xor_simplification) }
% 283.64/36.96 xor(and(X, not(X)), and(X, Y))
% 283.64/36.96 = { by lemma 158 }
% 283.64/36.96 xor(n0, and(X, Y))
% 283.64/36.96 = { by axiom 13 (xor_definition1) }
% 283.64/36.96 and(X, Y)
% 283.64/36.96
% 283.64/36.96 Lemma 188: xor(and(n6, i3), and(i1, i2)) = and(inv2, n6).
% 283.64/36.96 Proof:
% 283.64/36.96 xor(and(n6, i3), and(i1, i2))
% 283.64/36.96 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.96 xor(and(i1, i2), and(n6, i3))
% 283.64/36.96 = { by lemma 95 R->L }
% 283.64/36.96 xor(and(i1, i2), and(and(n6, i3), and(i1, i2)))
% 283.64/36.96 = { by lemma 62 }
% 283.64/36.96 and(and(i1, i2), not(and(n6, i3)))
% 283.64/36.96 = { by lemma 169 R->L }
% 283.64/36.96 and(and(i1, i2), or(not(n9), not(n20)))
% 283.64/36.96 = { by lemma 54 R->L }
% 283.64/36.96 and(and(i1, i2), xor(not(n9), xor(not(n20), and(not(n9), not(n20)))))
% 283.64/36.96 = { by lemma 67 }
% 283.64/36.96 and(and(i1, i2), xor(not(n9), xor(not(n20), and(inv1, inv2))))
% 283.64/36.96 = { by axiom 10 (xor_symmetry) }
% 283.64/36.96 and(and(i1, i2), xor(not(n9), xor(and(inv1, inv2), not(n20))))
% 283.64/36.96 = { by axiom 44 (xor_commutativity) }
% 283.64/36.96 and(and(i1, i2), xor(and(inv1, inv2), xor(not(n9), not(n20))))
% 283.64/36.96 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.96 and(and(i1, i2), xor(and(inv1, inv2), xor(not(n20), not(n9))))
% 283.64/36.96 = { by lemma 107 R->L }
% 283.64/36.96 and(and(i1, i2), xor(and(inv1, inv2), xor(or(n8, n2), not(not(n20)))))
% 283.64/36.96 = { by lemma 66 R->L }
% 283.64/36.96 and(and(i1, i2), xor(and(inv1, inv2), xor(or(n8, n2), or(n22, n14))))
% 283.64/36.96 = { by axiom 44 (xor_commutativity) R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), xor(and(inv1, inv2), or(n22, n14))))
% 283.64/36.96 = { by lemma 66 }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), xor(and(inv1, inv2), not(not(n20)))))
% 283.64/36.96 = { by lemma 59 R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(xor(and(inv1, inv2), not(n20)))))
% 283.64/36.96 = { by lemma 170 R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(and(not(n20), or(n8, n2)))))
% 283.64/36.96 = { by axiom 28 (and_simplification1) R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(and(not(n20), and(or(n8, n2), or(n8, n2))))))
% 283.64/36.96 = { by lemma 171 R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(and(and(not(n20), or(n8, n2)), or(n8, n2)))))
% 283.64/36.96 = { by lemma 170 }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(and(xor(and(inv1, inv2), not(n20)), or(n8, n2)))))
% 283.64/36.96 = { by axiom 28 (and_simplification1) R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(and(xor(and(inv1, inv2), not(n20)), and(or(n8, n2), or(n8, n2))))))
% 283.64/36.96 = { by lemma 65 }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(and(xor(and(inv1, inv2), not(n20)), and(not(not(n9)), or(n8, n2))))))
% 283.64/36.96 = { by lemma 171 R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(and(and(xor(and(inv1, inv2), not(n20)), or(n8, n2)), not(not(n9))))))
% 283.64/36.96 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(and(not(not(n9)), and(xor(and(inv1, inv2), not(n20)), or(n8, n2))))))
% 283.64/36.96 = { by axiom 13 (xor_definition1) R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(xor(n0, and(not(not(n9)), and(xor(and(inv1, inv2), not(n20)), or(n8, n2)))))))
% 283.64/36.96 = { by lemma 158 R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(xor(and(not(n9), not(not(n9))), and(not(not(n9)), and(xor(and(inv1, inv2), not(n20)), or(n8, n2)))))))
% 283.64/36.96 = { by lemma 81 }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(and(not(not(n9)), xor(not(n9), and(xor(and(inv1, inv2), not(n20)), or(n8, n2)))))))
% 283.64/36.96 = { by lemma 172 }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(and(not(not(n9)), or(not(n9), xor(and(inv1, inv2), not(n20)))))))
% 283.64/36.96 = { by lemma 65 R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(and(or(n8, n2), or(not(n9), xor(and(inv1, inv2), not(n20)))))))
% 283.64/36.96 = { by lemma 173 }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(and(or(n8, n2), not(and(n6, i3))))))
% 283.64/36.96 = { by lemma 174 }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), not(not(or(not(n9), and(n6, i3))))))
% 283.64/36.96 = { by lemma 51 }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(not(n9), and(n6, i3))))
% 283.64/36.96 = { by lemma 64 R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(and(n6, i3), not(n9))))
% 283.64/36.96 = { by axiom 11 (xor_definition2) R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(xor(and(n6, i3), n0), not(n9))))
% 283.64/36.96 = { by lemma 156 R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(xor(and(n6, i3), and(and(inv1, i2), and(i1, inv1))), not(n9))))
% 283.64/36.96 = { by lemma 147 }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(xor(and(n6, i3), and(and(i1, inv1), i2)), not(n9))))
% 283.64/36.96 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(xor(and(n6, i3), and(i2, and(i1, inv1))), not(n9))))
% 283.64/36.96 = { by lemma 177 R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(xor(and(and(i2, i3), and(n6, i3)), and(i2, and(i1, inv1))), not(n9))))
% 283.64/36.96 = { by lemma 176 R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(xor(and(and(i2, i3), and(i1, i2)), and(i2, and(i1, inv1))), not(n9))))
% 283.64/36.96 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(xor(and(and(i1, i2), and(i2, i3)), and(i2, and(i1, inv1))), not(n9))))
% 283.64/36.96 = { by axiom 41 (constructor9) R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(xor(and(n6, and(i2, i3)), and(i2, and(i1, inv1))), not(n9))))
% 283.64/36.96 = { by axiom 46 (and_commutativity) }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(xor(and(i2, and(n6, i3)), and(i2, and(i1, inv1))), not(n9))))
% 283.64/36.96 = { by axiom 29 (and_symmetry) }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(xor(and(and(n6, i3), i2), and(i2, and(i1, inv1))), not(n9))))
% 283.64/36.96 = { by lemma 81 }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(and(i2, xor(and(n6, i3), and(i1, inv1))), not(n9))))
% 283.64/36.96 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(and(i2, xor(and(i1, inv1), and(n6, i3))), not(n9))))
% 283.64/36.96 = { by lemma 178 R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(and(i2, xor(and(i1, inv1), and(and(n6, i3), i1))), not(n9))))
% 283.64/36.96 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(and(i2, xor(and(i1, inv1), and(i1, and(n6, i3)))), not(n9))))
% 283.64/36.96 = { by lemma 92 R->L }
% 283.64/36.96 and(and(i1, i2), xor(or(n8, n2), or(and(i2, xor(and(and(i1, inv1), i1), and(i1, and(n6, i3)))), not(n9))))
% 283.64/36.97 = { by lemma 81 }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(i2, and(i1, xor(and(i1, inv1), and(n6, i3)))), not(n9))))
% 283.64/36.97 = { by axiom 10 (xor_symmetry) }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(i2, and(i1, xor(and(n6, i3), and(i1, inv1)))), not(n9))))
% 283.64/36.97 = { by lemma 140 }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(i2, and(i1, or(n24, n7))), not(n9))))
% 283.64/36.97 = { by axiom 29 (and_symmetry) }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(i2, and(or(n24, n7), i1)), not(n9))))
% 283.64/36.97 = { by lemma 88 }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(or(n24, n7), and(i1, i2)), not(n9))))
% 283.64/36.97 = { by axiom 29 (and_symmetry) }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(and(i1, i2), or(n24, n7)), not(n9))))
% 283.64/36.97 = { by lemma 183 R->L }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(and(i1, i2), and(or(a1, n10), i1)), not(n9))))
% 283.64/36.97 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(or(a1, n10), and(and(i1, i2), i1)), not(n9))))
% 283.64/36.97 = { by lemma 92 }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(or(a1, n10), and(i1, i2)), not(n9))))
% 283.64/36.97 = { by lemma 112 R->L }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(and(i1, i2), and(or(a1, n10), i2)), not(n9))))
% 283.64/36.97 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(and(i1, i2), and(i2, or(a1, n10))), not(n9))))
% 283.64/36.97 = { by lemma 165 R->L }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(and(i1, i2), and(i2, xor(and(inv1, i3), or(n8, n2)))), not(n9))))
% 283.64/36.97 = { by lemma 81 R->L }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(and(i1, i2), xor(and(and(inv1, i3), i2), and(i2, or(n8, n2)))), not(n9))))
% 283.64/36.97 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(and(i1, i2), xor(and(i2, and(inv1, i3)), and(i2, or(n8, n2)))), not(n9))))
% 283.64/36.97 = { by lemma 113 R->L }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(and(i1, i2), xor(and(not(n20), and(i2, i3)), and(i2, or(n8, n2)))), not(n9))))
% 283.64/36.97 = { by axiom 29 (and_symmetry) }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(and(i1, i2), xor(and(and(i2, i3), not(n20)), and(i2, or(n8, n2)))), not(n9))))
% 283.64/36.97 = { by lemma 114 R->L }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(and(i1, i2), xor(and(and(inv1, i2), and(i2, i3)), and(i2, or(n8, n2)))), not(n9))))
% 283.64/36.97 = { by lemma 117 }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(and(i1, i2), xor(n0, and(i2, or(n8, n2)))), not(n9))))
% 283.64/36.97 = { by axiom 13 (xor_definition1) }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(and(i1, i2), and(i2, or(n8, n2))), not(n9))))
% 283.64/36.97 = { by axiom 29 (and_symmetry) }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(and(i1, i2), and(or(n8, n2), i2)), not(n9))))
% 283.64/36.97 = { by lemma 112 }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(or(n8, n2), and(i1, i2)), not(n9))))
% 283.64/36.97 = { by axiom 29 (and_symmetry) }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(and(i1, i2), or(n8, n2)), not(n9))))
% 283.64/36.97 = { by lemma 185 }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(xor(and(i1, i2), and(inv2, n6)), not(n9))))
% 283.64/36.97 = { by lemma 64 }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(not(n9), xor(and(i1, i2), and(inv2, n6)))))
% 283.64/36.97 = { by lemma 172 R->L }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), xor(not(n9), and(xor(and(i1, i2), and(inv2, n6)), or(n8, n2)))))
% 283.64/36.97 = { by lemma 185 R->L }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), xor(not(n9), and(and(and(i1, i2), or(n8, n2)), or(n8, n2)))))
% 283.64/36.97 = { by lemma 171 }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), xor(not(n9), and(and(i1, i2), and(or(n8, n2), or(n8, n2))))))
% 283.64/36.97 = { by axiom 28 (and_simplification1) }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), xor(not(n9), and(and(i1, i2), or(n8, n2)))))
% 283.64/36.97 = { by lemma 172 }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(not(n9), and(i1, i2))))
% 283.64/36.97 = { by lemma 64 R->L }
% 283.64/36.97 and(and(i1, i2), xor(or(n8, n2), or(and(i1, i2), not(n9))))
% 283.64/36.97 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.97 and(and(i1, i2), xor(or(and(i1, i2), not(n9)), or(n8, n2)))
% 283.64/36.97 = { by lemma 106 R->L }
% 283.64/36.97 and(and(i1, i2), xor(not(n9), not(or(and(i1, i2), not(n9)))))
% 283.64/36.97 = { by lemma 64 }
% 283.64/36.97 and(and(i1, i2), xor(not(n9), not(or(not(n9), and(i1, i2)))))
% 283.64/36.97 = { by lemma 186 }
% 283.64/36.97 and(and(i1, i2), not(and(and(i1, i2), not(not(n9)))))
% 283.64/36.97 = { by lemma 65 R->L }
% 283.64/36.97 and(and(i1, i2), not(and(and(i1, i2), or(n8, n2))))
% 283.64/36.97 = { by lemma 185 }
% 283.64/36.97 and(and(i1, i2), not(xor(and(i1, i2), and(inv2, n6))))
% 283.64/36.97 = { by lemma 59 }
% 283.64/36.97 and(and(i1, i2), xor(and(i1, i2), not(and(inv2, n6))))
% 283.64/36.97 = { by lemma 187 }
% 283.64/36.97 and(and(i1, i2), and(inv2, n6))
% 283.64/36.97 = { by lemma 184 R->L }
% 283.64/36.97 and(and(i1, i2), and(and(i1, i2), not(n9)))
% 283.64/36.97 = { by axiom 45 (and_simplification2) }
% 283.64/36.97 and(and(i1, i2), not(n9))
% 283.64/36.97 = { by lemma 184 }
% 283.64/36.97 and(inv2, n6)
% 283.64/36.97
% 283.64/36.97 Lemma 189: and(not(i3), or(n22, n14)) = and(inv2, n6).
% 283.64/36.97 Proof:
% 283.64/36.97 and(not(i3), or(n22, n14))
% 283.64/36.97 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.97 and(or(n22, n14), not(i3))
% 283.64/36.97 = { by lemma 83 R->L }
% 283.64/36.97 and(not(i3), xor(or(n22, n14), and(i2, i3)))
% 283.64/36.97 = { by axiom 10 (xor_symmetry) }
% 283.64/36.97 and(not(i3), xor(and(i2, i3), or(n22, n14)))
% 283.64/36.97 = { by axiom 43 (xor_simplification1) R->L }
% 283.64/36.97 and(not(i3), xor(and(i2, i3), xor(or(n23, n6), xor(or(n23, n6), or(n22, n14)))))
% 283.64/36.97 = { by lemma 104 R->L }
% 283.64/36.97 and(not(i3), xor(and(i2, i3), xor(or(n23, n6), xor(and(i2, i3), and(n6, i3)))))
% 283.64/36.97 = { by axiom 44 (xor_commutativity) }
% 283.64/36.97 and(not(i3), xor(and(i2, i3), xor(and(i2, i3), xor(or(n23, n6), and(n6, i3)))))
% 283.64/36.97 = { by axiom 10 (xor_symmetry) }
% 283.64/36.97 and(not(i3), xor(and(i2, i3), xor(and(i2, i3), xor(and(n6, i3), or(n23, n6)))))
% 283.64/36.97 = { by axiom 43 (xor_simplification1) }
% 283.64/36.97 and(not(i3), xor(and(n6, i3), or(n23, n6)))
% 283.64/36.97 = { by axiom 41 (constructor9) }
% 283.64/36.97 and(not(i3), xor(and(n6, i3), or(n23, and(i1, i2))))
% 283.64/36.97 = { by axiom 42 (constructor26) }
% 283.64/36.97 and(not(i3), xor(and(n6, i3), or(and(i1, i3), and(i1, i2))))
% 283.64/36.97 = { by lemma 57 R->L }
% 283.64/36.97 and(not(i3), xor(and(n6, i3), xor(and(i1, i3), and(and(i1, i2), not(and(i1, i3))))))
% 283.64/36.97 = { by axiom 42 (constructor26) R->L }
% 283.64/36.97 and(not(i3), xor(and(n6, i3), xor(and(i1, i3), and(and(i1, i2), not(n23)))))
% 283.64/36.97 = { by axiom 41 (constructor9) R->L }
% 283.64/36.97 and(not(i3), xor(and(n6, i3), xor(and(i1, i3), and(n6, not(n23)))))
% 283.64/36.97 = { by lemma 56 R->L }
% 283.64/36.97 and(not(i3), xor(and(n6, i3), xor(and(i1, i3), xor(n23, or(n23, n6)))))
% 283.64/36.97 = { by axiom 42 (constructor26) }
% 283.64/36.97 and(not(i3), xor(and(n6, i3), xor(and(i1, i3), xor(and(i1, i3), or(n23, n6)))))
% 283.64/36.97 = { by lemma 100 }
% 283.64/36.97 and(not(i3), xor(and(n6, i3), xor(and(i1, i3), xor(and(n6, i3), and(i1, i2)))))
% 283.64/36.97 = { by axiom 44 (xor_commutativity) }
% 283.64/36.97 and(not(i3), xor(and(n6, i3), xor(and(n6, i3), xor(and(i1, i3), and(i1, i2)))))
% 283.64/36.97 = { by axiom 10 (xor_symmetry) }
% 283.64/36.97 and(not(i3), xor(and(n6, i3), xor(and(n6, i3), xor(and(i1, i2), and(i1, i3)))))
% 283.64/36.97 = { by axiom 43 (xor_simplification1) }
% 283.64/36.97 and(not(i3), xor(and(i1, i2), and(i1, i3)))
% 283.64/36.97 = { by lemma 83 }
% 283.64/36.97 and(and(i1, i2), not(i3))
% 283.64/36.97 = { by lemma 105 R->L }
% 283.64/36.97 xor(and(n6, i3), and(i1, i2))
% 283.64/36.97 = { by lemma 188 }
% 283.64/36.97 and(inv2, n6)
% 283.64/36.97
% 283.64/36.97 Lemma 190: xor(and(inv1, X), not(n20)) = and(not(X), not(n20)).
% 283.64/36.97 Proof:
% 283.64/36.97 xor(and(inv1, X), not(n20))
% 283.64/36.97 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.97 xor(not(n20), and(inv1, X))
% 283.64/36.97 = { by axiom 8 (constructor29) }
% 283.64/36.97 xor(not(n20), and(not(n20), X))
% 283.64/36.97 = { by lemma 55 }
% 283.64/36.97 and(not(n20), not(X))
% 283.64/36.97 = { by axiom 29 (and_symmetry) }
% 283.64/36.97 and(not(X), not(n20))
% 283.64/36.97
% 283.64/36.97 Lemma 191: and(not(n9), xor(and(inv1, i3), X)) = and(X, not(n9)).
% 283.64/36.97 Proof:
% 283.64/36.97 and(not(n9), xor(and(inv1, i3), X))
% 283.64/36.97 = { by lemma 81 R->L }
% 283.64/36.97 xor(and(and(inv1, i3), not(n9)), and(not(n9), X))
% 283.64/36.97 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.97 xor(and(not(n9), and(inv1, i3)), and(not(n9), X))
% 283.64/36.97 = { by lemma 69 R->L }
% 283.64/36.97 xor(and(not(n9), and(and(inv1, i3), not(n20))), and(not(n9), X))
% 283.64/36.97 = { by lemma 68 }
% 283.64/36.97 xor(and(and(inv1, i3), and(inv1, inv2)), and(not(n9), X))
% 283.64/36.97 = { by lemma 73 }
% 283.64/36.97 xor(n0, and(not(n9), X))
% 283.64/36.97 = { by axiom 13 (xor_definition1) }
% 283.64/36.97 and(not(n9), X)
% 283.64/36.97 = { by axiom 29 (and_symmetry) }
% 283.64/36.97 and(X, not(n9))
% 283.64/36.97
% 283.64/36.97 Lemma 192: xor(or(a1, n24), or(a1, n10)) = and(n6, i3).
% 283.64/36.97 Proof:
% 283.64/36.97 xor(or(a1, n24), or(a1, n10))
% 283.64/36.97 = { by axiom 43 (xor_simplification1) R->L }
% 283.64/36.97 xor(and(i1, inv1), xor(and(i1, inv1), xor(or(a1, n24), or(a1, n10))))
% 283.64/36.97 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.97 xor(and(i1, inv1), xor(and(i1, inv1), xor(or(a1, n10), or(a1, n24))))
% 283.64/36.97 = { by axiom 44 (xor_commutativity) R->L }
% 283.64/36.97 xor(and(i1, inv1), xor(or(a1, n10), xor(and(i1, inv1), or(a1, n24))))
% 283.64/36.97 = { by lemma 142 }
% 283.64/36.97 xor(and(i1, inv1), xor(or(a1, n10), xor(or(a1, n10), or(n24, n7))))
% 283.64/36.97 = { by axiom 43 (xor_simplification1) }
% 283.64/36.97 xor(and(i1, inv1), or(n24, n7))
% 283.64/36.97 = { by lemma 139 }
% 283.64/36.97 and(n6, i3)
% 283.64/36.97
% 283.64/36.97 Lemma 193: and(not(i3), or(a1, n24)) = and(not(i3), or(a1, n10)).
% 283.64/36.97 Proof:
% 283.64/36.97 and(not(i3), or(a1, n24))
% 283.64/36.97 = { by axiom 13 (xor_definition1) R->L }
% 283.64/36.97 xor(n0, and(not(i3), or(a1, n24)))
% 283.64/36.97 = { by axiom 9 (xor_definition3) R->L }
% 283.64/36.97 xor(xor(and(n6, i3), and(n6, i3)), and(not(i3), or(a1, n24)))
% 283.64/36.97 = { by lemma 82 R->L }
% 283.64/36.97 xor(xor(and(n6, i3), and(and(n6, i3), i3)), and(not(i3), or(a1, n24)))
% 283.64/36.97 = { by lemma 55 }
% 283.64/36.97 xor(and(and(n6, i3), not(i3)), and(not(i3), or(a1, n24)))
% 283.64/36.97 = { by lemma 81 }
% 283.64/36.97 and(not(i3), xor(and(n6, i3), or(a1, n24)))
% 283.64/36.97 = { by axiom 10 (xor_symmetry) }
% 283.64/36.97 and(not(i3), xor(or(a1, n24), and(n6, i3)))
% 283.64/36.97 = { by lemma 192 R->L }
% 283.64/36.97 and(not(i3), xor(or(a1, n24), xor(or(a1, n24), or(a1, n10))))
% 283.64/36.97 = { by axiom 43 (xor_simplification1) }
% 283.64/36.97 and(not(i3), or(a1, n10))
% 283.64/36.97
% 283.64/36.97 Lemma 194: and(not(i3), or(a1, n24)) = and(not(i3), or(n8, n2)).
% 283.64/36.97 Proof:
% 283.64/36.97 and(not(i3), or(a1, n24))
% 283.64/36.97 = { by lemma 193 }
% 283.64/36.97 and(not(i3), or(a1, n10))
% 283.64/36.97 = { by lemma 165 R->L }
% 283.64/36.97 and(not(i3), xor(and(inv1, i3), or(n8, n2)))
% 283.64/36.97 = { by lemma 81 R->L }
% 283.64/36.97 xor(and(and(inv1, i3), not(i3)), and(not(i3), or(n8, n2)))
% 283.64/36.97 = { by lemma 55 R->L }
% 283.64/36.97 xor(xor(and(inv1, i3), and(and(inv1, i3), i3)), and(not(i3), or(n8, n2)))
% 283.64/36.97 = { by lemma 82 }
% 283.64/36.97 xor(xor(and(inv1, i3), and(inv1, i3)), and(not(i3), or(n8, n2)))
% 283.64/36.97 = { by axiom 9 (xor_definition3) }
% 283.64/36.97 xor(n0, and(not(i3), or(n8, n2)))
% 283.64/36.97 = { by axiom 13 (xor_definition1) }
% 283.64/36.97 and(not(i3), or(n8, n2))
% 283.64/36.97
% 283.64/36.97 Lemma 195: not(and(X, not(Y))) = or(not(X), Y).
% 283.64/36.97 Proof:
% 283.64/36.97 not(and(X, not(Y)))
% 283.64/36.97 = { by lemma 62 R->L }
% 283.64/36.97 not(xor(X, and(Y, X)))
% 283.64/36.97 = { by lemma 59 }
% 283.64/36.97 xor(X, not(and(Y, X)))
% 283.64/36.97 = { by axiom 29 (and_symmetry) }
% 283.64/36.97 xor(X, not(and(X, Y)))
% 283.64/36.97 = { by lemma 58 }
% 283.64/36.97 or(not(X), Y)
% 283.64/36.97
% 283.64/36.97 Lemma 196: and(or(n22, n14), X) = xor(and(X, inv1), X).
% 283.64/36.97 Proof:
% 283.64/36.97 and(or(n22, n14), X)
% 283.64/36.97 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.97 and(X, or(n22, n14))
% 283.64/36.97 = { by lemma 66 }
% 283.64/36.97 and(X, not(not(n20)))
% 283.64/36.97 = { by lemma 62 R->L }
% 283.64/36.97 xor(X, and(not(n20), X))
% 283.64/36.97 = { by lemma 136 }
% 283.64/36.97 xor(X, and(X, inv1))
% 283.64/36.97 = { by axiom 10 (xor_symmetry) }
% 283.64/36.97 xor(and(X, inv1), X)
% 283.64/36.97
% 283.64/36.97 Lemma 197: xor(and(i1, inv1), i1) = or(n23, n6).
% 283.64/36.97 Proof:
% 283.64/36.97 xor(and(i1, inv1), i1)
% 283.64/36.97 = { by lemma 151 R->L }
% 283.64/36.97 xor(and(i1, inv1), xor(and(i1, inv1), or(n23, n6)))
% 283.64/36.97 = { by axiom 43 (xor_simplification1) }
% 283.64/36.97 or(n23, n6)
% 283.64/36.97
% 283.64/36.97 Lemma 198: and(not(n9), and(X, and(i1, i2))) = and(X, and(inv2, n6)).
% 283.64/36.97 Proof:
% 283.64/36.97 and(not(n9), and(X, and(i1, i2)))
% 283.64/36.97 = { by axiom 41 (constructor9) R->L }
% 283.64/36.97 and(not(n9), and(X, n6))
% 283.64/36.97 = { by lemma 171 R->L }
% 283.64/36.97 and(and(not(n9), n6), X)
% 283.64/36.97 = { by axiom 7 (constructor30) R->L }
% 283.64/36.97 and(and(inv2, n6), X)
% 283.64/36.97 = { by axiom 29 (and_symmetry) }
% 283.64/36.97 and(X, and(inv2, n6))
% 283.64/36.97
% 283.64/36.97 Lemma 199: and(not(n20), xor(X, and(inv1, Y))) = xor(and(inv1, Y), and(X, not(n20))).
% 283.64/36.97 Proof:
% 283.64/36.97 and(not(n20), xor(X, and(inv1, Y)))
% 283.64/36.97 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.97 and(not(n20), xor(and(inv1, Y), X))
% 283.64/36.97 = { by lemma 81 R->L }
% 283.64/36.97 xor(and(and(inv1, Y), not(n20)), and(not(n20), X))
% 283.64/36.97 = { by lemma 69 }
% 283.64/36.97 xor(and(inv1, Y), and(not(n20), X))
% 283.64/36.97 = { by axiom 29 (and_symmetry) }
% 283.64/36.97 xor(and(inv1, Y), and(X, not(n20)))
% 283.64/36.97
% 283.64/36.97 Lemma 200: xor(X, and(X, not(n20))) = and(X, or(n22, n14)).
% 283.64/36.97 Proof:
% 283.64/36.97 xor(X, and(X, not(n20)))
% 283.64/36.97 = { by axiom 43 (xor_simplification1) R->L }
% 283.64/36.97 xor(X, xor(and(inv1, Y), xor(and(inv1, Y), and(X, not(n20)))))
% 283.64/36.97 = { by lemma 180 R->L }
% 283.64/36.97 xor(X, xor(xor(and(inv1, Y), and(X, not(n20))), and(inv1, Y)))
% 283.64/36.98 = { by lemma 180 R->L }
% 283.64/36.98 xor(xor(X, and(inv1, Y)), xor(and(inv1, Y), and(X, not(n20))))
% 283.64/36.98 = { by lemma 199 R->L }
% 283.64/36.98 xor(xor(X, and(inv1, Y)), and(not(n20), xor(X, and(inv1, Y))))
% 283.64/36.98 = { by lemma 62 }
% 283.64/36.98 and(xor(X, and(inv1, Y)), not(not(n20)))
% 283.64/36.98 = { by lemma 66 R->L }
% 283.64/36.98 and(xor(X, and(inv1, Y)), or(n22, n14))
% 283.64/36.98 = { by axiom 29 (and_symmetry) }
% 283.64/36.98 and(or(n22, n14), xor(X, and(inv1, Y)))
% 283.64/36.98 = { by lemma 110 }
% 283.64/36.98 and(X, or(n22, n14))
% 283.64/36.98
% 283.64/36.98 Lemma 201: xor(X, and(X, or(n22, n14))) = and(X, not(n20)).
% 283.64/36.98 Proof:
% 283.64/36.98 xor(X, and(X, or(n22, n14)))
% 283.64/36.98 = { by lemma 200 R->L }
% 283.64/36.98 xor(X, xor(X, and(X, not(n20))))
% 283.64/36.98 = { by axiom 43 (xor_simplification1) }
% 283.64/36.98 and(X, not(n20))
% 283.64/36.98
% 283.64/36.98 Lemma 202: or(not(n20), and(and(X, inv1), Y)) = not(n20).
% 283.64/36.98 Proof:
% 283.64/36.98 or(not(n20), and(and(X, inv1), Y))
% 283.64/36.98 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.98 or(not(n20), and(Y, and(X, inv1)))
% 283.64/36.98 = { by lemma 143 R->L }
% 283.64/36.98 or(not(n20), and(not(n20), and(Y, X)))
% 283.64/36.98 = { by lemma 84 }
% 283.64/36.98 not(n20)
% 283.64/36.98
% 283.64/36.98 Lemma 203: circuit(not(i3)) = circuit(o1).
% 283.64/36.98 Proof:
% 283.64/36.98 circuit(not(i3))
% 283.64/36.98 = { by axiom 43 (xor_simplification1) R->L }
% 283.64/36.98 circuit(xor(and(inv1, inv2), xor(and(inv1, inv2), not(i3))))
% 283.64/36.98 = { by lemma 53 R->L }
% 283.64/36.98 circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), i3)))
% 283.64/36.98 = { by axiom 11 (xor_definition2) R->L }
% 283.64/36.98 circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), xor(i3, n0))))
% 283.64/36.98 = { by lemma 73 R->L }
% 283.64/36.98 circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), xor(i3, and(and(inv1, i3), and(inv1, inv2))))))
% 283.64/36.98 = { by lemma 70 }
% 283.64/36.98 circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), xor(i3, and(and(inv1, i3), not(n9))))))
% 283.64/36.98 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.98 circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), xor(i3, and(not(n9), and(inv1, i3))))))
% 283.64/36.98 = { by axiom 8 (constructor29) }
% 283.64/36.98 circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), xor(i3, and(not(n9), and(not(n20), i3))))))
% 283.64/36.98 = { by lemma 74 }
% 283.64/36.98 circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), xor(i3, and(i3, and(inv1, inv2))))))
% 283.64/36.98 = { by axiom 29 (and_symmetry) }
% 283.64/36.98 circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), xor(i3, and(and(inv1, inv2), i3)))))
% 283.64/36.98 = { by lemma 62 }
% 283.64/36.98 circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), and(i3, not(and(inv1, inv2))))))
% 283.64/36.98 = { by lemma 62 }
% 283.64/36.98 circuit(xor(and(inv1, inv2), and(not(and(inv1, inv2)), not(i3))))
% 283.64/36.98 = { by axiom 29 (and_symmetry) }
% 283.64/36.98 circuit(xor(and(inv1, inv2), and(not(i3), not(and(inv1, inv2)))))
% 283.64/36.98 = { by lemma 57 }
% 283.64/36.98 circuit(or(and(inv1, inv2), not(i3)))
% 283.64/36.98 = { by lemma 77 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(and(inv1, inv2), not(i3))))
% 283.64/36.98 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), and(inv1, inv2))))
% 283.64/36.98 = { by lemma 78 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(and(inv1, inv2), and(inv2, n6))))))
% 283.64/36.98 = { by lemma 79 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(and(inv1, inv2), and(and(inv2, n6), not(n9)))))))
% 283.64/36.98 = { by lemma 80 }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), and(not(n9), xor(and(inv2, n6), not(n20)))))))
% 283.64/36.98 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), and(not(n9), xor(not(n20), and(inv2, n6)))))))
% 283.64/36.98 = { by lemma 189 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), and(not(n9), xor(not(n20), and(not(i3), or(n22, n14))))))))
% 283.64/36.98 = { by lemma 66 }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), and(not(n9), xor(not(n20), and(not(i3), not(not(n20)))))))))
% 283.64/36.98 = { by lemma 57 }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), and(not(n9), or(not(n20), not(i3)))))))
% 283.64/36.98 = { by lemma 64 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), and(not(n9), or(not(i3), not(n20)))))))
% 283.64/36.98 = { by lemma 54 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), and(not(n9), xor(not(i3), xor(not(n20), and(not(i3), not(n20)))))))))
% 283.64/36.98 = { by lemma 190 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), and(not(n9), xor(not(i3), xor(not(n20), xor(and(inv1, i3), not(n20)))))))))
% 283.64/36.98 = { by lemma 78 }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), and(not(n9), xor(not(i3), and(inv1, i3)))))))
% 283.64/36.98 = { by axiom 10 (xor_symmetry) }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), and(not(n9), xor(and(inv1, i3), not(i3)))))))
% 283.64/36.98 = { by lemma 191 }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), and(not(i3), not(n9))))))
% 283.64/36.98 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), and(not(n9), not(i3))))))
% 283.64/36.98 = { by axiom 43 (xor_simplification1) R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, xor(i3, and(not(n9), not(i3))))))))
% 283.64/36.98 = { by lemma 57 }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, or(i3, not(n9)))))))
% 283.64/36.98 = { by lemma 64 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, or(not(n9), i3))))))
% 283.64/36.98 = { by lemma 51 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(not(or(not(n9), i3))))))))
% 283.64/36.98 = { by lemma 174 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(and(or(n8, n2), not(i3))))))))
% 283.64/36.98 = { by axiom 29 (and_symmetry) }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(and(not(i3), or(n8, n2))))))))
% 283.64/36.98 = { by lemma 194 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(and(not(i3), or(a1, n24))))))))
% 283.64/36.98 = { by lemma 193 }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(and(not(i3), or(a1, n10))))))))
% 283.64/36.98 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(and(or(a1, n10), not(i3))))))))
% 283.64/36.98 = { by lemma 51 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(not(not(and(or(a1, n10), not(i3))))))))))
% 283.64/36.98 = { by lemma 195 }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(not(or(not(or(a1, n10)), i3))))))))
% 283.64/36.98 = { by lemma 60 }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), and(or(a1, n10), i3))))))))
% 283.64/36.98 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), and(i3, or(a1, n10)))))))))
% 283.64/36.98 = { by lemma 166 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), and(i3, xor(and(inv1, i2), or(n24, n7))))))))))
% 283.64/36.98 = { by lemma 81 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), xor(and(and(inv1, i2), i3), and(i3, or(n24, n7))))))))))
% 283.64/36.98 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), xor(and(i3, and(inv1, i2)), and(i3, or(n24, n7))))))))))
% 283.64/36.98 = { by lemma 133 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), xor(and(not(n20), and(i2, i3)), and(i3, or(n24, n7))))))))))
% 283.64/36.98 = { by axiom 29 (and_symmetry) }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), xor(and(and(i2, i3), not(n20)), and(i3, or(n24, n7))))))))))
% 283.64/36.98 = { by lemma 114 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), xor(and(and(inv1, i2), and(i2, i3)), and(i3, or(n24, n7))))))))))
% 283.64/36.98 = { by lemma 117 }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), xor(n0, and(i3, or(n24, n7))))))))))
% 283.64/36.98 = { by axiom 13 (xor_definition1) }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), and(i3, or(n24, n7)))))))))
% 283.64/36.98 = { by lemma 140 R->L }
% 283.64/36.98 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), and(i3, xor(and(n6, i3), and(i1, inv1))))))))))
% 283.64/36.99 = { by lemma 153 }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), xor(and(n6, i3), and(and(i1, inv1), i3)))))))))
% 283.64/36.99 = { by lemma 147 R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), xor(and(n6, i3), and(and(inv1, i3), and(i1, inv1))))))))))
% 283.64/36.99 = { by lemma 163 }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), xor(and(n6, i3), n0))))))))
% 283.64/36.99 = { by axiom 11 (xor_definition2) }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), and(n6, i3))))))))
% 283.64/36.99 = { by lemma 192 R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(xor(or(a1, n10), xor(or(a1, n24), or(a1, n10)))))))))
% 283.64/36.99 = { by lemma 78 }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(i3, not(or(a1, n24)))))))
% 283.64/36.99 = { by lemma 52 }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), not(i3))))))
% 283.64/36.99 = { by axiom 10 (xor_symmetry) }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(and(inv2, n6), xor(not(i3), or(a1, n24))))))
% 283.64/36.99 = { by axiom 44 (xor_commutativity) R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), or(a1, n24))))))
% 283.64/36.99 = { by axiom 11 (xor_definition2) R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), n0))))))
% 283.64/36.99 = { by axiom 31 (and_definition2) R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(or(a1, n24), n0)))))))
% 283.64/36.99 = { by axiom 31 (and_definition2) R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(or(a1, n24), and(and(i1, i2), n0))))))))
% 283.64/36.99 = { by lemma 109 R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(or(a1, n24), and(and(i1, i2), and(and(inv1, inv2), or(n22, n14))))))))))
% 283.64/36.99 = { by axiom 46 (and_commutativity) }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(or(a1, n24), and(and(inv1, inv2), and(and(i1, i2), or(n22, n14))))))))))
% 283.64/36.99 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(or(a1, n24), and(and(inv1, inv2), and(or(n22, n14), and(i1, i2))))))))))
% 283.64/36.99 = { by lemma 88 R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(or(a1, n24), and(and(inv1, inv2), and(i2, and(or(n22, n14), i1))))))))))
% 283.64/36.99 = { by lemma 196 }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(or(a1, n24), and(and(inv1, inv2), and(i2, xor(and(i1, inv1), i1))))))))))
% 283.64/36.99 = { by lemma 197 }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(or(a1, n24), and(and(inv1, inv2), and(i2, or(n23, n6))))))))))
% 283.64/36.99 = { by axiom 29 (and_symmetry) }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(or(a1, n24), and(and(inv1, inv2), and(or(n23, n6), i2)))))))))
% 283.64/36.99 = { by lemma 155 }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(or(a1, n24), and(and(inv1, inv2), and(i1, i2)))))))))
% 283.64/36.99 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(or(a1, n24), and(and(i1, i2), and(inv1, inv2)))))))))
% 283.64/36.99 = { by lemma 74 R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(or(a1, n24), and(not(n9), and(not(n20), and(i1, i2))))))))))
% 283.64/36.99 = { by lemma 198 }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(or(a1, n24), and(not(n20), and(inv2, n6)))))))))
% 283.64/36.99 = { by axiom 29 (and_symmetry) }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(or(a1, n24), and(and(inv2, n6), not(n20)))))))))
% 283.64/36.99 = { by axiom 46 (and_commutativity) }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(and(inv2, n6), and(or(a1, n24), not(n20)))))))))
% 283.64/36.99 = { by lemma 201 R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(and(inv2, n6), xor(or(a1, n24), and(or(a1, n24), or(n22, n14))))))))))
% 283.64/36.99 = { by lemma 111 R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(and(inv2, n6), xor(or(a1, n24), and(or(n22, n14), xor(and(inv1, i2), or(a1, n24)))))))))))
% 283.64/36.99 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(and(inv2, n6), xor(or(a1, n24), and(xor(and(inv1, i2), or(a1, n24)), or(n22, n14))))))))))
% 283.64/36.99 = { by lemma 66 }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(and(inv2, n6), xor(or(a1, n24), and(xor(and(inv1, i2), or(a1, n24)), not(not(n20)))))))))))
% 283.64/36.99 = { by lemma 56 R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(and(inv2, n6), xor(or(a1, n24), xor(not(n20), or(not(n20), xor(and(inv1, i2), or(a1, n24))))))))))))
% 283.64/36.99 = { by lemma 126 R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(and(inv2, n6), xor(or(a1, n24), xor(not(n20), or(not(n20), and(and(i1, inv1), not(and(inv1, i2)))))))))))))
% 283.64/36.99 = { by lemma 202 }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(and(inv2, n6), xor(or(a1, n24), xor(not(n20), not(n20))))))))))
% 283.64/36.99 = { by axiom 9 (xor_definition3) }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(and(inv2, n6), xor(or(a1, n24), n0))))))))
% 283.64/36.99 = { by axiom 11 (xor_definition2) }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), xor(or(a1, n24), and(and(inv2, n6), or(a1, n24))))))))
% 283.64/36.99 = { by lemma 62 }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), xor(and(inv2, n6), and(or(a1, n24), not(and(inv2, n6))))))))
% 283.64/36.99 = { by lemma 57 }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), or(and(inv2, n6), or(a1, n24))))))
% 283.64/36.99 = { by axiom 38 (constructor18) R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), or(n15, or(a1, n24))))))
% 283.64/36.99 = { by axiom 25 (constructor6) R->L }
% 283.64/36.99 circuit(or(and(inv1, inv2), xor(not(i3), xor(not(i3), or(n15, n3)))))
% 283.64/36.99 = { by axiom 43 (xor_simplification1) }
% 283.64/36.99 circuit(or(and(inv1, inv2), or(n15, n3)))
% 283.64/36.99 = { by lemma 64 }
% 283.64/36.99 circuit(or(or(n15, n3), and(inv1, inv2)))
% 283.64/36.99 = { by axiom 35 (constructor24) R->L }
% 283.64/36.99 circuit(or(or(n15, n3), n21))
% 283.64/36.99 = { by axiom 15 (constructor7) R->L }
% 283.64/36.99 circuit(or(n4, n21))
% 283.64/36.99 = { by axiom 14 (constructor8) R->L }
% 283.64/36.99 circuit(n5)
% 283.64/36.99 = { by axiom 3 (constructor3) R->L }
% 283.64/36.99 circuit(o3)
% 283.64/36.99 = { by axiom 6 (output3) }
% 283.64/36.99 true
% 283.64/36.99 = { by axiom 4 (output1) R->L }
% 283.64/36.99 circuit(o1)
% 283.64/36.99
% 283.64/36.99 Lemma 204: xor(X, not(or(X, Y))) = or(X, not(Y)).
% 283.64/36.99 Proof:
% 283.64/36.99 xor(X, not(or(X, Y)))
% 283.64/36.99 = { by lemma 59 R->L }
% 283.64/36.99 not(xor(X, or(X, Y)))
% 283.64/36.99 = { by lemma 56 }
% 283.64/36.99 not(and(Y, not(X)))
% 283.64/36.99 = { by lemma 195 }
% 283.64/36.99 or(not(Y), X)
% 283.64/36.99 = { by lemma 64 R->L }
% 283.64/36.99 or(X, not(Y))
% 283.64/36.99
% 283.64/36.99 Lemma 205: and(not(n9), X) = and(X, inv2).
% 283.64/36.99 Proof:
% 283.64/36.99 and(not(n9), X)
% 283.64/36.99 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.99 and(X, not(n9))
% 283.64/36.99 = { by axiom 7 (constructor30) R->L }
% 283.64/36.99 and(X, inv2)
% 283.64/36.99
% 283.64/36.99 Lemma 206: and(and(X, inv2), not(n9)) = and(X, inv2).
% 283.64/36.99 Proof:
% 283.64/36.99 and(and(X, inv2), not(n9))
% 283.64/36.99 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.99 and(not(n9), and(X, inv2))
% 283.64/36.99 = { by lemma 205 R->L }
% 283.64/36.99 and(not(n9), and(not(n9), X))
% 283.64/36.99 = { by axiom 45 (and_simplification2) }
% 283.64/36.99 and(not(n9), X)
% 283.64/36.99 = { by lemma 205 }
% 283.64/36.99 and(X, inv2)
% 283.64/36.99
% 283.64/36.99 Lemma 207: and(and(X, inv2), or(n8, n2)) = n0.
% 283.64/36.99 Proof:
% 283.64/36.99 and(and(X, inv2), or(n8, n2))
% 283.64/36.99 = { by lemma 65 }
% 283.64/36.99 and(and(X, inv2), not(not(n9)))
% 283.64/36.99 = { by lemma 55 R->L }
% 283.64/36.99 xor(and(X, inv2), and(and(X, inv2), not(n9)))
% 283.64/36.99 = { by lemma 206 }
% 283.64/36.99 xor(and(X, inv2), and(X, inv2))
% 283.64/36.99 = { by axiom 9 (xor_definition3) }
% 283.64/36.99 n0
% 283.64/36.99
% 283.64/36.99 Lemma 208: and(and(X, inv2), and(Y, or(n8, n2))) = n0.
% 283.64/36.99 Proof:
% 283.64/36.99 and(and(X, inv2), and(Y, or(n8, n2)))
% 283.64/36.99 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.99 and(Y, and(and(X, inv2), or(n8, n2)))
% 283.64/36.99 = { by lemma 207 }
% 283.64/36.99 and(Y, n0)
% 283.64/36.99 = { by axiom 31 (and_definition2) }
% 283.64/36.99 n0
% 283.64/36.99
% 283.64/36.99 Lemma 209: xor(and(Y, X), Y) = and(not(X), Y).
% 283.64/36.99 Proof:
% 283.64/36.99 xor(and(Y, X), Y)
% 283.64/36.99 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.99 xor(Y, and(Y, X))
% 283.64/36.99 = { by lemma 55 }
% 283.64/36.99 and(Y, not(X))
% 283.64/36.99 = { by axiom 29 (and_symmetry) }
% 283.64/36.99 and(not(X), Y)
% 283.64/36.99
% 283.64/36.99 Lemma 210: and(and(i1, inv1), not(and(inv1, i3))) = xor(and(inv1, i3), or(n2, n24)).
% 283.64/36.99 Proof:
% 283.64/36.99 and(and(i1, inv1), not(and(inv1, i3)))
% 283.64/36.99 = { by axiom 37 (constructor5) R->L }
% 283.64/36.99 and(and(i1, inv1), not(n2))
% 283.64/36.99 = { by axiom 40 (constructor27) R->L }
% 283.64/36.99 and(n24, not(n2))
% 283.64/36.99 = { by lemma 56 R->L }
% 283.64/36.99 xor(n2, or(n2, n24))
% 283.64/36.99 = { by axiom 37 (constructor5) }
% 283.64/36.99 xor(and(inv1, i3), or(n2, n24))
% 283.64/36.99
% 283.64/36.99 Lemma 211: xor(and(inv1, i3), or(n2, n24)) = and(i1, inv1).
% 283.64/36.99 Proof:
% 283.64/36.99 xor(and(inv1, i3), or(n2, n24))
% 283.64/36.99 = { by lemma 210 R->L }
% 283.64/36.99 and(and(i1, inv1), not(and(inv1, i3)))
% 283.64/36.99 = { by lemma 62 R->L }
% 283.64/36.99 xor(and(i1, inv1), and(and(inv1, i3), and(i1, inv1)))
% 283.64/36.99 = { by lemma 163 }
% 283.64/36.99 xor(and(i1, inv1), n0)
% 283.64/36.99 = { by axiom 11 (xor_definition2) }
% 283.64/36.99 and(i1, inv1)
% 283.64/36.99
% 283.64/36.99 Lemma 212: and(and(i1, inv1), and(not(i3), X)) = and(X, and(i1, inv1)).
% 283.64/36.99 Proof:
% 283.64/36.99 and(and(i1, inv1), and(not(i3), X))
% 283.64/36.99 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.99 and(and(i1, inv1), and(X, not(i3)))
% 283.64/36.99 = { by axiom 46 (and_commutativity) R->L }
% 283.64/36.99 and(X, and(and(i1, inv1), not(i3)))
% 283.64/36.99 = { by axiom 29 (and_symmetry) R->L }
% 283.64/36.99 and(X, and(not(i3), and(i1, inv1)))
% 283.64/36.99 = { by lemma 143 R->L }
% 283.64/36.99 and(X, and(not(n20), and(not(i3), i1)))
% 283.64/36.99 = { by lemma 209 R->L }
% 283.64/36.99 and(X, and(not(n20), xor(and(i1, i3), i1)))
% 283.64/36.99 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/36.99 and(X, and(not(n20), xor(i1, and(i1, i3))))
% 283.64/36.99 = { by axiom 48 (and_xor_simplification) }
% 283.64/36.99 and(X, xor(and(not(n20), i1), and(not(n20), and(i1, i3))))
% 283.64/36.99 = { by lemma 136 }
% 283.64/36.99 and(X, xor(and(i1, inv1), and(not(n20), and(i1, i3))))
% 283.64/36.99 = { by axiom 29 (and_symmetry) }
% 283.64/36.99 and(X, xor(and(i1, inv1), and(and(i1, i3), not(n20))))
% 283.64/36.99 = { by lemma 144 }
% 283.64/36.99 and(X, xor(and(i1, inv1), and(and(inv1, i3), i1)))
% 283.64/36.99 = { by lemma 145 R->L }
% 283.64/37.00 and(X, xor(and(i1, inv1), and(and(inv1, i3), and(i1, i3))))
% 283.64/37.00 = { by lemma 146 R->L }
% 283.64/37.00 and(X, xor(and(i1, inv1), and(and(inv1, i3), and(i1, inv1))))
% 283.64/37.00 = { by lemma 62 }
% 283.64/37.00 and(X, and(and(i1, inv1), not(and(inv1, i3))))
% 283.64/37.00 = { by lemma 210 }
% 283.64/37.00 and(X, xor(and(inv1, i3), or(n2, n24)))
% 283.64/37.00 = { by lemma 211 }
% 283.64/37.00 and(X, and(i1, inv1))
% 283.64/37.00
% 283.64/37.00 Lemma 213: and(and(i1, inv1), or(n8, n2)) = and(i1, inv1).
% 283.64/37.00 Proof:
% 283.64/37.00 and(and(i1, inv1), or(n8, n2))
% 283.64/37.00 = { by axiom 29 (and_symmetry) R->L }
% 283.64/37.00 and(or(n8, n2), and(i1, inv1))
% 283.64/37.00 = { by lemma 212 R->L }
% 283.64/37.00 and(and(i1, inv1), and(not(i3), or(n8, n2)))
% 283.64/37.00 = { by lemma 194 R->L }
% 283.64/37.00 and(and(i1, inv1), and(not(i3), or(a1, n24)))
% 283.64/37.00 = { by lemma 212 }
% 283.64/37.00 and(or(a1, n24), and(i1, inv1))
% 283.64/37.00 = { by axiom 29 (and_symmetry) }
% 283.64/37.00 and(and(i1, inv1), or(a1, n24))
% 283.64/37.00 = { by lemma 51 R->L }
% 283.64/37.00 and(and(i1, inv1), not(not(or(a1, n24))))
% 283.64/37.00 = { by lemma 55 R->L }
% 283.64/37.00 xor(and(i1, inv1), and(and(i1, inv1), not(or(a1, n24))))
% 283.64/37.00 = { by lemma 127 R->L }
% 283.64/37.00 xor(and(i1, inv1), and(and(i1, inv1), and(not(and(inv1, i2)), not(and(i1, inv1)))))
% 283.64/37.00 = { by lemma 159 }
% 283.64/37.00 xor(and(i1, inv1), n0)
% 283.64/37.00 = { by axiom 11 (xor_definition2) }
% 283.64/37.00 and(i1, inv1)
% 283.64/37.00
% 283.64/37.00 Lemma 214: and(and(inv1, inv2), and(X, inv1)) = and(and(X, inv1), not(n9)).
% 283.64/37.00 Proof:
% 283.64/37.00 and(and(inv1, inv2), and(X, inv1))
% 283.64/37.00 = { by axiom 29 (and_symmetry) R->L }
% 283.64/37.00 and(and(X, inv1), and(inv1, inv2))
% 283.64/37.00 = { by lemma 68 R->L }
% 283.64/37.00 and(not(n9), and(and(X, inv1), not(n20)))
% 283.64/37.00 = { by lemma 137 }
% 283.64/37.00 and(not(n9), and(X, inv1))
% 283.64/37.00 = { by axiom 29 (and_symmetry) }
% 283.64/37.00 and(and(X, inv1), not(n9))
% 283.64/37.00
% 283.64/37.00 Lemma 215: not(or(or(n8, n2), X)) = and(not(n9), not(X)).
% 283.64/37.00 Proof:
% 283.64/37.00 not(or(or(n8, n2), X))
% 283.64/37.00 = { by axiom 16 (constructor12) R->L }
% 283.64/37.00 not(or(n9, X))
% 283.64/37.00 = { by lemma 57 R->L }
% 283.64/37.00 not(xor(n9, and(X, not(n9))))
% 283.64/37.00 = { by axiom 16 (constructor12) }
% 283.64/37.00 not(xor(or(n8, n2), and(X, not(n9))))
% 283.64/37.00 = { by lemma 59 }
% 283.64/37.00 xor(or(n8, n2), not(and(X, not(n9))))
% 283.64/37.00 = { by lemma 107 }
% 283.64/37.00 xor(and(X, not(n9)), not(n9))
% 283.64/37.00 = { by axiom 10 (xor_symmetry) }
% 283.64/37.00 xor(not(n9), and(X, not(n9)))
% 283.64/37.00 = { by lemma 62 }
% 283.64/37.00 and(not(n9), not(X))
% 283.64/37.00
% 283.64/37.00 Lemma 216: and(not(n20), or(n2, n24)) = or(n2, n24).
% 283.64/37.00 Proof:
% 283.64/37.00 and(not(n20), or(n2, n24))
% 283.64/37.00 = { by axiom 29 (and_symmetry) R->L }
% 283.64/37.00 and(or(n2, n24), not(n20))
% 283.64/37.00 = { by lemma 201 R->L }
% 283.64/37.00 xor(or(n2, n24), and(or(n2, n24), or(n22, n14)))
% 283.64/37.00 = { by lemma 111 R->L }
% 283.64/37.00 xor(or(n2, n24), and(or(n22, n14), xor(and(inv1, i3), or(n2, n24))))
% 283.64/37.00 = { by axiom 29 (and_symmetry) R->L }
% 283.64/37.00 xor(or(n2, n24), and(xor(and(inv1, i3), or(n2, n24)), or(n22, n14)))
% 283.64/37.00 = { by lemma 66 }
% 283.64/37.00 xor(or(n2, n24), and(xor(and(inv1, i3), or(n2, n24)), not(not(n20))))
% 283.64/37.00 = { by lemma 56 R->L }
% 283.64/37.00 xor(or(n2, n24), xor(not(n20), or(not(n20), xor(and(inv1, i3), or(n2, n24)))))
% 283.64/37.00 = { by lemma 210 R->L }
% 283.64/37.00 xor(or(n2, n24), xor(not(n20), or(not(n20), and(and(i1, inv1), not(and(inv1, i3))))))
% 283.64/37.00 = { by lemma 202 }
% 283.64/37.00 xor(or(n2, n24), xor(not(n20), not(n20)))
% 283.64/37.00 = { by axiom 9 (xor_definition3) }
% 283.64/37.00 xor(or(n2, n24), n0)
% 283.64/37.00 = { by axiom 11 (xor_definition2) }
% 283.64/37.00 or(n2, n24)
% 283.64/37.00
% 283.64/37.00 Lemma 217: and(and(inv1, inv2), and(X, i3)) = n0.
% 283.64/37.00 Proof:
% 283.64/37.00 and(and(inv1, inv2), and(X, i3))
% 283.64/37.00 = { by lemma 112 R->L }
% 283.64/37.00 and(and(X, i3), and(and(inv1, inv2), i3))
% 283.64/37.00 = { by axiom 29 (and_symmetry) R->L }
% 283.64/37.00 and(and(X, i3), and(i3, and(inv1, inv2)))
% 283.64/37.00 = { by lemma 74 R->L }
% 283.64/37.00 and(and(X, i3), and(not(n9), and(not(n20), i3)))
% 283.64/37.00 = { by axiom 8 (constructor29) R->L }
% 283.64/37.00 and(and(X, i3), and(not(n9), and(inv1, i3)))
% 283.64/37.00 = { by axiom 29 (and_symmetry) }
% 283.64/37.00 and(and(X, i3), and(and(inv1, i3), not(n9)))
% 283.64/37.00 = { by lemma 70 R->L }
% 283.64/37.00 and(and(X, i3), and(and(inv1, i3), and(inv1, inv2)))
% 283.64/37.00 = { by lemma 73 }
% 283.64/37.00 and(and(X, i3), n0)
% 283.64/37.00 = { by axiom 31 (and_definition2) }
% 283.64/37.00 n0
% 283.64/37.00
% 283.64/37.00 Lemma 218: and(and(i1, i3), not(n9)) = and(n23, inv2).
% 283.64/37.00 Proof:
% 283.64/37.00 and(and(i1, i3), not(n9))
% 283.64/37.00 = { by axiom 42 (constructor26) R->L }
% 283.64/37.00 and(n23, not(n9))
% 283.64/37.00 = { by axiom 29 (and_symmetry) R->L }
% 283.64/37.00 and(not(n9), n23)
% 283.64/37.00 = { by lemma 205 }
% 283.64/37.00 and(n23, inv2)
% 283.64/37.00
% 283.64/37.00 Lemma 219: and(and(i1, i3), and(X, not(n9))) = and(X, and(n23, inv2)).
% 283.64/37.00 Proof:
% 283.64/37.00 and(and(i1, i3), and(X, not(n9)))
% 283.64/37.00 = { by axiom 46 (and_commutativity) R->L }
% 283.64/37.00 and(X, and(and(i1, i3), not(n9)))
% 283.64/37.00 = { by lemma 218 }
% 283.64/37.00 and(X, and(n23, inv2))
% 283.64/37.00
% 283.64/37.00 Lemma 220: and(not(n9), and(X, and(i1, i3))) = and(X, and(n23, inv2)).
% 283.64/37.00 Proof:
% 283.64/37.00 and(not(n9), and(X, and(i1, i3)))
% 283.64/37.00 = { by axiom 42 (constructor26) R->L }
% 283.64/37.00 and(not(n9), and(X, n23))
% 283.64/37.00 = { by lemma 171 R->L }
% 283.64/37.00 and(and(not(n9), n23), X)
% 283.64/37.00 = { by lemma 205 }
% 283.64/37.00 and(and(n23, inv2), X)
% 283.64/37.00 = { by axiom 29 (and_symmetry) }
% 283.64/37.00 and(X, and(n23, inv2))
% 283.64/37.00
% 283.64/37.00 Lemma 221: and(and(n23, inv2), not(n20)) = n0.
% 283.64/37.00 Proof:
% 283.64/37.00 and(and(n23, inv2), not(n20))
% 283.64/37.00 = { by axiom 29 (and_symmetry) R->L }
% 283.64/37.00 and(not(n20), and(n23, inv2))
% 283.64/37.00 = { by lemma 220 R->L }
% 283.64/37.00 and(not(n9), and(not(n20), and(i1, i3)))
% 283.64/37.00 = { by lemma 74 }
% 283.64/37.00 and(and(i1, i3), and(inv1, inv2))
% 283.64/37.00 = { by axiom 29 (and_symmetry) }
% 283.64/37.00 and(and(inv1, inv2), and(i1, i3))
% 283.64/37.00 = { by lemma 217 }
% 283.64/37.00 n0
% 283.64/37.00
% 283.64/37.00 Lemma 222: xor(or(n2, n24), or(n19, n25)) = and(n23, inv2).
% 283.64/37.00 Proof:
% 283.64/37.00 xor(or(n2, n24), or(n19, n25))
% 283.64/37.00 = { by axiom 43 (xor_simplification1) R->L }
% 283.64/37.00 xor(and(n23, inv2), xor(and(n23, inv2), xor(or(n2, n24), or(n19, n25))))
% 283.64/37.00 = { by axiom 44 (xor_commutativity) R->L }
% 283.64/37.00 xor(and(n23, inv2), xor(or(n2, n24), xor(and(n23, inv2), or(n19, n25))))
% 283.64/37.00 = { by axiom 33 (constructor22) R->L }
% 283.64/37.00 xor(and(n23, inv2), xor(or(n2, n24), xor(n19, or(n19, n25))))
% 283.64/37.00 = { by lemma 56 }
% 283.64/37.00 xor(and(n23, inv2), xor(or(n2, n24), and(n25, not(n19))))
% 283.64/37.00 = { by axiom 26 (constructor28) }
% 283.64/37.00 xor(and(n23, inv2), xor(or(n2, n24), and(or(n2, n24), not(n19))))
% 283.64/37.00 = { by axiom 33 (constructor22) }
% 283.64/37.00 xor(and(n23, inv2), xor(or(n2, n24), and(or(n2, n24), not(and(n23, inv2)))))
% 283.64/37.00 = { by lemma 55 }
% 283.64/37.00 xor(and(n23, inv2), and(or(n2, n24), not(not(and(n23, inv2)))))
% 283.64/37.00 = { by lemma 51 }
% 283.64/37.00 xor(and(n23, inv2), and(or(n2, n24), and(n23, inv2)))
% 283.64/37.00 = { by axiom 29 (and_symmetry) }
% 283.64/37.00 xor(and(n23, inv2), and(and(n23, inv2), or(n2, n24)))
% 283.64/37.00 = { by lemma 216 R->L }
% 283.64/37.00 xor(and(n23, inv2), and(and(n23, inv2), and(not(n20), or(n2, n24))))
% 283.64/37.00 = { by axiom 29 (and_symmetry) R->L }
% 283.64/37.00 xor(and(n23, inv2), and(and(n23, inv2), and(or(n2, n24), not(n20))))
% 283.64/37.00 = { by axiom 46 (and_commutativity) R->L }
% 283.64/37.00 xor(and(n23, inv2), and(or(n2, n24), and(and(n23, inv2), not(n20))))
% 283.64/37.00 = { by lemma 221 }
% 283.64/37.00 xor(and(n23, inv2), and(or(n2, n24), n0))
% 283.64/37.00 = { by axiom 31 (and_definition2) }
% 283.64/37.00 xor(and(n23, inv2), n0)
% 283.64/37.00 = { by axiom 11 (xor_definition2) }
% 283.64/37.00 and(n23, inv2)
% 283.64/37.00
% 283.64/37.00 Lemma 223: xor(and(n23, inv2), or(n2, n24)) = or(n19, n25).
% 283.64/37.00 Proof:
% 283.64/37.00 xor(and(n23, inv2), or(n2, n24))
% 283.64/37.00 = { by axiom 10 (xor_symmetry) R->L }
% 283.64/37.00 xor(or(n2, n24), and(n23, inv2))
% 283.64/37.00 = { by lemma 222 R->L }
% 283.64/37.00 xor(or(n2, n24), xor(or(n2, n24), or(n19, n25)))
% 283.64/37.00 = { by axiom 43 (xor_simplification1) }
% 283.64/37.00 or(n19, n25)
% 283.64/37.00
% 283.64/37.00 Lemma 224: and(and(inv1, inv2), not(or(n19, n25))) = xor(or(n18, n21), or(n19, n25)).
% 283.64/37.00 Proof:
% 283.64/37.00 and(and(inv1, inv2), not(or(n19, n25)))
% 283.64/37.00 = { by axiom 20 (constructor21) R->L }
% 283.64/37.00 and(and(inv1, inv2), not(n18))
% 283.64/37.00 = { by axiom 35 (constructor24) R->L }
% 283.64/37.00 and(n21, not(n18))
% 283.64/37.00 = { by lemma 56 R->L }
% 283.64/37.00 xor(n18, or(n18, n21))
% 283.64/37.00 = { by axiom 20 (constructor21) }
% 283.64/37.00 xor(or(n19, n25), or(n18, n21))
% 283.64/37.00 = { by axiom 10 (xor_symmetry) }
% 283.64/37.00 xor(or(n18, n21), or(n19, n25))
% 283.64/37.00
% 283.64/37.00 Lemma 225: and(and(inv2, X), or(n8, n2)) = n0.
% 283.64/37.00 Proof:
% 283.64/37.00 and(and(inv2, X), or(n8, n2))
% 283.64/37.00 = { by lemma 65 }
% 283.64/37.00 and(and(inv2, X), not(not(n9)))
% 283.64/37.00 = { by lemma 55 R->L }
% 283.64/37.00 xor(and(inv2, X), and(and(inv2, X), not(n9)))
% 283.64/37.00 = { by lemma 79 }
% 283.64/37.00 xor(and(inv2, X), and(inv2, X))
% 283.64/37.00 = { by axiom 9 (xor_definition3) }
% 283.64/37.00 n0
% 283.64/37.00
% 283.64/37.00 Lemma 226: and(and(i2, i3), and(n23, inv2)) = and(and(n6, i3), not(n9)).
% 283.64/37.00 Proof:
% 283.64/37.00 and(and(i2, i3), and(n23, inv2))
% 283.64/37.00 = { by lemma 220 R->L }
% 283.64/37.00 and(not(n9), and(and(i2, i3), and(i1, i3)))
% 283.64/37.00 = { by lemma 90 }
% 283.64/37.00 and(not(n9), and(n6, i3))
% 283.64/37.00 = { by axiom 29 (and_symmetry) }
% 283.64/37.00 and(and(n6, i3), not(n9))
% 283.64/37.00
% 283.64/37.00 Lemma 227: and(and(i2, i3), and(inv2, n6)) = and(and(i2, i3), and(n23, inv2)).
% 283.64/37.00 Proof:
% 283.64/37.00 and(and(i2, i3), and(inv2, n6))
% 283.64/37.00 = { by lemma 198 R->L }
% 283.64/37.00 and(not(n9), and(and(i2, i3), and(i1, i2)))
% 283.64/37.00 = { by lemma 176 }
% 283.64/37.00 and(not(n9), and(and(i2, i3), and(n6, i3)))
% 283.64/37.00 = { by lemma 177 }
% 283.64/37.00 and(not(n9), and(n6, i3))
% 283.64/37.00 = { by axiom 29 (and_symmetry) }
% 283.64/37.00 and(and(n6, i3), not(n9))
% 283.64/37.00 = { by lemma 226 R->L }
% 283.64/37.00 and(and(i2, i3), and(n23, inv2))
% 283.64/37.00
% 283.64/37.00 Lemma 228: and(and(i2, i3), not(n9)) = and(n14, inv2).
% 283.64/37.00 Proof:
% 283.64/37.00 and(and(i2, i3), not(n9))
% 283.64/37.00 = { by axiom 39 (constructor17) R->L }
% 283.64/37.00 and(n14, not(n9))
% 283.64/37.00 = { by axiom 29 (and_symmetry) R->L }
% 283.64/37.00 and(not(n9), n14)
% 283.64/37.00 = { by lemma 205 }
% 283.64/37.00 and(n14, inv2)
% 283.64/37.00
% 283.64/37.00 Lemma 229: and(and(i2, i3), and(X, not(n9))) = and(X, and(n14, inv2)).
% 283.64/37.00 Proof:
% 283.64/37.00 and(and(i2, i3), and(X, not(n9)))
% 283.64/37.00 = { by axiom 46 (and_commutativity) R->L }
% 283.64/37.00 and(X, and(and(i2, i3), not(n9)))
% 283.64/37.00 = { by lemma 228 }
% 283.64/37.00 and(X, and(n14, inv2))
% 283.64/37.00
% 283.64/37.00 Lemma 230: and(and(i2, i3), and(inv2, n6)) = n0.
% 283.64/37.00 Proof:
% 283.64/37.00 and(and(i2, i3), and(inv2, n6))
% 283.64/37.00 = { by lemma 227 }
% 283.64/37.00 and(and(i2, i3), and(n23, inv2))
% 283.64/37.00 = { by axiom 45 (and_simplification2) R->L }
% 283.64/37.00 and(and(i2, i3), and(and(i2, i3), and(n23, inv2)))
% 283.64/37.00 = { by lemma 226 }
% 283.64/37.00 and(and(i2, i3), and(and(n6, i3), not(n9)))
% 283.64/37.00 = { by lemma 229 }
% 283.64/37.00 and(and(n6, i3), and(n14, inv2))
% 283.64/37.00 = { by axiom 29 (and_symmetry) R->L }
% 283.64/37.00 and(and(n14, inv2), and(n6, i3))
% 283.64/37.00 = { by lemma 168 R->L }
% 283.64/37.00 and(and(n14, inv2), and(or(n8, n2), or(n22, n14)))
% 283.64/37.00 = { by axiom 29 (and_symmetry) R->L }
% 283.64/37.00 and(and(n14, inv2), and(or(n22, n14), or(n8, n2)))
% 283.64/37.00 = { by axiom 46 (and_commutativity) R->L }
% 283.64/37.00 and(or(n22, n14), and(and(n14, inv2), or(n8, n2)))
% 283.64/37.00 = { by lemma 207 }
% 283.64/37.00 and(or(n22, n14), n0)
% 283.64/37.00 = { by axiom 31 (and_definition2) }
% 284.41/37.00 n0
% 284.41/37.00
% 284.41/37.00 Lemma 231: xor(X, not(and(X, Y))) = or(Y, not(X)).
% 284.41/37.00 Proof:
% 284.41/37.00 xor(X, not(and(X, Y)))
% 284.41/37.00 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.00 xor(X, not(and(Y, X)))
% 284.41/37.00 = { by lemma 53 R->L }
% 284.41/37.00 xor(not(X), and(Y, X))
% 284.41/37.00 = { by lemma 51 R->L }
% 284.41/37.00 xor(not(X), and(Y, not(not(X))))
% 284.41/37.00 = { by lemma 57 }
% 284.41/37.00 or(not(X), Y)
% 284.41/37.00 = { by lemma 64 R->L }
% 284.41/37.00 or(Y, not(X))
% 284.41/37.00
% 284.41/37.00 Lemma 232: and(or(n8, n2), xor(X, and(Y, inv2))) = and(X, or(n8, n2)).
% 284.41/37.00 Proof:
% 284.41/37.00 and(or(n8, n2), xor(X, and(Y, inv2)))
% 284.41/37.00 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.00 and(or(n8, n2), xor(and(Y, inv2), X))
% 284.41/37.00 = { by lemma 81 R->L }
% 284.41/37.00 xor(and(and(Y, inv2), or(n8, n2)), and(or(n8, n2), X))
% 284.41/37.00 = { by lemma 207 }
% 284.41/37.00 xor(n0, and(or(n8, n2), X))
% 284.41/37.00 = { by axiom 13 (xor_definition1) }
% 284.41/37.00 and(or(n8, n2), X)
% 284.41/37.00 = { by axiom 29 (and_symmetry) }
% 284.41/37.00 and(X, or(n8, n2))
% 284.41/37.00
% 284.41/37.00 Lemma 233: xor(not(n20), not(X)) = xor(X, or(n22, n14)).
% 284.41/37.00 Proof:
% 284.41/37.00 xor(not(n20), not(X))
% 284.41/37.00 = { by lemma 52 }
% 284.41/37.00 xor(X, not(not(n20)))
% 284.41/37.00 = { by lemma 66 R->L }
% 284.41/37.00 xor(X, or(n22, n14))
% 284.41/37.00
% 284.41/37.01 Lemma 234: xor(not(n20), and(X, or(n22, n14))) = or(not(n20), X).
% 284.41/37.01 Proof:
% 284.41/37.01 xor(not(n20), and(X, or(n22, n14)))
% 284.41/37.01 = { by lemma 66 }
% 284.41/37.01 xor(not(n20), and(X, not(not(n20))))
% 284.41/37.01 = { by lemma 57 }
% 284.41/37.01 or(not(n20), X)
% 284.41/37.01
% 284.41/37.01 Lemma 235: xor(and(inv1, inv2), or(n8, n2)) = xor(and(n6, i3), not(n20)).
% 284.41/37.01 Proof:
% 284.41/37.01 xor(and(inv1, inv2), or(n8, n2))
% 284.41/37.01 = { by lemma 65 }
% 284.41/37.01 xor(and(inv1, inv2), not(not(n9)))
% 284.41/37.01 = { by lemma 59 R->L }
% 284.41/37.01 not(xor(and(inv1, inv2), not(n9)))
% 284.41/37.01 = { by lemma 108 R->L }
% 284.41/37.01 not(and(not(n9), or(n22, n14)))
% 284.41/37.01 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.01 not(and(or(n22, n14), not(n9)))
% 284.41/37.01 = { by axiom 16 (constructor12) }
% 284.41/37.01 not(and(or(n22, n14), not(or(n8, n2))))
% 284.41/37.01 = { by lemma 62 R->L }
% 284.41/37.01 not(xor(or(n22, n14), and(or(n8, n2), or(n22, n14))))
% 284.41/37.01 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.01 not(xor(and(or(n8, n2), or(n22, n14)), or(n22, n14)))
% 284.41/37.01 = { by lemma 233 R->L }
% 284.41/37.01 not(xor(not(n20), not(and(or(n8, n2), or(n22, n14)))))
% 284.41/37.01 = { by lemma 59 R->L }
% 284.41/37.01 not(not(xor(not(n20), and(or(n8, n2), or(n22, n14)))))
% 284.41/37.01 = { by lemma 234 }
% 284.41/37.01 not(not(or(not(n20), or(n8, n2))))
% 284.41/37.01 = { by lemma 51 }
% 284.41/37.01 or(not(n20), or(n8, n2))
% 284.41/37.01 = { by lemma 234 R->L }
% 284.41/37.01 xor(not(n20), and(or(n8, n2), or(n22, n14)))
% 284.41/37.01 = { by lemma 168 }
% 284.41/37.01 xor(not(n20), and(n6, i3))
% 284.41/37.01 = { by axiom 10 (xor_symmetry) }
% 284.41/37.01 xor(and(n6, i3), not(n20))
% 284.41/37.01
% 284.41/37.01 Lemma 236: and(and(i2, i3), or(n8, n2)) = xor(and(i2, i3), and(n14, inv2)).
% 284.41/37.01 Proof:
% 284.41/37.01 and(and(i2, i3), or(n8, n2))
% 284.41/37.01 = { by lemma 65 }
% 284.41/37.01 and(and(i2, i3), not(not(n9)))
% 284.41/37.01 = { by lemma 55 R->L }
% 284.41/37.01 xor(and(i2, i3), and(and(i2, i3), not(n9)))
% 284.41/37.01 = { by lemma 228 }
% 284.41/37.01 xor(and(i2, i3), and(n14, inv2))
% 284.41/37.01
% 284.41/37.01 Lemma 237: and(xor(and(i2, i3), and(n14, inv2)), X) = and(and(i2, i3), and(X, or(n8, n2))).
% 284.41/37.01 Proof:
% 284.41/37.01 and(xor(and(i2, i3), and(n14, inv2)), X)
% 284.41/37.01 = { by lemma 236 R->L }
% 284.41/37.01 and(and(and(i2, i3), or(n8, n2)), X)
% 284.41/37.01 = { by lemma 171 }
% 284.41/37.01 and(and(i2, i3), and(X, or(n8, n2)))
% 284.41/37.01
% 284.41/37.01 Lemma 238: xor(and(i2, i3), and(n14, inv2)) = and(n6, i3).
% 284.41/37.01 Proof:
% 284.41/37.01 xor(and(i2, i3), and(n14, inv2))
% 284.41/37.01 = { by axiom 13 (xor_definition1) R->L }
% 284.41/37.01 xor(and(i2, i3), xor(n0, and(n14, inv2)))
% 284.41/37.01 = { by axiom 31 (and_definition2) R->L }
% 284.41/37.01 xor(and(i2, i3), xor(and(or(n8, n2), n0), and(n14, inv2)))
% 284.41/37.01 = { by lemma 117 R->L }
% 284.41/37.01 xor(and(i2, i3), xor(and(or(n8, n2), and(and(inv1, i2), and(i2, i3))), and(n14, inv2)))
% 284.41/37.01 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.01 xor(and(i2, i3), xor(and(or(n8, n2), and(and(i2, i3), and(inv1, i2))), and(n14, inv2)))
% 284.41/37.01 = { by lemma 113 R->L }
% 284.41/37.01 xor(and(i2, i3), xor(and(or(n8, n2), and(not(n20), and(and(i2, i3), i2))), and(n14, inv2)))
% 284.41/37.01 = { by lemma 92 }
% 284.41/37.01 xor(and(i2, i3), xor(and(or(n8, n2), and(not(n20), and(i2, i3))), and(n14, inv2)))
% 284.41/37.01 = { by axiom 29 (and_symmetry) }
% 284.41/37.01 xor(and(i2, i3), xor(and(or(n8, n2), and(and(i2, i3), not(n20))), and(n14, inv2)))
% 284.41/37.01 = { by axiom 46 (and_commutativity) }
% 284.41/37.01 xor(and(i2, i3), xor(and(and(i2, i3), and(or(n8, n2), not(n20))), and(n14, inv2)))
% 284.41/37.01 = { by axiom 29 (and_symmetry) }
% 284.41/37.01 xor(and(i2, i3), xor(and(and(i2, i3), and(not(n20), or(n8, n2))), and(n14, inv2)))
% 284.41/37.01 = { by lemma 180 R->L }
% 284.41/37.01 xor(xor(and(i2, i3), and(n14, inv2)), and(and(i2, i3), and(not(n20), or(n8, n2))))
% 284.41/37.01 = { by lemma 237 R->L }
% 284.41/37.01 xor(xor(and(i2, i3), and(n14, inv2)), and(xor(and(i2, i3), and(n14, inv2)), not(n20)))
% 284.41/37.01 = { by lemma 200 }
% 284.41/37.01 and(xor(and(i2, i3), and(n14, inv2)), or(n22, n14))
% 284.41/37.01 = { by lemma 237 }
% 284.41/37.01 and(and(i2, i3), and(or(n22, n14), or(n8, n2)))
% 284.41/37.01 = { by axiom 29 (and_symmetry) }
% 284.41/37.01 and(and(i2, i3), and(or(n8, n2), or(n22, n14)))
% 284.41/37.01 = { by lemma 168 }
% 284.41/37.01 and(and(i2, i3), and(n6, i3))
% 284.41/37.01 = { by lemma 177 }
% 284.41/37.01 and(n6, i3)
% 284.41/37.01
% 284.41/37.01 Lemma 239: xor(and(X, inv1), not(n20)) = and(not(X), not(n20)).
% 284.41/37.01 Proof:
% 284.41/37.01 xor(and(X, inv1), not(n20))
% 284.41/37.01 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.01 xor(not(n20), and(X, inv1))
% 284.41/37.01 = { by lemma 136 R->L }
% 284.41/37.01 xor(not(n20), and(not(n20), X))
% 284.41/37.01 = { by lemma 55 }
% 284.41/37.01 and(not(n20), not(X))
% 284.41/37.01 = { by axiom 29 (and_symmetry) }
% 284.41/37.01 and(not(X), not(n20))
% 284.41/37.01
% 284.41/37.01 Lemma 240: xor(or(n22, n14), X) = xor(not(X), not(n20)).
% 284.41/37.01 Proof:
% 284.41/37.01 xor(or(n22, n14), X)
% 284.41/37.01 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.01 xor(X, or(n22, n14))
% 284.41/37.01 = { by lemma 66 }
% 284.41/37.01 xor(X, not(not(n20)))
% 284.41/37.01 = { by lemma 52 }
% 284.41/37.01 xor(not(n20), not(X))
% 284.41/37.01 = { by axiom 10 (xor_symmetry) }
% 284.41/37.01 xor(not(X), not(n20))
% 284.41/37.01
% 284.41/37.01 Lemma 241: xor(not(X), not(Y)) = xor(Y, X).
% 284.41/37.01 Proof:
% 284.41/37.01 xor(not(X), not(Y))
% 284.41/37.01 = { by lemma 52 }
% 284.41/37.01 xor(Y, not(not(X)))
% 284.41/37.01 = { by lemma 51 }
% 284.41/37.01 xor(Y, X)
% 284.41/37.01
% 284.41/37.01 Lemma 242: xor(not(X), or(n22, n14)) = xor(not(n20), X).
% 284.41/37.01 Proof:
% 284.41/37.01 xor(not(X), or(n22, n14))
% 284.41/37.01 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.01 xor(or(n22, n14), not(X))
% 284.41/37.01 = { by axiom 21 (constructor23) R->L }
% 284.41/37.01 xor(n20, not(X))
% 284.41/37.01 = { by lemma 52 R->L }
% 284.41/37.01 xor(X, not(n20))
% 284.41/37.01 = { by axiom 10 (xor_symmetry) }
% 284.41/37.01 xor(not(n20), X)
% 284.41/37.01
% 284.41/37.01 Lemma 243: xor(and(X, inv1), xor(not(X), or(n22, n14))) = or(not(n20), X).
% 284.41/37.01 Proof:
% 284.41/37.01 xor(and(X, inv1), xor(not(X), or(n22, n14)))
% 284.41/37.01 = { by lemma 242 }
% 284.41/37.01 xor(and(X, inv1), xor(not(n20), X))
% 284.41/37.01 = { by axiom 44 (xor_commutativity) R->L }
% 284.41/37.01 xor(not(n20), xor(and(X, inv1), X))
% 284.41/37.01 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.01 xor(not(n20), xor(X, and(X, inv1)))
% 284.41/37.01 = { by lemma 136 R->L }
% 284.41/37.01 xor(not(n20), xor(X, and(not(n20), X)))
% 284.41/37.01 = { by lemma 54 }
% 284.41/37.01 or(not(n20), X)
% 284.41/37.01
% 284.41/37.01 Lemma 244: and(not(X), or(n22, n14)) = not(or(not(n20), X)).
% 284.41/37.01 Proof:
% 284.41/37.01 and(not(X), or(n22, n14))
% 284.41/37.01 = { by lemma 66 }
% 284.41/37.01 and(not(X), not(not(n20)))
% 284.41/37.01 = { by lemma 55 R->L }
% 284.41/37.01 xor(not(X), and(not(X), not(n20)))
% 284.41/37.01 = { by lemma 239 R->L }
% 284.41/37.01 xor(not(X), xor(and(X, inv1), not(n20)))
% 284.41/37.01 = { by axiom 44 (xor_commutativity) }
% 284.41/37.01 xor(and(X, inv1), xor(not(X), not(n20)))
% 284.41/37.01 = { by lemma 240 R->L }
% 284.41/37.01 xor(and(X, inv1), xor(or(n22, n14), X))
% 284.41/37.01 = { by lemma 241 R->L }
% 284.41/37.01 xor(and(X, inv1), xor(not(X), not(or(n22, n14))))
% 284.41/37.01 = { by lemma 59 R->L }
% 284.41/37.01 xor(and(X, inv1), not(xor(not(X), or(n22, n14))))
% 284.41/37.01 = { by lemma 59 R->L }
% 284.41/37.01 not(xor(and(X, inv1), xor(not(X), or(n22, n14))))
% 284.41/37.01 = { by lemma 243 }
% 284.41/37.01 not(or(not(n20), X))
% 284.41/37.01
% 284.41/37.01 Lemma 245: xor(and(inv1, i2), and(n23, inv2)) = xor(not(i2), not(n20)).
% 284.41/37.01 Proof:
% 284.41/37.01 xor(and(inv1, i2), and(n23, inv2))
% 284.41/37.01 = { by axiom 43 (xor_simplification1) R->L }
% 284.41/37.01 xor(and(inv1, i2), xor(and(i1, i3), xor(and(i1, i3), and(n23, inv2))))
% 284.41/37.01 = { by lemma 218 R->L }
% 284.41/37.01 xor(and(inv1, i2), xor(and(i1, i3), xor(and(i1, i3), and(and(i1, i3), not(n9)))))
% 284.41/37.01 = { by lemma 55 }
% 284.41/37.01 xor(and(inv1, i2), xor(and(i1, i3), and(and(i1, i3), not(not(n9)))))
% 284.41/37.01 = { by lemma 65 R->L }
% 284.41/37.01 xor(and(inv1, i2), xor(and(i1, i3), and(and(i1, i3), or(n8, n2))))
% 284.41/37.01 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.01 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), and(i1, i3))))
% 284.41/37.01 = { by axiom 13 (xor_definition1) R->L }
% 284.41/37.01 xor(and(inv1, i2), xor(and(i1, i3), xor(n0, and(or(n8, n2), and(i1, i3)))))
% 284.41/37.01 = { by lemma 225 R->L }
% 284.41/37.01 xor(and(inv1, i2), xor(and(i1, i3), xor(and(and(inv2, n6), or(n8, n2)), and(or(n8, n2), and(i1, i3)))))
% 284.41/37.01 = { by lemma 81 }
% 284.41/37.01 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(inv2, n6), and(i1, i3)))))
% 284.41/37.01 = { by lemma 51 R->L }
% 284.41/37.01 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(inv2, n6), not(not(and(i1, i3)))))))
% 284.41/37.01 = { by lemma 50 R->L }
% 284.41/37.01 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(inv2, n6), not(xor(and(i1, i3), n1))))))
% 284.41/37.01 = { by lemma 49 R->L }
% 284.41/37.01 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(inv2, n6), not(xor(and(i1, i3), not(n0)))))))
% 284.41/37.01 = { by lemma 230 R->L }
% 284.41/37.01 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(inv2, n6), not(xor(and(i1, i3), not(and(and(i2, i3), and(inv2, n6)))))))))
% 284.41/37.01 = { by lemma 227 }
% 284.41/37.01 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(inv2, n6), not(xor(and(i1, i3), not(and(and(i2, i3), and(n23, inv2)))))))))
% 284.41/37.01 = { by lemma 220 R->L }
% 284.41/37.01 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(inv2, n6), not(xor(and(i1, i3), not(and(not(n9), and(and(i2, i3), and(i1, i3))))))))))
% 284.41/37.01 = { by lemma 93 }
% 284.41/37.01 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(inv2, n6), not(xor(and(i1, i3), not(and(not(n9), and(and(i1, i2), and(i1, i3))))))))))
% 284.41/37.01 = { by lemma 220 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(inv2, n6), not(xor(and(i1, i3), not(and(and(i1, i2), and(n23, inv2)))))))))
% 284.41/37.02 = { by lemma 219 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(inv2, n6), not(xor(and(i1, i3), not(and(and(i1, i3), and(and(i1, i2), not(n9))))))))))
% 284.41/37.02 = { by lemma 184 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(inv2, n6), not(xor(and(i1, i3), not(and(and(i1, i3), and(inv2, n6)))))))))
% 284.41/37.02 = { by lemma 231 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(inv2, n6), not(or(and(inv2, n6), not(and(i1, i3))))))))
% 284.41/37.02 = { by lemma 204 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), or(and(inv2, n6), not(not(and(i1, i3)))))))
% 284.41/37.02 = { by lemma 51 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), or(and(inv2, n6), and(i1, i3)))))
% 284.41/37.02 = { by lemma 64 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), or(and(i1, i3), and(inv2, n6)))))
% 284.41/37.02 = { by lemma 188 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), or(and(i1, i3), xor(and(n6, i3), and(i1, i2))))))
% 284.41/37.02 = { by lemma 100 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), or(and(i1, i3), xor(and(i1, i3), or(n23, n6))))))
% 284.41/37.02 = { by lemma 51 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), or(and(i1, i3), xor(and(i1, i3), not(not(or(n23, n6))))))))
% 284.41/37.02 = { by lemma 53 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), or(and(i1, i3), xor(not(and(i1, i3)), not(or(n23, n6)))))))
% 284.41/37.02 = { by lemma 75 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(i1, i3), and(not(and(i1, i3)), xor(not(and(i1, i3)), not(or(n23, n6))))))))
% 284.41/37.02 = { by lemma 187 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(i1, i3), and(not(and(i1, i3)), or(n23, n6))))))
% 284.41/37.02 = { by lemma 75 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), or(and(i1, i3), or(n23, n6)))))
% 284.41/37.02 = { by lemma 54 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(i1, i3), xor(or(n23, n6), and(and(i1, i3), or(n23, n6)))))))
% 284.41/37.02 = { by lemma 51 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(i1, i3), xor(or(n23, n6), and(and(i1, i3), not(not(or(n23, n6)))))))))
% 284.41/37.02 = { by lemma 55 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(i1, i3), xor(or(n23, n6), xor(and(i1, i3), and(and(i1, i3), not(or(n23, n6)))))))))
% 284.41/37.02 = { by lemma 162 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(i1, i3), xor(or(n23, n6), xor(and(i1, i3), n0))))))
% 284.41/37.02 = { by axiom 11 (xor_definition2) }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(i1, i3), xor(or(n23, n6), and(i1, i3))))))
% 284.41/37.02 = { by lemma 78 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), or(n23, n6))))
% 284.41/37.02 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n23, n6), or(n8, n2))))
% 284.41/37.02 = { by lemma 232 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(or(n23, n6), and(inv1, inv2)))))
% 284.41/37.02 = { by axiom 10 (xor_symmetry) }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(inv1, inv2), or(n23, n6)))))
% 284.41/37.02 = { by lemma 51 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(inv1, inv2), not(not(or(n23, n6)))))))
% 284.41/37.02 = { by lemma 59 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), not(xor(and(inv1, inv2), not(or(n23, n6)))))))
% 284.41/37.02 = { by lemma 50 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), not(xor(and(inv1, inv2), xor(or(n23, n6), n1))))))
% 284.41/37.02 = { by lemma 149 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), not(xor(and(inv1, inv2), xor(or(n23, n6), xor(n20, not(n20))))))))
% 284.41/37.02 = { by axiom 21 (constructor23) }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), not(xor(and(inv1, inv2), xor(or(n23, n6), xor(or(n22, n14), not(n20))))))))
% 284.41/37.02 = { by axiom 10 (xor_symmetry) }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), not(xor(and(inv1, inv2), xor(or(n23, n6), xor(not(n20), or(n22, n14))))))))
% 284.41/37.02 = { by axiom 44 (xor_commutativity) }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), not(xor(and(inv1, inv2), xor(not(n20), xor(or(n23, n6), or(n22, n14))))))))
% 284.41/37.02 = { by lemma 104 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), not(xor(and(inv1, inv2), xor(not(n20), xor(and(i2, i3), and(n6, i3))))))))
% 284.41/37.02 = { by axiom 44 (xor_commutativity) }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), not(xor(and(inv1, inv2), xor(and(i2, i3), xor(not(n20), and(n6, i3))))))))
% 284.41/37.02 = { by axiom 10 (xor_symmetry) }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), not(xor(and(inv1, inv2), xor(and(i2, i3), xor(and(n6, i3), not(n20))))))))
% 284.41/37.02 = { by lemma 235 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), not(xor(and(inv1, inv2), xor(and(i2, i3), xor(and(inv1, inv2), or(n8, n2))))))))
% 284.41/37.02 = { by axiom 44 (xor_commutativity) }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), not(xor(and(inv1, inv2), xor(and(inv1, inv2), xor(and(i2, i3), or(n8, n2))))))))
% 284.41/37.02 = { by axiom 43 (xor_simplification1) }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), not(xor(and(i2, i3), or(n8, n2))))))
% 284.41/37.02 = { by lemma 59 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(i2, i3), not(or(n8, n2))))))
% 284.41/37.02 = { by axiom 16 (constructor12) R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(and(i2, i3), not(n9)))))
% 284.41/37.02 = { by lemma 107 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), xor(or(n8, n2), not(and(i2, i3))))))
% 284.41/37.02 = { by lemma 187 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(or(n8, n2), and(i2, i3))))
% 284.41/37.02 = { by axiom 29 (and_symmetry) }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(and(i2, i3), or(n8, n2))))
% 284.41/37.02 = { by lemma 236 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), xor(and(i2, i3), and(n14, inv2))))
% 284.41/37.02 = { by lemma 238 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i3), and(n6, i3)))
% 284.41/37.02 = { by axiom 10 (xor_symmetry) }
% 284.41/37.02 xor(and(inv1, i2), xor(and(n6, i3), and(i1, i3)))
% 284.41/37.02 = { by lemma 94 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(and(i1, i2), or(n23, n6)))
% 284.41/37.02 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(or(n23, n6), and(i1, i2)))
% 284.41/37.02 = { by lemma 155 R->L }
% 284.41/37.02 xor(and(inv1, i2), xor(or(n23, n6), and(or(n23, n6), i2)))
% 284.41/37.02 = { by lemma 55 }
% 284.41/37.02 xor(and(inv1, i2), and(or(n23, n6), not(i2)))
% 284.41/37.02 = { by lemma 84 R->L }
% 284.41/37.02 xor(and(inv1, i2), and(or(n23, n6), not(or(i2, and(i2, i3)))))
% 284.41/37.02 = { by lemma 63 R->L }
% 284.41/37.02 xor(and(inv1, i2), and(or(n23, n6), and(not(i2), not(and(i2, i3)))))
% 284.41/37.02 = { by lemma 171 R->L }
% 284.41/37.02 xor(and(inv1, i2), and(and(or(n23, n6), not(and(i2, i3))), not(i2)))
% 284.41/37.02 = { by lemma 98 R->L }
% 284.41/37.02 xor(and(inv1, i2), and(not(i2), xor(and(i2, i3), and(or(n23, n6), not(and(i2, i3))))))
% 284.41/37.02 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.02 xor(and(inv1, i2), and(not(i2), xor(and(i2, i3), and(not(and(i2, i3)), or(n23, n6)))))
% 284.41/37.02 = { by lemma 51 R->L }
% 284.41/37.02 xor(and(inv1, i2), and(not(i2), xor(and(i2, i3), and(not(and(i2, i3)), not(not(or(n23, n6)))))))
% 284.41/37.02 = { by lemma 55 R->L }
% 284.41/37.02 xor(and(inv1, i2), and(not(i2), xor(and(i2, i3), xor(not(and(i2, i3)), and(not(and(i2, i3)), not(or(n23, n6)))))))
% 284.41/37.02 = { by lemma 115 }
% 284.41/37.02 xor(and(inv1, i2), and(not(i2), xor(and(i2, i3), xor(not(and(i2, i3)), not(n20)))))
% 284.41/37.02 = { by lemma 53 }
% 284.41/37.02 xor(and(inv1, i2), and(not(i2), xor(and(i2, i3), xor(and(i2, i3), not(not(n20))))))
% 284.41/37.02 = { by lemma 66 R->L }
% 284.41/37.02 xor(and(inv1, i2), and(not(i2), xor(and(i2, i3), xor(and(i2, i3), or(n22, n14)))))
% 284.41/37.02 = { by axiom 43 (xor_simplification1) }
% 284.41/37.02 xor(and(inv1, i2), and(not(i2), or(n22, n14)))
% 284.41/37.02 = { by lemma 244 }
% 284.41/37.02 xor(and(inv1, i2), not(or(not(n20), i2)))
% 284.41/37.02 = { by lemma 54 R->L }
% 284.41/37.02 xor(and(inv1, i2), not(xor(not(n20), xor(i2, and(not(n20), i2)))))
% 284.41/37.02 = { by axiom 8 (constructor29) R->L }
% 284.41/37.02 xor(and(inv1, i2), not(xor(not(n20), xor(i2, and(inv1, i2)))))
% 284.41/37.02 = { by axiom 10 (xor_symmetry) }
% 284.41/37.02 xor(and(inv1, i2), not(xor(not(n20), xor(and(inv1, i2), i2))))
% 284.41/37.02 = { by axiom 44 (xor_commutativity) }
% 284.41/37.02 xor(and(inv1, i2), not(xor(and(inv1, i2), xor(not(n20), i2))))
% 284.41/37.02 = { by lemma 242 R->L }
% 284.41/37.02 xor(and(inv1, i2), not(xor(and(inv1, i2), xor(not(i2), or(n22, n14)))))
% 284.41/37.02 = { by lemma 59 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(inv1, i2), not(xor(not(i2), or(n22, n14)))))
% 284.41/37.02 = { by lemma 59 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(inv1, i2), xor(not(i2), not(or(n22, n14)))))
% 284.41/37.02 = { by lemma 241 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(inv1, i2), xor(or(n22, n14), i2)))
% 284.41/37.02 = { by lemma 240 }
% 284.41/37.02 xor(and(inv1, i2), xor(and(inv1, i2), xor(not(i2), not(n20))))
% 284.41/37.02 = { by axiom 43 (xor_simplification1) }
% 284.41/37.02 xor(not(i2), not(n20))
% 284.41/37.02
% 284.41/37.02 Lemma 246: xor(or(n22, n14), and(X, not(n20))) = or(or(n22, n14), X).
% 284.41/37.02 Proof:
% 284.41/37.02 xor(or(n22, n14), and(X, not(n20)))
% 284.41/37.02 = { by axiom 21 (constructor23) R->L }
% 284.41/37.02 xor(n20, and(X, not(n20)))
% 284.41/37.02 = { by lemma 57 }
% 284.41/37.02 or(n20, X)
% 284.41/37.02 = { by axiom 21 (constructor23) }
% 284.41/37.02 or(or(n22, n14), X)
% 284.41/37.02
% 284.41/37.02 Lemma 247: xor(and(inv1, i2), xor(X, or(a1, n10))) = xor(X, or(n24, n7)).
% 284.41/37.02 Proof:
% 284.41/37.02 xor(and(inv1, i2), xor(X, or(a1, n10)))
% 284.41/37.02 = { by axiom 44 (xor_commutativity) R->L }
% 284.41/37.02 xor(X, xor(and(inv1, i2), or(a1, n10)))
% 284.41/37.02 = { by lemma 161 }
% 284.41/37.02 xor(X, or(n24, n7))
% 284.41/37.02
% 284.41/37.02 Lemma 248: and(and(X, inv2), and(i1, inv1)) = n0.
% 284.41/37.02 Proof:
% 284.41/37.02 and(and(X, inv2), and(i1, inv1))
% 284.41/37.02 = { by lemma 213 R->L }
% 284.41/37.02 and(and(X, inv2), and(and(i1, inv1), or(n8, n2)))
% 284.41/37.02 = { by lemma 208 }
% 284.41/37.02 n0
% 284.41/37.02
% 284.41/37.02 Lemma 249: xor(and(X, Z), and(Y, X)) = and(X, xor(Y, Z)).
% 284.41/37.02 Proof:
% 284.41/37.02 xor(and(X, Z), and(Y, X))
% 284.41/37.02 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.02 xor(and(X, Z), and(X, Y))
% 284.41/37.02 = { by axiom 48 (and_xor_simplification) R->L }
% 284.41/37.02 and(X, xor(Z, Y))
% 284.41/37.02 = { by axiom 10 (xor_symmetry) }
% 284.41/37.02 and(X, xor(Y, Z))
% 284.41/37.02
% 284.41/37.02 Lemma 250: and(and(inv1, i2), i1) = n0.
% 284.41/37.03 Proof:
% 284.41/37.03 and(and(inv1, i2), i1)
% 284.41/37.03 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.03 and(i1, and(inv1, i2))
% 284.41/37.03 = { by lemma 133 R->L }
% 284.41/37.03 and(not(n20), and(i2, i1))
% 284.41/37.03 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.03 and(not(n20), and(i1, i2))
% 284.41/37.03 = { by axiom 29 (and_symmetry) }
% 284.41/37.03 and(and(i1, i2), not(n20))
% 284.41/37.03 = { by lemma 132 R->L }
% 284.41/37.03 and(and(inv1, i2), and(i1, i2))
% 284.41/37.03 = { by lemma 146 R->L }
% 284.41/37.03 and(and(inv1, i2), and(i1, inv1))
% 284.41/37.03 = { by lemma 156 }
% 284.41/37.03 n0
% 284.41/37.03
% 284.41/37.03 Lemma 251: not(or(X, not(Y))) = and(Y, not(X)).
% 284.41/37.03 Proof:
% 284.41/37.03 not(or(X, not(Y)))
% 284.41/37.03 = { by lemma 64 }
% 284.41/37.03 not(or(not(Y), X))
% 284.41/37.03 = { by lemma 195 R->L }
% 284.41/37.03 not(not(and(Y, not(X))))
% 284.41/37.03 = { by lemma 51 }
% 284.41/37.03 and(Y, not(X))
% 284.41/37.03
% 284.41/37.03 Lemma 252: xor(and(i2, i3), and(n6, i3)) = and(not(i1), or(n22, n14)).
% 284.41/37.03 Proof:
% 284.41/37.03 xor(and(i2, i3), and(n6, i3))
% 284.41/37.03 = { by lemma 104 }
% 284.41/37.03 xor(or(n23, n6), or(n22, n14))
% 284.41/37.03 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.03 xor(or(n22, n14), or(n23, n6))
% 284.41/37.03 = { by lemma 197 R->L }
% 284.41/37.03 xor(or(n22, n14), xor(and(i1, inv1), i1))
% 284.41/37.03 = { by lemma 196 R->L }
% 284.41/37.03 xor(or(n22, n14), and(or(n22, n14), i1))
% 284.41/37.03 = { by lemma 60 R->L }
% 284.41/37.03 not(or(not(or(n22, n14)), i1))
% 284.41/37.03 = { by axiom 21 (constructor23) R->L }
% 284.41/37.03 not(or(not(n20), i1))
% 284.41/37.03 = { by lemma 244 R->L }
% 284.41/37.03 and(not(i1), or(n22, n14))
% 284.41/37.03
% 284.41/37.03 Lemma 253: xor(and(i2, X), and(n6, X)) = and(and(i2, X), not(i1)).
% 284.41/37.03 Proof:
% 284.41/37.03 xor(and(i2, X), and(n6, X))
% 284.41/37.03 = { by lemma 90 R->L }
% 284.41/37.03 xor(and(i2, X), and(and(i2, X), and(i1, X)))
% 284.41/37.03 = { by lemma 87 }
% 284.41/37.03 xor(and(i2, X), and(and(i2, X), i1))
% 284.41/37.03 = { by lemma 55 }
% 284.41/37.03 and(and(i2, X), not(i1))
% 284.41/37.03
% 284.41/37.03 Lemma 254: xor(and(i2, i3), and(n6, i3)) = and(n14, inv2).
% 284.41/37.03 Proof:
% 284.41/37.03 xor(and(i2, i3), and(n6, i3))
% 284.41/37.03 = { by lemma 238 R->L }
% 284.41/37.03 xor(and(i2, i3), xor(and(i2, i3), and(n14, inv2)))
% 284.41/37.03 = { by axiom 43 (xor_simplification1) }
% 284.41/37.03 and(n14, inv2)
% 284.41/37.03
% 284.41/37.03 Lemma 255: and(and(i2, i3), and(n14, inv2)) = and(n14, inv2).
% 284.41/37.03 Proof:
% 284.41/37.03 and(and(i2, i3), and(n14, inv2))
% 284.41/37.03 = { by lemma 228 R->L }
% 284.41/37.03 and(and(i2, i3), and(and(i2, i3), not(n9)))
% 284.41/37.03 = { by axiom 45 (and_simplification2) }
% 284.41/37.03 and(and(i2, i3), not(n9))
% 284.41/37.03 = { by lemma 228 }
% 284.41/37.03 and(n14, inv2)
% 284.41/37.03
% 284.41/37.03 Lemma 256: and(and(i2, i3), and(not(n9), X)) = and(X, and(n14, inv2)).
% 284.41/37.03 Proof:
% 284.41/37.03 and(and(i2, i3), and(not(n9), X))
% 284.41/37.03 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.03 and(and(i2, i3), and(X, not(n9)))
% 284.41/37.03 = { by lemma 229 }
% 284.41/37.03 and(X, and(n14, inv2))
% 284.41/37.03
% 284.41/37.03 Lemma 257: and(not(n9), xor(and(i2, i3), X)) = xor(and(n14, inv2), and(X, not(n9))).
% 284.41/37.03 Proof:
% 284.41/37.03 and(not(n9), xor(and(i2, i3), X))
% 284.41/37.03 = { by axiom 39 (constructor17) R->L }
% 284.41/37.03 and(not(n9), xor(n14, X))
% 284.41/37.03 = { by axiom 48 (and_xor_simplification) }
% 284.41/37.03 xor(and(not(n9), n14), and(not(n9), X))
% 284.41/37.03 = { by lemma 205 }
% 284.41/37.03 xor(and(n14, inv2), and(not(n9), X))
% 284.41/37.03 = { by axiom 29 (and_symmetry) }
% 284.41/37.03 xor(and(n14, inv2), and(X, not(n9)))
% 284.41/37.03
% 284.41/37.03 Lemma 258: or(i1, and(n14, inv2)) = xor(and(n14, inv2), i1).
% 284.41/37.03 Proof:
% 284.41/37.03 or(i1, and(n14, inv2))
% 284.41/37.03 = { by lemma 57 R->L }
% 284.41/37.03 xor(i1, and(and(n14, inv2), not(i1)))
% 284.41/37.03 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.03 xor(i1, and(not(i1), and(n14, inv2)))
% 284.41/37.03 = { by lemma 255 R->L }
% 284.41/37.03 xor(i1, and(not(i1), and(and(i2, i3), and(n14, inv2))))
% 284.41/37.03 = { by axiom 46 (and_commutativity) }
% 284.41/37.03 xor(i1, and(and(i2, i3), and(not(i1), and(n14, inv2))))
% 284.41/37.03 = { by axiom 29 (and_symmetry) }
% 284.41/37.03 xor(i1, and(and(i2, i3), and(and(n14, inv2), not(i1))))
% 284.41/37.03 = { by lemma 62 R->L }
% 284.41/37.03 xor(i1, and(and(i2, i3), xor(and(n14, inv2), and(i1, and(n14, inv2)))))
% 284.41/37.03 = { by lemma 256 R->L }
% 284.41/37.03 xor(i1, and(and(i2, i3), xor(and(n14, inv2), and(and(i2, i3), and(not(n9), i1)))))
% 284.41/37.03 = { by lemma 171 R->L }
% 284.41/37.03 xor(i1, and(and(i2, i3), xor(and(n14, inv2), and(and(and(i2, i3), i1), not(n9)))))
% 284.41/37.03 = { by lemma 257 R->L }
% 284.41/37.03 xor(i1, and(and(i2, i3), and(not(n9), xor(and(i2, i3), and(and(i2, i3), i1)))))
% 284.41/37.03 = { by lemma 55 }
% 284.41/37.03 xor(i1, and(and(i2, i3), and(not(n9), and(and(i2, i3), not(i1)))))
% 284.41/37.03 = { by lemma 253 R->L }
% 284.41/37.03 xor(i1, and(and(i2, i3), and(not(n9), xor(and(i2, i3), and(n6, i3)))))
% 284.41/37.03 = { by lemma 257 }
% 284.41/37.03 xor(i1, and(and(i2, i3), xor(and(n14, inv2), and(and(n6, i3), not(n9)))))
% 284.41/37.03 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.03 xor(i1, and(and(i2, i3), xor(and(n14, inv2), and(not(n9), and(n6, i3)))))
% 284.41/37.03 = { by lemma 90 R->L }
% 284.41/37.03 xor(i1, and(and(i2, i3), xor(and(n14, inv2), and(not(n9), and(and(i2, i3), and(i1, i3))))))
% 284.41/37.03 = { by lemma 220 }
% 284.41/37.03 xor(i1, and(and(i2, i3), xor(and(n14, inv2), and(and(i2, i3), and(n23, inv2)))))
% 284.41/37.03 = { by lemma 227 R->L }
% 284.41/37.03 xor(i1, and(and(i2, i3), xor(and(n14, inv2), and(and(i2, i3), and(inv2, n6)))))
% 284.41/37.03 = { by axiom 48 (and_xor_simplification) }
% 284.41/37.03 xor(i1, xor(and(and(i2, i3), and(n14, inv2)), and(and(i2, i3), and(and(i2, i3), and(inv2, n6)))))
% 284.41/37.03 = { by lemma 255 }
% 284.41/37.03 xor(i1, xor(and(n14, inv2), and(and(i2, i3), and(and(i2, i3), and(inv2, n6)))))
% 284.41/37.03 = { by lemma 230 }
% 284.41/37.03 xor(i1, xor(and(n14, inv2), and(and(i2, i3), n0)))
% 284.41/37.03 = { by axiom 31 (and_definition2) }
% 284.41/37.03 xor(i1, xor(and(n14, inv2), n0))
% 284.41/37.03 = { by axiom 11 (xor_definition2) }
% 284.41/37.03 xor(i1, and(n14, inv2))
% 284.41/37.03 = { by axiom 10 (xor_symmetry) }
% 284.41/37.03 xor(and(n14, inv2), i1)
% 284.41/37.03
% 284.41/37.03 Lemma 259: and(and(inv1, inv2), and(i2, i3)) = n0.
% 284.41/37.03 Proof:
% 284.41/37.03 and(and(inv1, inv2), and(i2, i3))
% 284.41/37.03 = { by lemma 51 R->L }
% 284.41/37.03 and(and(inv1, inv2), not(not(and(i2, i3))))
% 284.41/37.03 = { by lemma 55 R->L }
% 284.41/37.03 xor(and(inv1, inv2), and(and(inv1, inv2), not(and(i2, i3))))
% 284.41/37.03 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.03 xor(and(inv1, inv2), and(not(and(i2, i3)), and(inv1, inv2)))
% 284.41/37.03 = { by lemma 74 R->L }
% 284.41/37.03 xor(and(inv1, inv2), and(not(n9), and(not(n20), not(and(i2, i3)))))
% 284.41/37.03 = { by lemma 116 }
% 284.41/37.03 xor(and(inv1, inv2), and(not(n9), not(n20)))
% 284.41/37.03 = { by lemma 67 }
% 284.41/37.03 xor(and(inv1, inv2), and(inv1, inv2))
% 284.41/37.03 = { by axiom 9 (xor_definition3) }
% 284.41/37.03 n0
% 284.41/37.03
% 284.41/37.03 Lemma 260: xor(not(n20), and(or(n22, n14), X)) = or(not(n20), X).
% 284.41/37.03 Proof:
% 284.41/37.03 xor(not(n20), and(or(n22, n14), X))
% 284.41/37.03 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.03 xor(not(n20), and(X, or(n22, n14)))
% 284.41/37.03 = { by lemma 234 }
% 284.41/37.03 or(not(n20), X)
% 284.41/37.03
% 284.41/37.03 Lemma 261: xor(not(n20), or(n2, n24)) = and(not(i3), not(i1)).
% 284.41/37.03 Proof:
% 284.41/37.03 xor(not(n20), or(n2, n24))
% 284.41/37.03 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.03 xor(or(n2, n24), not(n20))
% 284.41/37.03 = { by axiom 21 (constructor23) }
% 284.41/37.03 xor(or(n2, n24), not(or(n22, n14)))
% 284.41/37.03 = { by lemma 59 R->L }
% 284.41/37.03 not(xor(or(n2, n24), or(n22, n14)))
% 284.41/37.03 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.03 not(xor(or(n22, n14), or(n2, n24)))
% 284.41/37.03 = { by lemma 216 R->L }
% 284.41/37.03 not(xor(or(n22, n14), and(not(n20), or(n2, n24))))
% 284.41/37.03 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.03 not(xor(or(n22, n14), and(or(n2, n24), not(n20))))
% 284.41/37.03 = { by lemma 246 }
% 284.41/37.03 not(or(or(n22, n14), or(n2, n24)))
% 284.41/37.03 = { by lemma 64 R->L }
% 284.41/37.03 not(or(or(n2, n24), or(n22, n14)))
% 284.41/37.03 = { by lemma 66 }
% 284.41/37.03 not(or(or(n2, n24), not(not(n20))))
% 284.41/37.03 = { by lemma 251 }
% 284.41/37.03 and(not(n20), not(or(n2, n24)))
% 284.41/37.03 = { by axiom 43 (xor_simplification1) R->L }
% 284.41/37.03 and(not(n20), xor(and(inv1, i3), xor(and(inv1, i3), not(or(n2, n24)))))
% 284.41/37.03 = { by lemma 59 R->L }
% 284.41/37.03 and(not(n20), xor(and(inv1, i3), not(xor(and(inv1, i3), or(n2, n24)))))
% 284.41/37.03 = { by lemma 53 R->L }
% 284.41/37.03 and(not(n20), xor(not(and(inv1, i3)), xor(and(inv1, i3), or(n2, n24))))
% 284.41/37.03 = { by lemma 211 }
% 284.41/37.03 and(not(n20), xor(not(and(inv1, i3)), and(i1, inv1)))
% 284.41/37.03 = { by lemma 53 }
% 284.41/37.03 and(not(n20), xor(and(inv1, i3), not(and(i1, inv1))))
% 284.41/37.03 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.03 and(not(n20), xor(not(and(i1, inv1)), and(inv1, i3)))
% 284.41/37.03 = { by lemma 199 }
% 284.41/37.03 xor(and(inv1, i3), and(not(and(i1, inv1)), not(n20)))
% 284.41/37.03 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.03 xor(and(inv1, i3), and(not(n20), not(and(i1, inv1))))
% 284.41/37.03 = { by axiom 8 (constructor29) }
% 284.41/37.03 xor(and(not(n20), i3), and(not(n20), not(and(i1, inv1))))
% 284.41/37.03 = { by axiom 48 (and_xor_simplification) R->L }
% 284.41/37.03 and(not(n20), xor(i3, not(and(i1, inv1))))
% 284.41/37.03 = { by lemma 52 R->L }
% 284.41/37.03 and(not(n20), xor(and(i1, inv1), not(i3)))
% 284.41/37.03 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.03 and(not(n20), xor(not(i3), and(i1, inv1)))
% 284.41/37.03 = { by lemma 138 }
% 284.41/37.03 xor(and(i1, inv1), and(not(i3), not(n20)))
% 284.41/37.03 = { by lemma 190 R->L }
% 284.41/37.03 xor(and(i1, inv1), xor(and(inv1, i3), not(n20)))
% 284.41/37.03 = { by axiom 44 (xor_commutativity) }
% 284.41/37.03 xor(and(inv1, i3), xor(and(i1, inv1), not(n20)))
% 284.41/37.03 = { by lemma 239 }
% 284.41/37.03 xor(and(inv1, i3), and(not(i1), not(n20)))
% 284.41/37.03 = { by lemma 187 R->L }
% 284.41/37.03 xor(and(inv1, i3), and(not(i1), xor(not(i1), not(not(n20)))))
% 284.41/37.03 = { by lemma 66 R->L }
% 284.41/37.03 xor(and(inv1, i3), and(not(i1), xor(not(i1), or(n22, n14))))
% 284.41/37.03 = { by axiom 43 (xor_simplification1) R->L }
% 284.41/37.03 xor(and(inv1, i3), and(not(i1), xor(and(i1, inv1), xor(and(i1, inv1), xor(not(i1), or(n22, n14))))))
% 284.41/37.03 = { by lemma 243 }
% 284.41/37.03 xor(and(inv1, i3), and(not(i1), xor(and(i1, inv1), or(not(n20), i1))))
% 284.41/37.03 = { by lemma 98 }
% 284.41/37.03 xor(and(inv1, i3), and(or(not(n20), i1), not(i1)))
% 284.41/37.03 = { by lemma 51 R->L }
% 284.41/37.03 xor(and(inv1, i3), and(not(not(or(not(n20), i1))), not(i1)))
% 284.41/37.03 = { by lemma 244 R->L }
% 284.41/37.03 xor(and(inv1, i3), and(not(and(not(i1), or(n22, n14))), not(i1)))
% 284.41/37.03 = { by lemma 252 R->L }
% 284.41/37.03 xor(and(inv1, i3), and(not(xor(and(i2, i3), and(n6, i3))), not(i1)))
% 284.41/37.03 = { by lemma 253 }
% 284.41/37.03 xor(and(inv1, i3), and(not(and(and(i2, i3), not(i1))), not(i1)))
% 284.41/37.03 = { by lemma 186 R->L }
% 284.41/37.03 xor(and(inv1, i3), and(xor(i1, not(or(i1, and(i2, i3)))), not(i1)))
% 284.41/37.04 = { by lemma 75 R->L }
% 284.41/37.04 xor(and(inv1, i3), and(xor(i1, not(xor(i1, and(not(i1), and(i2, i3))))), not(i1)))
% 284.41/37.04 = { by axiom 45 (and_simplification2) R->L }
% 284.41/37.04 xor(and(inv1, i3), and(xor(i1, not(xor(i1, and(not(i1), and(not(i1), and(i2, i3)))))), not(i1)))
% 284.41/37.04 = { by lemma 75 }
% 284.41/37.04 xor(and(inv1, i3), and(xor(i1, not(or(i1, and(not(i1), and(i2, i3))))), not(i1)))
% 284.41/37.04 = { by axiom 29 (and_symmetry) }
% 284.41/37.04 xor(and(inv1, i3), and(xor(i1, not(or(i1, and(and(i2, i3), not(i1))))), not(i1)))
% 284.41/37.04 = { by lemma 253 R->L }
% 284.41/37.04 xor(and(inv1, i3), and(xor(i1, not(or(i1, xor(and(i2, i3), and(n6, i3))))), not(i1)))
% 284.41/37.04 = { by lemma 254 }
% 284.41/37.04 xor(and(inv1, i3), and(xor(i1, not(or(i1, and(n14, inv2)))), not(i1)))
% 284.41/37.04 = { by lemma 258 }
% 284.41/37.04 xor(and(inv1, i3), and(xor(i1, not(xor(and(n14, inv2), i1))), not(i1)))
% 284.41/37.04 = { by lemma 52 }
% 284.41/37.04 xor(and(inv1, i3), and(xor(xor(and(n14, inv2), i1), not(i1)), not(i1)))
% 284.41/37.04 = { by lemma 180 }
% 284.41/37.04 xor(and(inv1, i3), and(xor(and(n14, inv2), xor(not(i1), i1)), not(i1)))
% 284.41/37.04 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.04 xor(and(inv1, i3), and(xor(and(n14, inv2), xor(i1, not(i1))), not(i1)))
% 284.41/37.04 = { by lemma 149 }
% 284.41/37.04 xor(and(inv1, i3), and(xor(and(n14, inv2), n1), not(i1)))
% 284.41/37.04 = { by lemma 50 }
% 284.41/37.04 xor(and(inv1, i3), and(not(and(n14, inv2)), not(i1)))
% 284.41/37.04 = { by axiom 29 (and_symmetry) }
% 284.41/37.04 xor(and(inv1, i3), and(not(i1), not(and(n14, inv2))))
% 284.41/37.04 = { by lemma 63 }
% 284.41/37.04 xor(and(inv1, i3), not(or(i1, and(n14, inv2))))
% 284.41/37.04 = { by lemma 258 }
% 284.41/37.04 xor(and(inv1, i3), not(xor(and(n14, inv2), i1)))
% 284.41/37.04 = { by lemma 59 }
% 284.41/37.04 xor(and(inv1, i3), xor(and(n14, inv2), not(i1)))
% 284.41/37.04 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.04 xor(and(inv1, i3), xor(not(i1), and(n14, inv2)))
% 284.41/37.04 = { by axiom 44 (xor_commutativity) R->L }
% 284.41/37.04 xor(not(i1), xor(and(inv1, i3), and(n14, inv2)))
% 284.41/37.04 = { by lemma 228 R->L }
% 284.41/37.04 xor(not(i1), xor(and(inv1, i3), and(and(i2, i3), not(n9))))
% 284.41/37.04 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.04 xor(not(i1), xor(and(inv1, i3), and(not(n9), and(i2, i3))))
% 284.41/37.04 = { by lemma 112 R->L }
% 284.41/37.04 xor(not(i1), xor(and(inv1, i3), and(and(i2, i3), and(not(n9), i3))))
% 284.41/37.04 = { by lemma 256 }
% 284.41/37.04 xor(not(i1), xor(and(inv1, i3), and(i3, and(n14, inv2))))
% 284.41/37.04 = { by axiom 8 (constructor29) }
% 284.41/37.04 xor(not(i1), xor(and(not(n20), i3), and(i3, and(n14, inv2))))
% 284.41/37.04 = { by lemma 81 }
% 284.41/37.04 xor(not(i1), and(i3, xor(not(n20), and(n14, inv2))))
% 284.41/37.04 = { by axiom 11 (xor_definition2) R->L }
% 284.41/37.04 xor(not(i1), and(i3, xor(not(n20), xor(and(n14, inv2), n0))))
% 284.41/37.04 = { by lemma 259 R->L }
% 284.41/37.04 xor(not(i1), and(i3, xor(not(n20), xor(and(n14, inv2), and(and(inv1, inv2), and(i2, i3))))))
% 284.41/37.04 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.04 xor(not(i1), and(i3, xor(not(n20), xor(and(n14, inv2), and(and(i2, i3), and(inv1, inv2))))))
% 284.41/37.04 = { by lemma 228 R->L }
% 284.41/37.04 xor(not(i1), and(i3, xor(not(n20), xor(and(and(i2, i3), not(n9)), and(and(i2, i3), and(inv1, inv2))))))
% 284.41/37.04 = { by axiom 48 (and_xor_simplification) R->L }
% 284.41/37.04 xor(not(i1), and(i3, xor(not(n20), and(and(i2, i3), xor(not(n9), and(inv1, inv2))))))
% 284.41/37.04 = { by axiom 10 (xor_symmetry) }
% 284.41/37.04 xor(not(i1), and(i3, xor(not(n20), and(and(i2, i3), xor(and(inv1, inv2), not(n9))))))
% 284.41/37.04 = { by lemma 108 R->L }
% 284.41/37.04 xor(not(i1), and(i3, xor(not(n20), and(and(i2, i3), and(not(n9), or(n22, n14))))))
% 284.41/37.04 = { by lemma 256 }
% 284.41/37.04 xor(not(i1), and(i3, xor(not(n20), and(or(n22, n14), and(n14, inv2)))))
% 284.41/37.04 = { by axiom 29 (and_symmetry) }
% 284.41/37.04 xor(not(i1), and(i3, xor(not(n20), and(and(n14, inv2), or(n22, n14)))))
% 284.41/37.04 = { by lemma 234 }
% 284.41/37.04 xor(not(i1), and(i3, or(not(n20), and(n14, inv2))))
% 284.41/37.04 = { by lemma 254 R->L }
% 284.41/37.04 xor(not(i1), and(i3, or(not(n20), xor(and(i2, i3), and(n6, i3)))))
% 284.41/37.04 = { by lemma 252 }
% 284.41/37.04 xor(not(i1), and(i3, or(not(n20), and(not(i1), or(n22, n14)))))
% 284.41/37.04 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.04 xor(not(i1), and(i3, or(not(n20), and(or(n22, n14), not(i1)))))
% 284.41/37.04 = { by lemma 260 R->L }
% 284.41/37.04 xor(not(i1), and(i3, xor(not(n20), and(or(n22, n14), and(or(n22, n14), not(i1))))))
% 284.41/37.04 = { by axiom 45 (and_simplification2) }
% 284.41/37.04 xor(not(i1), and(i3, xor(not(n20), and(or(n22, n14), not(i1)))))
% 284.41/37.04 = { by lemma 260 }
% 284.41/37.04 xor(not(i1), and(i3, or(not(n20), not(i1))))
% 284.41/37.04 = { by lemma 234 R->L }
% 284.41/37.04 xor(not(i1), and(i3, xor(not(n20), and(not(i1), or(n22, n14)))))
% 284.41/37.04 = { by lemma 244 }
% 284.41/37.04 xor(not(i1), and(i3, xor(not(n20), not(or(not(n20), i1)))))
% 284.41/37.04 = { by lemma 186 }
% 284.41/37.04 xor(not(i1), and(i3, not(and(i1, not(not(n20))))))
% 284.41/37.04 = { by lemma 66 R->L }
% 284.41/37.04 xor(not(i1), and(i3, not(and(i1, or(n22, n14)))))
% 284.41/37.04 = { by axiom 29 (and_symmetry) }
% 284.41/37.04 xor(not(i1), and(i3, not(and(or(n22, n14), i1))))
% 284.41/37.04 = { by lemma 196 }
% 284.41/37.04 xor(not(i1), and(i3, not(xor(and(i1, inv1), i1))))
% 284.41/37.04 = { by lemma 197 }
% 284.41/37.04 xor(not(i1), and(i3, not(or(n23, n6))))
% 284.41/37.04 = { by lemma 61 R->L }
% 284.41/37.04 xor(not(i1), not(or(not(i3), or(n23, n6))))
% 284.41/37.04 = { by lemma 197 R->L }
% 284.41/37.04 xor(not(i1), not(or(not(i3), xor(and(i1, inv1), i1))))
% 284.41/37.04 = { by lemma 58 R->L }
% 284.41/37.04 xor(not(i1), not(xor(i3, not(and(i3, xor(and(i1, inv1), i1))))))
% 284.41/37.04 = { by lemma 99 R->L }
% 284.41/37.04 xor(not(i1), not(xor(i3, not(xor(and(i1, i3), and(and(i1, inv1), i3))))))
% 284.41/37.04 = { by lemma 52 }
% 284.41/37.04 xor(not(i1), not(xor(xor(and(i1, i3), and(and(i1, inv1), i3)), not(i3))))
% 284.41/37.04 = { by lemma 180 }
% 284.41/37.04 xor(not(i1), not(xor(and(i1, i3), xor(not(i3), and(and(i1, inv1), i3)))))
% 284.41/37.04 = { by lemma 147 R->L }
% 284.41/37.04 xor(not(i1), not(xor(and(i1, i3), xor(not(i3), and(and(inv1, i3), and(i1, inv1))))))
% 284.41/37.04 = { by lemma 163 }
% 284.41/37.04 xor(not(i1), not(xor(and(i1, i3), xor(not(i3), n0))))
% 284.41/37.04 = { by axiom 11 (xor_definition2) }
% 284.41/37.04 xor(not(i1), not(xor(and(i1, i3), not(i3))))
% 284.41/37.04 = { by lemma 59 }
% 284.41/37.04 xor(not(i1), xor(and(i1, i3), not(not(i3))))
% 284.41/37.04 = { by lemma 51 }
% 284.41/37.04 xor(not(i1), xor(and(i1, i3), i3))
% 284.41/37.04 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.04 xor(not(i1), xor(i3, and(i1, i3)))
% 284.41/37.04 = { by lemma 62 }
% 284.41/37.04 xor(not(i1), and(i3, not(i1)))
% 284.41/37.04 = { by axiom 29 (and_symmetry) }
% 284.41/37.04 xor(not(i1), and(not(i1), i3))
% 284.41/37.04 = { by lemma 55 }
% 284.41/37.04 and(not(i1), not(i3))
% 284.41/37.04 = { by axiom 29 (and_symmetry) }
% 284.41/37.04 and(not(i3), not(i1))
% 284.41/37.04
% 284.41/37.04 Lemma 262: and(not(X), not(Y)) = not(or(Y, X)).
% 284.41/37.04 Proof:
% 284.41/37.04 and(not(X), not(Y))
% 284.41/37.04 = { by lemma 251 R->L }
% 284.41/37.04 not(or(Y, not(not(X))))
% 284.41/37.04 = { by lemma 51 }
% 284.41/37.05 not(or(Y, X))
% 284.41/37.05
% 284.41/37.05 Lemma 263: circuit(not(i3)) = circuit(not(i2)).
% 284.41/37.05 Proof:
% 284.41/37.05 circuit(not(i3))
% 284.41/37.05 = { by lemma 203 }
% 284.41/37.05 circuit(o1)
% 284.41/37.05 = { by axiom 4 (output1) }
% 284.41/37.05 true
% 284.41/37.05 = { by axiom 5 (output2) R->L }
% 284.41/37.05 circuit(o2)
% 284.41/37.05 = { by axiom 2 (constructor2) }
% 284.41/37.05 circuit(n17)
% 284.41/37.05 = { by axiom 19 (constructor20) }
% 284.41/37.05 circuit(or(n18, n21))
% 284.41/37.05 = { by axiom 20 (constructor21) }
% 284.41/37.05 circuit(or(or(n19, n25), n21))
% 284.41/37.05 = { by axiom 35 (constructor24) }
% 284.41/37.05 circuit(or(or(n19, n25), and(inv1, inv2)))
% 284.41/37.05 = { by lemma 64 R->L }
% 284.41/37.05 circuit(or(and(inv1, inv2), or(n19, n25)))
% 284.41/37.05 = { by lemma 51 R->L }
% 284.41/37.05 circuit(or(and(inv1, inv2), not(not(or(n19, n25)))))
% 284.41/37.05 = { by lemma 204 R->L }
% 284.41/37.05 circuit(xor(and(inv1, inv2), not(or(and(inv1, inv2), not(or(n19, n25))))))
% 284.41/37.05 = { by lemma 64 }
% 284.41/37.05 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), and(inv1, inv2)))))
% 284.41/37.05 = { by axiom 30 (and_definition4) R->L }
% 284.41/37.05 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), and(and(inv1, inv2), n1)))))
% 284.41/37.05 = { by lemma 49 R->L }
% 284.41/37.05 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), and(and(inv1, inv2), not(n0))))))
% 284.41/37.05 = { by lemma 208 R->L }
% 284.41/37.05 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), and(and(inv1, inv2), not(and(and(inv1, inv2), and(and(i1, inv1), or(n8, n2)))))))))
% 284.41/37.05 = { by lemma 123 }
% 284.41/37.05 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), and(and(inv1, inv2), not(and(and(i1, inv1), or(n8, n2))))))))
% 284.41/37.05 = { by lemma 213 }
% 284.41/37.05 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), and(and(inv1, inv2), not(and(i1, inv1)))))))
% 284.41/37.05 = { by lemma 55 R->L }
% 284.41/37.05 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(and(inv1, inv2), and(i1, inv1)))))))
% 284.41/37.05 = { by lemma 214 }
% 284.41/37.05 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(and(i1, inv1), not(n9)))))))
% 284.41/37.05 = { by axiom 16 (constructor12) }
% 284.41/37.05 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(and(i1, inv1), not(or(n8, n2))))))))
% 284.41/37.05 = { by lemma 85 R->L }
% 284.41/37.05 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(and(i1, inv1), not(or(or(n8, n2), and(and(inv1, i3), or(n8, n2))))))))))
% 284.41/37.05 = { by lemma 65 }
% 284.41/37.05 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(and(i1, inv1), not(or(or(n8, n2), and(and(inv1, i3), not(not(n9)))))))))))
% 284.41/37.05 = { by lemma 55 R->L }
% 284.41/37.05 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(and(i1, inv1), not(or(or(n8, n2), xor(and(inv1, i3), and(and(inv1, i3), not(n9)))))))))))
% 284.41/37.05 = { by lemma 70 R->L }
% 284.41/37.05 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(and(i1, inv1), not(or(or(n8, n2), xor(and(inv1, i3), and(and(inv1, i3), and(inv1, inv2)))))))))))
% 284.41/37.05 = { by lemma 73 }
% 284.41/37.05 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(and(i1, inv1), not(or(or(n8, n2), xor(and(inv1, i3), n0)))))))))
% 284.41/37.06 = { by axiom 11 (xor_definition2) }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(and(i1, inv1), not(or(or(n8, n2), and(inv1, i3)))))))))
% 284.41/37.06 = { by lemma 215 }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(and(i1, inv1), and(not(n9), not(and(inv1, i3)))))))))
% 284.41/37.06 = { by lemma 171 R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(and(and(i1, inv1), not(and(inv1, i3))), not(n9)))))))
% 284.41/37.06 = { by lemma 191 R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(not(n9), xor(and(inv1, i3), and(and(i1, inv1), not(and(inv1, i3))))))))))
% 284.41/37.06 = { by lemma 57 }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(not(n9), or(and(inv1, i3), and(i1, inv1))))))))
% 284.41/37.06 = { by axiom 40 (constructor27) R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(not(n9), or(and(inv1, i3), n24)))))))
% 284.41/37.06 = { by axiom 37 (constructor5) R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(not(n9), or(n2, n24)))))))
% 284.41/37.06 = { by lemma 216 R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(not(n9), and(not(n20), or(n2, n24))))))))
% 284.41/37.06 = { by lemma 74 }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(or(n2, n24), and(inv1, inv2)))))))
% 284.41/37.06 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(and(inv1, inv2), or(n2, n24)))))))
% 284.41/37.06 = { by axiom 13 (xor_definition1) R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), xor(n0, and(and(inv1, inv2), or(n2, n24))))))))
% 284.41/37.06 = { by lemma 217 R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), xor(and(and(inv1, inv2), and(i1, i3)), and(and(inv1, inv2), or(n2, n24))))))))
% 284.41/37.06 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), xor(and(and(i1, i3), and(inv1, inv2)), and(and(inv1, inv2), or(n2, n24))))))))
% 284.41/37.06 = { by lemma 206 R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), xor(and(and(i1, i3), and(and(inv1, inv2), not(n9))), and(and(inv1, inv2), or(n2, n24))))))))
% 284.41/37.06 = { by lemma 219 }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), xor(and(and(inv1, inv2), and(n23, inv2)), and(and(inv1, inv2), or(n2, n24))))))))
% 284.41/37.06 = { by axiom 48 (and_xor_simplification) R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(and(inv1, inv2), xor(and(n23, inv2), or(n2, n24))))))))
% 284.41/37.06 = { by lemma 223 }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(and(inv1, inv2), and(and(inv1, inv2), or(n19, n25)))))))
% 284.41/37.06 = { by lemma 60 R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), not(or(not(and(inv1, inv2)), or(n19, n25)))))))
% 284.41/37.06 = { by lemma 195 R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), not(not(and(and(inv1, inv2), not(or(n19, n25)))))))))
% 284.41/37.06 = { by lemma 224 }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), not(not(xor(or(n18, n21), or(n19, n25))))))))
% 284.41/37.06 = { by lemma 59 }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), not(xor(or(n18, n21), not(or(n19, n25))))))))
% 284.41/37.06 = { by lemma 59 }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(or(n18, n21), not(not(or(n19, n25))))))))
% 284.41/37.06 = { by lemma 51 }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), xor(or(n18, n21), or(n19, n25))))))
% 284.41/37.06 = { by lemma 224 R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(or(not(or(n19, n25)), and(and(inv1, inv2), not(or(n19, n25)))))))
% 284.41/37.06 = { by lemma 85 }
% 284.41/37.06 circuit(xor(and(inv1, inv2), not(not(or(n19, n25)))))
% 284.41/37.06 = { by lemma 51 }
% 284.41/37.06 circuit(xor(and(inv1, inv2), or(n19, n25)))
% 284.41/37.06 = { by lemma 223 R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), xor(and(n23, inv2), or(n2, n24))))
% 284.41/37.06 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.06 circuit(xor(and(inv1, inv2), xor(or(n2, n24), and(n23, inv2))))
% 284.41/37.06 = { by axiom 44 (xor_commutativity) R->L }
% 284.41/37.06 circuit(xor(or(n2, n24), xor(and(inv1, inv2), and(n23, inv2))))
% 284.41/37.06 = { by axiom 43 (xor_simplification1) R->L }
% 284.41/37.06 circuit(xor(or(n2, n24), xor(and(inv1, i2), xor(and(inv1, i2), xor(and(inv1, inv2), and(n23, inv2))))))
% 284.41/37.06 = { by lemma 180 R->L }
% 284.41/37.06 circuit(xor(or(n2, n24), xor(and(inv1, i2), xor(xor(and(inv1, i2), and(n23, inv2)), and(inv1, inv2)))))
% 284.41/37.06 = { by lemma 245 }
% 284.41/37.06 circuit(xor(or(n2, n24), xor(and(inv1, i2), xor(xor(not(i2), not(n20)), and(inv1, inv2)))))
% 284.41/37.06 = { by lemma 240 R->L }
% 284.41/37.06 circuit(xor(or(n2, n24), xor(and(inv1, i2), xor(xor(or(n22, n14), i2), and(inv1, inv2)))))
% 284.41/37.06 = { by lemma 180 }
% 284.41/37.06 circuit(xor(or(n2, n24), xor(and(inv1, i2), xor(or(n22, n14), xor(and(inv1, inv2), i2)))))
% 284.41/37.06 = { by lemma 180 R->L }
% 284.41/37.06 circuit(xor(or(n2, n24), xor(xor(and(inv1, i2), xor(and(inv1, inv2), i2)), or(n22, n14))))
% 284.41/37.06 = { by lemma 180 R->L }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(and(inv1, i2), xor(and(inv1, inv2), i2))))
% 284.41/37.06 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(and(inv1, i2), xor(i2, and(inv1, inv2)))))
% 284.41/37.06 = { by axiom 44 (xor_commutativity) R->L }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, xor(and(inv1, i2), and(inv1, inv2)))))
% 284.41/37.06 = { by lemma 51 R->L }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, xor(and(inv1, i2), not(not(and(inv1, inv2)))))))
% 284.41/37.06 = { by lemma 59 R->L }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(and(inv1, i2), not(and(inv1, inv2)))))))
% 284.41/37.06 = { by lemma 67 R->L }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(and(inv1, i2), not(and(not(n9), not(n20))))))))
% 284.41/37.06 = { by axiom 21 (constructor23) }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(and(inv1, i2), not(and(not(n9), not(or(n22, n14)))))))))
% 284.41/37.06 = { by lemma 215 R->L }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(and(inv1, i2), not(not(or(or(n8, n2), or(n22, n14)))))))))
% 284.41/37.06 = { by lemma 51 }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(and(inv1, i2), or(or(n8, n2), or(n22, n14)))))))
% 284.41/37.06 = { by lemma 64 }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(and(inv1, i2), or(or(n22, n14), or(n8, n2)))))))
% 284.41/37.06 = { by lemma 246 R->L }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(and(inv1, i2), xor(or(n22, n14), and(or(n8, n2), not(n20))))))))
% 284.41/37.06 = { by lemma 180 R->L }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(xor(and(inv1, i2), and(or(n8, n2), not(n20))), or(n22, n14))))))
% 284.41/37.06 = { by lemma 233 R->L }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(not(n20), not(xor(and(inv1, i2), and(or(n8, n2), not(n20)))))))))
% 284.41/37.06 = { by lemma 199 R->L }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(not(n20), not(and(not(n20), xor(or(n8, n2), and(inv1, i2)))))))))
% 284.41/37.06 = { by lemma 58 }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(not(not(n20)), xor(or(n8, n2), and(inv1, i2)))))))
% 284.41/37.06 = { by lemma 66 R->L }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(or(n8, n2), and(inv1, i2)))))))
% 284.41/37.06 = { by axiom 10 (xor_symmetry) }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i2), or(n8, n2)))))))
% 284.41/37.06 = { by axiom 43 (xor_simplification1) R->L }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i2), xor(and(inv1, i3), xor(and(inv1, i3), or(n8, n2)))))))))
% 284.41/37.06 = { by lemma 165 }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i2), xor(and(inv1, i3), or(a1, n10))))))))
% 284.41/37.06 = { by lemma 247 }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), or(n24, n7)))))))
% 284.41/37.06 = { by lemma 183 R->L }
% 284.41/37.06 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(or(a1, n10), i1)))))))
% 284.41/37.07 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, or(a1, n10))))))))
% 284.41/37.07 = { by axiom 13 (xor_definition1) R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(n0, and(i1, or(a1, n10)))))))))
% 284.41/37.07 = { by lemma 248 R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(and(inv1, inv2), and(i1, inv1)), and(i1, or(a1, n10)))))))))
% 284.41/37.07 = { by lemma 214 }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(and(i1, inv1), not(n9)), and(i1, or(a1, n10)))))))))
% 284.41/37.07 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(not(n9), and(i1, inv1)), and(i1, or(a1, n10)))))))))
% 284.41/37.07 = { by lemma 136 R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(not(n9), and(not(n20), i1)), and(i1, or(a1, n10)))))))))
% 284.41/37.07 = { by lemma 74 }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, and(inv1, inv2)), and(i1, or(a1, n10)))))))))
% 284.41/37.07 = { by axiom 29 (and_symmetry) }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(and(inv1, inv2), i1), and(i1, or(a1, n10)))))))))
% 284.41/37.07 = { by lemma 81 }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(inv1, inv2), or(a1, n10)))))))))
% 284.41/37.07 = { by lemma 165 R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(inv1, inv2), xor(and(inv1, i3), or(n8, n2))))))))))
% 284.41/37.07 = { by lemma 180 R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(xor(and(inv1, inv2), or(n8, n2)), and(inv1, i3)))))))))
% 284.41/37.07 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(inv1, i3), xor(and(inv1, inv2), or(n8, n2))))))))))
% 284.41/37.07 = { by lemma 235 }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(inv1, i3), xor(and(n6, i3), not(n20))))))))))
% 284.41/37.07 = { by axiom 44 (xor_commutativity) R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), xor(and(inv1, i3), not(n20))))))))))
% 284.41/37.07 = { by lemma 190 }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), and(not(i3), not(n20))))))))))
% 284.41/37.07 = { by lemma 201 R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), xor(not(i3), and(not(i3), or(n22, n14)))))))))))
% 284.41/37.07 = { by lemma 189 }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), xor(not(i3), and(inv2, n6))))))))))
% 284.41/37.07 = { by axiom 10 (xor_symmetry) }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), xor(and(inv2, n6), not(i3))))))))))
% 284.41/37.07 = { by lemma 59 R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(and(inv2, n6), i3))))))))))
% 284.41/37.07 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(inv2, n6)))))))))))
% 284.41/37.07 = { by axiom 30 (and_definition4) R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(inv2, n6), n1)))))))))))
% 284.41/37.07 = { by lemma 49 R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(inv2, n6), not(n0))))))))))))
% 284.41/37.07 = { by axiom 31 (and_definition2) R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(inv2, n6), not(and(xor(and(inv1, inv2), not(n20)), n0)))))))))))))
% 284.41/37.07 = { by lemma 225 R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(inv2, n6), not(and(xor(and(inv1, inv2), not(n20)), and(and(inv2, n6), or(n8, n2)))))))))))))))
% 284.41/37.07 = { by axiom 46 (and_commutativity) }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(inv2, n6), not(and(and(inv2, n6), and(xor(and(inv1, inv2), not(n20)), or(n8, n2)))))))))))))))
% 284.41/37.07 = { by lemma 65 }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(inv2, n6), not(and(and(inv2, n6), and(xor(and(inv1, inv2), not(n20)), not(not(n9))))))))))))))))
% 284.41/37.07 = { by lemma 56 R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(inv2, n6), not(and(and(inv2, n6), xor(not(n9), or(not(n9), xor(and(inv1, inv2), not(n20)))))))))))))))))
% 284.41/37.07 = { by axiom 48 (and_xor_simplification) }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(inv2, n6), not(xor(and(and(inv2, n6), not(n9)), and(and(inv2, n6), or(not(n9), xor(and(inv1, inv2), not(n20)))))))))))))))))
% 284.41/37.07 = { by lemma 79 }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(inv2, n6), not(xor(and(inv2, n6), and(and(inv2, n6), or(not(n9), xor(and(inv1, inv2), not(n20)))))))))))))))))
% 284.41/37.07 = { by lemma 55 }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(inv2, n6), not(and(and(inv2, n6), not(or(not(n9), xor(and(inv1, inv2), not(n20)))))))))))))))))
% 284.41/37.07 = { by lemma 123 }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(inv2, n6), not(not(or(not(n9), xor(and(inv1, inv2), not(n20))))))))))))))))
% 284.41/37.07 = { by lemma 51 }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(inv2, n6), or(not(n9), xor(and(inv1, inv2), not(n20))))))))))))))
% 284.41/37.07 = { by lemma 173 }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(inv2, n6), not(and(n6, i3)))))))))))))
% 284.41/37.07 = { by lemma 62 R->L }
% 284.41/37.07 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, xor(and(inv2, n6), and(and(n6, i3), and(inv2, n6)))))))))))))
% 284.41/37.08 = { by lemma 198 R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, xor(and(inv2, n6), and(not(n9), and(and(n6, i3), and(i1, i2))))))))))))))
% 284.41/37.08 = { by lemma 95 }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, xor(and(inv2, n6), and(not(n9), and(n6, i3)))))))))))))
% 284.41/37.08 = { by lemma 167 R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, xor(and(inv2, n6), and(and(i1, i2), and(not(n9), i3)))))))))))))
% 284.41/37.08 = { by axiom 29 (and_symmetry) }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, xor(and(inv2, n6), and(and(i1, i2), and(i3, not(n9))))))))))))))
% 284.41/37.08 = { by axiom 46 (and_commutativity) R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, xor(and(inv2, n6), and(i3, and(and(i1, i2), not(n9))))))))))))))
% 284.41/37.08 = { by lemma 184 }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, xor(and(inv2, n6), and(i3, and(inv2, n6)))))))))))))
% 284.41/37.08 = { by axiom 29 (and_symmetry) }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, xor(and(inv2, n6), and(and(inv2, n6), i3))))))))))))
% 284.41/37.08 = { by lemma 55 }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(inv2, n6), not(i3))))))))))))
% 284.41/37.08 = { by lemma 57 }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(or(i3, and(inv2, n6)))))))))))
% 284.41/37.08 = { by lemma 188 R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(or(i3, xor(and(n6, i3), and(i1, i2))))))))))))
% 284.41/37.08 = { by lemma 57 R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(xor(and(n6, i3), and(i1, i2)), not(i3))))))))))))
% 284.41/37.08 = { by lemma 105 }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(and(i1, i2), not(i3)), not(i3))))))))))))
% 284.41/37.08 = { by lemma 171 }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(i1, i2), and(not(i3), not(i3)))))))))))))
% 284.41/37.08 = { by axiom 28 (and_simplification1) }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(xor(i3, and(and(i1, i2), not(i3))))))))))))
% 284.41/37.08 = { by lemma 57 }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(or(i3, and(i1, i2)))))))))))
% 284.41/37.08 = { by lemma 64 R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(n6, i3), not(or(and(i1, i2), i3))))))))))
% 284.41/37.08 = { by lemma 59 R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, not(xor(and(n6, i3), or(and(i1, i2), i3))))))))))
% 284.41/37.08 = { by axiom 41 (constructor9) R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, not(xor(and(n6, i3), or(n6, i3))))))))))
% 284.41/37.08 = { by lemma 54 R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, not(xor(and(n6, i3), xor(n6, xor(i3, and(n6, i3))))))))))))
% 284.41/37.08 = { by axiom 41 (constructor9) }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, not(xor(and(n6, i3), xor(and(i1, i2), xor(i3, and(n6, i3))))))))))))
% 284.41/37.08 = { by axiom 10 (xor_symmetry) }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, not(xor(and(n6, i3), xor(and(i1, i2), xor(and(n6, i3), i3)))))))))))
% 284.41/37.08 = { by axiom 44 (xor_commutativity) }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, not(xor(and(n6, i3), xor(and(n6, i3), xor(and(i1, i2), i3)))))))))))
% 284.41/37.08 = { by axiom 43 (xor_simplification1) }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, not(xor(and(i1, i2), i3)))))))))
% 284.41/37.08 = { by lemma 59 }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(and(i1, i2), not(i3)))))))))
% 284.41/37.08 = { by lemma 81 R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(and(i1, i2), i1), and(i1, not(i3)))))))))
% 284.41/37.08 = { by lemma 92 }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i2), and(i1, not(i3)))))))))
% 284.41/37.08 = { by axiom 29 (and_symmetry) }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i2), and(not(i3), i1))))))))
% 284.41/37.08 = { by lemma 249 }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(not(i3), i2))))))))
% 284.41/37.08 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(i2, not(i3)))))))))
% 284.41/37.08 = { by lemma 52 R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(i3, not(i2)))))))))
% 284.41/37.08 = { by axiom 10 (xor_symmetry) }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), and(i1, xor(not(i2), i3))))))))
% 284.41/37.08 = { by lemma 249 R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), and(not(i2), i1))))))))
% 284.41/37.08 = { by lemma 209 R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, i2), i1))))))))
% 284.41/37.08 = { by axiom 43 (xor_simplification1) R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), xor(and(i1, inv1), xor(and(i1, i2), i1))))))))))
% 284.41/37.08 = { by lemma 209 }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), xor(and(i1, inv1), and(not(i2), i1))))))))))
% 284.41/37.08 = { by lemma 148 }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), and(i1, xor(not(i2), not(n20)))))))))))
% 284.41/37.08 = { by lemma 245 R->L }
% 284.41/37.08 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), and(i1, xor(and(inv1, i2), and(n23, inv2)))))))))))
% 284.41/37.09 = { by lemma 81 R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), xor(and(and(inv1, i2), i1), and(i1, and(n23, inv2)))))))))))
% 284.41/37.09 = { by lemma 250 }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), xor(n0, and(i1, and(n23, inv2)))))))))))
% 284.41/37.09 = { by axiom 13 (xor_definition1) }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), and(i1, and(n23, inv2))))))))))
% 284.41/37.09 = { by axiom 29 (and_symmetry) }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), and(and(n23, inv2), i1)))))))))
% 284.41/37.09 = { by lemma 51 R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), and(and(n23, inv2), not(not(i1)))))))))))
% 284.41/37.09 = { by lemma 55 R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), xor(and(n23, inv2), and(and(n23, inv2), not(i1)))))))))))
% 284.41/37.09 = { by lemma 56 R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), xor(and(n23, inv2), xor(i1, or(i1, and(n23, inv2))))))))))))
% 284.41/37.09 = { by lemma 218 R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), xor(and(n23, inv2), xor(i1, or(i1, and(and(i1, i3), not(n9)))))))))))))
% 284.41/37.09 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), xor(and(n23, inv2), xor(i1, or(i1, and(not(n9), and(i1, i3)))))))))))))
% 284.41/37.09 = { by lemma 101 }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), xor(and(n23, inv2), xor(i1, i1))))))))))
% 284.41/37.09 = { by axiom 9 (xor_definition3) }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), xor(and(n23, inv2), n0)))))))))
% 284.41/37.09 = { by axiom 11 (xor_definition2) }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(i1, inv1), and(n23, inv2)))))))))
% 284.41/37.09 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(n23, inv2), and(i1, inv1)))))))))
% 284.41/37.09 = { by lemma 211 R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(n23, inv2), xor(and(inv1, i3), or(n2, n24))))))))))
% 284.41/37.09 = { by axiom 44 (xor_commutativity) R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(inv1, i3), xor(and(n23, inv2), or(n2, n24))))))))))
% 284.41/37.09 = { by lemma 223 }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(i1, i3), xor(and(inv1, i3), or(n19, n25)))))))))
% 284.41/37.09 = { by axiom 44 (xor_commutativity) }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(inv1, i3), xor(and(inv1, i3), xor(and(i1, i3), or(n19, n25)))))))))
% 284.41/37.09 = { by axiom 43 (xor_simplification1) }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(and(i1, i3), or(n19, n25)))))))
% 284.41/37.09 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(or(n22, n14), xor(or(n19, n25), and(i1, i3)))))))
% 284.41/37.09 = { by lemma 64 }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(xor(or(n19, n25), and(i1, i3)), or(n22, n14))))))
% 284.41/37.09 = { by lemma 66 }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(xor(or(n19, n25), and(i1, i3)), not(not(n20)))))))
% 284.41/37.09 = { by lemma 231 R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(not(n20), not(and(not(n20), xor(or(n19, n25), and(i1, i3)))))))))
% 284.41/37.09 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(not(n20), not(and(not(n20), xor(and(i1, i3), or(n19, n25)))))))))
% 284.41/37.09 = { by lemma 81 R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(not(n20), not(xor(and(and(i1, i3), not(n20)), and(not(n20), or(n19, n25)))))))))
% 284.41/37.09 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(not(n20), not(xor(and(not(n20), and(i1, i3)), and(not(n20), or(n19, n25)))))))))
% 284.41/37.09 = { by lemma 113 }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(not(n20), not(xor(and(i1, and(inv1, i3)), and(not(n20), or(n19, n25)))))))))
% 284.41/37.09 = { by axiom 29 (and_symmetry) }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(not(n20), not(xor(and(and(inv1, i3), i1), and(not(n20), or(n19, n25)))))))))
% 284.41/37.09 = { by lemma 145 R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(not(n20), not(xor(and(and(inv1, i3), and(i1, i3)), and(not(n20), or(n19, n25)))))))))
% 284.41/37.09 = { by lemma 146 R->L }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(not(n20), not(xor(and(and(inv1, i3), and(i1, inv1)), and(not(n20), or(n19, n25)))))))))
% 284.41/37.09 = { by lemma 163 }
% 284.41/37.09 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(not(n20), not(xor(n0, and(not(n20), or(n19, n25)))))))))
% 284.41/37.10 = { by axiom 13 (xor_definition1) }
% 284.41/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(not(n20), not(and(not(n20), or(n19, n25))))))))
% 284.41/37.10 = { by axiom 29 (and_symmetry) }
% 284.41/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(not(n20), not(and(or(n19, n25), not(n20))))))))
% 284.41/37.10 = { by lemma 233 }
% 284.41/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(and(or(n19, n25), not(n20)), or(n22, n14))))))
% 284.41/37.10 = { by axiom 10 (xor_symmetry) }
% 284.41/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(or(n22, n14), and(or(n19, n25), not(n20)))))))
% 284.41/37.10 = { by axiom 29 (and_symmetry) R->L }
% 284.41/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(or(n22, n14), and(not(n20), or(n19, n25)))))))
% 284.41/37.10 = { by axiom 13 (xor_definition1) R->L }
% 284.41/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(or(n22, n14), xor(n0, and(not(n20), or(n19, n25))))))))
% 284.41/37.10 = { by lemma 221 R->L }
% 284.41/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(or(n22, n14), xor(and(and(n23, inv2), not(n20)), and(not(n20), or(n19, n25))))))))
% 284.41/37.10 = { by lemma 81 }
% 284.41/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(or(n22, n14), and(not(n20), xor(and(n23, inv2), or(n19, n25))))))))
% 284.41/37.10 = { by axiom 10 (xor_symmetry) R->L }
% 284.41/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(or(n22, n14), and(not(n20), xor(or(n19, n25), and(n23, inv2))))))))
% 284.41/37.10 = { by lemma 222 R->L }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(or(n22, n14), and(not(n20), xor(or(n19, n25), xor(or(n2, n24), or(n19, n25)))))))))
% 285.16/37.10 = { by lemma 78 }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(or(n22, n14), and(not(n20), or(n2, n24)))))))
% 285.16/37.10 = { by lemma 216 }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(or(n22, n14), or(n2, n24))))))
% 285.16/37.10 = { by axiom 10 (xor_symmetry) }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(xor(or(n2, n24), or(n22, n14))))))
% 285.16/37.10 = { by lemma 59 }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, xor(or(n2, n24), not(or(n22, n14))))))
% 285.16/37.10 = { by axiom 21 (constructor23) R->L }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, xor(or(n2, n24), not(n20)))))
% 285.16/37.10 = { by axiom 10 (xor_symmetry) }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, xor(not(n20), or(n2, n24)))))
% 285.16/37.10 = { by lemma 261 }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, and(not(i3), not(i1)))))
% 285.16/37.10 = { by lemma 262 }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(i2, not(or(i1, i3)))))
% 285.16/37.10 = { by lemma 52 }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(or(i1, i3), not(i2))))
% 285.16/37.10 = { by axiom 10 (xor_symmetry) }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(not(i2), or(i1, i3))))
% 285.16/37.10 = { by lemma 51 R->L }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(not(i2), not(not(or(i1, i3))))))
% 285.16/37.10 = { by lemma 262 R->L }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(not(i2), not(and(not(i3), not(i1))))))
% 285.16/37.10 = { by lemma 261 R->L }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(not(i2), not(xor(not(n20), or(n2, n24))))))
% 285.16/37.10 = { by lemma 59 }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(not(i2), xor(not(n20), not(or(n2, n24))))))
% 285.16/37.10 = { by lemma 233 }
% 285.16/37.10 circuit(xor(xor(or(n2, n24), or(n22, n14)), xor(not(i2), xor(or(n2, n24), or(n22, n14)))))
% 285.16/37.10 = { by lemma 78 }
% 285.16/37.10 circuit(not(i2))
% 285.16/37.10
% 285.16/37.10 Lemma 264: xor(and(inv1, i2), and(inv1, i3)) = or(a1, n2).
% 285.16/37.10 Proof:
% 285.16/37.10 xor(and(inv1, i2), and(inv1, i3))
% 285.16/37.10 = { by axiom 11 (xor_definition2) R->L }
% 285.16/37.10 xor(and(inv1, i2), xor(and(inv1, i3), n0))
% 285.16/37.10 = { by lemma 118 R->L }
% 285.16/37.10 xor(and(inv1, i2), xor(and(inv1, i3), and(and(inv1, i2), and(inv1, i3))))
% 285.16/37.10 = { by lemma 54 }
% 285.16/37.10 or(and(inv1, i2), and(inv1, i3))
% 285.16/37.10 = { by axiom 37 (constructor5) R->L }
% 285.16/37.10 or(and(inv1, i2), n2)
% 285.16/37.10 = { by axiom 36 (constructor4) R->L }
% 285.16/37.10 or(a1, n2)
% 285.16/37.10
% 285.16/37.10 Lemma 265: and(not(n9), xor(X, and(Y, inv2))) = xor(and(Y, inv2), and(X, not(n9))).
% 285.16/37.10 Proof:
% 285.16/37.10 and(not(n9), xor(X, and(Y, inv2)))
% 285.16/37.10 = { by axiom 10 (xor_symmetry) R->L }
% 285.16/37.10 and(not(n9), xor(and(Y, inv2), X))
% 285.16/37.10 = { by lemma 81 R->L }
% 285.16/37.10 xor(and(and(Y, inv2), not(n9)), and(not(n9), X))
% 285.16/37.10 = { by lemma 206 }
% 285.16/37.10 xor(and(Y, inv2), and(not(n9), X))
% 285.16/37.10 = { by axiom 29 (and_symmetry) }
% 285.16/37.10 xor(and(Y, inv2), and(X, not(n9)))
% 285.16/37.10
% 285.16/37.10 Lemma 266: and(not(and(n14, inv2)), not(or(a1, n2))) = not(or(n11, n16)).
% 285.16/37.10 Proof:
% 285.16/37.10 and(not(and(n14, inv2)), not(or(a1, n2)))
% 285.16/37.10 = { by axiom 29 (and_symmetry) R->L }
% 285.16/37.10 and(not(or(a1, n2)), not(and(n14, inv2)))
% 285.16/37.10 = { by lemma 62 R->L }
% 285.16/37.10 xor(not(or(a1, n2)), and(and(n14, inv2), not(or(a1, n2))))
% 285.16/37.10 = { by axiom 24 (constructor14) R->L }
% 285.16/37.10 xor(not(or(a1, n2)), and(and(n14, inv2), not(n11)))
% 285.16/37.10 = { by axiom 32 (constructor19) R->L }
% 285.16/37.10 xor(not(or(a1, n2)), and(n16, not(n11)))
% 285.16/37.10 = { by lemma 56 R->L }
% 285.16/37.10 xor(not(or(a1, n2)), xor(n11, or(n11, n16)))
% 285.16/37.10 = { by axiom 24 (constructor14) }
% 285.16/37.10 xor(not(or(a1, n2)), xor(or(a1, n2), or(n11, n16)))
% 285.16/37.10 = { by lemma 53 }
% 285.16/37.10 xor(or(a1, n2), not(xor(or(a1, n2), or(n11, n16))))
% 285.16/37.10 = { by lemma 59 }
% 285.16/37.10 xor(or(a1, n2), xor(or(a1, n2), not(or(n11, n16))))
% 285.16/37.10 = { by axiom 43 (xor_simplification1) }
% 285.16/37.10 not(or(n11, n16))
% 285.16/37.10
% 285.16/37.10 Goal 1 (prove_inversion): tuple(circuit(not(i2)), circuit(not(i3)), circuit(not(i1))) = tuple(true, true, true).
% 285.16/37.10 Proof:
% 285.16/37.10 tuple(circuit(not(i2)), circuit(not(i3)), circuit(not(i1)))
% 285.16/37.10 = { by axiom 11 (xor_definition2) R->L }
% 285.16/37.10 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(not(i1), n0)))
% 285.16/37.10 = { by lemma 248 R->L }
% 285.16/37.10 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(not(i1), and(and(inv1, inv2), and(i1, inv1)))))
% 285.16/37.10 = { by lemma 214 }
% 285.16/37.10 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(not(i1), and(and(i1, inv1), not(n9)))))
% 285.16/37.10 = { by axiom 29 (and_symmetry) R->L }
% 285.16/37.10 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(not(i1), and(not(n9), and(i1, inv1)))))
% 285.16/37.10 = { by lemma 136 R->L }
% 285.16/37.10 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(not(i1), and(not(n9), and(not(n20), i1)))))
% 285.16/37.10 = { by lemma 74 }
% 285.16/37.10 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(not(i1), and(i1, and(inv1, inv2)))))
% 285.16/37.10 = { by axiom 29 (and_symmetry) }
% 285.16/37.10 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(not(i1), and(and(inv1, inv2), i1))))
% 285.16/37.10 = { by lemma 182 }
% 285.16/37.10 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(not(i1), and(inv1, inv2))))
% 285.16/37.11 = { by lemma 64 R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), not(i1))))
% 285.16/37.11 = { by lemma 77 R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(and(inv1, inv2), not(i1)))))
% 285.16/37.11 = { by axiom 10 (xor_symmetry) R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), and(inv1, inv2)))))
% 285.16/37.11 = { by lemma 78 R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), and(n14, inv2)))))))
% 285.16/37.11 = { by axiom 11 (xor_definition2) R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), xor(and(n14, inv2), n0)))))))
% 285.16/37.11 = { by axiom 9 (xor_definition3) R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), xor(and(n14, inv2), xor(and(i1, inv1), and(i1, inv1)))))))))
% 285.16/37.11 = { by lemma 213 R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), xor(and(n14, inv2), xor(and(i1, inv1), and(and(i1, inv1), or(n8, n2))))))))))
% 285.16/37.11 = { by lemma 232 R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), xor(and(n14, inv2), xor(and(i1, inv1), and(or(n8, n2), xor(and(i1, inv1), and(X, inv2)))))))))))
% 285.16/37.11 = { by axiom 29 (and_symmetry) R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), xor(and(n14, inv2), xor(and(i1, inv1), and(xor(and(i1, inv1), and(X, inv2)), or(n8, n2))))))))))
% 285.16/37.11 = { by lemma 65 }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), xor(and(n14, inv2), xor(and(i1, inv1), and(xor(and(i1, inv1), and(X, inv2)), not(not(n9)))))))))))
% 285.16/37.11 = { by lemma 62 R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), xor(and(n14, inv2), xor(and(i1, inv1), xor(xor(and(i1, inv1), and(X, inv2)), and(not(n9), xor(and(i1, inv1), and(X, inv2))))))))))))
% 285.16/37.11 = { by lemma 265 }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), xor(and(n14, inv2), xor(and(i1, inv1), xor(xor(and(i1, inv1), and(X, inv2)), xor(and(X, inv2), and(and(i1, inv1), not(n9))))))))))))
% 285.16/37.11 = { by lemma 180 }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), xor(and(n14, inv2), xor(and(i1, inv1), xor(and(i1, inv1), xor(xor(and(X, inv2), and(and(i1, inv1), not(n9))), and(X, inv2)))))))))))
% 285.16/37.11 = { by lemma 180 }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), xor(and(n14, inv2), xor(and(i1, inv1), xor(and(i1, inv1), xor(and(X, inv2), xor(and(X, inv2), and(and(i1, inv1), not(n9)))))))))))))
% 285.16/37.11 = { by axiom 43 (xor_simplification1) }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), xor(and(n14, inv2), xor(and(i1, inv1), xor(and(i1, inv1), and(and(i1, inv1), not(n9)))))))))))
% 285.16/37.11 = { by axiom 43 (xor_simplification1) }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), xor(and(n14, inv2), and(and(i1, inv1), not(n9)))))))))
% 285.16/37.11 = { by lemma 265 R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), and(not(n9), xor(and(i1, inv1), and(n14, inv2)))))))))
% 285.16/37.11 = { by lemma 254 R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), and(not(n9), xor(and(i1, inv1), xor(and(i2, i3), and(n6, i3))))))))))
% 285.16/37.11 = { by lemma 252 }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), and(not(n9), xor(and(i1, inv1), and(not(i1), or(n22, n14))))))))))
% 285.16/37.11 = { by lemma 244 }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), and(not(n9), xor(and(i1, inv1), not(or(not(n20), i1))))))))))
% 285.16/37.11 = { by lemma 243 R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), and(not(n9), xor(and(i1, inv1), not(xor(and(i1, inv1), xor(not(i1), or(n22, n14))))))))))))
% 285.16/37.11 = { by lemma 59 }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), and(not(n9), xor(and(i1, inv1), xor(and(i1, inv1), not(xor(not(i1), or(n22, n14))))))))))))
% 285.16/37.11 = { by lemma 59 }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), and(not(n9), xor(and(i1, inv1), xor(and(i1, inv1), xor(not(i1), not(or(n22, n14))))))))))))
% 285.16/37.11 = { by lemma 241 }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), and(not(n9), xor(and(i1, inv1), xor(and(i1, inv1), xor(or(n22, n14), i1))))))))))
% 285.16/37.11 = { by lemma 240 }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), and(not(n9), xor(and(i1, inv1), xor(and(i1, inv1), xor(not(i1), not(n20)))))))))))
% 285.16/37.11 = { by axiom 43 (xor_simplification1) }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), and(not(n9), xor(not(i1), not(n20)))))))))
% 285.16/37.11 = { by lemma 80 R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(and(inv1, inv2), xor(and(inv1, inv2), and(not(i1), not(n9)))))))))
% 285.16/37.11 = { by axiom 43 (xor_simplification1) }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), not(n9)))))))
% 285.16/37.11 = { by axiom 29 (and_symmetry) R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(n9), not(i1)))))))
% 285.16/37.11 = { by lemma 181 R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(not(n9), and(n6, i3))))))))
% 285.16/37.11 = { by lemma 179 R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(and(i1, inv1), xor(not(n9), or(n24, n7)))))))))
% 285.16/37.11 = { by lemma 98 }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(xor(not(n9), or(n24, n7)), not(i1)))))))
% 285.16/37.11 = { by axiom 29 (and_symmetry) }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(not(n9), or(n24, n7))))))))
% 285.16/37.11 = { by lemma 247 R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(and(inv1, i2), xor(not(n9), or(a1, n10)))))))))
% 285.16/37.11 = { by axiom 43 (xor_simplification1) R->L }
% 285.16/37.11 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(and(inv1, i2), xor(and(inv1, i3), xor(and(inv1, i3), xor(not(n9), or(a1, n10)))))))))))
% 285.16/37.11 = { by axiom 10 (xor_symmetry) R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(and(inv1, i2), xor(and(inv1, i3), xor(and(inv1, i3), xor(or(a1, n10), not(n9)))))))))))
% 285.16/37.12 = { by axiom 16 (constructor12) }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(and(inv1, i2), xor(and(inv1, i3), xor(and(inv1, i3), xor(or(a1, n10), not(or(n8, n2))))))))))))
% 285.16/37.12 = { by lemma 59 R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(and(inv1, i2), xor(and(inv1, i3), xor(and(inv1, i3), not(xor(or(a1, n10), or(n8, n2))))))))))))
% 285.16/37.12 = { by lemma 59 R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(and(inv1, i2), xor(and(inv1, i3), not(xor(and(inv1, i3), xor(or(a1, n10), or(n8, n2))))))))))))
% 285.16/37.12 = { by lemma 71 R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(and(inv1, i2), xor(and(inv1, i3), not(xor(and(inv1, i3), and(and(inv1, i3), not(or(a1, n10)))))))))))))
% 285.16/37.12 = { by lemma 55 }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(and(inv1, i2), xor(and(inv1, i3), not(and(and(inv1, i3), not(not(or(a1, n10)))))))))))))
% 285.16/37.12 = { by lemma 51 }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(and(inv1, i2), xor(and(inv1, i3), not(and(and(inv1, i3), or(a1, n10)))))))))))
% 285.16/37.12 = { by lemma 164 }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(and(inv1, i2), xor(and(inv1, i3), not(n0)))))))))
% 285.16/37.12 = { by lemma 49 }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(and(inv1, i2), xor(and(inv1, i3), n1))))))))
% 285.16/37.12 = { by lemma 50 }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(and(inv1, i2), not(and(inv1, i3)))))))))
% 285.16/37.12 = { by lemma 53 R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(not(and(inv1, i2)), and(inv1, i3))))))))
% 285.16/37.12 = { by lemma 119 R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(not(and(inv1, i2)), and(and(inv1, i3), not(and(inv1, i2))))))))))
% 285.16/37.12 = { by axiom 36 (constructor4) R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(not(and(inv1, i2)), and(and(inv1, i3), not(a1)))))))))
% 285.16/37.12 = { by axiom 37 (constructor5) R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(not(and(inv1, i2)), and(n2, not(a1)))))))))
% 285.16/37.12 = { by lemma 56 R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(not(and(inv1, i2)), xor(a1, or(a1, n2)))))))))
% 285.16/37.12 = { by axiom 36 (constructor4) }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(not(and(inv1, i2)), xor(and(inv1, i2), or(a1, n2)))))))))
% 285.16/37.12 = { by lemma 53 }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(and(inv1, i2), not(xor(and(inv1, i2), or(a1, n2))))))))))
% 285.16/37.12 = { by lemma 59 }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), xor(and(inv1, i2), xor(and(inv1, i2), not(or(a1, n2))))))))))
% 285.16/37.12 = { by axiom 43 (xor_simplification1) }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), and(not(i1), not(or(a1, n2))))))))
% 285.16/37.12 = { by lemma 262 }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(or(or(a1, n2), i1)))))))
% 285.16/37.12 = { by lemma 64 }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(or(i1, or(a1, n2))))))))
% 285.16/37.12 = { by lemma 57 R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, and(or(a1, n2), not(i1)))))))))
% 285.16/37.12 = { by lemma 55 R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, xor(or(a1, n2), and(or(a1, n2), i1)))))))))
% 285.16/37.12 = { by axiom 29 (and_symmetry) R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, xor(or(a1, n2), and(i1, or(a1, n2))))))))))
% 285.16/37.12 = { by lemma 264 R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, xor(or(a1, n2), and(i1, xor(and(inv1, i2), and(inv1, i3)))))))))))
% 285.16/37.12 = { by axiom 10 (xor_symmetry) R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, xor(or(a1, n2), and(i1, xor(and(inv1, i3), and(inv1, i2)))))))))))
% 285.16/37.12 = { by lemma 81 R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, xor(or(a1, n2), xor(and(and(inv1, i3), i1), and(i1, and(inv1, i2)))))))))))
% 285.16/37.12 = { by lemma 144 R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, xor(or(a1, n2), xor(and(and(i1, i3), not(n20)), and(i1, and(inv1, i2)))))))))))
% 285.16/37.12 = { by axiom 29 (and_symmetry) R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, xor(or(a1, n2), xor(and(not(n20), and(i1, i3)), and(i1, and(inv1, i2)))))))))))
% 285.16/37.12 = { by lemma 82 R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, xor(or(a1, n2), xor(and(not(n20), and(and(i1, i3), i3)), and(i1, and(inv1, i2)))))))))))
% 285.16/37.12 = { by lemma 113 }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, xor(or(a1, n2), xor(and(and(i1, i3), and(inv1, i3)), and(i1, and(inv1, i2)))))))))))
% 285.16/37.12 = { by axiom 29 (and_symmetry) }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, xor(or(a1, n2), xor(and(and(inv1, i3), and(i1, i3)), and(i1, and(inv1, i2)))))))))))
% 285.16/37.12 = { by lemma 146 R->L }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, xor(or(a1, n2), xor(and(and(inv1, i3), and(i1, inv1)), and(i1, and(inv1, i2)))))))))))
% 285.16/37.12 = { by lemma 163 }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, xor(or(a1, n2), xor(n0, and(i1, and(inv1, i2)))))))))))
% 285.16/37.12 = { by axiom 13 (xor_definition1) }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, xor(or(a1, n2), and(i1, and(inv1, i2))))))))))
% 285.16/37.12 = { by axiom 29 (and_symmetry) }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, xor(or(a1, n2), and(and(inv1, i2), i1)))))))))
% 285.16/37.12 = { by lemma 250 }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, xor(or(a1, n2), n0))))))))
% 285.16/37.12 = { by axiom 11 (xor_definition2) }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(i1, or(a1, n2))))))))
% 285.16/37.12 = { by axiom 10 (xor_symmetry) }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), not(xor(or(a1, n2), i1)))))))
% 285.16/37.12 = { by lemma 59 }
% 285.16/37.12 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), not(i1)))))))
% 285.16/37.12 = { by axiom 10 (xor_symmetry) }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(and(n14, inv2), xor(not(i1), or(a1, n2)))))))
% 285.16/37.13 = { by axiom 44 (xor_commutativity) R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), or(a1, n2)))))))
% 285.16/37.13 = { by axiom 11 (xor_definition2) R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), n0)))))))
% 285.16/37.13 = { by axiom 31 (and_definition2) R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), and(or(a1, n2), n0))))))))
% 285.16/37.13 = { by lemma 259 R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), and(or(a1, n2), and(and(inv1, inv2), and(i2, i3))))))))))
% 285.16/37.13 = { by axiom 29 (and_symmetry) R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), and(or(a1, n2), and(and(i2, i3), and(inv1, inv2))))))))))
% 285.16/37.13 = { by lemma 74 R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), and(or(a1, n2), and(not(n9), and(not(n20), and(i2, i3)))))))))))
% 285.16/37.13 = { by axiom 39 (constructor17) R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), and(or(a1, n2), and(not(n9), and(not(n20), n14))))))))))
% 285.16/37.13 = { by lemma 171 R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), and(or(a1, n2), and(and(not(n9), n14), not(n20))))))))))
% 285.16/37.13 = { by lemma 205 }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), and(or(a1, n2), and(and(n14, inv2), not(n20))))))))))
% 285.16/37.13 = { by axiom 46 (and_commutativity) }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), and(and(n14, inv2), and(or(a1, n2), not(n20))))))))))
% 285.16/37.13 = { by axiom 29 (and_symmetry) }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), and(and(n14, inv2), and(not(n20), or(a1, n2))))))))))
% 285.16/37.13 = { by lemma 264 R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), and(and(n14, inv2), and(not(n20), xor(and(inv1, i2), and(inv1, i3)))))))))))
% 285.16/37.13 = { by lemma 199 }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), and(and(n14, inv2), xor(and(inv1, i3), and(and(inv1, i2), not(n20)))))))))))
% 285.16/37.13 = { by lemma 69 }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), and(and(n14, inv2), xor(and(inv1, i3), and(inv1, i2))))))))))
% 285.16/37.13 = { by axiom 10 (xor_symmetry) }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), and(and(n14, inv2), xor(and(inv1, i2), and(inv1, i3))))))))))
% 285.16/37.13 = { by lemma 264 }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(a1, n2), and(and(n14, inv2), or(a1, n2)))))))))
% 285.16/37.13 = { by lemma 62 }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), and(or(a1, n2), not(and(n14, inv2)))))))))
% 285.16/37.13 = { by axiom 29 (and_symmetry) R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), and(not(and(n14, inv2)), or(a1, n2))))))))
% 285.16/37.13 = { by lemma 51 R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), and(not(and(n14, inv2)), not(not(or(a1, n2))))))))))
% 285.16/37.13 = { by lemma 123 R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), and(not(and(n14, inv2)), not(and(not(and(n14, inv2)), not(or(a1, n2)))))))))))
% 285.16/37.13 = { by lemma 266 }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), and(not(and(n14, inv2)), not(not(or(n11, n16))))))))))
% 285.16/37.13 = { by lemma 51 }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), and(not(and(n14, inv2)), or(n11, n16))))))))
% 285.16/37.13 = { by axiom 29 (and_symmetry) }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), and(or(n11, n16), not(and(n14, inv2)))))))))
% 285.16/37.13 = { by lemma 57 }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), or(and(n14, inv2), or(n11, n16)))))))
% 285.16/37.13 = { by lemma 54 R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(n11, n16), and(and(n14, inv2), or(n11, n16)))))))))
% 285.16/37.13 = { by lemma 51 R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(n11, n16), and(and(n14, inv2), not(not(or(n11, n16)))))))))))
% 285.16/37.13 = { by lemma 55 R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(n11, n16), xor(and(n14, inv2), and(and(n14, inv2), not(or(n11, n16)))))))))))
% 285.16/37.13 = { by lemma 76 R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(n11, n16), xor(and(n14, inv2), and(and(n14, inv2), xor(and(n14, inv2), or(n11, n16)))))))))))
% 285.16/37.13 = { by lemma 51 R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(n11, n16), xor(and(n14, inv2), and(and(n14, inv2), xor(and(n14, inv2), not(not(or(n11, n16)))))))))))))
% 285.16/37.13 = { by lemma 53 R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(n11, n16), xor(and(n14, inv2), and(and(n14, inv2), xor(not(and(n14, inv2)), not(or(n11, n16))))))))))))
% 285.16/37.13 = { by lemma 266 R->L }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(n11, n16), xor(and(n14, inv2), and(and(n14, inv2), xor(not(and(n14, inv2)), and(not(and(n14, inv2)), not(or(a1, n2)))))))))))))
% 285.16/37.13 = { by lemma 55 }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(n11, n16), xor(and(n14, inv2), and(and(n14, inv2), and(not(and(n14, inv2)), not(not(or(a1, n2)))))))))))))
% 285.16/37.13 = { by lemma 51 }
% 285.16/37.13 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(n11, n16), xor(and(n14, inv2), and(and(n14, inv2), and(not(and(n14, inv2)), or(a1, n2)))))))))))
% 285.16/37.14 = { by axiom 29 (and_symmetry) }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(n11, n16), xor(and(n14, inv2), and(and(n14, inv2), and(or(a1, n2), not(and(n14, inv2))))))))))))
% 285.16/37.14 = { by lemma 159 }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(n11, n16), xor(and(n14, inv2), n0))))))))
% 285.16/37.14 = { by axiom 11 (xor_definition2) }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), xor(and(n14, inv2), xor(or(n11, n16), and(n14, inv2))))))))
% 285.16/37.14 = { by lemma 78 }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), xor(not(i1), xor(not(i1), or(n11, n16))))))
% 285.16/37.14 = { by axiom 43 (xor_simplification1) }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(and(inv1, inv2), or(n11, n16))))
% 285.16/37.14 = { by lemma 57 R->L }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(and(inv1, inv2), and(or(n11, n16), not(and(inv1, inv2))))))
% 285.16/37.14 = { by axiom 29 (and_symmetry) R->L }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(and(inv1, inv2), and(not(and(inv1, inv2)), or(n11, n16)))))
% 285.16/37.14 = { by lemma 51 R->L }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(and(inv1, inv2), and(not(and(inv1, inv2)), not(not(or(n11, n16)))))))
% 285.16/37.14 = { by lemma 55 R->L }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), and(not(and(inv1, inv2)), not(or(n11, n16)))))))
% 285.16/37.14 = { by axiom 29 (and_symmetry) R->L }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), and(not(or(n11, n16)), not(and(inv1, inv2)))))))
% 285.16/37.14 = { by lemma 62 R->L }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), xor(not(or(n11, n16)), and(and(inv1, inv2), not(or(n11, n16))))))))
% 285.16/37.14 = { by axiom 35 (constructor24) R->L }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), xor(not(or(n11, n16)), and(n21, not(or(n11, n16))))))))
% 285.16/37.14 = { by lemma 56 R->L }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), xor(not(or(n11, n16)), xor(or(n11, n16), or(or(n11, n16), n21)))))))
% 285.16/37.14 = { by axiom 17 (constructor15) R->L }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), xor(not(or(n11, n16)), xor(or(n11, n16), or(n12, n21)))))))
% 285.16/37.14 = { by lemma 53 }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), xor(or(n11, n16), not(xor(or(n11, n16), or(n12, n21))))))))
% 285.16/37.14 = { by lemma 59 }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), xor(or(n11, n16), xor(or(n11, n16), not(or(n12, n21))))))))
% 285.16/37.14 = { by axiom 43 (xor_simplification1) }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(and(inv1, inv2), xor(not(and(inv1, inv2)), not(or(n12, n21))))))
% 285.16/37.14 = { by lemma 53 }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(and(inv1, inv2), xor(and(inv1, inv2), not(not(or(n12, n21)))))))
% 285.16/37.14 = { by lemma 51 }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(xor(and(inv1, inv2), xor(and(inv1, inv2), or(n12, n21)))))
% 285.16/37.14 = { by axiom 43 (xor_simplification1) }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(or(n12, n21)))
% 285.16/37.14 = { by axiom 18 (constructor16) R->L }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(n13))
% 285.16/37.14 = { by axiom 1 (constructor1) R->L }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(o1))
% 285.16/37.14 = { by lemma 203 R->L }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i3)), circuit(not(i3)))
% 285.16/37.14 = { by lemma 263 }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i2)), circuit(not(i3)))
% 285.16/37.14 = { by lemma 263 }
% 285.16/37.14 tuple(circuit(not(i2)), circuit(not(i2)), circuit(not(i2)))
% 285.16/37.14 = { by lemma 263 R->L }
% 285.16/37.14 tuple(circuit(not(i3)), circuit(not(i2)), circuit(not(i2)))
% 285.16/37.14 = { by lemma 263 R->L }
% 285.16/37.14 tuple(circuit(not(i3)), circuit(not(i3)), circuit(not(i2)))
% 285.16/37.14 = { by lemma 263 R->L }
% 285.16/37.14 tuple(circuit(not(i3)), circuit(not(i3)), circuit(not(i3)))
% 285.16/37.14 = { by lemma 203 }
% 285.16/37.14 tuple(circuit(o1), circuit(not(i3)), circuit(not(i3)))
% 285.16/37.14 = { by lemma 203 }
% 285.16/37.14 tuple(circuit(o1), circuit(o1), circuit(not(i3)))
% 285.16/37.14 = { by lemma 203 }
% 285.16/37.14 tuple(circuit(o1), circuit(o1), circuit(o1))
% 285.16/37.14 = { by axiom 4 (output1) }
% 285.16/37.14 tuple(true, circuit(o1), circuit(o1))
% 285.16/37.14 = { by axiom 4 (output1) }
% 285.16/37.14 tuple(true, true, circuit(o1))
% 285.16/37.14 = { by axiom 4 (output1) }
% 285.16/37.14 tuple(true, true, true)
% 285.16/37.14 % SZS output end Proof
% 285.16/37.14
% 285.16/37.14 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------