TSTP Solution File: LCL513+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL513+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n020.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 08:19:16 EDT 2023
% Result : Theorem 159.13s 20.85s
% Output : Proof 162.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL513+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 01:06:30 EDT 2023
% 0.14/0.35 % CPUTime :
% 159.13/20.85 Command-line arguments: --no-flatten-goal
% 159.13/20.85
% 159.13/20.85 % SZS status Theorem
% 159.13/20.85
% 159.91/20.99 % SZS output start Proof
% 159.91/20.99 Take the following subset of the input axioms:
% 159.91/20.99 fof(and_1, axiom, and_1 <=> ![X, Y]: is_a_theorem(implies(and(X, Y), X))).
% 159.91/20.99 fof(and_2, axiom, and_2 <=> ![X2, Y2]: is_a_theorem(implies(and(X2, Y2), Y2))).
% 159.91/20.99 fof(equivalence_2, axiom, equivalence_2 <=> ![X2, Y2]: is_a_theorem(implies(equiv(X2, Y2), implies(Y2, X2)))).
% 159.91/20.99 fof(hilbert_equivalence_2, conjecture, equivalence_2).
% 159.91/20.99 fof(kn1, axiom, kn1 <=> ![P]: is_a_theorem(implies(P, and(P, P)))).
% 159.91/20.99 fof(kn2, axiom, kn2 <=> ![Q, P2]: is_a_theorem(implies(and(P2, Q), P2))).
% 159.91/20.99 fof(kn3, axiom, kn3 <=> ![R, P2, Q2]: is_a_theorem(implies(implies(P2, Q2), implies(not(and(Q2, R)), not(and(R, P2)))))).
% 159.91/20.99 fof(modus_ponens, axiom, modus_ponens <=> ![X2, Y2]: ((is_a_theorem(X2) & is_a_theorem(implies(X2, Y2))) => is_a_theorem(Y2))).
% 159.91/20.99 fof(op_equiv, axiom, op_equiv => ![X2, Y2]: equiv(X2, Y2)=and(implies(X2, Y2), implies(Y2, X2))).
% 159.91/20.99 fof(op_implies_and, axiom, op_implies_and => ![X2, Y2]: implies(X2, Y2)=not(and(X2, not(Y2)))).
% 159.91/20.99 fof(op_or, axiom, op_or => ![X2, Y2]: or(X2, Y2)=not(and(not(X2), not(Y2)))).
% 159.91/20.99 fof(r3, axiom, r3 <=> ![P2, Q2]: is_a_theorem(implies(or(P2, Q2), or(Q2, P2)))).
% 159.91/20.99 fof(rosser_kn1, axiom, kn1).
% 159.91/20.99 fof(rosser_kn2, axiom, kn2).
% 159.91/20.99 fof(rosser_kn3, axiom, kn3).
% 159.91/20.99 fof(rosser_modus_ponens, axiom, modus_ponens).
% 159.91/20.99 fof(rosser_op_equiv, axiom, op_equiv).
% 159.91/20.99 fof(rosser_op_implies_and, axiom, op_implies_and).
% 159.91/20.99 fof(rosser_op_or, axiom, op_or).
% 159.91/20.99
% 159.91/20.99 Now clausify the problem and encode Horn clauses using encoding 3 of
% 159.91/20.99 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 159.91/21.00 We repeatedly replace C & s=t => u=v by the two clauses:
% 159.91/21.00 fresh(y, y, x1...xn) = u
% 159.91/21.01 C => fresh(s, t, x1...xn) = v
% 159.91/21.01 where fresh is a fresh function symbol and x1..xn are the free
% 160.39/21.01 variables of u and v.
% 160.39/21.01 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 160.39/21.01 input problem has no model of domain size 1).
% 160.39/21.02
% 160.39/21.02 The encoding turns the above axioms into the following unit equations and goals:
% 160.39/21.02
% 160.39/21.02 Axiom 1 (rosser_modus_ponens): modus_ponens = true.
% 160.39/21.02 Axiom 2 (rosser_kn1): kn1 = true.
% 160.39/21.02 Axiom 3 (rosser_kn2): kn2 = true.
% 160.39/21.02 Axiom 4 (rosser_kn3): kn3 = true.
% 160.39/21.02 Axiom 5 (rosser_op_or): op_or = true.
% 160.39/21.02 Axiom 6 (rosser_op_implies_and): op_implies_and = true.
% 160.39/21.02 Axiom 7 (rosser_op_equiv): op_equiv = true.
% 160.39/21.02 Axiom 8 (and_1): fresh57(X, X) = true.
% 160.39/21.02 Axiom 9 (equivalence_2): fresh44(X, X) = true.
% 160.39/21.02 Axiom 10 (modus_ponens_2): fresh60(X, X, Y) = true.
% 160.39/21.02 Axiom 11 (kn1_1): fresh33(X, X, Y) = true.
% 160.39/21.02 Axiom 12 (modus_ponens_2): fresh28(X, X, Y) = is_a_theorem(Y).
% 160.39/21.02 Axiom 13 (modus_ponens_2): fresh59(X, X, Y, Z) = fresh60(modus_ponens, true, Z).
% 160.39/21.02 Axiom 14 (kn2_1): fresh31(X, X, Y, Z) = true.
% 160.39/21.02 Axiom 15 (op_equiv): fresh23(X, X, Y, Z) = equiv(Y, Z).
% 160.39/21.02 Axiom 16 (op_implies_and): fresh22(X, X, Y, Z) = implies(Y, Z).
% 160.39/21.02 Axiom 17 (op_or): fresh20(X, X, Y, Z) = or(Y, Z).
% 160.39/21.02 Axiom 18 (op_implies_and): fresh22(op_implies_and, true, X, Y) = not(and(X, not(Y))).
% 160.39/21.02 Axiom 19 (kn3_1): fresh29(X, X, Y, Z, W) = true.
% 160.39/21.02 Axiom 20 (op_or): fresh20(op_or, true, X, Y) = not(and(not(X), not(Y))).
% 160.39/21.02 Axiom 21 (kn1_1): fresh33(kn1, true, X) = is_a_theorem(implies(X, and(X, X))).
% 160.39/21.02 Axiom 22 (and_1_1): fresh58(and_1, true, X, Y) = is_a_theorem(implies(and(X, Y), X)).
% 160.39/21.02 Axiom 23 (kn2_1): fresh31(kn2, true, X, Y) = is_a_theorem(implies(and(X, Y), X)).
% 160.39/21.02 Axiom 24 (and_2_1): fresh55(and_2, true, X, Y) = is_a_theorem(implies(and(X, Y), Y)).
% 160.39/21.02 Axiom 25 (op_equiv): fresh23(op_equiv, true, X, Y) = and(implies(X, Y), implies(Y, X)).
% 160.39/21.02 Axiom 26 (modus_ponens_2): fresh59(is_a_theorem(implies(X, Y)), true, X, Y) = fresh28(is_a_theorem(X), true, Y).
% 160.39/21.02 Axiom 27 (and_1): fresh57(is_a_theorem(implies(and(x9, y9), x9)), true) = and_1.
% 160.39/21.02 Axiom 28 (equivalence_2_1): fresh43(equivalence_2, true, X, Y) = is_a_theorem(implies(equiv(X, Y), implies(Y, X))).
% 160.39/21.02 Axiom 29 (r3_1): fresh8(r3, true, X, Y) = is_a_theorem(implies(or(X, Y), or(Y, X))).
% 160.39/21.02 Axiom 30 (equivalence_2): fresh44(is_a_theorem(implies(equiv(x2, y2), implies(y2, x2))), true) = equivalence_2.
% 160.39/21.02 Axiom 31 (kn3_1): fresh29(kn3, true, X, Y, Z) = is_a_theorem(implies(implies(X, Y), implies(not(and(Y, Z)), not(and(Z, X))))).
% 160.39/21.02
% 160.39/21.02 Lemma 32: is_a_theorem(implies(and(X, Y), X)) = fresh58(and_1, modus_ponens, X, Y).
% 160.39/21.02 Proof:
% 160.39/21.02 is_a_theorem(implies(and(X, Y), X))
% 160.39/21.02 = { by axiom 22 (and_1_1) R->L }
% 160.39/21.02 fresh58(and_1, true, X, Y)
% 160.39/21.02 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.39/21.02 fresh58(and_1, modus_ponens, X, Y)
% 160.39/21.02
% 160.39/21.02 Lemma 33: fresh58(and_1, modus_ponens, X, Y) = modus_ponens.
% 160.39/21.02 Proof:
% 160.39/21.02 fresh58(and_1, modus_ponens, X, Y)
% 160.39/21.02 = { by lemma 32 R->L }
% 160.39/21.02 is_a_theorem(implies(and(X, Y), X))
% 160.39/21.02 = { by axiom 23 (kn2_1) R->L }
% 160.39/21.02 fresh31(kn2, true, X, Y)
% 160.39/21.02 = { by axiom 3 (rosser_kn2) }
% 160.39/21.02 fresh31(true, true, X, Y)
% 160.39/21.02 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.39/21.02 fresh31(modus_ponens, true, X, Y)
% 160.39/21.02 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.39/21.02 fresh31(modus_ponens, modus_ponens, X, Y)
% 160.39/21.02 = { by axiom 14 (kn2_1) }
% 160.39/21.02 true
% 160.39/21.02 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.39/21.02 modus_ponens
% 160.39/21.02
% 160.39/21.02 Lemma 34: modus_ponens = and_1.
% 160.39/21.02 Proof:
% 160.39/21.02 modus_ponens
% 160.39/21.02 = { by axiom 1 (rosser_modus_ponens) }
% 160.39/21.02 true
% 160.39/21.02 = { by axiom 8 (and_1) R->L }
% 160.39/21.02 fresh57(modus_ponens, modus_ponens)
% 160.39/21.02 = { by axiom 1 (rosser_modus_ponens) }
% 160.39/21.02 fresh57(modus_ponens, true)
% 160.39/21.02 = { by lemma 33 R->L }
% 160.39/21.02 fresh57(fresh58(and_1, modus_ponens, x9, y9), true)
% 160.39/21.02 = { by lemma 32 R->L }
% 160.39/21.02 fresh57(is_a_theorem(implies(and(x9, y9), x9)), true)
% 160.39/21.02 = { by axiom 27 (and_1) }
% 160.39/21.02 and_1
% 160.39/21.02
% 160.87/21.03 Lemma 35: fresh60(X, X, Y) = modus_ponens.
% 160.87/21.03 Proof:
% 160.87/21.03 fresh60(X, X, Y)
% 160.87/21.03 = { by axiom 10 (modus_ponens_2) }
% 160.87/21.03 true
% 160.87/21.03 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.03 modus_ponens
% 160.87/21.03
% 160.87/21.03 Lemma 36: not(and(X, not(Y))) = implies(X, Y).
% 160.87/21.03 Proof:
% 160.87/21.03 not(and(X, not(Y)))
% 160.87/21.03 = { by axiom 18 (op_implies_and) R->L }
% 160.87/21.03 fresh22(op_implies_and, true, X, Y)
% 160.87/21.03 = { by axiom 6 (rosser_op_implies_and) }
% 160.87/21.03 fresh22(true, true, X, Y)
% 160.87/21.03 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.03 fresh22(modus_ponens, true, X, Y)
% 160.87/21.03 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.03 fresh22(modus_ponens, modus_ponens, X, Y)
% 160.87/21.03 = { by axiom 16 (op_implies_and) }
% 160.87/21.03 implies(X, Y)
% 160.87/21.03
% 160.87/21.03 Lemma 37: implies(not(X), Y) = or(X, Y).
% 160.87/21.03 Proof:
% 160.87/21.03 implies(not(X), Y)
% 160.87/21.03 = { by lemma 36 R->L }
% 160.87/21.03 not(and(not(X), not(Y)))
% 160.87/21.03 = { by axiom 20 (op_or) R->L }
% 160.87/21.03 fresh20(op_or, true, X, Y)
% 160.87/21.03 = { by axiom 5 (rosser_op_or) }
% 160.87/21.03 fresh20(true, true, X, Y)
% 160.87/21.03 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.03 fresh20(modus_ponens, true, X, Y)
% 160.87/21.03 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.03 fresh20(modus_ponens, modus_ponens, X, Y)
% 160.87/21.03 = { by axiom 17 (op_or) }
% 160.87/21.03 or(X, Y)
% 160.87/21.03
% 160.87/21.03 Lemma 38: fresh59(is_a_theorem(implies(X, Y)), modus_ponens, X, Y) = fresh28(is_a_theorem(X), modus_ponens, Y).
% 160.87/21.03 Proof:
% 160.87/21.03 fresh59(is_a_theorem(implies(X, Y)), modus_ponens, X, Y)
% 160.87/21.03 = { by axiom 1 (rosser_modus_ponens) }
% 160.87/21.03 fresh59(is_a_theorem(implies(X, Y)), true, X, Y)
% 160.87/21.03 = { by axiom 26 (modus_ponens_2) }
% 160.87/21.03 fresh28(is_a_theorem(X), true, Y)
% 160.87/21.03 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.03 fresh28(is_a_theorem(X), modus_ponens, Y)
% 160.87/21.03
% 160.87/21.03 Lemma 39: or(and(X, not(Y)), Z) = implies(implies(X, Y), Z).
% 160.87/21.03 Proof:
% 160.87/21.03 or(and(X, not(Y)), Z)
% 160.87/21.03 = { by lemma 37 R->L }
% 160.87/21.03 implies(not(and(X, not(Y))), Z)
% 160.87/21.03 = { by lemma 36 }
% 160.87/21.03 implies(implies(X, Y), Z)
% 160.87/21.03
% 160.87/21.03 Lemma 40: is_a_theorem(implies(X, and(X, X))) = modus_ponens.
% 160.87/21.03 Proof:
% 160.87/21.03 is_a_theorem(implies(X, and(X, X)))
% 160.87/21.03 = { by axiom 21 (kn1_1) R->L }
% 160.87/21.03 fresh33(kn1, true, X)
% 160.87/21.03 = { by axiom 2 (rosser_kn1) }
% 160.87/21.03 fresh33(true, true, X)
% 160.87/21.03 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.03 fresh33(modus_ponens, true, X)
% 160.87/21.03 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.03 fresh33(modus_ponens, modus_ponens, X)
% 160.87/21.03 = { by axiom 11 (kn1_1) }
% 160.87/21.03 true
% 160.87/21.03 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.03 modus_ponens
% 160.87/21.03
% 160.87/21.03 Lemma 41: is_a_theorem(implies(implies(X, Y), or(and(Y, Z), not(and(Z, X))))) = and_1.
% 160.87/21.03 Proof:
% 160.87/21.03 is_a_theorem(implies(implies(X, Y), or(and(Y, Z), not(and(Z, X)))))
% 160.87/21.03 = { by lemma 37 R->L }
% 160.87/21.03 is_a_theorem(implies(implies(X, Y), implies(not(and(Y, Z)), not(and(Z, X)))))
% 160.87/21.03 = { by axiom 31 (kn3_1) R->L }
% 160.87/21.03 fresh29(kn3, true, X, Y, Z)
% 160.87/21.03 = { by axiom 4 (rosser_kn3) }
% 160.87/21.03 fresh29(true, true, X, Y, Z)
% 160.87/21.03 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.03 fresh29(modus_ponens, true, X, Y, Z)
% 160.87/21.03 = { by lemma 34 }
% 160.87/21.03 fresh29(and_1, true, X, Y, Z)
% 160.87/21.03 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.03 fresh29(and_1, modus_ponens, X, Y, Z)
% 160.87/21.03 = { by lemma 34 }
% 160.87/21.03 fresh29(and_1, and_1, X, Y, Z)
% 160.87/21.03 = { by axiom 19 (kn3_1) }
% 160.87/21.03 true
% 160.87/21.03 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.03 modus_ponens
% 160.87/21.03 = { by lemma 34 }
% 160.87/21.03 and_1
% 160.87/21.03
% 160.87/21.03 Lemma 42: is_a_theorem(implies(or(X, Y), or(and(Y, Z), implies(Z, X)))) = and_1.
% 160.87/21.03 Proof:
% 160.87/21.03 is_a_theorem(implies(or(X, Y), or(and(Y, Z), implies(Z, X))))
% 160.87/21.03 = { by lemma 37 R->L }
% 160.87/21.03 is_a_theorem(implies(implies(not(X), Y), or(and(Y, Z), implies(Z, X))))
% 160.87/21.03 = { by lemma 36 R->L }
% 160.87/21.03 is_a_theorem(implies(implies(not(X), Y), or(and(Y, Z), not(and(Z, not(X))))))
% 160.87/21.03 = { by lemma 41 }
% 160.87/21.03 and_1
% 160.87/21.03
% 160.87/21.03 Lemma 43: fresh59(X, X, Y, Z) = modus_ponens.
% 160.87/21.03 Proof:
% 160.87/21.03 fresh59(X, X, Y, Z)
% 160.87/21.03 = { by axiom 13 (modus_ponens_2) }
% 160.87/21.03 fresh60(modus_ponens, true, Z)
% 160.87/21.03 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.03 fresh60(modus_ponens, modus_ponens, Z)
% 160.87/21.03 = { by lemma 35 }
% 160.87/21.03 modus_ponens
% 160.87/21.03
% 160.87/21.03 Lemma 44: fresh28(is_a_theorem(or(X, Y)), and_1, or(and(Y, Z), implies(Z, X))) = and_1.
% 160.87/21.03 Proof:
% 160.87/21.03 fresh28(is_a_theorem(or(X, Y)), and_1, or(and(Y, Z), implies(Z, X)))
% 160.87/21.03 = { by lemma 34 R->L }
% 160.87/21.03 fresh28(is_a_theorem(or(X, Y)), modus_ponens, or(and(Y, Z), implies(Z, X)))
% 160.87/21.03 = { by lemma 38 R->L }
% 160.87/21.03 fresh59(is_a_theorem(implies(or(X, Y), or(and(Y, Z), implies(Z, X)))), modus_ponens, or(X, Y), or(and(Y, Z), implies(Z, X)))
% 160.87/21.03 = { by lemma 42 }
% 160.87/21.03 fresh59(and_1, modus_ponens, or(X, Y), or(and(Y, Z), implies(Z, X)))
% 160.87/21.03 = { by lemma 34 }
% 160.87/21.03 fresh59(and_1, and_1, or(X, Y), or(and(Y, Z), implies(Z, X)))
% 160.87/21.03 = { by lemma 43 }
% 160.87/21.03 modus_ponens
% 160.87/21.03 = { by lemma 34 }
% 160.87/21.03 and_1
% 160.87/21.03
% 160.87/21.03 Lemma 45: is_a_theorem(or(not(X), X)) = and_1.
% 160.87/21.03 Proof:
% 160.87/21.03 is_a_theorem(or(not(X), X))
% 160.87/21.03 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.03 fresh28(and_1, and_1, or(not(X), X))
% 160.87/21.03 = { by lemma 34 R->L }
% 160.87/21.03 fresh28(modus_ponens, and_1, or(not(X), X))
% 160.87/21.03 = { by lemma 33 R->L }
% 160.87/21.03 fresh28(fresh58(and_1, modus_ponens, not(X), not(X)), and_1, or(not(X), X))
% 160.87/21.03 = { by lemma 32 R->L }
% 160.87/21.03 fresh28(is_a_theorem(implies(and(not(X), not(X)), not(X))), and_1, or(not(X), X))
% 160.87/21.03 = { by lemma 34 R->L }
% 160.87/21.03 fresh28(is_a_theorem(implies(and(not(X), not(X)), not(X))), modus_ponens, or(not(X), X))
% 160.87/21.03 = { by lemma 38 R->L }
% 160.87/21.03 fresh59(is_a_theorem(implies(implies(and(not(X), not(X)), not(X)), or(not(X), X))), modus_ponens, implies(and(not(X), not(X)), not(X)), or(not(X), X))
% 160.87/21.03 = { by lemma 39 R->L }
% 160.87/21.03 fresh59(is_a_theorem(or(and(and(not(X), not(X)), not(not(X))), or(not(X), X))), modus_ponens, implies(and(not(X), not(X)), not(X)), or(not(X), X))
% 160.87/21.03 = { by lemma 37 R->L }
% 160.87/21.03 fresh59(is_a_theorem(or(and(and(not(X), not(X)), not(not(X))), implies(not(not(X)), X))), modus_ponens, implies(and(not(X), not(X)), not(X)), or(not(X), X))
% 160.87/21.03 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.03 fresh59(fresh28(and_1, and_1, or(and(and(not(X), not(X)), not(not(X))), implies(not(not(X)), X))), modus_ponens, implies(and(not(X), not(X)), not(X)), or(not(X), X))
% 160.87/21.03 = { by lemma 34 R->L }
% 160.87/21.04 fresh59(fresh28(modus_ponens, and_1, or(and(and(not(X), not(X)), not(not(X))), implies(not(not(X)), X))), modus_ponens, implies(and(not(X), not(X)), not(X)), or(not(X), X))
% 160.87/21.04 = { by lemma 40 R->L }
% 160.87/21.04 fresh59(fresh28(is_a_theorem(implies(not(X), and(not(X), not(X)))), and_1, or(and(and(not(X), not(X)), not(not(X))), implies(not(not(X)), X))), modus_ponens, implies(and(not(X), not(X)), not(X)), or(not(X), X))
% 160.87/21.04 = { by lemma 37 }
% 160.87/21.04 fresh59(fresh28(is_a_theorem(or(X, and(not(X), not(X)))), and_1, or(and(and(not(X), not(X)), not(not(X))), implies(not(not(X)), X))), modus_ponens, implies(and(not(X), not(X)), not(X)), or(not(X), X))
% 160.87/21.04 = { by lemma 44 }
% 160.87/21.04 fresh59(and_1, modus_ponens, implies(and(not(X), not(X)), not(X)), or(not(X), X))
% 160.87/21.04 = { by lemma 34 }
% 160.87/21.04 fresh59(and_1, and_1, implies(and(not(X), not(X)), not(X)), or(not(X), X))
% 160.87/21.04 = { by lemma 43 }
% 160.87/21.04 modus_ponens
% 160.87/21.04 = { by lemma 34 }
% 160.87/21.04 and_1
% 160.87/21.04
% 160.87/21.04 Lemma 46: fresh59(X, X, Y, Z) = and_1.
% 160.87/21.04 Proof:
% 160.87/21.04 fresh59(X, X, Y, Z)
% 160.87/21.04 = { by axiom 13 (modus_ponens_2) }
% 160.87/21.04 fresh60(modus_ponens, true, Z)
% 160.87/21.04 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.04 fresh60(modus_ponens, modus_ponens, Z)
% 160.87/21.04 = { by lemma 35 }
% 160.87/21.04 modus_ponens
% 160.87/21.04 = { by lemma 34 }
% 160.87/21.04 and_1
% 160.87/21.04
% 160.87/21.04 Lemma 47: is_a_theorem(implies(or(X, Y), or(Y, X))) = fresh8(r3, and_1, X, Y).
% 160.87/21.04 Proof:
% 160.87/21.04 is_a_theorem(implies(or(X, Y), or(Y, X)))
% 160.87/21.04 = { by axiom 29 (r3_1) R->L }
% 160.87/21.04 fresh8(r3, true, X, Y)
% 160.87/21.04 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.04 fresh8(r3, modus_ponens, X, Y)
% 160.87/21.04 = { by lemma 34 }
% 160.87/21.04 fresh8(r3, and_1, X, Y)
% 160.87/21.04
% 160.87/21.04 Lemma 48: fresh59(is_a_theorem(or(X, Y)), and_1, not(X), Y) = fresh28(is_a_theorem(not(X)), and_1, Y).
% 160.87/21.04 Proof:
% 160.87/21.04 fresh59(is_a_theorem(or(X, Y)), and_1, not(X), Y)
% 160.87/21.04 = { by lemma 34 R->L }
% 160.87/21.04 fresh59(is_a_theorem(or(X, Y)), modus_ponens, not(X), Y)
% 160.87/21.04 = { by lemma 37 R->L }
% 160.87/21.04 fresh59(is_a_theorem(implies(not(X), Y)), modus_ponens, not(X), Y)
% 160.87/21.04 = { by lemma 38 }
% 160.87/21.04 fresh28(is_a_theorem(not(X)), modus_ponens, Y)
% 160.87/21.04 = { by lemma 34 }
% 160.87/21.04 fresh28(is_a_theorem(not(X)), and_1, Y)
% 160.87/21.04
% 160.87/21.04 Lemma 49: fresh28(is_a_theorem(or(X, Y)), and_1, implies(implies(Y, Z), or(Z, X))) = and_1.
% 160.87/21.04 Proof:
% 160.87/21.04 fresh28(is_a_theorem(or(X, Y)), and_1, implies(implies(Y, Z), or(Z, X)))
% 160.87/21.04 = { by lemma 34 R->L }
% 160.87/21.04 fresh28(is_a_theorem(or(X, Y)), modus_ponens, implies(implies(Y, Z), or(Z, X)))
% 160.87/21.04 = { by lemma 38 R->L }
% 160.87/21.04 fresh59(is_a_theorem(implies(or(X, Y), implies(implies(Y, Z), or(Z, X)))), modus_ponens, or(X, Y), implies(implies(Y, Z), or(Z, X)))
% 160.87/21.04 = { by lemma 39 R->L }
% 160.87/21.04 fresh59(is_a_theorem(implies(or(X, Y), or(and(Y, not(Z)), or(Z, X)))), modus_ponens, or(X, Y), implies(implies(Y, Z), or(Z, X)))
% 160.87/21.04 = { by lemma 37 R->L }
% 160.87/21.04 fresh59(is_a_theorem(implies(or(X, Y), or(and(Y, not(Z)), implies(not(Z), X)))), modus_ponens, or(X, Y), implies(implies(Y, Z), or(Z, X)))
% 160.87/21.04 = { by lemma 42 }
% 160.87/21.04 fresh59(and_1, modus_ponens, or(X, Y), implies(implies(Y, Z), or(Z, X)))
% 160.87/21.04 = { by lemma 34 }
% 160.87/21.04 fresh59(and_1, and_1, or(X, Y), implies(implies(Y, Z), or(Z, X)))
% 160.87/21.04 = { by lemma 43 }
% 160.87/21.04 modus_ponens
% 160.87/21.04 = { by lemma 34 }
% 160.87/21.04 and_1
% 160.87/21.04
% 160.87/21.04 Lemma 50: fresh28(is_a_theorem(implies(X, Y)), and_1, or(Y, not(X))) = and_1.
% 160.87/21.04 Proof:
% 160.87/21.04 fresh28(is_a_theorem(implies(X, Y)), and_1, or(Y, not(X)))
% 160.87/21.04 = { by lemma 34 R->L }
% 160.87/21.04 fresh28(is_a_theorem(implies(X, Y)), modus_ponens, or(Y, not(X)))
% 160.87/21.04 = { by lemma 38 R->L }
% 160.87/21.04 fresh59(is_a_theorem(implies(implies(X, Y), or(Y, not(X)))), modus_ponens, implies(X, Y), or(Y, not(X)))
% 160.87/21.04 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.04 fresh59(fresh28(and_1, and_1, implies(implies(X, Y), or(Y, not(X)))), modus_ponens, implies(X, Y), or(Y, not(X)))
% 160.87/21.04 = { by lemma 45 R->L }
% 160.87/21.04 fresh59(fresh28(is_a_theorem(or(not(X), X)), and_1, implies(implies(X, Y), or(Y, not(X)))), modus_ponens, implies(X, Y), or(Y, not(X)))
% 160.87/21.04 = { by lemma 49 }
% 160.87/21.04 fresh59(and_1, modus_ponens, implies(X, Y), or(Y, not(X)))
% 160.87/21.04 = { by lemma 34 }
% 160.87/21.04 fresh59(and_1, and_1, implies(X, Y), or(Y, not(X)))
% 160.87/21.04 = { by lemma 43 }
% 160.87/21.04 modus_ponens
% 160.87/21.04 = { by lemma 34 }
% 160.87/21.04 and_1
% 160.87/21.04
% 160.87/21.04 Lemma 51: is_a_theorem(or(X, not(and(X, Y)))) = and_1.
% 160.87/21.04 Proof:
% 160.87/21.04 is_a_theorem(or(X, not(and(X, Y))))
% 160.87/21.04 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.04 fresh28(and_1, and_1, or(X, not(and(X, Y))))
% 160.87/21.04 = { by lemma 34 R->L }
% 160.87/21.04 fresh28(modus_ponens, and_1, or(X, not(and(X, Y))))
% 160.87/21.04 = { by lemma 33 R->L }
% 160.87/21.04 fresh28(fresh58(and_1, modus_ponens, X, Y), and_1, or(X, not(and(X, Y))))
% 160.87/21.04 = { by lemma 32 R->L }
% 160.87/21.04 fresh28(is_a_theorem(implies(and(X, Y), X)), and_1, or(X, not(and(X, Y))))
% 160.87/21.04 = { by lemma 50 }
% 160.87/21.04 and_1
% 160.87/21.04
% 160.87/21.04 Lemma 52: fresh59(is_a_theorem(implies(X, Y)), and_1, X, Y) = fresh28(is_a_theorem(X), and_1, Y).
% 160.87/21.04 Proof:
% 160.87/21.04 fresh59(is_a_theorem(implies(X, Y)), and_1, X, Y)
% 160.87/21.04 = { by lemma 34 R->L }
% 160.87/21.04 fresh59(is_a_theorem(implies(X, Y)), modus_ponens, X, Y)
% 160.87/21.04 = { by lemma 38 }
% 160.87/21.04 fresh28(is_a_theorem(X), modus_ponens, Y)
% 160.87/21.04 = { by lemma 34 }
% 160.87/21.04 fresh28(is_a_theorem(X), and_1, Y)
% 160.87/21.04
% 160.87/21.04 Lemma 53: fresh8(r3, and_1, X, Y) = and_1.
% 160.87/21.04 Proof:
% 160.87/21.04 fresh8(r3, and_1, X, Y)
% 160.87/21.04 = { by lemma 47 R->L }
% 160.87/21.04 is_a_theorem(implies(or(X, Y), or(Y, X)))
% 160.87/21.04 = { by lemma 37 R->L }
% 160.87/21.04 is_a_theorem(implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.04 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.04 fresh28(and_1, and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.04 = { by lemma 34 R->L }
% 160.87/21.04 fresh28(modus_ponens, and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.04 = { by lemma 43 R->L }
% 160.87/21.04 fresh28(fresh59(and_1, and_1, not(not(implies(not(X), not(X)))), implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.04 = { by lemma 45 R->L }
% 160.87/21.04 fresh28(fresh59(is_a_theorem(or(not(implies(not(X), not(X))), implies(not(X), not(X)))), and_1, not(not(implies(not(X), not(X)))), implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.04 = { by lemma 48 }
% 160.87/21.04 fresh28(fresh28(is_a_theorem(not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.04 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.04 fresh28(fresh28(fresh28(and_1, and_1, not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 46 R->L }
% 160.87/21.05 fresh28(fresh28(fresh28(fresh59(and_1, and_1, or(and(implies(not(X), not(X)), not(X)), implies(not(X), not(X))), or(implies(not(X), not(X)), implies(not(X), not(X)))), and_1, not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 49 R->L }
% 160.87/21.05 fresh28(fresh28(fresh28(fresh59(fresh28(is_a_theorem(or(implies(not(X), not(X)), not(and(implies(not(X), not(X)), not(X))))), and_1, implies(implies(not(and(implies(not(X), not(X)), not(X))), implies(not(X), not(X))), or(implies(not(X), not(X)), implies(not(X), not(X))))), and_1, or(and(implies(not(X), not(X)), not(X)), implies(not(X), not(X))), or(implies(not(X), not(X)), implies(not(X), not(X)))), and_1, not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 51 }
% 160.87/21.05 fresh28(fresh28(fresh28(fresh59(fresh28(and_1, and_1, implies(implies(not(and(implies(not(X), not(X)), not(X))), implies(not(X), not(X))), or(implies(not(X), not(X)), implies(not(X), not(X))))), and_1, or(and(implies(not(X), not(X)), not(X)), implies(not(X), not(X))), or(implies(not(X), not(X)), implies(not(X), not(X)))), and_1, not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by axiom 12 (modus_ponens_2) }
% 160.87/21.05 fresh28(fresh28(fresh28(fresh59(is_a_theorem(implies(implies(not(and(implies(not(X), not(X)), not(X))), implies(not(X), not(X))), or(implies(not(X), not(X)), implies(not(X), not(X))))), and_1, or(and(implies(not(X), not(X)), not(X)), implies(not(X), not(X))), or(implies(not(X), not(X)), implies(not(X), not(X)))), and_1, not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 37 }
% 160.87/21.05 fresh28(fresh28(fresh28(fresh59(is_a_theorem(implies(or(and(implies(not(X), not(X)), not(X)), implies(not(X), not(X))), or(implies(not(X), not(X)), implies(not(X), not(X))))), and_1, or(and(implies(not(X), not(X)), not(X)), implies(not(X), not(X))), or(implies(not(X), not(X)), implies(not(X), not(X)))), and_1, not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 52 }
% 160.87/21.05 fresh28(fresh28(fresh28(fresh28(is_a_theorem(or(and(implies(not(X), not(X)), not(X)), implies(not(X), not(X)))), and_1, or(implies(not(X), not(X)), implies(not(X), not(X)))), and_1, not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.05 fresh28(fresh28(fresh28(fresh28(fresh28(and_1, and_1, or(and(implies(not(X), not(X)), not(X)), implies(not(X), not(X)))), and_1, or(implies(not(X), not(X)), implies(not(X), not(X)))), and_1, not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 51 R->L }
% 160.87/21.05 fresh28(fresh28(fresh28(fresh28(fresh28(is_a_theorem(or(not(X), not(and(not(X), not(not(X)))))), and_1, or(and(implies(not(X), not(X)), not(X)), implies(not(X), not(X)))), and_1, or(implies(not(X), not(X)), implies(not(X), not(X)))), and_1, not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 36 }
% 160.87/21.05 fresh28(fresh28(fresh28(fresh28(fresh28(is_a_theorem(or(not(X), implies(not(X), not(X)))), and_1, or(and(implies(not(X), not(X)), not(X)), implies(not(X), not(X)))), and_1, or(implies(not(X), not(X)), implies(not(X), not(X)))), and_1, not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 44 }
% 160.87/21.05 fresh28(fresh28(fresh28(fresh28(and_1, and_1, or(implies(not(X), not(X)), implies(not(X), not(X)))), and_1, not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by axiom 12 (modus_ponens_2) }
% 160.87/21.05 fresh28(fresh28(fresh28(is_a_theorem(or(implies(not(X), not(X)), implies(not(X), not(X)))), and_1, not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 34 R->L }
% 160.87/21.05 fresh28(fresh28(fresh28(is_a_theorem(or(implies(not(X), not(X)), implies(not(X), not(X)))), modus_ponens, not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 38 R->L }
% 160.87/21.05 fresh28(fresh28(fresh59(is_a_theorem(implies(or(implies(not(X), not(X)), implies(not(X), not(X))), not(not(implies(not(X), not(X)))))), modus_ponens, or(implies(not(X), not(X)), implies(not(X), not(X))), not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 37 R->L }
% 160.87/21.05 fresh28(fresh28(fresh59(is_a_theorem(implies(implies(not(implies(not(X), not(X))), implies(not(X), not(X))), not(not(implies(not(X), not(X)))))), modus_ponens, or(implies(not(X), not(X)), implies(not(X), not(X))), not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 39 R->L }
% 160.87/21.05 fresh28(fresh28(fresh59(is_a_theorem(or(and(not(implies(not(X), not(X))), not(implies(not(X), not(X)))), not(not(implies(not(X), not(X)))))), modus_ponens, or(implies(not(X), not(X)), implies(not(X), not(X))), not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.05 fresh28(fresh28(fresh59(fresh28(and_1, and_1, or(and(not(implies(not(X), not(X))), not(implies(not(X), not(X)))), not(not(implies(not(X), not(X)))))), modus_ponens, or(implies(not(X), not(X)), implies(not(X), not(X))), not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 34 R->L }
% 160.87/21.05 fresh28(fresh28(fresh59(fresh28(modus_ponens, and_1, or(and(not(implies(not(X), not(X))), not(implies(not(X), not(X)))), not(not(implies(not(X), not(X)))))), modus_ponens, or(implies(not(X), not(X)), implies(not(X), not(X))), not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 40 R->L }
% 160.87/21.05 fresh28(fresh28(fresh59(fresh28(is_a_theorem(implies(not(implies(not(X), not(X))), and(not(implies(not(X), not(X))), not(implies(not(X), not(X)))))), and_1, or(and(not(implies(not(X), not(X))), not(implies(not(X), not(X)))), not(not(implies(not(X), not(X)))))), modus_ponens, or(implies(not(X), not(X)), implies(not(X), not(X))), not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 50 }
% 160.87/21.05 fresh28(fresh28(fresh59(and_1, modus_ponens, or(implies(not(X), not(X)), implies(not(X), not(X))), not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 34 }
% 160.87/21.05 fresh28(fresh28(fresh59(and_1, and_1, or(implies(not(X), not(X)), implies(not(X), not(X))), not(not(implies(not(X), not(X))))), and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 43 }
% 160.87/21.05 fresh28(fresh28(modus_ponens, and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 34 }
% 160.87/21.05 fresh28(fresh28(and_1, and_1, implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by axiom 12 (modus_ponens_2) }
% 160.87/21.05 fresh28(is_a_theorem(implies(not(X), not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 37 }
% 160.87/21.05 fresh28(is_a_theorem(or(X, not(X))), and_1, implies(implies(not(X), Y), or(Y, X)))
% 160.87/21.05 = { by lemma 49 }
% 160.87/21.05 and_1
% 160.87/21.05
% 160.87/21.05 Lemma 54: implies(X, and(Y, not(Z))) = not(and(X, implies(Y, Z))).
% 160.87/21.05 Proof:
% 160.87/21.05 implies(X, and(Y, not(Z)))
% 160.87/21.05 = { by lemma 36 R->L }
% 160.87/21.05 not(and(X, not(and(Y, not(Z)))))
% 160.87/21.05 = { by lemma 36 }
% 160.87/21.05 not(and(X, implies(Y, Z)))
% 160.87/21.05
% 160.87/21.05 Lemma 55: is_a_theorem(implies(equiv(X, Y), implies(Y, X))) = fresh43(equivalence_2, and_1, X, Y).
% 160.87/21.05 Proof:
% 160.87/21.05 is_a_theorem(implies(equiv(X, Y), implies(Y, X)))
% 160.87/21.05 = { by axiom 28 (equivalence_2_1) R->L }
% 160.87/21.06 fresh43(equivalence_2, true, X, Y)
% 160.87/21.06 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.06 fresh43(equivalence_2, modus_ponens, X, Y)
% 160.87/21.06 = { by lemma 34 }
% 160.87/21.06 fresh43(equivalence_2, and_1, X, Y)
% 160.87/21.06
% 160.87/21.06 Lemma 56: is_a_theorem(implies(or(X, Y), or(Y, X))) = and_1.
% 160.87/21.06 Proof:
% 160.87/21.06 is_a_theorem(implies(or(X, Y), or(Y, X)))
% 160.87/21.06 = { by axiom 29 (r3_1) R->L }
% 160.87/21.06 fresh8(r3, true, X, Y)
% 160.87/21.06 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.06 fresh8(r3, modus_ponens, X, Y)
% 160.87/21.06 = { by lemma 34 }
% 160.87/21.06 fresh8(r3, and_1, X, Y)
% 160.87/21.06 = { by lemma 53 }
% 160.87/21.06 and_1
% 160.87/21.06
% 160.87/21.06 Lemma 57: fresh28(is_a_theorem(not(and(X, Y))), and_1, implies(Y, not(X))) = and_1.
% 160.87/21.06 Proof:
% 160.87/21.06 fresh28(is_a_theorem(not(and(X, Y))), and_1, implies(Y, not(X)))
% 160.87/21.06 = { by lemma 48 R->L }
% 160.87/21.06 fresh59(is_a_theorem(or(and(X, Y), implies(Y, not(X)))), and_1, not(and(X, Y)), implies(Y, not(X)))
% 160.87/21.06 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.06 fresh59(fresh28(and_1, and_1, or(and(X, Y), implies(Y, not(X)))), and_1, not(and(X, Y)), implies(Y, not(X)))
% 160.87/21.06 = { by lemma 45 R->L }
% 160.87/21.06 fresh59(fresh28(is_a_theorem(or(not(X), X)), and_1, or(and(X, Y), implies(Y, not(X)))), and_1, not(and(X, Y)), implies(Y, not(X)))
% 160.87/21.06 = { by lemma 44 }
% 160.87/21.06 fresh59(and_1, and_1, not(and(X, Y)), implies(Y, not(X)))
% 160.87/21.06 = { by lemma 43 }
% 160.87/21.06 modus_ponens
% 160.87/21.06 = { by lemma 34 }
% 160.87/21.06 and_1
% 160.87/21.06
% 160.87/21.06 Lemma 58: fresh28(is_a_theorem(implies(X, Y)), and_1, or(and(Y, Z), not(and(Z, X)))) = and_1.
% 160.87/21.06 Proof:
% 160.87/21.06 fresh28(is_a_theorem(implies(X, Y)), and_1, or(and(Y, Z), not(and(Z, X))))
% 160.87/21.06 = { by lemma 34 R->L }
% 160.87/21.06 fresh28(is_a_theorem(implies(X, Y)), modus_ponens, or(and(Y, Z), not(and(Z, X))))
% 160.87/21.06 = { by lemma 38 R->L }
% 160.87/21.06 fresh59(is_a_theorem(implies(implies(X, Y), or(and(Y, Z), not(and(Z, X))))), modus_ponens, implies(X, Y), or(and(Y, Z), not(and(Z, X))))
% 160.87/21.06 = { by lemma 41 }
% 160.87/21.06 fresh59(and_1, modus_ponens, implies(X, Y), or(and(Y, Z), not(and(Z, X))))
% 160.87/21.06 = { by lemma 34 }
% 160.87/21.06 fresh59(and_1, and_1, implies(X, Y), or(and(Y, Z), not(and(Z, X))))
% 160.87/21.06 = { by lemma 43 }
% 160.87/21.06 modus_ponens
% 160.87/21.06 = { by lemma 34 }
% 160.87/21.06 and_1
% 160.87/21.06
% 160.87/21.06 Lemma 59: is_a_theorem(or(and(and(X, X), Y), not(and(Y, X)))) = and_1.
% 160.87/21.06 Proof:
% 160.87/21.06 is_a_theorem(or(and(and(X, X), Y), not(and(Y, X))))
% 160.87/21.06 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.06 fresh28(and_1, and_1, or(and(and(X, X), Y), not(and(Y, X))))
% 160.87/21.06 = { by lemma 34 R->L }
% 160.87/21.06 fresh28(modus_ponens, and_1, or(and(and(X, X), Y), not(and(Y, X))))
% 160.87/21.06 = { by lemma 40 R->L }
% 160.87/21.06 fresh28(is_a_theorem(implies(X, and(X, X))), and_1, or(and(and(X, X), Y), not(and(Y, X))))
% 160.87/21.06 = { by lemma 58 }
% 160.87/21.06 and_1
% 160.87/21.06
% 160.87/21.06 Lemma 60: fresh28(is_a_theorem(not(and(X, Y))), and_1, not(and(Y, and(X, Z)))) = and_1.
% 160.87/21.06 Proof:
% 160.87/21.06 fresh28(is_a_theorem(not(and(X, Y))), and_1, not(and(Y, and(X, Z))))
% 160.87/21.06 = { by lemma 48 R->L }
% 160.87/21.06 fresh59(is_a_theorem(or(and(X, Y), not(and(Y, and(X, Z))))), and_1, not(and(X, Y)), not(and(Y, and(X, Z))))
% 160.87/21.06 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.06 fresh59(fresh28(and_1, and_1, or(and(X, Y), not(and(Y, and(X, Z))))), and_1, not(and(X, Y)), not(and(Y, and(X, Z))))
% 160.87/21.06 = { by lemma 34 R->L }
% 160.87/21.06 fresh59(fresh28(modus_ponens, and_1, or(and(X, Y), not(and(Y, and(X, Z))))), and_1, not(and(X, Y)), not(and(Y, and(X, Z))))
% 160.87/21.06 = { by lemma 33 R->L }
% 160.87/21.06 fresh59(fresh28(fresh58(and_1, modus_ponens, X, Z), and_1, or(and(X, Y), not(and(Y, and(X, Z))))), and_1, not(and(X, Y)), not(and(Y, and(X, Z))))
% 160.87/21.06 = { by lemma 32 R->L }
% 160.87/21.06 fresh59(fresh28(is_a_theorem(implies(and(X, Z), X)), and_1, or(and(X, Y), not(and(Y, and(X, Z))))), and_1, not(and(X, Y)), not(and(Y, and(X, Z))))
% 160.87/21.06 = { by lemma 58 }
% 160.87/21.06 fresh59(and_1, and_1, not(and(X, Y)), not(and(Y, and(X, Z))))
% 160.87/21.06 = { by lemma 43 }
% 160.87/21.06 modus_ponens
% 160.87/21.06 = { by lemma 34 }
% 160.87/21.06 and_1
% 160.87/21.06
% 160.87/21.06 Lemma 61: fresh28(is_a_theorem(implies(and(X, X), Y)), and_1, not(and(not(Y), X))) = and_1.
% 160.87/21.06 Proof:
% 160.87/21.06 fresh28(is_a_theorem(implies(and(X, X), Y)), and_1, not(and(not(Y), X)))
% 160.87/21.06 = { by lemma 34 R->L }
% 160.87/21.06 fresh28(is_a_theorem(implies(and(X, X), Y)), modus_ponens, not(and(not(Y), X)))
% 160.87/21.06 = { by lemma 38 R->L }
% 160.87/21.06 fresh59(is_a_theorem(implies(implies(and(X, X), Y), not(and(not(Y), X)))), modus_ponens, implies(and(X, X), Y), not(and(not(Y), X)))
% 160.87/21.06 = { by lemma 39 R->L }
% 160.87/21.06 fresh59(is_a_theorem(or(and(and(X, X), not(Y)), not(and(not(Y), X)))), modus_ponens, implies(and(X, X), Y), not(and(not(Y), X)))
% 160.87/21.06 = { by lemma 59 }
% 160.87/21.06 fresh59(and_1, modus_ponens, implies(and(X, X), Y), not(and(not(Y), X)))
% 160.87/21.06 = { by lemma 34 }
% 160.87/21.06 fresh59(and_1, and_1, implies(and(X, X), Y), not(and(not(Y), X)))
% 160.87/21.06 = { by lemma 43 }
% 160.87/21.06 modus_ponens
% 160.87/21.06 = { by lemma 34 }
% 160.87/21.06 and_1
% 160.87/21.06
% 160.87/21.06 Lemma 62: fresh28(is_a_theorem(not(and(and(X, X), Y))), and_1, not(and(Y, X))) = and_1.
% 160.87/21.06 Proof:
% 160.87/21.06 fresh28(is_a_theorem(not(and(and(X, X), Y))), and_1, not(and(Y, X)))
% 160.87/21.06 = { by lemma 48 R->L }
% 160.87/21.06 fresh59(is_a_theorem(or(and(and(X, X), Y), not(and(Y, X)))), and_1, not(and(and(X, X), Y)), not(and(Y, X)))
% 160.87/21.06 = { by lemma 59 }
% 160.87/21.06 fresh59(and_1, and_1, not(and(and(X, X), Y)), not(and(Y, X)))
% 160.87/21.06 = { by lemma 43 }
% 160.87/21.06 modus_ponens
% 160.87/21.06 = { by lemma 34 }
% 160.87/21.07 and_1
% 160.87/21.07
% 160.87/21.07 Goal 1 (hilbert_equivalence_2): equivalence_2 = true.
% 160.87/21.07 Proof:
% 160.87/21.07 equivalence_2
% 160.87/21.07 = { by axiom 30 (equivalence_2) R->L }
% 160.87/21.07 fresh44(is_a_theorem(implies(equiv(x2, y2), implies(y2, x2))), true)
% 160.87/21.07 = { by lemma 55 }
% 160.87/21.07 fresh44(fresh43(equivalence_2, and_1, x2, y2), true)
% 160.87/21.07 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.07 fresh44(fresh43(equivalence_2, and_1, x2, y2), modus_ponens)
% 160.87/21.07 = { by lemma 34 }
% 160.87/21.07 fresh44(fresh43(equivalence_2, and_1, x2, y2), and_1)
% 160.87/21.07 = { by lemma 55 R->L }
% 160.87/21.07 fresh44(is_a_theorem(implies(equiv(x2, y2), implies(y2, x2))), and_1)
% 160.87/21.07 = { by axiom 15 (op_equiv) R->L }
% 160.87/21.07 fresh44(is_a_theorem(implies(fresh23(modus_ponens, modus_ponens, x2, y2), implies(y2, x2))), and_1)
% 160.87/21.07 = { by axiom 1 (rosser_modus_ponens) }
% 160.87/21.07 fresh44(is_a_theorem(implies(fresh23(modus_ponens, true, x2, y2), implies(y2, x2))), and_1)
% 160.87/21.07 = { by axiom 1 (rosser_modus_ponens) }
% 160.87/21.07 fresh44(is_a_theorem(implies(fresh23(true, true, x2, y2), implies(y2, x2))), and_1)
% 160.87/21.07 = { by axiom 7 (rosser_op_equiv) R->L }
% 160.87/21.07 fresh44(is_a_theorem(implies(fresh23(op_equiv, true, x2, y2), implies(y2, x2))), and_1)
% 160.87/21.07 = { by axiom 25 (op_equiv) }
% 160.87/21.07 fresh44(is_a_theorem(implies(and(implies(x2, y2), implies(y2, x2)), implies(y2, x2))), and_1)
% 160.87/21.07 = { by axiom 24 (and_2_1) R->L }
% 160.87/21.07 fresh44(fresh55(and_2, true, implies(x2, y2), implies(y2, x2)), and_1)
% 160.87/21.07 = { by axiom 1 (rosser_modus_ponens) R->L }
% 160.87/21.07 fresh44(fresh55(and_2, modus_ponens, implies(x2, y2), implies(y2, x2)), and_1)
% 160.87/21.07 = { by lemma 34 }
% 160.87/21.07 fresh44(fresh55(and_2, and_1, implies(x2, y2), implies(y2, x2)), and_1)
% 160.87/21.07 = { by lemma 36 R->L }
% 160.87/21.07 fresh44(fresh55(and_2, and_1, implies(x2, y2), not(and(y2, not(x2)))), and_1)
% 160.87/21.07 = { by lemma 36 R->L }
% 160.87/21.07 fresh44(fresh55(and_2, and_1, not(and(x2, not(y2))), not(and(y2, not(x2)))), and_1)
% 160.87/21.07 = { by lemma 34 R->L }
% 160.87/21.07 fresh44(fresh55(and_2, modus_ponens, not(and(x2, not(y2))), not(and(y2, not(x2)))), and_1)
% 160.87/21.07 = { by axiom 1 (rosser_modus_ponens) }
% 160.87/21.07 fresh44(fresh55(and_2, true, not(and(x2, not(y2))), not(and(y2, not(x2)))), and_1)
% 160.87/21.07 = { by axiom 24 (and_2_1) }
% 160.87/21.07 fresh44(is_a_theorem(implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.07 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.07 fresh44(fresh28(and_1, and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.08 = { by lemma 62 R->L }
% 160.87/21.08 fresh44(fresh28(fresh28(is_a_theorem(not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.08 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.08 fresh44(fresh28(fresh28(fresh28(and_1, and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.08 = { by lemma 60 R->L }
% 160.87/21.08 fresh44(fresh28(fresh28(fresh28(fresh28(is_a_theorem(not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))))), and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.08 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.08 fresh44(fresh28(fresh28(fresh28(fresh28(fresh28(and_1, and_1, not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))))), and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.08 = { by lemma 62 R->L }
% 160.87/21.08 fresh44(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(is_a_theorem(not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), or(and(x2, not(y2)), and(y2, not(x2)))))), and_1, not(and(or(and(x2, not(y2)), and(y2, not(x2))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))))), and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.08 = { by lemma 37 R->L }
% 160.87/21.09 fresh44(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(is_a_theorem(not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), implies(not(and(x2, not(y2))), and(y2, not(x2)))))), and_1, not(and(or(and(x2, not(y2)), and(y2, not(x2))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))))), and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.09 = { by lemma 54 R->L }
% 160.87/21.09 fresh44(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(is_a_theorem(implies(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), and_1, not(and(or(and(x2, not(y2)), and(y2, not(x2))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))))), and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.09 = { by lemma 32 }
% 160.87/21.09 fresh44(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(fresh58(and_1, modus_ponens, and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and_1, not(and(or(and(x2, not(y2)), and(y2, not(x2))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))))), and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.09 = { by lemma 33 }
% 160.87/21.09 fresh44(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(modus_ponens, and_1, not(and(or(and(x2, not(y2)), and(y2, not(x2))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))))), and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.09 = { by lemma 34 }
% 160.87/21.09 fresh44(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(and_1, and_1, not(and(or(and(x2, not(y2)), and(y2, not(x2))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))))), and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.09 = { by axiom 12 (modus_ponens_2) }
% 160.87/21.09 fresh44(fresh28(fresh28(fresh28(fresh28(fresh28(is_a_theorem(not(and(or(and(x2, not(y2)), and(y2, not(x2))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))))), and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.10 = { by lemma 48 R->L }
% 160.87/21.10 fresh44(fresh28(fresh28(fresh28(fresh28(fresh59(is_a_theorem(or(and(or(and(x2, not(y2)), and(y2, not(x2))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, not(and(or(and(x2, not(y2)), and(y2, not(x2))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))))), and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.10 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.10 fresh44(fresh28(fresh28(fresh28(fresh28(fresh59(fresh28(and_1, and_1, or(and(or(and(x2, not(y2)), and(y2, not(x2))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, not(and(or(and(x2, not(y2)), and(y2, not(x2))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))))), and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.10 = { by lemma 56 R->L }
% 160.87/21.10 fresh44(fresh28(fresh28(fresh28(fresh28(fresh59(fresh28(is_a_theorem(implies(or(and(y2, not(x2)), and(x2, not(y2))), or(and(x2, not(y2)), and(y2, not(x2))))), and_1, or(and(or(and(x2, not(y2)), and(y2, not(x2))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, not(and(or(and(x2, not(y2)), and(y2, not(x2))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))))), and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.10 = { by lemma 58 }
% 160.87/21.10 fresh44(fresh28(fresh28(fresh28(fresh28(fresh59(and_1, and_1, not(and(or(and(x2, not(y2)), and(y2, not(x2))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))))), and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.10 = { by lemma 46 }
% 160.87/21.10 fresh44(fresh28(fresh28(fresh28(fresh28(and_1, and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))))), and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.11 = { by axiom 12 (modus_ponens_2) }
% 160.87/21.11 fresh44(fresh28(fresh28(fresh28(is_a_theorem(not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))))), and_1, not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.11 = { by lemma 48 R->L }
% 160.87/21.11 fresh44(fresh28(fresh28(fresh59(is_a_theorem(or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.11 = { by axiom 12 (modus_ponens_2) R->L }
% 160.87/21.11 fresh44(fresh28(fresh28(fresh59(fresh28(and_1, and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.11 = { by lemma 46 R->L }
% 160.87/21.11 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(and_1, and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 160.87/21.12 = { by lemma 46 R->L }
% 161.65/21.12 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(and_1, and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 161.65/21.12 = { by lemma 46 R->L }
% 161.65/21.12 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh59(and_1, and_1, or(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2)))))), or(and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 161.65/21.13 = { by lemma 53 R->L }
% 161.65/21.13 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh59(fresh8(r3, and_1, or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, or(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2)))))), or(and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 161.65/21.13 = { by lemma 34 R->L }
% 161.65/21.15 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh59(fresh8(r3, and_1, or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2)))))), modus_ponens, or(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2)))))), or(and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 161.65/21.15 = { by lemma 47 R->L }
% 161.65/21.15 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh59(is_a_theorem(implies(or(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2)))))), or(and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))))), modus_ponens, or(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2)))))), or(and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 161.65/21.16 = { by lemma 38 }
% 161.65/21.16 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh28(is_a_theorem(or(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2))))))), modus_ponens, or(and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 161.65/21.16 = { by lemma 34 }
% 161.65/21.16 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh28(is_a_theorem(or(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 161.65/21.17 = { by lemma 39 }
% 161.65/21.17 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh28(is_a_theorem(or(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, implies(implies(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 161.65/21.17 = { by lemma 37 }
% 161.65/21.17 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh28(is_a_theorem(or(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, implies(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 161.65/21.17 = { by lemma 37 R->L }
% 161.65/21.18 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh28(is_a_theorem(implies(not(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, implies(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 161.65/21.18 = { by lemma 54 }
% 161.65/21.18 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh28(is_a_theorem(not(and(not(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), implies(not(not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, implies(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 161.65/21.18 = { by lemma 37 }
% 161.65/21.18 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh28(is_a_theorem(not(and(not(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, implies(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 161.65/21.19 = { by axiom 12 (modus_ponens_2) R->L }
% 161.65/21.19 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh28(fresh28(and_1, and_1, not(and(not(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, implies(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 161.65/21.19 = { by lemma 42 R->L }
% 161.65/21.19 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh28(fresh28(is_a_theorem(implies(or(or(and(y2, not(x2)), and(x2, not(y2))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, not(and(not(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, implies(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 161.65/21.19 = { by lemma 52 R->L }
% 162.23/21.19 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh28(fresh59(is_a_theorem(implies(implies(or(or(and(y2, not(x2)), and(x2, not(y2))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), not(and(not(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))))))), and_1, implies(or(or(and(y2, not(x2)), and(x2, not(y2))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), not(and(not(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, implies(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.20 = { by axiom 12 (modus_ponens_2) R->L }
% 162.23/21.20 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh28(fresh59(fresh28(and_1, and_1, implies(implies(or(or(and(y2, not(x2)), and(x2, not(y2))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), not(and(not(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))))))), and_1, implies(or(or(and(y2, not(x2)), and(x2, not(y2))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), not(and(not(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, implies(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.20 = { by lemma 56 R->L }
% 162.23/21.20 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh28(fresh59(fresh28(is_a_theorem(implies(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(or(and(y2, not(x2)), and(x2, not(y2))), not(or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, implies(implies(or(or(and(y2, not(x2)), and(x2, not(y2))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), not(and(not(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))))))), and_1, implies(or(or(and(y2, not(x2)), and(x2, not(y2))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), not(and(not(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, implies(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.20 = { by lemma 39 R->L }
% 162.23/21.20 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh28(fresh59(fresh28(is_a_theorem(implies(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(or(and(y2, not(x2)), and(x2, not(y2))), not(or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(and(or(or(and(y2, not(x2)), and(x2, not(y2))), not(or(and(y2, not(x2)), and(x2, not(y2))))), not(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), not(and(not(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))))))), and_1, implies(or(or(and(y2, not(x2)), and(x2, not(y2))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), not(and(not(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, implies(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.20 = { by lemma 58 }
% 162.23/21.21 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh28(fresh59(and_1, and_1, implies(or(or(and(y2, not(x2)), and(x2, not(y2))), not(or(and(y2, not(x2)), and(x2, not(y2))))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), not(and(not(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, implies(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.21 = { by lemma 46 }
% 162.23/21.21 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(fresh28(and_1, and_1, implies(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.21 = { by axiom 12 (modus_ponens_2) }
% 162.23/21.21 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh59(is_a_theorem(implies(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))))), and_1, or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2)))), or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.21 = { by lemma 52 }
% 162.23/21.21 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh28(is_a_theorem(or(not(or(and(y2, not(x2)), and(x2, not(y2)))), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.21 = { by lemma 45 }
% 162.23/21.21 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(fresh28(and_1, and_1, or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.21 = { by axiom 12 (modus_ponens_2) }
% 162.23/21.21 fresh44(fresh28(fresh28(fresh59(fresh28(fresh59(is_a_theorem(or(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2)))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2)))), implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.21 = { by lemma 48 }
% 162.23/21.21 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(is_a_theorem(not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))))), and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.22 = { by axiom 12 (modus_ponens_2) R->L }
% 162.23/21.22 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(fresh28(and_1, and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))))), and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.22 = { by lemma 57 R->L }
% 162.23/21.22 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(fresh28(fresh28(is_a_theorem(not(and(and(not(and(y2, not(x2))), not(and(x2, not(y2)))), and(and(y2, not(x2)), and(y2, not(x2)))))), and_1, implies(and(and(y2, not(x2)), and(y2, not(x2))), not(and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))))), and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.22 = { by axiom 12 (modus_ponens_2) R->L }
% 162.23/21.22 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(fresh28(fresh28(fresh28(and_1, and_1, not(and(and(not(and(y2, not(x2))), not(and(x2, not(y2)))), and(and(y2, not(x2)), and(y2, not(x2)))))), and_1, implies(and(and(y2, not(x2)), and(y2, not(x2))), not(and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))))), and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.22 = { by lemma 60 R->L }
% 162.23/21.22 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(is_a_theorem(not(and(not(and(y2, not(x2))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(and(not(and(y2, not(x2))), not(and(x2, not(y2)))), and(and(y2, not(x2)), and(y2, not(x2)))))), and_1, implies(and(and(y2, not(x2)), and(y2, not(x2))), not(and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))))), and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.23 = { by axiom 12 (modus_ponens_2) R->L }
% 162.23/21.23 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(and_1, and_1, not(and(not(and(y2, not(x2))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(and(not(and(y2, not(x2))), not(and(x2, not(y2)))), and(and(y2, not(x2)), and(y2, not(x2)))))), and_1, implies(and(and(y2, not(x2)), and(y2, not(x2))), not(and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))))), and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.23 = { by lemma 34 R->L }
% 162.23/21.23 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(modus_ponens, and_1, not(and(not(and(y2, not(x2))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(and(not(and(y2, not(x2))), not(and(x2, not(y2)))), and(and(y2, not(x2)), and(y2, not(x2)))))), and_1, implies(and(and(y2, not(x2)), and(y2, not(x2))), not(and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))))), and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.23 = { by lemma 33 R->L }
% 162.23/21.23 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(fresh58(and_1, modus_ponens, and(y2, not(x2)), and(y2, not(x2))), and_1, not(and(not(and(y2, not(x2))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(and(not(and(y2, not(x2))), not(and(x2, not(y2)))), and(and(y2, not(x2)), and(y2, not(x2)))))), and_1, implies(and(and(y2, not(x2)), and(y2, not(x2))), not(and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))))), and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.23 = { by lemma 32 R->L }
% 162.23/21.23 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(is_a_theorem(implies(and(and(y2, not(x2)), and(y2, not(x2))), and(y2, not(x2)))), and_1, not(and(not(and(y2, not(x2))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(and(not(and(y2, not(x2))), not(and(x2, not(y2)))), and(and(y2, not(x2)), and(y2, not(x2)))))), and_1, implies(and(and(y2, not(x2)), and(y2, not(x2))), not(and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))))), and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.23 = { by lemma 61 }
% 162.23/21.23 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(fresh28(fresh28(fresh28(fresh28(and_1, and_1, not(and(and(y2, not(x2)), and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(and(not(and(y2, not(x2))), not(and(x2, not(y2)))), and(and(y2, not(x2)), and(y2, not(x2)))))), and_1, implies(and(and(y2, not(x2)), and(y2, not(x2))), not(and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))))), and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.23 = { by axiom 12 (modus_ponens_2) }
% 162.23/21.24 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(fresh28(fresh28(fresh28(is_a_theorem(not(and(and(y2, not(x2)), and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(and(not(and(y2, not(x2))), not(and(x2, not(y2)))), and(and(y2, not(x2)), and(y2, not(x2)))))), and_1, implies(and(and(y2, not(x2)), and(y2, not(x2))), not(and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))))), and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.24 = { by lemma 60 }
% 162.23/21.24 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(fresh28(fresh28(and_1, and_1, implies(and(and(y2, not(x2)), and(y2, not(x2))), not(and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))))), and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.24 = { by axiom 12 (modus_ponens_2) }
% 162.23/21.24 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(fresh28(is_a_theorem(implies(and(and(y2, not(x2)), and(y2, not(x2))), not(and(not(and(y2, not(x2))), not(and(x2, not(y2))))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))))), and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.24 = { by lemma 36 }
% 162.23/21.24 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(fresh28(is_a_theorem(implies(and(and(y2, not(x2)), and(y2, not(x2))), implies(not(and(y2, not(x2))), and(x2, not(y2))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))))), and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.24 = { by lemma 37 }
% 162.23/21.24 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(fresh28(is_a_theorem(implies(and(and(y2, not(x2)), and(y2, not(x2))), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, not(and(not(or(and(y2, not(x2)), and(x2, not(y2)))), and(y2, not(x2))))), and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.24 = { by lemma 61 }
% 162.23/21.24 fresh44(fresh28(fresh28(fresh59(fresh28(fresh28(and_1, and_1, implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.24 = { by axiom 12 (modus_ponens_2) }
% 162.23/21.24 fresh44(fresh28(fresh28(fresh59(fresh28(is_a_theorem(implies(and(y2, not(x2)), or(and(y2, not(x2)), and(x2, not(y2))))), and_1, or(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2)))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2)))))), and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.24 = { by lemma 58 }
% 162.23/21.24 fresh44(fresh28(fresh28(fresh59(and_1, and_1, not(and(or(and(y2, not(x2)), and(x2, not(y2))), and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), not(and(and(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), and(not(and(x2, not(y2))), not(and(y2, not(x2))))), and(y2, not(x2))))), and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.24 = { by lemma 46 }
% 162.23/21.24 fresh44(fresh28(fresh28(and_1, and_1, not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.24 = { by axiom 12 (modus_ponens_2) }
% 162.23/21.24 fresh44(fresh28(is_a_theorem(not(and(and(y2, not(x2)), and(not(and(x2, not(y2))), not(and(y2, not(x2))))))), and_1, implies(and(not(and(x2, not(y2))), not(and(y2, not(x2)))), not(and(y2, not(x2))))), and_1)
% 162.23/21.24 = { by lemma 57 }
% 162.23/21.24 fresh44(and_1, and_1)
% 162.23/21.24 = { by axiom 9 (equivalence_2) }
% 162.23/21.24 true
% 162.23/21.24 % SZS output end Proof
% 162.23/21.24
% 162.23/21.24 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------